id	sid	tid	token	lemma	pos
fuelectenerg-1427	1	1	facta	facta	PROPN
fuelectenerg-1427	1	2	universitatis	universitatis	PROPN
fuelectenerg-1427	1	3	series	series	NOUN
fuelectenerg-1427	1	4	:	:	PUNCT
fuelectenerg-1427	1	5	electronics	electronic	NOUN
fuelectenerg-1427	1	6	and	and	CCONJ
fuelectenerg-1427	1	7	energetics	energetics	NOUN
fuelectenerg-1427	1	8	vol	vol	NOUN
fuelectenerg-1427	1	9	.	.	PROPN
fuelectenerg-1427	1	10	30	30	NUM
fuelectenerg-1427	1	11	,	,	PUNCT
fuelectenerg-1427	1	12	no	no	DET
fuelectenerg-1427	1	13	1	1	NUM
fuelectenerg-1427	1	14	,	,	PUNCT
fuelectenerg-1427	1	15	march	march	PROPN
fuelectenerg-1427	1	16	2017	2017	NUM
fuelectenerg-1427	1	17	,	,	PUNCT
fuelectenerg-1427	1	18	pp	pp	ADV
fuelectenerg-1427	1	19	.	.	PUNCT
fuelectenerg-1427	2	1	49	49	NUM
fuelectenerg-1427	2	2	66	66	NUM
fuelectenerg-1427	2	3	doi	doi	NOUN
fuelectenerg-1427	2	4	:	:	PUNCT
fuelectenerg-1427	2	5	10.2298	10.2298	NUM
fuelectenerg-1427	2	6	/	/	SYM
fuelectenerg-1427	2	7	fuee1701049a	fuee1701049a	PROPN
fuelectenerg-1427	2	8	anas	anas	PROPN
fuelectenerg-1427	2	9	n.	n.	PROPN
fuelectenerg-1427	2	10	al	al	PROPN
fuelectenerg-1427	2	11	-	-	PROPN
fuelectenerg-1427	2	12	rabadi1,2	rabadi1,2	PROPN
fuelectenerg-1427	2	13	received	receive	VERB
fuelectenerg-1427	2	14	november	november	PROPN
fuelectenerg-1427	2	15	28	28	NUM
fuelectenerg-1427	2	16	,	,	PUNCT
fuelectenerg-1427	2	17	2015	2015	NUM
fuelectenerg-1427	2	18	;	;	PUNCT
fuelectenerg-1427	2	19	received	receive	VERB
fuelectenerg-1427	2	20	in	in	ADP
fuelectenerg-1427	2	21	revised	revise	VERB
fuelectenerg-1427	2	22	form	form	NOUN
fuelectenerg-1427	2	23	april	april	PROPN
fuelectenerg-1427	2	24	13	13	NUM
fuelectenerg-1427	2	25	,	,	PUNCT
fuelectenerg-1427	2	26	2016	2016	NUM
fuelectenerg-1427	2	27	corresponding	correspond	VERB
fuelectenerg-1427	2	28	author	author	NOUN
fuelectenerg-1427	2	29	:	:	PUNCT
fuelectenerg-1427	2	30	anas	anas	PROPN
fuelectenerg-1427	2	31	n.	n.	PROPN
fuelectenerg-1427	2	32	al	al	PROPN
fuelectenerg-1427	2	33	-	-	PUNCT
fuelectenerg-1427	2	34	rabadi	rabadi	PROPN
fuelectenerg-1427	2	35	electrical	electrical	ADJ
fuelectenerg-1427	2	36	engineering	engineering	NOUN
fuelectenerg-1427	2	37	department	department	PROPN
fuelectenerg-1427	2	38	,	,	PUNCT
fuelectenerg-1427	2	39	philadelphia	philadelphia	PROPN
fuelectenerg-1427	2	40	university	university	PROPN
fuelectenerg-1427	2	41	,	,	PUNCT
fuelectenerg-1427	2	42	jordan	jordan	PROPN
fuelectenerg-1427	2	43	&	&	CCONJ
fuelectenerg-1427	2	44	computer	computer	PROPN
fuelectenerg-1427	2	45	engineering	engineering	PROPN
fuelectenerg-1427	2	46	department	department	PROPN
fuelectenerg-1427	2	47	,	,	PUNCT
fuelectenerg-1427	2	48	the	the	DET
fuelectenerg-1427	2	49	university	university	PROPN
fuelectenerg-1427	2	50	of	of	ADP
fuelectenerg-1427	2	51	jordan	jordan	PROPN
fuelectenerg-1427	2	52	,	,	PUNCT
fuelectenerg-1427	2	53	amman	amman	PROPN
fuelectenerg-1427	2	54	-	-	PUNCT
fuelectenerg-1427	2	55	jordan	jordan	PROPN
fuelectenerg-1427	2	56	(	(	PUNCT
fuelectenerg-1427	2	57	email	email	NOUN
fuelectenerg-1427	2	58	:	:	PUNCT
fuelectenerg-1427	2	59	alrabadi@yahoo.com	alrabadi@yahoo.com	X
fuelectenerg-1427	2	60	)	)	PUNCT
fuelectenerg-1427	2	61	facta	facta	PROPN
fuelectenerg-1427	2	62	universitatis	universitatis	PROPN
fuelectenerg-1427	2	63	series	series	NOUN
fuelectenerg-1427	2	64	:	:	PUNCT
fuelectenerg-1427	2	65	electronics	electronic	NOUN
fuelectenerg-1427	2	66	and	and	CCONJ
fuelectenerg-1427	2	67	energetics	energetics	NOUN
fuelectenerg-1427	2	68	vol	vol	NOUN
fuelectenerg-1427	2	69	.	.	PUNCT
fuelectenerg-1427	3	1	28	28	NUM
fuelectenerg-1427	3	2	,	,	PUNCT
fuelectenerg-1427	3	3	no	no	DET
fuelectenerg-1427	3	4	4	4	NUM
fuelectenerg-1427	3	5	,	,	PUNCT
fuelectenerg-1427	3	6	december	december	PROPN
fuelectenerg-1427	3	7	2015	2015	NUM
fuelectenerg-1427	3	8	,	,	PUNCT
fuelectenerg-1427	3	9	pp	pp	ADJ
fuelectenerg-1427	3	10	.	.	PUNCT
fuelectenerg-1427	4	1	507	507	NUM
fuelectenerg-1427	4	2	525	525	NUM
fuelectenerg-1427	4	3	doi	doi	NOUN
fuelectenerg-1427	4	4	:	:	PUNCT
fuelectenerg-1427	4	5	10.2298	10.2298	NUM
fuelectenerg-1427	4	6	/	/	SYM
fuelectenerg-1427	4	7	fuee1504507s	fuee1504507	VERB
fuelectenerg-1427	4	8	horizontal	horizontal	ADJ
fuelectenerg-1427	4	9	current	current	ADJ
fuelectenerg-1427	4	10	bipolar	bipolar	ADJ
fuelectenerg-1427	4	11	transistor	transistor	NOUN
fuelectenerg-1427	4	12	(	(	PUNCT
fuelectenerg-1427	4	13	hcbt	hcbt	NOUN
fuelectenerg-1427	4	14	)	)	PUNCT
fuelectenerg-1427	4	15	–	–	PUNCT
fuelectenerg-1427	4	16	a	a	DET
fuelectenerg-1427	4	17	low	low	ADJ
fuelectenerg-1427	4	18	-	-	PUNCT
fuelectenerg-1427	4	19	cost	cost	NOUN
fuelectenerg-1427	4	20	,	,	PUNCT
fuelectenerg-1427	4	21	high	high	ADJ
fuelectenerg-1427	4	22	-	-	PUNCT
fuelectenerg-1427	4	23	performance	performance	NOUN
fuelectenerg-1427	4	24	flexible	flexible	ADJ
fuelectenerg-1427	4	25	bicmos	bicmos	PROPN
fuelectenerg-1427	4	26	technology	technology	PROPN
fuelectenerg-1427	4	27	for	for	ADP
fuelectenerg-1427	4	28	rf	rf	NOUN
fuelectenerg-1427	4	29	communication	communication	NOUN
fuelectenerg-1427	4	30	applications	applications	X
fuelectenerg-1427	4	31	tomislav	tomislav	PROPN
fuelectenerg-1427	4	32	suligoj1	suligoj1	PROPN
fuelectenerg-1427	4	33	,	,	PUNCT
fuelectenerg-1427	4	34	marko	marko	PROPN
fuelectenerg-1427	4	35	koričić1	koričić1	PROPN
fuelectenerg-1427	4	36	,	,	PUNCT
fuelectenerg-1427	4	37	josip	josip	PROPN
fuelectenerg-1427	4	38	žilak1	žilak1	PROPN
fuelectenerg-1427	4	39	,	,	PUNCT
fuelectenerg-1427	4	40	hidenori	hidenori	PROPN
fuelectenerg-1427	4	41	mochizuki2	mochizuki2	PROPN
fuelectenerg-1427	4	42	,	,	PUNCT
fuelectenerg-1427	4	43	so	so	ADV
fuelectenerg-1427	4	44	-	-	PUNCT
fuelectenerg-1427	4	45	ichi	ichi	ADJ
fuelectenerg-1427	4	46	morita2	morita2	NOUN
fuelectenerg-1427	4	47	,	,	PUNCT
fuelectenerg-1427	4	48	katsumi	katsumi	PROPN
fuelectenerg-1427	4	49	shinomura2	shinomura2	PROPN
fuelectenerg-1427	4	50	,	,	PUNCT
fuelectenerg-1427	4	51	hisaya	hisaya	NOUN
fuelectenerg-1427	4	52	imai2	imai2	PROPN
fuelectenerg-1427	4	53	1university	1university	NUM
fuelectenerg-1427	4	54	of	of	ADP
fuelectenerg-1427	4	55	zagreb	zagreb	PROPN
fuelectenerg-1427	4	56	,	,	PUNCT
fuelectenerg-1427	4	57	faculty	faculty	NOUN
fuelectenerg-1427	4	58	of	of	ADP
fuelectenerg-1427	4	59	electrical	electrical	ADJ
fuelectenerg-1427	4	60	engineering	engineering	NOUN
fuelectenerg-1427	4	61	and	and	CCONJ
fuelectenerg-1427	4	62	computing	computing	NOUN
fuelectenerg-1427	4	63	,	,	PUNCT
fuelectenerg-1427	4	64	department	department	NOUN
fuelectenerg-1427	4	65	of	of	ADP
fuelectenerg-1427	4	66	electronics	electronic	NOUN
fuelectenerg-1427	4	67	,	,	PUNCT
fuelectenerg-1427	4	68	microand	microand	NOUN
fuelectenerg-1427	4	69	nano	nano	NOUN
fuelectenerg-1427	4	70	-	-	PUNCT
fuelectenerg-1427	4	71	electronics	electronic	NOUN
fuelectenerg-1427	4	72	laboratory	laboratory	NOUN
fuelectenerg-1427	4	73	,	,	PUNCT
fuelectenerg-1427	4	74	croatia	croatia	PROPN
fuelectenerg-1427	4	75	2asahi	2asahi	PROPN
fuelectenerg-1427	4	76	kasei	kasei	PROPN
fuelectenerg-1427	4	77	microdevices	microdevices	PROPN
fuelectenerg-1427	4	78	co.	co.	PROPN
fuelectenerg-1427	4	79	5	5	NUM
fuelectenerg-1427	4	80	-	-	SYM
fuelectenerg-1427	4	81	4960	4960	NUM
fuelectenerg-1427	4	82	,	,	PUNCT
fuelectenerg-1427	4	83	nobeoka	nobeoka	NOUN
fuelectenerg-1427	4	84	,	,	PUNCT
fuelectenerg-1427	4	85	miyazaki	miyazaki	PROPN
fuelectenerg-1427	4	86	,	,	PUNCT
fuelectenerg-1427	4	87	882	882	NUM
fuelectenerg-1427	4	88	-	-	SYM
fuelectenerg-1427	4	89	0031	0031	NUM
fuelectenerg-1427	4	90	,	,	PUNCT
fuelectenerg-1427	4	91	japan	japan	PROPN
fuelectenerg-1427	4	92	abstract	abstract	PROPN
fuelectenerg-1427	4	93	.	.	PUNCT
fuelectenerg-1427	5	1	in	in	ADP
fuelectenerg-1427	5	2	an	an	DET
fuelectenerg-1427	5	3	overview	overview	NOUN
fuelectenerg-1427	5	4	of	of	ADP
fuelectenerg-1427	5	5	horizontal	horizontal	ADJ
fuelectenerg-1427	5	6	current	current	ADJ
fuelectenerg-1427	5	7	bipolar	bipolar	ADJ
fuelectenerg-1427	5	8	transistor	transistor	NOUN
fuelectenerg-1427	5	9	(	(	PUNCT
fuelectenerg-1427	5	10	hcbt	hcbt	NOUN
fuelectenerg-1427	5	11	)	)	PUNCT
fuelectenerg-1427	5	12	technology	technology	NOUN
fuelectenerg-1427	5	13	,	,	PUNCT
fuelectenerg-1427	5	14	the	the	DET
fuelectenerg-1427	5	15	state	state	NOUN
fuelectenerg-1427	5	16	-	-	PUNCT
fuelectenerg-1427	5	17	of	of	ADP
fuelectenerg-1427	5	18	-	-	PUNCT
fuelectenerg-1427	5	19	the	the	DET
fuelectenerg-1427	5	20	-	-	PUNCT
fuelectenerg-1427	5	21	art	art	NOUN
fuelectenerg-1427	5	22	integrated	integrate	VERB
fuelectenerg-1427	5	23	silicon	silicon	NOUN
fuelectenerg-1427	5	24	bipolar	bipolar	ADJ
fuelectenerg-1427	5	25	transistors	transistor	NOUN
fuelectenerg-1427	5	26	are	be	AUX
fuelectenerg-1427	5	27	described	describe	VERB
fuelectenerg-1427	5	28	which	which	PRON
fuelectenerg-1427	5	29	exhibit	exhibit	VERB
fuelectenerg-1427	5	30	ft	ft	PROPN
fuelectenerg-1427	5	31	and	and	CCONJ
fuelectenerg-1427	5	32	fmax	fmax	PROPN
fuelectenerg-1427	5	33	of	of	ADP
fuelectenerg-1427	5	34	51	51	NUM
fuelectenerg-1427	5	35	ghz	ghz	NOUN
fuelectenerg-1427	5	36	and	and	CCONJ
fuelectenerg-1427	5	37	61	61	NUM
fuelectenerg-1427	5	38	ghz	ghz	NOUN
fuelectenerg-1427	5	39	and	and	CCONJ
fuelectenerg-1427	5	40	ftbvceo	ftbvceo	ADJ
fuelectenerg-1427	5	41	product	product	NOUN
fuelectenerg-1427	5	42	of	of	ADP
fuelectenerg-1427	5	43	173	173	NUM
fuelectenerg-1427	5	44	ghzv	ghzv	NOUN
fuelectenerg-1427	5	45	that	that	PRON
fuelectenerg-1427	5	46	are	be	AUX
fuelectenerg-1427	5	47	among	among	ADP
fuelectenerg-1427	5	48	the	the	DET
fuelectenerg-1427	5	49	highest	high	ADJ
fuelectenerg-1427	5	50	-	-	PUNCT
fuelectenerg-1427	5	51	performance	performance	NOUN
fuelectenerg-1427	5	52	implanted	implant	VERB
fuelectenerg-1427	5	53	-	-	PUNCT
fuelectenerg-1427	5	54	base	base	NOUN
fuelectenerg-1427	5	55	,	,	PUNCT
fuelectenerg-1427	5	56	silicon	silicon	NOUN
fuelectenerg-1427	5	57	bipolar	bipolar	ADJ
fuelectenerg-1427	5	58	transistors	transistor	NOUN
fuelectenerg-1427	5	59	.	.	PUNCT
fuelectenerg-1427	6	1	hbct	hbct	ADV
fuelectenerg-1427	6	2	is	be	AUX
fuelectenerg-1427	6	3	integrated	integrate	VERB
fuelectenerg-1427	6	4	with	with	ADP
fuelectenerg-1427	6	5	cmos	cmos	PROPN
fuelectenerg-1427	6	6	in	in	ADP
fuelectenerg-1427	6	7	a	a	DET
fuelectenerg-1427	6	8	considerably	considerably	ADV
fuelectenerg-1427	6	9	lower	low	ADJ
fuelectenerg-1427	6	10	-	-	PUNCT
fuelectenerg-1427	6	11	cost	cost	NOUN
fuelectenerg-1427	6	12	fabrication	fabrication	NOUN
fuelectenerg-1427	6	13	sequence	sequence	NOUN
fuelectenerg-1427	6	14	as	as	ADP
fuelectenerg-1427	6	15	compared	compare	VERB
fuelectenerg-1427	6	16	to	to	ADP
fuelectenerg-1427	6	17	standard	standard	ADJ
fuelectenerg-1427	6	18	vertical	vertical	ADJ
fuelectenerg-1427	6	19	-	-	PUNCT
fuelectenerg-1427	6	20	current	current	ADJ
fuelectenerg-1427	6	21	bipolar	bipolar	ADJ
fuelectenerg-1427	6	22	transistors	transistor	NOUN
fuelectenerg-1427	6	23	with	with	ADP
fuelectenerg-1427	6	24	only	only	ADV
fuelectenerg-1427	6	25	2	2	NUM
fuelectenerg-1427	6	26	or	or	CCONJ
fuelectenerg-1427	6	27	3	3	NUM
fuelectenerg-1427	6	28	additional	additional	ADJ
fuelectenerg-1427	6	29	masks	mask	NOUN
fuelectenerg-1427	6	30	and	and	CCONJ
fuelectenerg-1427	6	31	fewer	few	ADJ
fuelectenerg-1427	6	32	process	process	NOUN
fuelectenerg-1427	6	33	steps	step	NOUN
fuelectenerg-1427	6	34	.	.	PUNCT
fuelectenerg-1427	7	1	due	due	ADP
fuelectenerg-1427	7	2	to	to	ADP
fuelectenerg-1427	7	3	its	its	PRON
fuelectenerg-1427	7	4	specific	specific	ADJ
fuelectenerg-1427	7	5	structure	structure	NOUN
fuelectenerg-1427	7	6	,	,	PUNCT
fuelectenerg-1427	7	7	the	the	DET
fuelectenerg-1427	7	8	charge	charge	NOUN
fuelectenerg-1427	7	9	sharing	sharing	NOUN
fuelectenerg-1427	7	10	effect	effect	NOUN
fuelectenerg-1427	7	11	can	can	AUX
fuelectenerg-1427	7	12	be	be	AUX
fuelectenerg-1427	7	13	employed	employ	VERB
fuelectenerg-1427	7	14	to	to	PART
fuelectenerg-1427	7	15	increase	increase	VERB
fuelectenerg-1427	7	16	bvceo	bvceo	ADV
fuelectenerg-1427	7	17	without	without	ADP
fuelectenerg-1427	7	18	sacrificing	sacrifice	VERB
fuelectenerg-1427	7	19	ft	ft	X
fuelectenerg-1427	7	20	and	and	CCONJ
fuelectenerg-1427	7	21	fmax	fmax	PROPN
fuelectenerg-1427	7	22	.	.	PUNCT
fuelectenerg-1427	8	1	moreover	moreover	ADV
fuelectenerg-1427	8	2	,	,	PUNCT
fuelectenerg-1427	8	3	the	the	DET
fuelectenerg-1427	8	4	electric	electric	ADJ
fuelectenerg-1427	8	5	field	field	NOUN
fuelectenerg-1427	8	6	can	can	AUX
fuelectenerg-1427	8	7	be	be	AUX
fuelectenerg-1427	8	8	engineered	engineer	VERB
fuelectenerg-1427	8	9	just	just	ADV
fuelectenerg-1427	8	10	by	by	ADP
fuelectenerg-1427	8	11	manipulating	manipulate	VERB
fuelectenerg-1427	8	12	the	the	DET
fuelectenerg-1427	8	13	lithography	lithography	NOUN
fuelectenerg-1427	8	14	masks	mask	NOUN
fuelectenerg-1427	8	15	achieving	achieve	VERB
fuelectenerg-1427	8	16	the	the	DET
fuelectenerg-1427	8	17	high	high	ADJ
fuelectenerg-1427	8	18	-	-	PUNCT
fuelectenerg-1427	8	19	voltage	voltage	NOUN
fuelectenerg-1427	8	20	hcbts	hcbt	NOUN
fuelectenerg-1427	8	21	with	with	ADP
fuelectenerg-1427	8	22	breakdowns	breakdown	NOUN
fuelectenerg-1427	8	23	up	up	ADP
fuelectenerg-1427	8	24	to	to	PART
fuelectenerg-1427	8	25	36	36	NUM
fuelectenerg-1427	8	26	v	v	NOUN
fuelectenerg-1427	8	27	integrated	integrate	VERB
fuelectenerg-1427	8	28	in	in	ADP
fuelectenerg-1427	8	29	the	the	DET
fuelectenerg-1427	8	30	same	same	ADJ
fuelectenerg-1427	8	31	process	process	NOUN
fuelectenerg-1427	8	32	flow	flow	NOUN
fuelectenerg-1427	8	33	with	with	ADP
fuelectenerg-1427	8	34	high	high	ADJ
fuelectenerg-1427	8	35	-	-	PUNCT
fuelectenerg-1427	8	36	speed	speed	NOUN
fuelectenerg-1427	8	37	devices	device	NOUN
fuelectenerg-1427	8	38	,	,	PUNCT
fuelectenerg-1427	8	39	i.e.	i.e.	X
fuelectenerg-1427	8	40	at	at	ADP
fuelectenerg-1427	8	41	zero	zero	NUM
fuelectenerg-1427	8	42	additional	additional	ADJ
fuelectenerg-1427	8	43	costs	cost	NOUN
fuelectenerg-1427	8	44	.	.	PUNCT
fuelectenerg-1427	9	1	double	double	ADJ
fuelectenerg-1427	9	2	-	-	PUNCT
fuelectenerg-1427	9	3	balanced	balanced	ADJ
fuelectenerg-1427	9	4	active	active	ADJ
fuelectenerg-1427	9	5	mixer	mixer	NOUN
fuelectenerg-1427	9	6	circuit	circuit	NOUN
fuelectenerg-1427	9	7	is	be	AUX
fuelectenerg-1427	9	8	designed	design	VERB
fuelectenerg-1427	9	9	and	and	CCONJ
fuelectenerg-1427	9	10	fabricated	fabricate	VERB
fuelectenerg-1427	9	11	in	in	ADP
fuelectenerg-1427	9	12	hcbt	hcbt	NOUN
fuelectenerg-1427	9	13	technology	technology	NOUN
fuelectenerg-1427	9	14	.	.	PUNCT
fuelectenerg-1427	10	1	the	the	DET
fuelectenerg-1427	10	2	maximum	maximum	ADJ
fuelectenerg-1427	10	3	iip3	iip3	NOUN
fuelectenerg-1427	10	4	of	of	ADP
fuelectenerg-1427	10	5	17.7	17.7	NUM
fuelectenerg-1427	10	6	dbm	dbm	NOUN
fuelectenerg-1427	10	7	at	at	ADP
fuelectenerg-1427	10	8	mixer	mixer	PROPN
fuelectenerg-1427	10	9	current	current	ADJ
fuelectenerg-1427	10	10	of	of	ADP
fuelectenerg-1427	10	11	9.2	9.2	NUM
fuelectenerg-1427	10	12	ma	ma	PROPN
fuelectenerg-1427	10	13	and	and	CCONJ
fuelectenerg-1427	10	14	conversion	conversion	NOUN
fuelectenerg-1427	10	15	gain	gain	NOUN
fuelectenerg-1427	10	16	of	of	ADP
fuelectenerg-1427	10	17	-5	-5	INTJ
fuelectenerg-1427	10	18	db	db	PROPN
fuelectenerg-1427	10	19	are	be	AUX
fuelectenerg-1427	10	20	achieved	achieve	VERB
fuelectenerg-1427	10	21	.	.	PUNCT
fuelectenerg-1427	11	1	key	key	ADJ
fuelectenerg-1427	11	2	words	word	NOUN
fuelectenerg-1427	11	3	:	:	PUNCT
fuelectenerg-1427	11	4	bicmos	bicmos	ADJ
fuelectenerg-1427	11	5	technology	technology	NOUN
fuelectenerg-1427	11	6	,	,	PUNCT
fuelectenerg-1427	11	7	bipolar	bipolar	ADJ
fuelectenerg-1427	11	8	transistors	transistor	NOUN
fuelectenerg-1427	11	9	,	,	PUNCT
fuelectenerg-1427	11	10	horizontal	horizontal	ADJ
fuelectenerg-1427	11	11	current	current	ADJ
fuelectenerg-1427	11	12	bipolar	bipolar	ADJ
fuelectenerg-1427	11	13	transistor	transistor	NOUN
fuelectenerg-1427	11	14	,	,	PUNCT
fuelectenerg-1427	11	15	radio	radio	NOUN
fuelectenerg-1427	11	16	frequency	frequency	NOUN
fuelectenerg-1427	11	17	integrated	integrate	VERB
fuelectenerg-1427	11	18	circuits	circuit	NOUN
fuelectenerg-1427	11	19	,	,	PUNCT
fuelectenerg-1427	11	20	mixer	mixer	NOUN
fuelectenerg-1427	11	21	,	,	PUNCT
fuelectenerg-1427	11	22	high	high	ADJ
fuelectenerg-1427	11	23	-	-	PUNCT
fuelectenerg-1427	11	24	voltage	voltage	NOUN
fuelectenerg-1427	11	25	bipolar	bipolar	ADJ
fuelectenerg-1427	11	26	transistors	transistor	NOUN
fuelectenerg-1427	11	27	.	.	PUNCT
fuelectenerg-1427	12	1	1	1	X
fuelectenerg-1427	12	2	.	.	X
fuelectenerg-1427	12	3	introduction	introduction	NOUN
fuelectenerg-1427	12	4	in	in	ADP
fuelectenerg-1427	12	5	the	the	DET
fuelectenerg-1427	12	6	highly	highly	ADV
fuelectenerg-1427	12	7	competitive	competitive	ADJ
fuelectenerg-1427	12	8	wireless	wireless	ADJ
fuelectenerg-1427	12	9	communication	communication	NOUN
fuelectenerg-1427	12	10	markets	market	NOUN
fuelectenerg-1427	12	11	,	,	PUNCT
fuelectenerg-1427	12	12	the	the	DET
fuelectenerg-1427	12	13	rf	rf	ADJ
fuelectenerg-1427	12	14	circuits	circuit	NOUN
fuelectenerg-1427	12	15	and	and	CCONJ
fuelectenerg-1427	12	16	systems	system	NOUN
fuelectenerg-1427	12	17	are	be	AUX
fuelectenerg-1427	12	18	fabricated	fabricate	VERB
fuelectenerg-1427	12	19	in	in	ADP
fuelectenerg-1427	12	20	the	the	DET
fuelectenerg-1427	12	21	technologies	technology	NOUN
fuelectenerg-1427	12	22	that	that	PRON
fuelectenerg-1427	12	23	are	be	AUX
fuelectenerg-1427	12	24	very	very	ADV
fuelectenerg-1427	12	25	cost	cost	NOUN
fuelectenerg-1427	12	26	-	-	PUNCT
fuelectenerg-1427	12	27	sensitive	sensitive	ADJ
fuelectenerg-1427	12	28	.	.	PUNCT
fuelectenerg-1427	13	1	in	in	ADP
fuelectenerg-1427	13	2	order	order	NOUN
fuelectenerg-1427	13	3	to	to	PART
fuelectenerg-1427	13	4	minimize	minimize	VERB
fuelectenerg-1427	13	5	the	the	DET
fuelectenerg-1427	13	6	fabrication	fabrication	NOUN
fuelectenerg-1427	13	7	costs	cost	NOUN
fuelectenerg-1427	13	8	,	,	PUNCT
fuelectenerg-1427	13	9	the	the	DET
fuelectenerg-1427	13	10	sub-10	sub-10	NUM
fuelectenerg-1427	13	11	ghz	ghz	NOUN
fuelectenerg-1427	13	12	applications	application	NOUN
fuelectenerg-1427	13	13	can	can	AUX
fuelectenerg-1427	13	14	be	be	AUX
fuelectenerg-1427	13	15	processed	process	VERB
fuelectenerg-1427	13	16	by	by	ADP
fuelectenerg-1427	13	17	using	use	VERB
fuelectenerg-1427	13	18	the	the	DET
fuelectenerg-1427	13	19	high	high	ADJ
fuelectenerg-1427	13	20	-	-	PUNCT
fuelectenerg-1427	13	21	volume	volume	NOUN
fuelectenerg-1427	13	22	silicon	silicon	NOUN
fuelectenerg-1427	13	23	technologies	technology	NOUN
fuelectenerg-1427	13	24	.	.	PUNCT
fuelectenerg-1427	14	1	it	it	PRON
fuelectenerg-1427	14	2	has	have	AUX
fuelectenerg-1427	14	3	been	be	AUX
fuelectenerg-1427	14	4	identified	identify	VERB
fuelectenerg-1427	14	5	that	that	SCONJ
fuelectenerg-1427	14	6	the	the	DET
fuelectenerg-1427	14	7	optimum	optimum	ADJ
fuelectenerg-1427	14	8	solution	solution	NOUN
fuelectenerg-1427	14	9	might	might	AUX
fuelectenerg-1427	14	10	received	receive	VERB
fuelectenerg-1427	14	11	march	march	PROPN
fuelectenerg-1427	14	12	9	9	NUM
fuelectenerg-1427	14	13	,	,	PUNCT
fuelectenerg-1427	14	14	2015	2015	NUM
fuelectenerg-1427	14	15	corresponding	correspond	VERB
fuelectenerg-1427	14	16	author	author	NOUN
fuelectenerg-1427	14	17	:	:	PUNCT
fuelectenerg-1427	14	18	tomislav	tomislav	PROPN
fuelectenerg-1427	14	19	suligoj	suligoj	PROPN
fuelectenerg-1427	14	20	university	university	PROPN
fuelectenerg-1427	14	21	of	of	ADP
fuelectenerg-1427	14	22	zagreb	zagreb	PROPN
fuelectenerg-1427	14	23	,	,	PUNCT
fuelectenerg-1427	14	24	faculty	faculty	NOUN
fuelectenerg-1427	14	25	of	of	ADP
fuelectenerg-1427	14	26	electrical	electrical	ADJ
fuelectenerg-1427	14	27	engineering	engineering	NOUN
fuelectenerg-1427	14	28	and	and	CCONJ
fuelectenerg-1427	14	29	computing	computing	NOUN
fuelectenerg-1427	14	30	,	,	PUNCT
fuelectenerg-1427	14	31	department	department	NOUN
fuelectenerg-1427	14	32	of	of	ADP
fuelectenerg-1427	14	33	electronics	electronic	NOUN
fuelectenerg-1427	14	34	,	,	PUNCT
fuelectenerg-1427	14	35	microand	microand	NOUN
fuelectenerg-1427	14	36	nano	nano	NOUN
fuelectenerg-1427	14	37	-	-	PUNCT
fuelectenerg-1427	14	38	electronics	electronic	NOUN
fuelectenerg-1427	14	39	laboratory	laboratory	NOUN
fuelectenerg-1427	14	40	,	,	PUNCT
fuelectenerg-1427	14	41	croatia	croatia	PROPN
fuelectenerg-1427	14	42	(	(	PUNCT
fuelectenerg-1427	14	43	e	e	NOUN
fuelectenerg-1427	14	44	-	-	NOUN
fuelectenerg-1427	14	45	mail	mail	NOUN
fuelectenerg-1427	14	46	:	:	PUNCT
fuelectenerg-1427	14	47	tom@zemris.fer.hr	tom@zemris.fer.hr	X
fuelectenerg-1427	14	48	)	)	PUNCT
fuelectenerg-1427	14	49	an	an	DET
fuelectenerg-1427	14	50	extended	extend	VERB
fuelectenerg-1427	14	51	green	green	PROPN
fuelectenerg-1427	14	52	sasao	sasao	PROPN
fuelectenerg-1427	14	53	hierarchy	hierarchy	NOUN
fuelectenerg-1427	14	54	of	of	ADP
fuelectenerg-1427	14	55	canonical	canonical	ADJ
fuelectenerg-1427	14	56	ternary	ternary	ADJ
fuelectenerg-1427	14	57	galois	galois	NOUN
fuelectenerg-1427	14	58	forms	form	NOUN
fuelectenerg-1427	14	59	and	and	CCONJ
fuelectenerg-1427	14	60	universal	universal	ADJ
fuelectenerg-1427	14	61	logic	logic	NOUN
fuelectenerg-1427	14	62	modules	module	VERB
fuelectenerg-1427	14	63	1electrical	1electrical	NUM
fuelectenerg-1427	14	64	engineering	engineering	NOUN
fuelectenerg-1427	14	65	department	department	PROPN
fuelectenerg-1427	14	66	,	,	PUNCT
fuelectenerg-1427	14	67	philadelphia	philadelphia	PROPN
fuelectenerg-1427	14	68	university	university	PROPN
fuelectenerg-1427	14	69	,	,	PUNCT
fuelectenerg-1427	14	70	2jordan	2jordan	NUM
fuelectenerg-1427	14	71	&	&	CCONJ
fuelectenerg-1427	14	72	computer	computer	PROPN
fuelectenerg-1427	14	73	engineering	engineering	PROPN
fuelectenerg-1427	14	74	department	department	PROPN
fuelectenerg-1427	14	75	,	,	PUNCT
fuelectenerg-1427	14	76	the	the	DET
fuelectenerg-1427	14	77	university	university	PROPN
fuelectenerg-1427	14	78	of	of	ADP
fuelectenerg-1427	14	79	jordan	jordan	PROPN
fuelectenerg-1427	14	80	,	,	PUNCT
fuelectenerg-1427	14	81	amman	amman	PROPN
fuelectenerg-1427	14	82	-	-	PUNCT
fuelectenerg-1427	14	83	jordan	jordan	PROPN
fuelectenerg-1427	14	84	abstract	abstract	PROPN
fuelectenerg-1427	14	85	.	.	PUNCT
fuelectenerg-1427	15	1	a	a	DET
fuelectenerg-1427	15	2	new	new	ADJ
fuelectenerg-1427	15	3	extended	extended	ADJ
fuelectenerg-1427	15	4	green	green	ADJ
fuelectenerg-1427	15	5	-	-	PUNCT
fuelectenerg-1427	15	6	sasao	sasao	NOUN
fuelectenerg-1427	15	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	15	8	of	of	ADP
fuelectenerg-1427	15	9	families	family	NOUN
fuelectenerg-1427	15	10	and	and	CCONJ
fuelectenerg-1427	15	11	forms	form	NOUN
fuelectenerg-1427	15	12	with	with	ADP
fuelectenerg-1427	15	13	a	a	DET
fuelectenerg-1427	15	14	new	new	ADJ
fuelectenerg-1427	15	15	subfamily	subfamily	NOUN
fuelectenerg-1427	15	16	for	for	ADP
fuelectenerg-1427	15	17	multiple	multiple	ADV
fuelectenerg-1427	15	18	-	-	PUNCT
fuelectenerg-1427	15	19	valued	value	VERB
fuelectenerg-1427	15	20	reed	reed	NOUN
fuelectenerg-1427	15	21	-	-	PUNCT
fuelectenerg-1427	15	22	muller	muller	NOUN
fuelectenerg-1427	15	23	logic	logic	NOUN
fuelectenerg-1427	15	24	is	be	AUX
fuelectenerg-1427	15	25	introduced	introduce	VERB
fuelectenerg-1427	15	26	.	.	PUNCT
fuelectenerg-1427	16	1	recently	recently	ADV
fuelectenerg-1427	16	2	,	,	PUNCT
fuelectenerg-1427	16	3	two	two	NUM
fuelectenerg-1427	16	4	families	family	NOUN
fuelectenerg-1427	16	5	of	of	ADP
fuelectenerg-1427	16	6	binary	binary	ADJ
fuelectenerg-1427	16	7	canonical	canonical	ADJ
fuelectenerg-1427	16	8	reed	reed	NOUN
fuelectenerg-1427	16	9	-	-	PUNCT
fuelectenerg-1427	16	10	muller	muller	NOUN
fuelectenerg-1427	16	11	forms	form	NOUN
fuelectenerg-1427	16	12	,	,	PUNCT
fuelectenerg-1427	16	13	called	call	VERB
fuelectenerg-1427	16	14	inclusive	inclusive	ADJ
fuelectenerg-1427	16	15	forms	form	NOUN
fuelectenerg-1427	16	16	(	(	PUNCT
fuelectenerg-1427	16	17	ifs	ifs	PROPN
fuelectenerg-1427	16	18	)	)	PUNCT
fuelectenerg-1427	16	19	and	and	CCONJ
fuelectenerg-1427	16	20	generalized	generalized	ADJ
fuelectenerg-1427	16	21	inclusive	inclusive	ADJ
fuelectenerg-1427	16	22	forms	form	NOUN
fuelectenerg-1427	16	23	(	(	PUNCT
fuelectenerg-1427	16	24	gifs	gifs	PROPN
fuelectenerg-1427	16	25	)	)	PUNCT
fuelectenerg-1427	16	26	have	have	AUX
fuelectenerg-1427	16	27	been	be	AUX
fuelectenerg-1427	16	28	proposed	propose	VERB
fuelectenerg-1427	16	29	,	,	PUNCT
fuelectenerg-1427	16	30	where	where	SCONJ
fuelectenerg-1427	16	31	the	the	DET
fuelectenerg-1427	16	32	second	second	ADJ
fuelectenerg-1427	16	33	family	family	NOUN
fuelectenerg-1427	16	34	was	be	AUX
fuelectenerg-1427	16	35	the	the	DET
fuelectenerg-1427	16	36	first	first	ADJ
fuelectenerg-1427	16	37	to	to	PART
fuelectenerg-1427	16	38	include	include	VERB
fuelectenerg-1427	16	39	all	all	DET
fuelectenerg-1427	16	40	minimum	minimum	ADJ
fuelectenerg-1427	16	41	exclusive	exclusive	ADJ
fuelectenerg-1427	16	42	sum	sum	NOUN
fuelectenerg-1427	16	43	-	-	PUNCT
fuelectenerg-1427	16	44	of	of	ADP
fuelectenerg-1427	16	45	-	-	PUNCT
fuelectenerg-1427	16	46	products	product	NOUN
fuelectenerg-1427	16	47	(	(	PUNCT
fuelectenerg-1427	16	48	esops	esop	NOUN
fuelectenerg-1427	16	49	)	)	PUNCT
fuelectenerg-1427	16	50	.	.	PUNCT
fuelectenerg-1427	17	1	in	in	ADP
fuelectenerg-1427	17	2	this	this	DET
fuelectenerg-1427	17	3	paper	paper	NOUN
fuelectenerg-1427	17	4	,	,	PUNCT
fuelectenerg-1427	17	5	we	we	PRON
fuelectenerg-1427	17	6	propose	propose	VERB
fuelectenerg-1427	17	7	,	,	PUNCT
fuelectenerg-1427	17	8	analogously	analogously	ADV
fuelectenerg-1427	17	9	to	to	ADP
fuelectenerg-1427	17	10	the	the	DET
fuelectenerg-1427	17	11	binary	binary	ADJ
fuelectenerg-1427	17	12	case	case	NOUN
fuelectenerg-1427	17	13	,	,	PUNCT
fuelectenerg-1427	17	14	two	two	NUM
fuelectenerg-1427	17	15	general	general	ADJ
fuelectenerg-1427	17	16	families	family	NOUN
fuelectenerg-1427	17	17	of	of	ADP
fuelectenerg-1427	17	18	canonical	canonical	ADJ
fuelectenerg-1427	17	19	ternary	ternary	ADJ
fuelectenerg-1427	17	20	reed	reed	NOUN
fuelectenerg-1427	17	21	-	-	PUNCT
fuelectenerg-1427	17	22	muller	muller	NOUN
fuelectenerg-1427	17	23	forms	form	NOUN
fuelectenerg-1427	17	24	,	,	PUNCT
fuelectenerg-1427	17	25	called	call	VERB
fuelectenerg-1427	17	26	ternary	ternary	ADJ
fuelectenerg-1427	17	27	inclusive	inclusive	ADJ
fuelectenerg-1427	17	28	forms	form	NOUN
fuelectenerg-1427	17	29	(	(	PUNCT
fuelectenerg-1427	17	30	tifs	tifs	PROPN
fuelectenerg-1427	17	31	)	)	PUNCT
fuelectenerg-1427	17	32	and	and	CCONJ
fuelectenerg-1427	17	33	their	their	PRON
fuelectenerg-1427	17	34	generalization	generalization	NOUN
fuelectenerg-1427	17	35	of	of	ADP
fuelectenerg-1427	17	36	ternary	ternary	ADJ
fuelectenerg-1427	17	37	generalized	generalize	VERB
fuelectenerg-1427	17	38	inclusive	inclusive	ADJ
fuelectenerg-1427	17	39	forms	form	NOUN
fuelectenerg-1427	17	40	(	(	PUNCT
fuelectenerg-1427	17	41	tgifs	tgif	NOUN
fuelectenerg-1427	17	42	)	)	PUNCT
fuelectenerg-1427	17	43	,	,	PUNCT
fuelectenerg-1427	17	44	where	where	SCONJ
fuelectenerg-1427	17	45	the	the	DET
fuelectenerg-1427	17	46	second	second	ADJ
fuelectenerg-1427	17	47	family	family	NOUN
fuelectenerg-1427	17	48	includes	include	VERB
fuelectenerg-1427	17	49	minimum	minimum	ADJ
fuelectenerg-1427	17	50	galois	galois	PROPN
fuelectenerg-1427	17	51	field	field	NOUN
fuelectenerg-1427	17	52	sum	sum	NOUN
fuelectenerg-1427	17	53	-	-	PUNCT
fuelectenerg-1427	17	54	of	of	ADP
fuelectenerg-1427	17	55	-	-	PUNCT
fuelectenerg-1427	17	56	products	product	NOUN
fuelectenerg-1427	17	57	(	(	PUNCT
fuelectenerg-1427	17	58	gfsops	gfsop	NOUN
fuelectenerg-1427	17	59	)	)	PUNCT
fuelectenerg-1427	17	60	over	over	ADP
fuelectenerg-1427	17	61	ternary	ternary	ADJ
fuelectenerg-1427	17	62	galois	galois	PROPN
fuelectenerg-1427	17	63	field	field	NOUN
fuelectenerg-1427	17	64	gf(3	gf(3	PROPN
fuelectenerg-1427	17	65	)	)	PUNCT
fuelectenerg-1427	17	66	.	.	PUNCT
fuelectenerg-1427	18	1	one	one	NUM
fuelectenerg-1427	18	2	of	of	ADP
fuelectenerg-1427	18	3	the	the	DET
fuelectenerg-1427	18	4	basic	basic	ADJ
fuelectenerg-1427	18	5	motivations	motivation	NOUN
fuelectenerg-1427	18	6	in	in	ADP
fuelectenerg-1427	18	7	this	this	DET
fuelectenerg-1427	18	8	work	work	NOUN
fuelectenerg-1427	18	9	is	be	AUX
fuelectenerg-1427	18	10	the	the	DET
fuelectenerg-1427	18	11	application	application	NOUN
fuelectenerg-1427	18	12	of	of	ADP
fuelectenerg-1427	18	13	these	these	DET
fuelectenerg-1427	18	14	tifs	tif	NOUN
fuelectenerg-1427	18	15	and	and	CCONJ
fuelectenerg-1427	18	16	tgifs	tgif	NOUN
fuelectenerg-1427	18	17	to	to	PART
fuelectenerg-1427	18	18	find	find	VERB
fuelectenerg-1427	18	19	the	the	DET
fuelectenerg-1427	18	20	minimum	minimum	ADJ
fuelectenerg-1427	18	21	gfsop	gfsop	NOUN
fuelectenerg-1427	18	22	for	for	ADP
fuelectenerg-1427	18	23	multiple	multiple	ADV
fuelectenerg-1427	18	24	-	-	PUNCT
fuelectenerg-1427	18	25	valued	value	VERB
fuelectenerg-1427	18	26	input	input	NOUN
fuelectenerg-1427	18	27	-	-	PUNCT
fuelectenerg-1427	18	28	output	output	NOUN
fuelectenerg-1427	18	29	functions	function	NOUN
fuelectenerg-1427	18	30	within	within	ADP
fuelectenerg-1427	18	31	logic	logic	ADJ
fuelectenerg-1427	18	32	synthesis	synthesis	NOUN
fuelectenerg-1427	18	33	,	,	PUNCT
fuelectenerg-1427	18	34	where	where	SCONJ
fuelectenerg-1427	18	35	a	a	DET
fuelectenerg-1427	18	36	gfsop	gfsop	NOUN
fuelectenerg-1427	18	37	minimizer	minimizer	NOUN
fuelectenerg-1427	18	38	based	base	VERB
fuelectenerg-1427	18	39	on	on	ADP
fuelectenerg-1427	18	40	if	if	SCONJ
fuelectenerg-1427	18	41	polarity	polarity	NOUN
fuelectenerg-1427	18	42	can	can	AUX
fuelectenerg-1427	18	43	be	be	AUX
fuelectenerg-1427	18	44	used	use	VERB
fuelectenerg-1427	18	45	to	to	PART
fuelectenerg-1427	18	46	minimize	minimize	VERB
fuelectenerg-1427	18	47	the	the	DET
fuelectenerg-1427	18	48	multiple	multiple	ADV
fuelectenerg-1427	18	49	-	-	PUNCT
fuelectenerg-1427	18	50	valued	value	VERB
fuelectenerg-1427	18	51	gfsop	gfsop	NOUN
fuelectenerg-1427	18	52	expression	expression	NOUN
fuelectenerg-1427	18	53	for	for	ADP
fuelectenerg-1427	18	54	any	any	DET
fuelectenerg-1427	18	55	given	give	VERB
fuelectenerg-1427	18	56	function	function	NOUN
fuelectenerg-1427	18	57	.	.	PUNCT
fuelectenerg-1427	19	1	the	the	DET
fuelectenerg-1427	19	2	realization	realization	NOUN
fuelectenerg-1427	19	3	of	of	ADP
fuelectenerg-1427	19	4	the	the	DET
fuelectenerg-1427	19	5	presented	present	VERB
fuelectenerg-1427	19	6	shannon	shannon	NOUN
fuelectenerg-1427	19	7	-	-	PUNCT
fuelectenerg-1427	19	8	davio	davio	NOUN
fuelectenerg-1427	19	9	(	(	PUNCT
fuelectenerg-1427	19	10	s	s	NOUN
fuelectenerg-1427	19	11	/	/	SYM
fuelectenerg-1427	19	12	d	d	NOUN
fuelectenerg-1427	19	13	)	)	PUNCT
fuelectenerg-1427	19	14	trees	tree	NOUN
fuelectenerg-1427	19	15	using	use	VERB
fuelectenerg-1427	19	16	universal	universal	ADJ
fuelectenerg-1427	19	17	logic	logic	NOUN
fuelectenerg-1427	19	18	modules	module	NOUN
fuelectenerg-1427	19	19	(	(	PUNCT
fuelectenerg-1427	19	20	ulms	ulm	NOUN
fuelectenerg-1427	19	21	)	)	PUNCT
fuelectenerg-1427	19	22	is	be	AUX
fuelectenerg-1427	19	23	also	also	ADV
fuelectenerg-1427	19	24	introduced	introduce	VERB
fuelectenerg-1427	19	25	,	,	PUNCT
fuelectenerg-1427	19	26	where	where	SCONJ
fuelectenerg-1427	19	27	ulms	ulm	NOUN
fuelectenerg-1427	19	28	are	be	AUX
fuelectenerg-1427	19	29	complete	complete	ADJ
fuelectenerg-1427	19	30	systems	system	NOUN
fuelectenerg-1427	19	31	that	that	PRON
fuelectenerg-1427	19	32	can	can	AUX
fuelectenerg-1427	19	33	implement	implement	VERB
fuelectenerg-1427	19	34	all	all	DET
fuelectenerg-1427	19	35	possible	possible	ADJ
fuelectenerg-1427	19	36	logic	logic	NOUN
fuelectenerg-1427	19	37	functions	function	NOUN
fuelectenerg-1427	19	38	utilizing	utilize	VERB
fuelectenerg-1427	19	39	the	the	DET
fuelectenerg-1427	19	40	corresponding	correspond	VERB
fuelectenerg-1427	19	41	s	s	PROPN
fuelectenerg-1427	19	42	/	/	SYM
fuelectenerg-1427	19	43	d	d	NOUN
fuelectenerg-1427	19	44	expansions	expansion	NOUN
fuelectenerg-1427	19	45	of	of	ADP
fuelectenerg-1427	19	46	multiple	multiple	ADV
fuelectenerg-1427	19	47	-	-	PUNCT
fuelectenerg-1427	19	48	valued	value	VERB
fuelectenerg-1427	19	49	shannon	shannon	NOUN
fuelectenerg-1427	19	50	and	and	CCONJ
fuelectenerg-1427	19	51	davio	davio	PROPN
fuelectenerg-1427	19	52	spectral	spectral	ADJ
fuelectenerg-1427	19	53	transforms	transform	VERB
fuelectenerg-1427	19	54	.	.	PUNCT
fuelectenerg-1427	20	1	key	key	ADJ
fuelectenerg-1427	20	2	words	word	NOUN
fuelectenerg-1427	20	3	:	:	PUNCT
fuelectenerg-1427	20	4	canonical	canonical	ADJ
fuelectenerg-1427	20	5	forms	form	NOUN
fuelectenerg-1427	20	6	,	,	PUNCT
fuelectenerg-1427	20	7	galois	galois	PROPN
fuelectenerg-1427	20	8	field	field	NOUN
fuelectenerg-1427	20	9	forms	form	NOUN
fuelectenerg-1427	20	10	,	,	PUNCT
fuelectenerg-1427	20	11	green	green	ADJ
fuelectenerg-1427	20	12	-	-	PUNCT
fuelectenerg-1427	20	13	sasao	sasao	PROPN
fuelectenerg-1427	20	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	20	15	,	,	PUNCT
fuelectenerg-1427	20	16	inclusive	inclusive	ADJ
fuelectenerg-1427	20	17	forms	form	NOUN
fuelectenerg-1427	20	18	,	,	PUNCT
fuelectenerg-1427	20	19	multiple	multiple	ADV
fuelectenerg-1427	20	20	-	-	PUNCT
fuelectenerg-1427	20	21	valued	value	VERB
fuelectenerg-1427	20	22	logic	logic	NOUN
fuelectenerg-1427	20	23	,	,	PUNCT
fuelectenerg-1427	20	24	shannon	shannon	ADJ
fuelectenerg-1427	20	25	-	-	PUNCT
fuelectenerg-1427	20	26	davio	davio	NOUN
fuelectenerg-1427	20	27	trees	tree	NOUN
fuelectenerg-1427	20	28	,	,	PUNCT
fuelectenerg-1427	20	29	ternary	ternary	ADJ
fuelectenerg-1427	20	30	logic	logic	NOUN
fuelectenerg-1427	20	31	,	,	PUNCT
fuelectenerg-1427	20	32	universal	universal	ADJ
fuelectenerg-1427	20	33	logic	logic	NOUN
fuelectenerg-1427	20	34	modules	module	NOUN
fuelectenerg-1427	20	35	.	.	PUNCT
fuelectenerg-1427	21	1	an	an	DET
fuelectenerg-1427	21	2	extended	extend	VERB
fuelectenerg-1427	21	3	green	green	PROPN
fuelectenerg-1427	21	4	sasao	sasao	PROPN
fuelectenerg-1427	21	5	hierarchy	hierarchy	NOUN
fuelectenerg-1427	21	6	of	of	ADP
fuelectenerg-1427	21	7	canonical	canonical	ADJ
fuelectenerg-1427	21	8	ternary	ternary	ADJ
fuelectenerg-1427	21	9	galois	galois	NOUN
fuelectenerg-1427	21	10	forms	form	NOUN
fuelectenerg-1427	21	11	and	and	CCONJ
fuelectenerg-1427	21	12	universal	universal	ADJ
fuelectenerg-1427	21	13	logic	logic	NOUN
fuelectenerg-1427	21	14	modules	module	NOUN
fuelectenerg-1427	21	15	anas	anas	PROPN
fuelectenerg-1427	21	16	n.	n.	PROPN
fuelectenerg-1427	21	17	al	al	PROPN
fuelectenerg-1427	21	18	-	-	PUNCT
fuelectenerg-1427	21	19	rabadi	rabadi	PROPN
fuelectenerg-1427	21	20	∗	∗	NOUN
fuelectenerg-1427	21	21	electrical	electrical	ADJ
fuelectenerg-1427	21	22	engineering	engineering	NOUN
fuelectenerg-1427	21	23	department	department	PROPN
fuelectenerg-1427	21	24	,	,	PUNCT
fuelectenerg-1427	21	25	philadelphia	philadelphia	PROPN
fuelectenerg-1427	21	26	university	university	PROPN
fuelectenerg-1427	21	27	,	,	PUNCT
fuelectenerg-1427	21	28	jordan	jordan	PROPN
fuelectenerg-1427	21	29	&	&	CCONJ
fuelectenerg-1427	21	30	computer	computer	PROPN
fuelectenerg-1427	21	31	engineering	engineering	PROPN
fuelectenerg-1427	21	32	department	department	PROPN
fuelectenerg-1427	21	33	,	,	PUNCT
fuelectenerg-1427	21	34	the	the	DET
fuelectenerg-1427	21	35	university	university	PROPN
fuelectenerg-1427	21	36	of	of	ADP
fuelectenerg-1427	21	37	jordan	jordan	PROPN
fuelectenerg-1427	21	38	,	,	PUNCT
fuelectenerg-1427	21	39	amman	amman	PROPN
fuelectenerg-1427	21	40	-	-	PUNCT
fuelectenerg-1427	21	41	jordan	jordan	PROPN
fuelectenerg-1427	21	42	e	e	PROPN
fuelectenerg-1427	21	43	-	-	NOUN
fuelectenerg-1427	21	44	mail	mail	NOUN
fuelectenerg-1427	21	45	:	:	PUNCT
fuelectenerg-1427	21	46	alrabadi@yahoo.com	alrabadi@yahoo.com	X
fuelectenerg-1427	22	1	abstract	abstract	ADJ
fuelectenerg-1427	22	2	a	a	DET
fuelectenerg-1427	22	3	new	new	ADJ
fuelectenerg-1427	22	4	extended	extended	ADJ
fuelectenerg-1427	22	5	green	green	ADJ
fuelectenerg-1427	22	6	-	-	PUNCT
fuelectenerg-1427	22	7	sasao	sasao	NOUN
fuelectenerg-1427	22	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	22	9	of	of	ADP
fuelectenerg-1427	22	10	families	family	NOUN
fuelectenerg-1427	22	11	and	and	CCONJ
fuelectenerg-1427	22	12	forms	form	NOUN
fuelectenerg-1427	22	13	with	with	ADP
fuelectenerg-1427	22	14	a	a	DET
fuelectenerg-1427	22	15	new	new	ADJ
fuelectenerg-1427	22	16	subfamily	subfamily	NOUN
fuelectenerg-1427	22	17	for	for	ADP
fuelectenerg-1427	22	18	multiple	multiple	ADV
fuelectenerg-1427	22	19	-	-	PUNCT
fuelectenerg-1427	22	20	valued	value	VERB
fuelectenerg-1427	22	21	reed	reed	NOUN
fuelectenerg-1427	22	22	-	-	PUNCT
fuelectenerg-1427	22	23	muller	muller	NOUN
fuelectenerg-1427	22	24	logic	logic	NOUN
fuelectenerg-1427	22	25	is	be	AUX
fuelectenerg-1427	22	26	introduced	introduce	VERB
fuelectenerg-1427	22	27	.	.	PUNCT
fuelectenerg-1427	23	1	recently	recently	ADV
fuelectenerg-1427	23	2	,	,	PUNCT
fuelectenerg-1427	23	3	two	two	NUM
fuelectenerg-1427	23	4	families	family	NOUN
fuelectenerg-1427	23	5	of	of	ADP
fuelectenerg-1427	23	6	binary	binary	ADJ
fuelectenerg-1427	23	7	canonical	canonical	ADJ
fuelectenerg-1427	23	8	reed	reed	NOUN
fuelectenerg-1427	23	9	-	-	PUNCT
fuelectenerg-1427	23	10	muller	muller	NOUN
fuelectenerg-1427	23	11	forms	form	NOUN
fuelectenerg-1427	23	12	,	,	PUNCT
fuelectenerg-1427	23	13	called	call	VERB
fuelectenerg-1427	23	14	inclusive	inclusive	ADJ
fuelectenerg-1427	23	15	forms	form	NOUN
fuelectenerg-1427	23	16	(	(	PUNCT
fuelectenerg-1427	23	17	ifs	ifs	PROPN
fuelectenerg-1427	23	18	)	)	PUNCT
fuelectenerg-1427	23	19	and	and	CCONJ
fuelectenerg-1427	23	20	generalized	generalized	ADJ
fuelectenerg-1427	23	21	inclusive	inclusive	ADJ
fuelectenerg-1427	23	22	forms	form	NOUN
fuelectenerg-1427	23	23	(	(	PUNCT
fuelectenerg-1427	23	24	gifs	gifs	PROPN
fuelectenerg-1427	23	25	)	)	PUNCT
fuelectenerg-1427	23	26	have	have	AUX
fuelectenerg-1427	23	27	been	be	AUX
fuelectenerg-1427	23	28	proposed	propose	VERB
fuelectenerg-1427	23	29	,	,	PUNCT
fuelectenerg-1427	23	30	where	where	SCONJ
fuelectenerg-1427	23	31	the	the	DET
fuelectenerg-1427	23	32	second	second	ADJ
fuelectenerg-1427	23	33	family	family	NOUN
fuelectenerg-1427	23	34	was	be	AUX
fuelectenerg-1427	23	35	the	the	DET
fuelectenerg-1427	23	36	first	first	ADJ
fuelectenerg-1427	23	37	to	to	PART
fuelectenerg-1427	23	38	include	include	VERB
fuelectenerg-1427	23	39	all	all	DET
fuelectenerg-1427	23	40	minimum	minimum	ADJ
fuelectenerg-1427	23	41	exclusive	exclusive	ADJ
fuelectenerg-1427	23	42	sum	sum	NOUN
fuelectenerg-1427	23	43	-	-	PUNCT
fuelectenerg-1427	23	44	of	of	ADP
fuelectenerg-1427	23	45	-	-	PUNCT
fuelectenerg-1427	23	46	products	product	NOUN
fuelectenerg-1427	23	47	(	(	PUNCT
fuelectenerg-1427	23	48	esops	esop	NOUN
fuelectenerg-1427	23	49	)	)	PUNCT
fuelectenerg-1427	23	50	.	.	PUNCT
fuelectenerg-1427	24	1	in	in	ADP
fuelectenerg-1427	24	2	this	this	DET
fuelectenerg-1427	24	3	paper	paper	NOUN
fuelectenerg-1427	24	4	,	,	PUNCT
fuelectenerg-1427	24	5	we	we	PRON
fuelectenerg-1427	24	6	propose	propose	VERB
fuelectenerg-1427	24	7	,	,	PUNCT
fuelectenerg-1427	24	8	analogously	analogously	ADV
fuelectenerg-1427	24	9	to	to	ADP
fuelectenerg-1427	24	10	the	the	DET
fuelectenerg-1427	24	11	binary	binary	ADJ
fuelectenerg-1427	24	12	case	case	NOUN
fuelectenerg-1427	24	13	,	,	PUNCT
fuelectenerg-1427	24	14	two	two	NUM
fuelectenerg-1427	24	15	general	general	ADJ
fuelectenerg-1427	24	16	families	family	NOUN
fuelectenerg-1427	24	17	of	of	ADP
fuelectenerg-1427	24	18	canonical	canonical	ADJ
fuelectenerg-1427	24	19	ternary	ternary	ADJ
fuelectenerg-1427	24	20	reed	reed	NOUN
fuelectenerg-1427	24	21	-	-	PUNCT
fuelectenerg-1427	24	22	muller	muller	NOUN
fuelectenerg-1427	24	23	forms	form	NOUN
fuelectenerg-1427	24	24	,	,	PUNCT
fuelectenerg-1427	24	25	called	call	VERB
fuelectenerg-1427	24	26	ternary	ternary	ADJ
fuelectenerg-1427	24	27	inclusive	inclusive	ADJ
fuelectenerg-1427	24	28	forms	form	NOUN
fuelectenerg-1427	24	29	(	(	PUNCT
fuelectenerg-1427	24	30	tifs	tifs	PROPN
fuelectenerg-1427	24	31	)	)	PUNCT
fuelectenerg-1427	24	32	and	and	CCONJ
fuelectenerg-1427	24	33	their	their	PRON
fuelectenerg-1427	24	34	generalization	generalization	NOUN
fuelectenerg-1427	24	35	of	of	ADP
fuelectenerg-1427	24	36	ternary	ternary	ADJ
fuelectenerg-1427	24	37	generalized	generalize	VERB
fuelectenerg-1427	24	38	inclusive	inclusive	ADJ
fuelectenerg-1427	24	39	forms	form	NOUN
fuelectenerg-1427	24	40	(	(	PUNCT
fuelectenerg-1427	24	41	tgifs	tgif	NOUN
fuelectenerg-1427	24	42	)	)	PUNCT
fuelectenerg-1427	24	43	,	,	PUNCT
fuelectenerg-1427	24	44	where	where	SCONJ
fuelectenerg-1427	24	45	the	the	DET
fuelectenerg-1427	24	46	second	second	ADJ
fuelectenerg-1427	24	47	family	family	NOUN
fuelectenerg-1427	24	48	includes	include	VERB
fuelectenerg-1427	24	49	minimum	minimum	ADJ
fuelectenerg-1427	24	50	galois	galois	PROPN
fuelectenerg-1427	24	51	field	field	NOUN
fuelectenerg-1427	24	52	sum	sum	NOUN
fuelectenerg-1427	24	53	-	-	PUNCT
fuelectenerg-1427	24	54	of	of	ADP
fuelectenerg-1427	24	55	-	-	PUNCT
fuelectenerg-1427	24	56	products	product	NOUN
fuelectenerg-1427	24	57	(	(	PUNCT
fuelectenerg-1427	24	58	gfsops	gfsop	NOUN
fuelectenerg-1427	24	59	)	)	PUNCT
fuelectenerg-1427	24	60	over	over	ADP
fuelectenerg-1427	24	61	ternary	ternary	ADJ
fuelectenerg-1427	24	62	galois	galois	PROPN
fuelectenerg-1427	24	63	field	field	NOUN
fuelectenerg-1427	24	64	gf(3	gf(3	PROPN
fuelectenerg-1427	24	65	)	)	PUNCT
fuelectenerg-1427	24	66	.	.	PUNCT
fuelectenerg-1427	25	1	one	one	NUM
fuelectenerg-1427	25	2	of	of	ADP
fuelectenerg-1427	25	3	the	the	DET
fuelectenerg-1427	25	4	basic	basic	ADJ
fuelectenerg-1427	25	5	motivations	motivation	NOUN
fuelectenerg-1427	25	6	in	in	ADP
fuelectenerg-1427	25	7	this	this	DET
fuelectenerg-1427	25	8	work	work	NOUN
fuelectenerg-1427	25	9	is	be	AUX
fuelectenerg-1427	25	10	the	the	DET
fuelectenerg-1427	25	11	application	application	NOUN
fuelectenerg-1427	25	12	of	of	ADP
fuelectenerg-1427	25	13	these	these	DET
fuelectenerg-1427	25	14	tifs	tif	NOUN
fuelectenerg-1427	25	15	and	and	CCONJ
fuelectenerg-1427	25	16	tgifs	tgif	NOUN
fuelectenerg-1427	25	17	to	to	PART
fuelectenerg-1427	25	18	find	find	VERB
fuelectenerg-1427	25	19	the	the	DET
fuelectenerg-1427	25	20	minimum	minimum	ADJ
fuelectenerg-1427	25	21	gfsop	gfsop	NOUN
fuelectenerg-1427	25	22	for	for	ADP
fuelectenerg-1427	25	23	multiple	multiple	ADV
fuelectenerg-1427	25	24	-	-	PUNCT
fuelectenerg-1427	25	25	valued	value	VERB
fuelectenerg-1427	25	26	inputoutput	inputoutput	NOUN
fuelectenerg-1427	25	27	functions	function	NOUN
fuelectenerg-1427	25	28	within	within	ADP
fuelectenerg-1427	25	29	logic	logic	ADJ
fuelectenerg-1427	25	30	synthesis	synthesis	NOUN
fuelectenerg-1427	25	31	,	,	PUNCT
fuelectenerg-1427	25	32	where	where	SCONJ
fuelectenerg-1427	25	33	a	a	DET
fuelectenerg-1427	25	34	gfsop	gfsop	NOUN
fuelectenerg-1427	25	35	minimizer	minimizer	NOUN
fuelectenerg-1427	25	36	based	base	VERB
fuelectenerg-1427	25	37	on	on	ADP
fuelectenerg-1427	25	38	if	if	SCONJ
fuelectenerg-1427	25	39	polarity	polarity	NOUN
fuelectenerg-1427	25	40	can	can	AUX
fuelectenerg-1427	25	41	be	be	AUX
fuelectenerg-1427	25	42	used	use	VERB
fuelectenerg-1427	25	43	to	to	PART
fuelectenerg-1427	25	44	minimize	minimize	VERB
fuelectenerg-1427	25	45	the	the	DET
fuelectenerg-1427	25	46	multiple	multiple	ADV
fuelectenerg-1427	25	47	-	-	PUNCT
fuelectenerg-1427	25	48	valued	value	VERB
fuelectenerg-1427	25	49	gfsop	gfsop	NOUN
fuelectenerg-1427	25	50	expression	expression	NOUN
fuelectenerg-1427	25	51	for	for	ADP
fuelectenerg-1427	25	52	any	any	DET
fuelectenerg-1427	25	53	given	give	VERB
fuelectenerg-1427	25	54	function	function	NOUN
fuelectenerg-1427	25	55	.	.	PUNCT
fuelectenerg-1427	26	1	the	the	DET
fuelectenerg-1427	26	2	realization	realization	NOUN
fuelectenerg-1427	26	3	of	of	ADP
fuelectenerg-1427	26	4	the	the	DET
fuelectenerg-1427	26	5	presented	present	VERB
fuelectenerg-1427	26	6	shannon	shannon	NOUN
fuelectenerg-1427	26	7	-	-	PUNCT
fuelectenerg-1427	26	8	davio	davio	NOUN
fuelectenerg-1427	26	9	(	(	PUNCT
fuelectenerg-1427	26	10	s	s	NOUN
fuelectenerg-1427	26	11	/	/	SYM
fuelectenerg-1427	26	12	d	d	NOUN
fuelectenerg-1427	26	13	)	)	PUNCT
fuelectenerg-1427	26	14	trees	tree	NOUN
fuelectenerg-1427	26	15	using	use	VERB
fuelectenerg-1427	26	16	universal	universal	ADJ
fuelectenerg-1427	26	17	logic	logic	NOUN
fuelectenerg-1427	26	18	modules	module	NOUN
fuelectenerg-1427	26	19	(	(	PUNCT
fuelectenerg-1427	26	20	ulms	ulm	NOUN
fuelectenerg-1427	26	21	)	)	PUNCT
fuelectenerg-1427	26	22	is	be	AUX
fuelectenerg-1427	26	23	also	also	ADV
fuelectenerg-1427	26	24	introduced	introduce	VERB
fuelectenerg-1427	26	25	,	,	PUNCT
fuelectenerg-1427	26	26	where	where	SCONJ
fuelectenerg-1427	26	27	ulms	ulm	NOUN
fuelectenerg-1427	26	28	are	be	AUX
fuelectenerg-1427	26	29	complete	complete	ADJ
fuelectenerg-1427	26	30	systems	system	NOUN
fuelectenerg-1427	26	31	that	that	PRON
fuelectenerg-1427	26	32	can	can	AUX
fuelectenerg-1427	26	33	implement	implement	VERB
fuelectenerg-1427	26	34	all	all	DET
fuelectenerg-1427	26	35	possible	possible	ADJ
fuelectenerg-1427	26	36	logic	logic	NOUN
fuelectenerg-1427	26	37	functions	function	NOUN
fuelectenerg-1427	26	38	utilizing	utilize	VERB
fuelectenerg-1427	26	39	the	the	DET
fuelectenerg-1427	26	40	corresponding	correspond	VERB
fuelectenerg-1427	26	41	s	s	PROPN
fuelectenerg-1427	26	42	/	/	SYM
fuelectenerg-1427	26	43	d	d	NOUN
fuelectenerg-1427	26	44	expansions	expansion	NOUN
fuelectenerg-1427	26	45	of	of	ADP
fuelectenerg-1427	26	46	multiple	multiple	ADV
fuelectenerg-1427	26	47	-	-	PUNCT
fuelectenerg-1427	26	48	valued	value	VERB
fuelectenerg-1427	26	49	shannon	shannon	NOUN
fuelectenerg-1427	26	50	and	and	CCONJ
fuelectenerg-1427	26	51	davio	davio	PROPN
fuelectenerg-1427	26	52	spectral	spectral	ADJ
fuelectenerg-1427	26	53	transforms	transform	VERB
fuelectenerg-1427	26	54	.	.	PUNCT
fuelectenerg-1427	27	1	keywords	keyword	NOUN
fuelectenerg-1427	27	2	1	1	NUM
fuelectenerg-1427	27	3	.	.	PUNCT
fuelectenerg-1427	28	1	canonical	canonical	ADJ
fuelectenerg-1427	28	2	forms	form	NOUN
fuelectenerg-1427	28	3	,	,	PUNCT
fuelectenerg-1427	28	4	galois	galois	PROPN
fuelectenerg-1427	28	5	field	field	NOUN
fuelectenerg-1427	28	6	forms	form	NOUN
fuelectenerg-1427	28	7	,	,	PUNCT
fuelectenerg-1427	28	8	green	green	ADJ
fuelectenerg-1427	28	9	-	-	PUNCT
fuelectenerg-1427	28	10	sasao	sasao	PROPN
fuelectenerg-1427	28	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	28	12	,	,	PUNCT
fuelectenerg-1427	28	13	inclusive	inclusive	ADJ
fuelectenerg-1427	28	14	forms	form	NOUN
fuelectenerg-1427	28	15	,	,	PUNCT
fuelectenerg-1427	28	16	multiple	multiple	ADV
fuelectenerg-1427	28	17	-	-	PUNCT
fuelectenerg-1427	28	18	valued	value	VERB
fuelectenerg-1427	28	19	logic	logic	NOUN
fuelectenerg-1427	28	20	,	,	PUNCT
fuelectenerg-1427	28	21	shannon	shannon	ADJ
fuelectenerg-1427	28	22	-	-	PUNCT
fuelectenerg-1427	28	23	davio	davio	NOUN
fuelectenerg-1427	28	24	trees	tree	NOUN
fuelectenerg-1427	28	25	,	,	PUNCT
fuelectenerg-1427	28	26	ternary	ternary	ADJ
fuelectenerg-1427	28	27	logic	logic	NOUN
fuelectenerg-1427	28	28	,	,	PUNCT
fuelectenerg-1427	28	29	universal	universal	ADJ
fuelectenerg-1427	28	30	logic	logic	NOUN
fuelectenerg-1427	28	31	modules	module	NOUN
fuelectenerg-1427	28	32	.	.	PUNCT
fuelectenerg-1427	29	1	1	1	NUM
fuelectenerg-1427	29	2	normal	normal	ADJ
fuelectenerg-1427	29	3	galois	galois	PROPN
fuelectenerg-1427	29	4	forms	form	VERB
fuelectenerg-1427	29	5	reed	reed	NOUN
fuelectenerg-1427	29	6	-	-	PUNCT
fuelectenerg-1427	29	7	muller	muller	NOUN
fuelectenerg-1427	29	8	-	-	PUNCT
fuelectenerg-1427	29	9	like	like	ADJ
fuelectenerg-1427	29	10	spectral	spectral	ADJ
fuelectenerg-1427	29	11	transforms	transform	VERB
fuelectenerg-1427	29	12	[	[	X
fuelectenerg-1427	29	13	1	1	NUM
fuelectenerg-1427	29	14	-	-	SYM
fuelectenerg-1427	29	15	18	18	NUM
fuelectenerg-1427	29	16	]	]	PUNCT
fuelectenerg-1427	29	17	have	have	AUX
fuelectenerg-1427	29	18	found	find	VERB
fuelectenerg-1427	29	19	a	a	DET
fuelectenerg-1427	29	20	variety	variety	NOUN
fuelectenerg-1427	29	21	of	of	ADP
fuelectenerg-1427	29	22	useful	useful	ADJ
fuelectenerg-1427	29	23	applications	application	NOUN
fuelectenerg-1427	29	24	in	in	ADP
fuelectenerg-1427	29	25	minimizing	minimize	VERB
fuelectenerg-1427	29	26	exclusive	exclusive	ADJ
fuelectenerg-1427	29	27	sum	sum	NOUN
fuelectenerg-1427	29	28	-	-	PUNCT
fuelectenerg-1427	29	29	of	of	ADP
fuelectenerg-1427	29	30	-	-	PUNCT
fuelectenerg-1427	29	31	products	product	NOUN
fuelectenerg-1427	29	32	(	(	PUNCT
fuelectenerg-1427	29	33	esop	esop	PROPN
fuelectenerg-1427	29	34	)	)	PUNCT
fuelectenerg-1427	29	35	and	and	CCONJ
fuelectenerg-1427	29	36	galois	galois	PROPN
fuelectenerg-1427	29	37	field	field	NOUN
fuelectenerg-1427	29	38	sop	sop	PROPN
fuelectenerg-1427	29	39	(	(	PUNCT
fuelectenerg-1427	29	40	gfsop	gfsop	NOUN
fuelectenerg-1427	29	41	)	)	PUNCT
fuelectenerg-1427	29	42	expressions	expression	NOUN
fuelectenerg-1427	29	43	,	,	PUNCT
fuelectenerg-1427	29	44	creation	creation	NOUN
fuelectenerg-1427	29	45	of	of	ADP
fuelectenerg-1427	29	46	new	new	ADJ
fuelectenerg-1427	29	47	forms	form	NOUN
fuelectenerg-1427	29	48	,	,	PUNCT
fuelectenerg-1427	29	49	binary	binary	ADJ
fuelectenerg-1427	29	50	and	and	CCONJ
fuelectenerg-1427	29	51	spectral	spectral	ADJ
fuelectenerg-1427	29	52	decision	decision	NOUN
fuelectenerg-1427	29	53	diagrams	diagram	NOUN
fuelectenerg-1427	29	54	,	,	PUNCT
fuelectenerg-1427	29	55	regular	regular	ADJ
fuelectenerg-1427	29	56	structures	structure	NOUN
fuelectenerg-1427	29	57	,	,	PUNCT
fuelectenerg-1427	29	58	besides	besides	SCONJ
fuelectenerg-1427	29	59	the	the	DET
fuelectenerg-1427	29	60	well	well	ADV
fuelectenerg-1427	29	61	-	-	PUNCT
fuelectenerg-1427	29	62	known	know	VERB
fuelectenerg-1427	29	63	uses	use	NOUN
fuelectenerg-1427	29	64	in	in	ADP
fuelectenerg-1427	29	65	digital	digital	ADJ
fuelectenerg-1427	29	66	communications	communication	NOUN
fuelectenerg-1427	29	67	,	,	PUNCT
fuelectenerg-1427	29	68	digital	digital	ADJ
fuelectenerg-1427	29	69	signal	signal	NOUN
fuelectenerg-1427	29	70	∗received	∗receive	VERB
fuelectenerg-1427	29	71	:	:	PUNCT
fuelectenerg-1427	29	72	july	july	PROPN
fuelectenerg-1427	29	73	15	15	NUM
fuelectenerg-1427	29	74	,	,	PUNCT
fuelectenerg-1427	29	75	2015	2015	NUM
fuelectenerg-1427	29	76	101	101	NUM
fuelectenerg-1427	29	77	an	an	DET
fuelectenerg-1427	29	78	extended	extend	VERB
fuelectenerg-1427	29	79	green	green	ADJ
fuelectenerg-1427	29	80	sasao	sasao	PROPN
fuelectenerg-1427	29	81	hierarchy	hierarchy	NOUN
fuelectenerg-1427	29	82	of	of	ADP
fuelectenerg-1427	29	83	canonical	canonical	ADJ
fuelectenerg-1427	29	84	ternary	ternary	ADJ
fuelectenerg-1427	29	85	galois	galois	NOUN
fuelectenerg-1427	29	86	forms	form	NOUN
fuelectenerg-1427	29	87	...	...	PUNCT
fuelectenerg-1427	29	88	table	table	NOUN
fuelectenerg-1427	29	89	1	1	NUM
fuelectenerg-1427	29	90	:	:	PUNCT
fuelectenerg-1427	29	91	number	number	NOUN
fuelectenerg-1427	29	92	of	of	ADP
fuelectenerg-1427	29	93	product	product	NOUN
fuelectenerg-1427	29	94	terms	term	NOUN
fuelectenerg-1427	29	95	needed	need	VERB
fuelectenerg-1427	29	96	to	to	PART
fuelectenerg-1427	29	97	realize	realize	VERB
fuelectenerg-1427	29	98	some	some	DET
fuelectenerg-1427	29	99	arithmetic	arithmetic	ADJ
fuelectenerg-1427	29	100	functions	function	NOUN
fuelectenerg-1427	29	101	using	use	VERB
fuelectenerg-1427	29	102	various	various	ADJ
fuelectenerg-1427	29	103	expressions	expression	NOUN
fuelectenerg-1427	29	104	.	.	PUNCT
fuelectenerg-1427	30	1	function	function	NOUN
fuelectenerg-1427	30	2	pprm	pprm	PROPN
fuelectenerg-1427	30	3	fprm	fprm	PROPN
fuelectenerg-1427	30	4	grm	grm	PROPN
fuelectenerg-1427	30	5	esop	esop	PROPN
fuelectenerg-1427	30	6	sop	sop	PROPN
fuelectenerg-1427	30	7	adr4	adr4	PROPN
fuelectenerg-1427	30	8	34	34	NUM
fuelectenerg-1427	30	9	34	34	NUM
fuelectenerg-1427	30	10	34	34	NUM
fuelectenerg-1427	30	11	31	31	NUM
fuelectenerg-1427	30	12	75	75	NUM
fuelectenerg-1427	30	13	log8	log8	NOUN
fuelectenerg-1427	30	14	253	253	NUM
fuelectenerg-1427	30	15	193	193	NUM
fuelectenerg-1427	30	16	105	105	NUM
fuelectenerg-1427	30	17	96	96	NUM
fuelectenerg-1427	30	18	123	123	NUM
fuelectenerg-1427	30	19	nrm4	nrm4	NOUN
fuelectenerg-1427	30	20	216	216	NUM
fuelectenerg-1427	30	21	185	185	NUM
fuelectenerg-1427	30	22	96	96	NUM
fuelectenerg-1427	30	23	69	69	NUM
fuelectenerg-1427	30	24	120	120	NUM
fuelectenerg-1427	30	25	rdm8	rdm8	NOUN
fuelectenerg-1427	30	26	56	56	NUM
fuelectenerg-1427	30	27	56	56	NUM
fuelectenerg-1427	30	28	31	31	NUM
fuelectenerg-1427	30	29	31	31	NUM
fuelectenerg-1427	30	30	76	76	NUM
fuelectenerg-1427	30	31	rot8	rot8	NOUN
fuelectenerg-1427	30	32	225	225	NUM
fuelectenerg-1427	30	33	118	118	NUM
fuelectenerg-1427	30	34	51	51	NUM
fuelectenerg-1427	30	35	35	35	NUM
fuelectenerg-1427	30	36	57	57	NUM
fuelectenerg-1427	30	37	sym9	sym9	NOUN
fuelectenerg-1427	30	38	210	210	NUM
fuelectenerg-1427	30	39	173	173	NUM
fuelectenerg-1427	30	40	126	126	NUM
fuelectenerg-1427	30	41	51	51	NUM
fuelectenerg-1427	30	42	84	84	NUM
fuelectenerg-1427	30	43	wgt8	wgt8	NOUN
fuelectenerg-1427	30	44	107	107	NUM
fuelectenerg-1427	30	45	107	107	NUM
fuelectenerg-1427	30	46	107	107	NUM
fuelectenerg-1427	30	47	58	58	NUM
fuelectenerg-1427	30	48	255	255	NUM
fuelectenerg-1427	31	1	and	and	CCONJ
fuelectenerg-1427	31	2	image	image	NOUN
fuelectenerg-1427	31	3	processing	processing	NOUN
fuelectenerg-1427	31	4	,	,	PUNCT
fuelectenerg-1427	31	5	and	and	CCONJ
fuelectenerg-1427	31	6	fault	fault	VERB
fuelectenerg-1427	31	7	detection	detection	NOUN
fuelectenerg-1427	31	8	and	and	CCONJ
fuelectenerg-1427	31	9	testing	testing	NOUN
fuelectenerg-1427	32	1	[	[	X
fuelectenerg-1427	32	2	1	1	NUM
fuelectenerg-1427	32	3	-	-	SYM
fuelectenerg-1427	32	4	9	9	NUM
fuelectenerg-1427	32	5	,	,	PUNCT
fuelectenerg-1427	32	6	12	12	NUM
fuelectenerg-1427	32	7	-	-	SYM
fuelectenerg-1427	32	8	14	14	NUM
fuelectenerg-1427	32	9	,	,	PUNCT
fuelectenerg-1427	32	10	16	16	NUM
fuelectenerg-1427	32	11	,	,	PUNCT
fuelectenerg-1427	32	12	17	17	NUM
fuelectenerg-1427	32	13	,	,	PUNCT
fuelectenerg-1427	32	14	19	19	NUM
fuelectenerg-1427	32	15	,	,	PUNCT
fuelectenerg-1427	32	16	20	20	NUM
fuelectenerg-1427	32	17	,	,	PUNCT
fuelectenerg-1427	32	18	21	21	NUM
fuelectenerg-1427	32	19	]	]	PUNCT
fuelectenerg-1427	32	20	.	.	PUNCT
fuelectenerg-1427	33	1	the	the	DET
fuelectenerg-1427	33	2	method	method	NOUN
fuelectenerg-1427	33	3	of	of	ADP
fuelectenerg-1427	33	4	generating	generate	VERB
fuelectenerg-1427	33	5	the	the	DET
fuelectenerg-1427	33	6	new	new	ADJ
fuelectenerg-1427	33	7	families	family	NOUN
fuelectenerg-1427	33	8	of	of	ADP
fuelectenerg-1427	33	9	multiple	multiple	ADV
fuelectenerg-1427	33	10	-	-	PUNCT
fuelectenerg-1427	33	11	valued	value	VERB
fuelectenerg-1427	33	12	shannon	shannon	NOUN
fuelectenerg-1427	33	13	and	and	CCONJ
fuelectenerg-1427	33	14	davio	davio	PROPN
fuelectenerg-1427	33	15	spectral	spectral	ADJ
fuelectenerg-1427	33	16	transforms	transform	NOUN
fuelectenerg-1427	33	17	is	be	AUX
fuelectenerg-1427	33	18	based	base	VERB
fuelectenerg-1427	33	19	on	on	ADP
fuelectenerg-1427	33	20	the	the	DET
fuelectenerg-1427	33	21	fundamental	fundamental	ADJ
fuelectenerg-1427	33	22	multiple	multiple	ADV
fuelectenerg-1427	33	23	-	-	PUNCT
fuelectenerg-1427	33	24	valued	value	VERB
fuelectenerg-1427	33	25	shannon	shannon	NOUN
fuelectenerg-1427	33	26	and	and	CCONJ
fuelectenerg-1427	33	27	davio	davio	NOUN
fuelectenerg-1427	33	28	expansions	expansion	NOUN
fuelectenerg-1427	33	29	.	.	PUNCT
fuelectenerg-1427	34	1	dyadic	dyadic	ADJ
fuelectenerg-1427	34	2	families	family	NOUN
fuelectenerg-1427	34	3	of	of	ADP
fuelectenerg-1427	34	4	discrete	discrete	ADJ
fuelectenerg-1427	34	5	transforms	transform	NOUN
fuelectenerg-1427	34	6	;	;	PUNCT
fuelectenerg-1427	34	7	reed	reed	NOUN
fuelectenerg-1427	34	8	-	-	PUNCT
fuelectenerg-1427	34	9	muller	muller	NOUN
fuelectenerg-1427	34	10	and	and	CCONJ
fuelectenerg-1427	34	11	green	green	ADJ
fuelectenerg-1427	34	12	-	-	PUNCT
fuelectenerg-1427	34	13	sasao	sasao	PROPN
fuelectenerg-1427	34	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	34	15	,	,	PUNCT
fuelectenerg-1427	34	16	walsh	walsh	NOUN
fuelectenerg-1427	34	17	,	,	PUNCT
fuelectenerg-1427	34	18	arithmetic	arithmetic	ADJ
fuelectenerg-1427	34	19	,	,	PUNCT
fuelectenerg-1427	34	20	adding	add	VERB
fuelectenerg-1427	34	21	and	and	CCONJ
fuelectenerg-1427	34	22	haar	haar	PROPN
fuelectenerg-1427	34	23	transforms	transform	VERB
fuelectenerg-1427	34	24	and	and	CCONJ
fuelectenerg-1427	34	25	their	their	PRON
fuelectenerg-1427	34	26	generalizations	generalization	NOUN
fuelectenerg-1427	34	27	to	to	ADP
fuelectenerg-1427	34	28	multiple	multiple	ADV
fuelectenerg-1427	34	29	-	-	PUNCT
fuelectenerg-1427	34	30	valued	value	VERB
fuelectenerg-1427	34	31	transforms	transform	NOUN
fuelectenerg-1427	34	32	,	,	PUNCT
fuelectenerg-1427	34	33	have	have	AUX
fuelectenerg-1427	34	34	also	also	ADV
fuelectenerg-1427	34	35	found	find	VERB
fuelectenerg-1427	34	36	important	important	ADJ
fuelectenerg-1427	34	37	applications	application	NOUN
fuelectenerg-1427	34	38	in	in	ADP
fuelectenerg-1427	34	39	digital	digital	ADJ
fuelectenerg-1427	34	40	system	system	NOUN
fuelectenerg-1427	34	41	design	design	NOUN
fuelectenerg-1427	34	42	and	and	CCONJ
fuelectenerg-1427	34	43	optimization	optimization	NOUN
fuelectenerg-1427	34	44	[	[	X
fuelectenerg-1427	34	45	1	1	NUM
fuelectenerg-1427	34	46	,	,	PUNCT
fuelectenerg-1427	34	47	6	6	NUM
fuelectenerg-1427	34	48	,	,	PUNCT
fuelectenerg-1427	34	49	19	19	NUM
fuelectenerg-1427	34	50	,	,	PUNCT
fuelectenerg-1427	34	51	7	7	NUM
fuelectenerg-1427	34	52	-	-	SYM
fuelectenerg-1427	34	53	18	18	NUM
fuelectenerg-1427	34	54	,	,	PUNCT
fuelectenerg-1427	34	55	20	20	NUM
fuelectenerg-1427	34	56	-	-	SYM
fuelectenerg-1427	34	57	31	31	NUM
fuelectenerg-1427	34	58	]	]	PUNCT
fuelectenerg-1427	34	59	.	.	PUNCT
fuelectenerg-1427	35	1	normal	normal	ADJ
fuelectenerg-1427	35	2	canonical	canonical	ADJ
fuelectenerg-1427	35	3	forms	form	NOUN
fuelectenerg-1427	35	4	play	play	VERB
fuelectenerg-1427	35	5	an	an	DET
fuelectenerg-1427	35	6	important	important	ADJ
fuelectenerg-1427	35	7	role	role	NOUN
fuelectenerg-1427	35	8	in	in	ADP
fuelectenerg-1427	35	9	the	the	DET
fuelectenerg-1427	35	10	synthesis	synthesis	NOUN
fuelectenerg-1427	35	11	of	of	ADP
fuelectenerg-1427	35	12	logic	logic	NOUN
fuelectenerg-1427	35	13	circuits	circuit	NOUN
fuelectenerg-1427	35	14	which	which	PRON
fuelectenerg-1427	35	15	includes	include	VERB
fuelectenerg-1427	35	16	synthesis	synthesis	NOUN
fuelectenerg-1427	35	17	,	,	PUNCT
fuelectenerg-1427	35	18	testing	testing	NOUN
fuelectenerg-1427	35	19	and	and	CCONJ
fuelectenerg-1427	35	20	optimization	optimization	NOUN
fuelectenerg-1427	35	21	[	[	X
fuelectenerg-1427	35	22	1	1	NUM
fuelectenerg-1427	35	23	,	,	PUNCT
fuelectenerg-1427	35	24	9	9	NUM
fuelectenerg-1427	35	25	,	,	PUNCT
fuelectenerg-1427	35	26	12	12	NUM
fuelectenerg-1427	35	27	-	-	SYM
fuelectenerg-1427	35	28	15	15	NUM
fuelectenerg-1427	35	29	,	,	PUNCT
fuelectenerg-1427	35	30	17	17	NUM
fuelectenerg-1427	35	31	,	,	PUNCT
fuelectenerg-1427	35	32	21	21	NUM
fuelectenerg-1427	35	33	,	,	PUNCT
fuelectenerg-1427	35	34	22	22	NUM
fuelectenerg-1427	35	35	,	,	PUNCT
fuelectenerg-1427	35	36	26	26	NUM
fuelectenerg-1427	35	37	,	,	PUNCT
fuelectenerg-1427	35	38	27	27	NUM
fuelectenerg-1427	35	39	,	,	PUNCT
fuelectenerg-1427	35	40	31	31	NUM
fuelectenerg-1427	35	41	,	,	PUNCT
fuelectenerg-1427	35	42	32	32	NUM
fuelectenerg-1427	35	43	]	]	PUNCT
fuelectenerg-1427	35	44	.	.	PUNCT
fuelectenerg-1427	36	1	one	one	PRON
fuelectenerg-1427	36	2	can	can	AUX
fuelectenerg-1427	36	3	observe	observe	VERB
fuelectenerg-1427	36	4	that	that	SCONJ
fuelectenerg-1427	36	5	by	by	ADP
fuelectenerg-1427	36	6	going	go	VERB
fuelectenerg-1427	36	7	,	,	PUNCT
fuelectenerg-1427	36	8	for	for	ADP
fuelectenerg-1427	36	9	example	example	NOUN
fuelectenerg-1427	36	10	,	,	PUNCT
fuelectenerg-1427	36	11	from	from	ADP
fuelectenerg-1427	36	12	positive	positive	ADJ
fuelectenerg-1427	36	13	polarity	polarity	NOUN
fuelectenerg-1427	36	14	reed	reed	NOUN
fuelectenerg-1427	36	15	-	-	PUNCT
fuelectenerg-1427	36	16	muller	muller	NOUN
fuelectenerg-1427	36	17	(	(	PUNCT
fuelectenerg-1427	36	18	pprm	pprm	ADJ
fuelectenerg-1427	36	19	)	)	PUNCT
fuelectenerg-1427	36	20	form	form	NOUN
fuelectenerg-1427	36	21	to	to	ADP
fuelectenerg-1427	36	22	the	the	DET
fuelectenerg-1427	36	23	generalized	generalized	ADJ
fuelectenerg-1427	36	24	reed	reed	NOUN
fuelectenerg-1427	36	25	-	-	PUNCT
fuelectenerg-1427	36	26	muller	muller	NOUN
fuelectenerg-1427	36	27	(	(	PUNCT
fuelectenerg-1427	36	28	grm	grm	NOUN
fuelectenerg-1427	36	29	)	)	PUNCT
fuelectenerg-1427	36	30	form	form	NOUN
fuelectenerg-1427	36	31	,	,	PUNCT
fuelectenerg-1427	36	32	less	less	ADJ
fuelectenerg-1427	36	33	constraints	constraint	NOUN
fuelectenerg-1427	36	34	are	be	AUX
fuelectenerg-1427	36	35	imposed	impose	VERB
fuelectenerg-1427	36	36	on	on	ADP
fuelectenerg-1427	36	37	the	the	DET
fuelectenerg-1427	36	38	canonical	canonical	ADJ
fuelectenerg-1427	36	39	forms	form	NOUN
fuelectenerg-1427	36	40	due	due	ADJ
fuelectenerg-1427	36	41	to	to	ADP
fuelectenerg-1427	36	42	the	the	DET
fuelectenerg-1427	36	43	enlarged	enlarged	ADJ
fuelectenerg-1427	36	44	set	set	NOUN
fuelectenerg-1427	36	45	of	of	ADP
fuelectenerg-1427	36	46	polarities	polarity	NOUN
fuelectenerg-1427	36	47	that	that	PRON
fuelectenerg-1427	36	48	one	one	PRON
fuelectenerg-1427	36	49	can	can	AUX
fuelectenerg-1427	36	50	choose	choose	VERB
fuelectenerg-1427	36	51	from	from	ADP
fuelectenerg-1427	36	52	.	.	PUNCT
fuelectenerg-1427	37	1	the	the	DET
fuelectenerg-1427	37	2	gain	gain	NOUN
fuelectenerg-1427	37	3	of	of	ADP
fuelectenerg-1427	37	4	more	more	ADJ
fuelectenerg-1427	37	5	freedom	freedom	NOUN
fuelectenerg-1427	37	6	on	on	ADP
fuelectenerg-1427	37	7	the	the	DET
fuelectenerg-1427	37	8	polarity	polarity	NOUN
fuelectenerg-1427	37	9	of	of	ADP
fuelectenerg-1427	37	10	the	the	DET
fuelectenerg-1427	37	11	canonical	canonical	ADJ
fuelectenerg-1427	37	12	expansions	expansion	NOUN
fuelectenerg-1427	37	13	will	will	AUX
fuelectenerg-1427	37	14	provide	provide	VERB
fuelectenerg-1427	37	15	an	an	DET
fuelectenerg-1427	37	16	advantage	advantage	NOUN
fuelectenerg-1427	37	17	of	of	ADP
fuelectenerg-1427	37	18	obtaining	obtain	VERB
fuelectenerg-1427	37	19	exclusive	exclusive	ADJ
fuelectenerg-1427	37	20	-	-	PUNCT
fuelectenerg-1427	37	21	sum	sum	NOUN
fuelectenerg-1427	37	22	-	-	PUNCT
fuelectenerg-1427	37	23	of	of	ADP
fuelectenerg-1427	37	24	-	-	PUNCT
fuelectenerg-1427	37	25	product	product	NOUN
fuelectenerg-1427	37	26	(	(	PUNCT
fuelectenerg-1427	37	27	esop	esop	PROPN
fuelectenerg-1427	37	28	)	)	PUNCT
fuelectenerg-1427	37	29	expressions	expression	NOUN
fuelectenerg-1427	37	30	with	with	ADP
fuelectenerg-1427	37	31	less	less	ADJ
fuelectenerg-1427	37	32	number	number	NOUN
fuelectenerg-1427	37	33	of	of	ADP
fuelectenerg-1427	37	34	terms	term	NOUN
fuelectenerg-1427	37	35	and	and	CCONJ
fuelectenerg-1427	37	36	literals	literal	NOUN
fuelectenerg-1427	37	37	,	,	PUNCT
fuelectenerg-1427	37	38	and	and	CCONJ
fuelectenerg-1427	37	39	consequently	consequently	ADV
fuelectenerg-1427	37	40	expressing	express	VERB
fuelectenerg-1427	37	41	boolean	boolean	ADJ
fuelectenerg-1427	37	42	functions	function	NOUN
fuelectenerg-1427	37	43	using	use	VERB
fuelectenerg-1427	37	44	esop	esop	NOUN
fuelectenerg-1427	37	45	forms	form	NOUN
fuelectenerg-1427	37	46	will	will	AUX
fuelectenerg-1427	37	47	produce	produce	VERB
fuelectenerg-1427	37	48	on	on	ADP
fuelectenerg-1427	37	49	average	average	ADJ
fuelectenerg-1427	37	50	expressions	expression	NOUN
fuelectenerg-1427	37	51	with	with	ADP
fuelectenerg-1427	37	52	less	less	ADJ
fuelectenerg-1427	37	53	size	size	NOUN
fuelectenerg-1427	37	54	as	as	SCONJ
fuelectenerg-1427	37	55	if	if	SCONJ
fuelectenerg-1427	37	56	compared	compare	VERB
fuelectenerg-1427	37	57	to	to	ADP
fuelectenerg-1427	37	58	sum	sum	NOUN
fuelectenerg-1427	37	59	-	-	PUNCT
fuelectenerg-1427	37	60	of	of	ADP
fuelectenerg-1427	37	61	-	-	PUNCT
fuelectenerg-1427	37	62	product	product	NOUN
fuelectenerg-1427	37	63	(	(	PUNCT
fuelectenerg-1427	37	64	sop	sop	NOUN
fuelectenerg-1427	37	65	)	)	PUNCT
fuelectenerg-1427	37	66	expressions	expression	NOUN
fuelectenerg-1427	37	67	for	for	ADP
fuelectenerg-1427	37	68	example	example	NOUN
fuelectenerg-1427	37	69	.	.	PUNCT
fuelectenerg-1427	38	1	table	table	NOUN
fuelectenerg-1427	38	2	1	1	NUM
fuelectenerg-1427	38	3	illustrates	illustrate	VERB
fuelectenerg-1427	38	4	these	these	DET
fuelectenerg-1427	38	5	observations	observation	NOUN
fuelectenerg-1427	39	1	[	[	X
fuelectenerg-1427	39	2	1	1	NUM
fuelectenerg-1427	39	3	]	]	PUNCT
fuelectenerg-1427	39	4	.	.	PUNCT
fuelectenerg-1427	40	1	the	the	DET
fuelectenerg-1427	40	2	main	main	ADJ
fuelectenerg-1427	40	3	algebraic	algebraic	ADJ
fuelectenerg-1427	40	4	structure	structure	NOUN
fuelectenerg-1427	40	5	which	which	PRON
fuelectenerg-1427	40	6	is	be	AUX
fuelectenerg-1427	40	7	used	use	VERB
fuelectenerg-1427	40	8	in	in	ADP
fuelectenerg-1427	40	9	this	this	DET
fuelectenerg-1427	40	10	work	work	NOUN
fuelectenerg-1427	40	11	for	for	ADP
fuelectenerg-1427	40	12	developing	develop	VERB
fuelectenerg-1427	40	13	the	the	DET
fuelectenerg-1427	40	14	canonical	canonical	ADJ
fuelectenerg-1427	40	15	normal	normal	ADJ
fuelectenerg-1427	40	16	forms	form	NOUN
fuelectenerg-1427	40	17	is	be	AUX
fuelectenerg-1427	40	18	the	the	DET
fuelectenerg-1427	40	19	galois	galois	PROPN
fuelectenerg-1427	40	20	field	field	NOUN
fuelectenerg-1427	40	21	(	(	PUNCT
fuelectenerg-1427	40	22	gf	gf	NOUN
fuelectenerg-1427	40	23	)	)	PUNCT
fuelectenerg-1427	40	24	algebraic	algebraic	ADJ
fuelectenerg-1427	40	25	structure	structure	NOUN
fuelectenerg-1427	40	26	,	,	PUNCT
fuelectenerg-1427	40	27	which	which	PRON
fuelectenerg-1427	40	28	is	be	AUX
fuelectenerg-1427	40	29	a	a	DET
fuelectenerg-1427	40	30	fundamental	fundamental	ADJ
fuelectenerg-1427	40	31	algebraic	algebraic	ADJ
fuelectenerg-1427	40	32	structure	structure	NOUN
fuelectenerg-1427	40	33	in	in	ADP
fuelectenerg-1427	40	34	the	the	DET
fuelectenerg-1427	40	35	theory	theory	NOUN
fuelectenerg-1427	40	36	of	of	ADP
fuelectenerg-1427	40	37	algebra	algebra	NOUN
fuelectenerg-1427	40	38	[	[	X
fuelectenerg-1427	40	39	1	1	NUM
fuelectenerg-1427	40	40	,	,	PUNCT
fuelectenerg-1427	40	41	12	12	NUM
fuelectenerg-1427	40	42	,	,	PUNCT
fuelectenerg-1427	40	43	13	13	NUM
fuelectenerg-1427	40	44	,	,	PUNCT
fuelectenerg-1427	40	45	17	17	NUM
fuelectenerg-1427	40	46	,	,	PUNCT
fuelectenerg-1427	40	47	22	22	NUM
fuelectenerg-1427	40	48	,	,	PUNCT
fuelectenerg-1427	40	49	29	29	NUM
fuelectenerg-1427	40	50	,	,	PUNCT
fuelectenerg-1427	40	51	33	33	NUM
fuelectenerg-1427	40	52	,	,	PUNCT
fuelectenerg-1427	40	53	34	34	NUM
fuelectenerg-1427	40	54	]	]	PUNCT
fuelectenerg-1427	40	55	.	.	PUNCT
fuelectenerg-1427	41	1	the	the	DET
fuelectenerg-1427	41	2	importance	importance	NOUN
fuelectenerg-1427	41	3	of	of	ADP
fuelectenerg-1427	41	4	gf	gf	PROPN
fuelectenerg-1427	41	5	for	for	ADP
fuelectenerg-1427	41	6	logic	logic	ADJ
fuelectenerg-1427	41	7	synthesis	synthesis	NOUN
fuelectenerg-1427	41	8	results	result	NOUN
fuelectenerg-1427	41	9	from	from	ADP
fuelectenerg-1427	41	10	the	the	DET
fuelectenerg-1427	41	11	fact	fact	NOUN
fuelectenerg-1427	41	12	that	that	SCONJ
fuelectenerg-1427	41	13	every	every	DET
fuelectenerg-1427	41	14	finite	finite	ADJ
fuelectenerg-1427	41	15	field	field	NOUN
fuelectenerg-1427	41	16	is	be	AUX
fuelectenerg-1427	41	17	isomorphic	isomorphic	ADJ
fuelectenerg-1427	41	18	to	to	ADP
fuelectenerg-1427	41	19	a	a	DET
fuelectenerg-1427	41	20	galois	galois	PROPN
fuelectenerg-1427	41	21	field	field	NOUN
fuelectenerg-1427	41	22	.	.	PUNCT
fuelectenerg-1427	42	1	in	in	ADP
fuelectenerg-1427	42	2	general	general	ADJ
fuelectenerg-1427	42	3	,	,	PUNCT
fuelectenerg-1427	42	4	the	the	DET
fuelectenerg-1427	42	5	attractive	attractive	ADJ
fuelectenerg-1427	42	6	properties	property	NOUN
fuelectenerg-1427	42	7	of	of	ADP
fuelectenerg-1427	42	8	gf	gf	NOUN
fuelectenerg-1427	42	9	-	-	PUNCT
fuelectenerg-1427	42	10	based	base	VERB
fuelectenerg-1427	42	11	circuits	circuit	NOUN
fuelectenerg-1427	42	12	,	,	PUNCT
fuelectenerg-1427	42	13	such	such	ADJ
fuelectenerg-1427	42	14	as	as	ADP
fuelectenerg-1427	42	15	the	the	DET
fuelectenerg-1427	42	16	high	high	ADJ
fuelectenerg-1427	42	17	testability	testability	NOUN
fuelectenerg-1427	42	18	of	of	ADP
fuelectenerg-1427	42	19	such	such	ADJ
fuelectenerg-1427	42	20	circuits	circuit	NOUN
fuelectenerg-1427	42	21	,	,	PUNCT
fuelectenerg-1427	42	22	are	be	AUX
fuelectenerg-1427	42	23	mainly	mainly	ADV
fuelectenerg-1427	42	24	due	due	ADP
fuelectenerg-1427	42	25	to	to	ADP
fuelectenerg-1427	42	26	the	the	DET
fuelectenerg-1427	42	27	fact	fact	NOUN
fuelectenerg-1427	42	28	that	that	SCONJ
fuelectenerg-1427	42	29	the	the	DET
fuelectenerg-1427	42	30	gf	gf	PROPN
fuelectenerg-1427	42	31	operators	operator	NOUN
fuelectenerg-1427	42	32	exhibit	exhibit	VERB
fuelectenerg-1427	42	33	the	the	DET
fuelectenerg-1427	42	34	cyclic	cyclic	ADJ
fuelectenerg-1427	42	35	group	group	NOUN
fuelectenerg-1427	42	36	,	,	PUNCT
fuelectenerg-1427	42	37	also	also	ADV
fuelectenerg-1427	42	38	known	know	VERB
fuelectenerg-1427	42	39	as	as	ADP
fuelectenerg-1427	42	40	latin	latin	PROPN
fuelectenerg-1427	42	41	square	square	NOUN
fuelectenerg-1427	42	42	,	,	PUNCT
fuelectenerg-1427	42	43	property	property	NOUN
fuelectenerg-1427	42	44	.	.	PUNCT
fuelectenerg-1427	43	1	in	in	ADP
fuelectenerg-1427	43	2	binary	binary	NOUN
fuelectenerg-1427	43	3	,	,	PUNCT
fuelectenerg-1427	43	4	for	for	ADP
fuelectenerg-1427	43	5	example	example	NOUN
fuelectenerg-1427	43	6	,	,	PUNCT
fuelectenerg-1427	43	7	gf(2	gf(2	PROPN
fuelectenerg-1427	43	8	)	)	PUNCT
fuelectenerg-1427	43	9	addition	addition	NOUN
fuelectenerg-1427	43	10	gate	gate	NOUN
fuelectenerg-1427	43	11	,	,	PUNCT
fuelectenerg-1427	43	12	the	the	DET
fuelectenerg-1427	43	13	exor	exor	PROPN
fuelectenerg-1427	43	14	,	,	PUNCT
fuelectenerg-1427	43	15	has	have	VERB
fuelectenerg-1427	43	16	the	the	DET
fuelectenerg-1427	43	17	cyclic	cyclic	ADJ
fuelectenerg-1427	43	18	group	group	NOUN
fuelectenerg-1427	43	19	property	property	NOUN
fuelectenerg-1427	43	20	.	.	PUNCT
fuelectenerg-1427	44	1	the	the	DET
fuelectenerg-1427	44	2	cyclic	cyclic	PROPN
fuelectenerg-1427	44	3	group	group	NOUN
fuelectenerg-1427	44	4	property	property	NOUN
fuelectenerg-1427	44	5	can	can	AUX
fuelectenerg-1427	44	6	be	be	AUX
fuelectenerg-1427	44	7	explained	explain	VERB
fuelectenerg-1427	44	8	,	,	PUNCT
fuelectenerg-1427	44	9	for	for	ADP
fuelectenerg-1427	44	10	example	example	NOUN
fuelectenerg-1427	44	11	,	,	PUNCT
fuelectenerg-1427	44	12	using	use	VERB
fuelectenerg-1427	44	13	the	the	DET
fuelectenerg-1427	44	14	three	three	NUM
fuelectenerg-1427	44	15	-	-	PUNCT
fuelectenerg-1427	44	16	valued	value	VERB
fuelectenerg-1427	44	17	(	(	PUNCT
fuelectenerg-1427	44	18	ternary	ternary	ADJ
fuelectenerg-1427	44	19	)	)	PUNCT
fuelectenerg-1427	44	20	gf	gf	NOUN
fuelectenerg-1427	44	21	operators	operator	NOUN
fuelectenerg-1427	44	22	as	as	SCONJ
fuelectenerg-1427	44	23	shown	show	VERB
fuelectenerg-1427	44	24	in	in	ADP
fuelectenerg-1427	44	25	figures	figure	NOUN
fuelectenerg-1427	44	26	1(a	1(a	NUM
fuelectenerg-1427	44	27	)	)	PUNCT
fuelectenerg-1427	44	28	and	and	CCONJ
fuelectenerg-1427	44	29	1(b	1(b	NUM
fuelectenerg-1427	44	30	)	)	PUNCT
fuelectenerg-1427	44	31	,	,	PUNCT
fuelectenerg-1427	44	32	respectively	respectively	ADV
fuelectenerg-1427	44	33	.	.	PUNCT
fuelectenerg-1427	45	1	note	note	VERB
fuelectenerg-1427	45	2	that	that	SCONJ
fuelectenerg-1427	45	3	in	in	ADP
fuelectenerg-1427	45	4	any	any	DET
fuelectenerg-1427	45	5	row	row	NOUN
fuelectenerg-1427	45	6	and	and	CCONJ
fuelectenerg-1427	45	7	column	column	NOUN
fuelectenerg-1427	45	8	of	of	ADP
fuelectenerg-1427	45	9	the	the	DET
fuelectenerg-1427	45	10	addition	addition	NOUN
fuelectenerg-1427	45	11	table	table	NOUN
fuelectenerg-1427	45	12	in	in	ADP
fuelectenerg-1427	45	13	figure	figure	NOUN
fuelectenerg-1427	45	14	1(a	1(a	NUM
fuelectenerg-1427	45	15	)	)	PUNCT
fuelectenerg-1427	45	16	,	,	PUNCT
fuelectenerg-1427	45	17	the	the	DET
fuelectenerg-1427	45	18	elements	element	NOUN
fuelectenerg-1427	45	19	are	be	AUX
fuelectenerg-1427	45	20	all	all	ADV
fuelectenerg-1427	45	21	different	different	ADJ
fuelectenerg-1427	45	22	,	,	PUNCT
fuelectenerg-1427	45	23	which	which	PRON
fuelectenerg-1427	45	24	is	be	AUX
fuelectenerg-1427	45	25	cyclic	cyclic	ADJ
fuelectenerg-1427	45	26	,	,	PUNCT
fuelectenerg-1427	45	27	and	and	CCONJ
fuelectenerg-1427	45	28	that	that	SCONJ
fuelectenerg-1427	45	29	the	the	DET
fuelectenerg-1427	45	30	elements	element	NOUN
fuelectenerg-1427	45	31	have	have	VERB
fuelectenerg-1427	45	32	a	a	DET
fuelectenerg-1427	45	33	different	different	ADJ
fuelectenerg-1427	45	34	order	order	NOUN
fuelectenerg-1427	45	35	in	in	ADP
fuelectenerg-1427	45	36	each	each	DET
fuelectenerg-1427	45	37	row	row	NOUN
fuelectenerg-1427	45	38	and	and	CCONJ
fuelectenerg-1427	45	39	column	column	NOUN
fuelectenerg-1427	45	40	.	.	PUNCT
fuelectenerg-1427	46	1	another	another	DET
fuelectenerg-1427	46	2	cyclic	cyclic	ADJ
fuelectenerg-1427	46	3	group	group	NOUN
fuelectenerg-1427	46	4	can	can	AUX
fuelectenerg-1427	46	5	be	be	AUX
fuelectenerg-1427	46	6	observed	observe	VERB
fuelectenerg-1427	46	7	in	in	ADP
fuelectenerg-1427	46	8	the	the	DET
fuelectenerg-1427	46	9	multiplication	multiplication	NOUN
fuelectenerg-1427	46	10	table	table	NOUN
fuelectenerg-1427	46	11	;	;	PUNCT
fuelectenerg-1427	46	12	if	if	SCONJ
fuelectenerg-1427	46	13	the	the	DET
fuelectenerg-1427	46	14	zero	zero	NUM
fuelectenerg-1427	46	15	elements	element	NOUN
fuelectenerg-1427	46	16	are	be	AUX
fuelectenerg-1427	46	17	removed	remove	VERB
fuelectenerg-1427	46	18	from	from	ADP
fuelectenerg-1427	46	19	the	the	DET
fuelectenerg-1427	46	20	multiplication	multiplication	NOUN
fuelectenerg-1427	46	21	table	table	NOUN
fuelectenerg-1427	46	22	in	in	ADP
fuelectenerg-1427	46	23	figure	figure	NOUN
fuelectenerg-1427	46	24	1(b	1(b	NUM
fuelectenerg-1427	46	25	)	)	PUNCT
fuelectenerg-1427	46	26	,	,	PUNCT
fuelectenerg-1427	46	27	then	then	ADV
fuelectenerg-1427	46	28	the	the	DET
fuelectenerg-1427	46	29	remaining	remain	VERB
fuelectenerg-1427	46	30	elements	element	NOUN
fuelectenerg-1427	46	31	form	form	VERB
fuelectenerg-1427	46	32	a	a	DET
fuelectenerg-1427	46	33	cyclic	cyclic	ADJ
fuelectenerg-1427	46	34	group	group	NOUN
fuelectenerg-1427	46	35	.	.	PUNCT
fuelectenerg-1427	47	1	reed	reed	NOUN
fuelectenerg-1427	47	2	-	-	PUNCT
fuelectenerg-1427	47	3	muller	muller	NOUN
fuelectenerg-1427	47	4	normal	normal	ADJ
fuelectenerg-1427	47	5	forms	form	NOUN
fuelectenerg-1427	47	6	have	have	AUX
fuelectenerg-1427	47	7	been	be	AUX
fuelectenerg-1427	47	8	classified	classify	VERB
fuelectenerg-1427	47	9	using	use	VERB
fuelectenerg-1427	47	10	the	the	DET
fuelectenerg-1427	47	11	green	green	ADJ
fuelectenerg-1427	47	12	-	-	PUNCT
fuelectenerg-1427	47	13	sasao	sasao	NOUN
fuelectenerg-1427	47	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	48	1	[	[	X
fuelectenerg-1427	48	2	1	1	NUM
fuelectenerg-1427	48	3	,	,	PUNCT
fuelectenerg-1427	48	4	10	10	NUM
fuelectenerg-1427	48	5	,	,	PUNCT
fuelectenerg-1427	48	6	12	12	NUM
fuelectenerg-1427	48	7	,	,	PUNCT
fuelectenerg-1427	48	8	13	13	NUM
fuelectenerg-1427	48	9	,	,	PUNCT
fuelectenerg-1427	48	10	17	17	NUM
fuelectenerg-1427	48	11	]	]	PUNCT
fuelectenerg-1427	48	12	,	,	PUNCT
fuelectenerg-1427	48	13	where	where	SCONJ
fuelectenerg-1427	48	14	the	the	DET
fuelectenerg-1427	48	15	green	green	ADJ
fuelectenerg-1427	48	16	-	-	PUNCT
fuelectenerg-1427	48	17	sasao	sasao	PROPN
fuelectenerg-1427	48	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	48	19	of	of	ADP
fuelectenerg-1427	48	20	families	family	NOUN
fuelectenerg-1427	48	21	of	of	ADP
fuelectenerg-1427	48	22	canonical	canonical	ADJ
fuelectenerg-1427	48	23	forms	form	NOUN
fuelectenerg-1427	48	24	and	and	CCONJ
fuelectenerg-1427	48	25	corresponding	correspond	VERB
fuelectenerg-1427	48	26	decision	decision	NOUN
fuelectenerg-1427	48	27	diagrams	diagram	NOUN
fuelectenerg-1427	48	28	is	be	AUX
fuelectenerg-1427	48	29	based	base	VERB
fuelectenerg-1427	48	30	on	on	ADP
fuelectenerg-1427	48	31	three	three	NUM
fuelectenerg-1427	48	32	generic	generic	ADJ
fuelectenerg-1427	48	33	expansions	expansion	NOUN
fuelectenerg-1427	48	34	;	;	PUNCT
fuelectenerg-1427	48	35	shannon	shannon	PROPN
fuelectenerg-1427	48	36	,	,	PUNCT
fuelectenerg-1427	48	37	pos102	pos102	PROPN
fuelectenerg-1427	48	38	an	an	DET
fuelectenerg-1427	48	39	extended	extended	ADJ
fuelectenerg-1427	48	40	green	green	ADJ
fuelectenerg-1427	48	41	sasao	sasao	PROPN
fuelectenerg-1427	48	42	hierarchy	hierarchy	NOUN
fuelectenerg-1427	48	43	of	of	ADP
fuelectenerg-1427	48	44	canonical	canonical	ADJ
fuelectenerg-1427	48	45	ternary	ternary	ADJ
fuelectenerg-1427	48	46	galois	galois	NOUN
fuelectenerg-1427	48	47	forms	form	NOUN
fuelectenerg-1427	48	48	and	and	CCONJ
fuelectenerg-1427	48	49	universal	universal	ADJ
fuelectenerg-1427	48	50	logic	logic	NOUN
fuelectenerg-1427	48	51	modules	module	NOUN
fuelectenerg-1427	48	52	anas	anas	PROPN
fuelectenerg-1427	48	53	n.	n.	PROPN
fuelectenerg-1427	48	54	al	al	PROPN
fuelectenerg-1427	48	55	-	-	PUNCT
fuelectenerg-1427	48	56	rabadi	rabadi	PROPN
fuelectenerg-1427	48	57	∗	∗	NOUN
fuelectenerg-1427	48	58	electrical	electrical	ADJ
fuelectenerg-1427	48	59	engineering	engineering	NOUN
fuelectenerg-1427	48	60	department	department	PROPN
fuelectenerg-1427	48	61	,	,	PUNCT
fuelectenerg-1427	48	62	philadelphia	philadelphia	PROPN
fuelectenerg-1427	48	63	university	university	PROPN
fuelectenerg-1427	48	64	,	,	PUNCT
fuelectenerg-1427	48	65	jordan	jordan	PROPN
fuelectenerg-1427	48	66	&	&	CCONJ
fuelectenerg-1427	48	67	computer	computer	PROPN
fuelectenerg-1427	48	68	engineering	engineering	PROPN
fuelectenerg-1427	48	69	department	department	PROPN
fuelectenerg-1427	48	70	,	,	PUNCT
fuelectenerg-1427	48	71	the	the	DET
fuelectenerg-1427	48	72	university	university	PROPN
fuelectenerg-1427	48	73	of	of	ADP
fuelectenerg-1427	48	74	jordan	jordan	PROPN
fuelectenerg-1427	48	75	,	,	PUNCT
fuelectenerg-1427	48	76	amman	amman	PROPN
fuelectenerg-1427	48	77	-	-	PUNCT
fuelectenerg-1427	48	78	jordan	jordan	PROPN
fuelectenerg-1427	48	79	e	e	PROPN
fuelectenerg-1427	48	80	-	-	NOUN
fuelectenerg-1427	48	81	mail	mail	NOUN
fuelectenerg-1427	48	82	:	:	PUNCT
fuelectenerg-1427	48	83	alrabadi@yahoo.com	alrabadi@yahoo.com	X
fuelectenerg-1427	49	1	abstract	abstract	ADJ
fuelectenerg-1427	49	2	a	a	DET
fuelectenerg-1427	49	3	new	new	ADJ
fuelectenerg-1427	49	4	extended	extended	ADJ
fuelectenerg-1427	49	5	green	green	ADJ
fuelectenerg-1427	49	6	-	-	PUNCT
fuelectenerg-1427	49	7	sasao	sasao	NOUN
fuelectenerg-1427	49	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	49	9	of	of	ADP
fuelectenerg-1427	49	10	families	family	NOUN
fuelectenerg-1427	49	11	and	and	CCONJ
fuelectenerg-1427	49	12	forms	form	NOUN
fuelectenerg-1427	49	13	with	with	ADP
fuelectenerg-1427	49	14	a	a	DET
fuelectenerg-1427	49	15	new	new	ADJ
fuelectenerg-1427	49	16	subfamily	subfamily	NOUN
fuelectenerg-1427	49	17	for	for	ADP
fuelectenerg-1427	49	18	multiple	multiple	ADV
fuelectenerg-1427	49	19	-	-	PUNCT
fuelectenerg-1427	49	20	valued	value	VERB
fuelectenerg-1427	49	21	reed	reed	NOUN
fuelectenerg-1427	49	22	-	-	PUNCT
fuelectenerg-1427	49	23	muller	muller	NOUN
fuelectenerg-1427	49	24	logic	logic	NOUN
fuelectenerg-1427	49	25	is	be	AUX
fuelectenerg-1427	49	26	introduced	introduce	VERB
fuelectenerg-1427	49	27	.	.	PUNCT
fuelectenerg-1427	50	1	recently	recently	ADV
fuelectenerg-1427	50	2	,	,	PUNCT
fuelectenerg-1427	50	3	two	two	NUM
fuelectenerg-1427	50	4	families	family	NOUN
fuelectenerg-1427	50	5	of	of	ADP
fuelectenerg-1427	50	6	binary	binary	ADJ
fuelectenerg-1427	50	7	canonical	canonical	ADJ
fuelectenerg-1427	50	8	reed	reed	NOUN
fuelectenerg-1427	50	9	-	-	PUNCT
fuelectenerg-1427	50	10	muller	muller	NOUN
fuelectenerg-1427	50	11	forms	form	NOUN
fuelectenerg-1427	50	12	,	,	PUNCT
fuelectenerg-1427	50	13	called	call	VERB
fuelectenerg-1427	50	14	inclusive	inclusive	ADJ
fuelectenerg-1427	50	15	forms	form	NOUN
fuelectenerg-1427	50	16	(	(	PUNCT
fuelectenerg-1427	50	17	ifs	ifs	PROPN
fuelectenerg-1427	50	18	)	)	PUNCT
fuelectenerg-1427	50	19	and	and	CCONJ
fuelectenerg-1427	50	20	generalized	generalized	ADJ
fuelectenerg-1427	50	21	inclusive	inclusive	ADJ
fuelectenerg-1427	50	22	forms	form	NOUN
fuelectenerg-1427	50	23	(	(	PUNCT
fuelectenerg-1427	50	24	gifs	gifs	PROPN
fuelectenerg-1427	50	25	)	)	PUNCT
fuelectenerg-1427	50	26	have	have	AUX
fuelectenerg-1427	50	27	been	be	AUX
fuelectenerg-1427	50	28	proposed	propose	VERB
fuelectenerg-1427	50	29	,	,	PUNCT
fuelectenerg-1427	50	30	where	where	SCONJ
fuelectenerg-1427	50	31	the	the	DET
fuelectenerg-1427	50	32	second	second	ADJ
fuelectenerg-1427	50	33	family	family	NOUN
fuelectenerg-1427	50	34	was	be	AUX
fuelectenerg-1427	50	35	the	the	DET
fuelectenerg-1427	50	36	first	first	ADJ
fuelectenerg-1427	50	37	to	to	PART
fuelectenerg-1427	50	38	include	include	VERB
fuelectenerg-1427	50	39	all	all	DET
fuelectenerg-1427	50	40	minimum	minimum	ADJ
fuelectenerg-1427	50	41	exclusive	exclusive	ADJ
fuelectenerg-1427	50	42	sum	sum	NOUN
fuelectenerg-1427	50	43	-	-	PUNCT
fuelectenerg-1427	50	44	of	of	ADP
fuelectenerg-1427	50	45	-	-	PUNCT
fuelectenerg-1427	50	46	products	product	NOUN
fuelectenerg-1427	50	47	(	(	PUNCT
fuelectenerg-1427	50	48	esops	esop	NOUN
fuelectenerg-1427	50	49	)	)	PUNCT
fuelectenerg-1427	50	50	.	.	PUNCT
fuelectenerg-1427	51	1	in	in	ADP
fuelectenerg-1427	51	2	this	this	DET
fuelectenerg-1427	51	3	paper	paper	NOUN
fuelectenerg-1427	51	4	,	,	PUNCT
fuelectenerg-1427	51	5	we	we	PRON
fuelectenerg-1427	51	6	propose	propose	VERB
fuelectenerg-1427	51	7	,	,	PUNCT
fuelectenerg-1427	51	8	analogously	analogously	ADV
fuelectenerg-1427	51	9	to	to	ADP
fuelectenerg-1427	51	10	the	the	DET
fuelectenerg-1427	51	11	binary	binary	ADJ
fuelectenerg-1427	51	12	case	case	NOUN
fuelectenerg-1427	51	13	,	,	PUNCT
fuelectenerg-1427	51	14	two	two	NUM
fuelectenerg-1427	51	15	general	general	ADJ
fuelectenerg-1427	51	16	families	family	NOUN
fuelectenerg-1427	51	17	of	of	ADP
fuelectenerg-1427	51	18	canonical	canonical	ADJ
fuelectenerg-1427	51	19	ternary	ternary	ADJ
fuelectenerg-1427	51	20	reed	reed	NOUN
fuelectenerg-1427	51	21	-	-	PUNCT
fuelectenerg-1427	51	22	muller	muller	NOUN
fuelectenerg-1427	51	23	forms	form	NOUN
fuelectenerg-1427	51	24	,	,	PUNCT
fuelectenerg-1427	51	25	called	call	VERB
fuelectenerg-1427	51	26	ternary	ternary	ADJ
fuelectenerg-1427	51	27	inclusive	inclusive	ADJ
fuelectenerg-1427	51	28	forms	form	NOUN
fuelectenerg-1427	51	29	(	(	PUNCT
fuelectenerg-1427	51	30	tifs	tifs	PROPN
fuelectenerg-1427	51	31	)	)	PUNCT
fuelectenerg-1427	51	32	and	and	CCONJ
fuelectenerg-1427	51	33	their	their	PRON
fuelectenerg-1427	51	34	generalization	generalization	NOUN
fuelectenerg-1427	51	35	of	of	ADP
fuelectenerg-1427	51	36	ternary	ternary	ADJ
fuelectenerg-1427	51	37	generalized	generalize	VERB
fuelectenerg-1427	51	38	inclusive	inclusive	ADJ
fuelectenerg-1427	51	39	forms	form	NOUN
fuelectenerg-1427	51	40	(	(	PUNCT
fuelectenerg-1427	51	41	tgifs	tgif	NOUN
fuelectenerg-1427	51	42	)	)	PUNCT
fuelectenerg-1427	51	43	,	,	PUNCT
fuelectenerg-1427	51	44	where	where	SCONJ
fuelectenerg-1427	51	45	the	the	DET
fuelectenerg-1427	51	46	second	second	ADJ
fuelectenerg-1427	51	47	family	family	NOUN
fuelectenerg-1427	51	48	includes	include	VERB
fuelectenerg-1427	51	49	minimum	minimum	ADJ
fuelectenerg-1427	51	50	galois	galois	PROPN
fuelectenerg-1427	51	51	field	field	NOUN
fuelectenerg-1427	51	52	sum	sum	NOUN
fuelectenerg-1427	51	53	-	-	PUNCT
fuelectenerg-1427	51	54	of	of	ADP
fuelectenerg-1427	51	55	-	-	PUNCT
fuelectenerg-1427	51	56	products	product	NOUN
fuelectenerg-1427	51	57	(	(	PUNCT
fuelectenerg-1427	51	58	gfsops	gfsop	NOUN
fuelectenerg-1427	51	59	)	)	PUNCT
fuelectenerg-1427	51	60	over	over	ADP
fuelectenerg-1427	51	61	ternary	ternary	ADJ
fuelectenerg-1427	51	62	galois	galois	PROPN
fuelectenerg-1427	51	63	field	field	NOUN
fuelectenerg-1427	51	64	gf(3	gf(3	PROPN
fuelectenerg-1427	51	65	)	)	PUNCT
fuelectenerg-1427	51	66	.	.	PUNCT
fuelectenerg-1427	52	1	one	one	NUM
fuelectenerg-1427	52	2	of	of	ADP
fuelectenerg-1427	52	3	the	the	DET
fuelectenerg-1427	52	4	basic	basic	ADJ
fuelectenerg-1427	52	5	motivations	motivation	NOUN
fuelectenerg-1427	52	6	in	in	ADP
fuelectenerg-1427	52	7	this	this	DET
fuelectenerg-1427	52	8	work	work	NOUN
fuelectenerg-1427	52	9	is	be	AUX
fuelectenerg-1427	52	10	the	the	DET
fuelectenerg-1427	52	11	application	application	NOUN
fuelectenerg-1427	52	12	of	of	ADP
fuelectenerg-1427	52	13	these	these	DET
fuelectenerg-1427	52	14	tifs	tif	NOUN
fuelectenerg-1427	52	15	and	and	CCONJ
fuelectenerg-1427	52	16	tgifs	tgif	NOUN
fuelectenerg-1427	52	17	to	to	PART
fuelectenerg-1427	52	18	find	find	VERB
fuelectenerg-1427	52	19	the	the	DET
fuelectenerg-1427	52	20	minimum	minimum	ADJ
fuelectenerg-1427	52	21	gfsop	gfsop	NOUN
fuelectenerg-1427	52	22	for	for	ADP
fuelectenerg-1427	52	23	multiple	multiple	ADV
fuelectenerg-1427	52	24	-	-	PUNCT
fuelectenerg-1427	52	25	valued	value	VERB
fuelectenerg-1427	52	26	inputoutput	inputoutput	NOUN
fuelectenerg-1427	52	27	functions	function	NOUN
fuelectenerg-1427	52	28	within	within	ADP
fuelectenerg-1427	52	29	logic	logic	ADJ
fuelectenerg-1427	52	30	synthesis	synthesis	NOUN
fuelectenerg-1427	52	31	,	,	PUNCT
fuelectenerg-1427	52	32	where	where	SCONJ
fuelectenerg-1427	52	33	a	a	DET
fuelectenerg-1427	52	34	gfsop	gfsop	NOUN
fuelectenerg-1427	52	35	minimizer	minimizer	NOUN
fuelectenerg-1427	52	36	based	base	VERB
fuelectenerg-1427	52	37	on	on	ADP
fuelectenerg-1427	52	38	if	if	SCONJ
fuelectenerg-1427	52	39	polarity	polarity	NOUN
fuelectenerg-1427	52	40	can	can	AUX
fuelectenerg-1427	52	41	be	be	AUX
fuelectenerg-1427	52	42	used	use	VERB
fuelectenerg-1427	52	43	to	to	PART
fuelectenerg-1427	52	44	minimize	minimize	VERB
fuelectenerg-1427	52	45	the	the	DET
fuelectenerg-1427	52	46	multiple	multiple	ADV
fuelectenerg-1427	52	47	-	-	PUNCT
fuelectenerg-1427	52	48	valued	value	VERB
fuelectenerg-1427	52	49	gfsop	gfsop	NOUN
fuelectenerg-1427	52	50	expression	expression	NOUN
fuelectenerg-1427	52	51	for	for	ADP
fuelectenerg-1427	52	52	any	any	DET
fuelectenerg-1427	52	53	given	give	VERB
fuelectenerg-1427	52	54	function	function	NOUN
fuelectenerg-1427	52	55	.	.	PUNCT
fuelectenerg-1427	53	1	the	the	DET
fuelectenerg-1427	53	2	realization	realization	NOUN
fuelectenerg-1427	53	3	of	of	ADP
fuelectenerg-1427	53	4	the	the	DET
fuelectenerg-1427	53	5	presented	present	VERB
fuelectenerg-1427	53	6	shannon	shannon	NOUN
fuelectenerg-1427	53	7	-	-	PUNCT
fuelectenerg-1427	53	8	davio	davio	NOUN
fuelectenerg-1427	53	9	(	(	PUNCT
fuelectenerg-1427	53	10	s	s	NOUN
fuelectenerg-1427	53	11	/	/	SYM
fuelectenerg-1427	53	12	d	d	NOUN
fuelectenerg-1427	53	13	)	)	PUNCT
fuelectenerg-1427	53	14	trees	tree	NOUN
fuelectenerg-1427	53	15	using	use	VERB
fuelectenerg-1427	53	16	universal	universal	ADJ
fuelectenerg-1427	53	17	logic	logic	NOUN
fuelectenerg-1427	53	18	modules	module	NOUN
fuelectenerg-1427	53	19	(	(	PUNCT
fuelectenerg-1427	53	20	ulms	ulm	NOUN
fuelectenerg-1427	53	21	)	)	PUNCT
fuelectenerg-1427	53	22	is	be	AUX
fuelectenerg-1427	53	23	also	also	ADV
fuelectenerg-1427	53	24	introduced	introduce	VERB
fuelectenerg-1427	53	25	,	,	PUNCT
fuelectenerg-1427	53	26	where	where	SCONJ
fuelectenerg-1427	53	27	ulms	ulm	NOUN
fuelectenerg-1427	53	28	are	be	AUX
fuelectenerg-1427	53	29	complete	complete	ADJ
fuelectenerg-1427	53	30	systems	system	NOUN
fuelectenerg-1427	53	31	that	that	PRON
fuelectenerg-1427	53	32	can	can	AUX
fuelectenerg-1427	53	33	implement	implement	VERB
fuelectenerg-1427	53	34	all	all	DET
fuelectenerg-1427	53	35	possible	possible	ADJ
fuelectenerg-1427	53	36	logic	logic	NOUN
fuelectenerg-1427	53	37	functions	function	NOUN
fuelectenerg-1427	53	38	utilizing	utilize	VERB
fuelectenerg-1427	53	39	the	the	DET
fuelectenerg-1427	53	40	corresponding	correspond	VERB
fuelectenerg-1427	53	41	s	s	PROPN
fuelectenerg-1427	53	42	/	/	SYM
fuelectenerg-1427	53	43	d	d	NOUN
fuelectenerg-1427	53	44	expansions	expansion	NOUN
fuelectenerg-1427	53	45	of	of	ADP
fuelectenerg-1427	53	46	multiple	multiple	ADV
fuelectenerg-1427	53	47	-	-	PUNCT
fuelectenerg-1427	53	48	valued	value	VERB
fuelectenerg-1427	53	49	shannon	shannon	NOUN
fuelectenerg-1427	53	50	and	and	CCONJ
fuelectenerg-1427	53	51	davio	davio	PROPN
fuelectenerg-1427	53	52	spectral	spectral	ADJ
fuelectenerg-1427	53	53	transforms	transform	VERB
fuelectenerg-1427	53	54	.	.	PUNCT
fuelectenerg-1427	54	1	keywords	keyword	NOUN
fuelectenerg-1427	54	2	1	1	NUM
fuelectenerg-1427	54	3	.	.	PUNCT
fuelectenerg-1427	55	1	canonical	canonical	ADJ
fuelectenerg-1427	55	2	forms	form	NOUN
fuelectenerg-1427	55	3	,	,	PUNCT
fuelectenerg-1427	55	4	galois	galois	PROPN
fuelectenerg-1427	55	5	field	field	NOUN
fuelectenerg-1427	55	6	forms	form	NOUN
fuelectenerg-1427	55	7	,	,	PUNCT
fuelectenerg-1427	55	8	green	green	ADJ
fuelectenerg-1427	55	9	-	-	PUNCT
fuelectenerg-1427	55	10	sasao	sasao	PROPN
fuelectenerg-1427	55	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	55	12	,	,	PUNCT
fuelectenerg-1427	55	13	inclusive	inclusive	ADJ
fuelectenerg-1427	55	14	forms	form	NOUN
fuelectenerg-1427	55	15	,	,	PUNCT
fuelectenerg-1427	55	16	multiple	multiple	ADV
fuelectenerg-1427	55	17	-	-	PUNCT
fuelectenerg-1427	55	18	valued	value	VERB
fuelectenerg-1427	55	19	logic	logic	NOUN
fuelectenerg-1427	55	20	,	,	PUNCT
fuelectenerg-1427	55	21	shannon	shannon	ADJ
fuelectenerg-1427	55	22	-	-	PUNCT
fuelectenerg-1427	55	23	davio	davio	NOUN
fuelectenerg-1427	55	24	trees	tree	NOUN
fuelectenerg-1427	55	25	,	,	PUNCT
fuelectenerg-1427	55	26	ternary	ternary	ADJ
fuelectenerg-1427	55	27	logic	logic	NOUN
fuelectenerg-1427	55	28	,	,	PUNCT
fuelectenerg-1427	55	29	universal	universal	ADJ
fuelectenerg-1427	55	30	logic	logic	NOUN
fuelectenerg-1427	55	31	modules	module	NOUN
fuelectenerg-1427	55	32	.	.	PUNCT
fuelectenerg-1427	56	1	1	1	NUM
fuelectenerg-1427	56	2	normal	normal	ADJ
fuelectenerg-1427	56	3	galois	galois	PROPN
fuelectenerg-1427	56	4	forms	form	VERB
fuelectenerg-1427	56	5	reed	reed	NOUN
fuelectenerg-1427	56	6	-	-	PUNCT
fuelectenerg-1427	56	7	muller	muller	NOUN
fuelectenerg-1427	56	8	-	-	PUNCT
fuelectenerg-1427	56	9	like	like	ADJ
fuelectenerg-1427	56	10	spectral	spectral	ADJ
fuelectenerg-1427	56	11	transforms	transform	VERB
fuelectenerg-1427	56	12	[	[	X
fuelectenerg-1427	56	13	1	1	NUM
fuelectenerg-1427	56	14	-	-	SYM
fuelectenerg-1427	56	15	18	18	NUM
fuelectenerg-1427	56	16	]	]	PUNCT
fuelectenerg-1427	56	17	have	have	AUX
fuelectenerg-1427	56	18	found	find	VERB
fuelectenerg-1427	56	19	a	a	DET
fuelectenerg-1427	56	20	variety	variety	NOUN
fuelectenerg-1427	56	21	of	of	ADP
fuelectenerg-1427	56	22	useful	useful	ADJ
fuelectenerg-1427	56	23	applications	application	NOUN
fuelectenerg-1427	56	24	in	in	ADP
fuelectenerg-1427	56	25	minimizing	minimize	VERB
fuelectenerg-1427	56	26	exclusive	exclusive	ADJ
fuelectenerg-1427	56	27	sum	sum	NOUN
fuelectenerg-1427	56	28	-	-	PUNCT
fuelectenerg-1427	56	29	of	of	ADP
fuelectenerg-1427	56	30	-	-	PUNCT
fuelectenerg-1427	56	31	products	product	NOUN
fuelectenerg-1427	56	32	(	(	PUNCT
fuelectenerg-1427	56	33	esop	esop	PROPN
fuelectenerg-1427	56	34	)	)	PUNCT
fuelectenerg-1427	56	35	and	and	CCONJ
fuelectenerg-1427	56	36	galois	galois	PROPN
fuelectenerg-1427	56	37	field	field	NOUN
fuelectenerg-1427	56	38	sop	sop	PROPN
fuelectenerg-1427	56	39	(	(	PUNCT
fuelectenerg-1427	56	40	gfsop	gfsop	NOUN
fuelectenerg-1427	56	41	)	)	PUNCT
fuelectenerg-1427	56	42	expressions	expression	NOUN
fuelectenerg-1427	56	43	,	,	PUNCT
fuelectenerg-1427	56	44	creation	creation	NOUN
fuelectenerg-1427	56	45	of	of	ADP
fuelectenerg-1427	56	46	new	new	ADJ
fuelectenerg-1427	56	47	forms	form	NOUN
fuelectenerg-1427	56	48	,	,	PUNCT
fuelectenerg-1427	56	49	binary	binary	ADJ
fuelectenerg-1427	56	50	and	and	CCONJ
fuelectenerg-1427	56	51	spectral	spectral	ADJ
fuelectenerg-1427	56	52	decision	decision	NOUN
fuelectenerg-1427	56	53	diagrams	diagram	NOUN
fuelectenerg-1427	56	54	,	,	PUNCT
fuelectenerg-1427	56	55	regular	regular	ADJ
fuelectenerg-1427	56	56	structures	structure	NOUN
fuelectenerg-1427	56	57	,	,	PUNCT
fuelectenerg-1427	56	58	besides	besides	SCONJ
fuelectenerg-1427	56	59	the	the	DET
fuelectenerg-1427	56	60	well	well	ADV
fuelectenerg-1427	56	61	-	-	PUNCT
fuelectenerg-1427	56	62	known	know	VERB
fuelectenerg-1427	56	63	uses	use	NOUN
fuelectenerg-1427	56	64	in	in	ADP
fuelectenerg-1427	56	65	digital	digital	ADJ
fuelectenerg-1427	56	66	communications	communication	NOUN
fuelectenerg-1427	56	67	,	,	PUNCT
fuelectenerg-1427	56	68	digital	digital	ADJ
fuelectenerg-1427	56	69	signal	signal	NOUN
fuelectenerg-1427	56	70	∗received	∗receive	VERB
fuelectenerg-1427	56	71	:	:	PUNCT
fuelectenerg-1427	56	72	july	july	PROPN
fuelectenerg-1427	56	73	15	15	NUM
fuelectenerg-1427	56	74	,	,	PUNCT
fuelectenerg-1427	56	75	2015	2015	NUM
fuelectenerg-1427	56	76	101	101	NUM
fuelectenerg-1427	56	77	50	50	NUM
fuelectenerg-1427	56	78	a.	a.	NOUN
fuelectenerg-1427	56	79	n.	n.	PROPN
fuelectenerg-1427	56	80	al	al	PROPN
fuelectenerg-1427	56	81	-	-	PUNCT
fuelectenerg-1427	56	82	rabadi	rabadi	VERB
fuelectenerg-1427	56	83	an	an	DET
fuelectenerg-1427	56	84	extended	extended	ADJ
fuelectenerg-1427	56	85	green	green	ADJ
fuelectenerg-1427	56	86	sasao	sasao	PROPN
fuelectenerg-1427	56	87	hierarchy	hierarchy	NOUN
fuelectenerg-1427	56	88	of	of	ADP
fuelectenerg-1427	56	89	canonical	canonical	ADJ
fuelectenerg-1427	56	90	ternary	ternary	ADJ
fuelectenerg-1427	56	91	galois	galois	NOUN
fuelectenerg-1427	56	92	forms	form	NOUN
fuelectenerg-1427	56	93	and	and	CCONJ
fuelectenerg-1427	56	94	universal	universal	ADJ
fuelectenerg-1427	56	95	logic	logic	NOUN
fuelectenerg-1427	56	96	modules	module	NOUN
fuelectenerg-1427	56	97	51	51	NUM
fuelectenerg-1427	56	98	an	an	DET
fuelectenerg-1427	56	99	extended	extend	VERB
fuelectenerg-1427	56	100	green	green	ADJ
fuelectenerg-1427	56	101	sasao	sasao	PROPN
fuelectenerg-1427	56	102	hierarchy	hierarchy	NOUN
fuelectenerg-1427	56	103	of	of	ADP
fuelectenerg-1427	56	104	canonical	canonical	ADJ
fuelectenerg-1427	56	105	ternary	ternary	ADJ
fuelectenerg-1427	56	106	galois	galois	NOUN
fuelectenerg-1427	56	107	forms	form	NOUN
fuelectenerg-1427	56	108	...	...	PUNCT
fuelectenerg-1427	56	109	table	table	NOUN
fuelectenerg-1427	56	110	1	1	NUM
fuelectenerg-1427	56	111	:	:	PUNCT
fuelectenerg-1427	56	112	number	number	NOUN
fuelectenerg-1427	56	113	of	of	ADP
fuelectenerg-1427	56	114	product	product	NOUN
fuelectenerg-1427	56	115	terms	term	NOUN
fuelectenerg-1427	56	116	needed	need	VERB
fuelectenerg-1427	56	117	to	to	PART
fuelectenerg-1427	56	118	realize	realize	VERB
fuelectenerg-1427	56	119	some	some	DET
fuelectenerg-1427	56	120	arithmetic	arithmetic	ADJ
fuelectenerg-1427	56	121	functions	function	NOUN
fuelectenerg-1427	56	122	using	use	VERB
fuelectenerg-1427	56	123	various	various	ADJ
fuelectenerg-1427	56	124	expressions	expression	NOUN
fuelectenerg-1427	56	125	.	.	PUNCT
fuelectenerg-1427	57	1	function	function	NOUN
fuelectenerg-1427	57	2	pprm	pprm	PROPN
fuelectenerg-1427	57	3	fprm	fprm	PROPN
fuelectenerg-1427	57	4	grm	grm	PROPN
fuelectenerg-1427	57	5	esop	esop	PROPN
fuelectenerg-1427	57	6	sop	sop	PROPN
fuelectenerg-1427	57	7	adr4	adr4	PROPN
fuelectenerg-1427	57	8	34	34	NUM
fuelectenerg-1427	57	9	34	34	NUM
fuelectenerg-1427	57	10	34	34	NUM
fuelectenerg-1427	57	11	31	31	NUM
fuelectenerg-1427	57	12	75	75	NUM
fuelectenerg-1427	57	13	log8	log8	NOUN
fuelectenerg-1427	57	14	253	253	NUM
fuelectenerg-1427	57	15	193	193	NUM
fuelectenerg-1427	57	16	105	105	NUM
fuelectenerg-1427	57	17	96	96	NUM
fuelectenerg-1427	57	18	123	123	NUM
fuelectenerg-1427	57	19	nrm4	nrm4	NOUN
fuelectenerg-1427	57	20	216	216	NUM
fuelectenerg-1427	57	21	185	185	NUM
fuelectenerg-1427	57	22	96	96	NUM
fuelectenerg-1427	57	23	69	69	NUM
fuelectenerg-1427	57	24	120	120	NUM
fuelectenerg-1427	57	25	rdm8	rdm8	NOUN
fuelectenerg-1427	57	26	56	56	NUM
fuelectenerg-1427	57	27	56	56	NUM
fuelectenerg-1427	57	28	31	31	NUM
fuelectenerg-1427	57	29	31	31	NUM
fuelectenerg-1427	57	30	76	76	NUM
fuelectenerg-1427	57	31	rot8	rot8	NOUN
fuelectenerg-1427	57	32	225	225	NUM
fuelectenerg-1427	57	33	118	118	NUM
fuelectenerg-1427	57	34	51	51	NUM
fuelectenerg-1427	57	35	35	35	NUM
fuelectenerg-1427	57	36	57	57	NUM
fuelectenerg-1427	57	37	sym9	sym9	NOUN
fuelectenerg-1427	57	38	210	210	NUM
fuelectenerg-1427	57	39	173	173	NUM
fuelectenerg-1427	57	40	126	126	NUM
fuelectenerg-1427	57	41	51	51	NUM
fuelectenerg-1427	57	42	84	84	NUM
fuelectenerg-1427	57	43	wgt8	wgt8	NOUN
fuelectenerg-1427	57	44	107	107	NUM
fuelectenerg-1427	57	45	107	107	NUM
fuelectenerg-1427	57	46	107	107	NUM
fuelectenerg-1427	57	47	58	58	NUM
fuelectenerg-1427	57	48	255	255	NUM
fuelectenerg-1427	58	1	and	and	CCONJ
fuelectenerg-1427	58	2	image	image	NOUN
fuelectenerg-1427	58	3	processing	processing	NOUN
fuelectenerg-1427	58	4	,	,	PUNCT
fuelectenerg-1427	58	5	and	and	CCONJ
fuelectenerg-1427	58	6	fault	fault	VERB
fuelectenerg-1427	58	7	detection	detection	NOUN
fuelectenerg-1427	58	8	and	and	CCONJ
fuelectenerg-1427	58	9	testing	testing	NOUN
fuelectenerg-1427	59	1	[	[	X
fuelectenerg-1427	59	2	1	1	NUM
fuelectenerg-1427	59	3	-	-	SYM
fuelectenerg-1427	59	4	9	9	NUM
fuelectenerg-1427	59	5	,	,	PUNCT
fuelectenerg-1427	59	6	12	12	NUM
fuelectenerg-1427	59	7	-	-	SYM
fuelectenerg-1427	59	8	14	14	NUM
fuelectenerg-1427	59	9	,	,	PUNCT
fuelectenerg-1427	59	10	16	16	NUM
fuelectenerg-1427	59	11	,	,	PUNCT
fuelectenerg-1427	59	12	17	17	NUM
fuelectenerg-1427	59	13	,	,	PUNCT
fuelectenerg-1427	59	14	19	19	NUM
fuelectenerg-1427	59	15	,	,	PUNCT
fuelectenerg-1427	59	16	20	20	NUM
fuelectenerg-1427	59	17	,	,	PUNCT
fuelectenerg-1427	59	18	21	21	NUM
fuelectenerg-1427	59	19	]	]	PUNCT
fuelectenerg-1427	59	20	.	.	PUNCT
fuelectenerg-1427	60	1	the	the	DET
fuelectenerg-1427	60	2	method	method	NOUN
fuelectenerg-1427	60	3	of	of	ADP
fuelectenerg-1427	60	4	generating	generate	VERB
fuelectenerg-1427	60	5	the	the	DET
fuelectenerg-1427	60	6	new	new	ADJ
fuelectenerg-1427	60	7	families	family	NOUN
fuelectenerg-1427	60	8	of	of	ADP
fuelectenerg-1427	60	9	multiple	multiple	ADV
fuelectenerg-1427	60	10	-	-	PUNCT
fuelectenerg-1427	60	11	valued	value	VERB
fuelectenerg-1427	60	12	shannon	shannon	NOUN
fuelectenerg-1427	60	13	and	and	CCONJ
fuelectenerg-1427	60	14	davio	davio	PROPN
fuelectenerg-1427	60	15	spectral	spectral	ADJ
fuelectenerg-1427	60	16	transforms	transform	NOUN
fuelectenerg-1427	60	17	is	be	AUX
fuelectenerg-1427	60	18	based	base	VERB
fuelectenerg-1427	60	19	on	on	ADP
fuelectenerg-1427	60	20	the	the	DET
fuelectenerg-1427	60	21	fundamental	fundamental	ADJ
fuelectenerg-1427	60	22	multiple	multiple	ADV
fuelectenerg-1427	60	23	-	-	PUNCT
fuelectenerg-1427	60	24	valued	value	VERB
fuelectenerg-1427	60	25	shannon	shannon	NOUN
fuelectenerg-1427	60	26	and	and	CCONJ
fuelectenerg-1427	60	27	davio	davio	NOUN
fuelectenerg-1427	60	28	expansions	expansion	NOUN
fuelectenerg-1427	60	29	.	.	PUNCT
fuelectenerg-1427	61	1	dyadic	dyadic	ADJ
fuelectenerg-1427	61	2	families	family	NOUN
fuelectenerg-1427	61	3	of	of	ADP
fuelectenerg-1427	61	4	discrete	discrete	ADJ
fuelectenerg-1427	61	5	transforms	transform	NOUN
fuelectenerg-1427	61	6	;	;	PUNCT
fuelectenerg-1427	61	7	reed	reed	NOUN
fuelectenerg-1427	61	8	-	-	PUNCT
fuelectenerg-1427	61	9	muller	muller	NOUN
fuelectenerg-1427	61	10	and	and	CCONJ
fuelectenerg-1427	61	11	green	green	ADJ
fuelectenerg-1427	61	12	-	-	PUNCT
fuelectenerg-1427	61	13	sasao	sasao	PROPN
fuelectenerg-1427	61	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	61	15	,	,	PUNCT
fuelectenerg-1427	61	16	walsh	walsh	NOUN
fuelectenerg-1427	61	17	,	,	PUNCT
fuelectenerg-1427	61	18	arithmetic	arithmetic	ADJ
fuelectenerg-1427	61	19	,	,	PUNCT
fuelectenerg-1427	61	20	adding	add	VERB
fuelectenerg-1427	61	21	and	and	CCONJ
fuelectenerg-1427	61	22	haar	haar	PROPN
fuelectenerg-1427	61	23	transforms	transform	VERB
fuelectenerg-1427	61	24	and	and	CCONJ
fuelectenerg-1427	61	25	their	their	PRON
fuelectenerg-1427	61	26	generalizations	generalization	NOUN
fuelectenerg-1427	61	27	to	to	ADP
fuelectenerg-1427	61	28	multiple	multiple	ADV
fuelectenerg-1427	61	29	-	-	PUNCT
fuelectenerg-1427	61	30	valued	value	VERB
fuelectenerg-1427	61	31	transforms	transform	NOUN
fuelectenerg-1427	61	32	,	,	PUNCT
fuelectenerg-1427	61	33	have	have	AUX
fuelectenerg-1427	61	34	also	also	ADV
fuelectenerg-1427	61	35	found	find	VERB
fuelectenerg-1427	61	36	important	important	ADJ
fuelectenerg-1427	61	37	applications	application	NOUN
fuelectenerg-1427	61	38	in	in	ADP
fuelectenerg-1427	61	39	digital	digital	ADJ
fuelectenerg-1427	61	40	system	system	NOUN
fuelectenerg-1427	61	41	design	design	NOUN
fuelectenerg-1427	61	42	and	and	CCONJ
fuelectenerg-1427	61	43	optimization	optimization	NOUN
fuelectenerg-1427	61	44	[	[	X
fuelectenerg-1427	61	45	1	1	NUM
fuelectenerg-1427	61	46	,	,	PUNCT
fuelectenerg-1427	61	47	6	6	NUM
fuelectenerg-1427	61	48	,	,	PUNCT
fuelectenerg-1427	61	49	19	19	NUM
fuelectenerg-1427	61	50	,	,	PUNCT
fuelectenerg-1427	61	51	7	7	NUM
fuelectenerg-1427	61	52	-	-	SYM
fuelectenerg-1427	61	53	18	18	NUM
fuelectenerg-1427	61	54	,	,	PUNCT
fuelectenerg-1427	61	55	20	20	NUM
fuelectenerg-1427	61	56	-	-	SYM
fuelectenerg-1427	61	57	31	31	NUM
fuelectenerg-1427	61	58	]	]	PUNCT
fuelectenerg-1427	61	59	.	.	PUNCT
fuelectenerg-1427	62	1	normal	normal	ADJ
fuelectenerg-1427	62	2	canonical	canonical	ADJ
fuelectenerg-1427	62	3	forms	form	NOUN
fuelectenerg-1427	62	4	play	play	VERB
fuelectenerg-1427	62	5	an	an	DET
fuelectenerg-1427	62	6	important	important	ADJ
fuelectenerg-1427	62	7	role	role	NOUN
fuelectenerg-1427	62	8	in	in	ADP
fuelectenerg-1427	62	9	the	the	DET
fuelectenerg-1427	62	10	synthesis	synthesis	NOUN
fuelectenerg-1427	62	11	of	of	ADP
fuelectenerg-1427	62	12	logic	logic	NOUN
fuelectenerg-1427	62	13	circuits	circuit	NOUN
fuelectenerg-1427	62	14	which	which	PRON
fuelectenerg-1427	62	15	includes	include	VERB
fuelectenerg-1427	62	16	synthesis	synthesis	NOUN
fuelectenerg-1427	62	17	,	,	PUNCT
fuelectenerg-1427	62	18	testing	testing	NOUN
fuelectenerg-1427	62	19	and	and	CCONJ
fuelectenerg-1427	62	20	optimization	optimization	NOUN
fuelectenerg-1427	62	21	[	[	X
fuelectenerg-1427	62	22	1	1	NUM
fuelectenerg-1427	62	23	,	,	PUNCT
fuelectenerg-1427	62	24	9	9	NUM
fuelectenerg-1427	62	25	,	,	PUNCT
fuelectenerg-1427	62	26	12	12	NUM
fuelectenerg-1427	62	27	-	-	SYM
fuelectenerg-1427	62	28	15	15	NUM
fuelectenerg-1427	62	29	,	,	PUNCT
fuelectenerg-1427	62	30	17	17	NUM
fuelectenerg-1427	62	31	,	,	PUNCT
fuelectenerg-1427	62	32	21	21	NUM
fuelectenerg-1427	62	33	,	,	PUNCT
fuelectenerg-1427	62	34	22	22	NUM
fuelectenerg-1427	62	35	,	,	PUNCT
fuelectenerg-1427	62	36	26	26	NUM
fuelectenerg-1427	62	37	,	,	PUNCT
fuelectenerg-1427	62	38	27	27	NUM
fuelectenerg-1427	62	39	,	,	PUNCT
fuelectenerg-1427	62	40	31	31	NUM
fuelectenerg-1427	62	41	,	,	PUNCT
fuelectenerg-1427	62	42	32	32	NUM
fuelectenerg-1427	62	43	]	]	PUNCT
fuelectenerg-1427	62	44	.	.	PUNCT
fuelectenerg-1427	63	1	one	one	PRON
fuelectenerg-1427	63	2	can	can	AUX
fuelectenerg-1427	63	3	observe	observe	VERB
fuelectenerg-1427	63	4	that	that	SCONJ
fuelectenerg-1427	63	5	by	by	ADP
fuelectenerg-1427	63	6	going	go	VERB
fuelectenerg-1427	63	7	,	,	PUNCT
fuelectenerg-1427	63	8	for	for	ADP
fuelectenerg-1427	63	9	example	example	NOUN
fuelectenerg-1427	63	10	,	,	PUNCT
fuelectenerg-1427	63	11	from	from	ADP
fuelectenerg-1427	63	12	positive	positive	ADJ
fuelectenerg-1427	63	13	polarity	polarity	NOUN
fuelectenerg-1427	63	14	reed	reed	NOUN
fuelectenerg-1427	63	15	-	-	PUNCT
fuelectenerg-1427	63	16	muller	muller	NOUN
fuelectenerg-1427	63	17	(	(	PUNCT
fuelectenerg-1427	63	18	pprm	pprm	ADJ
fuelectenerg-1427	63	19	)	)	PUNCT
fuelectenerg-1427	63	20	form	form	NOUN
fuelectenerg-1427	63	21	to	to	ADP
fuelectenerg-1427	63	22	the	the	DET
fuelectenerg-1427	63	23	generalized	generalized	ADJ
fuelectenerg-1427	63	24	reed	reed	NOUN
fuelectenerg-1427	63	25	-	-	PUNCT
fuelectenerg-1427	63	26	muller	muller	NOUN
fuelectenerg-1427	63	27	(	(	PUNCT
fuelectenerg-1427	63	28	grm	grm	NOUN
fuelectenerg-1427	63	29	)	)	PUNCT
fuelectenerg-1427	63	30	form	form	NOUN
fuelectenerg-1427	63	31	,	,	PUNCT
fuelectenerg-1427	63	32	less	less	ADJ
fuelectenerg-1427	63	33	constraints	constraint	NOUN
fuelectenerg-1427	63	34	are	be	AUX
fuelectenerg-1427	63	35	imposed	impose	VERB
fuelectenerg-1427	63	36	on	on	ADP
fuelectenerg-1427	63	37	the	the	DET
fuelectenerg-1427	63	38	canonical	canonical	ADJ
fuelectenerg-1427	63	39	forms	form	NOUN
fuelectenerg-1427	63	40	due	due	ADJ
fuelectenerg-1427	63	41	to	to	ADP
fuelectenerg-1427	63	42	the	the	DET
fuelectenerg-1427	63	43	enlarged	enlarged	ADJ
fuelectenerg-1427	63	44	set	set	NOUN
fuelectenerg-1427	63	45	of	of	ADP
fuelectenerg-1427	63	46	polarities	polarity	NOUN
fuelectenerg-1427	63	47	that	that	PRON
fuelectenerg-1427	63	48	one	one	PRON
fuelectenerg-1427	63	49	can	can	AUX
fuelectenerg-1427	63	50	choose	choose	VERB
fuelectenerg-1427	63	51	from	from	ADP
fuelectenerg-1427	63	52	.	.	PUNCT
fuelectenerg-1427	64	1	the	the	DET
fuelectenerg-1427	64	2	gain	gain	NOUN
fuelectenerg-1427	64	3	of	of	ADP
fuelectenerg-1427	64	4	more	more	ADJ
fuelectenerg-1427	64	5	freedom	freedom	NOUN
fuelectenerg-1427	64	6	on	on	ADP
fuelectenerg-1427	64	7	the	the	DET
fuelectenerg-1427	64	8	polarity	polarity	NOUN
fuelectenerg-1427	64	9	of	of	ADP
fuelectenerg-1427	64	10	the	the	DET
fuelectenerg-1427	64	11	canonical	canonical	ADJ
fuelectenerg-1427	64	12	expansions	expansion	NOUN
fuelectenerg-1427	64	13	will	will	AUX
fuelectenerg-1427	64	14	provide	provide	VERB
fuelectenerg-1427	64	15	an	an	DET
fuelectenerg-1427	64	16	advantage	advantage	NOUN
fuelectenerg-1427	64	17	of	of	ADP
fuelectenerg-1427	64	18	obtaining	obtain	VERB
fuelectenerg-1427	64	19	exclusive	exclusive	ADJ
fuelectenerg-1427	64	20	-	-	PUNCT
fuelectenerg-1427	64	21	sum	sum	NOUN
fuelectenerg-1427	64	22	-	-	PUNCT
fuelectenerg-1427	64	23	of	of	ADP
fuelectenerg-1427	64	24	-	-	PUNCT
fuelectenerg-1427	64	25	product	product	NOUN
fuelectenerg-1427	64	26	(	(	PUNCT
fuelectenerg-1427	64	27	esop	esop	PROPN
fuelectenerg-1427	64	28	)	)	PUNCT
fuelectenerg-1427	64	29	expressions	expression	NOUN
fuelectenerg-1427	64	30	with	with	ADP
fuelectenerg-1427	64	31	less	less	ADJ
fuelectenerg-1427	64	32	number	number	NOUN
fuelectenerg-1427	64	33	of	of	ADP
fuelectenerg-1427	64	34	terms	term	NOUN
fuelectenerg-1427	64	35	and	and	CCONJ
fuelectenerg-1427	64	36	literals	literal	NOUN
fuelectenerg-1427	64	37	,	,	PUNCT
fuelectenerg-1427	64	38	and	and	CCONJ
fuelectenerg-1427	64	39	consequently	consequently	ADV
fuelectenerg-1427	64	40	expressing	express	VERB
fuelectenerg-1427	64	41	boolean	boolean	ADJ
fuelectenerg-1427	64	42	functions	function	NOUN
fuelectenerg-1427	64	43	using	use	VERB
fuelectenerg-1427	64	44	esop	esop	NOUN
fuelectenerg-1427	64	45	forms	form	NOUN
fuelectenerg-1427	64	46	will	will	AUX
fuelectenerg-1427	64	47	produce	produce	VERB
fuelectenerg-1427	64	48	on	on	ADP
fuelectenerg-1427	64	49	average	average	ADJ
fuelectenerg-1427	64	50	expressions	expression	NOUN
fuelectenerg-1427	64	51	with	with	ADP
fuelectenerg-1427	64	52	less	less	ADJ
fuelectenerg-1427	64	53	size	size	NOUN
fuelectenerg-1427	64	54	as	as	SCONJ
fuelectenerg-1427	64	55	if	if	SCONJ
fuelectenerg-1427	64	56	compared	compare	VERB
fuelectenerg-1427	64	57	to	to	ADP
fuelectenerg-1427	64	58	sum	sum	NOUN
fuelectenerg-1427	64	59	-	-	PUNCT
fuelectenerg-1427	64	60	of	of	ADP
fuelectenerg-1427	64	61	-	-	PUNCT
fuelectenerg-1427	64	62	product	product	NOUN
fuelectenerg-1427	64	63	(	(	PUNCT
fuelectenerg-1427	64	64	sop	sop	NOUN
fuelectenerg-1427	64	65	)	)	PUNCT
fuelectenerg-1427	64	66	expressions	expression	NOUN
fuelectenerg-1427	64	67	for	for	ADP
fuelectenerg-1427	64	68	example	example	NOUN
fuelectenerg-1427	64	69	.	.	PUNCT
fuelectenerg-1427	65	1	table	table	NOUN
fuelectenerg-1427	65	2	1	1	NUM
fuelectenerg-1427	65	3	illustrates	illustrate	VERB
fuelectenerg-1427	65	4	these	these	DET
fuelectenerg-1427	65	5	observations	observation	NOUN
fuelectenerg-1427	66	1	[	[	X
fuelectenerg-1427	66	2	1	1	NUM
fuelectenerg-1427	66	3	]	]	PUNCT
fuelectenerg-1427	66	4	.	.	PUNCT
fuelectenerg-1427	67	1	the	the	DET
fuelectenerg-1427	67	2	main	main	ADJ
fuelectenerg-1427	67	3	algebraic	algebraic	ADJ
fuelectenerg-1427	67	4	structure	structure	NOUN
fuelectenerg-1427	67	5	which	which	PRON
fuelectenerg-1427	67	6	is	be	AUX
fuelectenerg-1427	67	7	used	use	VERB
fuelectenerg-1427	67	8	in	in	ADP
fuelectenerg-1427	67	9	this	this	DET
fuelectenerg-1427	67	10	work	work	NOUN
fuelectenerg-1427	67	11	for	for	ADP
fuelectenerg-1427	67	12	developing	develop	VERB
fuelectenerg-1427	67	13	the	the	DET
fuelectenerg-1427	67	14	canonical	canonical	ADJ
fuelectenerg-1427	67	15	normal	normal	ADJ
fuelectenerg-1427	67	16	forms	form	NOUN
fuelectenerg-1427	67	17	is	be	AUX
fuelectenerg-1427	67	18	the	the	DET
fuelectenerg-1427	67	19	galois	galois	PROPN
fuelectenerg-1427	67	20	field	field	NOUN
fuelectenerg-1427	67	21	(	(	PUNCT
fuelectenerg-1427	67	22	gf	gf	NOUN
fuelectenerg-1427	67	23	)	)	PUNCT
fuelectenerg-1427	67	24	algebraic	algebraic	ADJ
fuelectenerg-1427	67	25	structure	structure	NOUN
fuelectenerg-1427	67	26	,	,	PUNCT
fuelectenerg-1427	67	27	which	which	PRON
fuelectenerg-1427	67	28	is	be	AUX
fuelectenerg-1427	67	29	a	a	DET
fuelectenerg-1427	67	30	fundamental	fundamental	ADJ
fuelectenerg-1427	67	31	algebraic	algebraic	ADJ
fuelectenerg-1427	67	32	structure	structure	NOUN
fuelectenerg-1427	67	33	in	in	ADP
fuelectenerg-1427	67	34	the	the	DET
fuelectenerg-1427	67	35	theory	theory	NOUN
fuelectenerg-1427	67	36	of	of	ADP
fuelectenerg-1427	67	37	algebra	algebra	NOUN
fuelectenerg-1427	67	38	[	[	X
fuelectenerg-1427	67	39	1	1	NUM
fuelectenerg-1427	67	40	,	,	PUNCT
fuelectenerg-1427	67	41	12	12	NUM
fuelectenerg-1427	67	42	,	,	PUNCT
fuelectenerg-1427	67	43	13	13	NUM
fuelectenerg-1427	67	44	,	,	PUNCT
fuelectenerg-1427	67	45	17	17	NUM
fuelectenerg-1427	67	46	,	,	PUNCT
fuelectenerg-1427	67	47	22	22	NUM
fuelectenerg-1427	67	48	,	,	PUNCT
fuelectenerg-1427	67	49	29	29	NUM
fuelectenerg-1427	67	50	,	,	PUNCT
fuelectenerg-1427	67	51	33	33	NUM
fuelectenerg-1427	67	52	,	,	PUNCT
fuelectenerg-1427	67	53	34	34	NUM
fuelectenerg-1427	67	54	]	]	PUNCT
fuelectenerg-1427	67	55	.	.	PUNCT
fuelectenerg-1427	68	1	the	the	DET
fuelectenerg-1427	68	2	importance	importance	NOUN
fuelectenerg-1427	68	3	of	of	ADP
fuelectenerg-1427	68	4	gf	gf	PROPN
fuelectenerg-1427	68	5	for	for	ADP
fuelectenerg-1427	68	6	logic	logic	ADJ
fuelectenerg-1427	68	7	synthesis	synthesis	NOUN
fuelectenerg-1427	68	8	results	result	NOUN
fuelectenerg-1427	68	9	from	from	ADP
fuelectenerg-1427	68	10	the	the	DET
fuelectenerg-1427	68	11	fact	fact	NOUN
fuelectenerg-1427	68	12	that	that	SCONJ
fuelectenerg-1427	68	13	every	every	DET
fuelectenerg-1427	68	14	finite	finite	ADJ
fuelectenerg-1427	68	15	field	field	NOUN
fuelectenerg-1427	68	16	is	be	AUX
fuelectenerg-1427	68	17	isomorphic	isomorphic	ADJ
fuelectenerg-1427	68	18	to	to	ADP
fuelectenerg-1427	68	19	a	a	DET
fuelectenerg-1427	68	20	galois	galois	PROPN
fuelectenerg-1427	68	21	field	field	NOUN
fuelectenerg-1427	68	22	.	.	PUNCT
fuelectenerg-1427	69	1	in	in	ADP
fuelectenerg-1427	69	2	general	general	ADJ
fuelectenerg-1427	69	3	,	,	PUNCT
fuelectenerg-1427	69	4	the	the	DET
fuelectenerg-1427	69	5	attractive	attractive	ADJ
fuelectenerg-1427	69	6	properties	property	NOUN
fuelectenerg-1427	69	7	of	of	ADP
fuelectenerg-1427	69	8	gf	gf	NOUN
fuelectenerg-1427	69	9	-	-	PUNCT
fuelectenerg-1427	69	10	based	base	VERB
fuelectenerg-1427	69	11	circuits	circuit	NOUN
fuelectenerg-1427	69	12	,	,	PUNCT
fuelectenerg-1427	69	13	such	such	ADJ
fuelectenerg-1427	69	14	as	as	ADP
fuelectenerg-1427	69	15	the	the	DET
fuelectenerg-1427	69	16	high	high	ADJ
fuelectenerg-1427	69	17	testability	testability	NOUN
fuelectenerg-1427	69	18	of	of	ADP
fuelectenerg-1427	69	19	such	such	ADJ
fuelectenerg-1427	69	20	circuits	circuit	NOUN
fuelectenerg-1427	69	21	,	,	PUNCT
fuelectenerg-1427	69	22	are	be	AUX
fuelectenerg-1427	69	23	mainly	mainly	ADV
fuelectenerg-1427	69	24	due	due	ADP
fuelectenerg-1427	69	25	to	to	ADP
fuelectenerg-1427	69	26	the	the	DET
fuelectenerg-1427	69	27	fact	fact	NOUN
fuelectenerg-1427	69	28	that	that	SCONJ
fuelectenerg-1427	69	29	the	the	DET
fuelectenerg-1427	69	30	gf	gf	PROPN
fuelectenerg-1427	69	31	operators	operator	NOUN
fuelectenerg-1427	69	32	exhibit	exhibit	VERB
fuelectenerg-1427	69	33	the	the	DET
fuelectenerg-1427	69	34	cyclic	cyclic	ADJ
fuelectenerg-1427	69	35	group	group	NOUN
fuelectenerg-1427	69	36	,	,	PUNCT
fuelectenerg-1427	69	37	also	also	ADV
fuelectenerg-1427	69	38	known	know	VERB
fuelectenerg-1427	69	39	as	as	ADP
fuelectenerg-1427	69	40	latin	latin	PROPN
fuelectenerg-1427	69	41	square	square	NOUN
fuelectenerg-1427	69	42	,	,	PUNCT
fuelectenerg-1427	69	43	property	property	NOUN
fuelectenerg-1427	69	44	.	.	PUNCT
fuelectenerg-1427	70	1	in	in	ADP
fuelectenerg-1427	70	2	binary	binary	NOUN
fuelectenerg-1427	70	3	,	,	PUNCT
fuelectenerg-1427	70	4	for	for	ADP
fuelectenerg-1427	70	5	example	example	NOUN
fuelectenerg-1427	70	6	,	,	PUNCT
fuelectenerg-1427	70	7	gf(2	gf(2	PROPN
fuelectenerg-1427	70	8	)	)	PUNCT
fuelectenerg-1427	70	9	addition	addition	NOUN
fuelectenerg-1427	70	10	gate	gate	NOUN
fuelectenerg-1427	70	11	,	,	PUNCT
fuelectenerg-1427	70	12	the	the	DET
fuelectenerg-1427	70	13	exor	exor	PROPN
fuelectenerg-1427	70	14	,	,	PUNCT
fuelectenerg-1427	70	15	has	have	VERB
fuelectenerg-1427	70	16	the	the	DET
fuelectenerg-1427	70	17	cyclic	cyclic	ADJ
fuelectenerg-1427	70	18	group	group	NOUN
fuelectenerg-1427	70	19	property	property	NOUN
fuelectenerg-1427	70	20	.	.	PUNCT
fuelectenerg-1427	71	1	the	the	DET
fuelectenerg-1427	71	2	cyclic	cyclic	PROPN
fuelectenerg-1427	71	3	group	group	NOUN
fuelectenerg-1427	71	4	property	property	NOUN
fuelectenerg-1427	71	5	can	can	AUX
fuelectenerg-1427	71	6	be	be	AUX
fuelectenerg-1427	71	7	explained	explain	VERB
fuelectenerg-1427	71	8	,	,	PUNCT
fuelectenerg-1427	71	9	for	for	ADP
fuelectenerg-1427	71	10	example	example	NOUN
fuelectenerg-1427	71	11	,	,	PUNCT
fuelectenerg-1427	71	12	using	use	VERB
fuelectenerg-1427	71	13	the	the	DET
fuelectenerg-1427	71	14	three	three	NUM
fuelectenerg-1427	71	15	-	-	PUNCT
fuelectenerg-1427	71	16	valued	value	VERB
fuelectenerg-1427	71	17	(	(	PUNCT
fuelectenerg-1427	71	18	ternary	ternary	ADJ
fuelectenerg-1427	71	19	)	)	PUNCT
fuelectenerg-1427	71	20	gf	gf	NOUN
fuelectenerg-1427	71	21	operators	operator	NOUN
fuelectenerg-1427	71	22	as	as	SCONJ
fuelectenerg-1427	71	23	shown	show	VERB
fuelectenerg-1427	71	24	in	in	ADP
fuelectenerg-1427	71	25	figures	figure	NOUN
fuelectenerg-1427	71	26	1(a	1(a	NUM
fuelectenerg-1427	71	27	)	)	PUNCT
fuelectenerg-1427	71	28	and	and	CCONJ
fuelectenerg-1427	71	29	1(b	1(b	NUM
fuelectenerg-1427	71	30	)	)	PUNCT
fuelectenerg-1427	71	31	,	,	PUNCT
fuelectenerg-1427	71	32	respectively	respectively	ADV
fuelectenerg-1427	71	33	.	.	PUNCT
fuelectenerg-1427	72	1	note	note	VERB
fuelectenerg-1427	72	2	that	that	SCONJ
fuelectenerg-1427	72	3	in	in	ADP
fuelectenerg-1427	72	4	any	any	DET
fuelectenerg-1427	72	5	row	row	NOUN
fuelectenerg-1427	72	6	and	and	CCONJ
fuelectenerg-1427	72	7	column	column	NOUN
fuelectenerg-1427	72	8	of	of	ADP
fuelectenerg-1427	72	9	the	the	DET
fuelectenerg-1427	72	10	addition	addition	NOUN
fuelectenerg-1427	72	11	table	table	NOUN
fuelectenerg-1427	72	12	in	in	ADP
fuelectenerg-1427	72	13	figure	figure	NOUN
fuelectenerg-1427	72	14	1(a	1(a	NUM
fuelectenerg-1427	72	15	)	)	PUNCT
fuelectenerg-1427	72	16	,	,	PUNCT
fuelectenerg-1427	72	17	the	the	DET
fuelectenerg-1427	72	18	elements	element	NOUN
fuelectenerg-1427	72	19	are	be	AUX
fuelectenerg-1427	72	20	all	all	ADV
fuelectenerg-1427	72	21	different	different	ADJ
fuelectenerg-1427	72	22	,	,	PUNCT
fuelectenerg-1427	72	23	which	which	PRON
fuelectenerg-1427	72	24	is	be	AUX
fuelectenerg-1427	72	25	cyclic	cyclic	ADJ
fuelectenerg-1427	72	26	,	,	PUNCT
fuelectenerg-1427	72	27	and	and	CCONJ
fuelectenerg-1427	72	28	that	that	SCONJ
fuelectenerg-1427	72	29	the	the	DET
fuelectenerg-1427	72	30	elements	element	NOUN
fuelectenerg-1427	72	31	have	have	VERB
fuelectenerg-1427	72	32	a	a	DET
fuelectenerg-1427	72	33	different	different	ADJ
fuelectenerg-1427	72	34	order	order	NOUN
fuelectenerg-1427	72	35	in	in	ADP
fuelectenerg-1427	72	36	each	each	DET
fuelectenerg-1427	72	37	row	row	NOUN
fuelectenerg-1427	72	38	and	and	CCONJ
fuelectenerg-1427	72	39	column	column	NOUN
fuelectenerg-1427	72	40	.	.	PUNCT
fuelectenerg-1427	73	1	another	another	DET
fuelectenerg-1427	73	2	cyclic	cyclic	ADJ
fuelectenerg-1427	73	3	group	group	NOUN
fuelectenerg-1427	73	4	can	can	AUX
fuelectenerg-1427	73	5	be	be	AUX
fuelectenerg-1427	73	6	observed	observe	VERB
fuelectenerg-1427	73	7	in	in	ADP
fuelectenerg-1427	73	8	the	the	DET
fuelectenerg-1427	73	9	multiplication	multiplication	NOUN
fuelectenerg-1427	73	10	table	table	NOUN
fuelectenerg-1427	73	11	;	;	PUNCT
fuelectenerg-1427	73	12	if	if	SCONJ
fuelectenerg-1427	73	13	the	the	DET
fuelectenerg-1427	73	14	zero	zero	NUM
fuelectenerg-1427	73	15	elements	element	NOUN
fuelectenerg-1427	73	16	are	be	AUX
fuelectenerg-1427	73	17	removed	remove	VERB
fuelectenerg-1427	73	18	from	from	ADP
fuelectenerg-1427	73	19	the	the	DET
fuelectenerg-1427	73	20	multiplication	multiplication	NOUN
fuelectenerg-1427	73	21	table	table	NOUN
fuelectenerg-1427	73	22	in	in	ADP
fuelectenerg-1427	73	23	figure	figure	NOUN
fuelectenerg-1427	73	24	1(b	1(b	NUM
fuelectenerg-1427	73	25	)	)	PUNCT
fuelectenerg-1427	73	26	,	,	PUNCT
fuelectenerg-1427	73	27	then	then	ADV
fuelectenerg-1427	73	28	the	the	DET
fuelectenerg-1427	73	29	remaining	remain	VERB
fuelectenerg-1427	73	30	elements	element	NOUN
fuelectenerg-1427	73	31	form	form	VERB
fuelectenerg-1427	73	32	a	a	DET
fuelectenerg-1427	73	33	cyclic	cyclic	ADJ
fuelectenerg-1427	73	34	group	group	NOUN
fuelectenerg-1427	73	35	.	.	PUNCT
fuelectenerg-1427	74	1	reed	reed	NOUN
fuelectenerg-1427	74	2	-	-	PUNCT
fuelectenerg-1427	74	3	muller	muller	NOUN
fuelectenerg-1427	74	4	normal	normal	ADJ
fuelectenerg-1427	74	5	forms	form	NOUN
fuelectenerg-1427	74	6	have	have	AUX
fuelectenerg-1427	74	7	been	be	AUX
fuelectenerg-1427	74	8	classified	classify	VERB
fuelectenerg-1427	74	9	using	use	VERB
fuelectenerg-1427	74	10	the	the	DET
fuelectenerg-1427	74	11	green	green	ADJ
fuelectenerg-1427	74	12	-	-	PUNCT
fuelectenerg-1427	74	13	sasao	sasao	NOUN
fuelectenerg-1427	74	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	75	1	[	[	X
fuelectenerg-1427	75	2	1	1	NUM
fuelectenerg-1427	75	3	,	,	PUNCT
fuelectenerg-1427	75	4	10	10	NUM
fuelectenerg-1427	75	5	,	,	PUNCT
fuelectenerg-1427	75	6	12	12	NUM
fuelectenerg-1427	75	7	,	,	PUNCT
fuelectenerg-1427	75	8	13	13	NUM
fuelectenerg-1427	75	9	,	,	PUNCT
fuelectenerg-1427	75	10	17	17	NUM
fuelectenerg-1427	75	11	]	]	PUNCT
fuelectenerg-1427	75	12	,	,	PUNCT
fuelectenerg-1427	75	13	where	where	SCONJ
fuelectenerg-1427	75	14	the	the	DET
fuelectenerg-1427	75	15	green	green	ADJ
fuelectenerg-1427	75	16	-	-	PUNCT
fuelectenerg-1427	75	17	sasao	sasao	PROPN
fuelectenerg-1427	75	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	75	19	of	of	ADP
fuelectenerg-1427	75	20	families	family	NOUN
fuelectenerg-1427	75	21	of	of	ADP
fuelectenerg-1427	75	22	canonical	canonical	ADJ
fuelectenerg-1427	75	23	forms	form	NOUN
fuelectenerg-1427	75	24	and	and	CCONJ
fuelectenerg-1427	75	25	corresponding	correspond	VERB
fuelectenerg-1427	75	26	decision	decision	NOUN
fuelectenerg-1427	75	27	diagrams	diagram	NOUN
fuelectenerg-1427	75	28	is	be	AUX
fuelectenerg-1427	75	29	based	base	VERB
fuelectenerg-1427	75	30	on	on	ADP
fuelectenerg-1427	75	31	three	three	NUM
fuelectenerg-1427	75	32	generic	generic	ADJ
fuelectenerg-1427	75	33	expansions	expansion	NOUN
fuelectenerg-1427	75	34	;	;	PUNCT
fuelectenerg-1427	75	35	shannon	shannon	PROPN
fuelectenerg-1427	75	36	,	,	PUNCT
fuelectenerg-1427	75	37	pos102	pos102	PROPN
fuelectenerg-1427	75	38	an	an	DET
fuelectenerg-1427	75	39	extended	extended	ADJ
fuelectenerg-1427	75	40	green	green	ADJ
fuelectenerg-1427	75	41	sasao	sasao	PROPN
fuelectenerg-1427	75	42	hierarchy	hierarchy	NOUN
fuelectenerg-1427	75	43	of	of	ADP
fuelectenerg-1427	75	44	canonical	canonical	ADJ
fuelectenerg-1427	75	45	ternary	ternary	ADJ
fuelectenerg-1427	75	46	galois	galois	NOUN
fuelectenerg-1427	75	47	forms	form	NOUN
fuelectenerg-1427	75	48	...	...	PUNCT
fuelectenerg-1427	75	49	table	table	NOUN
fuelectenerg-1427	75	50	1	1	NUM
fuelectenerg-1427	75	51	:	:	PUNCT
fuelectenerg-1427	75	52	number	number	NOUN
fuelectenerg-1427	75	53	of	of	ADP
fuelectenerg-1427	75	54	product	product	NOUN
fuelectenerg-1427	75	55	terms	term	NOUN
fuelectenerg-1427	75	56	needed	need	VERB
fuelectenerg-1427	75	57	to	to	PART
fuelectenerg-1427	75	58	realize	realize	VERB
fuelectenerg-1427	75	59	some	some	DET
fuelectenerg-1427	75	60	arithmetic	arithmetic	ADJ
fuelectenerg-1427	75	61	functions	function	NOUN
fuelectenerg-1427	75	62	using	use	VERB
fuelectenerg-1427	75	63	various	various	ADJ
fuelectenerg-1427	75	64	expressions	expression	NOUN
fuelectenerg-1427	75	65	.	.	PUNCT
fuelectenerg-1427	76	1	function	function	NOUN
fuelectenerg-1427	76	2	pprm	pprm	PROPN
fuelectenerg-1427	76	3	fprm	fprm	PROPN
fuelectenerg-1427	76	4	grm	grm	PROPN
fuelectenerg-1427	76	5	esop	esop	PROPN
fuelectenerg-1427	76	6	sop	sop	PROPN
fuelectenerg-1427	76	7	adr4	adr4	PROPN
fuelectenerg-1427	76	8	34	34	NUM
fuelectenerg-1427	76	9	34	34	NUM
fuelectenerg-1427	76	10	34	34	NUM
fuelectenerg-1427	76	11	31	31	NUM
fuelectenerg-1427	76	12	75	75	NUM
fuelectenerg-1427	76	13	log8	log8	NOUN
fuelectenerg-1427	76	14	253	253	NUM
fuelectenerg-1427	76	15	193	193	NUM
fuelectenerg-1427	76	16	105	105	NUM
fuelectenerg-1427	76	17	96	96	NUM
fuelectenerg-1427	76	18	123	123	NUM
fuelectenerg-1427	76	19	nrm4	nrm4	NOUN
fuelectenerg-1427	76	20	216	216	NUM
fuelectenerg-1427	76	21	185	185	NUM
fuelectenerg-1427	76	22	96	96	NUM
fuelectenerg-1427	76	23	69	69	NUM
fuelectenerg-1427	76	24	120	120	NUM
fuelectenerg-1427	76	25	rdm8	rdm8	NOUN
fuelectenerg-1427	76	26	56	56	NUM
fuelectenerg-1427	76	27	56	56	NUM
fuelectenerg-1427	76	28	31	31	NUM
fuelectenerg-1427	76	29	31	31	NUM
fuelectenerg-1427	76	30	76	76	NUM
fuelectenerg-1427	76	31	rot8	rot8	NOUN
fuelectenerg-1427	76	32	225	225	NUM
fuelectenerg-1427	76	33	118	118	NUM
fuelectenerg-1427	76	34	51	51	NUM
fuelectenerg-1427	76	35	35	35	NUM
fuelectenerg-1427	76	36	57	57	NUM
fuelectenerg-1427	76	37	sym9	sym9	NOUN
fuelectenerg-1427	76	38	210	210	NUM
fuelectenerg-1427	76	39	173	173	NUM
fuelectenerg-1427	76	40	126	126	NUM
fuelectenerg-1427	76	41	51	51	NUM
fuelectenerg-1427	76	42	84	84	NUM
fuelectenerg-1427	76	43	wgt8	wgt8	NOUN
fuelectenerg-1427	76	44	107	107	NUM
fuelectenerg-1427	76	45	107	107	NUM
fuelectenerg-1427	76	46	107	107	NUM
fuelectenerg-1427	76	47	58	58	NUM
fuelectenerg-1427	76	48	255	255	NUM
fuelectenerg-1427	77	1	and	and	CCONJ
fuelectenerg-1427	77	2	image	image	NOUN
fuelectenerg-1427	77	3	processing	processing	NOUN
fuelectenerg-1427	77	4	,	,	PUNCT
fuelectenerg-1427	77	5	and	and	CCONJ
fuelectenerg-1427	77	6	fault	fault	VERB
fuelectenerg-1427	77	7	detection	detection	NOUN
fuelectenerg-1427	77	8	and	and	CCONJ
fuelectenerg-1427	77	9	testing	testing	NOUN
fuelectenerg-1427	78	1	[	[	X
fuelectenerg-1427	78	2	1	1	NUM
fuelectenerg-1427	78	3	-	-	SYM
fuelectenerg-1427	78	4	9	9	NUM
fuelectenerg-1427	78	5	,	,	PUNCT
fuelectenerg-1427	78	6	12	12	NUM
fuelectenerg-1427	78	7	-	-	SYM
fuelectenerg-1427	78	8	14	14	NUM
fuelectenerg-1427	78	9	,	,	PUNCT
fuelectenerg-1427	78	10	16	16	NUM
fuelectenerg-1427	78	11	,	,	PUNCT
fuelectenerg-1427	78	12	17	17	NUM
fuelectenerg-1427	78	13	,	,	PUNCT
fuelectenerg-1427	78	14	19	19	NUM
fuelectenerg-1427	78	15	,	,	PUNCT
fuelectenerg-1427	78	16	20	20	NUM
fuelectenerg-1427	78	17	,	,	PUNCT
fuelectenerg-1427	78	18	21	21	NUM
fuelectenerg-1427	78	19	]	]	PUNCT
fuelectenerg-1427	78	20	.	.	PUNCT
fuelectenerg-1427	79	1	the	the	DET
fuelectenerg-1427	79	2	method	method	NOUN
fuelectenerg-1427	79	3	of	of	ADP
fuelectenerg-1427	79	4	generating	generate	VERB
fuelectenerg-1427	79	5	the	the	DET
fuelectenerg-1427	79	6	new	new	ADJ
fuelectenerg-1427	79	7	families	family	NOUN
fuelectenerg-1427	79	8	of	of	ADP
fuelectenerg-1427	79	9	multiple	multiple	ADV
fuelectenerg-1427	79	10	-	-	PUNCT
fuelectenerg-1427	79	11	valued	value	VERB
fuelectenerg-1427	79	12	shannon	shannon	NOUN
fuelectenerg-1427	79	13	and	and	CCONJ
fuelectenerg-1427	79	14	davio	davio	PROPN
fuelectenerg-1427	79	15	spectral	spectral	ADJ
fuelectenerg-1427	79	16	transforms	transform	NOUN
fuelectenerg-1427	79	17	is	be	AUX
fuelectenerg-1427	79	18	based	base	VERB
fuelectenerg-1427	79	19	on	on	ADP
fuelectenerg-1427	79	20	the	the	DET
fuelectenerg-1427	79	21	fundamental	fundamental	ADJ
fuelectenerg-1427	79	22	multiple	multiple	ADV
fuelectenerg-1427	79	23	-	-	PUNCT
fuelectenerg-1427	79	24	valued	value	VERB
fuelectenerg-1427	79	25	shannon	shannon	NOUN
fuelectenerg-1427	79	26	and	and	CCONJ
fuelectenerg-1427	79	27	davio	davio	NOUN
fuelectenerg-1427	79	28	expansions	expansion	NOUN
fuelectenerg-1427	79	29	.	.	PUNCT
fuelectenerg-1427	80	1	dyadic	dyadic	ADJ
fuelectenerg-1427	80	2	families	family	NOUN
fuelectenerg-1427	80	3	of	of	ADP
fuelectenerg-1427	80	4	discrete	discrete	ADJ
fuelectenerg-1427	80	5	transforms	transform	NOUN
fuelectenerg-1427	80	6	;	;	PUNCT
fuelectenerg-1427	80	7	reed	reed	NOUN
fuelectenerg-1427	80	8	-	-	PUNCT
fuelectenerg-1427	80	9	muller	muller	NOUN
fuelectenerg-1427	80	10	and	and	CCONJ
fuelectenerg-1427	80	11	green	green	ADJ
fuelectenerg-1427	80	12	-	-	PUNCT
fuelectenerg-1427	80	13	sasao	sasao	PROPN
fuelectenerg-1427	80	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	80	15	,	,	PUNCT
fuelectenerg-1427	80	16	walsh	walsh	NOUN
fuelectenerg-1427	80	17	,	,	PUNCT
fuelectenerg-1427	80	18	arithmetic	arithmetic	ADJ
fuelectenerg-1427	80	19	,	,	PUNCT
fuelectenerg-1427	80	20	adding	add	VERB
fuelectenerg-1427	80	21	and	and	CCONJ
fuelectenerg-1427	80	22	haar	haar	PROPN
fuelectenerg-1427	80	23	transforms	transform	VERB
fuelectenerg-1427	80	24	and	and	CCONJ
fuelectenerg-1427	80	25	their	their	PRON
fuelectenerg-1427	80	26	generalizations	generalization	NOUN
fuelectenerg-1427	80	27	to	to	ADP
fuelectenerg-1427	80	28	multiple	multiple	ADV
fuelectenerg-1427	80	29	-	-	PUNCT
fuelectenerg-1427	80	30	valued	value	VERB
fuelectenerg-1427	80	31	transforms	transform	NOUN
fuelectenerg-1427	80	32	,	,	PUNCT
fuelectenerg-1427	80	33	have	have	AUX
fuelectenerg-1427	80	34	also	also	ADV
fuelectenerg-1427	80	35	found	find	VERB
fuelectenerg-1427	80	36	important	important	ADJ
fuelectenerg-1427	80	37	applications	application	NOUN
fuelectenerg-1427	80	38	in	in	ADP
fuelectenerg-1427	80	39	digital	digital	ADJ
fuelectenerg-1427	80	40	system	system	NOUN
fuelectenerg-1427	80	41	design	design	NOUN
fuelectenerg-1427	80	42	and	and	CCONJ
fuelectenerg-1427	80	43	optimization	optimization	NOUN
fuelectenerg-1427	80	44	[	[	X
fuelectenerg-1427	80	45	1	1	NUM
fuelectenerg-1427	80	46	,	,	PUNCT
fuelectenerg-1427	80	47	6	6	NUM
fuelectenerg-1427	80	48	,	,	PUNCT
fuelectenerg-1427	80	49	19	19	NUM
fuelectenerg-1427	80	50	,	,	PUNCT
fuelectenerg-1427	80	51	7	7	NUM
fuelectenerg-1427	80	52	-	-	SYM
fuelectenerg-1427	80	53	18	18	NUM
fuelectenerg-1427	80	54	,	,	PUNCT
fuelectenerg-1427	80	55	20	20	NUM
fuelectenerg-1427	80	56	-	-	SYM
fuelectenerg-1427	80	57	31	31	NUM
fuelectenerg-1427	80	58	]	]	PUNCT
fuelectenerg-1427	80	59	.	.	PUNCT
fuelectenerg-1427	81	1	normal	normal	ADJ
fuelectenerg-1427	81	2	canonical	canonical	ADJ
fuelectenerg-1427	81	3	forms	form	NOUN
fuelectenerg-1427	81	4	play	play	VERB
fuelectenerg-1427	81	5	an	an	DET
fuelectenerg-1427	81	6	important	important	ADJ
fuelectenerg-1427	81	7	role	role	NOUN
fuelectenerg-1427	81	8	in	in	ADP
fuelectenerg-1427	81	9	the	the	DET
fuelectenerg-1427	81	10	synthesis	synthesis	NOUN
fuelectenerg-1427	81	11	of	of	ADP
fuelectenerg-1427	81	12	logic	logic	NOUN
fuelectenerg-1427	81	13	circuits	circuit	NOUN
fuelectenerg-1427	81	14	which	which	PRON
fuelectenerg-1427	81	15	includes	include	VERB
fuelectenerg-1427	81	16	synthesis	synthesis	NOUN
fuelectenerg-1427	81	17	,	,	PUNCT
fuelectenerg-1427	81	18	testing	testing	NOUN
fuelectenerg-1427	81	19	and	and	CCONJ
fuelectenerg-1427	81	20	optimization	optimization	NOUN
fuelectenerg-1427	81	21	[	[	X
fuelectenerg-1427	81	22	1	1	NUM
fuelectenerg-1427	81	23	,	,	PUNCT
fuelectenerg-1427	81	24	9	9	NUM
fuelectenerg-1427	81	25	,	,	PUNCT
fuelectenerg-1427	81	26	12	12	NUM
fuelectenerg-1427	81	27	-	-	SYM
fuelectenerg-1427	81	28	15	15	NUM
fuelectenerg-1427	81	29	,	,	PUNCT
fuelectenerg-1427	81	30	17	17	NUM
fuelectenerg-1427	81	31	,	,	PUNCT
fuelectenerg-1427	81	32	21	21	NUM
fuelectenerg-1427	81	33	,	,	PUNCT
fuelectenerg-1427	81	34	22	22	NUM
fuelectenerg-1427	81	35	,	,	PUNCT
fuelectenerg-1427	81	36	26	26	NUM
fuelectenerg-1427	81	37	,	,	PUNCT
fuelectenerg-1427	81	38	27	27	NUM
fuelectenerg-1427	81	39	,	,	PUNCT
fuelectenerg-1427	81	40	31	31	NUM
fuelectenerg-1427	81	41	,	,	PUNCT
fuelectenerg-1427	81	42	32	32	NUM
fuelectenerg-1427	81	43	]	]	PUNCT
fuelectenerg-1427	81	44	.	.	PUNCT
fuelectenerg-1427	82	1	one	one	PRON
fuelectenerg-1427	82	2	can	can	AUX
fuelectenerg-1427	82	3	observe	observe	VERB
fuelectenerg-1427	82	4	that	that	SCONJ
fuelectenerg-1427	82	5	by	by	ADP
fuelectenerg-1427	82	6	going	go	VERB
fuelectenerg-1427	82	7	,	,	PUNCT
fuelectenerg-1427	82	8	for	for	ADP
fuelectenerg-1427	82	9	example	example	NOUN
fuelectenerg-1427	82	10	,	,	PUNCT
fuelectenerg-1427	82	11	from	from	ADP
fuelectenerg-1427	82	12	positive	positive	ADJ
fuelectenerg-1427	82	13	polarity	polarity	NOUN
fuelectenerg-1427	82	14	reed	reed	NOUN
fuelectenerg-1427	82	15	-	-	PUNCT
fuelectenerg-1427	82	16	muller	muller	NOUN
fuelectenerg-1427	82	17	(	(	PUNCT
fuelectenerg-1427	82	18	pprm	pprm	ADJ
fuelectenerg-1427	82	19	)	)	PUNCT
fuelectenerg-1427	82	20	form	form	NOUN
fuelectenerg-1427	82	21	to	to	ADP
fuelectenerg-1427	82	22	the	the	DET
fuelectenerg-1427	82	23	generalized	generalized	ADJ
fuelectenerg-1427	82	24	reed	reed	NOUN
fuelectenerg-1427	82	25	-	-	PUNCT
fuelectenerg-1427	82	26	muller	muller	NOUN
fuelectenerg-1427	82	27	(	(	PUNCT
fuelectenerg-1427	82	28	grm	grm	NOUN
fuelectenerg-1427	82	29	)	)	PUNCT
fuelectenerg-1427	82	30	form	form	NOUN
fuelectenerg-1427	82	31	,	,	PUNCT
fuelectenerg-1427	82	32	less	less	ADJ
fuelectenerg-1427	82	33	constraints	constraint	NOUN
fuelectenerg-1427	82	34	are	be	AUX
fuelectenerg-1427	82	35	imposed	impose	VERB
fuelectenerg-1427	82	36	on	on	ADP
fuelectenerg-1427	82	37	the	the	DET
fuelectenerg-1427	82	38	canonical	canonical	ADJ
fuelectenerg-1427	82	39	forms	form	NOUN
fuelectenerg-1427	82	40	due	due	ADJ
fuelectenerg-1427	82	41	to	to	ADP
fuelectenerg-1427	82	42	the	the	DET
fuelectenerg-1427	82	43	enlarged	enlarged	ADJ
fuelectenerg-1427	82	44	set	set	NOUN
fuelectenerg-1427	82	45	of	of	ADP
fuelectenerg-1427	82	46	polarities	polarity	NOUN
fuelectenerg-1427	82	47	that	that	PRON
fuelectenerg-1427	82	48	one	one	PRON
fuelectenerg-1427	82	49	can	can	AUX
fuelectenerg-1427	82	50	choose	choose	VERB
fuelectenerg-1427	82	51	from	from	ADP
fuelectenerg-1427	82	52	.	.	PUNCT
fuelectenerg-1427	83	1	the	the	DET
fuelectenerg-1427	83	2	gain	gain	NOUN
fuelectenerg-1427	83	3	of	of	ADP
fuelectenerg-1427	83	4	more	more	ADJ
fuelectenerg-1427	83	5	freedom	freedom	NOUN
fuelectenerg-1427	83	6	on	on	ADP
fuelectenerg-1427	83	7	the	the	DET
fuelectenerg-1427	83	8	polarity	polarity	NOUN
fuelectenerg-1427	83	9	of	of	ADP
fuelectenerg-1427	83	10	the	the	DET
fuelectenerg-1427	83	11	canonical	canonical	ADJ
fuelectenerg-1427	83	12	expansions	expansion	NOUN
fuelectenerg-1427	83	13	will	will	AUX
fuelectenerg-1427	83	14	provide	provide	VERB
fuelectenerg-1427	83	15	an	an	DET
fuelectenerg-1427	83	16	advantage	advantage	NOUN
fuelectenerg-1427	83	17	of	of	ADP
fuelectenerg-1427	83	18	obtaining	obtain	VERB
fuelectenerg-1427	83	19	exclusive	exclusive	ADJ
fuelectenerg-1427	83	20	-	-	PUNCT
fuelectenerg-1427	83	21	sum	sum	NOUN
fuelectenerg-1427	83	22	-	-	PUNCT
fuelectenerg-1427	83	23	of	of	ADP
fuelectenerg-1427	83	24	-	-	PUNCT
fuelectenerg-1427	83	25	product	product	NOUN
fuelectenerg-1427	83	26	(	(	PUNCT
fuelectenerg-1427	83	27	esop	esop	PROPN
fuelectenerg-1427	83	28	)	)	PUNCT
fuelectenerg-1427	83	29	expressions	expression	NOUN
fuelectenerg-1427	83	30	with	with	ADP
fuelectenerg-1427	83	31	less	less	ADJ
fuelectenerg-1427	83	32	number	number	NOUN
fuelectenerg-1427	83	33	of	of	ADP
fuelectenerg-1427	83	34	terms	term	NOUN
fuelectenerg-1427	83	35	and	and	CCONJ
fuelectenerg-1427	83	36	literals	literal	NOUN
fuelectenerg-1427	83	37	,	,	PUNCT
fuelectenerg-1427	83	38	and	and	CCONJ
fuelectenerg-1427	83	39	consequently	consequently	ADV
fuelectenerg-1427	83	40	expressing	express	VERB
fuelectenerg-1427	83	41	boolean	boolean	ADJ
fuelectenerg-1427	83	42	functions	function	NOUN
fuelectenerg-1427	83	43	using	use	VERB
fuelectenerg-1427	83	44	esop	esop	NOUN
fuelectenerg-1427	83	45	forms	form	NOUN
fuelectenerg-1427	83	46	will	will	AUX
fuelectenerg-1427	83	47	produce	produce	VERB
fuelectenerg-1427	83	48	on	on	ADP
fuelectenerg-1427	83	49	average	average	ADJ
fuelectenerg-1427	83	50	expressions	expression	NOUN
fuelectenerg-1427	83	51	with	with	ADP
fuelectenerg-1427	83	52	less	less	ADJ
fuelectenerg-1427	83	53	size	size	NOUN
fuelectenerg-1427	83	54	as	as	SCONJ
fuelectenerg-1427	83	55	if	if	SCONJ
fuelectenerg-1427	83	56	compared	compare	VERB
fuelectenerg-1427	83	57	to	to	ADP
fuelectenerg-1427	83	58	sum	sum	NOUN
fuelectenerg-1427	83	59	-	-	PUNCT
fuelectenerg-1427	83	60	of	of	ADP
fuelectenerg-1427	83	61	-	-	PUNCT
fuelectenerg-1427	83	62	product	product	NOUN
fuelectenerg-1427	83	63	(	(	PUNCT
fuelectenerg-1427	83	64	sop	sop	NOUN
fuelectenerg-1427	83	65	)	)	PUNCT
fuelectenerg-1427	83	66	expressions	expression	NOUN
fuelectenerg-1427	83	67	for	for	ADP
fuelectenerg-1427	83	68	example	example	NOUN
fuelectenerg-1427	83	69	.	.	PUNCT
fuelectenerg-1427	84	1	table	table	NOUN
fuelectenerg-1427	84	2	1	1	NUM
fuelectenerg-1427	84	3	illustrates	illustrate	VERB
fuelectenerg-1427	84	4	these	these	DET
fuelectenerg-1427	84	5	observations	observation	NOUN
fuelectenerg-1427	85	1	[	[	X
fuelectenerg-1427	85	2	1	1	NUM
fuelectenerg-1427	85	3	]	]	PUNCT
fuelectenerg-1427	85	4	.	.	PUNCT
fuelectenerg-1427	86	1	the	the	DET
fuelectenerg-1427	86	2	main	main	ADJ
fuelectenerg-1427	86	3	algebraic	algebraic	ADJ
fuelectenerg-1427	86	4	structure	structure	NOUN
fuelectenerg-1427	86	5	which	which	PRON
fuelectenerg-1427	86	6	is	be	AUX
fuelectenerg-1427	86	7	used	use	VERB
fuelectenerg-1427	86	8	in	in	ADP
fuelectenerg-1427	86	9	this	this	DET
fuelectenerg-1427	86	10	work	work	NOUN
fuelectenerg-1427	86	11	for	for	ADP
fuelectenerg-1427	86	12	developing	develop	VERB
fuelectenerg-1427	86	13	the	the	DET
fuelectenerg-1427	86	14	canonical	canonical	ADJ
fuelectenerg-1427	86	15	normal	normal	ADJ
fuelectenerg-1427	86	16	forms	form	NOUN
fuelectenerg-1427	86	17	is	be	AUX
fuelectenerg-1427	86	18	the	the	DET
fuelectenerg-1427	86	19	galois	galois	PROPN
fuelectenerg-1427	86	20	field	field	NOUN
fuelectenerg-1427	86	21	(	(	PUNCT
fuelectenerg-1427	86	22	gf	gf	NOUN
fuelectenerg-1427	86	23	)	)	PUNCT
fuelectenerg-1427	86	24	algebraic	algebraic	ADJ
fuelectenerg-1427	86	25	structure	structure	NOUN
fuelectenerg-1427	86	26	,	,	PUNCT
fuelectenerg-1427	86	27	which	which	PRON
fuelectenerg-1427	86	28	is	be	AUX
fuelectenerg-1427	86	29	a	a	DET
fuelectenerg-1427	86	30	fundamental	fundamental	ADJ
fuelectenerg-1427	86	31	algebraic	algebraic	ADJ
fuelectenerg-1427	86	32	structure	structure	NOUN
fuelectenerg-1427	86	33	in	in	ADP
fuelectenerg-1427	86	34	the	the	DET
fuelectenerg-1427	86	35	theory	theory	NOUN
fuelectenerg-1427	86	36	of	of	ADP
fuelectenerg-1427	86	37	algebra	algebra	NOUN
fuelectenerg-1427	86	38	[	[	X
fuelectenerg-1427	86	39	1	1	NUM
fuelectenerg-1427	86	40	,	,	PUNCT
fuelectenerg-1427	86	41	12	12	NUM
fuelectenerg-1427	86	42	,	,	PUNCT
fuelectenerg-1427	86	43	13	13	NUM
fuelectenerg-1427	86	44	,	,	PUNCT
fuelectenerg-1427	86	45	17	17	NUM
fuelectenerg-1427	86	46	,	,	PUNCT
fuelectenerg-1427	86	47	22	22	NUM
fuelectenerg-1427	86	48	,	,	PUNCT
fuelectenerg-1427	86	49	29	29	NUM
fuelectenerg-1427	86	50	,	,	PUNCT
fuelectenerg-1427	86	51	33	33	NUM
fuelectenerg-1427	86	52	,	,	PUNCT
fuelectenerg-1427	86	53	34	34	NUM
fuelectenerg-1427	86	54	]	]	PUNCT
fuelectenerg-1427	86	55	.	.	PUNCT
fuelectenerg-1427	87	1	the	the	DET
fuelectenerg-1427	87	2	importance	importance	NOUN
fuelectenerg-1427	87	3	of	of	ADP
fuelectenerg-1427	87	4	gf	gf	PROPN
fuelectenerg-1427	87	5	for	for	ADP
fuelectenerg-1427	87	6	logic	logic	ADJ
fuelectenerg-1427	87	7	synthesis	synthesis	NOUN
fuelectenerg-1427	87	8	results	result	NOUN
fuelectenerg-1427	87	9	from	from	ADP
fuelectenerg-1427	87	10	the	the	DET
fuelectenerg-1427	87	11	fact	fact	NOUN
fuelectenerg-1427	87	12	that	that	SCONJ
fuelectenerg-1427	87	13	every	every	DET
fuelectenerg-1427	87	14	finite	finite	ADJ
fuelectenerg-1427	87	15	field	field	NOUN
fuelectenerg-1427	87	16	is	be	AUX
fuelectenerg-1427	87	17	isomorphic	isomorphic	ADJ
fuelectenerg-1427	87	18	to	to	ADP
fuelectenerg-1427	87	19	a	a	DET
fuelectenerg-1427	87	20	galois	galois	PROPN
fuelectenerg-1427	87	21	field	field	NOUN
fuelectenerg-1427	87	22	.	.	PUNCT
fuelectenerg-1427	88	1	in	in	ADP
fuelectenerg-1427	88	2	general	general	ADJ
fuelectenerg-1427	88	3	,	,	PUNCT
fuelectenerg-1427	88	4	the	the	DET
fuelectenerg-1427	88	5	attractive	attractive	ADJ
fuelectenerg-1427	88	6	properties	property	NOUN
fuelectenerg-1427	88	7	of	of	ADP
fuelectenerg-1427	88	8	gf	gf	NOUN
fuelectenerg-1427	88	9	-	-	PUNCT
fuelectenerg-1427	88	10	based	base	VERB
fuelectenerg-1427	88	11	circuits	circuit	NOUN
fuelectenerg-1427	88	12	,	,	PUNCT
fuelectenerg-1427	88	13	such	such	ADJ
fuelectenerg-1427	88	14	as	as	ADP
fuelectenerg-1427	88	15	the	the	DET
fuelectenerg-1427	88	16	high	high	ADJ
fuelectenerg-1427	88	17	testability	testability	NOUN
fuelectenerg-1427	88	18	of	of	ADP
fuelectenerg-1427	88	19	such	such	ADJ
fuelectenerg-1427	88	20	circuits	circuit	NOUN
fuelectenerg-1427	88	21	,	,	PUNCT
fuelectenerg-1427	88	22	are	be	AUX
fuelectenerg-1427	88	23	mainly	mainly	ADV
fuelectenerg-1427	88	24	due	due	ADP
fuelectenerg-1427	88	25	to	to	ADP
fuelectenerg-1427	88	26	the	the	DET
fuelectenerg-1427	88	27	fact	fact	NOUN
fuelectenerg-1427	88	28	that	that	SCONJ
fuelectenerg-1427	88	29	the	the	DET
fuelectenerg-1427	88	30	gf	gf	PROPN
fuelectenerg-1427	88	31	operators	operator	NOUN
fuelectenerg-1427	88	32	exhibit	exhibit	VERB
fuelectenerg-1427	88	33	the	the	DET
fuelectenerg-1427	88	34	cyclic	cyclic	ADJ
fuelectenerg-1427	88	35	group	group	NOUN
fuelectenerg-1427	88	36	,	,	PUNCT
fuelectenerg-1427	88	37	also	also	ADV
fuelectenerg-1427	88	38	known	know	VERB
fuelectenerg-1427	88	39	as	as	ADP
fuelectenerg-1427	88	40	latin	latin	PROPN
fuelectenerg-1427	88	41	square	square	NOUN
fuelectenerg-1427	88	42	,	,	PUNCT
fuelectenerg-1427	88	43	property	property	NOUN
fuelectenerg-1427	88	44	.	.	PUNCT
fuelectenerg-1427	89	1	in	in	ADP
fuelectenerg-1427	89	2	binary	binary	NOUN
fuelectenerg-1427	89	3	,	,	PUNCT
fuelectenerg-1427	89	4	for	for	ADP
fuelectenerg-1427	89	5	example	example	NOUN
fuelectenerg-1427	89	6	,	,	PUNCT
fuelectenerg-1427	89	7	gf(2	gf(2	PROPN
fuelectenerg-1427	89	8	)	)	PUNCT
fuelectenerg-1427	89	9	addition	addition	NOUN
fuelectenerg-1427	89	10	gate	gate	NOUN
fuelectenerg-1427	89	11	,	,	PUNCT
fuelectenerg-1427	89	12	the	the	DET
fuelectenerg-1427	89	13	exor	exor	PROPN
fuelectenerg-1427	89	14	,	,	PUNCT
fuelectenerg-1427	89	15	has	have	VERB
fuelectenerg-1427	89	16	the	the	DET
fuelectenerg-1427	89	17	cyclic	cyclic	ADJ
fuelectenerg-1427	89	18	group	group	NOUN
fuelectenerg-1427	89	19	property	property	NOUN
fuelectenerg-1427	89	20	.	.	PUNCT
fuelectenerg-1427	90	1	the	the	DET
fuelectenerg-1427	90	2	cyclic	cyclic	PROPN
fuelectenerg-1427	90	3	group	group	NOUN
fuelectenerg-1427	90	4	property	property	NOUN
fuelectenerg-1427	90	5	can	can	AUX
fuelectenerg-1427	90	6	be	be	AUX
fuelectenerg-1427	90	7	explained	explain	VERB
fuelectenerg-1427	90	8	,	,	PUNCT
fuelectenerg-1427	90	9	for	for	ADP
fuelectenerg-1427	90	10	example	example	NOUN
fuelectenerg-1427	90	11	,	,	PUNCT
fuelectenerg-1427	90	12	using	use	VERB
fuelectenerg-1427	90	13	the	the	DET
fuelectenerg-1427	90	14	three	three	NUM
fuelectenerg-1427	90	15	-	-	PUNCT
fuelectenerg-1427	90	16	valued	value	VERB
fuelectenerg-1427	90	17	(	(	PUNCT
fuelectenerg-1427	90	18	ternary	ternary	ADJ
fuelectenerg-1427	90	19	)	)	PUNCT
fuelectenerg-1427	90	20	gf	gf	NOUN
fuelectenerg-1427	90	21	operators	operator	NOUN
fuelectenerg-1427	90	22	as	as	SCONJ
fuelectenerg-1427	90	23	shown	show	VERB
fuelectenerg-1427	90	24	in	in	ADP
fuelectenerg-1427	90	25	figures	figure	NOUN
fuelectenerg-1427	90	26	1(a	1(a	NUM
fuelectenerg-1427	90	27	)	)	PUNCT
fuelectenerg-1427	90	28	and	and	CCONJ
fuelectenerg-1427	90	29	1(b	1(b	NUM
fuelectenerg-1427	90	30	)	)	PUNCT
fuelectenerg-1427	90	31	,	,	PUNCT
fuelectenerg-1427	90	32	respectively	respectively	ADV
fuelectenerg-1427	90	33	.	.	PUNCT
fuelectenerg-1427	91	1	note	note	VERB
fuelectenerg-1427	91	2	that	that	SCONJ
fuelectenerg-1427	91	3	in	in	ADP
fuelectenerg-1427	91	4	any	any	DET
fuelectenerg-1427	91	5	row	row	NOUN
fuelectenerg-1427	91	6	and	and	CCONJ
fuelectenerg-1427	91	7	column	column	NOUN
fuelectenerg-1427	91	8	of	of	ADP
fuelectenerg-1427	91	9	the	the	DET
fuelectenerg-1427	91	10	addition	addition	NOUN
fuelectenerg-1427	91	11	table	table	NOUN
fuelectenerg-1427	91	12	in	in	ADP
fuelectenerg-1427	91	13	figure	figure	NOUN
fuelectenerg-1427	91	14	1(a	1(a	NUM
fuelectenerg-1427	91	15	)	)	PUNCT
fuelectenerg-1427	91	16	,	,	PUNCT
fuelectenerg-1427	91	17	the	the	DET
fuelectenerg-1427	91	18	elements	element	NOUN
fuelectenerg-1427	91	19	are	be	AUX
fuelectenerg-1427	91	20	all	all	ADV
fuelectenerg-1427	91	21	different	different	ADJ
fuelectenerg-1427	91	22	,	,	PUNCT
fuelectenerg-1427	91	23	which	which	PRON
fuelectenerg-1427	91	24	is	be	AUX
fuelectenerg-1427	91	25	cyclic	cyclic	ADJ
fuelectenerg-1427	91	26	,	,	PUNCT
fuelectenerg-1427	91	27	and	and	CCONJ
fuelectenerg-1427	91	28	that	that	SCONJ
fuelectenerg-1427	91	29	the	the	DET
fuelectenerg-1427	91	30	elements	element	NOUN
fuelectenerg-1427	91	31	have	have	VERB
fuelectenerg-1427	91	32	a	a	DET
fuelectenerg-1427	91	33	different	different	ADJ
fuelectenerg-1427	91	34	order	order	NOUN
fuelectenerg-1427	91	35	in	in	ADP
fuelectenerg-1427	91	36	each	each	DET
fuelectenerg-1427	91	37	row	row	NOUN
fuelectenerg-1427	91	38	and	and	CCONJ
fuelectenerg-1427	91	39	column	column	NOUN
fuelectenerg-1427	91	40	.	.	PUNCT
fuelectenerg-1427	92	1	another	another	DET
fuelectenerg-1427	92	2	cyclic	cyclic	ADJ
fuelectenerg-1427	92	3	group	group	NOUN
fuelectenerg-1427	92	4	can	can	AUX
fuelectenerg-1427	92	5	be	be	AUX
fuelectenerg-1427	92	6	observed	observe	VERB
fuelectenerg-1427	92	7	in	in	ADP
fuelectenerg-1427	92	8	the	the	DET
fuelectenerg-1427	92	9	multiplication	multiplication	NOUN
fuelectenerg-1427	92	10	table	table	NOUN
fuelectenerg-1427	92	11	;	;	PUNCT
fuelectenerg-1427	92	12	if	if	SCONJ
fuelectenerg-1427	92	13	the	the	DET
fuelectenerg-1427	92	14	zero	zero	NUM
fuelectenerg-1427	92	15	elements	element	NOUN
fuelectenerg-1427	92	16	are	be	AUX
fuelectenerg-1427	92	17	removed	remove	VERB
fuelectenerg-1427	92	18	from	from	ADP
fuelectenerg-1427	92	19	the	the	DET
fuelectenerg-1427	92	20	multiplication	multiplication	NOUN
fuelectenerg-1427	92	21	table	table	NOUN
fuelectenerg-1427	92	22	in	in	ADP
fuelectenerg-1427	92	23	figure	figure	NOUN
fuelectenerg-1427	92	24	1(b	1(b	NUM
fuelectenerg-1427	92	25	)	)	PUNCT
fuelectenerg-1427	92	26	,	,	PUNCT
fuelectenerg-1427	92	27	then	then	ADV
fuelectenerg-1427	92	28	the	the	DET
fuelectenerg-1427	92	29	remaining	remain	VERB
fuelectenerg-1427	92	30	elements	element	NOUN
fuelectenerg-1427	92	31	form	form	VERB
fuelectenerg-1427	92	32	a	a	DET
fuelectenerg-1427	92	33	cyclic	cyclic	ADJ
fuelectenerg-1427	92	34	group	group	NOUN
fuelectenerg-1427	92	35	.	.	PUNCT
fuelectenerg-1427	93	1	reed	reed	NOUN
fuelectenerg-1427	93	2	-	-	PUNCT
fuelectenerg-1427	93	3	muller	muller	NOUN
fuelectenerg-1427	93	4	normal	normal	ADJ
fuelectenerg-1427	93	5	forms	form	NOUN
fuelectenerg-1427	93	6	have	have	AUX
fuelectenerg-1427	93	7	been	be	AUX
fuelectenerg-1427	93	8	classified	classify	VERB
fuelectenerg-1427	93	9	using	use	VERB
fuelectenerg-1427	93	10	the	the	DET
fuelectenerg-1427	93	11	green	green	ADJ
fuelectenerg-1427	93	12	-	-	PUNCT
fuelectenerg-1427	93	13	sasao	sasao	NOUN
fuelectenerg-1427	93	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	94	1	[	[	X
fuelectenerg-1427	94	2	1	1	NUM
fuelectenerg-1427	94	3	,	,	PUNCT
fuelectenerg-1427	94	4	10	10	NUM
fuelectenerg-1427	94	5	,	,	PUNCT
fuelectenerg-1427	94	6	12	12	NUM
fuelectenerg-1427	94	7	,	,	PUNCT
fuelectenerg-1427	94	8	13	13	NUM
fuelectenerg-1427	94	9	,	,	PUNCT
fuelectenerg-1427	94	10	17	17	NUM
fuelectenerg-1427	94	11	]	]	PUNCT
fuelectenerg-1427	94	12	,	,	PUNCT
fuelectenerg-1427	94	13	where	where	SCONJ
fuelectenerg-1427	94	14	the	the	DET
fuelectenerg-1427	94	15	green	green	ADJ
fuelectenerg-1427	94	16	-	-	PUNCT
fuelectenerg-1427	94	17	sasao	sasao	PROPN
fuelectenerg-1427	94	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	94	19	of	of	ADP
fuelectenerg-1427	94	20	families	family	NOUN
fuelectenerg-1427	94	21	of	of	ADP
fuelectenerg-1427	94	22	canonical	canonical	ADJ
fuelectenerg-1427	94	23	forms	form	NOUN
fuelectenerg-1427	94	24	and	and	CCONJ
fuelectenerg-1427	94	25	corresponding	correspond	VERB
fuelectenerg-1427	94	26	decision	decision	NOUN
fuelectenerg-1427	94	27	diagrams	diagram	NOUN
fuelectenerg-1427	94	28	is	be	AUX
fuelectenerg-1427	94	29	based	base	VERB
fuelectenerg-1427	94	30	on	on	ADP
fuelectenerg-1427	94	31	three	three	NUM
fuelectenerg-1427	94	32	generic	generic	ADJ
fuelectenerg-1427	94	33	expansions	expansion	NOUN
fuelectenerg-1427	94	34	;	;	PUNCT
fuelectenerg-1427	94	35	shannon	shannon	PROPN
fuelectenerg-1427	94	36	,	,	PUNCT
fuelectenerg-1427	94	37	pos102	pos102	PROPN
fuelectenerg-1427	94	38	an	an	DET
fuelectenerg-1427	94	39	extended	extended	ADJ
fuelectenerg-1427	94	40	green	green	ADJ
fuelectenerg-1427	94	41	sasao	sasao	PROPN
fuelectenerg-1427	94	42	hierarchy	hierarchy	NOUN
fuelectenerg-1427	94	43	of	of	ADP
fuelectenerg-1427	94	44	canonical	canonical	ADJ
fuelectenerg-1427	94	45	ternary	ternary	ADJ
fuelectenerg-1427	94	46	galois	galois	NOUN
fuelectenerg-1427	94	47	forms	form	NOUN
fuelectenerg-1427	94	48	...	...	PUNCT
fuelectenerg-1427	95	1	+	+	CCONJ
fuelectenerg-1427	95	2	0	0	NUM
fuelectenerg-1427	95	3	1	1	NUM
fuelectenerg-1427	95	4	2	2	NUM
fuelectenerg-1427	95	5	0	0	NUM
fuelectenerg-1427	95	6	0	0	NUM
fuelectenerg-1427	95	7	1	1	NUM
fuelectenerg-1427	95	8	2	2	NUM
fuelectenerg-1427	95	9	1	1	NUM
fuelectenerg-1427	95	10	1	1	NUM
fuelectenerg-1427	95	11	2	2	NUM
fuelectenerg-1427	95	12	0	0	NUM
fuelectenerg-1427	95	13	2	2	NUM
fuelectenerg-1427	95	14	2	2	NUM
fuelectenerg-1427	95	15	0	0	NUM
fuelectenerg-1427	95	16	1	1	NUM
fuelectenerg-1427	95	17	∗	∗	NOUN
fuelectenerg-1427	95	18	0	0	NUM
fuelectenerg-1427	95	19	1	1	NUM
fuelectenerg-1427	95	20	2	2	NUM
fuelectenerg-1427	95	21	0	0	NUM
fuelectenerg-1427	95	22	0	0	NUM
fuelectenerg-1427	95	23	0	0	NUM
fuelectenerg-1427	95	24	0	0	NUM
fuelectenerg-1427	95	25	1	1	NUM
fuelectenerg-1427	95	26	0	0	NUM
fuelectenerg-1427	95	27	1	1	NUM
fuelectenerg-1427	95	28	2	2	NUM
fuelectenerg-1427	95	29	2	2	NUM
fuelectenerg-1427	95	30	0	0	NUM
fuelectenerg-1427	95	31	2	2	NUM
fuelectenerg-1427	95	32	1	1	NUM
fuelectenerg-1427	95	33	(	(	PUNCT
fuelectenerg-1427	95	34	a	a	NOUN
fuelectenerg-1427	95	35	)	)	PUNCT
fuelectenerg-1427	95	36	(	(	PUNCT
fuelectenerg-1427	95	37	b	b	X
fuelectenerg-1427	95	38	)	)	PUNCT
fuelectenerg-1427	95	39	figure	figure	NOUN
fuelectenerg-1427	95	40	1	1	NUM
fuelectenerg-1427	95	41	:	:	PUNCT
fuelectenerg-1427	95	42	third	third	ADJ
fuelectenerg-1427	95	43	radix	radix	PROPN
fuelectenerg-1427	95	44	galois	galois	PROPN
fuelectenerg-1427	95	45	field	field	NOUN
fuelectenerg-1427	95	46	addition	addition	NOUN
fuelectenerg-1427	95	47	and	and	CCONJ
fuelectenerg-1427	95	48	multiplication	multiplication	NOUN
fuelectenerg-1427	95	49	tables	table	NOUN
fuelectenerg-1427	95	50	:	:	PUNCT
fuelectenerg-1427	95	51	(	(	PUNCT
fuelectenerg-1427	95	52	a	a	X
fuelectenerg-1427	95	53	)	)	PUNCT
fuelectenerg-1427	95	54	addition	addition	NOUN
fuelectenerg-1427	95	55	and	and	CCONJ
fuelectenerg-1427	95	56	(	(	PUNCT
fuelectenerg-1427	95	57	b	b	NOUN
fuelectenerg-1427	95	58	)	)	PUNCT
fuelectenerg-1427	95	59	multiplication	multiplication	NOUN
fuelectenerg-1427	95	60	.	.	PUNCT
fuelectenerg-1427	96	1	itive	itive	ADJ
fuelectenerg-1427	96	2	davio	davio	NOUN
fuelectenerg-1427	96	3	and	and	CCONJ
fuelectenerg-1427	96	4	negative	negative	ADJ
fuelectenerg-1427	96	5	davio	davio	NOUN
fuelectenerg-1427	96	6	expansions	expansion	NOUN
fuelectenerg-1427	96	7	.	.	PUNCT
fuelectenerg-1427	97	1	the	the	DET
fuelectenerg-1427	97	2	two	two	NUM
fuelectenerg-1427	97	3	-	-	PUNCT
fuelectenerg-1427	97	4	valued	value	VERB
fuelectenerg-1427	97	5	shannon	shannon	NOUN
fuelectenerg-1427	97	6	,	,	PUNCT
fuelectenerg-1427	97	7	positive	positive	ADJ
fuelectenerg-1427	97	8	davio	davio	NOUN
fuelectenerg-1427	97	9	and	and	CCONJ
fuelectenerg-1427	97	10	negative	negative	ADJ
fuelectenerg-1427	97	11	davio	davio	NOUN
fuelectenerg-1427	97	12	expansions	expansion	NOUN
fuelectenerg-1427	97	13	are	be	AUX
fuelectenerg-1427	97	14	given	give	VERB
fuelectenerg-1427	97	15	as	as	ADP
fuelectenerg-1427	97	16	follows	follow	NOUN
fuelectenerg-1427	97	17	,	,	PUNCT
fuelectenerg-1427	97	18	respectively	respectively	ADV
fuelectenerg-1427	97	19	:	:	PUNCT
fuelectenerg-1427	97	20	f	f	PROPN
fuelectenerg-1427	97	21	(	(	PUNCT
fuelectenerg-1427	97	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	97	23	,	,	PUNCT
fuelectenerg-1427	97	24	.	.	PUNCT
fuelectenerg-1427	97	25	.	.	PUNCT
fuelectenerg-1427	97	26	.	.	PUNCT
fuelectenerg-1427	98	1	,	,	PUNCT
fuelectenerg-1427	98	2	xn	xn	X
fuelectenerg-1427	98	3	)	)	PUNCT
fuelectenerg-1427	98	4	=	=	SYM
fuelectenerg-1427	98	5	x̄1	x̄1	NOUN
fuelectenerg-1427	98	6	·	·	PUNCT
fuelectenerg-1427	98	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	98	8	,	,	PUNCT
fuelectenerg-1427	98	9	.	.	PUNCT
fuelectenerg-1427	98	10	.	.	PUNCT
fuelectenerg-1427	98	11	.	.	PUNCT
fuelectenerg-1427	99	1	,	,	PUNCT
fuelectenerg-1427	99	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	99	3	x1	x1	PRON
fuelectenerg-1427	99	4	·	·	PUNCT
fuelectenerg-1427	99	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	99	6	,	,	PUNCT
fuelectenerg-1427	99	7	.	.	PUNCT
fuelectenerg-1427	99	8	.	.	PUNCT
fuelectenerg-1427	99	9	.	.	PUNCT
fuelectenerg-1427	100	1	,	,	PUNCT
fuelectenerg-1427	100	2	xn	xn	X
fuelectenerg-1427	100	3	)	)	PUNCT
fuelectenerg-1427	100	4	=	=	NOUN
fuelectenerg-1427	101	1	[	[	PUNCT
fuelectenerg-1427	101	2	x̄1	x̄1	X
fuelectenerg-1427	101	3	x1	x1	X
fuelectenerg-1427	101	4	]	]	PUNCT
fuelectenerg-1427	101	5	[	[	PUNCT
fuelectenerg-1427	101	6	1	1	NUM
fuelectenerg-1427	101	7	0	0	NUM
fuelectenerg-1427	101	8	0	0	NUM
fuelectenerg-1427	101	9	1	1	NUM
fuelectenerg-1427	101	10	]	]	PUNCT
fuelectenerg-1427	101	11	[	[	PUNCT
fuelectenerg-1427	101	12	f0	f0	PROPN
fuelectenerg-1427	101	13	f1	f1	NOUN
fuelectenerg-1427	101	14	]	]	PUNCT
fuelectenerg-1427	101	15	,	,	PUNCT
fuelectenerg-1427	101	16	(	(	PUNCT
fuelectenerg-1427	101	17	1	1	X
fuelectenerg-1427	101	18	)	)	PUNCT
fuelectenerg-1427	101	19	f	f	NOUN
fuelectenerg-1427	101	20	(	(	PUNCT
fuelectenerg-1427	101	21	x1,x2	x1,x2	PROPN
fuelectenerg-1427	101	22	,	,	PUNCT
fuelectenerg-1427	101	23	.	.	PUNCT
fuelectenerg-1427	101	24	.	.	PUNCT
fuelectenerg-1427	101	25	.	.	PUNCT
fuelectenerg-1427	102	1	,	,	PUNCT
fuelectenerg-1427	102	2	xn	xn	X
fuelectenerg-1427	102	3	)	)	PUNCT
fuelectenerg-1427	102	4	=	=	SYM
fuelectenerg-1427	102	5	1	1	NUM
fuelectenerg-1427	102	6	·	·	PUNCT
fuelectenerg-1427	102	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	102	8	,	,	PUNCT
fuelectenerg-1427	102	9	.	.	PUNCT
fuelectenerg-1427	102	10	.	.	PUNCT
fuelectenerg-1427	102	11	.	.	PUNCT
fuelectenerg-1427	103	1	,	,	PUNCT
fuelectenerg-1427	103	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	103	3	x1	x1	PRON
fuelectenerg-1427	103	4	·	·	PUNCT
fuelectenerg-1427	103	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	103	6	,	,	PUNCT
fuelectenerg-1427	103	7	.	.	PUNCT
fuelectenerg-1427	103	8	.	.	PUNCT
fuelectenerg-1427	103	9	.	.	PUNCT
fuelectenerg-1427	104	1	,	,	PUNCT
fuelectenerg-1427	104	2	xn	xn	X
fuelectenerg-1427	104	3	)	)	PUNCT
fuelectenerg-1427	105	1	=	=	NOUN
fuelectenerg-1427	105	2	[	[	PUNCT
fuelectenerg-1427	105	3	1	1	NUM
fuelectenerg-1427	105	4	x1	x1	NOUN
fuelectenerg-1427	105	5	]	]	PUNCT
fuelectenerg-1427	105	6	[	[	PUNCT
fuelectenerg-1427	105	7	1	1	NUM
fuelectenerg-1427	105	8	0	0	NUM
fuelectenerg-1427	105	9	1	1	NUM
fuelectenerg-1427	105	10	1	1	NUM
fuelectenerg-1427	105	11	]	]	PUNCT
fuelectenerg-1427	105	12	[	[	PUNCT
fuelectenerg-1427	105	13	f0	f0	PROPN
fuelectenerg-1427	105	14	f1	f1	NOUN
fuelectenerg-1427	105	15	]	]	PUNCT
fuelectenerg-1427	105	16	,	,	PUNCT
fuelectenerg-1427	105	17	(	(	PUNCT
fuelectenerg-1427	105	18	2	2	X
fuelectenerg-1427	105	19	)	)	PUNCT
fuelectenerg-1427	105	20	f	f	NOUN
fuelectenerg-1427	105	21	(	(	PUNCT
fuelectenerg-1427	105	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	105	23	,	,	PUNCT
fuelectenerg-1427	105	24	.	.	PUNCT
fuelectenerg-1427	105	25	.	.	PUNCT
fuelectenerg-1427	105	26	.	.	PUNCT
fuelectenerg-1427	106	1	,	,	PUNCT
fuelectenerg-1427	106	2	xn	xn	X
fuelectenerg-1427	106	3	)	)	PUNCT
fuelectenerg-1427	106	4	=	=	SYM
fuelectenerg-1427	106	5	1	1	X
fuelectenerg-1427	106	6	·	·	PUNCT
fuelectenerg-1427	106	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	106	8	,	,	PUNCT
fuelectenerg-1427	106	9	.	.	PUNCT
fuelectenerg-1427	106	10	.	.	PUNCT
fuelectenerg-1427	106	11	.	.	PUNCT
fuelectenerg-1427	107	1	,	,	PUNCT
fuelectenerg-1427	107	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	107	3	x̄1	x̄1	PROPN
fuelectenerg-1427	107	4	·	·	PUNCT
fuelectenerg-1427	107	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	107	6	,	,	PUNCT
fuelectenerg-1427	107	7	.	.	PUNCT
fuelectenerg-1427	107	8	.	.	PUNCT
fuelectenerg-1427	107	9	.	.	PUNCT
fuelectenerg-1427	108	1	,	,	PUNCT
fuelectenerg-1427	108	2	xn	xn	X
fuelectenerg-1427	108	3	)	)	PUNCT
fuelectenerg-1427	109	1	=	=	PUNCT
fuelectenerg-1427	109	2	[	[	PUNCT
fuelectenerg-1427	109	3	1	1	NUM
fuelectenerg-1427	109	4	x̄1	x̄1	NOUN
fuelectenerg-1427	109	5	]	]	PUNCT
fuelectenerg-1427	110	1	[	[	PUNCT
fuelectenerg-1427	110	2	0	0	NUM
fuelectenerg-1427	110	3	1	1	NUM
fuelectenerg-1427	110	4	1	1	NUM
fuelectenerg-1427	110	5	1	1	NUM
fuelectenerg-1427	110	6	]	]	PUNCT
fuelectenerg-1427	110	7	[	[	PUNCT
fuelectenerg-1427	110	8	f0	f0	PROPN
fuelectenerg-1427	110	9	f1	f1	NOUN
fuelectenerg-1427	110	10	]	]	PUNCT
fuelectenerg-1427	110	11	,	,	PUNCT
fuelectenerg-1427	110	12	(	(	PUNCT
fuelectenerg-1427	110	13	3	3	X
fuelectenerg-1427	110	14	)	)	PUNCT
fuelectenerg-1427	110	15	where	where	SCONJ
fuelectenerg-1427	110	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1427	110	17	,	,	PUNCT
fuelectenerg-1427	110	18	.	.	PUNCT
fuelectenerg-1427	110	19	.	.	PUNCT
fuelectenerg-1427	110	20	.	.	PUNCT
fuelectenerg-1427	111	1	,	,	PUNCT
fuelectenerg-1427	111	2	xn	xn	X
fuelectenerg-1427	111	3	)	)	PUNCT
fuelectenerg-1427	111	4	=	=	SYM
fuelectenerg-1427	111	5	f	f	PROPN
fuelectenerg-1427	111	6	(	(	PUNCT
fuelectenerg-1427	111	7	0,x2	0,x2	NOUN
fuelectenerg-1427	111	8	,	,	PUNCT
fuelectenerg-1427	111	9	.	.	PUNCT
fuelectenerg-1427	111	10	.	.	PUNCT
fuelectenerg-1427	111	11	.	.	PUNCT
fuelectenerg-1427	112	1	,	,	PUNCT
fuelectenerg-1427	112	2	xn	xn	X
fuelectenerg-1427	112	3	)	)	PUNCT
fuelectenerg-1427	112	4	=	=	SYM
fuelectenerg-1427	112	5	f0	f0	PROPN
fuelectenerg-1427	112	6	is	be	AUX
fuelectenerg-1427	112	7	the	the	DET
fuelectenerg-1427	112	8	negative	negative	ADJ
fuelectenerg-1427	112	9	cofactor	cofactor	NOUN
fuelectenerg-1427	112	10	of	of	ADP
fuelectenerg-1427	112	11	variable	variable	ADJ
fuelectenerg-1427	112	12	x1	x1	PROPN
fuelectenerg-1427	112	13	,	,	PUNCT
fuelectenerg-1427	112	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	112	15	,	,	PUNCT
fuelectenerg-1427	112	16	.	.	PUNCT
fuelectenerg-1427	112	17	.	.	PUNCT
fuelectenerg-1427	113	1	.	.	PUNCT
fuelectenerg-1427	114	1	,	,	PUNCT
fuelectenerg-1427	114	2	xn	xn	X
fuelectenerg-1427	114	3	)	)	PUNCT
fuelectenerg-1427	114	4	=	=	SYM
fuelectenerg-1427	114	5	f	f	PROPN
fuelectenerg-1427	114	6	(	(	PUNCT
fuelectenerg-1427	114	7	1,x2	1,x2	NUM
fuelectenerg-1427	114	8	,	,	PUNCT
fuelectenerg-1427	114	9	.	.	PUNCT
fuelectenerg-1427	114	10	.	.	PUNCT
fuelectenerg-1427	114	11	.	.	PUNCT
fuelectenerg-1427	115	1	,	,	PUNCT
fuelectenerg-1427	115	2	xn	xn	X
fuelectenerg-1427	115	3	)	)	PUNCT
fuelectenerg-1427	115	4	=	=	SYM
fuelectenerg-1427	115	5	f1	f1	NOUN
fuelectenerg-1427	115	6	is	be	AUX
fuelectenerg-1427	115	7	the	the	DET
fuelectenerg-1427	115	8	positive	positive	ADJ
fuelectenerg-1427	115	9	cofactor	cofactor	NOUN
fuelectenerg-1427	115	10	of	of	ADP
fuelectenerg-1427	115	11	variable	variable	NOUN
fuelectenerg-1427	115	12	x1	x1	PROPN
fuelectenerg-1427	115	13	,	,	PUNCT
fuelectenerg-1427	115	14	and	and	CCONJ
fuelectenerg-1427	115	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	115	16	,	,	PUNCT
fuelectenerg-1427	115	17	.	.	PUNCT
fuelectenerg-1427	115	18	.	.	PUNCT
fuelectenerg-1427	116	1	.	.	PUNCT
fuelectenerg-1427	117	1	,	,	PUNCT
fuelectenerg-1427	117	2	xn	xn	X
fuelectenerg-1427	117	3	)	)	PUNCT
fuelectenerg-1427	117	4	=	=	SYM
fuelectenerg-1427	117	5	f	f	PROPN
fuelectenerg-1427	117	6	(	(	PUNCT
fuelectenerg-1427	117	7	0,x2	0,x2	NOUN
fuelectenerg-1427	117	8	,	,	PUNCT
fuelectenerg-1427	117	9	.	.	PUNCT
fuelectenerg-1427	117	10	.	.	PUNCT
fuelectenerg-1427	117	11	.	.	PUNCT
fuelectenerg-1427	118	1	,	,	PUNCT
fuelectenerg-1427	118	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	118	3	f	f	PROPN
fuelectenerg-1427	118	4	(	(	PUNCT
fuelectenerg-1427	118	5	1,x2	1,x2	NUM
fuelectenerg-1427	118	6	,	,	PUNCT
fuelectenerg-1427	118	7	.	.	PUNCT
fuelectenerg-1427	118	8	.	.	PUNCT
fuelectenerg-1427	118	9	.	.	PUNCT
fuelectenerg-1427	119	1	,	,	PUNCT
fuelectenerg-1427	119	2	xn	xn	X
fuelectenerg-1427	119	3	)	)	PUNCT
fuelectenerg-1427	119	4	=	=	SYM
fuelectenerg-1427	119	5	f0	f0	PROPN
fuelectenerg-1427	119	6	⊕	⊕	PROPN
fuelectenerg-1427	119	7	f1	f1	NOUN
fuelectenerg-1427	119	8	.	.	PUNCT
fuelectenerg-1427	120	1	in	in	ADP
fuelectenerg-1427	120	2	addition	addition	NOUN
fuelectenerg-1427	120	3	,	,	PUNCT
fuelectenerg-1427	120	4	an	an	DET
fuelectenerg-1427	120	5	arbitrary	arbitrary	ADJ
fuelectenerg-1427	120	6	n	n	CCONJ
fuelectenerg-1427	120	7	-	-	PUNCT
fuelectenerg-1427	120	8	variable	variable	ADJ
fuelectenerg-1427	120	9	function	function	NOUN
fuelectenerg-1427	120	10	f	f	PROPN
fuelectenerg-1427	120	11	(	(	PUNCT
fuelectenerg-1427	120	12	x1	x1	PROPN
fuelectenerg-1427	120	13	,	,	PUNCT
fuelectenerg-1427	120	14	.	.	PUNCT
fuelectenerg-1427	120	15	.	.	PUNCT
fuelectenerg-1427	120	16	.	.	PUNCT
fuelectenerg-1427	121	1	,	,	PUNCT
fuelectenerg-1427	121	2	xn	xn	X
fuelectenerg-1427	121	3	)	)	PUNCT
fuelectenerg-1427	121	4	can	can	AUX
fuelectenerg-1427	121	5	be	be	AUX
fuelectenerg-1427	121	6	represented	represent	VERB
fuelectenerg-1427	121	7	using	use	VERB
fuelectenerg-1427	121	8	pprm	pprm	ADJ
fuelectenerg-1427	121	9	expansion	expansion	NOUN
fuelectenerg-1427	121	10	as	as	ADP
fuelectenerg-1427	121	11	[	[	X
fuelectenerg-1427	121	12	2	2	NUM
fuelectenerg-1427	121	13	,	,	PUNCT
fuelectenerg-1427	121	14	31	31	NUM
fuelectenerg-1427	121	15	]	]	SYM
fuelectenerg-1427	121	16	:	:	PUNCT
fuelectenerg-1427	121	17	f	f	X
fuelectenerg-1427	121	18	(	(	PUNCT
fuelectenerg-1427	121	19	x1,x2	x1,x2	PROPN
fuelectenerg-1427	121	20	,	,	PUNCT
fuelectenerg-1427	121	21	.	.	PUNCT
fuelectenerg-1427	121	22	.	.	PUNCT
fuelectenerg-1427	121	23	.	.	PUNCT
fuelectenerg-1427	122	1	,	,	PUNCT
fuelectenerg-1427	122	2	xn	xn	X
fuelectenerg-1427	122	3	)	)	PUNCT
fuelectenerg-1427	123	1	=	=	PROPN
fuelectenerg-1427	123	2	a0	a0	PROPN
fuelectenerg-1427	123	3	⊕	⊕	PROPN
fuelectenerg-1427	123	4	a1x1	a1x1	PROPN
fuelectenerg-1427	123	5	⊕	⊕	PROPN
fuelectenerg-1427	123	6	.	.	PUNCT
fuelectenerg-1427	123	7	.	.	PUNCT
fuelectenerg-1427	124	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1427	124	2	⊕a12x1x2	⊕a12x1x2	X
fuelectenerg-1427	124	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1427	124	4	⊕an−1,nxn−1xn⊕	⊕an−1,nxn−1xn⊕	ADJ
fuelectenerg-1427	124	5	.	.	PUNCT
fuelectenerg-1427	124	6	.	.	PUNCT
fuelectenerg-1427	125	1	.⊕	.⊕	PROPN
fuelectenerg-1427	125	2	a12	a12	PROPN
fuelectenerg-1427	125	3	...	...	PUNCT
fuelectenerg-1427	125	4	nx1x2	nx1x2	X
fuelectenerg-1427	125	5	.	.	PUNCT
fuelectenerg-1427	125	6	.	.	PUNCT
fuelectenerg-1427	126	1	.xn	.xn	PROPN
fuelectenerg-1427	126	2	.	.	PUNCT
fuelectenerg-1427	127	1	(	(	PUNCT
fuelectenerg-1427	127	2	4	4	X
fuelectenerg-1427	127	3	)	)	PUNCT
fuelectenerg-1427	127	4	for	for	ADP
fuelectenerg-1427	127	5	each	each	DET
fuelectenerg-1427	127	6	function	function	NOUN
fuelectenerg-1427	127	7	f	f	PROPN
fuelectenerg-1427	127	8	,	,	PUNCT
fuelectenerg-1427	127	9	the	the	DET
fuelectenerg-1427	127	10	coefficients	coefficient	NOUN
fuelectenerg-1427	127	11	ai	ai	VERB
fuelectenerg-1427	127	12	in	in	ADP
fuelectenerg-1427	127	13	equation	equation	NOUN
fuelectenerg-1427	127	14	(	(	PUNCT
fuelectenerg-1427	127	15	4	4	X
fuelectenerg-1427	127	16	)	)	PUNCT
fuelectenerg-1427	127	17	are	be	AUX
fuelectenerg-1427	127	18	determined	determine	VERB
fuelectenerg-1427	127	19	uniquely	uniquely	ADV
fuelectenerg-1427	127	20	,	,	PUNCT
fuelectenerg-1427	127	21	so	so	ADV
fuelectenerg-1427	127	22	pprm	pprm	ADJ
fuelectenerg-1427	127	23	is	be	AUX
fuelectenerg-1427	127	24	a	a	DET
fuelectenerg-1427	127	25	canonical	canonical	ADJ
fuelectenerg-1427	127	26	form	form	NOUN
fuelectenerg-1427	127	27	.	.	PUNCT
fuelectenerg-1427	128	1	for	for	ADP
fuelectenerg-1427	128	2	example	example	NOUN
fuelectenerg-1427	128	3	,	,	PUNCT
fuelectenerg-1427	128	4	if	if	SCONJ
fuelectenerg-1427	128	5	we	we	PRON
fuelectenerg-1427	128	6	use	use	VERB
fuelectenerg-1427	128	7	either	either	CCONJ
fuelectenerg-1427	128	8	only	only	ADV
fuelectenerg-1427	128	9	the	the	DET
fuelectenerg-1427	128	10	positive	positive	ADJ
fuelectenerg-1427	128	11	literal	literal	NOUN
fuelectenerg-1427	128	12	or	or	CCONJ
fuelectenerg-1427	128	13	only	only	ADV
fuelectenerg-1427	128	14	the	the	DET
fuelectenerg-1427	128	15	negative	negative	ADJ
fuelectenerg-1427	128	16	literal	literal	NOUN
fuelectenerg-1427	128	17	for	for	ADP
fuelectenerg-1427	128	18	each	each	DET
fuelectenerg-1427	128	19	variable	variable	NOUN
fuelectenerg-1427	128	20	in	in	ADP
fuelectenerg-1427	128	21	equation	equation	NOUN
fuelectenerg-1427	128	22	(	(	PUNCT
fuelectenerg-1427	128	23	4	4	X
fuelectenerg-1427	128	24	)	)	PUNCT
fuelectenerg-1427	128	25	we	we	PRON
fuelectenerg-1427	128	26	obtain	obtain	VERB
fuelectenerg-1427	128	27	the	the	DET
fuelectenerg-1427	128	28	fixed	fix	VERB
fuelectenerg-1427	128	29	polarity	polarity	NOUN
fuelectenerg-1427	128	30	reed	reed	NOUN
fuelectenerg-1427	128	31	-	-	PUNCT
fuelectenerg-1427	128	32	muller	muller	NOUN
fuelectenerg-1427	128	33	(	(	PUNCT
fuelectenerg-1427	128	34	fprm	fprm	PROPN
fuelectenerg-1427	128	35	)	)	PUNCT
fuelectenerg-1427	128	36	form	form	NOUN
fuelectenerg-1427	128	37	.	.	PUNCT
fuelectenerg-1427	129	1	the	the	DET
fuelectenerg-1427	129	2	good	good	ADJ
fuelectenerg-1427	129	3	selection	selection	NOUN
fuelectenerg-1427	129	4	of	of	ADP
fuelectenerg-1427	129	5	different	different	ADJ
fuelectenerg-1427	129	6	permutations	permutation	NOUN
fuelectenerg-1427	129	7	using	use	VERB
fuelectenerg-1427	129	8	shannon	shannon	PROPN
fuelectenerg-1427	129	9	and	and	CCONJ
fuelectenerg-1427	129	10	davio	davio	NOUN
fuelectenerg-1427	129	11	expansions	expansion	NOUN
fuelectenerg-1427	129	12	like	like	ADP
fuelectenerg-1427	129	13	other	other	ADJ
fuelectenerg-1427	129	14	expansions	expansion	NOUN
fuelectenerg-1427	129	15	such	such	ADJ
fuelectenerg-1427	129	16	as	as	ADP
fuelectenerg-1427	129	17	walsh	walsh	NOUN
fuelectenerg-1427	129	18	and	and	CCONJ
fuelectenerg-1427	129	19	arithmetic	arithmetic	ADJ
fuelectenerg-1427	129	20	expansions	expansion	NOUN
fuelectenerg-1427	129	21	as	as	ADP
fuelectenerg-1427	129	22	internal	internal	ADJ
fuelectenerg-1427	129	23	nodes	node	NOUN
fuelectenerg-1427	129	24	in	in	ADP
fuelectenerg-1427	129	25	decision	decision	NOUN
fuelectenerg-1427	129	26	trees	tree	NOUN
fuelectenerg-1427	129	27	(	(	PUNCT
fuelectenerg-1427	129	28	dts	dts	NOUN
fuelectenerg-1427	129	29	)	)	PUNCT
fuelectenerg-1427	129	30	and	and	CCONJ
fuelectenerg-1427	129	31	diagrams	diagram	NOUN
fuelectenerg-1427	129	32	(	(	PUNCT
fuelectenerg-1427	129	33	dds	dds	PROPN
fuelectenerg-1427	129	34	)	)	PUNCT
fuelectenerg-1427	129	35	will	will	AUX
fuelectenerg-1427	129	36	result	result	VERB
fuelectenerg-1427	129	37	in	in	ADP
fuelectenerg-1427	129	38	dts	dts	NOUN
fuelectenerg-1427	129	39	and	and	CCONJ
fuelectenerg-1427	129	40	dds	dds	PROPN
fuelectenerg-1427	129	41	that	that	PRON
fuelectenerg-1427	129	42	represent	represent	VERB
fuelectenerg-1427	129	43	the	the	DET
fuelectenerg-1427	129	44	corresponding	corresponding	ADJ
fuelectenerg-1427	129	45	logic	logic	NOUN
fuelectenerg-1427	129	46	functions	function	NOUN
fuelectenerg-1427	129	47	with	with	ADP
fuelectenerg-1427	129	48	smaller	small	ADJ
fuelectenerg-1427	129	49	sizes	size	NOUN
fuelectenerg-1427	129	50	in	in	ADP
fuelectenerg-1427	129	51	terms	term	NOUN
fuelectenerg-1427	129	52	of	of	ADP
fuelectenerg-1427	129	53	the	the	DET
fuelectenerg-1427	129	54	total	total	ADJ
fuelectenerg-1427	129	55	number	number	NOUN
fuelectenerg-1427	129	56	of	of	ADP
fuelectenerg-1427	129	57	hierarchical	hierarchical	ADJ
fuelectenerg-1427	129	58	levels	level	NOUN
fuelectenerg-1427	129	59	used	use	VERB
fuelectenerg-1427	129	60	,	,	PUNCT
fuelectenerg-1427	129	61	and	and	CCONJ
fuelectenerg-1427	129	62	the	the	DET
fuelectenerg-1427	129	63	total	total	ADJ
fuelectenerg-1427	129	64	number	number	NOUN
fuelectenerg-1427	129	65	of	of	ADP
fuelectenerg-1427	129	66	internal	internal	ADJ
fuelectenerg-1427	129	67	nodes	node	NOUN
fuelectenerg-1427	129	68	needed	need	VERB
fuelectenerg-1427	129	69	.	.	PUNCT
fuelectenerg-1427	130	1	in	in	ADP
fuelectenerg-1427	130	2	general	general	ADJ
fuelectenerg-1427	130	3	,	,	PUNCT
fuelectenerg-1427	130	4	a	a	DET
fuelectenerg-1427	130	5	literal	literal	NOUN
fuelectenerg-1427	130	6	can	can	AUX
fuelectenerg-1427	130	7	be	be	AUX
fuelectenerg-1427	130	8	defined	define	VERB
fuelectenerg-1427	130	9	as	as	ADP
fuelectenerg-1427	130	10	any	any	DET
fuelectenerg-1427	130	11	function	function	NOUN
fuelectenerg-1427	130	12	of	of	ADP
fuelectenerg-1427	130	13	a	a	DET
fuelectenerg-1427	130	14	single	single	ADJ
fuelectenerg-1427	130	15	variable	variable	NOUN
fuelectenerg-1427	130	16	.	.	PUNCT
fuelectenerg-1427	131	1	basis	basis	NOUN
fuelectenerg-1427	131	2	functions	function	NOUN
fuelectenerg-1427	131	3	in	in	ADP
fuelectenerg-1427	131	4	the	the	DET
fuelectenerg-1427	131	5	general	general	ADJ
fuelectenerg-1427	131	6	case	case	NOUN
fuelectenerg-1427	131	7	of	of	ADP
fuelectenerg-1427	131	8	multiple	multiple	ADV
fuelectenerg-1427	131	9	-	-	PUNCT
fuelectenerg-1427	131	10	valued	value	VERB
fuelectenerg-1427	131	11	expansions	expansion	NOUN
fuelectenerg-1427	131	12	are	be	AUX
fuelectenerg-1427	131	13	constructed	construct	VERB
fuelectenerg-1427	131	14	using	use	VERB
fuelectenerg-1427	131	15	these	these	DET
fuelectenerg-1427	131	16	103	103	NUM
fuelectenerg-1427	131	17	50	50	NUM
fuelectenerg-1427	131	18	a.	a.	NOUN
fuelectenerg-1427	131	19	n.	n.	PROPN
fuelectenerg-1427	131	20	al	al	PROPN
fuelectenerg-1427	131	21	-	-	PUNCT
fuelectenerg-1427	131	22	rabadi	rabadi	VERB
fuelectenerg-1427	131	23	an	an	DET
fuelectenerg-1427	131	24	extended	extended	ADJ
fuelectenerg-1427	131	25	green	green	ADJ
fuelectenerg-1427	131	26	sasao	sasao	PROPN
fuelectenerg-1427	131	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	131	28	of	of	ADP
fuelectenerg-1427	131	29	canonical	canonical	ADJ
fuelectenerg-1427	131	30	ternary	ternary	ADJ
fuelectenerg-1427	131	31	galois	galois	NOUN
fuelectenerg-1427	131	32	forms	form	NOUN
fuelectenerg-1427	131	33	and	and	CCONJ
fuelectenerg-1427	131	34	universal	universal	ADJ
fuelectenerg-1427	131	35	logic	logic	NOUN
fuelectenerg-1427	131	36	modules	module	NOUN
fuelectenerg-1427	131	37	51	51	NUM
fuelectenerg-1427	131	38	an	an	DET
fuelectenerg-1427	131	39	extended	extend	VERB
fuelectenerg-1427	131	40	green	green	ADJ
fuelectenerg-1427	131	41	sasao	sasao	PROPN
fuelectenerg-1427	131	42	hierarchy	hierarchy	NOUN
fuelectenerg-1427	131	43	of	of	ADP
fuelectenerg-1427	131	44	canonical	canonical	ADJ
fuelectenerg-1427	131	45	ternary	ternary	ADJ
fuelectenerg-1427	131	46	galois	galois	NOUN
fuelectenerg-1427	131	47	forms	form	NOUN
fuelectenerg-1427	131	48	...	...	PUNCT
fuelectenerg-1427	132	1	+	+	CCONJ
fuelectenerg-1427	132	2	0	0	NUM
fuelectenerg-1427	132	3	1	1	NUM
fuelectenerg-1427	132	4	2	2	NUM
fuelectenerg-1427	132	5	0	0	NUM
fuelectenerg-1427	132	6	0	0	NUM
fuelectenerg-1427	132	7	1	1	NUM
fuelectenerg-1427	132	8	2	2	NUM
fuelectenerg-1427	132	9	1	1	NUM
fuelectenerg-1427	132	10	1	1	NUM
fuelectenerg-1427	132	11	2	2	NUM
fuelectenerg-1427	132	12	0	0	NUM
fuelectenerg-1427	132	13	2	2	NUM
fuelectenerg-1427	132	14	2	2	NUM
fuelectenerg-1427	132	15	0	0	NUM
fuelectenerg-1427	132	16	1	1	NUM
fuelectenerg-1427	132	17	∗	∗	NOUN
fuelectenerg-1427	132	18	0	0	NUM
fuelectenerg-1427	132	19	1	1	NUM
fuelectenerg-1427	132	20	2	2	NUM
fuelectenerg-1427	132	21	0	0	NUM
fuelectenerg-1427	132	22	0	0	NUM
fuelectenerg-1427	132	23	0	0	NUM
fuelectenerg-1427	132	24	0	0	NUM
fuelectenerg-1427	132	25	1	1	NUM
fuelectenerg-1427	132	26	0	0	NUM
fuelectenerg-1427	132	27	1	1	NUM
fuelectenerg-1427	132	28	2	2	NUM
fuelectenerg-1427	132	29	2	2	NUM
fuelectenerg-1427	132	30	0	0	NUM
fuelectenerg-1427	132	31	2	2	NUM
fuelectenerg-1427	132	32	1	1	NUM
fuelectenerg-1427	132	33	(	(	PUNCT
fuelectenerg-1427	132	34	a	a	NOUN
fuelectenerg-1427	132	35	)	)	PUNCT
fuelectenerg-1427	132	36	(	(	PUNCT
fuelectenerg-1427	132	37	b	b	X
fuelectenerg-1427	132	38	)	)	PUNCT
fuelectenerg-1427	132	39	figure	figure	NOUN
fuelectenerg-1427	132	40	1	1	NUM
fuelectenerg-1427	132	41	:	:	PUNCT
fuelectenerg-1427	132	42	third	third	ADJ
fuelectenerg-1427	132	43	radix	radix	PROPN
fuelectenerg-1427	132	44	galois	galois	PROPN
fuelectenerg-1427	132	45	field	field	NOUN
fuelectenerg-1427	132	46	addition	addition	NOUN
fuelectenerg-1427	132	47	and	and	CCONJ
fuelectenerg-1427	132	48	multiplication	multiplication	NOUN
fuelectenerg-1427	132	49	tables	table	NOUN
fuelectenerg-1427	132	50	:	:	PUNCT
fuelectenerg-1427	132	51	(	(	PUNCT
fuelectenerg-1427	132	52	a	a	X
fuelectenerg-1427	132	53	)	)	PUNCT
fuelectenerg-1427	132	54	addition	addition	NOUN
fuelectenerg-1427	132	55	and	and	CCONJ
fuelectenerg-1427	132	56	(	(	PUNCT
fuelectenerg-1427	132	57	b	b	NOUN
fuelectenerg-1427	132	58	)	)	PUNCT
fuelectenerg-1427	132	59	multiplication	multiplication	NOUN
fuelectenerg-1427	132	60	.	.	PUNCT
fuelectenerg-1427	133	1	itive	itive	ADJ
fuelectenerg-1427	133	2	davio	davio	NOUN
fuelectenerg-1427	133	3	and	and	CCONJ
fuelectenerg-1427	133	4	negative	negative	ADJ
fuelectenerg-1427	133	5	davio	davio	NOUN
fuelectenerg-1427	133	6	expansions	expansion	NOUN
fuelectenerg-1427	133	7	.	.	PUNCT
fuelectenerg-1427	134	1	the	the	DET
fuelectenerg-1427	134	2	two	two	NUM
fuelectenerg-1427	134	3	-	-	PUNCT
fuelectenerg-1427	134	4	valued	value	VERB
fuelectenerg-1427	134	5	shannon	shannon	NOUN
fuelectenerg-1427	134	6	,	,	PUNCT
fuelectenerg-1427	134	7	positive	positive	ADJ
fuelectenerg-1427	134	8	davio	davio	NOUN
fuelectenerg-1427	134	9	and	and	CCONJ
fuelectenerg-1427	134	10	negative	negative	ADJ
fuelectenerg-1427	134	11	davio	davio	NOUN
fuelectenerg-1427	134	12	expansions	expansion	NOUN
fuelectenerg-1427	134	13	are	be	AUX
fuelectenerg-1427	134	14	given	give	VERB
fuelectenerg-1427	134	15	as	as	ADP
fuelectenerg-1427	134	16	follows	follow	NOUN
fuelectenerg-1427	134	17	,	,	PUNCT
fuelectenerg-1427	134	18	respectively	respectively	ADV
fuelectenerg-1427	134	19	:	:	PUNCT
fuelectenerg-1427	134	20	f	f	PROPN
fuelectenerg-1427	134	21	(	(	PUNCT
fuelectenerg-1427	134	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	134	23	,	,	PUNCT
fuelectenerg-1427	134	24	.	.	PUNCT
fuelectenerg-1427	134	25	.	.	PUNCT
fuelectenerg-1427	134	26	.	.	PUNCT
fuelectenerg-1427	135	1	,	,	PUNCT
fuelectenerg-1427	135	2	xn	xn	X
fuelectenerg-1427	135	3	)	)	PUNCT
fuelectenerg-1427	135	4	=	=	SYM
fuelectenerg-1427	135	5	x̄1	x̄1	NOUN
fuelectenerg-1427	135	6	·	·	PUNCT
fuelectenerg-1427	135	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	135	8	,	,	PUNCT
fuelectenerg-1427	135	9	.	.	PUNCT
fuelectenerg-1427	135	10	.	.	PUNCT
fuelectenerg-1427	135	11	.	.	PUNCT
fuelectenerg-1427	136	1	,	,	PUNCT
fuelectenerg-1427	136	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	136	3	x1	x1	PRON
fuelectenerg-1427	136	4	·	·	PUNCT
fuelectenerg-1427	136	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	136	6	,	,	PUNCT
fuelectenerg-1427	136	7	.	.	PUNCT
fuelectenerg-1427	136	8	.	.	PUNCT
fuelectenerg-1427	136	9	.	.	PUNCT
fuelectenerg-1427	137	1	,	,	PUNCT
fuelectenerg-1427	137	2	xn	xn	X
fuelectenerg-1427	137	3	)	)	PUNCT
fuelectenerg-1427	137	4	=	=	NOUN
fuelectenerg-1427	138	1	[	[	PUNCT
fuelectenerg-1427	138	2	x̄1	x̄1	X
fuelectenerg-1427	138	3	x1	x1	X
fuelectenerg-1427	138	4	]	]	PUNCT
fuelectenerg-1427	138	5	[	[	PUNCT
fuelectenerg-1427	138	6	1	1	NUM
fuelectenerg-1427	138	7	0	0	NUM
fuelectenerg-1427	138	8	0	0	NUM
fuelectenerg-1427	138	9	1	1	NUM
fuelectenerg-1427	138	10	]	]	PUNCT
fuelectenerg-1427	138	11	[	[	PUNCT
fuelectenerg-1427	138	12	f0	f0	PROPN
fuelectenerg-1427	138	13	f1	f1	NOUN
fuelectenerg-1427	138	14	]	]	PUNCT
fuelectenerg-1427	138	15	,	,	PUNCT
fuelectenerg-1427	138	16	(	(	PUNCT
fuelectenerg-1427	138	17	1	1	X
fuelectenerg-1427	138	18	)	)	PUNCT
fuelectenerg-1427	138	19	f	f	NOUN
fuelectenerg-1427	138	20	(	(	PUNCT
fuelectenerg-1427	138	21	x1,x2	x1,x2	PROPN
fuelectenerg-1427	138	22	,	,	PUNCT
fuelectenerg-1427	138	23	.	.	PUNCT
fuelectenerg-1427	138	24	.	.	PUNCT
fuelectenerg-1427	138	25	.	.	PUNCT
fuelectenerg-1427	139	1	,	,	PUNCT
fuelectenerg-1427	139	2	xn	xn	X
fuelectenerg-1427	139	3	)	)	PUNCT
fuelectenerg-1427	139	4	=	=	SYM
fuelectenerg-1427	139	5	1	1	NUM
fuelectenerg-1427	139	6	·	·	PUNCT
fuelectenerg-1427	139	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	139	8	,	,	PUNCT
fuelectenerg-1427	139	9	.	.	PUNCT
fuelectenerg-1427	139	10	.	.	PUNCT
fuelectenerg-1427	139	11	.	.	PUNCT
fuelectenerg-1427	140	1	,	,	PUNCT
fuelectenerg-1427	140	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	140	3	x1	x1	PRON
fuelectenerg-1427	140	4	·	·	PUNCT
fuelectenerg-1427	140	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	140	6	,	,	PUNCT
fuelectenerg-1427	140	7	.	.	PUNCT
fuelectenerg-1427	140	8	.	.	PUNCT
fuelectenerg-1427	140	9	.	.	PUNCT
fuelectenerg-1427	141	1	,	,	PUNCT
fuelectenerg-1427	141	2	xn	xn	X
fuelectenerg-1427	141	3	)	)	PUNCT
fuelectenerg-1427	142	1	=	=	NOUN
fuelectenerg-1427	142	2	[	[	PUNCT
fuelectenerg-1427	142	3	1	1	NUM
fuelectenerg-1427	142	4	x1	x1	NOUN
fuelectenerg-1427	142	5	]	]	PUNCT
fuelectenerg-1427	142	6	[	[	PUNCT
fuelectenerg-1427	142	7	1	1	NUM
fuelectenerg-1427	142	8	0	0	NUM
fuelectenerg-1427	142	9	1	1	NUM
fuelectenerg-1427	142	10	1	1	NUM
fuelectenerg-1427	142	11	]	]	PUNCT
fuelectenerg-1427	142	12	[	[	PUNCT
fuelectenerg-1427	142	13	f0	f0	PROPN
fuelectenerg-1427	142	14	f1	f1	NOUN
fuelectenerg-1427	142	15	]	]	PUNCT
fuelectenerg-1427	142	16	,	,	PUNCT
fuelectenerg-1427	142	17	(	(	PUNCT
fuelectenerg-1427	142	18	2	2	X
fuelectenerg-1427	142	19	)	)	PUNCT
fuelectenerg-1427	142	20	f	f	NOUN
fuelectenerg-1427	142	21	(	(	PUNCT
fuelectenerg-1427	142	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	142	23	,	,	PUNCT
fuelectenerg-1427	142	24	.	.	PUNCT
fuelectenerg-1427	142	25	.	.	PUNCT
fuelectenerg-1427	142	26	.	.	PUNCT
fuelectenerg-1427	143	1	,	,	PUNCT
fuelectenerg-1427	143	2	xn	xn	X
fuelectenerg-1427	143	3	)	)	PUNCT
fuelectenerg-1427	143	4	=	=	SYM
fuelectenerg-1427	143	5	1	1	X
fuelectenerg-1427	143	6	·	·	PUNCT
fuelectenerg-1427	143	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	143	8	,	,	PUNCT
fuelectenerg-1427	143	9	.	.	PUNCT
fuelectenerg-1427	143	10	.	.	PUNCT
fuelectenerg-1427	143	11	.	.	PUNCT
fuelectenerg-1427	144	1	,	,	PUNCT
fuelectenerg-1427	144	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	144	3	x̄1	x̄1	PROPN
fuelectenerg-1427	144	4	·	·	PUNCT
fuelectenerg-1427	144	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	144	6	,	,	PUNCT
fuelectenerg-1427	144	7	.	.	PUNCT
fuelectenerg-1427	144	8	.	.	PUNCT
fuelectenerg-1427	144	9	.	.	PUNCT
fuelectenerg-1427	145	1	,	,	PUNCT
fuelectenerg-1427	145	2	xn	xn	X
fuelectenerg-1427	145	3	)	)	PUNCT
fuelectenerg-1427	146	1	=	=	PUNCT
fuelectenerg-1427	146	2	[	[	PUNCT
fuelectenerg-1427	146	3	1	1	NUM
fuelectenerg-1427	146	4	x̄1	x̄1	NOUN
fuelectenerg-1427	146	5	]	]	PUNCT
fuelectenerg-1427	147	1	[	[	PUNCT
fuelectenerg-1427	147	2	0	0	NUM
fuelectenerg-1427	147	3	1	1	NUM
fuelectenerg-1427	147	4	1	1	NUM
fuelectenerg-1427	147	5	1	1	NUM
fuelectenerg-1427	147	6	]	]	PUNCT
fuelectenerg-1427	147	7	[	[	PUNCT
fuelectenerg-1427	147	8	f0	f0	PROPN
fuelectenerg-1427	147	9	f1	f1	NOUN
fuelectenerg-1427	147	10	]	]	PUNCT
fuelectenerg-1427	147	11	,	,	PUNCT
fuelectenerg-1427	147	12	(	(	PUNCT
fuelectenerg-1427	147	13	3	3	X
fuelectenerg-1427	147	14	)	)	PUNCT
fuelectenerg-1427	147	15	where	where	SCONJ
fuelectenerg-1427	147	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1427	147	17	,	,	PUNCT
fuelectenerg-1427	147	18	.	.	PUNCT
fuelectenerg-1427	147	19	.	.	PUNCT
fuelectenerg-1427	147	20	.	.	PUNCT
fuelectenerg-1427	148	1	,	,	PUNCT
fuelectenerg-1427	148	2	xn	xn	X
fuelectenerg-1427	148	3	)	)	PUNCT
fuelectenerg-1427	148	4	=	=	SYM
fuelectenerg-1427	148	5	f	f	PROPN
fuelectenerg-1427	148	6	(	(	PUNCT
fuelectenerg-1427	148	7	0,x2	0,x2	NOUN
fuelectenerg-1427	148	8	,	,	PUNCT
fuelectenerg-1427	148	9	.	.	PUNCT
fuelectenerg-1427	148	10	.	.	PUNCT
fuelectenerg-1427	148	11	.	.	PUNCT
fuelectenerg-1427	149	1	,	,	PUNCT
fuelectenerg-1427	149	2	xn	xn	X
fuelectenerg-1427	149	3	)	)	PUNCT
fuelectenerg-1427	149	4	=	=	SYM
fuelectenerg-1427	149	5	f0	f0	PROPN
fuelectenerg-1427	149	6	is	be	AUX
fuelectenerg-1427	149	7	the	the	DET
fuelectenerg-1427	149	8	negative	negative	ADJ
fuelectenerg-1427	149	9	cofactor	cofactor	NOUN
fuelectenerg-1427	149	10	of	of	ADP
fuelectenerg-1427	149	11	variable	variable	ADJ
fuelectenerg-1427	149	12	x1	x1	PROPN
fuelectenerg-1427	149	13	,	,	PUNCT
fuelectenerg-1427	149	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	149	15	,	,	PUNCT
fuelectenerg-1427	149	16	.	.	PUNCT
fuelectenerg-1427	149	17	.	.	PUNCT
fuelectenerg-1427	150	1	.	.	PUNCT
fuelectenerg-1427	151	1	,	,	PUNCT
fuelectenerg-1427	151	2	xn	xn	X
fuelectenerg-1427	151	3	)	)	PUNCT
fuelectenerg-1427	151	4	=	=	SYM
fuelectenerg-1427	151	5	f	f	PROPN
fuelectenerg-1427	151	6	(	(	PUNCT
fuelectenerg-1427	151	7	1,x2	1,x2	NUM
fuelectenerg-1427	151	8	,	,	PUNCT
fuelectenerg-1427	151	9	.	.	PUNCT
fuelectenerg-1427	151	10	.	.	PUNCT
fuelectenerg-1427	151	11	.	.	PUNCT
fuelectenerg-1427	152	1	,	,	PUNCT
fuelectenerg-1427	152	2	xn	xn	X
fuelectenerg-1427	152	3	)	)	PUNCT
fuelectenerg-1427	152	4	=	=	SYM
fuelectenerg-1427	152	5	f1	f1	NOUN
fuelectenerg-1427	152	6	is	be	AUX
fuelectenerg-1427	152	7	the	the	DET
fuelectenerg-1427	152	8	positive	positive	ADJ
fuelectenerg-1427	152	9	cofactor	cofactor	NOUN
fuelectenerg-1427	152	10	of	of	ADP
fuelectenerg-1427	152	11	variable	variable	NOUN
fuelectenerg-1427	152	12	x1	x1	PROPN
fuelectenerg-1427	152	13	,	,	PUNCT
fuelectenerg-1427	152	14	and	and	CCONJ
fuelectenerg-1427	152	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	152	16	,	,	PUNCT
fuelectenerg-1427	152	17	.	.	PUNCT
fuelectenerg-1427	152	18	.	.	PUNCT
fuelectenerg-1427	153	1	.	.	PUNCT
fuelectenerg-1427	154	1	,	,	PUNCT
fuelectenerg-1427	154	2	xn	xn	X
fuelectenerg-1427	154	3	)	)	PUNCT
fuelectenerg-1427	154	4	=	=	SYM
fuelectenerg-1427	154	5	f	f	PROPN
fuelectenerg-1427	154	6	(	(	PUNCT
fuelectenerg-1427	154	7	0,x2	0,x2	NOUN
fuelectenerg-1427	154	8	,	,	PUNCT
fuelectenerg-1427	154	9	.	.	PUNCT
fuelectenerg-1427	154	10	.	.	PUNCT
fuelectenerg-1427	154	11	.	.	PUNCT
fuelectenerg-1427	155	1	,	,	PUNCT
fuelectenerg-1427	155	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	155	3	f	f	PROPN
fuelectenerg-1427	155	4	(	(	PUNCT
fuelectenerg-1427	155	5	1,x2	1,x2	NUM
fuelectenerg-1427	155	6	,	,	PUNCT
fuelectenerg-1427	155	7	.	.	PUNCT
fuelectenerg-1427	155	8	.	.	PUNCT
fuelectenerg-1427	155	9	.	.	PUNCT
fuelectenerg-1427	156	1	,	,	PUNCT
fuelectenerg-1427	156	2	xn	xn	X
fuelectenerg-1427	156	3	)	)	PUNCT
fuelectenerg-1427	156	4	=	=	SYM
fuelectenerg-1427	156	5	f0	f0	PROPN
fuelectenerg-1427	156	6	⊕	⊕	PROPN
fuelectenerg-1427	156	7	f1	f1	NOUN
fuelectenerg-1427	156	8	.	.	PUNCT
fuelectenerg-1427	157	1	in	in	ADP
fuelectenerg-1427	157	2	addition	addition	NOUN
fuelectenerg-1427	157	3	,	,	PUNCT
fuelectenerg-1427	157	4	an	an	DET
fuelectenerg-1427	157	5	arbitrary	arbitrary	ADJ
fuelectenerg-1427	157	6	n	n	CCONJ
fuelectenerg-1427	157	7	-	-	PUNCT
fuelectenerg-1427	157	8	variable	variable	ADJ
fuelectenerg-1427	157	9	function	function	NOUN
fuelectenerg-1427	157	10	f	f	PROPN
fuelectenerg-1427	157	11	(	(	PUNCT
fuelectenerg-1427	157	12	x1	x1	PROPN
fuelectenerg-1427	157	13	,	,	PUNCT
fuelectenerg-1427	157	14	.	.	PUNCT
fuelectenerg-1427	157	15	.	.	PUNCT
fuelectenerg-1427	157	16	.	.	PUNCT
fuelectenerg-1427	158	1	,	,	PUNCT
fuelectenerg-1427	158	2	xn	xn	X
fuelectenerg-1427	158	3	)	)	PUNCT
fuelectenerg-1427	158	4	can	can	AUX
fuelectenerg-1427	158	5	be	be	AUX
fuelectenerg-1427	158	6	represented	represent	VERB
fuelectenerg-1427	158	7	using	use	VERB
fuelectenerg-1427	158	8	pprm	pprm	ADJ
fuelectenerg-1427	158	9	expansion	expansion	NOUN
fuelectenerg-1427	158	10	as	as	ADP
fuelectenerg-1427	158	11	[	[	X
fuelectenerg-1427	158	12	2	2	NUM
fuelectenerg-1427	158	13	,	,	PUNCT
fuelectenerg-1427	158	14	31	31	NUM
fuelectenerg-1427	158	15	]	]	SYM
fuelectenerg-1427	158	16	:	:	PUNCT
fuelectenerg-1427	158	17	f	f	X
fuelectenerg-1427	158	18	(	(	PUNCT
fuelectenerg-1427	158	19	x1,x2	x1,x2	PROPN
fuelectenerg-1427	158	20	,	,	PUNCT
fuelectenerg-1427	158	21	.	.	PUNCT
fuelectenerg-1427	158	22	.	.	PUNCT
fuelectenerg-1427	158	23	.	.	PUNCT
fuelectenerg-1427	159	1	,	,	PUNCT
fuelectenerg-1427	159	2	xn	xn	X
fuelectenerg-1427	159	3	)	)	PUNCT
fuelectenerg-1427	160	1	=	=	PROPN
fuelectenerg-1427	160	2	a0	a0	PROPN
fuelectenerg-1427	160	3	⊕	⊕	PROPN
fuelectenerg-1427	160	4	a1x1	a1x1	PROPN
fuelectenerg-1427	160	5	⊕	⊕	PROPN
fuelectenerg-1427	160	6	.	.	PUNCT
fuelectenerg-1427	160	7	.	.	PUNCT
fuelectenerg-1427	161	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1427	161	2	⊕a12x1x2	⊕a12x1x2	X
fuelectenerg-1427	161	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1427	161	4	⊕an−1,nxn−1xn⊕	⊕an−1,nxn−1xn⊕	ADJ
fuelectenerg-1427	161	5	.	.	PUNCT
fuelectenerg-1427	161	6	.	.	PUNCT
fuelectenerg-1427	162	1	.⊕	.⊕	PROPN
fuelectenerg-1427	162	2	a12	a12	PROPN
fuelectenerg-1427	162	3	...	...	PUNCT
fuelectenerg-1427	162	4	nx1x2	nx1x2	X
fuelectenerg-1427	162	5	.	.	PUNCT
fuelectenerg-1427	162	6	.	.	PUNCT
fuelectenerg-1427	163	1	.xn	.xn	PROPN
fuelectenerg-1427	163	2	.	.	PUNCT
fuelectenerg-1427	164	1	(	(	PUNCT
fuelectenerg-1427	164	2	4	4	X
fuelectenerg-1427	164	3	)	)	PUNCT
fuelectenerg-1427	164	4	for	for	ADP
fuelectenerg-1427	164	5	each	each	DET
fuelectenerg-1427	164	6	function	function	NOUN
fuelectenerg-1427	164	7	f	f	PROPN
fuelectenerg-1427	164	8	,	,	PUNCT
fuelectenerg-1427	164	9	the	the	DET
fuelectenerg-1427	164	10	coefficients	coefficient	NOUN
fuelectenerg-1427	164	11	ai	ai	VERB
fuelectenerg-1427	164	12	in	in	ADP
fuelectenerg-1427	164	13	equation	equation	NOUN
fuelectenerg-1427	164	14	(	(	PUNCT
fuelectenerg-1427	164	15	4	4	X
fuelectenerg-1427	164	16	)	)	PUNCT
fuelectenerg-1427	164	17	are	be	AUX
fuelectenerg-1427	164	18	determined	determine	VERB
fuelectenerg-1427	164	19	uniquely	uniquely	ADV
fuelectenerg-1427	164	20	,	,	PUNCT
fuelectenerg-1427	164	21	so	so	ADV
fuelectenerg-1427	164	22	pprm	pprm	ADJ
fuelectenerg-1427	164	23	is	be	AUX
fuelectenerg-1427	164	24	a	a	DET
fuelectenerg-1427	164	25	canonical	canonical	ADJ
fuelectenerg-1427	164	26	form	form	NOUN
fuelectenerg-1427	164	27	.	.	PUNCT
fuelectenerg-1427	165	1	for	for	ADP
fuelectenerg-1427	165	2	example	example	NOUN
fuelectenerg-1427	165	3	,	,	PUNCT
fuelectenerg-1427	165	4	if	if	SCONJ
fuelectenerg-1427	165	5	we	we	PRON
fuelectenerg-1427	165	6	use	use	VERB
fuelectenerg-1427	165	7	either	either	CCONJ
fuelectenerg-1427	165	8	only	only	ADV
fuelectenerg-1427	165	9	the	the	DET
fuelectenerg-1427	165	10	positive	positive	ADJ
fuelectenerg-1427	165	11	literal	literal	NOUN
fuelectenerg-1427	165	12	or	or	CCONJ
fuelectenerg-1427	165	13	only	only	ADV
fuelectenerg-1427	165	14	the	the	DET
fuelectenerg-1427	165	15	negative	negative	ADJ
fuelectenerg-1427	165	16	literal	literal	NOUN
fuelectenerg-1427	165	17	for	for	ADP
fuelectenerg-1427	165	18	each	each	DET
fuelectenerg-1427	165	19	variable	variable	NOUN
fuelectenerg-1427	165	20	in	in	ADP
fuelectenerg-1427	165	21	equation	equation	NOUN
fuelectenerg-1427	165	22	(	(	PUNCT
fuelectenerg-1427	165	23	4	4	X
fuelectenerg-1427	165	24	)	)	PUNCT
fuelectenerg-1427	165	25	we	we	PRON
fuelectenerg-1427	165	26	obtain	obtain	VERB
fuelectenerg-1427	165	27	the	the	DET
fuelectenerg-1427	165	28	fixed	fix	VERB
fuelectenerg-1427	165	29	polarity	polarity	NOUN
fuelectenerg-1427	165	30	reed	reed	NOUN
fuelectenerg-1427	165	31	-	-	PUNCT
fuelectenerg-1427	165	32	muller	muller	NOUN
fuelectenerg-1427	165	33	(	(	PUNCT
fuelectenerg-1427	165	34	fprm	fprm	PROPN
fuelectenerg-1427	165	35	)	)	PUNCT
fuelectenerg-1427	165	36	form	form	NOUN
fuelectenerg-1427	165	37	.	.	PUNCT
fuelectenerg-1427	166	1	the	the	DET
fuelectenerg-1427	166	2	good	good	ADJ
fuelectenerg-1427	166	3	selection	selection	NOUN
fuelectenerg-1427	166	4	of	of	ADP
fuelectenerg-1427	166	5	different	different	ADJ
fuelectenerg-1427	166	6	permutations	permutation	NOUN
fuelectenerg-1427	166	7	using	use	VERB
fuelectenerg-1427	166	8	shannon	shannon	PROPN
fuelectenerg-1427	166	9	and	and	CCONJ
fuelectenerg-1427	166	10	davio	davio	NOUN
fuelectenerg-1427	166	11	expansions	expansion	NOUN
fuelectenerg-1427	166	12	like	like	ADP
fuelectenerg-1427	166	13	other	other	ADJ
fuelectenerg-1427	166	14	expansions	expansion	NOUN
fuelectenerg-1427	166	15	such	such	ADJ
fuelectenerg-1427	166	16	as	as	ADP
fuelectenerg-1427	166	17	walsh	walsh	NOUN
fuelectenerg-1427	166	18	and	and	CCONJ
fuelectenerg-1427	166	19	arithmetic	arithmetic	ADJ
fuelectenerg-1427	166	20	expansions	expansion	NOUN
fuelectenerg-1427	166	21	as	as	ADP
fuelectenerg-1427	166	22	internal	internal	ADJ
fuelectenerg-1427	166	23	nodes	node	NOUN
fuelectenerg-1427	166	24	in	in	ADP
fuelectenerg-1427	166	25	decision	decision	NOUN
fuelectenerg-1427	166	26	trees	tree	NOUN
fuelectenerg-1427	166	27	(	(	PUNCT
fuelectenerg-1427	166	28	dts	dts	NOUN
fuelectenerg-1427	166	29	)	)	PUNCT
fuelectenerg-1427	166	30	and	and	CCONJ
fuelectenerg-1427	166	31	diagrams	diagram	NOUN
fuelectenerg-1427	166	32	(	(	PUNCT
fuelectenerg-1427	166	33	dds	dds	PROPN
fuelectenerg-1427	166	34	)	)	PUNCT
fuelectenerg-1427	166	35	will	will	AUX
fuelectenerg-1427	166	36	result	result	VERB
fuelectenerg-1427	166	37	in	in	ADP
fuelectenerg-1427	166	38	dts	dts	NOUN
fuelectenerg-1427	166	39	and	and	CCONJ
fuelectenerg-1427	166	40	dds	dds	PROPN
fuelectenerg-1427	166	41	that	that	PRON
fuelectenerg-1427	166	42	represent	represent	VERB
fuelectenerg-1427	166	43	the	the	DET
fuelectenerg-1427	166	44	corresponding	corresponding	ADJ
fuelectenerg-1427	166	45	logic	logic	NOUN
fuelectenerg-1427	166	46	functions	function	NOUN
fuelectenerg-1427	166	47	with	with	ADP
fuelectenerg-1427	166	48	smaller	small	ADJ
fuelectenerg-1427	166	49	sizes	size	NOUN
fuelectenerg-1427	166	50	in	in	ADP
fuelectenerg-1427	166	51	terms	term	NOUN
fuelectenerg-1427	166	52	of	of	ADP
fuelectenerg-1427	166	53	the	the	DET
fuelectenerg-1427	166	54	total	total	ADJ
fuelectenerg-1427	166	55	number	number	NOUN
fuelectenerg-1427	166	56	of	of	ADP
fuelectenerg-1427	166	57	hierarchical	hierarchical	ADJ
fuelectenerg-1427	166	58	levels	level	NOUN
fuelectenerg-1427	166	59	used	use	VERB
fuelectenerg-1427	166	60	,	,	PUNCT
fuelectenerg-1427	166	61	and	and	CCONJ
fuelectenerg-1427	166	62	the	the	DET
fuelectenerg-1427	166	63	total	total	ADJ
fuelectenerg-1427	166	64	number	number	NOUN
fuelectenerg-1427	166	65	of	of	ADP
fuelectenerg-1427	166	66	internal	internal	ADJ
fuelectenerg-1427	166	67	nodes	node	NOUN
fuelectenerg-1427	166	68	needed	need	VERB
fuelectenerg-1427	166	69	.	.	PUNCT
fuelectenerg-1427	167	1	in	in	ADP
fuelectenerg-1427	167	2	general	general	ADJ
fuelectenerg-1427	167	3	,	,	PUNCT
fuelectenerg-1427	167	4	a	a	DET
fuelectenerg-1427	167	5	literal	literal	NOUN
fuelectenerg-1427	167	6	can	can	AUX
fuelectenerg-1427	167	7	be	be	AUX
fuelectenerg-1427	167	8	defined	define	VERB
fuelectenerg-1427	167	9	as	as	ADP
fuelectenerg-1427	167	10	any	any	DET
fuelectenerg-1427	167	11	function	function	NOUN
fuelectenerg-1427	167	12	of	of	ADP
fuelectenerg-1427	167	13	a	a	DET
fuelectenerg-1427	167	14	single	single	ADJ
fuelectenerg-1427	167	15	variable	variable	NOUN
fuelectenerg-1427	167	16	.	.	PUNCT
fuelectenerg-1427	168	1	basis	basis	NOUN
fuelectenerg-1427	168	2	functions	function	NOUN
fuelectenerg-1427	168	3	in	in	ADP
fuelectenerg-1427	168	4	the	the	DET
fuelectenerg-1427	168	5	general	general	ADJ
fuelectenerg-1427	168	6	case	case	NOUN
fuelectenerg-1427	168	7	of	of	ADP
fuelectenerg-1427	168	8	multiple	multiple	ADV
fuelectenerg-1427	168	9	-	-	PUNCT
fuelectenerg-1427	168	10	valued	value	VERB
fuelectenerg-1427	168	11	expansions	expansion	NOUN
fuelectenerg-1427	168	12	are	be	AUX
fuelectenerg-1427	168	13	constructed	construct	VERB
fuelectenerg-1427	168	14	using	use	VERB
fuelectenerg-1427	168	15	these	these	DET
fuelectenerg-1427	168	16	103	103	NUM
fuelectenerg-1427	168	17	an	an	DET
fuelectenerg-1427	168	18	extended	extended	ADJ
fuelectenerg-1427	168	19	green	green	ADJ
fuelectenerg-1427	168	20	sasao	sasao	PROPN
fuelectenerg-1427	168	21	hierarchy	hierarchy	NOUN
fuelectenerg-1427	168	22	of	of	ADP
fuelectenerg-1427	168	23	canonical	canonical	ADJ
fuelectenerg-1427	168	24	ternary	ternary	ADJ
fuelectenerg-1427	168	25	galois	galois	NOUN
fuelectenerg-1427	168	26	forms	form	NOUN
fuelectenerg-1427	168	27	...	...	PUNCT
fuelectenerg-1427	169	1	+	+	CCONJ
fuelectenerg-1427	169	2	0	0	NUM
fuelectenerg-1427	169	3	1	1	NUM
fuelectenerg-1427	169	4	2	2	NUM
fuelectenerg-1427	169	5	0	0	NUM
fuelectenerg-1427	169	6	0	0	NUM
fuelectenerg-1427	169	7	1	1	NUM
fuelectenerg-1427	169	8	2	2	NUM
fuelectenerg-1427	169	9	1	1	NUM
fuelectenerg-1427	169	10	1	1	NUM
fuelectenerg-1427	169	11	2	2	NUM
fuelectenerg-1427	169	12	0	0	NUM
fuelectenerg-1427	169	13	2	2	NUM
fuelectenerg-1427	169	14	2	2	NUM
fuelectenerg-1427	169	15	0	0	NUM
fuelectenerg-1427	169	16	1	1	NUM
fuelectenerg-1427	169	17	∗	∗	NOUN
fuelectenerg-1427	169	18	0	0	NUM
fuelectenerg-1427	169	19	1	1	NUM
fuelectenerg-1427	169	20	2	2	NUM
fuelectenerg-1427	169	21	0	0	NUM
fuelectenerg-1427	169	22	0	0	NUM
fuelectenerg-1427	169	23	0	0	NUM
fuelectenerg-1427	169	24	0	0	NUM
fuelectenerg-1427	169	25	1	1	NUM
fuelectenerg-1427	169	26	0	0	NUM
fuelectenerg-1427	169	27	1	1	NUM
fuelectenerg-1427	169	28	2	2	NUM
fuelectenerg-1427	169	29	2	2	NUM
fuelectenerg-1427	169	30	0	0	NUM
fuelectenerg-1427	169	31	2	2	NUM
fuelectenerg-1427	169	32	1	1	NUM
fuelectenerg-1427	169	33	(	(	PUNCT
fuelectenerg-1427	169	34	a	a	NOUN
fuelectenerg-1427	169	35	)	)	PUNCT
fuelectenerg-1427	169	36	(	(	PUNCT
fuelectenerg-1427	169	37	b	b	X
fuelectenerg-1427	169	38	)	)	PUNCT
fuelectenerg-1427	169	39	figure	figure	NOUN
fuelectenerg-1427	169	40	1	1	NUM
fuelectenerg-1427	169	41	:	:	PUNCT
fuelectenerg-1427	169	42	third	third	ADJ
fuelectenerg-1427	169	43	radix	radix	PROPN
fuelectenerg-1427	169	44	galois	galois	PROPN
fuelectenerg-1427	169	45	field	field	NOUN
fuelectenerg-1427	169	46	addition	addition	NOUN
fuelectenerg-1427	169	47	and	and	CCONJ
fuelectenerg-1427	169	48	multiplication	multiplication	NOUN
fuelectenerg-1427	169	49	tables	table	NOUN
fuelectenerg-1427	169	50	:	:	PUNCT
fuelectenerg-1427	169	51	(	(	PUNCT
fuelectenerg-1427	169	52	a	a	X
fuelectenerg-1427	169	53	)	)	PUNCT
fuelectenerg-1427	169	54	addition	addition	NOUN
fuelectenerg-1427	169	55	and	and	CCONJ
fuelectenerg-1427	169	56	(	(	PUNCT
fuelectenerg-1427	169	57	b	b	NOUN
fuelectenerg-1427	169	58	)	)	PUNCT
fuelectenerg-1427	169	59	multiplication	multiplication	NOUN
fuelectenerg-1427	169	60	.	.	PUNCT
fuelectenerg-1427	170	1	itive	itive	ADJ
fuelectenerg-1427	170	2	davio	davio	NOUN
fuelectenerg-1427	170	3	and	and	CCONJ
fuelectenerg-1427	170	4	negative	negative	ADJ
fuelectenerg-1427	170	5	davio	davio	NOUN
fuelectenerg-1427	170	6	expansions	expansion	NOUN
fuelectenerg-1427	170	7	.	.	PUNCT
fuelectenerg-1427	171	1	the	the	DET
fuelectenerg-1427	171	2	two	two	NUM
fuelectenerg-1427	171	3	-	-	PUNCT
fuelectenerg-1427	171	4	valued	value	VERB
fuelectenerg-1427	171	5	shannon	shannon	NOUN
fuelectenerg-1427	171	6	,	,	PUNCT
fuelectenerg-1427	171	7	positive	positive	ADJ
fuelectenerg-1427	171	8	davio	davio	NOUN
fuelectenerg-1427	171	9	and	and	CCONJ
fuelectenerg-1427	171	10	negative	negative	ADJ
fuelectenerg-1427	171	11	davio	davio	NOUN
fuelectenerg-1427	171	12	expansions	expansion	NOUN
fuelectenerg-1427	171	13	are	be	AUX
fuelectenerg-1427	171	14	given	give	VERB
fuelectenerg-1427	171	15	as	as	ADP
fuelectenerg-1427	171	16	follows	follow	NOUN
fuelectenerg-1427	171	17	,	,	PUNCT
fuelectenerg-1427	171	18	respectively	respectively	ADV
fuelectenerg-1427	171	19	:	:	PUNCT
fuelectenerg-1427	171	20	f	f	PROPN
fuelectenerg-1427	171	21	(	(	PUNCT
fuelectenerg-1427	171	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	171	23	,	,	PUNCT
fuelectenerg-1427	171	24	.	.	PUNCT
fuelectenerg-1427	171	25	.	.	PUNCT
fuelectenerg-1427	171	26	.	.	PUNCT
fuelectenerg-1427	172	1	,	,	PUNCT
fuelectenerg-1427	172	2	xn	xn	X
fuelectenerg-1427	172	3	)	)	PUNCT
fuelectenerg-1427	172	4	=	=	SYM
fuelectenerg-1427	172	5	x̄1	x̄1	NOUN
fuelectenerg-1427	172	6	·	·	PUNCT
fuelectenerg-1427	172	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	172	8	,	,	PUNCT
fuelectenerg-1427	172	9	.	.	PUNCT
fuelectenerg-1427	172	10	.	.	PUNCT
fuelectenerg-1427	172	11	.	.	PUNCT
fuelectenerg-1427	173	1	,	,	PUNCT
fuelectenerg-1427	173	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	173	3	x1	x1	PRON
fuelectenerg-1427	173	4	·	·	PUNCT
fuelectenerg-1427	173	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	173	6	,	,	PUNCT
fuelectenerg-1427	173	7	.	.	PUNCT
fuelectenerg-1427	173	8	.	.	PUNCT
fuelectenerg-1427	173	9	.	.	PUNCT
fuelectenerg-1427	174	1	,	,	PUNCT
fuelectenerg-1427	174	2	xn	xn	X
fuelectenerg-1427	174	3	)	)	PUNCT
fuelectenerg-1427	174	4	=	=	NOUN
fuelectenerg-1427	175	1	[	[	PUNCT
fuelectenerg-1427	175	2	x̄1	x̄1	X
fuelectenerg-1427	175	3	x1	x1	X
fuelectenerg-1427	175	4	]	]	PUNCT
fuelectenerg-1427	175	5	[	[	PUNCT
fuelectenerg-1427	175	6	1	1	NUM
fuelectenerg-1427	175	7	0	0	NUM
fuelectenerg-1427	175	8	0	0	NUM
fuelectenerg-1427	175	9	1	1	NUM
fuelectenerg-1427	175	10	]	]	PUNCT
fuelectenerg-1427	175	11	[	[	PUNCT
fuelectenerg-1427	175	12	f0	f0	PROPN
fuelectenerg-1427	175	13	f1	f1	NOUN
fuelectenerg-1427	175	14	]	]	PUNCT
fuelectenerg-1427	175	15	,	,	PUNCT
fuelectenerg-1427	175	16	(	(	PUNCT
fuelectenerg-1427	175	17	1	1	X
fuelectenerg-1427	175	18	)	)	PUNCT
fuelectenerg-1427	175	19	f	f	NOUN
fuelectenerg-1427	175	20	(	(	PUNCT
fuelectenerg-1427	175	21	x1,x2	x1,x2	PROPN
fuelectenerg-1427	175	22	,	,	PUNCT
fuelectenerg-1427	175	23	.	.	PUNCT
fuelectenerg-1427	175	24	.	.	PUNCT
fuelectenerg-1427	175	25	.	.	PUNCT
fuelectenerg-1427	176	1	,	,	PUNCT
fuelectenerg-1427	176	2	xn	xn	X
fuelectenerg-1427	176	3	)	)	PUNCT
fuelectenerg-1427	176	4	=	=	SYM
fuelectenerg-1427	176	5	1	1	NUM
fuelectenerg-1427	176	6	·	·	PUNCT
fuelectenerg-1427	176	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	176	8	,	,	PUNCT
fuelectenerg-1427	176	9	.	.	PUNCT
fuelectenerg-1427	176	10	.	.	PUNCT
fuelectenerg-1427	176	11	.	.	PUNCT
fuelectenerg-1427	177	1	,	,	PUNCT
fuelectenerg-1427	177	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	177	3	x1	x1	PRON
fuelectenerg-1427	177	4	·	·	PUNCT
fuelectenerg-1427	177	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	177	6	,	,	PUNCT
fuelectenerg-1427	177	7	.	.	PUNCT
fuelectenerg-1427	177	8	.	.	PUNCT
fuelectenerg-1427	177	9	.	.	PUNCT
fuelectenerg-1427	178	1	,	,	PUNCT
fuelectenerg-1427	178	2	xn	xn	X
fuelectenerg-1427	178	3	)	)	PUNCT
fuelectenerg-1427	179	1	=	=	NOUN
fuelectenerg-1427	179	2	[	[	PUNCT
fuelectenerg-1427	179	3	1	1	NUM
fuelectenerg-1427	179	4	x1	x1	NOUN
fuelectenerg-1427	179	5	]	]	PUNCT
fuelectenerg-1427	179	6	[	[	PUNCT
fuelectenerg-1427	179	7	1	1	NUM
fuelectenerg-1427	179	8	0	0	NUM
fuelectenerg-1427	179	9	1	1	NUM
fuelectenerg-1427	179	10	1	1	NUM
fuelectenerg-1427	179	11	]	]	PUNCT
fuelectenerg-1427	179	12	[	[	PUNCT
fuelectenerg-1427	179	13	f0	f0	PROPN
fuelectenerg-1427	179	14	f1	f1	NOUN
fuelectenerg-1427	179	15	]	]	PUNCT
fuelectenerg-1427	179	16	,	,	PUNCT
fuelectenerg-1427	179	17	(	(	PUNCT
fuelectenerg-1427	179	18	2	2	X
fuelectenerg-1427	179	19	)	)	PUNCT
fuelectenerg-1427	179	20	f	f	NOUN
fuelectenerg-1427	179	21	(	(	PUNCT
fuelectenerg-1427	179	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	179	23	,	,	PUNCT
fuelectenerg-1427	179	24	.	.	PUNCT
fuelectenerg-1427	179	25	.	.	PUNCT
fuelectenerg-1427	179	26	.	.	PUNCT
fuelectenerg-1427	180	1	,	,	PUNCT
fuelectenerg-1427	180	2	xn	xn	X
fuelectenerg-1427	180	3	)	)	PUNCT
fuelectenerg-1427	180	4	=	=	SYM
fuelectenerg-1427	180	5	1	1	X
fuelectenerg-1427	180	6	·	·	PUNCT
fuelectenerg-1427	180	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	180	8	,	,	PUNCT
fuelectenerg-1427	180	9	.	.	PUNCT
fuelectenerg-1427	180	10	.	.	PUNCT
fuelectenerg-1427	180	11	.	.	PUNCT
fuelectenerg-1427	181	1	,	,	PUNCT
fuelectenerg-1427	181	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	181	3	x̄1	x̄1	PROPN
fuelectenerg-1427	181	4	·	·	PUNCT
fuelectenerg-1427	181	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	181	6	,	,	PUNCT
fuelectenerg-1427	181	7	.	.	PUNCT
fuelectenerg-1427	181	8	.	.	PUNCT
fuelectenerg-1427	181	9	.	.	PUNCT
fuelectenerg-1427	182	1	,	,	PUNCT
fuelectenerg-1427	182	2	xn	xn	X
fuelectenerg-1427	182	3	)	)	PUNCT
fuelectenerg-1427	183	1	=	=	PUNCT
fuelectenerg-1427	183	2	[	[	PUNCT
fuelectenerg-1427	183	3	1	1	NUM
fuelectenerg-1427	183	4	x̄1	x̄1	NOUN
fuelectenerg-1427	183	5	]	]	PUNCT
fuelectenerg-1427	184	1	[	[	PUNCT
fuelectenerg-1427	184	2	0	0	NUM
fuelectenerg-1427	184	3	1	1	NUM
fuelectenerg-1427	184	4	1	1	NUM
fuelectenerg-1427	184	5	1	1	NUM
fuelectenerg-1427	184	6	]	]	PUNCT
fuelectenerg-1427	184	7	[	[	PUNCT
fuelectenerg-1427	184	8	f0	f0	PROPN
fuelectenerg-1427	184	9	f1	f1	NOUN
fuelectenerg-1427	184	10	]	]	PUNCT
fuelectenerg-1427	184	11	,	,	PUNCT
fuelectenerg-1427	184	12	(	(	PUNCT
fuelectenerg-1427	184	13	3	3	X
fuelectenerg-1427	184	14	)	)	PUNCT
fuelectenerg-1427	184	15	where	where	SCONJ
fuelectenerg-1427	184	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1427	184	17	,	,	PUNCT
fuelectenerg-1427	184	18	.	.	PUNCT
fuelectenerg-1427	184	19	.	.	PUNCT
fuelectenerg-1427	184	20	.	.	PUNCT
fuelectenerg-1427	185	1	,	,	PUNCT
fuelectenerg-1427	185	2	xn	xn	X
fuelectenerg-1427	185	3	)	)	PUNCT
fuelectenerg-1427	185	4	=	=	SYM
fuelectenerg-1427	185	5	f	f	PROPN
fuelectenerg-1427	185	6	(	(	PUNCT
fuelectenerg-1427	185	7	0,x2	0,x2	NOUN
fuelectenerg-1427	185	8	,	,	PUNCT
fuelectenerg-1427	185	9	.	.	PUNCT
fuelectenerg-1427	185	10	.	.	PUNCT
fuelectenerg-1427	185	11	.	.	PUNCT
fuelectenerg-1427	186	1	,	,	PUNCT
fuelectenerg-1427	186	2	xn	xn	X
fuelectenerg-1427	186	3	)	)	PUNCT
fuelectenerg-1427	186	4	=	=	SYM
fuelectenerg-1427	186	5	f0	f0	PROPN
fuelectenerg-1427	186	6	is	be	AUX
fuelectenerg-1427	186	7	the	the	DET
fuelectenerg-1427	186	8	negative	negative	ADJ
fuelectenerg-1427	186	9	cofactor	cofactor	NOUN
fuelectenerg-1427	186	10	of	of	ADP
fuelectenerg-1427	186	11	variable	variable	ADJ
fuelectenerg-1427	186	12	x1	x1	PROPN
fuelectenerg-1427	186	13	,	,	PUNCT
fuelectenerg-1427	186	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	186	15	,	,	PUNCT
fuelectenerg-1427	186	16	.	.	PUNCT
fuelectenerg-1427	186	17	.	.	PUNCT
fuelectenerg-1427	187	1	.	.	PUNCT
fuelectenerg-1427	188	1	,	,	PUNCT
fuelectenerg-1427	188	2	xn	xn	X
fuelectenerg-1427	188	3	)	)	PUNCT
fuelectenerg-1427	188	4	=	=	SYM
fuelectenerg-1427	188	5	f	f	PROPN
fuelectenerg-1427	188	6	(	(	PUNCT
fuelectenerg-1427	188	7	1,x2	1,x2	NUM
fuelectenerg-1427	188	8	,	,	PUNCT
fuelectenerg-1427	188	9	.	.	PUNCT
fuelectenerg-1427	188	10	.	.	PUNCT
fuelectenerg-1427	188	11	.	.	PUNCT
fuelectenerg-1427	189	1	,	,	PUNCT
fuelectenerg-1427	189	2	xn	xn	X
fuelectenerg-1427	189	3	)	)	PUNCT
fuelectenerg-1427	189	4	=	=	SYM
fuelectenerg-1427	189	5	f1	f1	NOUN
fuelectenerg-1427	189	6	is	be	AUX
fuelectenerg-1427	189	7	the	the	DET
fuelectenerg-1427	189	8	positive	positive	ADJ
fuelectenerg-1427	189	9	cofactor	cofactor	NOUN
fuelectenerg-1427	189	10	of	of	ADP
fuelectenerg-1427	189	11	variable	variable	NOUN
fuelectenerg-1427	189	12	x1	x1	PROPN
fuelectenerg-1427	189	13	,	,	PUNCT
fuelectenerg-1427	189	14	and	and	CCONJ
fuelectenerg-1427	189	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	189	16	,	,	PUNCT
fuelectenerg-1427	189	17	.	.	PUNCT
fuelectenerg-1427	189	18	.	.	PUNCT
fuelectenerg-1427	190	1	.	.	PUNCT
fuelectenerg-1427	191	1	,	,	PUNCT
fuelectenerg-1427	191	2	xn	xn	X
fuelectenerg-1427	191	3	)	)	PUNCT
fuelectenerg-1427	191	4	=	=	SYM
fuelectenerg-1427	191	5	f	f	PROPN
fuelectenerg-1427	191	6	(	(	PUNCT
fuelectenerg-1427	191	7	0,x2	0,x2	NOUN
fuelectenerg-1427	191	8	,	,	PUNCT
fuelectenerg-1427	191	9	.	.	PUNCT
fuelectenerg-1427	191	10	.	.	PUNCT
fuelectenerg-1427	191	11	.	.	PUNCT
fuelectenerg-1427	192	1	,	,	PUNCT
fuelectenerg-1427	192	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	192	3	f	f	PROPN
fuelectenerg-1427	192	4	(	(	PUNCT
fuelectenerg-1427	192	5	1,x2	1,x2	NUM
fuelectenerg-1427	192	6	,	,	PUNCT
fuelectenerg-1427	192	7	.	.	PUNCT
fuelectenerg-1427	192	8	.	.	PUNCT
fuelectenerg-1427	192	9	.	.	PUNCT
fuelectenerg-1427	193	1	,	,	PUNCT
fuelectenerg-1427	193	2	xn	xn	X
fuelectenerg-1427	193	3	)	)	PUNCT
fuelectenerg-1427	193	4	=	=	SYM
fuelectenerg-1427	193	5	f0	f0	PROPN
fuelectenerg-1427	193	6	⊕	⊕	PROPN
fuelectenerg-1427	193	7	f1	f1	NOUN
fuelectenerg-1427	193	8	.	.	PUNCT
fuelectenerg-1427	194	1	in	in	ADP
fuelectenerg-1427	194	2	addition	addition	NOUN
fuelectenerg-1427	194	3	,	,	PUNCT
fuelectenerg-1427	194	4	an	an	DET
fuelectenerg-1427	194	5	arbitrary	arbitrary	ADJ
fuelectenerg-1427	194	6	n	n	CCONJ
fuelectenerg-1427	194	7	-	-	PUNCT
fuelectenerg-1427	194	8	variable	variable	ADJ
fuelectenerg-1427	194	9	function	function	NOUN
fuelectenerg-1427	194	10	f	f	PROPN
fuelectenerg-1427	194	11	(	(	PUNCT
fuelectenerg-1427	194	12	x1	x1	PROPN
fuelectenerg-1427	194	13	,	,	PUNCT
fuelectenerg-1427	194	14	.	.	PUNCT
fuelectenerg-1427	194	15	.	.	PUNCT
fuelectenerg-1427	194	16	.	.	PUNCT
fuelectenerg-1427	195	1	,	,	PUNCT
fuelectenerg-1427	195	2	xn	xn	X
fuelectenerg-1427	195	3	)	)	PUNCT
fuelectenerg-1427	195	4	can	can	AUX
fuelectenerg-1427	195	5	be	be	AUX
fuelectenerg-1427	195	6	represented	represent	VERB
fuelectenerg-1427	195	7	using	use	VERB
fuelectenerg-1427	195	8	pprm	pprm	ADJ
fuelectenerg-1427	195	9	expansion	expansion	NOUN
fuelectenerg-1427	195	10	as	as	ADP
fuelectenerg-1427	195	11	[	[	X
fuelectenerg-1427	195	12	2	2	NUM
fuelectenerg-1427	195	13	,	,	PUNCT
fuelectenerg-1427	195	14	31	31	NUM
fuelectenerg-1427	195	15	]	]	SYM
fuelectenerg-1427	195	16	:	:	PUNCT
fuelectenerg-1427	195	17	f	f	X
fuelectenerg-1427	195	18	(	(	PUNCT
fuelectenerg-1427	195	19	x1,x2	x1,x2	PROPN
fuelectenerg-1427	195	20	,	,	PUNCT
fuelectenerg-1427	195	21	.	.	PUNCT
fuelectenerg-1427	195	22	.	.	PUNCT
fuelectenerg-1427	195	23	.	.	PUNCT
fuelectenerg-1427	196	1	,	,	PUNCT
fuelectenerg-1427	196	2	xn	xn	X
fuelectenerg-1427	196	3	)	)	PUNCT
fuelectenerg-1427	197	1	=	=	PROPN
fuelectenerg-1427	197	2	a0	a0	PROPN
fuelectenerg-1427	197	3	⊕	⊕	PROPN
fuelectenerg-1427	197	4	a1x1	a1x1	PROPN
fuelectenerg-1427	197	5	⊕	⊕	PROPN
fuelectenerg-1427	197	6	.	.	PUNCT
fuelectenerg-1427	197	7	.	.	PUNCT
fuelectenerg-1427	198	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1427	198	2	⊕a12x1x2	⊕a12x1x2	X
fuelectenerg-1427	198	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1427	198	4	⊕an−1,nxn−1xn⊕	⊕an−1,nxn−1xn⊕	ADJ
fuelectenerg-1427	198	5	.	.	PUNCT
fuelectenerg-1427	198	6	.	.	PUNCT
fuelectenerg-1427	199	1	.⊕	.⊕	PROPN
fuelectenerg-1427	199	2	a12	a12	PROPN
fuelectenerg-1427	199	3	...	...	PUNCT
fuelectenerg-1427	199	4	nx1x2	nx1x2	X
fuelectenerg-1427	199	5	.	.	PUNCT
fuelectenerg-1427	199	6	.	.	PUNCT
fuelectenerg-1427	200	1	.xn	.xn	PROPN
fuelectenerg-1427	200	2	.	.	PUNCT
fuelectenerg-1427	201	1	(	(	PUNCT
fuelectenerg-1427	201	2	4	4	X
fuelectenerg-1427	201	3	)	)	PUNCT
fuelectenerg-1427	201	4	for	for	ADP
fuelectenerg-1427	201	5	each	each	DET
fuelectenerg-1427	201	6	function	function	NOUN
fuelectenerg-1427	201	7	f	f	PROPN
fuelectenerg-1427	201	8	,	,	PUNCT
fuelectenerg-1427	201	9	the	the	DET
fuelectenerg-1427	201	10	coefficients	coefficient	NOUN
fuelectenerg-1427	201	11	ai	ai	VERB
fuelectenerg-1427	201	12	in	in	ADP
fuelectenerg-1427	201	13	equation	equation	NOUN
fuelectenerg-1427	201	14	(	(	PUNCT
fuelectenerg-1427	201	15	4	4	X
fuelectenerg-1427	201	16	)	)	PUNCT
fuelectenerg-1427	201	17	are	be	AUX
fuelectenerg-1427	201	18	determined	determine	VERB
fuelectenerg-1427	201	19	uniquely	uniquely	ADV
fuelectenerg-1427	201	20	,	,	PUNCT
fuelectenerg-1427	201	21	so	so	ADV
fuelectenerg-1427	201	22	pprm	pprm	ADJ
fuelectenerg-1427	201	23	is	be	AUX
fuelectenerg-1427	201	24	a	a	DET
fuelectenerg-1427	201	25	canonical	canonical	ADJ
fuelectenerg-1427	201	26	form	form	NOUN
fuelectenerg-1427	201	27	.	.	PUNCT
fuelectenerg-1427	202	1	for	for	ADP
fuelectenerg-1427	202	2	example	example	NOUN
fuelectenerg-1427	202	3	,	,	PUNCT
fuelectenerg-1427	202	4	if	if	SCONJ
fuelectenerg-1427	202	5	we	we	PRON
fuelectenerg-1427	202	6	use	use	VERB
fuelectenerg-1427	202	7	either	either	CCONJ
fuelectenerg-1427	202	8	only	only	ADV
fuelectenerg-1427	202	9	the	the	DET
fuelectenerg-1427	202	10	positive	positive	ADJ
fuelectenerg-1427	202	11	literal	literal	NOUN
fuelectenerg-1427	202	12	or	or	CCONJ
fuelectenerg-1427	202	13	only	only	ADV
fuelectenerg-1427	202	14	the	the	DET
fuelectenerg-1427	202	15	negative	negative	ADJ
fuelectenerg-1427	202	16	literal	literal	NOUN
fuelectenerg-1427	202	17	for	for	ADP
fuelectenerg-1427	202	18	each	each	DET
fuelectenerg-1427	202	19	variable	variable	NOUN
fuelectenerg-1427	202	20	in	in	ADP
fuelectenerg-1427	202	21	equation	equation	NOUN
fuelectenerg-1427	202	22	(	(	PUNCT
fuelectenerg-1427	202	23	4	4	X
fuelectenerg-1427	202	24	)	)	PUNCT
fuelectenerg-1427	202	25	we	we	PRON
fuelectenerg-1427	202	26	obtain	obtain	VERB
fuelectenerg-1427	202	27	the	the	DET
fuelectenerg-1427	202	28	fixed	fix	VERB
fuelectenerg-1427	202	29	polarity	polarity	NOUN
fuelectenerg-1427	202	30	reed	reed	NOUN
fuelectenerg-1427	202	31	-	-	PUNCT
fuelectenerg-1427	202	32	muller	muller	NOUN
fuelectenerg-1427	202	33	(	(	PUNCT
fuelectenerg-1427	202	34	fprm	fprm	PROPN
fuelectenerg-1427	202	35	)	)	PUNCT
fuelectenerg-1427	202	36	form	form	NOUN
fuelectenerg-1427	202	37	.	.	PUNCT
fuelectenerg-1427	203	1	the	the	DET
fuelectenerg-1427	203	2	good	good	ADJ
fuelectenerg-1427	203	3	selection	selection	NOUN
fuelectenerg-1427	203	4	of	of	ADP
fuelectenerg-1427	203	5	different	different	ADJ
fuelectenerg-1427	203	6	permutations	permutation	NOUN
fuelectenerg-1427	203	7	using	use	VERB
fuelectenerg-1427	203	8	shannon	shannon	PROPN
fuelectenerg-1427	203	9	and	and	CCONJ
fuelectenerg-1427	203	10	davio	davio	NOUN
fuelectenerg-1427	203	11	expansions	expansion	NOUN
fuelectenerg-1427	203	12	like	like	ADP
fuelectenerg-1427	203	13	other	other	ADJ
fuelectenerg-1427	203	14	expansions	expansion	NOUN
fuelectenerg-1427	203	15	such	such	ADJ
fuelectenerg-1427	203	16	as	as	ADP
fuelectenerg-1427	203	17	walsh	walsh	NOUN
fuelectenerg-1427	203	18	and	and	CCONJ
fuelectenerg-1427	203	19	arithmetic	arithmetic	ADJ
fuelectenerg-1427	203	20	expansions	expansion	NOUN
fuelectenerg-1427	203	21	as	as	ADP
fuelectenerg-1427	203	22	internal	internal	ADJ
fuelectenerg-1427	203	23	nodes	node	NOUN
fuelectenerg-1427	203	24	in	in	ADP
fuelectenerg-1427	203	25	decision	decision	NOUN
fuelectenerg-1427	203	26	trees	tree	NOUN
fuelectenerg-1427	203	27	(	(	PUNCT
fuelectenerg-1427	203	28	dts	dts	NOUN
fuelectenerg-1427	203	29	)	)	PUNCT
fuelectenerg-1427	203	30	and	and	CCONJ
fuelectenerg-1427	203	31	diagrams	diagram	NOUN
fuelectenerg-1427	203	32	(	(	PUNCT
fuelectenerg-1427	203	33	dds	dds	PROPN
fuelectenerg-1427	203	34	)	)	PUNCT
fuelectenerg-1427	203	35	will	will	AUX
fuelectenerg-1427	203	36	result	result	VERB
fuelectenerg-1427	203	37	in	in	ADP
fuelectenerg-1427	203	38	dts	dts	NOUN
fuelectenerg-1427	203	39	and	and	CCONJ
fuelectenerg-1427	203	40	dds	dds	PROPN
fuelectenerg-1427	203	41	that	that	PRON
fuelectenerg-1427	203	42	represent	represent	VERB
fuelectenerg-1427	203	43	the	the	DET
fuelectenerg-1427	203	44	corresponding	corresponding	ADJ
fuelectenerg-1427	203	45	logic	logic	NOUN
fuelectenerg-1427	203	46	functions	function	NOUN
fuelectenerg-1427	203	47	with	with	ADP
fuelectenerg-1427	203	48	smaller	small	ADJ
fuelectenerg-1427	203	49	sizes	size	NOUN
fuelectenerg-1427	203	50	in	in	ADP
fuelectenerg-1427	203	51	terms	term	NOUN
fuelectenerg-1427	203	52	of	of	ADP
fuelectenerg-1427	203	53	the	the	DET
fuelectenerg-1427	203	54	total	total	ADJ
fuelectenerg-1427	203	55	number	number	NOUN
fuelectenerg-1427	203	56	of	of	ADP
fuelectenerg-1427	203	57	hierarchical	hierarchical	ADJ
fuelectenerg-1427	203	58	levels	level	NOUN
fuelectenerg-1427	203	59	used	use	VERB
fuelectenerg-1427	203	60	,	,	PUNCT
fuelectenerg-1427	203	61	and	and	CCONJ
fuelectenerg-1427	203	62	the	the	DET
fuelectenerg-1427	203	63	total	total	ADJ
fuelectenerg-1427	203	64	number	number	NOUN
fuelectenerg-1427	203	65	of	of	ADP
fuelectenerg-1427	203	66	internal	internal	ADJ
fuelectenerg-1427	203	67	nodes	node	NOUN
fuelectenerg-1427	203	68	needed	need	VERB
fuelectenerg-1427	203	69	.	.	PUNCT
fuelectenerg-1427	204	1	in	in	ADP
fuelectenerg-1427	204	2	general	general	ADJ
fuelectenerg-1427	204	3	,	,	PUNCT
fuelectenerg-1427	204	4	a	a	DET
fuelectenerg-1427	204	5	literal	literal	NOUN
fuelectenerg-1427	204	6	can	can	AUX
fuelectenerg-1427	204	7	be	be	AUX
fuelectenerg-1427	204	8	defined	define	VERB
fuelectenerg-1427	204	9	as	as	ADP
fuelectenerg-1427	204	10	any	any	DET
fuelectenerg-1427	204	11	function	function	NOUN
fuelectenerg-1427	204	12	of	of	ADP
fuelectenerg-1427	204	13	a	a	DET
fuelectenerg-1427	204	14	single	single	ADJ
fuelectenerg-1427	204	15	variable	variable	NOUN
fuelectenerg-1427	204	16	.	.	PUNCT
fuelectenerg-1427	205	1	basis	basis	NOUN
fuelectenerg-1427	205	2	functions	function	NOUN
fuelectenerg-1427	205	3	in	in	ADP
fuelectenerg-1427	205	4	the	the	DET
fuelectenerg-1427	205	5	general	general	ADJ
fuelectenerg-1427	205	6	case	case	NOUN
fuelectenerg-1427	205	7	of	of	ADP
fuelectenerg-1427	205	8	multiple	multiple	ADV
fuelectenerg-1427	205	9	-	-	PUNCT
fuelectenerg-1427	205	10	valued	value	VERB
fuelectenerg-1427	205	11	expansions	expansion	NOUN
fuelectenerg-1427	205	12	are	be	AUX
fuelectenerg-1427	205	13	constructed	construct	VERB
fuelectenerg-1427	205	14	using	use	VERB
fuelectenerg-1427	205	15	these	these	DET
fuelectenerg-1427	205	16	103	103	NUM
fuelectenerg-1427	205	17	an	an	DET
fuelectenerg-1427	205	18	extended	extended	ADJ
fuelectenerg-1427	205	19	green	green	ADJ
fuelectenerg-1427	205	20	sasao	sasao	PROPN
fuelectenerg-1427	205	21	hierarchy	hierarchy	NOUN
fuelectenerg-1427	205	22	of	of	ADP
fuelectenerg-1427	205	23	canonical	canonical	ADJ
fuelectenerg-1427	205	24	ternary	ternary	ADJ
fuelectenerg-1427	205	25	galois	galois	NOUN
fuelectenerg-1427	205	26	forms	form	NOUN
fuelectenerg-1427	205	27	...	...	PUNCT
fuelectenerg-1427	206	1	+	+	CCONJ
fuelectenerg-1427	206	2	0	0	NUM
fuelectenerg-1427	206	3	1	1	NUM
fuelectenerg-1427	206	4	2	2	NUM
fuelectenerg-1427	206	5	0	0	NUM
fuelectenerg-1427	206	6	0	0	NUM
fuelectenerg-1427	206	7	1	1	NUM
fuelectenerg-1427	206	8	2	2	NUM
fuelectenerg-1427	206	9	1	1	NUM
fuelectenerg-1427	206	10	1	1	NUM
fuelectenerg-1427	206	11	2	2	NUM
fuelectenerg-1427	206	12	0	0	NUM
fuelectenerg-1427	206	13	2	2	NUM
fuelectenerg-1427	206	14	2	2	NUM
fuelectenerg-1427	206	15	0	0	NUM
fuelectenerg-1427	206	16	1	1	NUM
fuelectenerg-1427	206	17	∗	∗	NOUN
fuelectenerg-1427	206	18	0	0	NUM
fuelectenerg-1427	206	19	1	1	NUM
fuelectenerg-1427	206	20	2	2	NUM
fuelectenerg-1427	206	21	0	0	NUM
fuelectenerg-1427	206	22	0	0	NUM
fuelectenerg-1427	206	23	0	0	NUM
fuelectenerg-1427	206	24	0	0	NUM
fuelectenerg-1427	206	25	1	1	NUM
fuelectenerg-1427	206	26	0	0	NUM
fuelectenerg-1427	206	27	1	1	NUM
fuelectenerg-1427	206	28	2	2	NUM
fuelectenerg-1427	206	29	2	2	NUM
fuelectenerg-1427	206	30	0	0	NUM
fuelectenerg-1427	206	31	2	2	NUM
fuelectenerg-1427	206	32	1	1	NUM
fuelectenerg-1427	206	33	(	(	PUNCT
fuelectenerg-1427	206	34	a	a	NOUN
fuelectenerg-1427	206	35	)	)	PUNCT
fuelectenerg-1427	206	36	(	(	PUNCT
fuelectenerg-1427	206	37	b	b	X
fuelectenerg-1427	206	38	)	)	PUNCT
fuelectenerg-1427	206	39	figure	figure	NOUN
fuelectenerg-1427	206	40	1	1	NUM
fuelectenerg-1427	206	41	:	:	PUNCT
fuelectenerg-1427	206	42	third	third	ADJ
fuelectenerg-1427	206	43	radix	radix	PROPN
fuelectenerg-1427	206	44	galois	galois	PROPN
fuelectenerg-1427	206	45	field	field	NOUN
fuelectenerg-1427	206	46	addition	addition	NOUN
fuelectenerg-1427	206	47	and	and	CCONJ
fuelectenerg-1427	206	48	multiplication	multiplication	NOUN
fuelectenerg-1427	206	49	tables	table	NOUN
fuelectenerg-1427	206	50	:	:	PUNCT
fuelectenerg-1427	206	51	(	(	PUNCT
fuelectenerg-1427	206	52	a	a	X
fuelectenerg-1427	206	53	)	)	PUNCT
fuelectenerg-1427	206	54	addition	addition	NOUN
fuelectenerg-1427	206	55	and	and	CCONJ
fuelectenerg-1427	206	56	(	(	PUNCT
fuelectenerg-1427	206	57	b	b	NOUN
fuelectenerg-1427	206	58	)	)	PUNCT
fuelectenerg-1427	206	59	multiplication	multiplication	NOUN
fuelectenerg-1427	206	60	.	.	PUNCT
fuelectenerg-1427	207	1	itive	itive	ADJ
fuelectenerg-1427	207	2	davio	davio	NOUN
fuelectenerg-1427	207	3	and	and	CCONJ
fuelectenerg-1427	207	4	negative	negative	ADJ
fuelectenerg-1427	207	5	davio	davio	NOUN
fuelectenerg-1427	207	6	expansions	expansion	NOUN
fuelectenerg-1427	207	7	.	.	PUNCT
fuelectenerg-1427	208	1	the	the	DET
fuelectenerg-1427	208	2	two	two	NUM
fuelectenerg-1427	208	3	-	-	PUNCT
fuelectenerg-1427	208	4	valued	value	VERB
fuelectenerg-1427	208	5	shannon	shannon	NOUN
fuelectenerg-1427	208	6	,	,	PUNCT
fuelectenerg-1427	208	7	positive	positive	ADJ
fuelectenerg-1427	208	8	davio	davio	NOUN
fuelectenerg-1427	208	9	and	and	CCONJ
fuelectenerg-1427	208	10	negative	negative	ADJ
fuelectenerg-1427	208	11	davio	davio	NOUN
fuelectenerg-1427	208	12	expansions	expansion	NOUN
fuelectenerg-1427	208	13	are	be	AUX
fuelectenerg-1427	208	14	given	give	VERB
fuelectenerg-1427	208	15	as	as	ADP
fuelectenerg-1427	208	16	follows	follow	NOUN
fuelectenerg-1427	208	17	,	,	PUNCT
fuelectenerg-1427	208	18	respectively	respectively	ADV
fuelectenerg-1427	208	19	:	:	PUNCT
fuelectenerg-1427	208	20	f	f	PROPN
fuelectenerg-1427	208	21	(	(	PUNCT
fuelectenerg-1427	208	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	208	23	,	,	PUNCT
fuelectenerg-1427	208	24	.	.	PUNCT
fuelectenerg-1427	208	25	.	.	PUNCT
fuelectenerg-1427	208	26	.	.	PUNCT
fuelectenerg-1427	209	1	,	,	PUNCT
fuelectenerg-1427	209	2	xn	xn	X
fuelectenerg-1427	209	3	)	)	PUNCT
fuelectenerg-1427	209	4	=	=	SYM
fuelectenerg-1427	209	5	x̄1	x̄1	NOUN
fuelectenerg-1427	209	6	·	·	PUNCT
fuelectenerg-1427	209	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	209	8	,	,	PUNCT
fuelectenerg-1427	209	9	.	.	PUNCT
fuelectenerg-1427	209	10	.	.	PUNCT
fuelectenerg-1427	209	11	.	.	PUNCT
fuelectenerg-1427	210	1	,	,	PUNCT
fuelectenerg-1427	210	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	210	3	x1	x1	PRON
fuelectenerg-1427	210	4	·	·	PUNCT
fuelectenerg-1427	210	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	210	6	,	,	PUNCT
fuelectenerg-1427	210	7	.	.	PUNCT
fuelectenerg-1427	210	8	.	.	PUNCT
fuelectenerg-1427	210	9	.	.	PUNCT
fuelectenerg-1427	211	1	,	,	PUNCT
fuelectenerg-1427	211	2	xn	xn	X
fuelectenerg-1427	211	3	)	)	PUNCT
fuelectenerg-1427	211	4	=	=	NOUN
fuelectenerg-1427	212	1	[	[	PUNCT
fuelectenerg-1427	212	2	x̄1	x̄1	X
fuelectenerg-1427	212	3	x1	x1	X
fuelectenerg-1427	212	4	]	]	PUNCT
fuelectenerg-1427	212	5	[	[	PUNCT
fuelectenerg-1427	212	6	1	1	NUM
fuelectenerg-1427	212	7	0	0	NUM
fuelectenerg-1427	212	8	0	0	NUM
fuelectenerg-1427	212	9	1	1	NUM
fuelectenerg-1427	212	10	]	]	PUNCT
fuelectenerg-1427	212	11	[	[	PUNCT
fuelectenerg-1427	212	12	f0	f0	PROPN
fuelectenerg-1427	212	13	f1	f1	NOUN
fuelectenerg-1427	212	14	]	]	PUNCT
fuelectenerg-1427	212	15	,	,	PUNCT
fuelectenerg-1427	212	16	(	(	PUNCT
fuelectenerg-1427	212	17	1	1	X
fuelectenerg-1427	212	18	)	)	PUNCT
fuelectenerg-1427	212	19	f	f	NOUN
fuelectenerg-1427	212	20	(	(	PUNCT
fuelectenerg-1427	212	21	x1,x2	x1,x2	PROPN
fuelectenerg-1427	212	22	,	,	PUNCT
fuelectenerg-1427	212	23	.	.	PUNCT
fuelectenerg-1427	212	24	.	.	PUNCT
fuelectenerg-1427	212	25	.	.	PUNCT
fuelectenerg-1427	213	1	,	,	PUNCT
fuelectenerg-1427	213	2	xn	xn	X
fuelectenerg-1427	213	3	)	)	PUNCT
fuelectenerg-1427	213	4	=	=	SYM
fuelectenerg-1427	213	5	1	1	NUM
fuelectenerg-1427	213	6	·	·	PUNCT
fuelectenerg-1427	213	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	213	8	,	,	PUNCT
fuelectenerg-1427	213	9	.	.	PUNCT
fuelectenerg-1427	213	10	.	.	PUNCT
fuelectenerg-1427	213	11	.	.	PUNCT
fuelectenerg-1427	214	1	,	,	PUNCT
fuelectenerg-1427	214	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	214	3	x1	x1	PRON
fuelectenerg-1427	214	4	·	·	PUNCT
fuelectenerg-1427	214	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	214	6	,	,	PUNCT
fuelectenerg-1427	214	7	.	.	PUNCT
fuelectenerg-1427	214	8	.	.	PUNCT
fuelectenerg-1427	214	9	.	.	PUNCT
fuelectenerg-1427	215	1	,	,	PUNCT
fuelectenerg-1427	215	2	xn	xn	X
fuelectenerg-1427	215	3	)	)	PUNCT
fuelectenerg-1427	216	1	=	=	NOUN
fuelectenerg-1427	216	2	[	[	PUNCT
fuelectenerg-1427	216	3	1	1	NUM
fuelectenerg-1427	216	4	x1	x1	NOUN
fuelectenerg-1427	216	5	]	]	PUNCT
fuelectenerg-1427	216	6	[	[	PUNCT
fuelectenerg-1427	216	7	1	1	NUM
fuelectenerg-1427	216	8	0	0	NUM
fuelectenerg-1427	216	9	1	1	NUM
fuelectenerg-1427	216	10	1	1	NUM
fuelectenerg-1427	216	11	]	]	PUNCT
fuelectenerg-1427	216	12	[	[	PUNCT
fuelectenerg-1427	216	13	f0	f0	PROPN
fuelectenerg-1427	216	14	f1	f1	NOUN
fuelectenerg-1427	216	15	]	]	PUNCT
fuelectenerg-1427	216	16	,	,	PUNCT
fuelectenerg-1427	216	17	(	(	PUNCT
fuelectenerg-1427	216	18	2	2	X
fuelectenerg-1427	216	19	)	)	PUNCT
fuelectenerg-1427	216	20	f	f	NOUN
fuelectenerg-1427	216	21	(	(	PUNCT
fuelectenerg-1427	216	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	216	23	,	,	PUNCT
fuelectenerg-1427	216	24	.	.	PUNCT
fuelectenerg-1427	216	25	.	.	PUNCT
fuelectenerg-1427	216	26	.	.	PUNCT
fuelectenerg-1427	217	1	,	,	PUNCT
fuelectenerg-1427	217	2	xn	xn	X
fuelectenerg-1427	217	3	)	)	PUNCT
fuelectenerg-1427	217	4	=	=	SYM
fuelectenerg-1427	217	5	1	1	X
fuelectenerg-1427	217	6	·	·	PUNCT
fuelectenerg-1427	217	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	217	8	,	,	PUNCT
fuelectenerg-1427	217	9	.	.	PUNCT
fuelectenerg-1427	217	10	.	.	PUNCT
fuelectenerg-1427	217	11	.	.	PUNCT
fuelectenerg-1427	218	1	,	,	PUNCT
fuelectenerg-1427	218	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	218	3	x̄1	x̄1	PROPN
fuelectenerg-1427	218	4	·	·	PUNCT
fuelectenerg-1427	218	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	218	6	,	,	PUNCT
fuelectenerg-1427	218	7	.	.	PUNCT
fuelectenerg-1427	218	8	.	.	PUNCT
fuelectenerg-1427	218	9	.	.	PUNCT
fuelectenerg-1427	219	1	,	,	PUNCT
fuelectenerg-1427	219	2	xn	xn	X
fuelectenerg-1427	219	3	)	)	PUNCT
fuelectenerg-1427	220	1	=	=	PUNCT
fuelectenerg-1427	220	2	[	[	PUNCT
fuelectenerg-1427	220	3	1	1	NUM
fuelectenerg-1427	220	4	x̄1	x̄1	NOUN
fuelectenerg-1427	220	5	]	]	PUNCT
fuelectenerg-1427	221	1	[	[	PUNCT
fuelectenerg-1427	221	2	0	0	NUM
fuelectenerg-1427	221	3	1	1	NUM
fuelectenerg-1427	221	4	1	1	NUM
fuelectenerg-1427	221	5	1	1	NUM
fuelectenerg-1427	221	6	]	]	PUNCT
fuelectenerg-1427	221	7	[	[	PUNCT
fuelectenerg-1427	221	8	f0	f0	PROPN
fuelectenerg-1427	221	9	f1	f1	NOUN
fuelectenerg-1427	221	10	]	]	PUNCT
fuelectenerg-1427	221	11	,	,	PUNCT
fuelectenerg-1427	221	12	(	(	PUNCT
fuelectenerg-1427	221	13	3	3	X
fuelectenerg-1427	221	14	)	)	PUNCT
fuelectenerg-1427	221	15	where	where	SCONJ
fuelectenerg-1427	221	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1427	221	17	,	,	PUNCT
fuelectenerg-1427	221	18	.	.	PUNCT
fuelectenerg-1427	221	19	.	.	PUNCT
fuelectenerg-1427	221	20	.	.	PUNCT
fuelectenerg-1427	222	1	,	,	PUNCT
fuelectenerg-1427	222	2	xn	xn	X
fuelectenerg-1427	222	3	)	)	PUNCT
fuelectenerg-1427	222	4	=	=	SYM
fuelectenerg-1427	222	5	f	f	PROPN
fuelectenerg-1427	222	6	(	(	PUNCT
fuelectenerg-1427	222	7	0,x2	0,x2	NOUN
fuelectenerg-1427	222	8	,	,	PUNCT
fuelectenerg-1427	222	9	.	.	PUNCT
fuelectenerg-1427	222	10	.	.	PUNCT
fuelectenerg-1427	222	11	.	.	PUNCT
fuelectenerg-1427	223	1	,	,	PUNCT
fuelectenerg-1427	223	2	xn	xn	X
fuelectenerg-1427	223	3	)	)	PUNCT
fuelectenerg-1427	223	4	=	=	SYM
fuelectenerg-1427	223	5	f0	f0	PROPN
fuelectenerg-1427	223	6	is	be	AUX
fuelectenerg-1427	223	7	the	the	DET
fuelectenerg-1427	223	8	negative	negative	ADJ
fuelectenerg-1427	223	9	cofactor	cofactor	NOUN
fuelectenerg-1427	223	10	of	of	ADP
fuelectenerg-1427	223	11	variable	variable	ADJ
fuelectenerg-1427	223	12	x1	x1	PROPN
fuelectenerg-1427	223	13	,	,	PUNCT
fuelectenerg-1427	223	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	223	15	,	,	PUNCT
fuelectenerg-1427	223	16	.	.	PUNCT
fuelectenerg-1427	223	17	.	.	PUNCT
fuelectenerg-1427	224	1	.	.	PUNCT
fuelectenerg-1427	225	1	,	,	PUNCT
fuelectenerg-1427	225	2	xn	xn	X
fuelectenerg-1427	225	3	)	)	PUNCT
fuelectenerg-1427	225	4	=	=	SYM
fuelectenerg-1427	225	5	f	f	PROPN
fuelectenerg-1427	225	6	(	(	PUNCT
fuelectenerg-1427	225	7	1,x2	1,x2	NUM
fuelectenerg-1427	225	8	,	,	PUNCT
fuelectenerg-1427	225	9	.	.	PUNCT
fuelectenerg-1427	225	10	.	.	PUNCT
fuelectenerg-1427	225	11	.	.	PUNCT
fuelectenerg-1427	226	1	,	,	PUNCT
fuelectenerg-1427	226	2	xn	xn	X
fuelectenerg-1427	226	3	)	)	PUNCT
fuelectenerg-1427	226	4	=	=	SYM
fuelectenerg-1427	226	5	f1	f1	NOUN
fuelectenerg-1427	226	6	is	be	AUX
fuelectenerg-1427	226	7	the	the	DET
fuelectenerg-1427	226	8	positive	positive	ADJ
fuelectenerg-1427	226	9	cofactor	cofactor	NOUN
fuelectenerg-1427	226	10	of	of	ADP
fuelectenerg-1427	226	11	variable	variable	NOUN
fuelectenerg-1427	226	12	x1	x1	PROPN
fuelectenerg-1427	226	13	,	,	PUNCT
fuelectenerg-1427	226	14	and	and	CCONJ
fuelectenerg-1427	226	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	226	16	,	,	PUNCT
fuelectenerg-1427	226	17	.	.	PUNCT
fuelectenerg-1427	226	18	.	.	PUNCT
fuelectenerg-1427	227	1	.	.	PUNCT
fuelectenerg-1427	228	1	,	,	PUNCT
fuelectenerg-1427	228	2	xn	xn	X
fuelectenerg-1427	228	3	)	)	PUNCT
fuelectenerg-1427	228	4	=	=	SYM
fuelectenerg-1427	228	5	f	f	PROPN
fuelectenerg-1427	228	6	(	(	PUNCT
fuelectenerg-1427	228	7	0,x2	0,x2	NOUN
fuelectenerg-1427	228	8	,	,	PUNCT
fuelectenerg-1427	228	9	.	.	PUNCT
fuelectenerg-1427	228	10	.	.	PUNCT
fuelectenerg-1427	228	11	.	.	PUNCT
fuelectenerg-1427	229	1	,	,	PUNCT
fuelectenerg-1427	229	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	229	3	f	f	PROPN
fuelectenerg-1427	229	4	(	(	PUNCT
fuelectenerg-1427	229	5	1,x2	1,x2	NUM
fuelectenerg-1427	229	6	,	,	PUNCT
fuelectenerg-1427	229	7	.	.	PUNCT
fuelectenerg-1427	229	8	.	.	PUNCT
fuelectenerg-1427	229	9	.	.	PUNCT
fuelectenerg-1427	230	1	,	,	PUNCT
fuelectenerg-1427	230	2	xn	xn	X
fuelectenerg-1427	230	3	)	)	PUNCT
fuelectenerg-1427	230	4	=	=	SYM
fuelectenerg-1427	230	5	f0	f0	PROPN
fuelectenerg-1427	230	6	⊕	⊕	PROPN
fuelectenerg-1427	230	7	f1	f1	NOUN
fuelectenerg-1427	230	8	.	.	PUNCT
fuelectenerg-1427	231	1	in	in	ADP
fuelectenerg-1427	231	2	addition	addition	NOUN
fuelectenerg-1427	231	3	,	,	PUNCT
fuelectenerg-1427	231	4	an	an	DET
fuelectenerg-1427	231	5	arbitrary	arbitrary	ADJ
fuelectenerg-1427	231	6	n	n	CCONJ
fuelectenerg-1427	231	7	-	-	PUNCT
fuelectenerg-1427	231	8	variable	variable	ADJ
fuelectenerg-1427	231	9	function	function	NOUN
fuelectenerg-1427	231	10	f	f	PROPN
fuelectenerg-1427	231	11	(	(	PUNCT
fuelectenerg-1427	231	12	x1	x1	PROPN
fuelectenerg-1427	231	13	,	,	PUNCT
fuelectenerg-1427	231	14	.	.	PUNCT
fuelectenerg-1427	231	15	.	.	PUNCT
fuelectenerg-1427	231	16	.	.	PUNCT
fuelectenerg-1427	232	1	,	,	PUNCT
fuelectenerg-1427	232	2	xn	xn	X
fuelectenerg-1427	232	3	)	)	PUNCT
fuelectenerg-1427	232	4	can	can	AUX
fuelectenerg-1427	232	5	be	be	AUX
fuelectenerg-1427	232	6	represented	represent	VERB
fuelectenerg-1427	232	7	using	use	VERB
fuelectenerg-1427	232	8	pprm	pprm	ADJ
fuelectenerg-1427	232	9	expansion	expansion	NOUN
fuelectenerg-1427	232	10	as	as	ADP
fuelectenerg-1427	232	11	[	[	X
fuelectenerg-1427	232	12	2	2	NUM
fuelectenerg-1427	232	13	,	,	PUNCT
fuelectenerg-1427	232	14	31	31	NUM
fuelectenerg-1427	232	15	]	]	SYM
fuelectenerg-1427	232	16	:	:	PUNCT
fuelectenerg-1427	232	17	f	f	X
fuelectenerg-1427	232	18	(	(	PUNCT
fuelectenerg-1427	232	19	x1,x2	x1,x2	PROPN
fuelectenerg-1427	232	20	,	,	PUNCT
fuelectenerg-1427	232	21	.	.	PUNCT
fuelectenerg-1427	232	22	.	.	PUNCT
fuelectenerg-1427	232	23	.	.	PUNCT
fuelectenerg-1427	233	1	,	,	PUNCT
fuelectenerg-1427	233	2	xn	xn	X
fuelectenerg-1427	233	3	)	)	PUNCT
fuelectenerg-1427	234	1	=	=	PROPN
fuelectenerg-1427	234	2	a0	a0	PROPN
fuelectenerg-1427	234	3	⊕	⊕	PROPN
fuelectenerg-1427	234	4	a1x1	a1x1	PROPN
fuelectenerg-1427	234	5	⊕	⊕	PROPN
fuelectenerg-1427	234	6	.	.	PUNCT
fuelectenerg-1427	234	7	.	.	PUNCT
fuelectenerg-1427	235	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1427	235	2	⊕a12x1x2	⊕a12x1x2	X
fuelectenerg-1427	235	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1427	235	4	⊕an−1,nxn−1xn⊕	⊕an−1,nxn−1xn⊕	ADJ
fuelectenerg-1427	235	5	.	.	PUNCT
fuelectenerg-1427	235	6	.	.	PUNCT
fuelectenerg-1427	236	1	.⊕	.⊕	PROPN
fuelectenerg-1427	236	2	a12	a12	PROPN
fuelectenerg-1427	236	3	...	...	PUNCT
fuelectenerg-1427	236	4	nx1x2	nx1x2	X
fuelectenerg-1427	236	5	.	.	PUNCT
fuelectenerg-1427	236	6	.	.	PUNCT
fuelectenerg-1427	237	1	.xn	.xn	PROPN
fuelectenerg-1427	237	2	.	.	PUNCT
fuelectenerg-1427	238	1	(	(	PUNCT
fuelectenerg-1427	238	2	4	4	X
fuelectenerg-1427	238	3	)	)	PUNCT
fuelectenerg-1427	238	4	for	for	ADP
fuelectenerg-1427	238	5	each	each	DET
fuelectenerg-1427	238	6	function	function	NOUN
fuelectenerg-1427	238	7	f	f	PROPN
fuelectenerg-1427	238	8	,	,	PUNCT
fuelectenerg-1427	238	9	the	the	DET
fuelectenerg-1427	238	10	coefficients	coefficient	NOUN
fuelectenerg-1427	238	11	ai	ai	VERB
fuelectenerg-1427	238	12	in	in	ADP
fuelectenerg-1427	238	13	equation	equation	NOUN
fuelectenerg-1427	238	14	(	(	PUNCT
fuelectenerg-1427	238	15	4	4	X
fuelectenerg-1427	238	16	)	)	PUNCT
fuelectenerg-1427	238	17	are	be	AUX
fuelectenerg-1427	238	18	determined	determine	VERB
fuelectenerg-1427	238	19	uniquely	uniquely	ADV
fuelectenerg-1427	238	20	,	,	PUNCT
fuelectenerg-1427	238	21	so	so	ADV
fuelectenerg-1427	238	22	pprm	pprm	ADJ
fuelectenerg-1427	238	23	is	be	AUX
fuelectenerg-1427	238	24	a	a	DET
fuelectenerg-1427	238	25	canonical	canonical	ADJ
fuelectenerg-1427	238	26	form	form	NOUN
fuelectenerg-1427	238	27	.	.	PUNCT
fuelectenerg-1427	239	1	for	for	ADP
fuelectenerg-1427	239	2	example	example	NOUN
fuelectenerg-1427	239	3	,	,	PUNCT
fuelectenerg-1427	239	4	if	if	SCONJ
fuelectenerg-1427	239	5	we	we	PRON
fuelectenerg-1427	239	6	use	use	VERB
fuelectenerg-1427	239	7	either	either	CCONJ
fuelectenerg-1427	239	8	only	only	ADV
fuelectenerg-1427	239	9	the	the	DET
fuelectenerg-1427	239	10	positive	positive	ADJ
fuelectenerg-1427	239	11	literal	literal	NOUN
fuelectenerg-1427	239	12	or	or	CCONJ
fuelectenerg-1427	239	13	only	only	ADV
fuelectenerg-1427	239	14	the	the	DET
fuelectenerg-1427	239	15	negative	negative	ADJ
fuelectenerg-1427	239	16	literal	literal	NOUN
fuelectenerg-1427	239	17	for	for	ADP
fuelectenerg-1427	239	18	each	each	DET
fuelectenerg-1427	239	19	variable	variable	NOUN
fuelectenerg-1427	239	20	in	in	ADP
fuelectenerg-1427	239	21	equation	equation	NOUN
fuelectenerg-1427	239	22	(	(	PUNCT
fuelectenerg-1427	239	23	4	4	X
fuelectenerg-1427	239	24	)	)	PUNCT
fuelectenerg-1427	239	25	we	we	PRON
fuelectenerg-1427	239	26	obtain	obtain	VERB
fuelectenerg-1427	239	27	the	the	DET
fuelectenerg-1427	239	28	fixed	fix	VERB
fuelectenerg-1427	239	29	polarity	polarity	NOUN
fuelectenerg-1427	239	30	reed	reed	NOUN
fuelectenerg-1427	239	31	-	-	PUNCT
fuelectenerg-1427	239	32	muller	muller	NOUN
fuelectenerg-1427	239	33	(	(	PUNCT
fuelectenerg-1427	239	34	fprm	fprm	PROPN
fuelectenerg-1427	239	35	)	)	PUNCT
fuelectenerg-1427	239	36	form	form	NOUN
fuelectenerg-1427	239	37	.	.	PUNCT
fuelectenerg-1427	240	1	the	the	DET
fuelectenerg-1427	240	2	good	good	ADJ
fuelectenerg-1427	240	3	selection	selection	NOUN
fuelectenerg-1427	240	4	of	of	ADP
fuelectenerg-1427	240	5	different	different	ADJ
fuelectenerg-1427	240	6	permutations	permutation	NOUN
fuelectenerg-1427	240	7	using	use	VERB
fuelectenerg-1427	240	8	shannon	shannon	PROPN
fuelectenerg-1427	240	9	and	and	CCONJ
fuelectenerg-1427	240	10	davio	davio	NOUN
fuelectenerg-1427	240	11	expansions	expansion	NOUN
fuelectenerg-1427	240	12	like	like	ADP
fuelectenerg-1427	240	13	other	other	ADJ
fuelectenerg-1427	240	14	expansions	expansion	NOUN
fuelectenerg-1427	240	15	such	such	ADJ
fuelectenerg-1427	240	16	as	as	ADP
fuelectenerg-1427	240	17	walsh	walsh	NOUN
fuelectenerg-1427	240	18	and	and	CCONJ
fuelectenerg-1427	240	19	arithmetic	arithmetic	ADJ
fuelectenerg-1427	240	20	expansions	expansion	NOUN
fuelectenerg-1427	240	21	as	as	ADP
fuelectenerg-1427	240	22	internal	internal	ADJ
fuelectenerg-1427	240	23	nodes	node	NOUN
fuelectenerg-1427	240	24	in	in	ADP
fuelectenerg-1427	240	25	decision	decision	NOUN
fuelectenerg-1427	240	26	trees	tree	NOUN
fuelectenerg-1427	240	27	(	(	PUNCT
fuelectenerg-1427	240	28	dts	dts	NOUN
fuelectenerg-1427	240	29	)	)	PUNCT
fuelectenerg-1427	240	30	and	and	CCONJ
fuelectenerg-1427	240	31	diagrams	diagram	NOUN
fuelectenerg-1427	240	32	(	(	PUNCT
fuelectenerg-1427	240	33	dds	dds	PROPN
fuelectenerg-1427	240	34	)	)	PUNCT
fuelectenerg-1427	240	35	will	will	AUX
fuelectenerg-1427	240	36	result	result	VERB
fuelectenerg-1427	240	37	in	in	ADP
fuelectenerg-1427	240	38	dts	dts	NOUN
fuelectenerg-1427	240	39	and	and	CCONJ
fuelectenerg-1427	240	40	dds	dds	PROPN
fuelectenerg-1427	240	41	that	that	PRON
fuelectenerg-1427	240	42	represent	represent	VERB
fuelectenerg-1427	240	43	the	the	DET
fuelectenerg-1427	240	44	corresponding	corresponding	ADJ
fuelectenerg-1427	240	45	logic	logic	NOUN
fuelectenerg-1427	240	46	functions	function	NOUN
fuelectenerg-1427	240	47	with	with	ADP
fuelectenerg-1427	240	48	smaller	small	ADJ
fuelectenerg-1427	240	49	sizes	size	NOUN
fuelectenerg-1427	240	50	in	in	ADP
fuelectenerg-1427	240	51	terms	term	NOUN
fuelectenerg-1427	240	52	of	of	ADP
fuelectenerg-1427	240	53	the	the	DET
fuelectenerg-1427	240	54	total	total	ADJ
fuelectenerg-1427	240	55	number	number	NOUN
fuelectenerg-1427	240	56	of	of	ADP
fuelectenerg-1427	240	57	hierarchical	hierarchical	ADJ
fuelectenerg-1427	240	58	levels	level	NOUN
fuelectenerg-1427	240	59	used	use	VERB
fuelectenerg-1427	240	60	,	,	PUNCT
fuelectenerg-1427	240	61	and	and	CCONJ
fuelectenerg-1427	240	62	the	the	DET
fuelectenerg-1427	240	63	total	total	ADJ
fuelectenerg-1427	240	64	number	number	NOUN
fuelectenerg-1427	240	65	of	of	ADP
fuelectenerg-1427	240	66	internal	internal	ADJ
fuelectenerg-1427	240	67	nodes	node	NOUN
fuelectenerg-1427	240	68	needed	need	VERB
fuelectenerg-1427	240	69	.	.	PUNCT
fuelectenerg-1427	241	1	in	in	ADP
fuelectenerg-1427	241	2	general	general	ADJ
fuelectenerg-1427	241	3	,	,	PUNCT
fuelectenerg-1427	241	4	a	a	DET
fuelectenerg-1427	241	5	literal	literal	NOUN
fuelectenerg-1427	241	6	can	can	AUX
fuelectenerg-1427	241	7	be	be	AUX
fuelectenerg-1427	241	8	defined	define	VERB
fuelectenerg-1427	241	9	as	as	ADP
fuelectenerg-1427	241	10	any	any	DET
fuelectenerg-1427	241	11	function	function	NOUN
fuelectenerg-1427	241	12	of	of	ADP
fuelectenerg-1427	241	13	a	a	DET
fuelectenerg-1427	241	14	single	single	ADJ
fuelectenerg-1427	241	15	variable	variable	NOUN
fuelectenerg-1427	241	16	.	.	PUNCT
fuelectenerg-1427	242	1	basis	basis	NOUN
fuelectenerg-1427	242	2	functions	function	NOUN
fuelectenerg-1427	242	3	in	in	ADP
fuelectenerg-1427	242	4	the	the	DET
fuelectenerg-1427	242	5	general	general	ADJ
fuelectenerg-1427	242	6	case	case	NOUN
fuelectenerg-1427	242	7	of	of	ADP
fuelectenerg-1427	242	8	multiple	multiple	ADV
fuelectenerg-1427	242	9	-	-	PUNCT
fuelectenerg-1427	242	10	valued	value	VERB
fuelectenerg-1427	242	11	expansions	expansion	NOUN
fuelectenerg-1427	242	12	are	be	AUX
fuelectenerg-1427	242	13	constructed	construct	VERB
fuelectenerg-1427	242	14	using	use	VERB
fuelectenerg-1427	242	15	these	these	DET
fuelectenerg-1427	242	16	103	103	NUM
fuelectenerg-1427	242	17	an	an	DET
fuelectenerg-1427	242	18	extended	extended	ADJ
fuelectenerg-1427	242	19	green	green	ADJ
fuelectenerg-1427	242	20	sasao	sasao	PROPN
fuelectenerg-1427	242	21	hierarchy	hierarchy	NOUN
fuelectenerg-1427	242	22	of	of	ADP
fuelectenerg-1427	242	23	canonical	canonical	ADJ
fuelectenerg-1427	242	24	ternary	ternary	ADJ
fuelectenerg-1427	242	25	galois	galois	NOUN
fuelectenerg-1427	242	26	forms	form	NOUN
fuelectenerg-1427	242	27	...	...	PUNCT
fuelectenerg-1427	243	1	+	+	CCONJ
fuelectenerg-1427	243	2	0	0	NUM
fuelectenerg-1427	243	3	1	1	NUM
fuelectenerg-1427	243	4	2	2	NUM
fuelectenerg-1427	243	5	0	0	NUM
fuelectenerg-1427	243	6	0	0	NUM
fuelectenerg-1427	243	7	1	1	NUM
fuelectenerg-1427	243	8	2	2	NUM
fuelectenerg-1427	243	9	1	1	NUM
fuelectenerg-1427	243	10	1	1	NUM
fuelectenerg-1427	243	11	2	2	NUM
fuelectenerg-1427	243	12	0	0	NUM
fuelectenerg-1427	243	13	2	2	NUM
fuelectenerg-1427	243	14	2	2	NUM
fuelectenerg-1427	243	15	0	0	NUM
fuelectenerg-1427	243	16	1	1	NUM
fuelectenerg-1427	243	17	∗	∗	NOUN
fuelectenerg-1427	243	18	0	0	NUM
fuelectenerg-1427	243	19	1	1	NUM
fuelectenerg-1427	243	20	2	2	NUM
fuelectenerg-1427	243	21	0	0	NUM
fuelectenerg-1427	243	22	0	0	NUM
fuelectenerg-1427	243	23	0	0	NUM
fuelectenerg-1427	243	24	0	0	NUM
fuelectenerg-1427	243	25	1	1	NUM
fuelectenerg-1427	243	26	0	0	NUM
fuelectenerg-1427	243	27	1	1	NUM
fuelectenerg-1427	243	28	2	2	NUM
fuelectenerg-1427	243	29	2	2	NUM
fuelectenerg-1427	243	30	0	0	NUM
fuelectenerg-1427	243	31	2	2	NUM
fuelectenerg-1427	243	32	1	1	NUM
fuelectenerg-1427	243	33	(	(	PUNCT
fuelectenerg-1427	243	34	a	a	NOUN
fuelectenerg-1427	243	35	)	)	PUNCT
fuelectenerg-1427	243	36	(	(	PUNCT
fuelectenerg-1427	243	37	b	b	X
fuelectenerg-1427	243	38	)	)	PUNCT
fuelectenerg-1427	243	39	figure	figure	NOUN
fuelectenerg-1427	243	40	1	1	NUM
fuelectenerg-1427	243	41	:	:	PUNCT
fuelectenerg-1427	243	42	third	third	ADJ
fuelectenerg-1427	243	43	radix	radix	PROPN
fuelectenerg-1427	243	44	galois	galois	PROPN
fuelectenerg-1427	243	45	field	field	NOUN
fuelectenerg-1427	243	46	addition	addition	NOUN
fuelectenerg-1427	243	47	and	and	CCONJ
fuelectenerg-1427	243	48	multiplication	multiplication	NOUN
fuelectenerg-1427	243	49	tables	table	NOUN
fuelectenerg-1427	243	50	:	:	PUNCT
fuelectenerg-1427	243	51	(	(	PUNCT
fuelectenerg-1427	243	52	a	a	X
fuelectenerg-1427	243	53	)	)	PUNCT
fuelectenerg-1427	243	54	addition	addition	NOUN
fuelectenerg-1427	243	55	and	and	CCONJ
fuelectenerg-1427	243	56	(	(	PUNCT
fuelectenerg-1427	243	57	b	b	NOUN
fuelectenerg-1427	243	58	)	)	PUNCT
fuelectenerg-1427	243	59	multiplication	multiplication	NOUN
fuelectenerg-1427	243	60	.	.	PUNCT
fuelectenerg-1427	244	1	itive	itive	ADJ
fuelectenerg-1427	244	2	davio	davio	NOUN
fuelectenerg-1427	244	3	and	and	CCONJ
fuelectenerg-1427	244	4	negative	negative	ADJ
fuelectenerg-1427	244	5	davio	davio	NOUN
fuelectenerg-1427	244	6	expansions	expansion	NOUN
fuelectenerg-1427	244	7	.	.	PUNCT
fuelectenerg-1427	245	1	the	the	DET
fuelectenerg-1427	245	2	two	two	NUM
fuelectenerg-1427	245	3	-	-	PUNCT
fuelectenerg-1427	245	4	valued	value	VERB
fuelectenerg-1427	245	5	shannon	shannon	NOUN
fuelectenerg-1427	245	6	,	,	PUNCT
fuelectenerg-1427	245	7	positive	positive	ADJ
fuelectenerg-1427	245	8	davio	davio	NOUN
fuelectenerg-1427	245	9	and	and	CCONJ
fuelectenerg-1427	245	10	negative	negative	ADJ
fuelectenerg-1427	245	11	davio	davio	NOUN
fuelectenerg-1427	245	12	expansions	expansion	NOUN
fuelectenerg-1427	245	13	are	be	AUX
fuelectenerg-1427	245	14	given	give	VERB
fuelectenerg-1427	245	15	as	as	ADP
fuelectenerg-1427	245	16	follows	follow	NOUN
fuelectenerg-1427	245	17	,	,	PUNCT
fuelectenerg-1427	245	18	respectively	respectively	ADV
fuelectenerg-1427	245	19	:	:	PUNCT
fuelectenerg-1427	245	20	f	f	PROPN
fuelectenerg-1427	245	21	(	(	PUNCT
fuelectenerg-1427	245	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	245	23	,	,	PUNCT
fuelectenerg-1427	245	24	.	.	PUNCT
fuelectenerg-1427	245	25	.	.	PUNCT
fuelectenerg-1427	245	26	.	.	PUNCT
fuelectenerg-1427	246	1	,	,	PUNCT
fuelectenerg-1427	246	2	xn	xn	X
fuelectenerg-1427	246	3	)	)	PUNCT
fuelectenerg-1427	246	4	=	=	SYM
fuelectenerg-1427	246	5	x̄1	x̄1	NOUN
fuelectenerg-1427	246	6	·	·	PUNCT
fuelectenerg-1427	246	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	246	8	,	,	PUNCT
fuelectenerg-1427	246	9	.	.	PUNCT
fuelectenerg-1427	246	10	.	.	PUNCT
fuelectenerg-1427	246	11	.	.	PUNCT
fuelectenerg-1427	247	1	,	,	PUNCT
fuelectenerg-1427	247	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	247	3	x1	x1	PRON
fuelectenerg-1427	247	4	·	·	PUNCT
fuelectenerg-1427	247	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	247	6	,	,	PUNCT
fuelectenerg-1427	247	7	.	.	PUNCT
fuelectenerg-1427	247	8	.	.	PUNCT
fuelectenerg-1427	247	9	.	.	PUNCT
fuelectenerg-1427	248	1	,	,	PUNCT
fuelectenerg-1427	248	2	xn	xn	X
fuelectenerg-1427	248	3	)	)	PUNCT
fuelectenerg-1427	248	4	=	=	NOUN
fuelectenerg-1427	249	1	[	[	PUNCT
fuelectenerg-1427	249	2	x̄1	x̄1	X
fuelectenerg-1427	249	3	x1	x1	X
fuelectenerg-1427	249	4	]	]	PUNCT
fuelectenerg-1427	249	5	[	[	PUNCT
fuelectenerg-1427	249	6	1	1	NUM
fuelectenerg-1427	249	7	0	0	NUM
fuelectenerg-1427	249	8	0	0	NUM
fuelectenerg-1427	249	9	1	1	NUM
fuelectenerg-1427	249	10	]	]	PUNCT
fuelectenerg-1427	249	11	[	[	PUNCT
fuelectenerg-1427	249	12	f0	f0	PROPN
fuelectenerg-1427	249	13	f1	f1	NOUN
fuelectenerg-1427	249	14	]	]	PUNCT
fuelectenerg-1427	249	15	,	,	PUNCT
fuelectenerg-1427	249	16	(	(	PUNCT
fuelectenerg-1427	249	17	1	1	X
fuelectenerg-1427	249	18	)	)	PUNCT
fuelectenerg-1427	249	19	f	f	NOUN
fuelectenerg-1427	249	20	(	(	PUNCT
fuelectenerg-1427	249	21	x1,x2	x1,x2	PROPN
fuelectenerg-1427	249	22	,	,	PUNCT
fuelectenerg-1427	249	23	.	.	PUNCT
fuelectenerg-1427	249	24	.	.	PUNCT
fuelectenerg-1427	249	25	.	.	PUNCT
fuelectenerg-1427	250	1	,	,	PUNCT
fuelectenerg-1427	250	2	xn	xn	X
fuelectenerg-1427	250	3	)	)	PUNCT
fuelectenerg-1427	250	4	=	=	SYM
fuelectenerg-1427	250	5	1	1	NUM
fuelectenerg-1427	250	6	·	·	PUNCT
fuelectenerg-1427	250	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1427	250	8	,	,	PUNCT
fuelectenerg-1427	250	9	.	.	PUNCT
fuelectenerg-1427	250	10	.	.	PUNCT
fuelectenerg-1427	250	11	.	.	PUNCT
fuelectenerg-1427	251	1	,	,	PUNCT
fuelectenerg-1427	251	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	251	3	x1	x1	PRON
fuelectenerg-1427	251	4	·	·	PUNCT
fuelectenerg-1427	251	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	251	6	,	,	PUNCT
fuelectenerg-1427	251	7	.	.	PUNCT
fuelectenerg-1427	251	8	.	.	PUNCT
fuelectenerg-1427	251	9	.	.	PUNCT
fuelectenerg-1427	252	1	,	,	PUNCT
fuelectenerg-1427	252	2	xn	xn	X
fuelectenerg-1427	252	3	)	)	PUNCT
fuelectenerg-1427	253	1	=	=	NOUN
fuelectenerg-1427	253	2	[	[	PUNCT
fuelectenerg-1427	253	3	1	1	NUM
fuelectenerg-1427	253	4	x1	x1	NOUN
fuelectenerg-1427	253	5	]	]	PUNCT
fuelectenerg-1427	253	6	[	[	PUNCT
fuelectenerg-1427	253	7	1	1	NUM
fuelectenerg-1427	253	8	0	0	NUM
fuelectenerg-1427	253	9	1	1	NUM
fuelectenerg-1427	253	10	1	1	NUM
fuelectenerg-1427	253	11	]	]	PUNCT
fuelectenerg-1427	253	12	[	[	PUNCT
fuelectenerg-1427	253	13	f0	f0	PROPN
fuelectenerg-1427	253	14	f1	f1	NOUN
fuelectenerg-1427	253	15	]	]	PUNCT
fuelectenerg-1427	253	16	,	,	PUNCT
fuelectenerg-1427	253	17	(	(	PUNCT
fuelectenerg-1427	253	18	2	2	X
fuelectenerg-1427	253	19	)	)	PUNCT
fuelectenerg-1427	253	20	f	f	NOUN
fuelectenerg-1427	253	21	(	(	PUNCT
fuelectenerg-1427	253	22	x1,x2	x1,x2	PROPN
fuelectenerg-1427	253	23	,	,	PUNCT
fuelectenerg-1427	253	24	.	.	PUNCT
fuelectenerg-1427	253	25	.	.	PUNCT
fuelectenerg-1427	253	26	.	.	PUNCT
fuelectenerg-1427	254	1	,	,	PUNCT
fuelectenerg-1427	254	2	xn	xn	X
fuelectenerg-1427	254	3	)	)	PUNCT
fuelectenerg-1427	254	4	=	=	SYM
fuelectenerg-1427	254	5	1	1	X
fuelectenerg-1427	254	6	·	·	PUNCT
fuelectenerg-1427	254	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	254	8	,	,	PUNCT
fuelectenerg-1427	254	9	.	.	PUNCT
fuelectenerg-1427	254	10	.	.	PUNCT
fuelectenerg-1427	254	11	.	.	PUNCT
fuelectenerg-1427	255	1	,	,	PUNCT
fuelectenerg-1427	255	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	255	3	x̄1	x̄1	PROPN
fuelectenerg-1427	255	4	·	·	PUNCT
fuelectenerg-1427	255	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	255	6	,	,	PUNCT
fuelectenerg-1427	255	7	.	.	PUNCT
fuelectenerg-1427	255	8	.	.	PUNCT
fuelectenerg-1427	255	9	.	.	PUNCT
fuelectenerg-1427	256	1	,	,	PUNCT
fuelectenerg-1427	256	2	xn	xn	X
fuelectenerg-1427	256	3	)	)	PUNCT
fuelectenerg-1427	257	1	=	=	PUNCT
fuelectenerg-1427	257	2	[	[	PUNCT
fuelectenerg-1427	257	3	1	1	NUM
fuelectenerg-1427	257	4	x̄1	x̄1	NOUN
fuelectenerg-1427	257	5	]	]	PUNCT
fuelectenerg-1427	258	1	[	[	PUNCT
fuelectenerg-1427	258	2	0	0	NUM
fuelectenerg-1427	258	3	1	1	NUM
fuelectenerg-1427	258	4	1	1	NUM
fuelectenerg-1427	258	5	1	1	NUM
fuelectenerg-1427	258	6	]	]	PUNCT
fuelectenerg-1427	258	7	[	[	PUNCT
fuelectenerg-1427	258	8	f0	f0	PROPN
fuelectenerg-1427	258	9	f1	f1	NOUN
fuelectenerg-1427	258	10	]	]	PUNCT
fuelectenerg-1427	258	11	,	,	PUNCT
fuelectenerg-1427	258	12	(	(	PUNCT
fuelectenerg-1427	258	13	3	3	X
fuelectenerg-1427	258	14	)	)	PUNCT
fuelectenerg-1427	258	15	where	where	SCONJ
fuelectenerg-1427	258	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1427	258	17	,	,	PUNCT
fuelectenerg-1427	258	18	.	.	PUNCT
fuelectenerg-1427	258	19	.	.	PUNCT
fuelectenerg-1427	258	20	.	.	PUNCT
fuelectenerg-1427	259	1	,	,	PUNCT
fuelectenerg-1427	259	2	xn	xn	X
fuelectenerg-1427	259	3	)	)	PUNCT
fuelectenerg-1427	259	4	=	=	SYM
fuelectenerg-1427	259	5	f	f	PROPN
fuelectenerg-1427	259	6	(	(	PUNCT
fuelectenerg-1427	259	7	0,x2	0,x2	NOUN
fuelectenerg-1427	259	8	,	,	PUNCT
fuelectenerg-1427	259	9	.	.	PUNCT
fuelectenerg-1427	259	10	.	.	PUNCT
fuelectenerg-1427	259	11	.	.	PUNCT
fuelectenerg-1427	260	1	,	,	PUNCT
fuelectenerg-1427	260	2	xn	xn	X
fuelectenerg-1427	260	3	)	)	PUNCT
fuelectenerg-1427	260	4	=	=	SYM
fuelectenerg-1427	260	5	f0	f0	PROPN
fuelectenerg-1427	260	6	is	be	AUX
fuelectenerg-1427	260	7	the	the	DET
fuelectenerg-1427	260	8	negative	negative	ADJ
fuelectenerg-1427	260	9	cofactor	cofactor	NOUN
fuelectenerg-1427	260	10	of	of	ADP
fuelectenerg-1427	260	11	variable	variable	ADJ
fuelectenerg-1427	260	12	x1	x1	PROPN
fuelectenerg-1427	260	13	,	,	PUNCT
fuelectenerg-1427	260	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1427	260	15	,	,	PUNCT
fuelectenerg-1427	260	16	.	.	PUNCT
fuelectenerg-1427	260	17	.	.	PUNCT
fuelectenerg-1427	261	1	.	.	PUNCT
fuelectenerg-1427	262	1	,	,	PUNCT
fuelectenerg-1427	262	2	xn	xn	X
fuelectenerg-1427	262	3	)	)	PUNCT
fuelectenerg-1427	262	4	=	=	SYM
fuelectenerg-1427	262	5	f	f	PROPN
fuelectenerg-1427	262	6	(	(	PUNCT
fuelectenerg-1427	262	7	1,x2	1,x2	NUM
fuelectenerg-1427	262	8	,	,	PUNCT
fuelectenerg-1427	262	9	.	.	PUNCT
fuelectenerg-1427	262	10	.	.	PUNCT
fuelectenerg-1427	262	11	.	.	PUNCT
fuelectenerg-1427	263	1	,	,	PUNCT
fuelectenerg-1427	263	2	xn	xn	X
fuelectenerg-1427	263	3	)	)	PUNCT
fuelectenerg-1427	263	4	=	=	SYM
fuelectenerg-1427	263	5	f1	f1	NOUN
fuelectenerg-1427	263	6	is	be	AUX
fuelectenerg-1427	263	7	the	the	DET
fuelectenerg-1427	263	8	positive	positive	ADJ
fuelectenerg-1427	263	9	cofactor	cofactor	NOUN
fuelectenerg-1427	263	10	of	of	ADP
fuelectenerg-1427	263	11	variable	variable	NOUN
fuelectenerg-1427	263	12	x1	x1	PROPN
fuelectenerg-1427	263	13	,	,	PUNCT
fuelectenerg-1427	263	14	and	and	CCONJ
fuelectenerg-1427	263	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1427	263	16	,	,	PUNCT
fuelectenerg-1427	263	17	.	.	PUNCT
fuelectenerg-1427	263	18	.	.	PUNCT
fuelectenerg-1427	264	1	.	.	PUNCT
fuelectenerg-1427	265	1	,	,	PUNCT
fuelectenerg-1427	265	2	xn	xn	X
fuelectenerg-1427	265	3	)	)	PUNCT
fuelectenerg-1427	265	4	=	=	SYM
fuelectenerg-1427	265	5	f	f	PROPN
fuelectenerg-1427	265	6	(	(	PUNCT
fuelectenerg-1427	265	7	0,x2	0,x2	NOUN
fuelectenerg-1427	265	8	,	,	PUNCT
fuelectenerg-1427	265	9	.	.	PUNCT
fuelectenerg-1427	265	10	.	.	PUNCT
fuelectenerg-1427	265	11	.	.	PUNCT
fuelectenerg-1427	266	1	,	,	PUNCT
fuelectenerg-1427	266	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1427	266	3	f	f	PROPN
fuelectenerg-1427	266	4	(	(	PUNCT
fuelectenerg-1427	266	5	1,x2	1,x2	NUM
fuelectenerg-1427	266	6	,	,	PUNCT
fuelectenerg-1427	266	7	.	.	PUNCT
fuelectenerg-1427	266	8	.	.	PUNCT
fuelectenerg-1427	266	9	.	.	PUNCT
fuelectenerg-1427	267	1	,	,	PUNCT
fuelectenerg-1427	267	2	xn	xn	X
fuelectenerg-1427	267	3	)	)	PUNCT
fuelectenerg-1427	267	4	=	=	SYM
fuelectenerg-1427	267	5	f0	f0	PROPN
fuelectenerg-1427	267	6	⊕	⊕	PROPN
fuelectenerg-1427	267	7	f1	f1	NOUN
fuelectenerg-1427	267	8	.	.	PUNCT
fuelectenerg-1427	268	1	in	in	ADP
fuelectenerg-1427	268	2	addition	addition	NOUN
fuelectenerg-1427	268	3	,	,	PUNCT
fuelectenerg-1427	268	4	an	an	DET
fuelectenerg-1427	268	5	arbitrary	arbitrary	ADJ
fuelectenerg-1427	268	6	n	n	CCONJ
fuelectenerg-1427	268	7	-	-	PUNCT
fuelectenerg-1427	268	8	variable	variable	ADJ
fuelectenerg-1427	268	9	function	function	NOUN
fuelectenerg-1427	268	10	f	f	PROPN
fuelectenerg-1427	268	11	(	(	PUNCT
fuelectenerg-1427	268	12	x1	x1	PROPN
fuelectenerg-1427	268	13	,	,	PUNCT
fuelectenerg-1427	268	14	.	.	PUNCT
fuelectenerg-1427	268	15	.	.	PUNCT
fuelectenerg-1427	268	16	.	.	PUNCT
fuelectenerg-1427	269	1	,	,	PUNCT
fuelectenerg-1427	269	2	xn	xn	X
fuelectenerg-1427	269	3	)	)	PUNCT
fuelectenerg-1427	269	4	can	can	AUX
fuelectenerg-1427	269	5	be	be	AUX
fuelectenerg-1427	269	6	represented	represent	VERB
fuelectenerg-1427	269	7	using	use	VERB
fuelectenerg-1427	269	8	pprm	pprm	ADJ
fuelectenerg-1427	269	9	expansion	expansion	NOUN
fuelectenerg-1427	269	10	as	as	ADP
fuelectenerg-1427	269	11	[	[	X
fuelectenerg-1427	269	12	2	2	NUM
fuelectenerg-1427	269	13	,	,	PUNCT
fuelectenerg-1427	269	14	31	31	NUM
fuelectenerg-1427	269	15	]	]	SYM
fuelectenerg-1427	269	16	:	:	PUNCT
fuelectenerg-1427	269	17	f	f	X
fuelectenerg-1427	269	18	(	(	PUNCT
fuelectenerg-1427	269	19	x1,x2	x1,x2	PROPN
fuelectenerg-1427	269	20	,	,	PUNCT
fuelectenerg-1427	269	21	.	.	PUNCT
fuelectenerg-1427	269	22	.	.	PUNCT
fuelectenerg-1427	269	23	.	.	PUNCT
fuelectenerg-1427	270	1	,	,	PUNCT
fuelectenerg-1427	270	2	xn	xn	X
fuelectenerg-1427	270	3	)	)	PUNCT
fuelectenerg-1427	271	1	=	=	PROPN
fuelectenerg-1427	271	2	a0	a0	PROPN
fuelectenerg-1427	271	3	⊕	⊕	PROPN
fuelectenerg-1427	271	4	a1x1	a1x1	PROPN
fuelectenerg-1427	271	5	⊕	⊕	PROPN
fuelectenerg-1427	271	6	.	.	PUNCT
fuelectenerg-1427	271	7	.	.	PUNCT
fuelectenerg-1427	272	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1427	272	2	⊕a12x1x2	⊕a12x1x2	X
fuelectenerg-1427	272	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1427	272	4	⊕an−1,nxn−1xn⊕	⊕an−1,nxn−1xn⊕	ADJ
fuelectenerg-1427	272	5	.	.	PUNCT
fuelectenerg-1427	272	6	.	.	PUNCT
fuelectenerg-1427	273	1	.⊕	.⊕	PROPN
fuelectenerg-1427	273	2	a12	a12	PROPN
fuelectenerg-1427	273	3	...	...	PUNCT
fuelectenerg-1427	273	4	nx1x2	nx1x2	X
fuelectenerg-1427	273	5	.	.	PUNCT
fuelectenerg-1427	273	6	.	.	PUNCT
fuelectenerg-1427	274	1	.xn	.xn	PROPN
fuelectenerg-1427	274	2	.	.	PUNCT
fuelectenerg-1427	275	1	(	(	PUNCT
fuelectenerg-1427	275	2	4	4	X
fuelectenerg-1427	275	3	)	)	PUNCT
fuelectenerg-1427	275	4	for	for	ADP
fuelectenerg-1427	275	5	each	each	DET
fuelectenerg-1427	275	6	function	function	NOUN
fuelectenerg-1427	275	7	f	f	PROPN
fuelectenerg-1427	275	8	,	,	PUNCT
fuelectenerg-1427	275	9	the	the	DET
fuelectenerg-1427	275	10	coefficients	coefficient	NOUN
fuelectenerg-1427	275	11	ai	ai	VERB
fuelectenerg-1427	275	12	in	in	ADP
fuelectenerg-1427	275	13	equation	equation	NOUN
fuelectenerg-1427	275	14	(	(	PUNCT
fuelectenerg-1427	275	15	4	4	X
fuelectenerg-1427	275	16	)	)	PUNCT
fuelectenerg-1427	275	17	are	be	AUX
fuelectenerg-1427	275	18	determined	determine	VERB
fuelectenerg-1427	275	19	uniquely	uniquely	ADV
fuelectenerg-1427	275	20	,	,	PUNCT
fuelectenerg-1427	275	21	so	so	ADV
fuelectenerg-1427	275	22	pprm	pprm	ADJ
fuelectenerg-1427	275	23	is	be	AUX
fuelectenerg-1427	275	24	a	a	DET
fuelectenerg-1427	275	25	canonical	canonical	ADJ
fuelectenerg-1427	275	26	form	form	NOUN
fuelectenerg-1427	275	27	.	.	PUNCT
fuelectenerg-1427	276	1	for	for	ADP
fuelectenerg-1427	276	2	example	example	NOUN
fuelectenerg-1427	276	3	,	,	PUNCT
fuelectenerg-1427	276	4	if	if	SCONJ
fuelectenerg-1427	276	5	we	we	PRON
fuelectenerg-1427	276	6	use	use	VERB
fuelectenerg-1427	276	7	either	either	CCONJ
fuelectenerg-1427	276	8	only	only	ADV
fuelectenerg-1427	276	9	the	the	DET
fuelectenerg-1427	276	10	positive	positive	ADJ
fuelectenerg-1427	276	11	literal	literal	NOUN
fuelectenerg-1427	276	12	or	or	CCONJ
fuelectenerg-1427	276	13	only	only	ADV
fuelectenerg-1427	276	14	the	the	DET
fuelectenerg-1427	276	15	negative	negative	ADJ
fuelectenerg-1427	276	16	literal	literal	NOUN
fuelectenerg-1427	276	17	for	for	ADP
fuelectenerg-1427	276	18	each	each	DET
fuelectenerg-1427	276	19	variable	variable	NOUN
fuelectenerg-1427	276	20	in	in	ADP
fuelectenerg-1427	276	21	equation	equation	NOUN
fuelectenerg-1427	276	22	(	(	PUNCT
fuelectenerg-1427	276	23	4	4	X
fuelectenerg-1427	276	24	)	)	PUNCT
fuelectenerg-1427	276	25	we	we	PRON
fuelectenerg-1427	276	26	obtain	obtain	VERB
fuelectenerg-1427	276	27	the	the	DET
fuelectenerg-1427	276	28	fixed	fix	VERB
fuelectenerg-1427	276	29	polarity	polarity	NOUN
fuelectenerg-1427	276	30	reed	reed	NOUN
fuelectenerg-1427	276	31	-	-	PUNCT
fuelectenerg-1427	276	32	muller	muller	NOUN
fuelectenerg-1427	276	33	(	(	PUNCT
fuelectenerg-1427	276	34	fprm	fprm	PROPN
fuelectenerg-1427	276	35	)	)	PUNCT
fuelectenerg-1427	276	36	form	form	NOUN
fuelectenerg-1427	276	37	.	.	PUNCT
fuelectenerg-1427	277	1	the	the	DET
fuelectenerg-1427	277	2	good	good	ADJ
fuelectenerg-1427	277	3	selection	selection	NOUN
fuelectenerg-1427	277	4	of	of	ADP
fuelectenerg-1427	277	5	different	different	ADJ
fuelectenerg-1427	277	6	permutations	permutation	NOUN
fuelectenerg-1427	277	7	using	use	VERB
fuelectenerg-1427	277	8	shannon	shannon	PROPN
fuelectenerg-1427	277	9	and	and	CCONJ
fuelectenerg-1427	277	10	davio	davio	NOUN
fuelectenerg-1427	277	11	expansions	expansion	NOUN
fuelectenerg-1427	277	12	like	like	ADP
fuelectenerg-1427	277	13	other	other	ADJ
fuelectenerg-1427	277	14	expansions	expansion	NOUN
fuelectenerg-1427	277	15	such	such	ADJ
fuelectenerg-1427	277	16	as	as	ADP
fuelectenerg-1427	277	17	walsh	walsh	NOUN
fuelectenerg-1427	277	18	and	and	CCONJ
fuelectenerg-1427	277	19	arithmetic	arithmetic	ADJ
fuelectenerg-1427	277	20	expansions	expansion	NOUN
fuelectenerg-1427	277	21	as	as	ADP
fuelectenerg-1427	277	22	internal	internal	ADJ
fuelectenerg-1427	277	23	nodes	node	NOUN
fuelectenerg-1427	277	24	in	in	ADP
fuelectenerg-1427	277	25	decision	decision	NOUN
fuelectenerg-1427	277	26	trees	tree	NOUN
fuelectenerg-1427	277	27	(	(	PUNCT
fuelectenerg-1427	277	28	dts	dts	NOUN
fuelectenerg-1427	277	29	)	)	PUNCT
fuelectenerg-1427	277	30	and	and	CCONJ
fuelectenerg-1427	277	31	diagrams	diagram	NOUN
fuelectenerg-1427	277	32	(	(	PUNCT
fuelectenerg-1427	277	33	dds	dds	PROPN
fuelectenerg-1427	277	34	)	)	PUNCT
fuelectenerg-1427	277	35	will	will	AUX
fuelectenerg-1427	277	36	result	result	VERB
fuelectenerg-1427	277	37	in	in	ADP
fuelectenerg-1427	277	38	dts	dts	NOUN
fuelectenerg-1427	277	39	and	and	CCONJ
fuelectenerg-1427	277	40	dds	dds	PROPN
fuelectenerg-1427	277	41	that	that	PRON
fuelectenerg-1427	277	42	represent	represent	VERB
fuelectenerg-1427	277	43	the	the	DET
fuelectenerg-1427	277	44	corresponding	corresponding	ADJ
fuelectenerg-1427	277	45	logic	logic	NOUN
fuelectenerg-1427	277	46	functions	function	NOUN
fuelectenerg-1427	277	47	with	with	ADP
fuelectenerg-1427	277	48	smaller	small	ADJ
fuelectenerg-1427	277	49	sizes	size	NOUN
fuelectenerg-1427	277	50	in	in	ADP
fuelectenerg-1427	277	51	terms	term	NOUN
fuelectenerg-1427	277	52	of	of	ADP
fuelectenerg-1427	277	53	the	the	DET
fuelectenerg-1427	277	54	total	total	ADJ
fuelectenerg-1427	277	55	number	number	NOUN
fuelectenerg-1427	277	56	of	of	ADP
fuelectenerg-1427	277	57	hierarchical	hierarchical	ADJ
fuelectenerg-1427	277	58	levels	level	NOUN
fuelectenerg-1427	277	59	used	use	VERB
fuelectenerg-1427	277	60	,	,	PUNCT
fuelectenerg-1427	277	61	and	and	CCONJ
fuelectenerg-1427	277	62	the	the	DET
fuelectenerg-1427	277	63	total	total	ADJ
fuelectenerg-1427	277	64	number	number	NOUN
fuelectenerg-1427	277	65	of	of	ADP
fuelectenerg-1427	277	66	internal	internal	ADJ
fuelectenerg-1427	277	67	nodes	node	NOUN
fuelectenerg-1427	277	68	needed	need	VERB
fuelectenerg-1427	277	69	.	.	PUNCT
fuelectenerg-1427	278	1	in	in	ADP
fuelectenerg-1427	278	2	general	general	ADJ
fuelectenerg-1427	278	3	,	,	PUNCT
fuelectenerg-1427	278	4	a	a	DET
fuelectenerg-1427	278	5	literal	literal	NOUN
fuelectenerg-1427	278	6	can	can	AUX
fuelectenerg-1427	278	7	be	be	AUX
fuelectenerg-1427	278	8	defined	define	VERB
fuelectenerg-1427	278	9	as	as	ADP
fuelectenerg-1427	278	10	any	any	DET
fuelectenerg-1427	278	11	function	function	NOUN
fuelectenerg-1427	278	12	of	of	ADP
fuelectenerg-1427	278	13	a	a	DET
fuelectenerg-1427	278	14	single	single	ADJ
fuelectenerg-1427	278	15	variable	variable	NOUN
fuelectenerg-1427	278	16	.	.	PUNCT
fuelectenerg-1427	279	1	basis	basis	NOUN
fuelectenerg-1427	279	2	functions	function	NOUN
fuelectenerg-1427	279	3	in	in	ADP
fuelectenerg-1427	279	4	the	the	DET
fuelectenerg-1427	279	5	general	general	ADJ
fuelectenerg-1427	279	6	case	case	NOUN
fuelectenerg-1427	279	7	of	of	ADP
fuelectenerg-1427	279	8	multiple	multiple	ADV
fuelectenerg-1427	279	9	-	-	PUNCT
fuelectenerg-1427	279	10	valued	value	VERB
fuelectenerg-1427	279	11	expansions	expansion	NOUN
fuelectenerg-1427	279	12	are	be	AUX
fuelectenerg-1427	279	13	constructed	construct	VERB
fuelectenerg-1427	279	14	using	use	VERB
fuelectenerg-1427	279	15	these	these	DET
fuelectenerg-1427	279	16	103	103	NUM
fuelectenerg-1427	280	1	[	[	SYM
fuelectenerg-1427	280	2	1	1	NUM
fuelectenerg-1427	280	3	,	,	PUNCT
fuelectenerg-1427	280	4	17	17	NUM
fuelectenerg-1427	280	5	]	]	SYM
fuelectenerg-1427	280	6	:	:	PUNCT
fuelectenerg-1427	280	7	52	52	NUM
fuelectenerg-1427	280	8	a.	a.	NOUN
fuelectenerg-1427	280	9	n.	n.	PROPN
fuelectenerg-1427	280	10	al	al	PROPN
fuelectenerg-1427	280	11	-	-	PUNCT
fuelectenerg-1427	280	12	rabadi	rabadi	VERB
fuelectenerg-1427	280	13	an	an	DET
fuelectenerg-1427	280	14	extended	extended	ADJ
fuelectenerg-1427	280	15	green	green	ADJ
fuelectenerg-1427	280	16	sasao	sasao	PROPN
fuelectenerg-1427	280	17	hierarchy	hierarchy	NOUN
fuelectenerg-1427	280	18	of	of	ADP
fuelectenerg-1427	280	19	canonical	canonical	ADJ
fuelectenerg-1427	280	20	ternary	ternary	ADJ
fuelectenerg-1427	280	21	galois	galois	NOUN
fuelectenerg-1427	280	22	forms	form	NOUN
fuelectenerg-1427	280	23	and	and	CCONJ
fuelectenerg-1427	280	24	universal	universal	ADJ
fuelectenerg-1427	280	25	logic	logic	NOUN
fuelectenerg-1427	280	26	modules	module	NOUN
fuelectenerg-1427	280	27	53	53	NUM
fuelectenerg-1427	280	28	an	an	DET
fuelectenerg-1427	280	29	extended	extend	VERB
fuelectenerg-1427	280	30	green	green	ADJ
fuelectenerg-1427	280	31	sasao	sasao	PROPN
fuelectenerg-1427	280	32	hierarchy	hierarchy	NOUN
fuelectenerg-1427	280	33	of	of	ADP
fuelectenerg-1427	280	34	canonical	canonical	ADJ
fuelectenerg-1427	280	35	ternary	ternary	ADJ
fuelectenerg-1427	280	36	galois	galois	NOUN
fuelectenerg-1427	280	37	forms	form	NOUN
fuelectenerg-1427	280	38	...	...	PUNCT
fuelectenerg-1427	280	39	literals	literal	NOUN
fuelectenerg-1427	280	40	.	.	PUNCT
fuelectenerg-1427	281	1	galois	galois	PROPN
fuelectenerg-1427	281	2	field	field	NOUN
fuelectenerg-1427	281	3	sum	sum	NOUN
fuelectenerg-1427	281	4	-	-	PUNCT
fuelectenerg-1427	281	5	of	of	ADP
fuelectenerg-1427	281	6	-	-	PUNCT
fuelectenerg-1427	281	7	products	product	NOUN
fuelectenerg-1427	281	8	expansions	expansion	NOUN
fuelectenerg-1427	281	9	can	can	AUX
fuelectenerg-1427	281	10	be	be	AUX
fuelectenerg-1427	281	11	performed	perform	VERB
fuelectenerg-1427	281	12	utilizing	utilize	VERB
fuelectenerg-1427	281	13	variety	variety	NOUN
fuelectenerg-1427	281	14	uses	use	NOUN
fuelectenerg-1427	281	15	of	of	ADP
fuelectenerg-1427	281	16	literals	literal	NOUN
fuelectenerg-1427	281	17	.	.	PUNCT
fuelectenerg-1427	282	1	for	for	ADP
fuelectenerg-1427	282	2	example	example	NOUN
fuelectenerg-1427	282	3	,	,	PUNCT
fuelectenerg-1427	282	4	one	one	PRON
fuelectenerg-1427	282	5	can	can	AUX
fuelectenerg-1427	282	6	use	use	VERB
fuelectenerg-1427	282	7	k	k	ADV
fuelectenerg-1427	282	8	-	-	PUNCT
fuelectenerg-1427	282	9	reduced	reduce	VERB
fuelectenerg-1427	282	10	post	post	NOUN
fuelectenerg-1427	282	11	literal	literal	ADJ
fuelectenerg-1427	282	12	(	(	PUNCT
fuelectenerg-1427	282	13	k	k	X
fuelectenerg-1427	282	14	-	-	NOUN
fuelectenerg-1427	282	15	rpl	rpl	NOUN
fuelectenerg-1427	282	16	)	)	PUNCT
fuelectenerg-1427	282	17	to	to	PART
fuelectenerg-1427	282	18	produce	produce	VERB
fuelectenerg-1427	282	19	k	k	ADJ
fuelectenerg-1427	282	20	-	-	ADJ
fuelectenerg-1427	282	21	rpl	rpl	PROPN
fuelectenerg-1427	282	22	gfsop	gfsop	NOUN
fuelectenerg-1427	282	23	,	,	PUNCT
fuelectenerg-1427	282	24	generalized	generalize	VERB
fuelectenerg-1427	282	25	(	(	PUNCT
fuelectenerg-1427	282	26	post	post	ADJ
fuelectenerg-1427	282	27	)	)	PUNCT
fuelectenerg-1427	282	28	literal	literal	ADJ
fuelectenerg-1427	282	29	(	(	PUNCT
fuelectenerg-1427	282	30	gl	gl	NOUN
fuelectenerg-1427	282	31	)	)	PUNCT
fuelectenerg-1427	282	32	to	to	PART
fuelectenerg-1427	282	33	produce	produce	VERB
fuelectenerg-1427	282	34	gl	gl	NOUN
fuelectenerg-1427	282	35	gfsop	gfsop	PROPN
fuelectenerg-1427	282	36	,	,	PUNCT
fuelectenerg-1427	282	37	and	and	CCONJ
fuelectenerg-1427	282	38	universal	universal	ADJ
fuelectenerg-1427	282	39	literal	literal	ADJ
fuelectenerg-1427	282	40	(	(	PUNCT
fuelectenerg-1427	282	41	ul	ul	INTJ
fuelectenerg-1427	282	42	)	)	PUNCT
fuelectenerg-1427	282	43	to	to	PART
fuelectenerg-1427	282	44	produce	produce	VERB
fuelectenerg-1427	282	45	ul	ul	INTJ
fuelectenerg-1427	282	46	gfsop	gfsop	PROPN
fuelectenerg-1427	282	47	.	.	PUNCT
fuelectenerg-1427	282	48	example	example	NOUN
fuelectenerg-1427	283	1	1	1	NUM
fuelectenerg-1427	283	2	.	.	PUNCT
fuelectenerg-1427	283	3	figure	figure	NOUN
fuelectenerg-1427	283	4	2	2	NUM
fuelectenerg-1427	283	5	demonstrates	demonstrate	VERB
fuelectenerg-1427	283	6	several	several	ADJ
fuelectenerg-1427	283	7	literal	literal	ADJ
fuelectenerg-1427	283	8	types	type	NOUN
fuelectenerg-1427	283	9	,	,	PUNCT
fuelectenerg-1427	283	10	where	where	SCONJ
fuelectenerg-1427	283	11	one	one	NUM
fuelectenerg-1427	283	12	proceeds	proceed	VERB
fuelectenerg-1427	283	13	from	from	ADP
fuelectenerg-1427	283	14	the	the	DET
fuelectenerg-1427	283	15	simplest	simple	ADJ
fuelectenerg-1427	283	16	literal	literal	NOUN
fuelectenerg-1427	283	17	in	in	ADP
fuelectenerg-1427	283	18	figure	figure	NOUN
fuelectenerg-1427	283	19	2(a	2(a	NUM
fuelectenerg-1427	283	20	)	)	PUNCT
fuelectenerg-1427	283	21	(	(	PUNCT
fuelectenerg-1427	283	22	i.e.	i.e.	X
fuelectenerg-1427	283	23	,	,	PUNCT
fuelectenerg-1427	283	24	rpl	rpl	PROPN
fuelectenerg-1427	283	25	)	)	PUNCT
fuelectenerg-1427	283	26	to	to	ADP
fuelectenerg-1427	283	27	the	the	DET
fuelectenerg-1427	283	28	most	most	ADV
fuelectenerg-1427	283	29	complex	complex	ADJ
fuelectenerg-1427	283	30	universal	universal	ADJ
fuelectenerg-1427	283	31	literal	literal	NOUN
fuelectenerg-1427	283	32	in	in	ADP
fuelectenerg-1427	283	33	figure	figure	NOUN
fuelectenerg-1427	283	34	2(c	2(c	NUM
fuelectenerg-1427	283	35	)	)	PUNCT
fuelectenerg-1427	283	36	.	.	PUNCT
fuelectenerg-1427	284	1	for	for	ADP
fuelectenerg-1427	284	2	rpl	rpl	NOUN
fuelectenerg-1427	284	3	in	in	ADP
fuelectenerg-1427	284	4	figure	figure	NOUN
fuelectenerg-1427	284	5	2(a	2(a	NUM
fuelectenerg-1427	284	6	)	)	PUNCT
fuelectenerg-1427	284	7	,	,	PUNCT
fuelectenerg-1427	284	8	a	a	DET
fuelectenerg-1427	284	9	value	value	NOUN
fuelectenerg-1427	284	10	k	k	NOUN
fuelectenerg-1427	284	11	is	be	AUX
fuelectenerg-1427	284	12	produced	produce	VERB
fuelectenerg-1427	284	13	by	by	ADP
fuelectenerg-1427	284	14	the	the	DET
fuelectenerg-1427	284	15	literal	literal	NOUN
fuelectenerg-1427	284	16	when	when	SCONJ
fuelectenerg-1427	284	17	the	the	DET
fuelectenerg-1427	284	18	value	value	NOUN
fuelectenerg-1427	284	19	of	of	ADP
fuelectenerg-1427	284	20	the	the	DET
fuelectenerg-1427	284	21	variable	variable	NOUN
fuelectenerg-1427	284	22	is	be	AUX
fuelectenerg-1427	284	23	equal	equal	ADJ
fuelectenerg-1427	284	24	to	to	ADP
fuelectenerg-1427	284	25	a	a	DET
fuelectenerg-1427	284	26	specific	specific	ADJ
fuelectenerg-1427	284	27	state	state	NOUN
fuelectenerg-1427	284	28	,	,	PUNCT
fuelectenerg-1427	284	29	and	and	CCONJ
fuelectenerg-1427	284	30	in	in	ADP
fuelectenerg-1427	284	31	this	this	DET
fuelectenerg-1427	284	32	particular	particular	ADJ
fuelectenerg-1427	284	33	example	example	NOUN
fuelectenerg-1427	284	34	a	a	DET
fuelectenerg-1427	284	35	value	value	NOUN
fuelectenerg-1427	284	36	of	of	ADP
fuelectenerg-1427	284	37	k	k	PROPN
fuelectenerg-1427	284	38	=	=	SYM
fuelectenerg-1427	284	39	1	1	NUM
fuelectenerg-1427	284	40	is	be	AUX
fuelectenerg-1427	284	41	generated	generate	VERB
fuelectenerg-1427	284	42	by	by	ADP
fuelectenerg-1427	284	43	the	the	DET
fuelectenerg-1427	284	44	1	1	NUM
fuelectenerg-1427	284	45	-	-	PUNCT
fuelectenerg-1427	284	46	rpl	rpl	NOUN
fuelectenerg-1427	284	47	when	when	SCONJ
fuelectenerg-1427	284	48	the	the	DET
fuelectenerg-1427	284	49	value	value	NOUN
fuelectenerg-1427	284	50	of	of	ADP
fuelectenerg-1427	284	51	variable	variable	NOUN
fuelectenerg-1427	284	52	x	x	PUNCT
fuelectenerg-1427	284	53	is	be	AUX
fuelectenerg-1427	284	54	equal	equal	ADJ
fuelectenerg-1427	284	55	to	to	ADP
fuelectenerg-1427	284	56	certain	certain	ADJ
fuelectenerg-1427	284	57	state	state	NOUN
fuelectenerg-1427	284	58	where	where	SCONJ
fuelectenerg-1427	284	59	this	this	DET
fuelectenerg-1427	284	60	state	state	NOUN
fuelectenerg-1427	284	61	here	here	ADV
fuelectenerg-1427	284	62	equals	equal	VERB
fuelectenerg-1427	284	63	to	to	ADP
fuelectenerg-1427	284	64	one	one	NUM
fuelectenerg-1427	284	65	.	.	PUNCT
fuelectenerg-1427	285	1	the	the	DET
fuelectenerg-1427	285	2	gl	gl	PROPN
fuelectenerg-1427	285	3	in	in	ADP
fuelectenerg-1427	285	4	figure	figure	NOUN
fuelectenerg-1427	285	5	2(b	2(b	NUM
fuelectenerg-1427	285	6	)	)	PUNCT
fuelectenerg-1427	285	7	produces	produce	VERB
fuelectenerg-1427	285	8	a	a	DET
fuelectenerg-1427	285	9	value	value	NOUN
fuelectenerg-1427	285	10	of	of	ADP
fuelectenerg-1427	285	11	radix	radix	NOUN
fuelectenerg-1427	285	12	for	for	ADP
fuelectenerg-1427	285	13	a	a	DET
fuelectenerg-1427	285	14	set	set	NOUN
fuelectenerg-1427	285	15	of	of	ADP
fuelectenerg-1427	285	16	distinct	distinct	ADJ
fuelectenerg-1427	285	17	states	state	NOUN
fuelectenerg-1427	285	18	.	.	PUNCT
fuelectenerg-1427	286	1	one	one	NUM
fuelectenerg-1427	286	2	notes	note	VERB
fuelectenerg-1427	286	3	that	that	SCONJ
fuelectenerg-1427	286	4	,	,	PUNCT
fuelectenerg-1427	286	5	in	in	ADP
fuelectenerg-1427	286	6	contrast	contrast	NOUN
fuelectenerg-1427	286	7	to	to	ADP
fuelectenerg-1427	286	8	the	the	DET
fuelectenerg-1427	286	9	other	other	ADJ
fuelectenerg-1427	286	10	literals	literal	NOUN
fuelectenerg-1427	286	11	,	,	PUNCT
fuelectenerg-1427	286	12	ul	ul	INTJ
fuelectenerg-1427	286	13	in	in	ADP
fuelectenerg-1427	286	14	figure	figure	NOUN
fuelectenerg-1427	286	15	2(c	2(c	NUM
fuelectenerg-1427	286	16	)	)	PUNCT
fuelectenerg-1427	286	17	can	can	AUX
fuelectenerg-1427	286	18	have	have	VERB
fuelectenerg-1427	286	19	any	any	DET
fuelectenerg-1427	286	20	value	value	NOUN
fuelectenerg-1427	286	21	of	of	ADP
fuelectenerg-1427	286	22	the	the	DET
fuelectenerg-1427	286	23	logic	logic	NOUN
fuelectenerg-1427	286	24	system	system	NOUN
fuelectenerg-1427	286	25	at	at	ADP
fuelectenerg-1427	286	26	distinct	distinct	ADJ
fuelectenerg-1427	286	27	states	state	NOUN
fuelectenerg-1427	286	28	,	,	PUNCT
fuelectenerg-1427	286	29	and	and	CCONJ
fuelectenerg-1427	286	30	thus	thus	ADV
fuelectenerg-1427	286	31	ul	ul	INTJ
fuelectenerg-1427	286	32	has	have	VERB
fuelectenerg-1427	286	33	the	the	DET
fuelectenerg-1427	286	34	highest	high	ADJ
fuelectenerg-1427	286	35	complexity	complexity	NOUN
fuelectenerg-1427	286	36	among	among	ADP
fuelectenerg-1427	286	37	the	the	DET
fuelectenerg-1427	286	38	different	different	ADJ
fuelectenerg-1427	286	39	types	type	NOUN
fuelectenerg-1427	286	40	of	of	ADP
fuelectenerg-1427	286	41	literals	literal	NOUN
fuelectenerg-1427	286	42	.	.	PUNCT
fuelectenerg-1427	287	1	0	0	NUM
fuelectenerg-1427	287	2	0	0	NUM
fuelectenerg-1427	288	1	01	01	NUM
fuelectenerg-1427	288	2	1	1	NUM
fuelectenerg-1427	288	3	1	1	NUM
fuelectenerg-1427	288	4	1	1	NUM
fuelectenerg-1427	288	5	1	1	NUM
fuelectenerg-1427	288	6	12	12	NUM
fuelectenerg-1427	288	7	2	2	NUM
fuelectenerg-1427	288	8	2	2	NUM
fuelectenerg-1427	288	9	2	2	NUM
fuelectenerg-1427	288	10	2	2	NUM
fuelectenerg-1427	288	11	23	23	NUM
fuelectenerg-1427	288	12	3	3	NUM
fuelectenerg-1427	288	13	3	3	NUM
fuelectenerg-1427	288	14	3	3	NUM
fuelectenerg-1427	288	15	3	3	NUM
fuelectenerg-1427	288	16	34	34	NUM
fuelectenerg-1427	288	17	4	4	NUM
fuelectenerg-1427	288	18	4	4	NUM
fuelectenerg-1427	288	19	4	4	NUM
fuelectenerg-1427	288	20	4	4	NUM
fuelectenerg-1427	288	21	4x	4x	NOUN
fuelectenerg-1427	288	22	x	x	SYM
fuelectenerg-1427	288	23	x	x	SYM
fuelectenerg-1427	288	24	1	1	NUM
fuelectenerg-1427	288	25	x	x	SYM
fuelectenerg-1427	288	26	l	l	NOUN
fuelectenerg-1427	288	27	(	(	PUNCT
fuelectenerg-1427	288	28	)	)	PUNCT
fuelectenerg-1427	288	29	{	{	PUNCT
fuelectenerg-1427	288	30	1,3	1,3	NUM
fuelectenerg-1427	288	31	}	}	PUNCT
fuelectenerg-1427	288	32	x	x	X
fuelectenerg-1427	288	33	l	l	NOUN
fuelectenerg-1427	288	34	(	(	PUNCT
fuelectenerg-1427	288	35	)	)	PUNCT
fuelectenerg-1427	288	36	<	<	X
fuelectenerg-1427	288	37	2,0,4,3,1	2,0,4,3,1	X
fuelectenerg-1427	288	38	>	>	X
fuelectenerg-1427	288	39	x	x	X
fuelectenerg-1427	288	40	(	(	PUNCT
fuelectenerg-1427	288	41	)	)	PUNCT
fuelectenerg-1427	288	42	a	a	DET
fuelectenerg-1427	288	43	(	(	PUNCT
fuelectenerg-1427	288	44	)	)	SYM
fuelectenerg-1427	288	45	b	b	NOUN
fuelectenerg-1427	288	46	(	(	PUNCT
fuelectenerg-1427	288	47	)	)	PUNCT
fuelectenerg-1427	288	48	c	c	NOUN
fuelectenerg-1427	288	49	figure	figure	NOUN
fuelectenerg-1427	288	50	2	2	NUM
fuelectenerg-1427	288	51	:	:	PUNCT
fuelectenerg-1427	288	52	an	an	DET
fuelectenerg-1427	288	53	illustrating	illustrate	VERB
fuelectenerg-1427	288	54	example	example	NOUN
fuelectenerg-1427	288	55	of	of	ADP
fuelectenerg-1427	288	56	the	the	DET
fuelectenerg-1427	288	57	different	different	ADJ
fuelectenerg-1427	288	58	types	type	NOUN
fuelectenerg-1427	288	59	of	of	ADP
fuelectenerg-1427	288	60	literals	literal	NOUN
fuelectenerg-1427	288	61	over	over	ADP
fuelectenerg-1427	288	62	an	an	DET
fuelectenerg-1427	288	63	arbitrary	arbitrary	ADJ
fuelectenerg-1427	288	64	five	five	NUM
fuelectenerg-1427	288	65	-	-	PUNCT
fuelectenerg-1427	288	66	radix	radix	NOUN
fuelectenerg-1427	288	67	logic	logic	NOUN
fuelectenerg-1427	288	68	:	:	PUNCT
fuelectenerg-1427	288	69	(	(	PUNCT
fuelectenerg-1427	288	70	a	a	X
fuelectenerg-1427	288	71	)	)	PUNCT
fuelectenerg-1427	288	72	1	1	NUM
fuelectenerg-1427	288	73	-	-	PUNCT
fuelectenerg-1427	288	74	reduced	reduce	VERB
fuelectenerg-1427	288	75	post	post	NOUN
fuelectenerg-1427	288	76	literal	literal	ADJ
fuelectenerg-1427	288	77	(	(	PUNCT
fuelectenerg-1427	288	78	1	1	NUM
fuelectenerg-1427	288	79	-	-	PUNCT
fuelectenerg-1427	288	80	rpl	rpl	NOUN
fuelectenerg-1427	288	81	)	)	PUNCT
fuelectenerg-1427	288	82	,	,	PUNCT
fuelectenerg-1427	288	83	(	(	PUNCT
fuelectenerg-1427	288	84	b	b	X
fuelectenerg-1427	288	85	)	)	PUNCT
fuelectenerg-1427	288	86	generalized	generalized	ADJ
fuelectenerg-1427	288	87	(	(	PUNCT
fuelectenerg-1427	288	88	post	post	ADJ
fuelectenerg-1427	288	89	)	)	PUNCT
fuelectenerg-1427	288	90	literal	literal	ADJ
fuelectenerg-1427	288	91	(	(	PUNCT
fuelectenerg-1427	288	92	gl	gl	NOUN
fuelectenerg-1427	288	93	)	)	PUNCT
fuelectenerg-1427	288	94	,	,	PUNCT
fuelectenerg-1427	288	95	and	and	CCONJ
fuelectenerg-1427	288	96	(	(	PUNCT
fuelectenerg-1427	288	97	c	c	X
fuelectenerg-1427	288	98	)	)	PUNCT
fuelectenerg-1427	288	99	universal	universal	ADJ
fuelectenerg-1427	288	100	literal	literal	ADJ
fuelectenerg-1427	288	101	(	(	PUNCT
fuelectenerg-1427	288	102	ul	ul	INTJ
fuelectenerg-1427	288	103	)	)	PUNCT
fuelectenerg-1427	288	104	.	.	PUNCT
fuelectenerg-1427	289	1	since	since	SCONJ
fuelectenerg-1427	289	2	k	k	PROPN
fuelectenerg-1427	289	3	-	-	PROPN
fuelectenerg-1427	289	4	rpl	rpl	PROPN
fuelectenerg-1427	289	5	gfsop	gfsop	NOUN
fuelectenerg-1427	289	6	is	be	AUX
fuelectenerg-1427	289	7	simpler	simple	ADJ
fuelectenerg-1427	289	8	from	from	ADP
fuelectenerg-1427	289	9	implementation	implementation	NOUN
fuelectenerg-1427	289	10	point	point	NOUN
fuelectenerg-1427	289	11	of	of	ADP
fuelectenerg-1427	289	12	view	view	NOUN
fuelectenerg-1427	289	13	than	than	ADP
fuelectenerg-1427	289	14	gl	gl	INTJ
fuelectenerg-1427	289	15	or	or	CCONJ
fuelectenerg-1427	289	16	ul	ul	INTJ
fuelectenerg-1427	289	17	,	,	PUNCT
fuelectenerg-1427	289	18	we	we	PRON
fuelectenerg-1427	289	19	will	will	AUX
fuelectenerg-1427	289	20	perform	perform	VERB
fuelectenerg-1427	289	21	all	all	DET
fuelectenerg-1427	289	22	the	the	DET
fuelectenerg-1427	289	23	gfsop	gfsop	NOUN
fuelectenerg-1427	289	24	expansions	expansion	NOUN
fuelectenerg-1427	289	25	utilizing	utilize	VERB
fuelectenerg-1427	289	26	the	the	DET
fuelectenerg-1427	289	27	1	1	NUM
fuelectenerg-1427	289	28	-	-	PUNCT
fuelectenerg-1427	289	29	rpl	rpl	NOUN
fuelectenerg-1427	289	30	gfsop	gfsop	NOUN
fuelectenerg-1427	289	31	.	.	PUNCT
fuelectenerg-1427	290	1	let	let	VERB
fuelectenerg-1427	290	2	us	we	PRON
fuelectenerg-1427	290	3	define	define	VERB
fuelectenerg-1427	290	4	1	1	NUM
fuelectenerg-1427	290	5	-	-	PUNCT
fuelectenerg-1427	290	6	rpl	rpl	NOUN
fuelectenerg-1427	290	7	[	[	X
fuelectenerg-1427	290	8	1	1	NUM
fuelectenerg-1427	290	9	,	,	PUNCT
fuelectenerg-1427	290	10	17	17	NUM
fuelectenerg-1427	290	11	]	]	PUNCT
fuelectenerg-1427	290	12	as	as	ADP
fuelectenerg-1427	290	13	:	:	PUNCT
fuelectenerg-1427	290	14	ix	ix	PROPN
fuelectenerg-1427	290	15	=	=	SYM
fuelectenerg-1427	290	16	1	1	NUM
fuelectenerg-1427	290	17	iff	iff	NOUN
fuelectenerg-1427	290	18	x	x	PROPN
fuelectenerg-1427	291	1	=	=	PUNCT
fuelectenerg-1427	292	1	i	i	PRON
fuelectenerg-1427	292	2	else	else	ADV
fuelectenerg-1427	292	3	ix	ix	ADP
fuelectenerg-1427	292	4	=	=	NOUN
fuelectenerg-1427	292	5	0	0	PROPN
fuelectenerg-1427	292	6	.	.	PUNCT
fuelectenerg-1427	293	1	(	(	PUNCT
fuelectenerg-1427	293	2	5	5	NUM
fuelectenerg-1427	293	3	)	)	PUNCT
fuelectenerg-1427	293	4	for	for	ADP
fuelectenerg-1427	293	5	example	example	NOUN
fuelectenerg-1427	293	6	{	{	PUNCT
fuelectenerg-1427	293	7	0x	0x	NOUN
fuelectenerg-1427	293	8	,	,	PUNCT
fuelectenerg-1427	293	9	1x	1x	NUM
fuelectenerg-1427	293	10	,	,	PUNCT
fuelectenerg-1427	293	11	2x	2x	NUM
fuelectenerg-1427	293	12	}	}	PUNCT
fuelectenerg-1427	293	13	are	be	AUX
fuelectenerg-1427	293	14	the	the	DET
fuelectenerg-1427	293	15	zero	zero	NUM
fuelectenerg-1427	293	16	,	,	PUNCT
fuelectenerg-1427	293	17	first	first	ADV
fuelectenerg-1427	293	18	,	,	PUNCT
fuelectenerg-1427	293	19	and	and	CCONJ
fuelectenerg-1427	293	20	second	second	ADJ
fuelectenerg-1427	293	21	polarities	polarity	NOUN
fuelectenerg-1427	293	22	of	of	ADP
fuelectenerg-1427	293	23	the	the	DET
fuelectenerg-1427	293	24	1	1	NUM
fuelectenerg-1427	293	25	-	-	PUNCT
fuelectenerg-1427	293	26	rpl	rpl	NOUN
fuelectenerg-1427	293	27	,	,	PUNCT
fuelectenerg-1427	293	28	respectively	respectively	ADV
fuelectenerg-1427	293	29	.	.	PUNCT
fuelectenerg-1427	294	1	also	also	ADV
fuelectenerg-1427	294	2	,	,	PUNCT
fuelectenerg-1427	294	3	let	let	VERB
fuelectenerg-1427	294	4	us	we	PRON
fuelectenerg-1427	294	5	define	define	VERB
fuelectenerg-1427	294	6	the	the	DET
fuelectenerg-1427	294	7	ternary	ternary	ADJ
fuelectenerg-1427	294	8	shifts	shift	NOUN
fuelectenerg-1427	294	9	over	over	ADP
fuelectenerg-1427	294	10	variable	variable	ADJ
fuelectenerg-1427	294	11	x	x	NOUN
fuelectenerg-1427	294	12	as	as	ADP
fuelectenerg-1427	294	13	{	{	PUNCT
fuelectenerg-1427	294	14	x	x	NOUN
fuelectenerg-1427	294	15	,	,	PUNCT
fuelectenerg-1427	294	16	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	294	17	}	}	PUNCT
fuelectenerg-1427	294	18	as	as	ADP
fuelectenerg-1427	294	19	the	the	DET
fuelectenerg-1427	294	20	zero	zero	NUM
fuelectenerg-1427	294	21	,	,	PUNCT
fuelectenerg-1427	294	22	first	first	ADJ
fuelectenerg-1427	294	23	and	and	CCONJ
fuelectenerg-1427	294	24	second	second	ADJ
fuelectenerg-1427	294	25	shifts	shift	NOUN
fuelectenerg-1427	294	26	of	of	ADP
fuelectenerg-1427	294	27	the	the	DET
fuelectenerg-1427	294	28	variable	variable	NOUN
fuelectenerg-1427	294	29	x	x	PUNCT
fuelectenerg-1427	294	30	respectively	respectively	ADV
fuelectenerg-1427	294	31	,	,	PUNCT
fuelectenerg-1427	294	32	i.e.	i.e.	X
fuelectenerg-1427	294	33	,	,	PUNCT
fuelectenerg-1427	294	34	x	x	SYM
fuelectenerg-1427	294	35	=	=	SYM
fuelectenerg-1427	294	36	x+	x+	PUNCT
fuelectenerg-1427	294	37	0	0	NUM
fuelectenerg-1427	294	38	,	,	PUNCT
fuelectenerg-1427	294	39	x′	x′	PROPN
fuelectenerg-1427	295	1	=	=	PUNCT
fuelectenerg-1427	295	2	x+	x+	SYM
fuelectenerg-1427	295	3	1	1	NUM
fuelectenerg-1427	295	4	and	and	CCONJ
fuelectenerg-1427	295	5	x′′	x′′	PROPN
fuelectenerg-1427	295	6	=	=	PUNCT
fuelectenerg-1427	295	7	x+	x+	PROPN
fuelectenerg-1427	295	8	2	2	NUM
fuelectenerg-1427	295	9	,	,	PUNCT
fuelectenerg-1427	295	10	and	and	CCONJ
fuelectenerg-1427	295	11	x	x	PRON
fuelectenerg-1427	295	12	can	can	AUX
fuelectenerg-1427	295	13	take	take	VERB
fuelectenerg-1427	295	14	any	any	DET
fuelectenerg-1427	295	15	value	value	NOUN
fuelectenerg-1427	295	16	in	in	ADP
fuelectenerg-1427	295	17	the	the	DET
fuelectenerg-1427	295	18	set	set	NOUN
fuelectenerg-1427	295	19	{	{	PUNCT
fuelectenerg-1427	295	20	0,1,2	0,1,2	NUM
fuelectenerg-1427	295	21	}	}	PUNCT
fuelectenerg-1427	295	22	.	.	PUNCT
fuelectenerg-1427	296	1	we	we	PRON
fuelectenerg-1427	296	2	chose	choose	VERB
fuelectenerg-1427	296	3	to	to	PART
fuelectenerg-1427	296	4	represent	represent	VERB
fuelectenerg-1427	296	5	the	the	DET
fuelectenerg-1427	296	6	1	1	NUM
fuelectenerg-1427	296	7	-	-	PUNCT
fuelectenerg-1427	296	8	reduced	reduce	VERB
fuelectenerg-1427	296	9	post	post	NOUN
fuelectenerg-1427	296	10	literals	literal	NOUN
fuelectenerg-1427	296	11	in	in	ADP
fuelectenerg-1427	296	12	terms	term	NOUN
fuelectenerg-1427	296	13	of	of	ADP
fuelectenerg-1427	296	14	shifts	shift	NOUN
fuelectenerg-1427	296	15	and	and	CCONJ
fuelectenerg-1427	296	16	powers	power	NOUN
fuelectenerg-1427	296	17	,	,	PUNCT
fuelectenerg-1427	296	18	among	among	ADP
fuelectenerg-1427	296	19	others	other	NOUN
fuelectenerg-1427	296	20	,	,	PUNCT
fuelectenerg-1427	296	21	because	because	SCONJ
fuelectenerg-1427	296	22	of	of	ADP
fuelectenerg-1427	296	23	the	the	DET
fuelectenerg-1427	296	24	ease	ease	NOUN
fuelectenerg-1427	296	25	of	of	ADP
fuelectenerg-1427	296	26	the	the	DET
fuelectenerg-1427	296	27	implementation	implementation	NOUN
fuelectenerg-1427	296	28	of	of	ADP
fuelectenerg-1427	296	29	powers	power	NOUN
fuelectenerg-1427	296	30	of	of	ADP
fuelectenerg-1427	296	31	shifted	shift	VERB
fuelectenerg-1427	296	32	variables	variable	NOUN
fuelectenerg-1427	296	33	in	in	ADP
fuelectenerg-1427	296	34	hardware	hardware	NOUN
fuelectenerg-1427	296	35	as	as	SCONJ
fuelectenerg-1427	296	36	will	will	AUX
fuelectenerg-1427	296	37	be	be	AUX
fuelectenerg-1427	296	38	seen	see	VERB
fuelectenerg-1427	296	39	in	in	ADP
fuelectenerg-1427	296	40	section	section	NOUN
fuelectenerg-1427	296	41	3	3	NUM
fuelectenerg-1427	296	42	within	within	ADP
fuelectenerg-1427	296	43	universal	universal	ADJ
fuelectenerg-1427	296	44	logic	logic	NOUN
fuelectenerg-1427	296	45	modules	module	NOUN
fuelectenerg-1427	296	46	(	(	PUNCT
fuelectenerg-1427	296	47	ulms	ulm	NOUN
fuelectenerg-1427	296	48	)	)	PUNCT
fuelectenerg-1427	296	49	for	for	ADP
fuelectenerg-1427	296	50	the	the	DET
fuelectenerg-1427	296	51	production	production	NOUN
fuelectenerg-1427	296	52	of	of	ADP
fuelectenerg-1427	296	53	rpl	rpl	NOUN
fuelectenerg-1427	296	54	.	.	PUNCT
fuelectenerg-1427	297	1	the	the	DET
fuelectenerg-1427	297	2	fundamental	fundamental	ADJ
fuelectenerg-1427	297	3	shannon	shannon	PROPN
fuelectenerg-1427	297	4	expansion	expansion	NOUN
fuelectenerg-1427	297	5	over	over	ADP
fuelectenerg-1427	297	6	gf(3	gf(3	PROPN
fuelectenerg-1427	297	7	)	)	PUNCT
fuelectenerg-1427	297	8	for	for	ADP
fuelectenerg-1427	297	9	a	a	DET
fuelectenerg-1427	297	10	ternary	ternary	ADJ
fuelectenerg-1427	297	11	function	function	NOUN
fuelectenerg-1427	297	12	with	with	ADP
fuelectenerg-1427	297	13	a	a	DET
fuelectenerg-1427	297	14	single	single	ADJ
fuelectenerg-1427	297	15	variable	variable	NOUN
fuelectenerg-1427	297	16	is	be	AUX
fuelectenerg-1427	297	17	shown	show	VERB
fuelectenerg-1427	297	18	in	in	ADP
fuelectenerg-1427	297	19	theorem	theorem	ADJ
fuelectenerg-1427	297	20	1	1	NUM
fuelectenerg-1427	297	21	.	.	PUNCT
fuelectenerg-1427	297	22	theorem	theorem	NOUN
fuelectenerg-1427	297	23	1	1	NUM
fuelectenerg-1427	297	24	.	.	PUNCT
fuelectenerg-1427	297	25	shannon	shannon	PROPN
fuelectenerg-1427	297	26	expansion	expansion	PROPN
fuelectenerg-1427	297	27	over	over	ADP
fuelectenerg-1427	297	28	gf(3	gf(3	PROPN
fuelectenerg-1427	297	29	)	)	PUNCT
fuelectenerg-1427	297	30	for	for	ADP
fuelectenerg-1427	297	31	a	a	DET
fuelectenerg-1427	297	32	function	function	NOUN
fuelectenerg-1427	297	33	with	with	ADP
fuelectenerg-1427	297	34	a	a	DET
fuelectenerg-1427	297	35	single	single	ADJ
fuelectenerg-1427	297	36	variable	variable	NOUN
fuelectenerg-1427	297	37	is	be	AUX
fuelectenerg-1427	297	38	:	:	PUNCT
fuelectenerg-1427	297	39	f	f	X
fuelectenerg-1427	298	1	=	=	SYM
fuelectenerg-1427	298	2	0x	0x	NUM
fuelectenerg-1427	298	3	f0	f0	PROPN
fuelectenerg-1427	298	4	+	+	CCONJ
fuelectenerg-1427	298	5	1x	1x	NUM
fuelectenerg-1427	298	6	f1	f1	NOUN
fuelectenerg-1427	298	7	+	+	CCONJ
fuelectenerg-1427	298	8	2x	2x	NUM
fuelectenerg-1427	298	9	f2	f2	PROPN
fuelectenerg-1427	298	10	,	,	PUNCT
fuelectenerg-1427	298	11	(	(	PUNCT
fuelectenerg-1427	298	12	6	6	NUM
fuelectenerg-1427	298	13	)	)	PUNCT
fuelectenerg-1427	298	14	where	where	SCONJ
fuelectenerg-1427	298	15	f0	f0	PROPN
fuelectenerg-1427	298	16	is	be	AUX
fuelectenerg-1427	298	17	cofactor	cofactor	NOUN
fuelectenerg-1427	298	18	of	of	ADP
fuelectenerg-1427	298	19	f	f	PROPN
fuelectenerg-1427	298	20	with	with	ADP
fuelectenerg-1427	298	21	respect	respect	NOUN
fuelectenerg-1427	298	22	to	to	ADP
fuelectenerg-1427	298	23	variable	variable	NOUN
fuelectenerg-1427	298	24	x	x	PUNCT
fuelectenerg-1427	298	25	of	of	ADP
fuelectenerg-1427	298	26	value	value	NOUN
fuelectenerg-1427	298	27	0	0	NUM
fuelectenerg-1427	298	28	,	,	PUNCT
fuelectenerg-1427	298	29	f1	f1	NOUN
fuelectenerg-1427	298	30	is	be	AUX
fuelectenerg-1427	298	31	cofactor	cofactor	NOUN
fuelectenerg-1427	298	32	of	of	ADP
fuelectenerg-1427	298	33	f	f	PROPN
fuelectenerg-1427	298	34	with	with	ADP
fuelectenerg-1427	298	35	respect	respect	NOUN
fuelectenerg-1427	298	36	to	to	ADP
fuelectenerg-1427	298	37	variable	variable	NOUN
fuelectenerg-1427	298	38	x	x	PUNCT
fuelectenerg-1427	298	39	of	of	ADP
fuelectenerg-1427	298	40	value	value	NOUN
fuelectenerg-1427	298	41	1	1	NUM
fuelectenerg-1427	298	42	,	,	PUNCT
fuelectenerg-1427	298	43	and	and	CCONJ
fuelectenerg-1427	298	44	f2	f2	PROPN
fuelectenerg-1427	298	45	is	be	AUX
fuelectenerg-1427	298	46	cofactor	cofactor	NOUN
fuelectenerg-1427	298	47	of	of	ADP
fuelectenerg-1427	298	48	f	f	PROPN
fuelectenerg-1427	298	49	with	with	ADP
fuelectenerg-1427	298	50	respect	respect	NOUN
fuelectenerg-1427	298	51	to	to	ADP
fuelectenerg-1427	298	52	variable	variable	NOUN
fuelectenerg-1427	298	53	x	x	PUNCT
fuelectenerg-1427	298	54	of	of	ADP
fuelectenerg-1427	298	55	value	value	NOUN
fuelectenerg-1427	298	56	2	2	NUM
fuelectenerg-1427	298	57	.	.	NOUN
fuelectenerg-1427	298	58	104	104	NUM
fuelectenerg-1427	298	59	an	an	DET
fuelectenerg-1427	298	60	extended	extend	VERB
fuelectenerg-1427	298	61	green	green	ADJ
fuelectenerg-1427	298	62	sasao	sasao	PROPN
fuelectenerg-1427	298	63	hierarchy	hierarchy	NOUN
fuelectenerg-1427	298	64	of	of	ADP
fuelectenerg-1427	298	65	canonical	canonical	ADJ
fuelectenerg-1427	298	66	ternary	ternary	ADJ
fuelectenerg-1427	298	67	galois	galois	NOUN
fuelectenerg-1427	298	68	forms	form	NOUN
fuelectenerg-1427	298	69	...	...	PUNCT
fuelectenerg-1427	298	70	literals	literal	NOUN
fuelectenerg-1427	298	71	.	.	PUNCT
fuelectenerg-1427	299	1	galois	galois	PROPN
fuelectenerg-1427	299	2	field	field	NOUN
fuelectenerg-1427	299	3	sum	sum	NOUN
fuelectenerg-1427	299	4	-	-	PUNCT
fuelectenerg-1427	299	5	of	of	ADP
fuelectenerg-1427	299	6	-	-	PUNCT
fuelectenerg-1427	299	7	products	product	NOUN
fuelectenerg-1427	299	8	expansions	expansion	NOUN
fuelectenerg-1427	299	9	can	can	AUX
fuelectenerg-1427	299	10	be	be	AUX
fuelectenerg-1427	299	11	performed	perform	VERB
fuelectenerg-1427	299	12	utilizing	utilize	VERB
fuelectenerg-1427	299	13	variety	variety	NOUN
fuelectenerg-1427	299	14	uses	use	NOUN
fuelectenerg-1427	299	15	of	of	ADP
fuelectenerg-1427	299	16	literals	literal	NOUN
fuelectenerg-1427	299	17	.	.	PUNCT
fuelectenerg-1427	300	1	for	for	ADP
fuelectenerg-1427	300	2	example	example	NOUN
fuelectenerg-1427	300	3	,	,	PUNCT
fuelectenerg-1427	300	4	one	one	PRON
fuelectenerg-1427	300	5	can	can	AUX
fuelectenerg-1427	300	6	use	use	VERB
fuelectenerg-1427	300	7	k	k	ADV
fuelectenerg-1427	300	8	-	-	PUNCT
fuelectenerg-1427	300	9	reduced	reduce	VERB
fuelectenerg-1427	300	10	post	post	NOUN
fuelectenerg-1427	300	11	literal	literal	ADJ
fuelectenerg-1427	300	12	(	(	PUNCT
fuelectenerg-1427	300	13	k	k	X
fuelectenerg-1427	300	14	-	-	NOUN
fuelectenerg-1427	300	15	rpl	rpl	NOUN
fuelectenerg-1427	300	16	)	)	PUNCT
fuelectenerg-1427	300	17	to	to	PART
fuelectenerg-1427	300	18	produce	produce	VERB
fuelectenerg-1427	300	19	k	k	ADJ
fuelectenerg-1427	300	20	-	-	ADJ
fuelectenerg-1427	300	21	rpl	rpl	PROPN
fuelectenerg-1427	300	22	gfsop	gfsop	NOUN
fuelectenerg-1427	300	23	,	,	PUNCT
fuelectenerg-1427	300	24	generalized	generalize	VERB
fuelectenerg-1427	300	25	(	(	PUNCT
fuelectenerg-1427	300	26	post	post	ADJ
fuelectenerg-1427	300	27	)	)	PUNCT
fuelectenerg-1427	300	28	literal	literal	ADJ
fuelectenerg-1427	300	29	(	(	PUNCT
fuelectenerg-1427	300	30	gl	gl	NOUN
fuelectenerg-1427	300	31	)	)	PUNCT
fuelectenerg-1427	300	32	to	to	PART
fuelectenerg-1427	300	33	produce	produce	VERB
fuelectenerg-1427	300	34	gl	gl	NOUN
fuelectenerg-1427	300	35	gfsop	gfsop	PROPN
fuelectenerg-1427	300	36	,	,	PUNCT
fuelectenerg-1427	300	37	and	and	CCONJ
fuelectenerg-1427	300	38	universal	universal	ADJ
fuelectenerg-1427	300	39	literal	literal	ADJ
fuelectenerg-1427	300	40	(	(	PUNCT
fuelectenerg-1427	300	41	ul	ul	INTJ
fuelectenerg-1427	300	42	)	)	PUNCT
fuelectenerg-1427	300	43	to	to	PART
fuelectenerg-1427	300	44	produce	produce	VERB
fuelectenerg-1427	300	45	ul	ul	INTJ
fuelectenerg-1427	300	46	gfsop	gfsop	PROPN
fuelectenerg-1427	300	47	.	.	PUNCT
fuelectenerg-1427	300	48	example	example	NOUN
fuelectenerg-1427	301	1	1	1	NUM
fuelectenerg-1427	301	2	.	.	PUNCT
fuelectenerg-1427	301	3	figure	figure	NOUN
fuelectenerg-1427	301	4	2	2	NUM
fuelectenerg-1427	301	5	demonstrates	demonstrate	VERB
fuelectenerg-1427	301	6	several	several	ADJ
fuelectenerg-1427	301	7	literal	literal	ADJ
fuelectenerg-1427	301	8	types	type	NOUN
fuelectenerg-1427	301	9	,	,	PUNCT
fuelectenerg-1427	301	10	where	where	SCONJ
fuelectenerg-1427	301	11	one	one	NUM
fuelectenerg-1427	301	12	proceeds	proceed	VERB
fuelectenerg-1427	301	13	from	from	ADP
fuelectenerg-1427	301	14	the	the	DET
fuelectenerg-1427	301	15	simplest	simple	ADJ
fuelectenerg-1427	301	16	literal	literal	NOUN
fuelectenerg-1427	301	17	in	in	ADP
fuelectenerg-1427	301	18	figure	figure	NOUN
fuelectenerg-1427	301	19	2(a	2(a	NUM
fuelectenerg-1427	301	20	)	)	PUNCT
fuelectenerg-1427	301	21	(	(	PUNCT
fuelectenerg-1427	301	22	i.e.	i.e.	X
fuelectenerg-1427	301	23	,	,	PUNCT
fuelectenerg-1427	301	24	rpl	rpl	PROPN
fuelectenerg-1427	301	25	)	)	PUNCT
fuelectenerg-1427	301	26	to	to	ADP
fuelectenerg-1427	301	27	the	the	DET
fuelectenerg-1427	301	28	most	most	ADV
fuelectenerg-1427	301	29	complex	complex	ADJ
fuelectenerg-1427	301	30	universal	universal	ADJ
fuelectenerg-1427	301	31	literal	literal	NOUN
fuelectenerg-1427	301	32	in	in	ADP
fuelectenerg-1427	301	33	figure	figure	NOUN
fuelectenerg-1427	301	34	2(c	2(c	NUM
fuelectenerg-1427	301	35	)	)	PUNCT
fuelectenerg-1427	301	36	.	.	PUNCT
fuelectenerg-1427	302	1	for	for	ADP
fuelectenerg-1427	302	2	rpl	rpl	NOUN
fuelectenerg-1427	302	3	in	in	ADP
fuelectenerg-1427	302	4	figure	figure	NOUN
fuelectenerg-1427	302	5	2(a	2(a	NUM
fuelectenerg-1427	302	6	)	)	PUNCT
fuelectenerg-1427	302	7	,	,	PUNCT
fuelectenerg-1427	302	8	a	a	DET
fuelectenerg-1427	302	9	value	value	NOUN
fuelectenerg-1427	302	10	k	k	NOUN
fuelectenerg-1427	302	11	is	be	AUX
fuelectenerg-1427	302	12	produced	produce	VERB
fuelectenerg-1427	302	13	by	by	ADP
fuelectenerg-1427	302	14	the	the	DET
fuelectenerg-1427	302	15	literal	literal	NOUN
fuelectenerg-1427	302	16	when	when	SCONJ
fuelectenerg-1427	302	17	the	the	DET
fuelectenerg-1427	302	18	value	value	NOUN
fuelectenerg-1427	302	19	of	of	ADP
fuelectenerg-1427	302	20	the	the	DET
fuelectenerg-1427	302	21	variable	variable	NOUN
fuelectenerg-1427	302	22	is	be	AUX
fuelectenerg-1427	302	23	equal	equal	ADJ
fuelectenerg-1427	302	24	to	to	ADP
fuelectenerg-1427	302	25	a	a	DET
fuelectenerg-1427	302	26	specific	specific	ADJ
fuelectenerg-1427	302	27	state	state	NOUN
fuelectenerg-1427	302	28	,	,	PUNCT
fuelectenerg-1427	302	29	and	and	CCONJ
fuelectenerg-1427	302	30	in	in	ADP
fuelectenerg-1427	302	31	this	this	DET
fuelectenerg-1427	302	32	particular	particular	ADJ
fuelectenerg-1427	302	33	example	example	NOUN
fuelectenerg-1427	302	34	a	a	DET
fuelectenerg-1427	302	35	value	value	NOUN
fuelectenerg-1427	302	36	of	of	ADP
fuelectenerg-1427	302	37	k	k	PROPN
fuelectenerg-1427	302	38	=	=	SYM
fuelectenerg-1427	302	39	1	1	NUM
fuelectenerg-1427	302	40	is	be	AUX
fuelectenerg-1427	302	41	generated	generate	VERB
fuelectenerg-1427	302	42	by	by	ADP
fuelectenerg-1427	302	43	the	the	DET
fuelectenerg-1427	302	44	1	1	NUM
fuelectenerg-1427	302	45	-	-	PUNCT
fuelectenerg-1427	302	46	rpl	rpl	NOUN
fuelectenerg-1427	302	47	when	when	SCONJ
fuelectenerg-1427	302	48	the	the	DET
fuelectenerg-1427	302	49	value	value	NOUN
fuelectenerg-1427	302	50	of	of	ADP
fuelectenerg-1427	302	51	variable	variable	NOUN
fuelectenerg-1427	302	52	x	x	PUNCT
fuelectenerg-1427	302	53	is	be	AUX
fuelectenerg-1427	302	54	equal	equal	ADJ
fuelectenerg-1427	302	55	to	to	ADP
fuelectenerg-1427	302	56	certain	certain	ADJ
fuelectenerg-1427	302	57	state	state	NOUN
fuelectenerg-1427	302	58	where	where	SCONJ
fuelectenerg-1427	302	59	this	this	DET
fuelectenerg-1427	302	60	state	state	NOUN
fuelectenerg-1427	302	61	here	here	ADV
fuelectenerg-1427	302	62	equals	equal	VERB
fuelectenerg-1427	302	63	to	to	ADP
fuelectenerg-1427	302	64	one	one	NUM
fuelectenerg-1427	302	65	.	.	PUNCT
fuelectenerg-1427	303	1	the	the	DET
fuelectenerg-1427	303	2	gl	gl	PROPN
fuelectenerg-1427	303	3	in	in	ADP
fuelectenerg-1427	303	4	figure	figure	NOUN
fuelectenerg-1427	303	5	2(b	2(b	NUM
fuelectenerg-1427	303	6	)	)	PUNCT
fuelectenerg-1427	303	7	produces	produce	VERB
fuelectenerg-1427	303	8	a	a	DET
fuelectenerg-1427	303	9	value	value	NOUN
fuelectenerg-1427	303	10	of	of	ADP
fuelectenerg-1427	303	11	radix	radix	NOUN
fuelectenerg-1427	303	12	for	for	ADP
fuelectenerg-1427	303	13	a	a	DET
fuelectenerg-1427	303	14	set	set	NOUN
fuelectenerg-1427	303	15	of	of	ADP
fuelectenerg-1427	303	16	distinct	distinct	ADJ
fuelectenerg-1427	303	17	states	state	NOUN
fuelectenerg-1427	303	18	.	.	PUNCT
fuelectenerg-1427	304	1	one	one	NUM
fuelectenerg-1427	304	2	notes	note	VERB
fuelectenerg-1427	304	3	that	that	SCONJ
fuelectenerg-1427	304	4	,	,	PUNCT
fuelectenerg-1427	304	5	in	in	ADP
fuelectenerg-1427	304	6	contrast	contrast	NOUN
fuelectenerg-1427	304	7	to	to	ADP
fuelectenerg-1427	304	8	the	the	DET
fuelectenerg-1427	304	9	other	other	ADJ
fuelectenerg-1427	304	10	literals	literal	NOUN
fuelectenerg-1427	304	11	,	,	PUNCT
fuelectenerg-1427	304	12	ul	ul	INTJ
fuelectenerg-1427	304	13	in	in	ADP
fuelectenerg-1427	304	14	figure	figure	NOUN
fuelectenerg-1427	304	15	2(c	2(c	NUM
fuelectenerg-1427	304	16	)	)	PUNCT
fuelectenerg-1427	304	17	can	can	AUX
fuelectenerg-1427	304	18	have	have	VERB
fuelectenerg-1427	304	19	any	any	DET
fuelectenerg-1427	304	20	value	value	NOUN
fuelectenerg-1427	304	21	of	of	ADP
fuelectenerg-1427	304	22	the	the	DET
fuelectenerg-1427	304	23	logic	logic	NOUN
fuelectenerg-1427	304	24	system	system	NOUN
fuelectenerg-1427	304	25	at	at	ADP
fuelectenerg-1427	304	26	distinct	distinct	ADJ
fuelectenerg-1427	304	27	states	state	NOUN
fuelectenerg-1427	304	28	,	,	PUNCT
fuelectenerg-1427	304	29	and	and	CCONJ
fuelectenerg-1427	304	30	thus	thus	ADV
fuelectenerg-1427	304	31	ul	ul	INTJ
fuelectenerg-1427	304	32	has	have	VERB
fuelectenerg-1427	304	33	the	the	DET
fuelectenerg-1427	304	34	highest	high	ADJ
fuelectenerg-1427	304	35	complexity	complexity	NOUN
fuelectenerg-1427	304	36	among	among	ADP
fuelectenerg-1427	304	37	the	the	DET
fuelectenerg-1427	304	38	different	different	ADJ
fuelectenerg-1427	304	39	types	type	NOUN
fuelectenerg-1427	304	40	of	of	ADP
fuelectenerg-1427	304	41	literals	literal	NOUN
fuelectenerg-1427	304	42	.	.	PUNCT
fuelectenerg-1427	305	1	0	0	NUM
fuelectenerg-1427	305	2	0	0	NUM
fuelectenerg-1427	306	1	01	01	NUM
fuelectenerg-1427	306	2	1	1	NUM
fuelectenerg-1427	306	3	1	1	NUM
fuelectenerg-1427	306	4	1	1	NUM
fuelectenerg-1427	306	5	1	1	NUM
fuelectenerg-1427	306	6	12	12	NUM
fuelectenerg-1427	306	7	2	2	NUM
fuelectenerg-1427	306	8	2	2	NUM
fuelectenerg-1427	306	9	2	2	NUM
fuelectenerg-1427	306	10	2	2	NUM
fuelectenerg-1427	306	11	23	23	NUM
fuelectenerg-1427	306	12	3	3	NUM
fuelectenerg-1427	306	13	3	3	NUM
fuelectenerg-1427	306	14	3	3	NUM
fuelectenerg-1427	306	15	3	3	NUM
fuelectenerg-1427	306	16	34	34	NUM
fuelectenerg-1427	306	17	4	4	NUM
fuelectenerg-1427	306	18	4	4	NUM
fuelectenerg-1427	306	19	4	4	NUM
fuelectenerg-1427	306	20	4	4	NUM
fuelectenerg-1427	306	21	4x	4x	NOUN
fuelectenerg-1427	306	22	x	x	SYM
fuelectenerg-1427	306	23	x	x	SYM
fuelectenerg-1427	306	24	1	1	NUM
fuelectenerg-1427	306	25	x	x	SYM
fuelectenerg-1427	306	26	l	l	NOUN
fuelectenerg-1427	306	27	(	(	PUNCT
fuelectenerg-1427	306	28	)	)	PUNCT
fuelectenerg-1427	306	29	{	{	PUNCT
fuelectenerg-1427	306	30	1,3	1,3	NUM
fuelectenerg-1427	306	31	}	}	PUNCT
fuelectenerg-1427	306	32	x	x	X
fuelectenerg-1427	306	33	l	l	NOUN
fuelectenerg-1427	306	34	(	(	PUNCT
fuelectenerg-1427	306	35	)	)	PUNCT
fuelectenerg-1427	306	36	<	<	X
fuelectenerg-1427	306	37	2,0,4,3,1	2,0,4,3,1	X
fuelectenerg-1427	306	38	>	>	X
fuelectenerg-1427	306	39	x	x	X
fuelectenerg-1427	306	40	(	(	PUNCT
fuelectenerg-1427	306	41	)	)	PUNCT
fuelectenerg-1427	306	42	a	a	DET
fuelectenerg-1427	306	43	(	(	PUNCT
fuelectenerg-1427	306	44	)	)	SYM
fuelectenerg-1427	306	45	b	b	NOUN
fuelectenerg-1427	306	46	(	(	PUNCT
fuelectenerg-1427	306	47	)	)	PUNCT
fuelectenerg-1427	306	48	c	c	NOUN
fuelectenerg-1427	306	49	figure	figure	NOUN
fuelectenerg-1427	306	50	2	2	NUM
fuelectenerg-1427	306	51	:	:	PUNCT
fuelectenerg-1427	306	52	an	an	DET
fuelectenerg-1427	306	53	illustrating	illustrate	VERB
fuelectenerg-1427	306	54	example	example	NOUN
fuelectenerg-1427	306	55	of	of	ADP
fuelectenerg-1427	306	56	the	the	DET
fuelectenerg-1427	306	57	different	different	ADJ
fuelectenerg-1427	306	58	types	type	NOUN
fuelectenerg-1427	306	59	of	of	ADP
fuelectenerg-1427	306	60	literals	literal	NOUN
fuelectenerg-1427	306	61	over	over	ADP
fuelectenerg-1427	306	62	an	an	DET
fuelectenerg-1427	306	63	arbitrary	arbitrary	ADJ
fuelectenerg-1427	306	64	five	five	NUM
fuelectenerg-1427	306	65	-	-	PUNCT
fuelectenerg-1427	306	66	radix	radix	NOUN
fuelectenerg-1427	306	67	logic	logic	NOUN
fuelectenerg-1427	306	68	:	:	PUNCT
fuelectenerg-1427	306	69	(	(	PUNCT
fuelectenerg-1427	306	70	a	a	X
fuelectenerg-1427	306	71	)	)	PUNCT
fuelectenerg-1427	306	72	1	1	NUM
fuelectenerg-1427	306	73	-	-	PUNCT
fuelectenerg-1427	306	74	reduced	reduce	VERB
fuelectenerg-1427	306	75	post	post	NOUN
fuelectenerg-1427	306	76	literal	literal	ADJ
fuelectenerg-1427	306	77	(	(	PUNCT
fuelectenerg-1427	306	78	1	1	NUM
fuelectenerg-1427	306	79	-	-	PUNCT
fuelectenerg-1427	306	80	rpl	rpl	NOUN
fuelectenerg-1427	306	81	)	)	PUNCT
fuelectenerg-1427	306	82	,	,	PUNCT
fuelectenerg-1427	306	83	(	(	PUNCT
fuelectenerg-1427	306	84	b	b	X
fuelectenerg-1427	306	85	)	)	PUNCT
fuelectenerg-1427	306	86	generalized	generalized	ADJ
fuelectenerg-1427	306	87	(	(	PUNCT
fuelectenerg-1427	306	88	post	post	ADJ
fuelectenerg-1427	306	89	)	)	PUNCT
fuelectenerg-1427	306	90	literal	literal	ADJ
fuelectenerg-1427	306	91	(	(	PUNCT
fuelectenerg-1427	306	92	gl	gl	NOUN
fuelectenerg-1427	306	93	)	)	PUNCT
fuelectenerg-1427	306	94	,	,	PUNCT
fuelectenerg-1427	306	95	and	and	CCONJ
fuelectenerg-1427	306	96	(	(	PUNCT
fuelectenerg-1427	306	97	c	c	X
fuelectenerg-1427	306	98	)	)	PUNCT
fuelectenerg-1427	306	99	universal	universal	ADJ
fuelectenerg-1427	306	100	literal	literal	ADJ
fuelectenerg-1427	306	101	(	(	PUNCT
fuelectenerg-1427	306	102	ul	ul	INTJ
fuelectenerg-1427	306	103	)	)	PUNCT
fuelectenerg-1427	306	104	.	.	PUNCT
fuelectenerg-1427	307	1	since	since	SCONJ
fuelectenerg-1427	307	2	k	k	PROPN
fuelectenerg-1427	307	3	-	-	PROPN
fuelectenerg-1427	307	4	rpl	rpl	PROPN
fuelectenerg-1427	307	5	gfsop	gfsop	NOUN
fuelectenerg-1427	307	6	is	be	AUX
fuelectenerg-1427	307	7	simpler	simple	ADJ
fuelectenerg-1427	307	8	from	from	ADP
fuelectenerg-1427	307	9	implementation	implementation	NOUN
fuelectenerg-1427	307	10	point	point	NOUN
fuelectenerg-1427	307	11	of	of	ADP
fuelectenerg-1427	307	12	view	view	NOUN
fuelectenerg-1427	307	13	than	than	ADP
fuelectenerg-1427	307	14	gl	gl	INTJ
fuelectenerg-1427	307	15	or	or	CCONJ
fuelectenerg-1427	307	16	ul	ul	INTJ
fuelectenerg-1427	307	17	,	,	PUNCT
fuelectenerg-1427	307	18	we	we	PRON
fuelectenerg-1427	307	19	will	will	AUX
fuelectenerg-1427	307	20	perform	perform	VERB
fuelectenerg-1427	307	21	all	all	DET
fuelectenerg-1427	307	22	the	the	DET
fuelectenerg-1427	307	23	gfsop	gfsop	NOUN
fuelectenerg-1427	307	24	expansions	expansion	NOUN
fuelectenerg-1427	307	25	utilizing	utilize	VERB
fuelectenerg-1427	307	26	the	the	DET
fuelectenerg-1427	307	27	1	1	NUM
fuelectenerg-1427	307	28	-	-	PUNCT
fuelectenerg-1427	307	29	rpl	rpl	NOUN
fuelectenerg-1427	307	30	gfsop	gfsop	NOUN
fuelectenerg-1427	307	31	.	.	PUNCT
fuelectenerg-1427	308	1	let	let	VERB
fuelectenerg-1427	308	2	us	we	PRON
fuelectenerg-1427	308	3	define	define	VERB
fuelectenerg-1427	308	4	1	1	NUM
fuelectenerg-1427	308	5	-	-	PUNCT
fuelectenerg-1427	308	6	rpl	rpl	NOUN
fuelectenerg-1427	308	7	[	[	X
fuelectenerg-1427	308	8	1	1	NUM
fuelectenerg-1427	308	9	,	,	PUNCT
fuelectenerg-1427	308	10	17	17	NUM
fuelectenerg-1427	308	11	]	]	PUNCT
fuelectenerg-1427	308	12	as	as	ADP
fuelectenerg-1427	308	13	:	:	PUNCT
fuelectenerg-1427	308	14	ix	ix	PROPN
fuelectenerg-1427	308	15	=	=	SYM
fuelectenerg-1427	308	16	1	1	NUM
fuelectenerg-1427	308	17	iff	iff	NOUN
fuelectenerg-1427	308	18	x	x	PROPN
fuelectenerg-1427	309	1	=	=	PUNCT
fuelectenerg-1427	310	1	i	i	PRON
fuelectenerg-1427	310	2	else	else	ADV
fuelectenerg-1427	310	3	ix	ix	ADP
fuelectenerg-1427	310	4	=	=	NOUN
fuelectenerg-1427	310	5	0	0	PROPN
fuelectenerg-1427	310	6	.	.	PUNCT
fuelectenerg-1427	311	1	(	(	PUNCT
fuelectenerg-1427	311	2	5	5	NUM
fuelectenerg-1427	311	3	)	)	PUNCT
fuelectenerg-1427	311	4	for	for	ADP
fuelectenerg-1427	311	5	example	example	NOUN
fuelectenerg-1427	311	6	{	{	PUNCT
fuelectenerg-1427	311	7	0x	0x	NOUN
fuelectenerg-1427	311	8	,	,	PUNCT
fuelectenerg-1427	311	9	1x	1x	NUM
fuelectenerg-1427	311	10	,	,	PUNCT
fuelectenerg-1427	311	11	2x	2x	NUM
fuelectenerg-1427	311	12	}	}	PUNCT
fuelectenerg-1427	311	13	are	be	AUX
fuelectenerg-1427	311	14	the	the	DET
fuelectenerg-1427	311	15	zero	zero	NUM
fuelectenerg-1427	311	16	,	,	PUNCT
fuelectenerg-1427	311	17	first	first	ADV
fuelectenerg-1427	311	18	,	,	PUNCT
fuelectenerg-1427	311	19	and	and	CCONJ
fuelectenerg-1427	311	20	second	second	ADJ
fuelectenerg-1427	311	21	polarities	polarity	NOUN
fuelectenerg-1427	311	22	of	of	ADP
fuelectenerg-1427	311	23	the	the	DET
fuelectenerg-1427	311	24	1	1	NUM
fuelectenerg-1427	311	25	-	-	PUNCT
fuelectenerg-1427	311	26	rpl	rpl	NOUN
fuelectenerg-1427	311	27	,	,	PUNCT
fuelectenerg-1427	311	28	respectively	respectively	ADV
fuelectenerg-1427	311	29	.	.	PUNCT
fuelectenerg-1427	312	1	also	also	ADV
fuelectenerg-1427	312	2	,	,	PUNCT
fuelectenerg-1427	312	3	let	let	VERB
fuelectenerg-1427	312	4	us	we	PRON
fuelectenerg-1427	312	5	define	define	VERB
fuelectenerg-1427	312	6	the	the	DET
fuelectenerg-1427	312	7	ternary	ternary	ADJ
fuelectenerg-1427	312	8	shifts	shift	NOUN
fuelectenerg-1427	312	9	over	over	ADP
fuelectenerg-1427	312	10	variable	variable	ADJ
fuelectenerg-1427	312	11	x	x	NOUN
fuelectenerg-1427	312	12	as	as	ADP
fuelectenerg-1427	312	13	{	{	PUNCT
fuelectenerg-1427	312	14	x	x	NOUN
fuelectenerg-1427	312	15	,	,	PUNCT
fuelectenerg-1427	312	16	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	312	17	}	}	PUNCT
fuelectenerg-1427	312	18	as	as	ADP
fuelectenerg-1427	312	19	the	the	DET
fuelectenerg-1427	312	20	zero	zero	NUM
fuelectenerg-1427	312	21	,	,	PUNCT
fuelectenerg-1427	312	22	first	first	ADJ
fuelectenerg-1427	312	23	and	and	CCONJ
fuelectenerg-1427	312	24	second	second	ADJ
fuelectenerg-1427	312	25	shifts	shift	NOUN
fuelectenerg-1427	312	26	of	of	ADP
fuelectenerg-1427	312	27	the	the	DET
fuelectenerg-1427	312	28	variable	variable	NOUN
fuelectenerg-1427	312	29	x	x	PUNCT
fuelectenerg-1427	312	30	respectively	respectively	ADV
fuelectenerg-1427	312	31	,	,	PUNCT
fuelectenerg-1427	312	32	i.e.	i.e.	X
fuelectenerg-1427	312	33	,	,	PUNCT
fuelectenerg-1427	312	34	x	x	SYM
fuelectenerg-1427	312	35	=	=	SYM
fuelectenerg-1427	312	36	x+	x+	PUNCT
fuelectenerg-1427	312	37	0	0	NUM
fuelectenerg-1427	312	38	,	,	PUNCT
fuelectenerg-1427	312	39	x′	x′	PROPN
fuelectenerg-1427	313	1	=	=	PUNCT
fuelectenerg-1427	313	2	x+	x+	SYM
fuelectenerg-1427	313	3	1	1	NUM
fuelectenerg-1427	313	4	and	and	CCONJ
fuelectenerg-1427	313	5	x′′	x′′	PROPN
fuelectenerg-1427	313	6	=	=	PUNCT
fuelectenerg-1427	313	7	x+	x+	PROPN
fuelectenerg-1427	313	8	2	2	NUM
fuelectenerg-1427	313	9	,	,	PUNCT
fuelectenerg-1427	313	10	and	and	CCONJ
fuelectenerg-1427	313	11	x	x	PRON
fuelectenerg-1427	313	12	can	can	AUX
fuelectenerg-1427	313	13	take	take	VERB
fuelectenerg-1427	313	14	any	any	DET
fuelectenerg-1427	313	15	value	value	NOUN
fuelectenerg-1427	313	16	in	in	ADP
fuelectenerg-1427	313	17	the	the	DET
fuelectenerg-1427	313	18	set	set	NOUN
fuelectenerg-1427	313	19	{	{	PUNCT
fuelectenerg-1427	313	20	0,1,2	0,1,2	NUM
fuelectenerg-1427	313	21	}	}	PUNCT
fuelectenerg-1427	313	22	.	.	PUNCT
fuelectenerg-1427	314	1	we	we	PRON
fuelectenerg-1427	314	2	chose	choose	VERB
fuelectenerg-1427	314	3	to	to	PART
fuelectenerg-1427	314	4	represent	represent	VERB
fuelectenerg-1427	314	5	the	the	DET
fuelectenerg-1427	314	6	1	1	NUM
fuelectenerg-1427	314	7	-	-	PUNCT
fuelectenerg-1427	314	8	reduced	reduce	VERB
fuelectenerg-1427	314	9	post	post	NOUN
fuelectenerg-1427	314	10	literals	literal	NOUN
fuelectenerg-1427	314	11	in	in	ADP
fuelectenerg-1427	314	12	terms	term	NOUN
fuelectenerg-1427	314	13	of	of	ADP
fuelectenerg-1427	314	14	shifts	shift	NOUN
fuelectenerg-1427	314	15	and	and	CCONJ
fuelectenerg-1427	314	16	powers	power	NOUN
fuelectenerg-1427	314	17	,	,	PUNCT
fuelectenerg-1427	314	18	among	among	ADP
fuelectenerg-1427	314	19	others	other	NOUN
fuelectenerg-1427	314	20	,	,	PUNCT
fuelectenerg-1427	314	21	because	because	SCONJ
fuelectenerg-1427	314	22	of	of	ADP
fuelectenerg-1427	314	23	the	the	DET
fuelectenerg-1427	314	24	ease	ease	NOUN
fuelectenerg-1427	314	25	of	of	ADP
fuelectenerg-1427	314	26	the	the	DET
fuelectenerg-1427	314	27	implementation	implementation	NOUN
fuelectenerg-1427	314	28	of	of	ADP
fuelectenerg-1427	314	29	powers	power	NOUN
fuelectenerg-1427	314	30	of	of	ADP
fuelectenerg-1427	314	31	shifted	shift	VERB
fuelectenerg-1427	314	32	variables	variable	NOUN
fuelectenerg-1427	314	33	in	in	ADP
fuelectenerg-1427	314	34	hardware	hardware	NOUN
fuelectenerg-1427	314	35	as	as	SCONJ
fuelectenerg-1427	314	36	will	will	AUX
fuelectenerg-1427	314	37	be	be	AUX
fuelectenerg-1427	314	38	seen	see	VERB
fuelectenerg-1427	314	39	in	in	ADP
fuelectenerg-1427	314	40	section	section	NOUN
fuelectenerg-1427	314	41	3	3	NUM
fuelectenerg-1427	314	42	within	within	ADP
fuelectenerg-1427	314	43	universal	universal	ADJ
fuelectenerg-1427	314	44	logic	logic	NOUN
fuelectenerg-1427	314	45	modules	module	NOUN
fuelectenerg-1427	314	46	(	(	PUNCT
fuelectenerg-1427	314	47	ulms	ulm	NOUN
fuelectenerg-1427	314	48	)	)	PUNCT
fuelectenerg-1427	314	49	for	for	ADP
fuelectenerg-1427	314	50	the	the	DET
fuelectenerg-1427	314	51	production	production	NOUN
fuelectenerg-1427	314	52	of	of	ADP
fuelectenerg-1427	314	53	rpl	rpl	NOUN
fuelectenerg-1427	314	54	.	.	PUNCT
fuelectenerg-1427	315	1	the	the	DET
fuelectenerg-1427	315	2	fundamental	fundamental	ADJ
fuelectenerg-1427	315	3	shannon	shannon	PROPN
fuelectenerg-1427	315	4	expansion	expansion	NOUN
fuelectenerg-1427	315	5	over	over	ADP
fuelectenerg-1427	315	6	gf(3	gf(3	PROPN
fuelectenerg-1427	315	7	)	)	PUNCT
fuelectenerg-1427	315	8	for	for	ADP
fuelectenerg-1427	315	9	a	a	DET
fuelectenerg-1427	315	10	ternary	ternary	ADJ
fuelectenerg-1427	315	11	function	function	NOUN
fuelectenerg-1427	315	12	with	with	ADP
fuelectenerg-1427	315	13	a	a	DET
fuelectenerg-1427	315	14	single	single	ADJ
fuelectenerg-1427	315	15	variable	variable	NOUN
fuelectenerg-1427	315	16	is	be	AUX
fuelectenerg-1427	315	17	shown	show	VERB
fuelectenerg-1427	315	18	in	in	ADP
fuelectenerg-1427	315	19	theorem	theorem	ADJ
fuelectenerg-1427	315	20	1	1	NUM
fuelectenerg-1427	315	21	.	.	PUNCT
fuelectenerg-1427	315	22	theorem	theorem	NOUN
fuelectenerg-1427	315	23	1	1	NUM
fuelectenerg-1427	315	24	.	.	PUNCT
fuelectenerg-1427	315	25	shannon	shannon	PROPN
fuelectenerg-1427	315	26	expansion	expansion	PROPN
fuelectenerg-1427	315	27	over	over	ADP
fuelectenerg-1427	315	28	gf(3	gf(3	PROPN
fuelectenerg-1427	315	29	)	)	PUNCT
fuelectenerg-1427	315	30	for	for	ADP
fuelectenerg-1427	315	31	a	a	DET
fuelectenerg-1427	315	32	function	function	NOUN
fuelectenerg-1427	315	33	with	with	ADP
fuelectenerg-1427	315	34	a	a	DET
fuelectenerg-1427	315	35	single	single	ADJ
fuelectenerg-1427	315	36	variable	variable	NOUN
fuelectenerg-1427	315	37	is	be	AUX
fuelectenerg-1427	315	38	:	:	PUNCT
fuelectenerg-1427	315	39	f	f	X
fuelectenerg-1427	316	1	=	=	SYM
fuelectenerg-1427	316	2	0x	0x	NUM
fuelectenerg-1427	316	3	f0	f0	PROPN
fuelectenerg-1427	316	4	+	+	CCONJ
fuelectenerg-1427	316	5	1x	1x	NUM
fuelectenerg-1427	316	6	f1	f1	NOUN
fuelectenerg-1427	316	7	+	+	CCONJ
fuelectenerg-1427	316	8	2x	2x	NUM
fuelectenerg-1427	316	9	f2	f2	PROPN
fuelectenerg-1427	316	10	,	,	PUNCT
fuelectenerg-1427	316	11	(	(	PUNCT
fuelectenerg-1427	316	12	6	6	NUM
fuelectenerg-1427	316	13	)	)	PUNCT
fuelectenerg-1427	316	14	where	where	SCONJ
fuelectenerg-1427	316	15	f0	f0	PROPN
fuelectenerg-1427	316	16	is	be	AUX
fuelectenerg-1427	316	17	cofactor	cofactor	NOUN
fuelectenerg-1427	316	18	of	of	ADP
fuelectenerg-1427	316	19	f	f	PROPN
fuelectenerg-1427	316	20	with	with	ADP
fuelectenerg-1427	316	21	respect	respect	NOUN
fuelectenerg-1427	316	22	to	to	ADP
fuelectenerg-1427	316	23	variable	variable	NOUN
fuelectenerg-1427	316	24	x	x	PUNCT
fuelectenerg-1427	316	25	of	of	ADP
fuelectenerg-1427	316	26	value	value	NOUN
fuelectenerg-1427	316	27	0	0	NUM
fuelectenerg-1427	316	28	,	,	PUNCT
fuelectenerg-1427	316	29	f1	f1	NOUN
fuelectenerg-1427	316	30	is	be	AUX
fuelectenerg-1427	316	31	cofactor	cofactor	NOUN
fuelectenerg-1427	316	32	of	of	ADP
fuelectenerg-1427	316	33	f	f	PROPN
fuelectenerg-1427	316	34	with	with	ADP
fuelectenerg-1427	316	35	respect	respect	NOUN
fuelectenerg-1427	316	36	to	to	ADP
fuelectenerg-1427	316	37	variable	variable	NOUN
fuelectenerg-1427	316	38	x	x	PUNCT
fuelectenerg-1427	316	39	of	of	ADP
fuelectenerg-1427	316	40	value	value	NOUN
fuelectenerg-1427	316	41	1	1	NUM
fuelectenerg-1427	316	42	,	,	PUNCT
fuelectenerg-1427	316	43	and	and	CCONJ
fuelectenerg-1427	316	44	f2	f2	PROPN
fuelectenerg-1427	316	45	is	be	AUX
fuelectenerg-1427	316	46	cofactor	cofactor	NOUN
fuelectenerg-1427	316	47	of	of	ADP
fuelectenerg-1427	316	48	f	f	PROPN
fuelectenerg-1427	316	49	with	with	ADP
fuelectenerg-1427	316	50	respect	respect	NOUN
fuelectenerg-1427	316	51	to	to	ADP
fuelectenerg-1427	316	52	variable	variable	NOUN
fuelectenerg-1427	316	53	x	x	PUNCT
fuelectenerg-1427	316	54	of	of	ADP
fuelectenerg-1427	316	55	value	value	NOUN
fuelectenerg-1427	316	56	2	2	NUM
fuelectenerg-1427	316	57	.	.	NOUN
fuelectenerg-1427	316	58	104	104	NUM
fuelectenerg-1427	316	59	an	an	DET
fuelectenerg-1427	316	60	extended	extend	VERB
fuelectenerg-1427	316	61	green	green	ADJ
fuelectenerg-1427	316	62	sasao	sasao	PROPN
fuelectenerg-1427	316	63	hierarchy	hierarchy	NOUN
fuelectenerg-1427	316	64	of	of	ADP
fuelectenerg-1427	316	65	canonical	canonical	ADJ
fuelectenerg-1427	316	66	ternary	ternary	ADJ
fuelectenerg-1427	316	67	galois	galois	NOUN
fuelectenerg-1427	316	68	forms	form	NOUN
fuelectenerg-1427	316	69	...	...	PUNCT
fuelectenerg-1427	316	70	literals	literal	NOUN
fuelectenerg-1427	316	71	.	.	PUNCT
fuelectenerg-1427	317	1	galois	galois	PROPN
fuelectenerg-1427	317	2	field	field	NOUN
fuelectenerg-1427	317	3	sum	sum	NOUN
fuelectenerg-1427	317	4	-	-	PUNCT
fuelectenerg-1427	317	5	of	of	ADP
fuelectenerg-1427	317	6	-	-	PUNCT
fuelectenerg-1427	317	7	products	product	NOUN
fuelectenerg-1427	317	8	expansions	expansion	NOUN
fuelectenerg-1427	317	9	can	can	AUX
fuelectenerg-1427	317	10	be	be	AUX
fuelectenerg-1427	317	11	performed	perform	VERB
fuelectenerg-1427	317	12	utilizing	utilize	VERB
fuelectenerg-1427	317	13	variety	variety	NOUN
fuelectenerg-1427	317	14	uses	use	NOUN
fuelectenerg-1427	317	15	of	of	ADP
fuelectenerg-1427	317	16	literals	literal	NOUN
fuelectenerg-1427	317	17	.	.	PUNCT
fuelectenerg-1427	318	1	for	for	ADP
fuelectenerg-1427	318	2	example	example	NOUN
fuelectenerg-1427	318	3	,	,	PUNCT
fuelectenerg-1427	318	4	one	one	PRON
fuelectenerg-1427	318	5	can	can	AUX
fuelectenerg-1427	318	6	use	use	VERB
fuelectenerg-1427	318	7	k	k	ADV
fuelectenerg-1427	318	8	-	-	PUNCT
fuelectenerg-1427	318	9	reduced	reduce	VERB
fuelectenerg-1427	318	10	post	post	NOUN
fuelectenerg-1427	318	11	literal	literal	ADJ
fuelectenerg-1427	318	12	(	(	PUNCT
fuelectenerg-1427	318	13	k	k	X
fuelectenerg-1427	318	14	-	-	NOUN
fuelectenerg-1427	318	15	rpl	rpl	NOUN
fuelectenerg-1427	318	16	)	)	PUNCT
fuelectenerg-1427	318	17	to	to	PART
fuelectenerg-1427	318	18	produce	produce	VERB
fuelectenerg-1427	318	19	k	k	ADJ
fuelectenerg-1427	318	20	-	-	ADJ
fuelectenerg-1427	318	21	rpl	rpl	PROPN
fuelectenerg-1427	318	22	gfsop	gfsop	NOUN
fuelectenerg-1427	318	23	,	,	PUNCT
fuelectenerg-1427	318	24	generalized	generalize	VERB
fuelectenerg-1427	318	25	(	(	PUNCT
fuelectenerg-1427	318	26	post	post	ADJ
fuelectenerg-1427	318	27	)	)	PUNCT
fuelectenerg-1427	318	28	literal	literal	ADJ
fuelectenerg-1427	318	29	(	(	PUNCT
fuelectenerg-1427	318	30	gl	gl	NOUN
fuelectenerg-1427	318	31	)	)	PUNCT
fuelectenerg-1427	318	32	to	to	PART
fuelectenerg-1427	318	33	produce	produce	VERB
fuelectenerg-1427	318	34	gl	gl	NOUN
fuelectenerg-1427	318	35	gfsop	gfsop	PROPN
fuelectenerg-1427	318	36	,	,	PUNCT
fuelectenerg-1427	318	37	and	and	CCONJ
fuelectenerg-1427	318	38	universal	universal	ADJ
fuelectenerg-1427	318	39	literal	literal	ADJ
fuelectenerg-1427	318	40	(	(	PUNCT
fuelectenerg-1427	318	41	ul	ul	INTJ
fuelectenerg-1427	318	42	)	)	PUNCT
fuelectenerg-1427	318	43	to	to	PART
fuelectenerg-1427	318	44	produce	produce	VERB
fuelectenerg-1427	318	45	ul	ul	INTJ
fuelectenerg-1427	318	46	gfsop	gfsop	PROPN
fuelectenerg-1427	318	47	.	.	PUNCT
fuelectenerg-1427	318	48	example	example	NOUN
fuelectenerg-1427	319	1	1	1	NUM
fuelectenerg-1427	319	2	.	.	PUNCT
fuelectenerg-1427	319	3	figure	figure	NOUN
fuelectenerg-1427	319	4	2	2	NUM
fuelectenerg-1427	319	5	demonstrates	demonstrate	VERB
fuelectenerg-1427	319	6	several	several	ADJ
fuelectenerg-1427	319	7	literal	literal	ADJ
fuelectenerg-1427	319	8	types	type	NOUN
fuelectenerg-1427	319	9	,	,	PUNCT
fuelectenerg-1427	319	10	where	where	SCONJ
fuelectenerg-1427	319	11	one	one	NUM
fuelectenerg-1427	319	12	proceeds	proceed	VERB
fuelectenerg-1427	319	13	from	from	ADP
fuelectenerg-1427	319	14	the	the	DET
fuelectenerg-1427	319	15	simplest	simple	ADJ
fuelectenerg-1427	319	16	literal	literal	NOUN
fuelectenerg-1427	319	17	in	in	ADP
fuelectenerg-1427	319	18	figure	figure	NOUN
fuelectenerg-1427	319	19	2(a	2(a	NUM
fuelectenerg-1427	319	20	)	)	PUNCT
fuelectenerg-1427	319	21	(	(	PUNCT
fuelectenerg-1427	319	22	i.e.	i.e.	X
fuelectenerg-1427	319	23	,	,	PUNCT
fuelectenerg-1427	319	24	rpl	rpl	PROPN
fuelectenerg-1427	319	25	)	)	PUNCT
fuelectenerg-1427	319	26	to	to	ADP
fuelectenerg-1427	319	27	the	the	DET
fuelectenerg-1427	319	28	most	most	ADV
fuelectenerg-1427	319	29	complex	complex	ADJ
fuelectenerg-1427	319	30	universal	universal	ADJ
fuelectenerg-1427	319	31	literal	literal	NOUN
fuelectenerg-1427	319	32	in	in	ADP
fuelectenerg-1427	319	33	figure	figure	NOUN
fuelectenerg-1427	319	34	2(c	2(c	NUM
fuelectenerg-1427	319	35	)	)	PUNCT
fuelectenerg-1427	319	36	.	.	PUNCT
fuelectenerg-1427	320	1	for	for	ADP
fuelectenerg-1427	320	2	rpl	rpl	NOUN
fuelectenerg-1427	320	3	in	in	ADP
fuelectenerg-1427	320	4	figure	figure	NOUN
fuelectenerg-1427	320	5	2(a	2(a	NUM
fuelectenerg-1427	320	6	)	)	PUNCT
fuelectenerg-1427	320	7	,	,	PUNCT
fuelectenerg-1427	320	8	a	a	DET
fuelectenerg-1427	320	9	value	value	NOUN
fuelectenerg-1427	320	10	k	k	NOUN
fuelectenerg-1427	320	11	is	be	AUX
fuelectenerg-1427	320	12	produced	produce	VERB
fuelectenerg-1427	320	13	by	by	ADP
fuelectenerg-1427	320	14	the	the	DET
fuelectenerg-1427	320	15	literal	literal	NOUN
fuelectenerg-1427	320	16	when	when	SCONJ
fuelectenerg-1427	320	17	the	the	DET
fuelectenerg-1427	320	18	value	value	NOUN
fuelectenerg-1427	320	19	of	of	ADP
fuelectenerg-1427	320	20	the	the	DET
fuelectenerg-1427	320	21	variable	variable	NOUN
fuelectenerg-1427	320	22	is	be	AUX
fuelectenerg-1427	320	23	equal	equal	ADJ
fuelectenerg-1427	320	24	to	to	ADP
fuelectenerg-1427	320	25	a	a	DET
fuelectenerg-1427	320	26	specific	specific	ADJ
fuelectenerg-1427	320	27	state	state	NOUN
fuelectenerg-1427	320	28	,	,	PUNCT
fuelectenerg-1427	320	29	and	and	CCONJ
fuelectenerg-1427	320	30	in	in	ADP
fuelectenerg-1427	320	31	this	this	DET
fuelectenerg-1427	320	32	particular	particular	ADJ
fuelectenerg-1427	320	33	example	example	NOUN
fuelectenerg-1427	320	34	a	a	DET
fuelectenerg-1427	320	35	value	value	NOUN
fuelectenerg-1427	320	36	of	of	ADP
fuelectenerg-1427	320	37	k	k	PROPN
fuelectenerg-1427	320	38	=	=	SYM
fuelectenerg-1427	320	39	1	1	NUM
fuelectenerg-1427	320	40	is	be	AUX
fuelectenerg-1427	320	41	generated	generate	VERB
fuelectenerg-1427	320	42	by	by	ADP
fuelectenerg-1427	320	43	the	the	DET
fuelectenerg-1427	320	44	1	1	NUM
fuelectenerg-1427	320	45	-	-	PUNCT
fuelectenerg-1427	320	46	rpl	rpl	NOUN
fuelectenerg-1427	320	47	when	when	SCONJ
fuelectenerg-1427	320	48	the	the	DET
fuelectenerg-1427	320	49	value	value	NOUN
fuelectenerg-1427	320	50	of	of	ADP
fuelectenerg-1427	320	51	variable	variable	NOUN
fuelectenerg-1427	320	52	x	x	PUNCT
fuelectenerg-1427	320	53	is	be	AUX
fuelectenerg-1427	320	54	equal	equal	ADJ
fuelectenerg-1427	320	55	to	to	ADP
fuelectenerg-1427	320	56	certain	certain	ADJ
fuelectenerg-1427	320	57	state	state	NOUN
fuelectenerg-1427	320	58	where	where	SCONJ
fuelectenerg-1427	320	59	this	this	DET
fuelectenerg-1427	320	60	state	state	NOUN
fuelectenerg-1427	320	61	here	here	ADV
fuelectenerg-1427	320	62	equals	equal	VERB
fuelectenerg-1427	320	63	to	to	ADP
fuelectenerg-1427	320	64	one	one	NUM
fuelectenerg-1427	320	65	.	.	PUNCT
fuelectenerg-1427	321	1	the	the	DET
fuelectenerg-1427	321	2	gl	gl	PROPN
fuelectenerg-1427	321	3	in	in	ADP
fuelectenerg-1427	321	4	figure	figure	NOUN
fuelectenerg-1427	321	5	2(b	2(b	NUM
fuelectenerg-1427	321	6	)	)	PUNCT
fuelectenerg-1427	321	7	produces	produce	VERB
fuelectenerg-1427	321	8	a	a	DET
fuelectenerg-1427	321	9	value	value	NOUN
fuelectenerg-1427	321	10	of	of	ADP
fuelectenerg-1427	321	11	radix	radix	NOUN
fuelectenerg-1427	321	12	for	for	ADP
fuelectenerg-1427	321	13	a	a	DET
fuelectenerg-1427	321	14	set	set	NOUN
fuelectenerg-1427	321	15	of	of	ADP
fuelectenerg-1427	321	16	distinct	distinct	ADJ
fuelectenerg-1427	321	17	states	state	NOUN
fuelectenerg-1427	321	18	.	.	PUNCT
fuelectenerg-1427	322	1	one	one	NUM
fuelectenerg-1427	322	2	notes	note	VERB
fuelectenerg-1427	322	3	that	that	SCONJ
fuelectenerg-1427	322	4	,	,	PUNCT
fuelectenerg-1427	322	5	in	in	ADP
fuelectenerg-1427	322	6	contrast	contrast	NOUN
fuelectenerg-1427	322	7	to	to	ADP
fuelectenerg-1427	322	8	the	the	DET
fuelectenerg-1427	322	9	other	other	ADJ
fuelectenerg-1427	322	10	literals	literal	NOUN
fuelectenerg-1427	322	11	,	,	PUNCT
fuelectenerg-1427	322	12	ul	ul	INTJ
fuelectenerg-1427	322	13	in	in	ADP
fuelectenerg-1427	322	14	figure	figure	NOUN
fuelectenerg-1427	322	15	2(c	2(c	NUM
fuelectenerg-1427	322	16	)	)	PUNCT
fuelectenerg-1427	322	17	can	can	AUX
fuelectenerg-1427	322	18	have	have	VERB
fuelectenerg-1427	322	19	any	any	DET
fuelectenerg-1427	322	20	value	value	NOUN
fuelectenerg-1427	322	21	of	of	ADP
fuelectenerg-1427	322	22	the	the	DET
fuelectenerg-1427	322	23	logic	logic	NOUN
fuelectenerg-1427	322	24	system	system	NOUN
fuelectenerg-1427	322	25	at	at	ADP
fuelectenerg-1427	322	26	distinct	distinct	ADJ
fuelectenerg-1427	322	27	states	state	NOUN
fuelectenerg-1427	322	28	,	,	PUNCT
fuelectenerg-1427	322	29	and	and	CCONJ
fuelectenerg-1427	322	30	thus	thus	ADV
fuelectenerg-1427	322	31	ul	ul	INTJ
fuelectenerg-1427	322	32	has	have	VERB
fuelectenerg-1427	322	33	the	the	DET
fuelectenerg-1427	322	34	highest	high	ADJ
fuelectenerg-1427	322	35	complexity	complexity	NOUN
fuelectenerg-1427	322	36	among	among	ADP
fuelectenerg-1427	322	37	the	the	DET
fuelectenerg-1427	322	38	different	different	ADJ
fuelectenerg-1427	322	39	types	type	NOUN
fuelectenerg-1427	322	40	of	of	ADP
fuelectenerg-1427	322	41	literals	literal	NOUN
fuelectenerg-1427	322	42	.	.	PUNCT
fuelectenerg-1427	323	1	0	0	NUM
fuelectenerg-1427	323	2	0	0	NUM
fuelectenerg-1427	324	1	01	01	NUM
fuelectenerg-1427	324	2	1	1	NUM
fuelectenerg-1427	324	3	1	1	NUM
fuelectenerg-1427	324	4	1	1	NUM
fuelectenerg-1427	324	5	1	1	NUM
fuelectenerg-1427	324	6	12	12	NUM
fuelectenerg-1427	324	7	2	2	NUM
fuelectenerg-1427	324	8	2	2	NUM
fuelectenerg-1427	324	9	2	2	NUM
fuelectenerg-1427	324	10	2	2	NUM
fuelectenerg-1427	324	11	23	23	NUM
fuelectenerg-1427	324	12	3	3	NUM
fuelectenerg-1427	324	13	3	3	NUM
fuelectenerg-1427	324	14	3	3	NUM
fuelectenerg-1427	324	15	3	3	NUM
fuelectenerg-1427	324	16	34	34	NUM
fuelectenerg-1427	324	17	4	4	NUM
fuelectenerg-1427	324	18	4	4	NUM
fuelectenerg-1427	324	19	4	4	NUM
fuelectenerg-1427	324	20	4	4	NUM
fuelectenerg-1427	324	21	4x	4x	NOUN
fuelectenerg-1427	324	22	x	x	SYM
fuelectenerg-1427	324	23	x	x	SYM
fuelectenerg-1427	324	24	1	1	NUM
fuelectenerg-1427	324	25	x	x	SYM
fuelectenerg-1427	324	26	l	l	NOUN
fuelectenerg-1427	324	27	(	(	PUNCT
fuelectenerg-1427	324	28	)	)	PUNCT
fuelectenerg-1427	324	29	{	{	PUNCT
fuelectenerg-1427	324	30	1,3	1,3	NUM
fuelectenerg-1427	324	31	}	}	PUNCT
fuelectenerg-1427	324	32	x	x	X
fuelectenerg-1427	324	33	l	l	NOUN
fuelectenerg-1427	324	34	(	(	PUNCT
fuelectenerg-1427	324	35	)	)	PUNCT
fuelectenerg-1427	324	36	<	<	X
fuelectenerg-1427	324	37	2,0,4,3,1	2,0,4,3,1	X
fuelectenerg-1427	324	38	>	>	X
fuelectenerg-1427	324	39	x	x	X
fuelectenerg-1427	324	40	(	(	PUNCT
fuelectenerg-1427	324	41	)	)	PUNCT
fuelectenerg-1427	324	42	a	a	DET
fuelectenerg-1427	324	43	(	(	PUNCT
fuelectenerg-1427	324	44	)	)	SYM
fuelectenerg-1427	324	45	b	b	NOUN
fuelectenerg-1427	324	46	(	(	PUNCT
fuelectenerg-1427	324	47	)	)	PUNCT
fuelectenerg-1427	324	48	c	c	NOUN
fuelectenerg-1427	324	49	figure	figure	NOUN
fuelectenerg-1427	324	50	2	2	NUM
fuelectenerg-1427	324	51	:	:	PUNCT
fuelectenerg-1427	324	52	an	an	DET
fuelectenerg-1427	324	53	illustrating	illustrate	VERB
fuelectenerg-1427	324	54	example	example	NOUN
fuelectenerg-1427	324	55	of	of	ADP
fuelectenerg-1427	324	56	the	the	DET
fuelectenerg-1427	324	57	different	different	ADJ
fuelectenerg-1427	324	58	types	type	NOUN
fuelectenerg-1427	324	59	of	of	ADP
fuelectenerg-1427	324	60	literals	literal	NOUN
fuelectenerg-1427	324	61	over	over	ADP
fuelectenerg-1427	324	62	an	an	DET
fuelectenerg-1427	324	63	arbitrary	arbitrary	ADJ
fuelectenerg-1427	324	64	five	five	NUM
fuelectenerg-1427	324	65	-	-	PUNCT
fuelectenerg-1427	324	66	radix	radix	NOUN
fuelectenerg-1427	324	67	logic	logic	NOUN
fuelectenerg-1427	324	68	:	:	PUNCT
fuelectenerg-1427	324	69	(	(	PUNCT
fuelectenerg-1427	324	70	a	a	X
fuelectenerg-1427	324	71	)	)	PUNCT
fuelectenerg-1427	324	72	1	1	NUM
fuelectenerg-1427	324	73	-	-	PUNCT
fuelectenerg-1427	324	74	reduced	reduce	VERB
fuelectenerg-1427	324	75	post	post	NOUN
fuelectenerg-1427	324	76	literal	literal	ADJ
fuelectenerg-1427	324	77	(	(	PUNCT
fuelectenerg-1427	324	78	1	1	NUM
fuelectenerg-1427	324	79	-	-	PUNCT
fuelectenerg-1427	324	80	rpl	rpl	NOUN
fuelectenerg-1427	324	81	)	)	PUNCT
fuelectenerg-1427	324	82	,	,	PUNCT
fuelectenerg-1427	324	83	(	(	PUNCT
fuelectenerg-1427	324	84	b	b	X
fuelectenerg-1427	324	85	)	)	PUNCT
fuelectenerg-1427	324	86	generalized	generalized	ADJ
fuelectenerg-1427	324	87	(	(	PUNCT
fuelectenerg-1427	324	88	post	post	ADJ
fuelectenerg-1427	324	89	)	)	PUNCT
fuelectenerg-1427	324	90	literal	literal	ADJ
fuelectenerg-1427	324	91	(	(	PUNCT
fuelectenerg-1427	324	92	gl	gl	NOUN
fuelectenerg-1427	324	93	)	)	PUNCT
fuelectenerg-1427	324	94	,	,	PUNCT
fuelectenerg-1427	324	95	and	and	CCONJ
fuelectenerg-1427	324	96	(	(	PUNCT
fuelectenerg-1427	324	97	c	c	X
fuelectenerg-1427	324	98	)	)	PUNCT
fuelectenerg-1427	324	99	universal	universal	ADJ
fuelectenerg-1427	324	100	literal	literal	ADJ
fuelectenerg-1427	324	101	(	(	PUNCT
fuelectenerg-1427	324	102	ul	ul	INTJ
fuelectenerg-1427	324	103	)	)	PUNCT
fuelectenerg-1427	324	104	.	.	PUNCT
fuelectenerg-1427	325	1	since	since	SCONJ
fuelectenerg-1427	325	2	k	k	PROPN
fuelectenerg-1427	325	3	-	-	PROPN
fuelectenerg-1427	325	4	rpl	rpl	PROPN
fuelectenerg-1427	325	5	gfsop	gfsop	NOUN
fuelectenerg-1427	325	6	is	be	AUX
fuelectenerg-1427	325	7	simpler	simple	ADJ
fuelectenerg-1427	325	8	from	from	ADP
fuelectenerg-1427	325	9	implementation	implementation	NOUN
fuelectenerg-1427	325	10	point	point	NOUN
fuelectenerg-1427	325	11	of	of	ADP
fuelectenerg-1427	325	12	view	view	NOUN
fuelectenerg-1427	325	13	than	than	ADP
fuelectenerg-1427	325	14	gl	gl	INTJ
fuelectenerg-1427	325	15	or	or	CCONJ
fuelectenerg-1427	325	16	ul	ul	INTJ
fuelectenerg-1427	325	17	,	,	PUNCT
fuelectenerg-1427	325	18	we	we	PRON
fuelectenerg-1427	325	19	will	will	AUX
fuelectenerg-1427	325	20	perform	perform	VERB
fuelectenerg-1427	325	21	all	all	DET
fuelectenerg-1427	325	22	the	the	DET
fuelectenerg-1427	325	23	gfsop	gfsop	NOUN
fuelectenerg-1427	325	24	expansions	expansion	NOUN
fuelectenerg-1427	325	25	utilizing	utilize	VERB
fuelectenerg-1427	325	26	the	the	DET
fuelectenerg-1427	325	27	1	1	NUM
fuelectenerg-1427	325	28	-	-	PUNCT
fuelectenerg-1427	325	29	rpl	rpl	NOUN
fuelectenerg-1427	325	30	gfsop	gfsop	NOUN
fuelectenerg-1427	325	31	.	.	PUNCT
fuelectenerg-1427	326	1	let	let	VERB
fuelectenerg-1427	326	2	us	we	PRON
fuelectenerg-1427	326	3	define	define	VERB
fuelectenerg-1427	326	4	1	1	NUM
fuelectenerg-1427	326	5	-	-	PUNCT
fuelectenerg-1427	326	6	rpl	rpl	NOUN
fuelectenerg-1427	326	7	[	[	X
fuelectenerg-1427	326	8	1	1	NUM
fuelectenerg-1427	326	9	,	,	PUNCT
fuelectenerg-1427	326	10	17	17	NUM
fuelectenerg-1427	326	11	]	]	PUNCT
fuelectenerg-1427	326	12	as	as	ADP
fuelectenerg-1427	326	13	:	:	PUNCT
fuelectenerg-1427	326	14	ix	ix	PROPN
fuelectenerg-1427	326	15	=	=	SYM
fuelectenerg-1427	326	16	1	1	NUM
fuelectenerg-1427	326	17	iff	iff	NOUN
fuelectenerg-1427	326	18	x	x	PROPN
fuelectenerg-1427	327	1	=	=	PUNCT
fuelectenerg-1427	328	1	i	i	PRON
fuelectenerg-1427	328	2	else	else	ADV
fuelectenerg-1427	328	3	ix	ix	ADP
fuelectenerg-1427	328	4	=	=	NOUN
fuelectenerg-1427	328	5	0	0	PROPN
fuelectenerg-1427	328	6	.	.	PUNCT
fuelectenerg-1427	329	1	(	(	PUNCT
fuelectenerg-1427	329	2	5	5	NUM
fuelectenerg-1427	329	3	)	)	PUNCT
fuelectenerg-1427	329	4	for	for	ADP
fuelectenerg-1427	329	5	example	example	NOUN
fuelectenerg-1427	329	6	{	{	PUNCT
fuelectenerg-1427	329	7	0x	0x	NOUN
fuelectenerg-1427	329	8	,	,	PUNCT
fuelectenerg-1427	329	9	1x	1x	NUM
fuelectenerg-1427	329	10	,	,	PUNCT
fuelectenerg-1427	329	11	2x	2x	NUM
fuelectenerg-1427	329	12	}	}	PUNCT
fuelectenerg-1427	329	13	are	be	AUX
fuelectenerg-1427	329	14	the	the	DET
fuelectenerg-1427	329	15	zero	zero	NUM
fuelectenerg-1427	329	16	,	,	PUNCT
fuelectenerg-1427	329	17	first	first	ADV
fuelectenerg-1427	329	18	,	,	PUNCT
fuelectenerg-1427	329	19	and	and	CCONJ
fuelectenerg-1427	329	20	second	second	ADJ
fuelectenerg-1427	329	21	polarities	polarity	NOUN
fuelectenerg-1427	329	22	of	of	ADP
fuelectenerg-1427	329	23	the	the	DET
fuelectenerg-1427	329	24	1	1	NUM
fuelectenerg-1427	329	25	-	-	PUNCT
fuelectenerg-1427	329	26	rpl	rpl	NOUN
fuelectenerg-1427	329	27	,	,	PUNCT
fuelectenerg-1427	329	28	respectively	respectively	ADV
fuelectenerg-1427	329	29	.	.	PUNCT
fuelectenerg-1427	330	1	also	also	ADV
fuelectenerg-1427	330	2	,	,	PUNCT
fuelectenerg-1427	330	3	let	let	VERB
fuelectenerg-1427	330	4	us	we	PRON
fuelectenerg-1427	330	5	define	define	VERB
fuelectenerg-1427	330	6	the	the	DET
fuelectenerg-1427	330	7	ternary	ternary	ADJ
fuelectenerg-1427	330	8	shifts	shift	NOUN
fuelectenerg-1427	330	9	over	over	ADP
fuelectenerg-1427	330	10	variable	variable	ADJ
fuelectenerg-1427	330	11	x	x	NOUN
fuelectenerg-1427	330	12	as	as	ADP
fuelectenerg-1427	330	13	{	{	PUNCT
fuelectenerg-1427	330	14	x	x	NOUN
fuelectenerg-1427	330	15	,	,	PUNCT
fuelectenerg-1427	330	16	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	330	17	}	}	PUNCT
fuelectenerg-1427	330	18	as	as	ADP
fuelectenerg-1427	330	19	the	the	DET
fuelectenerg-1427	330	20	zero	zero	NUM
fuelectenerg-1427	330	21	,	,	PUNCT
fuelectenerg-1427	330	22	first	first	ADJ
fuelectenerg-1427	330	23	and	and	CCONJ
fuelectenerg-1427	330	24	second	second	ADJ
fuelectenerg-1427	330	25	shifts	shift	NOUN
fuelectenerg-1427	330	26	of	of	ADP
fuelectenerg-1427	330	27	the	the	DET
fuelectenerg-1427	330	28	variable	variable	NOUN
fuelectenerg-1427	330	29	x	x	PUNCT
fuelectenerg-1427	330	30	respectively	respectively	ADV
fuelectenerg-1427	330	31	,	,	PUNCT
fuelectenerg-1427	330	32	i.e.	i.e.	X
fuelectenerg-1427	330	33	,	,	PUNCT
fuelectenerg-1427	330	34	x	x	SYM
fuelectenerg-1427	330	35	=	=	SYM
fuelectenerg-1427	330	36	x+	x+	PUNCT
fuelectenerg-1427	330	37	0	0	NUM
fuelectenerg-1427	330	38	,	,	PUNCT
fuelectenerg-1427	330	39	x′	x′	PROPN
fuelectenerg-1427	331	1	=	=	PUNCT
fuelectenerg-1427	331	2	x+	x+	SYM
fuelectenerg-1427	331	3	1	1	NUM
fuelectenerg-1427	331	4	and	and	CCONJ
fuelectenerg-1427	331	5	x′′	x′′	PROPN
fuelectenerg-1427	331	6	=	=	PUNCT
fuelectenerg-1427	331	7	x+	x+	PROPN
fuelectenerg-1427	331	8	2	2	NUM
fuelectenerg-1427	331	9	,	,	PUNCT
fuelectenerg-1427	331	10	and	and	CCONJ
fuelectenerg-1427	331	11	x	x	PRON
fuelectenerg-1427	331	12	can	can	AUX
fuelectenerg-1427	331	13	take	take	VERB
fuelectenerg-1427	331	14	any	any	DET
fuelectenerg-1427	331	15	value	value	NOUN
fuelectenerg-1427	331	16	in	in	ADP
fuelectenerg-1427	331	17	the	the	DET
fuelectenerg-1427	331	18	set	set	NOUN
fuelectenerg-1427	331	19	{	{	PUNCT
fuelectenerg-1427	331	20	0,1,2	0,1,2	NUM
fuelectenerg-1427	331	21	}	}	PUNCT
fuelectenerg-1427	331	22	.	.	PUNCT
fuelectenerg-1427	332	1	we	we	PRON
fuelectenerg-1427	332	2	chose	choose	VERB
fuelectenerg-1427	332	3	to	to	PART
fuelectenerg-1427	332	4	represent	represent	VERB
fuelectenerg-1427	332	5	the	the	DET
fuelectenerg-1427	332	6	1	1	NUM
fuelectenerg-1427	332	7	-	-	PUNCT
fuelectenerg-1427	332	8	reduced	reduce	VERB
fuelectenerg-1427	332	9	post	post	NOUN
fuelectenerg-1427	332	10	literals	literal	NOUN
fuelectenerg-1427	332	11	in	in	ADP
fuelectenerg-1427	332	12	terms	term	NOUN
fuelectenerg-1427	332	13	of	of	ADP
fuelectenerg-1427	332	14	shifts	shift	NOUN
fuelectenerg-1427	332	15	and	and	CCONJ
fuelectenerg-1427	332	16	powers	power	NOUN
fuelectenerg-1427	332	17	,	,	PUNCT
fuelectenerg-1427	332	18	among	among	ADP
fuelectenerg-1427	332	19	others	other	NOUN
fuelectenerg-1427	332	20	,	,	PUNCT
fuelectenerg-1427	332	21	because	because	SCONJ
fuelectenerg-1427	332	22	of	of	ADP
fuelectenerg-1427	332	23	the	the	DET
fuelectenerg-1427	332	24	ease	ease	NOUN
fuelectenerg-1427	332	25	of	of	ADP
fuelectenerg-1427	332	26	the	the	DET
fuelectenerg-1427	332	27	implementation	implementation	NOUN
fuelectenerg-1427	332	28	of	of	ADP
fuelectenerg-1427	332	29	powers	power	NOUN
fuelectenerg-1427	332	30	of	of	ADP
fuelectenerg-1427	332	31	shifted	shift	VERB
fuelectenerg-1427	332	32	variables	variable	NOUN
fuelectenerg-1427	332	33	in	in	ADP
fuelectenerg-1427	332	34	hardware	hardware	NOUN
fuelectenerg-1427	332	35	as	as	SCONJ
fuelectenerg-1427	332	36	will	will	AUX
fuelectenerg-1427	332	37	be	be	AUX
fuelectenerg-1427	332	38	seen	see	VERB
fuelectenerg-1427	332	39	in	in	ADP
fuelectenerg-1427	332	40	section	section	NOUN
fuelectenerg-1427	332	41	3	3	NUM
fuelectenerg-1427	332	42	within	within	ADP
fuelectenerg-1427	332	43	universal	universal	ADJ
fuelectenerg-1427	332	44	logic	logic	NOUN
fuelectenerg-1427	332	45	modules	module	NOUN
fuelectenerg-1427	332	46	(	(	PUNCT
fuelectenerg-1427	332	47	ulms	ulm	NOUN
fuelectenerg-1427	332	48	)	)	PUNCT
fuelectenerg-1427	332	49	for	for	ADP
fuelectenerg-1427	332	50	the	the	DET
fuelectenerg-1427	332	51	production	production	NOUN
fuelectenerg-1427	332	52	of	of	ADP
fuelectenerg-1427	332	53	rpl	rpl	NOUN
fuelectenerg-1427	332	54	.	.	PUNCT
fuelectenerg-1427	333	1	the	the	DET
fuelectenerg-1427	333	2	fundamental	fundamental	ADJ
fuelectenerg-1427	333	3	shannon	shannon	PROPN
fuelectenerg-1427	333	4	expansion	expansion	NOUN
fuelectenerg-1427	333	5	over	over	ADP
fuelectenerg-1427	333	6	gf(3	gf(3	PROPN
fuelectenerg-1427	333	7	)	)	PUNCT
fuelectenerg-1427	333	8	for	for	ADP
fuelectenerg-1427	333	9	a	a	DET
fuelectenerg-1427	333	10	ternary	ternary	ADJ
fuelectenerg-1427	333	11	function	function	NOUN
fuelectenerg-1427	333	12	with	with	ADP
fuelectenerg-1427	333	13	a	a	DET
fuelectenerg-1427	333	14	single	single	ADJ
fuelectenerg-1427	333	15	variable	variable	NOUN
fuelectenerg-1427	333	16	is	be	AUX
fuelectenerg-1427	333	17	shown	show	VERB
fuelectenerg-1427	333	18	in	in	ADP
fuelectenerg-1427	333	19	theorem	theorem	ADJ
fuelectenerg-1427	333	20	1	1	NUM
fuelectenerg-1427	333	21	.	.	PUNCT
fuelectenerg-1427	333	22	theorem	theorem	NOUN
fuelectenerg-1427	333	23	1	1	NUM
fuelectenerg-1427	333	24	.	.	PUNCT
fuelectenerg-1427	333	25	shannon	shannon	PROPN
fuelectenerg-1427	333	26	expansion	expansion	PROPN
fuelectenerg-1427	333	27	over	over	ADP
fuelectenerg-1427	333	28	gf(3	gf(3	PROPN
fuelectenerg-1427	333	29	)	)	PUNCT
fuelectenerg-1427	333	30	for	for	ADP
fuelectenerg-1427	333	31	a	a	DET
fuelectenerg-1427	333	32	function	function	NOUN
fuelectenerg-1427	333	33	with	with	ADP
fuelectenerg-1427	333	34	a	a	DET
fuelectenerg-1427	333	35	single	single	ADJ
fuelectenerg-1427	333	36	variable	variable	NOUN
fuelectenerg-1427	333	37	is	be	AUX
fuelectenerg-1427	333	38	:	:	PUNCT
fuelectenerg-1427	333	39	f	f	X
fuelectenerg-1427	334	1	=	=	SYM
fuelectenerg-1427	334	2	0x	0x	NUM
fuelectenerg-1427	334	3	f0	f0	PROPN
fuelectenerg-1427	334	4	+	+	CCONJ
fuelectenerg-1427	334	5	1x	1x	NUM
fuelectenerg-1427	334	6	f1	f1	NOUN
fuelectenerg-1427	334	7	+	+	CCONJ
fuelectenerg-1427	334	8	2x	2x	NUM
fuelectenerg-1427	334	9	f2	f2	PROPN
fuelectenerg-1427	334	10	,	,	PUNCT
fuelectenerg-1427	334	11	(	(	PUNCT
fuelectenerg-1427	334	12	6	6	NUM
fuelectenerg-1427	334	13	)	)	PUNCT
fuelectenerg-1427	334	14	where	where	SCONJ
fuelectenerg-1427	334	15	f0	f0	PROPN
fuelectenerg-1427	334	16	is	be	AUX
fuelectenerg-1427	334	17	cofactor	cofactor	NOUN
fuelectenerg-1427	334	18	of	of	ADP
fuelectenerg-1427	334	19	f	f	PROPN
fuelectenerg-1427	334	20	with	with	ADP
fuelectenerg-1427	334	21	respect	respect	NOUN
fuelectenerg-1427	334	22	to	to	ADP
fuelectenerg-1427	334	23	variable	variable	NOUN
fuelectenerg-1427	334	24	x	x	PUNCT
fuelectenerg-1427	334	25	of	of	ADP
fuelectenerg-1427	334	26	value	value	NOUN
fuelectenerg-1427	334	27	0	0	NUM
fuelectenerg-1427	334	28	,	,	PUNCT
fuelectenerg-1427	334	29	f1	f1	NOUN
fuelectenerg-1427	334	30	is	be	AUX
fuelectenerg-1427	334	31	cofactor	cofactor	NOUN
fuelectenerg-1427	334	32	of	of	ADP
fuelectenerg-1427	334	33	f	f	PROPN
fuelectenerg-1427	334	34	with	with	ADP
fuelectenerg-1427	334	35	respect	respect	NOUN
fuelectenerg-1427	334	36	to	to	ADP
fuelectenerg-1427	334	37	variable	variable	NOUN
fuelectenerg-1427	334	38	x	x	PUNCT
fuelectenerg-1427	334	39	of	of	ADP
fuelectenerg-1427	334	40	value	value	NOUN
fuelectenerg-1427	334	41	1	1	NUM
fuelectenerg-1427	334	42	,	,	PUNCT
fuelectenerg-1427	334	43	and	and	CCONJ
fuelectenerg-1427	334	44	f2	f2	PROPN
fuelectenerg-1427	334	45	is	be	AUX
fuelectenerg-1427	334	46	cofactor	cofactor	NOUN
fuelectenerg-1427	334	47	of	of	ADP
fuelectenerg-1427	334	48	f	f	PROPN
fuelectenerg-1427	334	49	with	with	ADP
fuelectenerg-1427	334	50	respect	respect	NOUN
fuelectenerg-1427	334	51	to	to	ADP
fuelectenerg-1427	334	52	variable	variable	NOUN
fuelectenerg-1427	334	53	x	x	PUNCT
fuelectenerg-1427	334	54	of	of	ADP
fuelectenerg-1427	334	55	value	value	NOUN
fuelectenerg-1427	334	56	2	2	NUM
fuelectenerg-1427	334	57	.	.	NOUN
fuelectenerg-1427	334	58	104	104	NUM
fuelectenerg-1427	334	59	an	an	DET
fuelectenerg-1427	334	60	extended	extend	VERB
fuelectenerg-1427	334	61	green	green	ADJ
fuelectenerg-1427	334	62	sasao	sasao	PROPN
fuelectenerg-1427	334	63	hierarchy	hierarchy	NOUN
fuelectenerg-1427	334	64	of	of	ADP
fuelectenerg-1427	334	65	canonical	canonical	ADJ
fuelectenerg-1427	334	66	ternary	ternary	ADJ
fuelectenerg-1427	334	67	galois	galois	NOUN
fuelectenerg-1427	334	68	forms	form	NOUN
fuelectenerg-1427	334	69	...	...	PUNCT
fuelectenerg-1427	334	70	literals	literal	NOUN
fuelectenerg-1427	334	71	.	.	PUNCT
fuelectenerg-1427	335	1	galois	galois	PROPN
fuelectenerg-1427	335	2	field	field	NOUN
fuelectenerg-1427	335	3	sum	sum	NOUN
fuelectenerg-1427	335	4	-	-	PUNCT
fuelectenerg-1427	335	5	of	of	ADP
fuelectenerg-1427	335	6	-	-	PUNCT
fuelectenerg-1427	335	7	products	product	NOUN
fuelectenerg-1427	335	8	expansions	expansion	NOUN
fuelectenerg-1427	335	9	can	can	AUX
fuelectenerg-1427	335	10	be	be	AUX
fuelectenerg-1427	335	11	performed	perform	VERB
fuelectenerg-1427	335	12	utilizing	utilize	VERB
fuelectenerg-1427	335	13	variety	variety	NOUN
fuelectenerg-1427	335	14	uses	use	NOUN
fuelectenerg-1427	335	15	of	of	ADP
fuelectenerg-1427	335	16	literals	literal	NOUN
fuelectenerg-1427	335	17	.	.	PUNCT
fuelectenerg-1427	336	1	for	for	ADP
fuelectenerg-1427	336	2	example	example	NOUN
fuelectenerg-1427	336	3	,	,	PUNCT
fuelectenerg-1427	336	4	one	one	PRON
fuelectenerg-1427	336	5	can	can	AUX
fuelectenerg-1427	336	6	use	use	VERB
fuelectenerg-1427	336	7	k	k	ADV
fuelectenerg-1427	336	8	-	-	PUNCT
fuelectenerg-1427	336	9	reduced	reduce	VERB
fuelectenerg-1427	336	10	post	post	NOUN
fuelectenerg-1427	336	11	literal	literal	ADJ
fuelectenerg-1427	336	12	(	(	PUNCT
fuelectenerg-1427	336	13	k	k	X
fuelectenerg-1427	336	14	-	-	NOUN
fuelectenerg-1427	336	15	rpl	rpl	NOUN
fuelectenerg-1427	336	16	)	)	PUNCT
fuelectenerg-1427	336	17	to	to	PART
fuelectenerg-1427	336	18	produce	produce	VERB
fuelectenerg-1427	336	19	k	k	ADJ
fuelectenerg-1427	336	20	-	-	ADJ
fuelectenerg-1427	336	21	rpl	rpl	PROPN
fuelectenerg-1427	336	22	gfsop	gfsop	NOUN
fuelectenerg-1427	336	23	,	,	PUNCT
fuelectenerg-1427	336	24	generalized	generalize	VERB
fuelectenerg-1427	336	25	(	(	PUNCT
fuelectenerg-1427	336	26	post	post	ADJ
fuelectenerg-1427	336	27	)	)	PUNCT
fuelectenerg-1427	336	28	literal	literal	ADJ
fuelectenerg-1427	336	29	(	(	PUNCT
fuelectenerg-1427	336	30	gl	gl	NOUN
fuelectenerg-1427	336	31	)	)	PUNCT
fuelectenerg-1427	336	32	to	to	PART
fuelectenerg-1427	336	33	produce	produce	VERB
fuelectenerg-1427	336	34	gl	gl	NOUN
fuelectenerg-1427	336	35	gfsop	gfsop	PROPN
fuelectenerg-1427	336	36	,	,	PUNCT
fuelectenerg-1427	336	37	and	and	CCONJ
fuelectenerg-1427	336	38	universal	universal	ADJ
fuelectenerg-1427	336	39	literal	literal	ADJ
fuelectenerg-1427	336	40	(	(	PUNCT
fuelectenerg-1427	336	41	ul	ul	INTJ
fuelectenerg-1427	336	42	)	)	PUNCT
fuelectenerg-1427	336	43	to	to	PART
fuelectenerg-1427	336	44	produce	produce	VERB
fuelectenerg-1427	336	45	ul	ul	INTJ
fuelectenerg-1427	336	46	gfsop	gfsop	PROPN
fuelectenerg-1427	336	47	.	.	PUNCT
fuelectenerg-1427	336	48	example	example	NOUN
fuelectenerg-1427	337	1	1	1	NUM
fuelectenerg-1427	337	2	.	.	PUNCT
fuelectenerg-1427	337	3	figure	figure	NOUN
fuelectenerg-1427	337	4	2	2	NUM
fuelectenerg-1427	337	5	demonstrates	demonstrate	VERB
fuelectenerg-1427	337	6	several	several	ADJ
fuelectenerg-1427	337	7	literal	literal	ADJ
fuelectenerg-1427	337	8	types	type	NOUN
fuelectenerg-1427	337	9	,	,	PUNCT
fuelectenerg-1427	337	10	where	where	SCONJ
fuelectenerg-1427	337	11	one	one	NUM
fuelectenerg-1427	337	12	proceeds	proceed	VERB
fuelectenerg-1427	337	13	from	from	ADP
fuelectenerg-1427	337	14	the	the	DET
fuelectenerg-1427	337	15	simplest	simple	ADJ
fuelectenerg-1427	337	16	literal	literal	NOUN
fuelectenerg-1427	337	17	in	in	ADP
fuelectenerg-1427	337	18	figure	figure	NOUN
fuelectenerg-1427	337	19	2(a	2(a	NUM
fuelectenerg-1427	337	20	)	)	PUNCT
fuelectenerg-1427	337	21	(	(	PUNCT
fuelectenerg-1427	337	22	i.e.	i.e.	X
fuelectenerg-1427	337	23	,	,	PUNCT
fuelectenerg-1427	337	24	rpl	rpl	PROPN
fuelectenerg-1427	337	25	)	)	PUNCT
fuelectenerg-1427	337	26	to	to	ADP
fuelectenerg-1427	337	27	the	the	DET
fuelectenerg-1427	337	28	most	most	ADV
fuelectenerg-1427	337	29	complex	complex	ADJ
fuelectenerg-1427	337	30	universal	universal	ADJ
fuelectenerg-1427	337	31	literal	literal	NOUN
fuelectenerg-1427	337	32	in	in	ADP
fuelectenerg-1427	337	33	figure	figure	NOUN
fuelectenerg-1427	337	34	2(c	2(c	NUM
fuelectenerg-1427	337	35	)	)	PUNCT
fuelectenerg-1427	337	36	.	.	PUNCT
fuelectenerg-1427	338	1	for	for	ADP
fuelectenerg-1427	338	2	rpl	rpl	NOUN
fuelectenerg-1427	338	3	in	in	ADP
fuelectenerg-1427	338	4	figure	figure	NOUN
fuelectenerg-1427	338	5	2(a	2(a	NUM
fuelectenerg-1427	338	6	)	)	PUNCT
fuelectenerg-1427	338	7	,	,	PUNCT
fuelectenerg-1427	338	8	a	a	DET
fuelectenerg-1427	338	9	value	value	NOUN
fuelectenerg-1427	338	10	k	k	NOUN
fuelectenerg-1427	338	11	is	be	AUX
fuelectenerg-1427	338	12	produced	produce	VERB
fuelectenerg-1427	338	13	by	by	ADP
fuelectenerg-1427	338	14	the	the	DET
fuelectenerg-1427	338	15	literal	literal	NOUN
fuelectenerg-1427	338	16	when	when	SCONJ
fuelectenerg-1427	338	17	the	the	DET
fuelectenerg-1427	338	18	value	value	NOUN
fuelectenerg-1427	338	19	of	of	ADP
fuelectenerg-1427	338	20	the	the	DET
fuelectenerg-1427	338	21	variable	variable	NOUN
fuelectenerg-1427	338	22	is	be	AUX
fuelectenerg-1427	338	23	equal	equal	ADJ
fuelectenerg-1427	338	24	to	to	ADP
fuelectenerg-1427	338	25	a	a	DET
fuelectenerg-1427	338	26	specific	specific	ADJ
fuelectenerg-1427	338	27	state	state	NOUN
fuelectenerg-1427	338	28	,	,	PUNCT
fuelectenerg-1427	338	29	and	and	CCONJ
fuelectenerg-1427	338	30	in	in	ADP
fuelectenerg-1427	338	31	this	this	DET
fuelectenerg-1427	338	32	particular	particular	ADJ
fuelectenerg-1427	338	33	example	example	NOUN
fuelectenerg-1427	338	34	a	a	DET
fuelectenerg-1427	338	35	value	value	NOUN
fuelectenerg-1427	338	36	of	of	ADP
fuelectenerg-1427	338	37	k	k	PROPN
fuelectenerg-1427	338	38	=	=	SYM
fuelectenerg-1427	338	39	1	1	NUM
fuelectenerg-1427	338	40	is	be	AUX
fuelectenerg-1427	338	41	generated	generate	VERB
fuelectenerg-1427	338	42	by	by	ADP
fuelectenerg-1427	338	43	the	the	DET
fuelectenerg-1427	338	44	1	1	NUM
fuelectenerg-1427	338	45	-	-	PUNCT
fuelectenerg-1427	338	46	rpl	rpl	NOUN
fuelectenerg-1427	338	47	when	when	SCONJ
fuelectenerg-1427	338	48	the	the	DET
fuelectenerg-1427	338	49	value	value	NOUN
fuelectenerg-1427	338	50	of	of	ADP
fuelectenerg-1427	338	51	variable	variable	NOUN
fuelectenerg-1427	338	52	x	x	PUNCT
fuelectenerg-1427	338	53	is	be	AUX
fuelectenerg-1427	338	54	equal	equal	ADJ
fuelectenerg-1427	338	55	to	to	ADP
fuelectenerg-1427	338	56	certain	certain	ADJ
fuelectenerg-1427	338	57	state	state	NOUN
fuelectenerg-1427	338	58	where	where	SCONJ
fuelectenerg-1427	338	59	this	this	DET
fuelectenerg-1427	338	60	state	state	NOUN
fuelectenerg-1427	338	61	here	here	ADV
fuelectenerg-1427	338	62	equals	equal	VERB
fuelectenerg-1427	338	63	to	to	ADP
fuelectenerg-1427	338	64	one	one	NUM
fuelectenerg-1427	338	65	.	.	PUNCT
fuelectenerg-1427	339	1	the	the	DET
fuelectenerg-1427	339	2	gl	gl	PROPN
fuelectenerg-1427	339	3	in	in	ADP
fuelectenerg-1427	339	4	figure	figure	NOUN
fuelectenerg-1427	339	5	2(b	2(b	NUM
fuelectenerg-1427	339	6	)	)	PUNCT
fuelectenerg-1427	339	7	produces	produce	VERB
fuelectenerg-1427	339	8	a	a	DET
fuelectenerg-1427	339	9	value	value	NOUN
fuelectenerg-1427	339	10	of	of	ADP
fuelectenerg-1427	339	11	radix	radix	NOUN
fuelectenerg-1427	339	12	for	for	ADP
fuelectenerg-1427	339	13	a	a	DET
fuelectenerg-1427	339	14	set	set	NOUN
fuelectenerg-1427	339	15	of	of	ADP
fuelectenerg-1427	339	16	distinct	distinct	ADJ
fuelectenerg-1427	339	17	states	state	NOUN
fuelectenerg-1427	339	18	.	.	PUNCT
fuelectenerg-1427	340	1	one	one	NUM
fuelectenerg-1427	340	2	notes	note	VERB
fuelectenerg-1427	340	3	that	that	SCONJ
fuelectenerg-1427	340	4	,	,	PUNCT
fuelectenerg-1427	340	5	in	in	ADP
fuelectenerg-1427	340	6	contrast	contrast	NOUN
fuelectenerg-1427	340	7	to	to	ADP
fuelectenerg-1427	340	8	the	the	DET
fuelectenerg-1427	340	9	other	other	ADJ
fuelectenerg-1427	340	10	literals	literal	NOUN
fuelectenerg-1427	340	11	,	,	PUNCT
fuelectenerg-1427	340	12	ul	ul	INTJ
fuelectenerg-1427	340	13	in	in	ADP
fuelectenerg-1427	340	14	figure	figure	NOUN
fuelectenerg-1427	340	15	2(c	2(c	NUM
fuelectenerg-1427	340	16	)	)	PUNCT
fuelectenerg-1427	340	17	can	can	AUX
fuelectenerg-1427	340	18	have	have	VERB
fuelectenerg-1427	340	19	any	any	DET
fuelectenerg-1427	340	20	value	value	NOUN
fuelectenerg-1427	340	21	of	of	ADP
fuelectenerg-1427	340	22	the	the	DET
fuelectenerg-1427	340	23	logic	logic	NOUN
fuelectenerg-1427	340	24	system	system	NOUN
fuelectenerg-1427	340	25	at	at	ADP
fuelectenerg-1427	340	26	distinct	distinct	ADJ
fuelectenerg-1427	340	27	states	state	NOUN
fuelectenerg-1427	340	28	,	,	PUNCT
fuelectenerg-1427	340	29	and	and	CCONJ
fuelectenerg-1427	340	30	thus	thus	ADV
fuelectenerg-1427	340	31	ul	ul	INTJ
fuelectenerg-1427	340	32	has	have	VERB
fuelectenerg-1427	340	33	the	the	DET
fuelectenerg-1427	340	34	highest	high	ADJ
fuelectenerg-1427	340	35	complexity	complexity	NOUN
fuelectenerg-1427	340	36	among	among	ADP
fuelectenerg-1427	340	37	the	the	DET
fuelectenerg-1427	340	38	different	different	ADJ
fuelectenerg-1427	340	39	types	type	NOUN
fuelectenerg-1427	340	40	of	of	ADP
fuelectenerg-1427	340	41	literals	literal	NOUN
fuelectenerg-1427	340	42	.	.	PUNCT
fuelectenerg-1427	341	1	0	0	NUM
fuelectenerg-1427	341	2	0	0	NUM
fuelectenerg-1427	342	1	01	01	NUM
fuelectenerg-1427	342	2	1	1	NUM
fuelectenerg-1427	342	3	1	1	NUM
fuelectenerg-1427	342	4	1	1	NUM
fuelectenerg-1427	342	5	1	1	NUM
fuelectenerg-1427	342	6	12	12	NUM
fuelectenerg-1427	342	7	2	2	NUM
fuelectenerg-1427	342	8	2	2	NUM
fuelectenerg-1427	342	9	2	2	NUM
fuelectenerg-1427	342	10	2	2	NUM
fuelectenerg-1427	342	11	23	23	NUM
fuelectenerg-1427	342	12	3	3	NUM
fuelectenerg-1427	342	13	3	3	NUM
fuelectenerg-1427	342	14	3	3	NUM
fuelectenerg-1427	342	15	3	3	NUM
fuelectenerg-1427	342	16	34	34	NUM
fuelectenerg-1427	342	17	4	4	NUM
fuelectenerg-1427	342	18	4	4	NUM
fuelectenerg-1427	342	19	4	4	NUM
fuelectenerg-1427	342	20	4	4	NUM
fuelectenerg-1427	342	21	4x	4x	NOUN
fuelectenerg-1427	342	22	x	x	SYM
fuelectenerg-1427	342	23	x	x	SYM
fuelectenerg-1427	342	24	1	1	NUM
fuelectenerg-1427	342	25	x	x	SYM
fuelectenerg-1427	342	26	l	l	NOUN
fuelectenerg-1427	342	27	(	(	PUNCT
fuelectenerg-1427	342	28	)	)	PUNCT
fuelectenerg-1427	342	29	{	{	PUNCT
fuelectenerg-1427	342	30	1,3	1,3	NUM
fuelectenerg-1427	342	31	}	}	PUNCT
fuelectenerg-1427	342	32	x	x	X
fuelectenerg-1427	342	33	l	l	NOUN
fuelectenerg-1427	342	34	(	(	PUNCT
fuelectenerg-1427	342	35	)	)	PUNCT
fuelectenerg-1427	342	36	<	<	X
fuelectenerg-1427	342	37	2,0,4,3,1	2,0,4,3,1	X
fuelectenerg-1427	342	38	>	>	X
fuelectenerg-1427	342	39	x	x	X
fuelectenerg-1427	342	40	(	(	PUNCT
fuelectenerg-1427	342	41	)	)	PUNCT
fuelectenerg-1427	342	42	a	a	DET
fuelectenerg-1427	342	43	(	(	PUNCT
fuelectenerg-1427	342	44	)	)	SYM
fuelectenerg-1427	342	45	b	b	NOUN
fuelectenerg-1427	342	46	(	(	PUNCT
fuelectenerg-1427	342	47	)	)	PUNCT
fuelectenerg-1427	342	48	c	c	NOUN
fuelectenerg-1427	342	49	figure	figure	NOUN
fuelectenerg-1427	342	50	2	2	NUM
fuelectenerg-1427	342	51	:	:	PUNCT
fuelectenerg-1427	342	52	an	an	DET
fuelectenerg-1427	342	53	illustrating	illustrate	VERB
fuelectenerg-1427	342	54	example	example	NOUN
fuelectenerg-1427	342	55	of	of	ADP
fuelectenerg-1427	342	56	the	the	DET
fuelectenerg-1427	342	57	different	different	ADJ
fuelectenerg-1427	342	58	types	type	NOUN
fuelectenerg-1427	342	59	of	of	ADP
fuelectenerg-1427	342	60	literals	literal	NOUN
fuelectenerg-1427	342	61	over	over	ADP
fuelectenerg-1427	342	62	an	an	DET
fuelectenerg-1427	342	63	arbitrary	arbitrary	ADJ
fuelectenerg-1427	342	64	five	five	NUM
fuelectenerg-1427	342	65	-	-	PUNCT
fuelectenerg-1427	342	66	radix	radix	NOUN
fuelectenerg-1427	342	67	logic	logic	NOUN
fuelectenerg-1427	342	68	:	:	PUNCT
fuelectenerg-1427	342	69	(	(	PUNCT
fuelectenerg-1427	342	70	a	a	X
fuelectenerg-1427	342	71	)	)	PUNCT
fuelectenerg-1427	342	72	1	1	NUM
fuelectenerg-1427	342	73	-	-	PUNCT
fuelectenerg-1427	342	74	reduced	reduce	VERB
fuelectenerg-1427	342	75	post	post	NOUN
fuelectenerg-1427	342	76	literal	literal	ADJ
fuelectenerg-1427	342	77	(	(	PUNCT
fuelectenerg-1427	342	78	1	1	NUM
fuelectenerg-1427	342	79	-	-	PUNCT
fuelectenerg-1427	342	80	rpl	rpl	NOUN
fuelectenerg-1427	342	81	)	)	PUNCT
fuelectenerg-1427	342	82	,	,	PUNCT
fuelectenerg-1427	342	83	(	(	PUNCT
fuelectenerg-1427	342	84	b	b	X
fuelectenerg-1427	342	85	)	)	PUNCT
fuelectenerg-1427	342	86	generalized	generalized	ADJ
fuelectenerg-1427	342	87	(	(	PUNCT
fuelectenerg-1427	342	88	post	post	ADJ
fuelectenerg-1427	342	89	)	)	PUNCT
fuelectenerg-1427	342	90	literal	literal	ADJ
fuelectenerg-1427	342	91	(	(	PUNCT
fuelectenerg-1427	342	92	gl	gl	NOUN
fuelectenerg-1427	342	93	)	)	PUNCT
fuelectenerg-1427	342	94	,	,	PUNCT
fuelectenerg-1427	342	95	and	and	CCONJ
fuelectenerg-1427	342	96	(	(	PUNCT
fuelectenerg-1427	342	97	c	c	X
fuelectenerg-1427	342	98	)	)	PUNCT
fuelectenerg-1427	342	99	universal	universal	ADJ
fuelectenerg-1427	342	100	literal	literal	ADJ
fuelectenerg-1427	342	101	(	(	PUNCT
fuelectenerg-1427	342	102	ul	ul	INTJ
fuelectenerg-1427	342	103	)	)	PUNCT
fuelectenerg-1427	342	104	.	.	PUNCT
fuelectenerg-1427	343	1	since	since	SCONJ
fuelectenerg-1427	343	2	k	k	PROPN
fuelectenerg-1427	343	3	-	-	PROPN
fuelectenerg-1427	343	4	rpl	rpl	PROPN
fuelectenerg-1427	343	5	gfsop	gfsop	NOUN
fuelectenerg-1427	343	6	is	be	AUX
fuelectenerg-1427	343	7	simpler	simple	ADJ
fuelectenerg-1427	343	8	from	from	ADP
fuelectenerg-1427	343	9	implementation	implementation	NOUN
fuelectenerg-1427	343	10	point	point	NOUN
fuelectenerg-1427	343	11	of	of	ADP
fuelectenerg-1427	343	12	view	view	NOUN
fuelectenerg-1427	343	13	than	than	ADP
fuelectenerg-1427	343	14	gl	gl	INTJ
fuelectenerg-1427	343	15	or	or	CCONJ
fuelectenerg-1427	343	16	ul	ul	INTJ
fuelectenerg-1427	343	17	,	,	PUNCT
fuelectenerg-1427	343	18	we	we	PRON
fuelectenerg-1427	343	19	will	will	AUX
fuelectenerg-1427	343	20	perform	perform	VERB
fuelectenerg-1427	343	21	all	all	DET
fuelectenerg-1427	343	22	the	the	DET
fuelectenerg-1427	343	23	gfsop	gfsop	NOUN
fuelectenerg-1427	343	24	expansions	expansion	NOUN
fuelectenerg-1427	343	25	utilizing	utilize	VERB
fuelectenerg-1427	343	26	the	the	DET
fuelectenerg-1427	343	27	1	1	NUM
fuelectenerg-1427	343	28	-	-	PUNCT
fuelectenerg-1427	343	29	rpl	rpl	NOUN
fuelectenerg-1427	343	30	gfsop	gfsop	NOUN
fuelectenerg-1427	343	31	.	.	PUNCT
fuelectenerg-1427	344	1	let	let	VERB
fuelectenerg-1427	344	2	us	we	PRON
fuelectenerg-1427	344	3	define	define	VERB
fuelectenerg-1427	344	4	1	1	NUM
fuelectenerg-1427	344	5	-	-	PUNCT
fuelectenerg-1427	344	6	rpl	rpl	NOUN
fuelectenerg-1427	344	7	[	[	X
fuelectenerg-1427	344	8	1	1	NUM
fuelectenerg-1427	344	9	,	,	PUNCT
fuelectenerg-1427	344	10	17	17	NUM
fuelectenerg-1427	344	11	]	]	PUNCT
fuelectenerg-1427	344	12	as	as	ADP
fuelectenerg-1427	344	13	:	:	PUNCT
fuelectenerg-1427	344	14	ix	ix	PROPN
fuelectenerg-1427	344	15	=	=	SYM
fuelectenerg-1427	344	16	1	1	NUM
fuelectenerg-1427	344	17	iff	iff	NOUN
fuelectenerg-1427	344	18	x	x	PROPN
fuelectenerg-1427	345	1	=	=	PUNCT
fuelectenerg-1427	346	1	i	i	PRON
fuelectenerg-1427	346	2	else	else	ADV
fuelectenerg-1427	346	3	ix	ix	ADP
fuelectenerg-1427	346	4	=	=	NOUN
fuelectenerg-1427	346	5	0	0	PROPN
fuelectenerg-1427	346	6	.	.	PUNCT
fuelectenerg-1427	347	1	(	(	PUNCT
fuelectenerg-1427	347	2	5	5	NUM
fuelectenerg-1427	347	3	)	)	PUNCT
fuelectenerg-1427	347	4	for	for	ADP
fuelectenerg-1427	347	5	example	example	NOUN
fuelectenerg-1427	347	6	{	{	PUNCT
fuelectenerg-1427	347	7	0x	0x	NOUN
fuelectenerg-1427	347	8	,	,	PUNCT
fuelectenerg-1427	347	9	1x	1x	NUM
fuelectenerg-1427	347	10	,	,	PUNCT
fuelectenerg-1427	347	11	2x	2x	NUM
fuelectenerg-1427	347	12	}	}	PUNCT
fuelectenerg-1427	347	13	are	be	AUX
fuelectenerg-1427	347	14	the	the	DET
fuelectenerg-1427	347	15	zero	zero	NUM
fuelectenerg-1427	347	16	,	,	PUNCT
fuelectenerg-1427	347	17	first	first	ADV
fuelectenerg-1427	347	18	,	,	PUNCT
fuelectenerg-1427	347	19	and	and	CCONJ
fuelectenerg-1427	347	20	second	second	ADJ
fuelectenerg-1427	347	21	polarities	polarity	NOUN
fuelectenerg-1427	347	22	of	of	ADP
fuelectenerg-1427	347	23	the	the	DET
fuelectenerg-1427	347	24	1	1	NUM
fuelectenerg-1427	347	25	-	-	PUNCT
fuelectenerg-1427	347	26	rpl	rpl	NOUN
fuelectenerg-1427	347	27	,	,	PUNCT
fuelectenerg-1427	347	28	respectively	respectively	ADV
fuelectenerg-1427	347	29	.	.	PUNCT
fuelectenerg-1427	348	1	also	also	ADV
fuelectenerg-1427	348	2	,	,	PUNCT
fuelectenerg-1427	348	3	let	let	VERB
fuelectenerg-1427	348	4	us	we	PRON
fuelectenerg-1427	348	5	define	define	VERB
fuelectenerg-1427	348	6	the	the	DET
fuelectenerg-1427	348	7	ternary	ternary	ADJ
fuelectenerg-1427	348	8	shifts	shift	NOUN
fuelectenerg-1427	348	9	over	over	ADP
fuelectenerg-1427	348	10	variable	variable	ADJ
fuelectenerg-1427	348	11	x	x	NOUN
fuelectenerg-1427	348	12	as	as	ADP
fuelectenerg-1427	348	13	{	{	PUNCT
fuelectenerg-1427	348	14	x	x	NOUN
fuelectenerg-1427	348	15	,	,	PUNCT
fuelectenerg-1427	348	16	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	348	17	}	}	PUNCT
fuelectenerg-1427	348	18	as	as	ADP
fuelectenerg-1427	348	19	the	the	DET
fuelectenerg-1427	348	20	zero	zero	NUM
fuelectenerg-1427	348	21	,	,	PUNCT
fuelectenerg-1427	348	22	first	first	ADJ
fuelectenerg-1427	348	23	and	and	CCONJ
fuelectenerg-1427	348	24	second	second	ADJ
fuelectenerg-1427	348	25	shifts	shift	NOUN
fuelectenerg-1427	348	26	of	of	ADP
fuelectenerg-1427	348	27	the	the	DET
fuelectenerg-1427	348	28	variable	variable	NOUN
fuelectenerg-1427	348	29	x	x	PUNCT
fuelectenerg-1427	348	30	respectively	respectively	ADV
fuelectenerg-1427	348	31	,	,	PUNCT
fuelectenerg-1427	348	32	i.e.	i.e.	X
fuelectenerg-1427	348	33	,	,	PUNCT
fuelectenerg-1427	348	34	x	x	SYM
fuelectenerg-1427	348	35	=	=	SYM
fuelectenerg-1427	348	36	x+	x+	PUNCT
fuelectenerg-1427	348	37	0	0	NUM
fuelectenerg-1427	348	38	,	,	PUNCT
fuelectenerg-1427	348	39	x′	x′	PROPN
fuelectenerg-1427	349	1	=	=	PUNCT
fuelectenerg-1427	349	2	x+	x+	SYM
fuelectenerg-1427	349	3	1	1	NUM
fuelectenerg-1427	349	4	and	and	CCONJ
fuelectenerg-1427	349	5	x′′	x′′	PROPN
fuelectenerg-1427	349	6	=	=	PUNCT
fuelectenerg-1427	349	7	x+	x+	PROPN
fuelectenerg-1427	349	8	2	2	NUM
fuelectenerg-1427	349	9	,	,	PUNCT
fuelectenerg-1427	349	10	and	and	CCONJ
fuelectenerg-1427	349	11	x	x	PRON
fuelectenerg-1427	349	12	can	can	AUX
fuelectenerg-1427	349	13	take	take	VERB
fuelectenerg-1427	349	14	any	any	DET
fuelectenerg-1427	349	15	value	value	NOUN
fuelectenerg-1427	349	16	in	in	ADP
fuelectenerg-1427	349	17	the	the	DET
fuelectenerg-1427	349	18	set	set	NOUN
fuelectenerg-1427	349	19	{	{	PUNCT
fuelectenerg-1427	349	20	0,1,2	0,1,2	NUM
fuelectenerg-1427	349	21	}	}	PUNCT
fuelectenerg-1427	349	22	.	.	PUNCT
fuelectenerg-1427	350	1	we	we	PRON
fuelectenerg-1427	350	2	chose	choose	VERB
fuelectenerg-1427	350	3	to	to	PART
fuelectenerg-1427	350	4	represent	represent	VERB
fuelectenerg-1427	350	5	the	the	DET
fuelectenerg-1427	350	6	1	1	NUM
fuelectenerg-1427	350	7	-	-	PUNCT
fuelectenerg-1427	350	8	reduced	reduce	VERB
fuelectenerg-1427	350	9	post	post	NOUN
fuelectenerg-1427	350	10	literals	literal	NOUN
fuelectenerg-1427	350	11	in	in	ADP
fuelectenerg-1427	350	12	terms	term	NOUN
fuelectenerg-1427	350	13	of	of	ADP
fuelectenerg-1427	350	14	shifts	shift	NOUN
fuelectenerg-1427	350	15	and	and	CCONJ
fuelectenerg-1427	350	16	powers	power	NOUN
fuelectenerg-1427	350	17	,	,	PUNCT
fuelectenerg-1427	350	18	among	among	ADP
fuelectenerg-1427	350	19	others	other	NOUN
fuelectenerg-1427	350	20	,	,	PUNCT
fuelectenerg-1427	350	21	because	because	SCONJ
fuelectenerg-1427	350	22	of	of	ADP
fuelectenerg-1427	350	23	the	the	DET
fuelectenerg-1427	350	24	ease	ease	NOUN
fuelectenerg-1427	350	25	of	of	ADP
fuelectenerg-1427	350	26	the	the	DET
fuelectenerg-1427	350	27	implementation	implementation	NOUN
fuelectenerg-1427	350	28	of	of	ADP
fuelectenerg-1427	350	29	powers	power	NOUN
fuelectenerg-1427	350	30	of	of	ADP
fuelectenerg-1427	350	31	shifted	shift	VERB
fuelectenerg-1427	350	32	variables	variable	NOUN
fuelectenerg-1427	350	33	in	in	ADP
fuelectenerg-1427	350	34	hardware	hardware	NOUN
fuelectenerg-1427	350	35	as	as	SCONJ
fuelectenerg-1427	350	36	will	will	AUX
fuelectenerg-1427	350	37	be	be	AUX
fuelectenerg-1427	350	38	seen	see	VERB
fuelectenerg-1427	350	39	in	in	ADP
fuelectenerg-1427	350	40	section	section	NOUN
fuelectenerg-1427	350	41	3	3	NUM
fuelectenerg-1427	350	42	within	within	ADP
fuelectenerg-1427	350	43	universal	universal	ADJ
fuelectenerg-1427	350	44	logic	logic	NOUN
fuelectenerg-1427	350	45	modules	module	NOUN
fuelectenerg-1427	350	46	(	(	PUNCT
fuelectenerg-1427	350	47	ulms	ulm	NOUN
fuelectenerg-1427	350	48	)	)	PUNCT
fuelectenerg-1427	350	49	for	for	ADP
fuelectenerg-1427	350	50	the	the	DET
fuelectenerg-1427	350	51	production	production	NOUN
fuelectenerg-1427	350	52	of	of	ADP
fuelectenerg-1427	350	53	rpl	rpl	NOUN
fuelectenerg-1427	350	54	.	.	PUNCT
fuelectenerg-1427	351	1	the	the	DET
fuelectenerg-1427	351	2	fundamental	fundamental	ADJ
fuelectenerg-1427	351	3	shannon	shannon	PROPN
fuelectenerg-1427	351	4	expansion	expansion	NOUN
fuelectenerg-1427	351	5	over	over	ADP
fuelectenerg-1427	351	6	gf(3	gf(3	PROPN
fuelectenerg-1427	351	7	)	)	PUNCT
fuelectenerg-1427	351	8	for	for	ADP
fuelectenerg-1427	351	9	a	a	DET
fuelectenerg-1427	351	10	ternary	ternary	ADJ
fuelectenerg-1427	351	11	function	function	NOUN
fuelectenerg-1427	351	12	with	with	ADP
fuelectenerg-1427	351	13	a	a	DET
fuelectenerg-1427	351	14	single	single	ADJ
fuelectenerg-1427	351	15	variable	variable	NOUN
fuelectenerg-1427	351	16	is	be	AUX
fuelectenerg-1427	351	17	shown	show	VERB
fuelectenerg-1427	351	18	in	in	ADP
fuelectenerg-1427	351	19	theorem	theorem	ADJ
fuelectenerg-1427	351	20	1	1	NUM
fuelectenerg-1427	351	21	.	.	PUNCT
fuelectenerg-1427	351	22	theorem	theorem	NOUN
fuelectenerg-1427	351	23	1	1	NUM
fuelectenerg-1427	351	24	.	.	PUNCT
fuelectenerg-1427	351	25	shannon	shannon	PROPN
fuelectenerg-1427	351	26	expansion	expansion	PROPN
fuelectenerg-1427	351	27	over	over	ADP
fuelectenerg-1427	351	28	gf(3	gf(3	PROPN
fuelectenerg-1427	351	29	)	)	PUNCT
fuelectenerg-1427	351	30	for	for	ADP
fuelectenerg-1427	351	31	a	a	DET
fuelectenerg-1427	351	32	function	function	NOUN
fuelectenerg-1427	351	33	with	with	ADP
fuelectenerg-1427	351	34	a	a	DET
fuelectenerg-1427	351	35	single	single	ADJ
fuelectenerg-1427	351	36	variable	variable	NOUN
fuelectenerg-1427	351	37	is	be	AUX
fuelectenerg-1427	351	38	:	:	PUNCT
fuelectenerg-1427	351	39	f	f	X
fuelectenerg-1427	352	1	=	=	SYM
fuelectenerg-1427	352	2	0x	0x	NUM
fuelectenerg-1427	352	3	f0	f0	PROPN
fuelectenerg-1427	352	4	+	+	CCONJ
fuelectenerg-1427	352	5	1x	1x	NUM
fuelectenerg-1427	352	6	f1	f1	NOUN
fuelectenerg-1427	352	7	+	+	CCONJ
fuelectenerg-1427	352	8	2x	2x	NUM
fuelectenerg-1427	352	9	f2	f2	PROPN
fuelectenerg-1427	352	10	,	,	PUNCT
fuelectenerg-1427	352	11	(	(	PUNCT
fuelectenerg-1427	352	12	6	6	NUM
fuelectenerg-1427	352	13	)	)	PUNCT
fuelectenerg-1427	352	14	where	where	SCONJ
fuelectenerg-1427	352	15	f0	f0	PROPN
fuelectenerg-1427	352	16	is	be	AUX
fuelectenerg-1427	352	17	cofactor	cofactor	NOUN
fuelectenerg-1427	352	18	of	of	ADP
fuelectenerg-1427	352	19	f	f	PROPN
fuelectenerg-1427	352	20	with	with	ADP
fuelectenerg-1427	352	21	respect	respect	NOUN
fuelectenerg-1427	352	22	to	to	ADP
fuelectenerg-1427	352	23	variable	variable	NOUN
fuelectenerg-1427	352	24	x	x	PUNCT
fuelectenerg-1427	352	25	of	of	ADP
fuelectenerg-1427	352	26	value	value	NOUN
fuelectenerg-1427	352	27	0	0	NUM
fuelectenerg-1427	352	28	,	,	PUNCT
fuelectenerg-1427	352	29	f1	f1	NOUN
fuelectenerg-1427	352	30	is	be	AUX
fuelectenerg-1427	352	31	cofactor	cofactor	NOUN
fuelectenerg-1427	352	32	of	of	ADP
fuelectenerg-1427	352	33	f	f	PROPN
fuelectenerg-1427	352	34	with	with	ADP
fuelectenerg-1427	352	35	respect	respect	NOUN
fuelectenerg-1427	352	36	to	to	ADP
fuelectenerg-1427	352	37	variable	variable	NOUN
fuelectenerg-1427	352	38	x	x	PUNCT
fuelectenerg-1427	352	39	of	of	ADP
fuelectenerg-1427	352	40	value	value	NOUN
fuelectenerg-1427	352	41	1	1	NUM
fuelectenerg-1427	352	42	,	,	PUNCT
fuelectenerg-1427	352	43	and	and	CCONJ
fuelectenerg-1427	352	44	f2	f2	PROPN
fuelectenerg-1427	352	45	is	be	AUX
fuelectenerg-1427	352	46	cofactor	cofactor	NOUN
fuelectenerg-1427	352	47	of	of	ADP
fuelectenerg-1427	352	48	f	f	PROPN
fuelectenerg-1427	352	49	with	with	ADP
fuelectenerg-1427	352	50	respect	respect	NOUN
fuelectenerg-1427	352	51	to	to	ADP
fuelectenerg-1427	352	52	variable	variable	NOUN
fuelectenerg-1427	352	53	x	x	PUNCT
fuelectenerg-1427	352	54	of	of	ADP
fuelectenerg-1427	352	55	value	value	NOUN
fuelectenerg-1427	352	56	2	2	NUM
fuelectenerg-1427	352	57	.	.	NOUN
fuelectenerg-1427	352	58	104	104	NUM
fuelectenerg-1427	352	59	an	an	DET
fuelectenerg-1427	352	60	extended	extend	VERB
fuelectenerg-1427	352	61	green	green	ADJ
fuelectenerg-1427	352	62	sasao	sasao	PROPN
fuelectenerg-1427	352	63	hierarchy	hierarchy	NOUN
fuelectenerg-1427	352	64	of	of	ADP
fuelectenerg-1427	352	65	canonical	canonical	ADJ
fuelectenerg-1427	352	66	ternary	ternary	ADJ
fuelectenerg-1427	352	67	galois	galois	NOUN
fuelectenerg-1427	352	68	forms	form	NOUN
fuelectenerg-1427	352	69	...	...	PUNCT
fuelectenerg-1427	352	70	literals	literal	NOUN
fuelectenerg-1427	352	71	.	.	PUNCT
fuelectenerg-1427	353	1	galois	galois	PROPN
fuelectenerg-1427	353	2	field	field	NOUN
fuelectenerg-1427	353	3	sum	sum	NOUN
fuelectenerg-1427	353	4	-	-	PUNCT
fuelectenerg-1427	353	5	of	of	ADP
fuelectenerg-1427	353	6	-	-	PUNCT
fuelectenerg-1427	353	7	products	product	NOUN
fuelectenerg-1427	353	8	expansions	expansion	NOUN
fuelectenerg-1427	353	9	can	can	AUX
fuelectenerg-1427	353	10	be	be	AUX
fuelectenerg-1427	353	11	performed	perform	VERB
fuelectenerg-1427	353	12	utilizing	utilize	VERB
fuelectenerg-1427	353	13	variety	variety	NOUN
fuelectenerg-1427	353	14	uses	use	NOUN
fuelectenerg-1427	353	15	of	of	ADP
fuelectenerg-1427	353	16	literals	literal	NOUN
fuelectenerg-1427	353	17	.	.	PUNCT
fuelectenerg-1427	354	1	for	for	ADP
fuelectenerg-1427	354	2	example	example	NOUN
fuelectenerg-1427	354	3	,	,	PUNCT
fuelectenerg-1427	354	4	one	one	PRON
fuelectenerg-1427	354	5	can	can	AUX
fuelectenerg-1427	354	6	use	use	VERB
fuelectenerg-1427	354	7	k	k	ADV
fuelectenerg-1427	354	8	-	-	PUNCT
fuelectenerg-1427	354	9	reduced	reduce	VERB
fuelectenerg-1427	354	10	post	post	NOUN
fuelectenerg-1427	354	11	literal	literal	ADJ
fuelectenerg-1427	354	12	(	(	PUNCT
fuelectenerg-1427	354	13	k	k	X
fuelectenerg-1427	354	14	-	-	NOUN
fuelectenerg-1427	354	15	rpl	rpl	NOUN
fuelectenerg-1427	354	16	)	)	PUNCT
fuelectenerg-1427	354	17	to	to	PART
fuelectenerg-1427	354	18	produce	produce	VERB
fuelectenerg-1427	354	19	k	k	ADJ
fuelectenerg-1427	354	20	-	-	ADJ
fuelectenerg-1427	354	21	rpl	rpl	PROPN
fuelectenerg-1427	354	22	gfsop	gfsop	NOUN
fuelectenerg-1427	354	23	,	,	PUNCT
fuelectenerg-1427	354	24	generalized	generalize	VERB
fuelectenerg-1427	354	25	(	(	PUNCT
fuelectenerg-1427	354	26	post	post	ADJ
fuelectenerg-1427	354	27	)	)	PUNCT
fuelectenerg-1427	354	28	literal	literal	ADJ
fuelectenerg-1427	354	29	(	(	PUNCT
fuelectenerg-1427	354	30	gl	gl	NOUN
fuelectenerg-1427	354	31	)	)	PUNCT
fuelectenerg-1427	354	32	to	to	PART
fuelectenerg-1427	354	33	produce	produce	VERB
fuelectenerg-1427	354	34	gl	gl	NOUN
fuelectenerg-1427	354	35	gfsop	gfsop	PROPN
fuelectenerg-1427	354	36	,	,	PUNCT
fuelectenerg-1427	354	37	and	and	CCONJ
fuelectenerg-1427	354	38	universal	universal	ADJ
fuelectenerg-1427	354	39	literal	literal	ADJ
fuelectenerg-1427	354	40	(	(	PUNCT
fuelectenerg-1427	354	41	ul	ul	INTJ
fuelectenerg-1427	354	42	)	)	PUNCT
fuelectenerg-1427	354	43	to	to	PART
fuelectenerg-1427	354	44	produce	produce	VERB
fuelectenerg-1427	354	45	ul	ul	INTJ
fuelectenerg-1427	354	46	gfsop	gfsop	PROPN
fuelectenerg-1427	354	47	.	.	PUNCT
fuelectenerg-1427	354	48	example	example	NOUN
fuelectenerg-1427	355	1	1	1	NUM
fuelectenerg-1427	355	2	.	.	PUNCT
fuelectenerg-1427	355	3	figure	figure	NOUN
fuelectenerg-1427	355	4	2	2	NUM
fuelectenerg-1427	355	5	demonstrates	demonstrate	VERB
fuelectenerg-1427	355	6	several	several	ADJ
fuelectenerg-1427	355	7	literal	literal	ADJ
fuelectenerg-1427	355	8	types	type	NOUN
fuelectenerg-1427	355	9	,	,	PUNCT
fuelectenerg-1427	355	10	where	where	SCONJ
fuelectenerg-1427	355	11	one	one	NUM
fuelectenerg-1427	355	12	proceeds	proceed	VERB
fuelectenerg-1427	355	13	from	from	ADP
fuelectenerg-1427	355	14	the	the	DET
fuelectenerg-1427	355	15	simplest	simple	ADJ
fuelectenerg-1427	355	16	literal	literal	NOUN
fuelectenerg-1427	355	17	in	in	ADP
fuelectenerg-1427	355	18	figure	figure	NOUN
fuelectenerg-1427	355	19	2(a	2(a	NUM
fuelectenerg-1427	355	20	)	)	PUNCT
fuelectenerg-1427	355	21	(	(	PUNCT
fuelectenerg-1427	355	22	i.e.	i.e.	X
fuelectenerg-1427	355	23	,	,	PUNCT
fuelectenerg-1427	355	24	rpl	rpl	PROPN
fuelectenerg-1427	355	25	)	)	PUNCT
fuelectenerg-1427	355	26	to	to	ADP
fuelectenerg-1427	355	27	the	the	DET
fuelectenerg-1427	355	28	most	most	ADV
fuelectenerg-1427	355	29	complex	complex	ADJ
fuelectenerg-1427	355	30	universal	universal	ADJ
fuelectenerg-1427	355	31	literal	literal	NOUN
fuelectenerg-1427	355	32	in	in	ADP
fuelectenerg-1427	355	33	figure	figure	NOUN
fuelectenerg-1427	355	34	2(c	2(c	NUM
fuelectenerg-1427	355	35	)	)	PUNCT
fuelectenerg-1427	355	36	.	.	PUNCT
fuelectenerg-1427	356	1	for	for	ADP
fuelectenerg-1427	356	2	rpl	rpl	NOUN
fuelectenerg-1427	356	3	in	in	ADP
fuelectenerg-1427	356	4	figure	figure	NOUN
fuelectenerg-1427	356	5	2(a	2(a	NUM
fuelectenerg-1427	356	6	)	)	PUNCT
fuelectenerg-1427	356	7	,	,	PUNCT
fuelectenerg-1427	356	8	a	a	DET
fuelectenerg-1427	356	9	value	value	NOUN
fuelectenerg-1427	356	10	k	k	NOUN
fuelectenerg-1427	356	11	is	be	AUX
fuelectenerg-1427	356	12	produced	produce	VERB
fuelectenerg-1427	356	13	by	by	ADP
fuelectenerg-1427	356	14	the	the	DET
fuelectenerg-1427	356	15	literal	literal	NOUN
fuelectenerg-1427	356	16	when	when	SCONJ
fuelectenerg-1427	356	17	the	the	DET
fuelectenerg-1427	356	18	value	value	NOUN
fuelectenerg-1427	356	19	of	of	ADP
fuelectenerg-1427	356	20	the	the	DET
fuelectenerg-1427	356	21	variable	variable	NOUN
fuelectenerg-1427	356	22	is	be	AUX
fuelectenerg-1427	356	23	equal	equal	ADJ
fuelectenerg-1427	356	24	to	to	ADP
fuelectenerg-1427	356	25	a	a	DET
fuelectenerg-1427	356	26	specific	specific	ADJ
fuelectenerg-1427	356	27	state	state	NOUN
fuelectenerg-1427	356	28	,	,	PUNCT
fuelectenerg-1427	356	29	and	and	CCONJ
fuelectenerg-1427	356	30	in	in	ADP
fuelectenerg-1427	356	31	this	this	DET
fuelectenerg-1427	356	32	particular	particular	ADJ
fuelectenerg-1427	356	33	example	example	NOUN
fuelectenerg-1427	356	34	a	a	DET
fuelectenerg-1427	356	35	value	value	NOUN
fuelectenerg-1427	356	36	of	of	ADP
fuelectenerg-1427	356	37	k	k	PROPN
fuelectenerg-1427	356	38	=	=	SYM
fuelectenerg-1427	356	39	1	1	NUM
fuelectenerg-1427	356	40	is	be	AUX
fuelectenerg-1427	356	41	generated	generate	VERB
fuelectenerg-1427	356	42	by	by	ADP
fuelectenerg-1427	356	43	the	the	DET
fuelectenerg-1427	356	44	1	1	NUM
fuelectenerg-1427	356	45	-	-	PUNCT
fuelectenerg-1427	356	46	rpl	rpl	NOUN
fuelectenerg-1427	356	47	when	when	SCONJ
fuelectenerg-1427	356	48	the	the	DET
fuelectenerg-1427	356	49	value	value	NOUN
fuelectenerg-1427	356	50	of	of	ADP
fuelectenerg-1427	356	51	variable	variable	NOUN
fuelectenerg-1427	356	52	x	x	PUNCT
fuelectenerg-1427	356	53	is	be	AUX
fuelectenerg-1427	356	54	equal	equal	ADJ
fuelectenerg-1427	356	55	to	to	ADP
fuelectenerg-1427	356	56	certain	certain	ADJ
fuelectenerg-1427	356	57	state	state	NOUN
fuelectenerg-1427	356	58	where	where	SCONJ
fuelectenerg-1427	356	59	this	this	DET
fuelectenerg-1427	356	60	state	state	NOUN
fuelectenerg-1427	356	61	here	here	ADV
fuelectenerg-1427	356	62	equals	equal	VERB
fuelectenerg-1427	356	63	to	to	ADP
fuelectenerg-1427	356	64	one	one	NUM
fuelectenerg-1427	356	65	.	.	PUNCT
fuelectenerg-1427	357	1	the	the	DET
fuelectenerg-1427	357	2	gl	gl	PROPN
fuelectenerg-1427	357	3	in	in	ADP
fuelectenerg-1427	357	4	figure	figure	NOUN
fuelectenerg-1427	357	5	2(b	2(b	NUM
fuelectenerg-1427	357	6	)	)	PUNCT
fuelectenerg-1427	357	7	produces	produce	VERB
fuelectenerg-1427	357	8	a	a	DET
fuelectenerg-1427	357	9	value	value	NOUN
fuelectenerg-1427	357	10	of	of	ADP
fuelectenerg-1427	357	11	radix	radix	NOUN
fuelectenerg-1427	357	12	for	for	ADP
fuelectenerg-1427	357	13	a	a	DET
fuelectenerg-1427	357	14	set	set	NOUN
fuelectenerg-1427	357	15	of	of	ADP
fuelectenerg-1427	357	16	distinct	distinct	ADJ
fuelectenerg-1427	357	17	states	state	NOUN
fuelectenerg-1427	357	18	.	.	PUNCT
fuelectenerg-1427	358	1	one	one	NUM
fuelectenerg-1427	358	2	notes	note	VERB
fuelectenerg-1427	358	3	that	that	SCONJ
fuelectenerg-1427	358	4	,	,	PUNCT
fuelectenerg-1427	358	5	in	in	ADP
fuelectenerg-1427	358	6	contrast	contrast	NOUN
fuelectenerg-1427	358	7	to	to	ADP
fuelectenerg-1427	358	8	the	the	DET
fuelectenerg-1427	358	9	other	other	ADJ
fuelectenerg-1427	358	10	literals	literal	NOUN
fuelectenerg-1427	358	11	,	,	PUNCT
fuelectenerg-1427	358	12	ul	ul	INTJ
fuelectenerg-1427	358	13	in	in	ADP
fuelectenerg-1427	358	14	figure	figure	NOUN
fuelectenerg-1427	358	15	2(c	2(c	NUM
fuelectenerg-1427	358	16	)	)	PUNCT
fuelectenerg-1427	358	17	can	can	AUX
fuelectenerg-1427	358	18	have	have	VERB
fuelectenerg-1427	358	19	any	any	DET
fuelectenerg-1427	358	20	value	value	NOUN
fuelectenerg-1427	358	21	of	of	ADP
fuelectenerg-1427	358	22	the	the	DET
fuelectenerg-1427	358	23	logic	logic	NOUN
fuelectenerg-1427	358	24	system	system	NOUN
fuelectenerg-1427	358	25	at	at	ADP
fuelectenerg-1427	358	26	distinct	distinct	ADJ
fuelectenerg-1427	358	27	states	state	NOUN
fuelectenerg-1427	358	28	,	,	PUNCT
fuelectenerg-1427	358	29	and	and	CCONJ
fuelectenerg-1427	358	30	thus	thus	ADV
fuelectenerg-1427	358	31	ul	ul	INTJ
fuelectenerg-1427	358	32	has	have	VERB
fuelectenerg-1427	358	33	the	the	DET
fuelectenerg-1427	358	34	highest	high	ADJ
fuelectenerg-1427	358	35	complexity	complexity	NOUN
fuelectenerg-1427	358	36	among	among	ADP
fuelectenerg-1427	358	37	the	the	DET
fuelectenerg-1427	358	38	different	different	ADJ
fuelectenerg-1427	358	39	types	type	NOUN
fuelectenerg-1427	358	40	of	of	ADP
fuelectenerg-1427	358	41	literals	literal	NOUN
fuelectenerg-1427	358	42	.	.	PUNCT
fuelectenerg-1427	359	1	0	0	NUM
fuelectenerg-1427	359	2	0	0	NUM
fuelectenerg-1427	360	1	01	01	NUM
fuelectenerg-1427	360	2	1	1	NUM
fuelectenerg-1427	360	3	1	1	NUM
fuelectenerg-1427	360	4	1	1	NUM
fuelectenerg-1427	360	5	1	1	NUM
fuelectenerg-1427	360	6	12	12	NUM
fuelectenerg-1427	360	7	2	2	NUM
fuelectenerg-1427	360	8	2	2	NUM
fuelectenerg-1427	360	9	2	2	NUM
fuelectenerg-1427	360	10	2	2	NUM
fuelectenerg-1427	360	11	23	23	NUM
fuelectenerg-1427	360	12	3	3	NUM
fuelectenerg-1427	360	13	3	3	NUM
fuelectenerg-1427	360	14	3	3	NUM
fuelectenerg-1427	360	15	3	3	NUM
fuelectenerg-1427	360	16	34	34	NUM
fuelectenerg-1427	360	17	4	4	NUM
fuelectenerg-1427	360	18	4	4	NUM
fuelectenerg-1427	360	19	4	4	NUM
fuelectenerg-1427	360	20	4	4	NUM
fuelectenerg-1427	360	21	4x	4x	NOUN
fuelectenerg-1427	360	22	x	x	SYM
fuelectenerg-1427	360	23	x	x	SYM
fuelectenerg-1427	360	24	1	1	NUM
fuelectenerg-1427	360	25	x	x	SYM
fuelectenerg-1427	360	26	l	l	NOUN
fuelectenerg-1427	360	27	(	(	PUNCT
fuelectenerg-1427	360	28	)	)	PUNCT
fuelectenerg-1427	360	29	{	{	PUNCT
fuelectenerg-1427	360	30	1,3	1,3	NUM
fuelectenerg-1427	360	31	}	}	PUNCT
fuelectenerg-1427	360	32	x	x	X
fuelectenerg-1427	360	33	l	l	NOUN
fuelectenerg-1427	360	34	(	(	PUNCT
fuelectenerg-1427	360	35	)	)	PUNCT
fuelectenerg-1427	360	36	<	<	X
fuelectenerg-1427	360	37	2,0,4,3,1	2,0,4,3,1	X
fuelectenerg-1427	360	38	>	>	X
fuelectenerg-1427	360	39	x	x	X
fuelectenerg-1427	360	40	(	(	PUNCT
fuelectenerg-1427	360	41	)	)	PUNCT
fuelectenerg-1427	360	42	a	a	DET
fuelectenerg-1427	360	43	(	(	PUNCT
fuelectenerg-1427	360	44	)	)	SYM
fuelectenerg-1427	360	45	b	b	NOUN
fuelectenerg-1427	360	46	(	(	PUNCT
fuelectenerg-1427	360	47	)	)	PUNCT
fuelectenerg-1427	360	48	c	c	NOUN
fuelectenerg-1427	360	49	figure	figure	NOUN
fuelectenerg-1427	360	50	2	2	NUM
fuelectenerg-1427	360	51	:	:	PUNCT
fuelectenerg-1427	360	52	an	an	DET
fuelectenerg-1427	360	53	illustrating	illustrate	VERB
fuelectenerg-1427	360	54	example	example	NOUN
fuelectenerg-1427	360	55	of	of	ADP
fuelectenerg-1427	360	56	the	the	DET
fuelectenerg-1427	360	57	different	different	ADJ
fuelectenerg-1427	360	58	types	type	NOUN
fuelectenerg-1427	360	59	of	of	ADP
fuelectenerg-1427	360	60	literals	literal	NOUN
fuelectenerg-1427	360	61	over	over	ADP
fuelectenerg-1427	360	62	an	an	DET
fuelectenerg-1427	360	63	arbitrary	arbitrary	ADJ
fuelectenerg-1427	360	64	five	five	NUM
fuelectenerg-1427	360	65	-	-	PUNCT
fuelectenerg-1427	360	66	radix	radix	NOUN
fuelectenerg-1427	360	67	logic	logic	NOUN
fuelectenerg-1427	360	68	:	:	PUNCT
fuelectenerg-1427	360	69	(	(	PUNCT
fuelectenerg-1427	360	70	a	a	X
fuelectenerg-1427	360	71	)	)	PUNCT
fuelectenerg-1427	360	72	1	1	NUM
fuelectenerg-1427	360	73	-	-	PUNCT
fuelectenerg-1427	360	74	reduced	reduce	VERB
fuelectenerg-1427	360	75	post	post	NOUN
fuelectenerg-1427	360	76	literal	literal	ADJ
fuelectenerg-1427	360	77	(	(	PUNCT
fuelectenerg-1427	360	78	1	1	NUM
fuelectenerg-1427	360	79	-	-	PUNCT
fuelectenerg-1427	360	80	rpl	rpl	NOUN
fuelectenerg-1427	360	81	)	)	PUNCT
fuelectenerg-1427	360	82	,	,	PUNCT
fuelectenerg-1427	360	83	(	(	PUNCT
fuelectenerg-1427	360	84	b	b	X
fuelectenerg-1427	360	85	)	)	PUNCT
fuelectenerg-1427	360	86	generalized	generalized	ADJ
fuelectenerg-1427	360	87	(	(	PUNCT
fuelectenerg-1427	360	88	post	post	ADJ
fuelectenerg-1427	360	89	)	)	PUNCT
fuelectenerg-1427	360	90	literal	literal	ADJ
fuelectenerg-1427	360	91	(	(	PUNCT
fuelectenerg-1427	360	92	gl	gl	NOUN
fuelectenerg-1427	360	93	)	)	PUNCT
fuelectenerg-1427	360	94	,	,	PUNCT
fuelectenerg-1427	360	95	and	and	CCONJ
fuelectenerg-1427	360	96	(	(	PUNCT
fuelectenerg-1427	360	97	c	c	X
fuelectenerg-1427	360	98	)	)	PUNCT
fuelectenerg-1427	360	99	universal	universal	ADJ
fuelectenerg-1427	360	100	literal	literal	ADJ
fuelectenerg-1427	360	101	(	(	PUNCT
fuelectenerg-1427	360	102	ul	ul	INTJ
fuelectenerg-1427	360	103	)	)	PUNCT
fuelectenerg-1427	360	104	.	.	PUNCT
fuelectenerg-1427	361	1	since	since	SCONJ
fuelectenerg-1427	361	2	k	k	PROPN
fuelectenerg-1427	361	3	-	-	PROPN
fuelectenerg-1427	361	4	rpl	rpl	PROPN
fuelectenerg-1427	361	5	gfsop	gfsop	NOUN
fuelectenerg-1427	361	6	is	be	AUX
fuelectenerg-1427	361	7	simpler	simple	ADJ
fuelectenerg-1427	361	8	from	from	ADP
fuelectenerg-1427	361	9	implementation	implementation	NOUN
fuelectenerg-1427	361	10	point	point	NOUN
fuelectenerg-1427	361	11	of	of	ADP
fuelectenerg-1427	361	12	view	view	NOUN
fuelectenerg-1427	361	13	than	than	ADP
fuelectenerg-1427	361	14	gl	gl	INTJ
fuelectenerg-1427	361	15	or	or	CCONJ
fuelectenerg-1427	361	16	ul	ul	INTJ
fuelectenerg-1427	361	17	,	,	PUNCT
fuelectenerg-1427	361	18	we	we	PRON
fuelectenerg-1427	361	19	will	will	AUX
fuelectenerg-1427	361	20	perform	perform	VERB
fuelectenerg-1427	361	21	all	all	DET
fuelectenerg-1427	361	22	the	the	DET
fuelectenerg-1427	361	23	gfsop	gfsop	NOUN
fuelectenerg-1427	361	24	expansions	expansion	NOUN
fuelectenerg-1427	361	25	utilizing	utilize	VERB
fuelectenerg-1427	361	26	the	the	DET
fuelectenerg-1427	361	27	1	1	NUM
fuelectenerg-1427	361	28	-	-	PUNCT
fuelectenerg-1427	361	29	rpl	rpl	NOUN
fuelectenerg-1427	361	30	gfsop	gfsop	NOUN
fuelectenerg-1427	361	31	.	.	PUNCT
fuelectenerg-1427	362	1	let	let	VERB
fuelectenerg-1427	362	2	us	we	PRON
fuelectenerg-1427	362	3	define	define	VERB
fuelectenerg-1427	362	4	1	1	NUM
fuelectenerg-1427	362	5	-	-	PUNCT
fuelectenerg-1427	362	6	rpl	rpl	NOUN
fuelectenerg-1427	362	7	[	[	X
fuelectenerg-1427	362	8	1	1	NUM
fuelectenerg-1427	362	9	,	,	PUNCT
fuelectenerg-1427	362	10	17	17	NUM
fuelectenerg-1427	362	11	]	]	PUNCT
fuelectenerg-1427	362	12	as	as	ADP
fuelectenerg-1427	362	13	:	:	PUNCT
fuelectenerg-1427	362	14	ix	ix	PROPN
fuelectenerg-1427	362	15	=	=	SYM
fuelectenerg-1427	362	16	1	1	NUM
fuelectenerg-1427	362	17	iff	iff	NOUN
fuelectenerg-1427	362	18	x	x	PROPN
fuelectenerg-1427	363	1	=	=	PUNCT
fuelectenerg-1427	364	1	i	i	PRON
fuelectenerg-1427	364	2	else	else	ADV
fuelectenerg-1427	364	3	ix	ix	ADP
fuelectenerg-1427	364	4	=	=	NOUN
fuelectenerg-1427	364	5	0	0	PROPN
fuelectenerg-1427	364	6	.	.	PUNCT
fuelectenerg-1427	365	1	(	(	PUNCT
fuelectenerg-1427	365	2	5	5	NUM
fuelectenerg-1427	365	3	)	)	PUNCT
fuelectenerg-1427	365	4	for	for	ADP
fuelectenerg-1427	365	5	example	example	NOUN
fuelectenerg-1427	365	6	{	{	PUNCT
fuelectenerg-1427	365	7	0x	0x	NOUN
fuelectenerg-1427	365	8	,	,	PUNCT
fuelectenerg-1427	365	9	1x	1x	NUM
fuelectenerg-1427	365	10	,	,	PUNCT
fuelectenerg-1427	365	11	2x	2x	NUM
fuelectenerg-1427	365	12	}	}	PUNCT
fuelectenerg-1427	365	13	are	be	AUX
fuelectenerg-1427	365	14	the	the	DET
fuelectenerg-1427	365	15	zero	zero	NUM
fuelectenerg-1427	365	16	,	,	PUNCT
fuelectenerg-1427	365	17	first	first	ADV
fuelectenerg-1427	365	18	,	,	PUNCT
fuelectenerg-1427	365	19	and	and	CCONJ
fuelectenerg-1427	365	20	second	second	ADJ
fuelectenerg-1427	365	21	polarities	polarity	NOUN
fuelectenerg-1427	365	22	of	of	ADP
fuelectenerg-1427	365	23	the	the	DET
fuelectenerg-1427	365	24	1	1	NUM
fuelectenerg-1427	365	25	-	-	PUNCT
fuelectenerg-1427	365	26	rpl	rpl	NOUN
fuelectenerg-1427	365	27	,	,	PUNCT
fuelectenerg-1427	365	28	respectively	respectively	ADV
fuelectenerg-1427	365	29	.	.	PUNCT
fuelectenerg-1427	366	1	also	also	ADV
fuelectenerg-1427	366	2	,	,	PUNCT
fuelectenerg-1427	366	3	let	let	VERB
fuelectenerg-1427	366	4	us	we	PRON
fuelectenerg-1427	366	5	define	define	VERB
fuelectenerg-1427	366	6	the	the	DET
fuelectenerg-1427	366	7	ternary	ternary	ADJ
fuelectenerg-1427	366	8	shifts	shift	NOUN
fuelectenerg-1427	366	9	over	over	ADP
fuelectenerg-1427	366	10	variable	variable	ADJ
fuelectenerg-1427	366	11	x	x	NOUN
fuelectenerg-1427	366	12	as	as	ADP
fuelectenerg-1427	366	13	{	{	PUNCT
fuelectenerg-1427	366	14	x	x	NOUN
fuelectenerg-1427	366	15	,	,	PUNCT
fuelectenerg-1427	366	16	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	366	17	}	}	PUNCT
fuelectenerg-1427	366	18	as	as	ADP
fuelectenerg-1427	366	19	the	the	DET
fuelectenerg-1427	366	20	zero	zero	NUM
fuelectenerg-1427	366	21	,	,	PUNCT
fuelectenerg-1427	366	22	first	first	ADJ
fuelectenerg-1427	366	23	and	and	CCONJ
fuelectenerg-1427	366	24	second	second	ADJ
fuelectenerg-1427	366	25	shifts	shift	NOUN
fuelectenerg-1427	366	26	of	of	ADP
fuelectenerg-1427	366	27	the	the	DET
fuelectenerg-1427	366	28	variable	variable	NOUN
fuelectenerg-1427	366	29	x	x	PUNCT
fuelectenerg-1427	366	30	respectively	respectively	ADV
fuelectenerg-1427	366	31	,	,	PUNCT
fuelectenerg-1427	366	32	i.e.	i.e.	X
fuelectenerg-1427	366	33	,	,	PUNCT
fuelectenerg-1427	366	34	x	x	SYM
fuelectenerg-1427	366	35	=	=	SYM
fuelectenerg-1427	366	36	x+	x+	PUNCT
fuelectenerg-1427	366	37	0	0	NUM
fuelectenerg-1427	366	38	,	,	PUNCT
fuelectenerg-1427	366	39	x′	x′	PROPN
fuelectenerg-1427	367	1	=	=	PUNCT
fuelectenerg-1427	367	2	x+	x+	SYM
fuelectenerg-1427	367	3	1	1	NUM
fuelectenerg-1427	367	4	and	and	CCONJ
fuelectenerg-1427	367	5	x′′	x′′	PROPN
fuelectenerg-1427	367	6	=	=	PUNCT
fuelectenerg-1427	367	7	x+	x+	PROPN
fuelectenerg-1427	367	8	2	2	NUM
fuelectenerg-1427	367	9	,	,	PUNCT
fuelectenerg-1427	367	10	and	and	CCONJ
fuelectenerg-1427	367	11	x	x	PRON
fuelectenerg-1427	367	12	can	can	AUX
fuelectenerg-1427	367	13	take	take	VERB
fuelectenerg-1427	367	14	any	any	DET
fuelectenerg-1427	367	15	value	value	NOUN
fuelectenerg-1427	367	16	in	in	ADP
fuelectenerg-1427	367	17	the	the	DET
fuelectenerg-1427	367	18	set	set	NOUN
fuelectenerg-1427	367	19	{	{	PUNCT
fuelectenerg-1427	367	20	0,1,2	0,1,2	NUM
fuelectenerg-1427	367	21	}	}	PUNCT
fuelectenerg-1427	367	22	.	.	PUNCT
fuelectenerg-1427	368	1	we	we	PRON
fuelectenerg-1427	368	2	chose	choose	VERB
fuelectenerg-1427	368	3	to	to	PART
fuelectenerg-1427	368	4	represent	represent	VERB
fuelectenerg-1427	368	5	the	the	DET
fuelectenerg-1427	368	6	1	1	NUM
fuelectenerg-1427	368	7	-	-	PUNCT
fuelectenerg-1427	368	8	reduced	reduce	VERB
fuelectenerg-1427	368	9	post	post	NOUN
fuelectenerg-1427	368	10	literals	literal	NOUN
fuelectenerg-1427	368	11	in	in	ADP
fuelectenerg-1427	368	12	terms	term	NOUN
fuelectenerg-1427	368	13	of	of	ADP
fuelectenerg-1427	368	14	shifts	shift	NOUN
fuelectenerg-1427	368	15	and	and	CCONJ
fuelectenerg-1427	368	16	powers	power	NOUN
fuelectenerg-1427	368	17	,	,	PUNCT
fuelectenerg-1427	368	18	among	among	ADP
fuelectenerg-1427	368	19	others	other	NOUN
fuelectenerg-1427	368	20	,	,	PUNCT
fuelectenerg-1427	368	21	because	because	SCONJ
fuelectenerg-1427	368	22	of	of	ADP
fuelectenerg-1427	368	23	the	the	DET
fuelectenerg-1427	368	24	ease	ease	NOUN
fuelectenerg-1427	368	25	of	of	ADP
fuelectenerg-1427	368	26	the	the	DET
fuelectenerg-1427	368	27	implementation	implementation	NOUN
fuelectenerg-1427	368	28	of	of	ADP
fuelectenerg-1427	368	29	powers	power	NOUN
fuelectenerg-1427	368	30	of	of	ADP
fuelectenerg-1427	368	31	shifted	shift	VERB
fuelectenerg-1427	368	32	variables	variable	NOUN
fuelectenerg-1427	368	33	in	in	ADP
fuelectenerg-1427	368	34	hardware	hardware	NOUN
fuelectenerg-1427	368	35	as	as	SCONJ
fuelectenerg-1427	368	36	will	will	AUX
fuelectenerg-1427	368	37	be	be	AUX
fuelectenerg-1427	368	38	seen	see	VERB
fuelectenerg-1427	368	39	in	in	ADP
fuelectenerg-1427	368	40	section	section	NOUN
fuelectenerg-1427	368	41	3	3	NUM
fuelectenerg-1427	368	42	within	within	ADP
fuelectenerg-1427	368	43	universal	universal	ADJ
fuelectenerg-1427	368	44	logic	logic	NOUN
fuelectenerg-1427	368	45	modules	module	NOUN
fuelectenerg-1427	368	46	(	(	PUNCT
fuelectenerg-1427	368	47	ulms	ulm	NOUN
fuelectenerg-1427	368	48	)	)	PUNCT
fuelectenerg-1427	368	49	for	for	ADP
fuelectenerg-1427	368	50	the	the	DET
fuelectenerg-1427	368	51	production	production	NOUN
fuelectenerg-1427	368	52	of	of	ADP
fuelectenerg-1427	368	53	rpl	rpl	NOUN
fuelectenerg-1427	368	54	.	.	PUNCT
fuelectenerg-1427	369	1	the	the	DET
fuelectenerg-1427	369	2	fundamental	fundamental	ADJ
fuelectenerg-1427	369	3	shannon	shannon	PROPN
fuelectenerg-1427	369	4	expansion	expansion	NOUN
fuelectenerg-1427	369	5	over	over	ADP
fuelectenerg-1427	369	6	gf(3	gf(3	PROPN
fuelectenerg-1427	369	7	)	)	PUNCT
fuelectenerg-1427	369	8	for	for	ADP
fuelectenerg-1427	369	9	a	a	DET
fuelectenerg-1427	369	10	ternary	ternary	ADJ
fuelectenerg-1427	369	11	function	function	NOUN
fuelectenerg-1427	369	12	with	with	ADP
fuelectenerg-1427	369	13	a	a	DET
fuelectenerg-1427	369	14	single	single	ADJ
fuelectenerg-1427	369	15	variable	variable	NOUN
fuelectenerg-1427	369	16	is	be	AUX
fuelectenerg-1427	369	17	shown	show	VERB
fuelectenerg-1427	369	18	in	in	ADP
fuelectenerg-1427	369	19	theorem	theorem	ADJ
fuelectenerg-1427	369	20	1	1	NUM
fuelectenerg-1427	369	21	.	.	PUNCT
fuelectenerg-1427	369	22	theorem	theorem	NOUN
fuelectenerg-1427	369	23	1	1	NUM
fuelectenerg-1427	369	24	.	.	PUNCT
fuelectenerg-1427	369	25	shannon	shannon	PROPN
fuelectenerg-1427	369	26	expansion	expansion	PROPN
fuelectenerg-1427	369	27	over	over	ADP
fuelectenerg-1427	369	28	gf(3	gf(3	PROPN
fuelectenerg-1427	369	29	)	)	PUNCT
fuelectenerg-1427	369	30	for	for	ADP
fuelectenerg-1427	369	31	a	a	DET
fuelectenerg-1427	369	32	function	function	NOUN
fuelectenerg-1427	369	33	with	with	ADP
fuelectenerg-1427	369	34	a	a	DET
fuelectenerg-1427	369	35	single	single	ADJ
fuelectenerg-1427	369	36	variable	variable	NOUN
fuelectenerg-1427	369	37	is	be	AUX
fuelectenerg-1427	369	38	:	:	PUNCT
fuelectenerg-1427	369	39	f	f	X
fuelectenerg-1427	370	1	=	=	SYM
fuelectenerg-1427	370	2	0x	0x	NUM
fuelectenerg-1427	370	3	f0	f0	PROPN
fuelectenerg-1427	370	4	+	+	CCONJ
fuelectenerg-1427	370	5	1x	1x	NUM
fuelectenerg-1427	370	6	f1	f1	NOUN
fuelectenerg-1427	370	7	+	+	CCONJ
fuelectenerg-1427	370	8	2x	2x	NUM
fuelectenerg-1427	370	9	f2	f2	PROPN
fuelectenerg-1427	370	10	,	,	PUNCT
fuelectenerg-1427	370	11	(	(	PUNCT
fuelectenerg-1427	370	12	6	6	NUM
fuelectenerg-1427	370	13	)	)	PUNCT
fuelectenerg-1427	370	14	where	where	SCONJ
fuelectenerg-1427	370	15	f0	f0	PROPN
fuelectenerg-1427	370	16	is	be	AUX
fuelectenerg-1427	370	17	cofactor	cofactor	NOUN
fuelectenerg-1427	370	18	of	of	ADP
fuelectenerg-1427	370	19	f	f	PROPN
fuelectenerg-1427	370	20	with	with	ADP
fuelectenerg-1427	370	21	respect	respect	NOUN
fuelectenerg-1427	370	22	to	to	ADP
fuelectenerg-1427	370	23	variable	variable	NOUN
fuelectenerg-1427	370	24	x	x	PUNCT
fuelectenerg-1427	370	25	of	of	ADP
fuelectenerg-1427	370	26	value	value	NOUN
fuelectenerg-1427	370	27	0	0	NUM
fuelectenerg-1427	370	28	,	,	PUNCT
fuelectenerg-1427	370	29	f1	f1	NOUN
fuelectenerg-1427	370	30	is	be	AUX
fuelectenerg-1427	370	31	cofactor	cofactor	NOUN
fuelectenerg-1427	370	32	of	of	ADP
fuelectenerg-1427	370	33	f	f	PROPN
fuelectenerg-1427	370	34	with	with	ADP
fuelectenerg-1427	370	35	respect	respect	NOUN
fuelectenerg-1427	370	36	to	to	ADP
fuelectenerg-1427	370	37	variable	variable	NOUN
fuelectenerg-1427	370	38	x	x	PUNCT
fuelectenerg-1427	370	39	of	of	ADP
fuelectenerg-1427	370	40	value	value	NOUN
fuelectenerg-1427	370	41	1	1	NUM
fuelectenerg-1427	370	42	,	,	PUNCT
fuelectenerg-1427	370	43	and	and	CCONJ
fuelectenerg-1427	370	44	f2	f2	PROPN
fuelectenerg-1427	370	45	is	be	AUX
fuelectenerg-1427	370	46	cofactor	cofactor	NOUN
fuelectenerg-1427	370	47	of	of	ADP
fuelectenerg-1427	370	48	f	f	PROPN
fuelectenerg-1427	370	49	with	with	ADP
fuelectenerg-1427	370	50	respect	respect	NOUN
fuelectenerg-1427	370	51	to	to	ADP
fuelectenerg-1427	370	52	variable	variable	NOUN
fuelectenerg-1427	370	53	x	x	PUNCT
fuelectenerg-1427	370	54	of	of	ADP
fuelectenerg-1427	370	55	value	value	NOUN
fuelectenerg-1427	370	56	2	2	NUM
fuelectenerg-1427	370	57	.	.	NOUN
fuelectenerg-1427	370	58	104	104	NUM
fuelectenerg-1427	370	59	an	an	DET
fuelectenerg-1427	370	60	extended	extend	VERB
fuelectenerg-1427	370	61	green	green	ADJ
fuelectenerg-1427	370	62	sasao	sasao	PROPN
fuelectenerg-1427	370	63	hierarchy	hierarchy	NOUN
fuelectenerg-1427	370	64	of	of	ADP
fuelectenerg-1427	370	65	canonical	canonical	ADJ
fuelectenerg-1427	370	66	ternary	ternary	ADJ
fuelectenerg-1427	370	67	galois	galois	NOUN
fuelectenerg-1427	370	68	forms	form	NOUN
fuelectenerg-1427	370	69	...	...	PUNCT
fuelectenerg-1427	371	1	proof	proof	NOUN
fuelectenerg-1427	371	2	.	.	PUNCT
fuelectenerg-1427	372	1	from	from	ADP
fuelectenerg-1427	372	2	equation	equation	NOUN
fuelectenerg-1427	372	3	(	(	PUNCT
fuelectenerg-1427	372	4	5	5	NUM
fuelectenerg-1427	372	5	)	)	PUNCT
fuelectenerg-1427	372	6	,	,	PUNCT
fuelectenerg-1427	372	7	if	if	SCONJ
fuelectenerg-1427	372	8	we	we	PRON
fuelectenerg-1427	372	9	substitute	substitute	VERB
fuelectenerg-1427	372	10	the	the	DET
fuelectenerg-1427	372	11	values	value	NOUN
fuelectenerg-1427	372	12	of	of	ADP
fuelectenerg-1427	372	13	the	the	DET
fuelectenerg-1427	372	14	1	1	NUM
fuelectenerg-1427	372	15	-	-	PUNCT
fuelectenerg-1427	372	16	rpl	rpl	NOUN
fuelectenerg-1427	372	17	in	in	ADP
fuelectenerg-1427	372	18	equation	equation	NOUN
fuelectenerg-1427	372	19	(	(	PUNCT
fuelectenerg-1427	372	20	6	6	NUM
fuelectenerg-1427	372	21	)	)	PUNCT
fuelectenerg-1427	372	22	,	,	PUNCT
fuelectenerg-1427	372	23	we	we	PRON
fuelectenerg-1427	372	24	obtain	obtain	VERB
fuelectenerg-1427	372	25	the	the	DET
fuelectenerg-1427	372	26	following	follow	VERB
fuelectenerg-1427	372	27	{	{	PUNCT
fuelectenerg-1427	372	28	x	x	SYM
fuelectenerg-1427	372	29	=	=	SYM
fuelectenerg-1427	372	30	0	0	NUM
fuelectenerg-1427	372	31	⇒	⇒	NOUN
fuelectenerg-1427	372	32	fx=0	fx=0	ADV
fuelectenerg-1427	372	33	=	=	SYM
fuelectenerg-1427	372	34	f0,x	f0,x	NOUN
fuelectenerg-1427	372	35	=	=	SYM
fuelectenerg-1427	372	36	1	1	NUM
fuelectenerg-1427	372	37	⇒	⇒	X
fuelectenerg-1427	372	38	fx=1	fx=1	ADJ
fuelectenerg-1427	372	39	=	=	SYM
fuelectenerg-1427	372	40	f1,x	f1,x	NOUN
fuelectenerg-1427	372	41	=	=	SYM
fuelectenerg-1427	372	42	2	2	NUM
fuelectenerg-1427	372	43	⇒	⇒	NOUN
fuelectenerg-1427	372	44	fx=2	fx=2	NOUN
fuelectenerg-1427	372	45	=	=	PUNCT
fuelectenerg-1427	372	46	f2	f2	PROPN
fuelectenerg-1427	372	47	}	}	PUNCT
fuelectenerg-1427	372	48	which	which	PRON
fuelectenerg-1427	372	49	are	be	AUX
fuelectenerg-1427	372	50	the	the	DET
fuelectenerg-1427	372	51	cofactors	cofactor	NOUN
fuelectenerg-1427	372	52	of	of	ADP
fuelectenerg-1427	372	53	variable	variable	ADJ
fuelectenerg-1427	372	54	x	x	X
fuelectenerg-1427	372	55	of	of	ADP
fuelectenerg-1427	372	56	values	value	NOUN
fuelectenerg-1427	372	57	{	{	PUNCT
fuelectenerg-1427	372	58	0,1,2	0,1,2	NUM
fuelectenerg-1427	372	59	}	}	PUNCT
fuelectenerg-1427	372	60	,	,	PUNCT
fuelectenerg-1427	372	61	respectively	respectively	ADV
fuelectenerg-1427	372	62	.	.	PUNCT
fuelectenerg-1427	372	63	example	example	NOUN
fuelectenerg-1427	373	1	2	2	NUM
fuelectenerg-1427	373	2	.	.	PUNCT
fuelectenerg-1427	373	3	let	let	VERB
fuelectenerg-1427	373	4	f	f	PROPN
fuelectenerg-1427	373	5	(	(	PUNCT
fuelectenerg-1427	373	6	x1,x2	x1,x2	PROPN
fuelectenerg-1427	373	7	)	)	PUNCT
fuelectenerg-1427	374	1	=	=	SYM
fuelectenerg-1427	374	2	x′1x2	x′1x2	X
fuelectenerg-1427	375	1	+	+	SYM
fuelectenerg-1427	376	1	x′′2x1	x′′2x1	PROPN
fuelectenerg-1427	376	2	.	.	PUNCT
fuelectenerg-1427	377	1	then	then	ADV
fuelectenerg-1427	377	2	,	,	PUNCT
fuelectenerg-1427	377	3	using	use	VERB
fuelectenerg-1427	377	4	figure	figure	NOUN
fuelectenerg-1427	377	5	1	1	NUM
fuelectenerg-1427	377	6	,	,	PUNCT
fuelectenerg-1427	377	7	the	the	DET
fuelectenerg-1427	377	8	ternary	ternary	ADJ
fuelectenerg-1427	377	9	truth	truth	NOUN
fuelectenerg-1427	377	10	vector	vector	NOUN
fuelectenerg-1427	377	11	with	with	ADP
fuelectenerg-1427	377	12	the	the	DET
fuelectenerg-1427	377	13	variable	variable	ADJ
fuelectenerg-1427	377	14	order	order	NOUN
fuelectenerg-1427	377	15	{	{	PUNCT
fuelectenerg-1427	377	16	x1,x2	x1,x2	PROPN
fuelectenerg-1427	377	17	}	}	PUNCT
fuelectenerg-1427	377	18	is	be	AUX
fuelectenerg-1427	377	19	f	f	X
fuelectenerg-1427	377	20	=	=	PUNCT
fuelectenerg-1427	378	1	[	[	PUNCT
fuelectenerg-1427	378	2	0,2,1,1,2,0,2,2,2]t	0,2,1,1,2,0,2,2,2]t	PROPN
fuelectenerg-1427	378	3	.	.	PUNCT
fuelectenerg-1427	379	1	using	use	VERB
fuelectenerg-1427	379	2	equation	equation	NOUN
fuelectenerg-1427	379	3	(	(	PUNCT
fuelectenerg-1427	379	4	6	6	NUM
fuelectenerg-1427	379	5	)	)	PUNCT
fuelectenerg-1427	379	6	,	,	PUNCT
fuelectenerg-1427	379	7	we	we	PRON
fuelectenerg-1427	379	8	obtain	obtain	VERB
fuelectenerg-1427	379	9	the	the	DET
fuelectenerg-1427	379	10	following	following	ADJ
fuelectenerg-1427	379	11	gf(3	gf(3	PROPN
fuelectenerg-1427	379	12	)	)	PUNCT
fuelectenerg-1427	379	13	shannon	shannon	PROPN
fuelectenerg-1427	379	14	expansion	expansion	NOUN
fuelectenerg-1427	379	15	f	f	PROPN
fuelectenerg-1427	379	16	(	(	PUNCT
fuelectenerg-1427	379	17	x1,x2	x1,x2	PROPN
fuelectenerg-1427	379	18	)	)	PUNCT
fuelectenerg-1427	380	1	=	=	PUNCT
fuelectenerg-1427	380	2	0x1	0x1	NOUN
fuelectenerg-1427	380	3	1x2	1x2	NUM
fuelectenerg-1427	381	1	+	+	CCONJ
fuelectenerg-1427	381	2	2	2	NUM
fuelectenerg-1427	381	3	·	·	PUNCT
fuelectenerg-1427	381	4	0x1	0x1	NOUN
fuelectenerg-1427	381	5	2x2	2x2	NUM
fuelectenerg-1427	382	1	+	+	CCONJ
fuelectenerg-1427	382	2	2	2	NUM
fuelectenerg-1427	382	3	·	·	SYM
fuelectenerg-1427	382	4	1x1	1x1	NUM
fuelectenerg-1427	382	5	0x2	0x2	NOUN
fuelectenerg-1427	382	6	+2	+2	PROPN
fuelectenerg-1427	382	7	·	·	PUNCT
fuelectenerg-1427	382	8	1x1	1x1	NUM
fuelectenerg-1427	382	9	1x2	1x2	NUM
fuelectenerg-1427	382	10	+2	+2	PRON
fuelectenerg-1427	382	11	·	·	PUNCT
fuelectenerg-1427	383	1	1x1	1x1	NUM
fuelectenerg-1427	383	2	2x2	2x2	NUM
fuelectenerg-1427	383	3	+	+	SYM
fuelectenerg-1427	383	4	2x1	2x1	NUM
fuelectenerg-1427	383	5	0x2	0x2	NOUN
fuelectenerg-1427	383	6	+2	+2	PROPN
fuelectenerg-1427	383	7	·	·	PUNCT
fuelectenerg-1427	383	8	2x1	2x1	NUM
fuelectenerg-1427	383	9	2x2	2x2	NUM
fuelectenerg-1427	383	10	.	.	PUNCT
fuelectenerg-1427	384	1	by	by	ADP
fuelectenerg-1427	384	2	using	use	VERB
fuelectenerg-1427	384	3	the	the	DET
fuelectenerg-1427	384	4	addition	addition	NOUN
fuelectenerg-1427	384	5	and	and	CCONJ
fuelectenerg-1427	384	6	multiplication	multiplication	NOUN
fuelectenerg-1427	384	7	over	over	ADP
fuelectenerg-1427	384	8	gf(3	gf(3	PROPN
fuelectenerg-1427	384	9	)	)	PUNCT
fuelectenerg-1427	384	10	utilizing	utilize	VERB
fuelectenerg-1427	384	11	figure	figure	NOUN
fuelectenerg-1427	384	12	1	1	NUM
fuelectenerg-1427	384	13	,	,	PUNCT
fuelectenerg-1427	384	14	the	the	DET
fuelectenerg-1427	384	15	1	1	NUM
fuelectenerg-1427	384	16	-	-	PUNCT
fuelectenerg-1427	384	17	rpl	rpl	NOUN
fuelectenerg-1427	384	18	which	which	PRON
fuelectenerg-1427	384	19	is	be	AUX
fuelectenerg-1427	384	20	defined	define	VERB
fuelectenerg-1427	384	21	in	in	ADP
fuelectenerg-1427	384	22	equation	equation	NOUN
fuelectenerg-1427	384	23	(	(	PUNCT
fuelectenerg-1427	384	24	5	5	NUM
fuelectenerg-1427	384	25	)	)	PUNCT
fuelectenerg-1427	384	26	is	be	AUX
fuelectenerg-1427	384	27	related	relate	VERB
fuelectenerg-1427	384	28	to	to	ADP
fuelectenerg-1427	384	29	the	the	DET
fuelectenerg-1427	384	30	shifts	shift	NOUN
fuelectenerg-1427	384	31	of	of	ADP
fuelectenerg-1427	384	32	variables	variable	NOUN
fuelectenerg-1427	384	33	over	over	ADP
fuelectenerg-1427	384	34	gf(3	gf(3	PROPN
fuelectenerg-1427	384	35	)	)	PUNCT
fuelectenerg-1427	384	36	in	in	ADP
fuelectenerg-1427	384	37	terms	term	NOUN
fuelectenerg-1427	384	38	of	of	ADP
fuelectenerg-1427	384	39	powers	power	NOUN
fuelectenerg-1427	384	40	as	as	SCONJ
fuelectenerg-1427	384	41	follows	follow	VERB
fuelectenerg-1427	384	42	:	:	PUNCT
fuelectenerg-1427	385	1	0x	0x	NUM
fuelectenerg-1427	385	2	=	=	NOUN
fuelectenerg-1427	385	3	2(x)2	2(x)2	NOUN
fuelectenerg-1427	385	4	+1	+1	X
fuelectenerg-1427	385	5	,	,	PUNCT
fuelectenerg-1427	385	6	(	(	PUNCT
fuelectenerg-1427	385	7	7	7	X
fuelectenerg-1427	385	8	)	)	PUNCT
fuelectenerg-1427	385	9	0x	0x	NOUN
fuelectenerg-1427	385	10	=	=	NOUN
fuelectenerg-1427	385	11	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	385	12	+2(x′	+2(x′	NUM
fuelectenerg-1427	385	13	)	)	PUNCT
fuelectenerg-1427	385	14	,	,	PUNCT
fuelectenerg-1427	385	15	(	(	PUNCT
fuelectenerg-1427	385	16	8)	8)	NUM
fuelectenerg-1427	385	17	0x	0x	NUM
fuelectenerg-1427	385	18	=	=	SYM
fuelectenerg-1427	385	19	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	385	20	+	+	CCONJ
fuelectenerg-1427	385	21	x′′	x′′	PROPN
fuelectenerg-1427	385	22	,	,	PUNCT
fuelectenerg-1427	385	23	(	(	PUNCT
fuelectenerg-1427	385	24	9	9	NUM
fuelectenerg-1427	385	25	)	)	PUNCT
fuelectenerg-1427	385	26	1x	1x	NOUN
fuelectenerg-1427	386	1	=	=	NOUN
fuelectenerg-1427	386	2	2(x)2	2(x)2	NOUN
fuelectenerg-1427	386	3	+2(x	+2(x	NOUN
fuelectenerg-1427	386	4	)	)	PUNCT
fuelectenerg-1427	386	5	,	,	PUNCT
fuelectenerg-1427	386	6	(	(	PUNCT
fuelectenerg-1427	386	7	10	10	NUM
fuelectenerg-1427	386	8	)	)	PUNCT
fuelectenerg-1427	386	9	1x	1x	NOUN
fuelectenerg-1427	387	1	=	=	NOUN
fuelectenerg-1427	387	2	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	387	3	+	+	X
fuelectenerg-1427	387	4	x′	x′	NUM
fuelectenerg-1427	387	5	,	,	PUNCT
fuelectenerg-1427	387	6	(	(	PUNCT
fuelectenerg-1427	387	7	11	11	NUM
fuelectenerg-1427	387	8	)	)	PUNCT
fuelectenerg-1427	387	9	1x	1x	NOUN
fuelectenerg-1427	388	1	=	=	SYM
fuelectenerg-1427	388	2	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	388	3	+1	+1	PROPN
fuelectenerg-1427	388	4	,	,	PUNCT
fuelectenerg-1427	388	5	(	(	PUNCT
fuelectenerg-1427	388	6	12	12	NUM
fuelectenerg-1427	388	7	)	)	PUNCT
fuelectenerg-1427	388	8	2x	2x	NOUN
fuelectenerg-1427	389	1	=	=	NOUN
fuelectenerg-1427	389	2	2(x)2	2(x)2	NOUN
fuelectenerg-1427	389	3	+	+	CCONJ
fuelectenerg-1427	389	4	x	x	X
fuelectenerg-1427	389	5	,	,	PUNCT
fuelectenerg-1427	389	6	(	(	PUNCT
fuelectenerg-1427	389	7	13	13	NUM
fuelectenerg-1427	389	8	)	)	PUNCT
fuelectenerg-1427	389	9	2x	2x	NOUN
fuelectenerg-1427	390	1	=	=	NOUN
fuelectenerg-1427	390	2	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	390	3	+1	+1	PROPN
fuelectenerg-1427	390	4	,	,	PUNCT
fuelectenerg-1427	390	5	(	(	PUNCT
fuelectenerg-1427	390	6	14	14	NUM
fuelectenerg-1427	390	7	)	)	PUNCT
fuelectenerg-1427	390	8	2x	2x	NUM
fuelectenerg-1427	390	9	=	=	NOUN
fuelectenerg-1427	390	10	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	390	11	+2(x′′	+2(x′′	NUM
fuelectenerg-1427	390	12	)	)	PUNCT
fuelectenerg-1427	390	13	.	.	PUNCT
fuelectenerg-1427	391	1	(	(	PUNCT
fuelectenerg-1427	391	2	15	15	NUM
fuelectenerg-1427	391	3	)	)	PUNCT
fuelectenerg-1427	391	4	after	after	ADP
fuelectenerg-1427	391	5	the	the	DET
fuelectenerg-1427	391	6	substitution	substitution	NOUN
fuelectenerg-1427	391	7	of	of	ADP
fuelectenerg-1427	391	8	equations	equation	NOUN
fuelectenerg-1427	391	9	(	(	PUNCT
fuelectenerg-1427	391	10	7	7	NUM
fuelectenerg-1427	391	11	)	)	PUNCT
fuelectenerg-1427	391	12	(	(	PUNCT
fuelectenerg-1427	391	13	15	15	NUM
fuelectenerg-1427	391	14	)	)	PUNCT
fuelectenerg-1427	391	15	in	in	ADP
fuelectenerg-1427	391	16	equation	equation	NOUN
fuelectenerg-1427	391	17	(	(	PUNCT
fuelectenerg-1427	391	18	6	6	NUM
fuelectenerg-1427	391	19	)	)	PUNCT
fuelectenerg-1427	391	20	,	,	PUNCT
fuelectenerg-1427	391	21	and	and	CCONJ
fuelectenerg-1427	391	22	after	after	ADP
fuelectenerg-1427	391	23	the	the	DET
fuelectenerg-1427	391	24	minimization	minimization	NOUN
fuelectenerg-1427	391	25	of	of	ADP
fuelectenerg-1427	391	26	the	the	DET
fuelectenerg-1427	391	27	terms	term	NOUN
fuelectenerg-1427	391	28	according	accord	VERB
fuelectenerg-1427	391	29	to	to	ADP
fuelectenerg-1427	391	30	the	the	DET
fuelectenerg-1427	391	31	gf	gf	PROPN
fuelectenerg-1427	391	32	operations	operation	NOUN
fuelectenerg-1427	391	33	in	in	ADP
fuelectenerg-1427	391	34	figure	figure	NOUN
fuelectenerg-1427	391	35	1	1	NUM
fuelectenerg-1427	391	36	,	,	PUNCT
fuelectenerg-1427	391	37	one	one	NOUN
fuelectenerg-1427	391	38	obtains	obtain	VERB
fuelectenerg-1427	391	39	the	the	DET
fuelectenerg-1427	391	40	following	follow	VERB
fuelectenerg-1427	391	41	equations	equation	NOUN
fuelectenerg-1427	391	42	:	:	PUNCT
fuelectenerg-1427	391	43	f	f	PROPN
fuelectenerg-1427	391	44	=	=	SYM
fuelectenerg-1427	391	45	1	1	NUM
fuelectenerg-1427	391	46	·	·	PUNCT
fuelectenerg-1427	391	47	f0	f0	PROPN
fuelectenerg-1427	391	48	+	+	CCONJ
fuelectenerg-1427	391	49	x	x	X
fuelectenerg-1427	391	50	·	·	PUNCT
fuelectenerg-1427	391	51	(	(	PUNCT
fuelectenerg-1427	391	52	2	2	NUM
fuelectenerg-1427	391	53	f1	f1	NOUN
fuelectenerg-1427	391	54	+	+	X
fuelectenerg-1427	391	55	f2)+2(x)2	f2)+2(x)2	PROPN
fuelectenerg-1427	391	56	(	(	PUNCT
fuelectenerg-1427	391	57	f0	f0	PROPN
fuelectenerg-1427	391	58	+	+	CCONJ
fuelectenerg-1427	391	59	f1	f1	NOUN
fuelectenerg-1427	391	60	+	+	CCONJ
fuelectenerg-1427	391	61	f2	f2	PROPN
fuelectenerg-1427	391	62	)	)	PUNCT
fuelectenerg-1427	391	63	,	,	PUNCT
fuelectenerg-1427	391	64	(	(	PUNCT
fuelectenerg-1427	391	65	16	16	NUM
fuelectenerg-1427	391	66	)	)	PUNCT
fuelectenerg-1427	391	67	f	f	NOUN
fuelectenerg-1427	392	1	=	=	SYM
fuelectenerg-1427	392	2	1	1	X
fuelectenerg-1427	392	3	·	·	PUNCT
fuelectenerg-1427	392	4	f2	f2	PROPN
fuelectenerg-1427	392	5	+	+	NOUN
fuelectenerg-1427	392	6	x′	x′	PROPN
fuelectenerg-1427	392	7	·	·	PUNCT
fuelectenerg-1427	392	8	(	(	PUNCT
fuelectenerg-1427	392	9	2	2	NUM
fuelectenerg-1427	392	10	f0	f0	PROPN
fuelectenerg-1427	392	11	+	+	CCONJ
fuelectenerg-1427	392	12	f1)+2(x′)2	f1)+2(x′)2	PROPN
fuelectenerg-1427	392	13	(	(	PUNCT
fuelectenerg-1427	392	14	f0	f0	PROPN
fuelectenerg-1427	392	15	+	+	CCONJ
fuelectenerg-1427	392	16	f1	f1	NOUN
fuelectenerg-1427	392	17	+	+	CCONJ
fuelectenerg-1427	392	18	f2	f2	PROPN
fuelectenerg-1427	392	19	)	)	PUNCT
fuelectenerg-1427	392	20	,	,	PUNCT
fuelectenerg-1427	392	21	(	(	PUNCT
fuelectenerg-1427	392	22	17	17	NUM
fuelectenerg-1427	392	23	)	)	PUNCT
fuelectenerg-1427	392	24	f	f	NOUN
fuelectenerg-1427	393	1	=	=	SYM
fuelectenerg-1427	393	2	1	1	NUM
fuelectenerg-1427	393	3	·	·	PUNCT
fuelectenerg-1427	393	4	f1	f1	NOUN
fuelectenerg-1427	393	5	+	+	CCONJ
fuelectenerg-1427	393	6	x	x	X
fuelectenerg-1427	393	7	”	"	PUNCT
fuelectenerg-1427	393	8	·	·	PUNCT
fuelectenerg-1427	393	9	(	(	PUNCT
fuelectenerg-1427	393	10	2	2	NUM
fuelectenerg-1427	393	11	f2	f2	NOUN
fuelectenerg-1427	393	12	+	+	CCONJ
fuelectenerg-1427	393	13	f0)+2(x′′)2	f0)+2(x′′)2	PROPN
fuelectenerg-1427	393	14	(	(	PUNCT
fuelectenerg-1427	393	15	f0	f0	PROPN
fuelectenerg-1427	393	16	+	+	CCONJ
fuelectenerg-1427	393	17	f1	f1	NOUN
fuelectenerg-1427	393	18	+	+	CCONJ
fuelectenerg-1427	393	19	f2	f2	PROPN
fuelectenerg-1427	393	20	)	)	PUNCT
fuelectenerg-1427	393	21	.	.	PUNCT
fuelectenerg-1427	394	1	(	(	PUNCT
fuelectenerg-1427	394	2	18	18	NUM
fuelectenerg-1427	394	3	)	)	PUNCT
fuelectenerg-1427	394	4	equations	equation	NOUN
fuelectenerg-1427	394	5	(	(	PUNCT
fuelectenerg-1427	394	6	6	6	NUM
fuelectenerg-1427	394	7	)	)	PUNCT
fuelectenerg-1427	394	8	and	and	CCONJ
fuelectenerg-1427	394	9	(	(	PUNCT
fuelectenerg-1427	394	10	16	16	NUM
fuelectenerg-1427	394	11	)	)	PUNCT
fuelectenerg-1427	394	12	(	(	PUNCT
fuelectenerg-1427	394	13	18	18	NUM
fuelectenerg-1427	394	14	)	)	PUNCT
fuelectenerg-1427	394	15	are	be	AUX
fuelectenerg-1427	394	16	the	the	DET
fuelectenerg-1427	394	17	ternary	ternary	ADJ
fuelectenerg-1427	394	18	fundamental	fundamental	ADJ
fuelectenerg-1427	394	19	shannon	shannon	NOUN
fuelectenerg-1427	394	20	and	and	CCONJ
fuelectenerg-1427	394	21	davio	davio	NOUN
fuelectenerg-1427	394	22	expansions	expansion	NOUN
fuelectenerg-1427	394	23	for	for	ADP
fuelectenerg-1427	394	24	a	a	DET
fuelectenerg-1427	394	25	single	single	ADJ
fuelectenerg-1427	394	26	variable	variable	NOUN
fuelectenerg-1427	394	27	,	,	PUNCT
fuelectenerg-1427	394	28	respectively	respectively	ADV
fuelectenerg-1427	394	29	.	.	PUNCT
fuelectenerg-1427	395	1	these	these	DET
fuelectenerg-1427	395	2	equations	equation	NOUN
fuelectenerg-1427	395	3	can	can	AUX
fuelectenerg-1427	395	4	be	be	AUX
fuelectenerg-1427	395	5	re	re	VERB
fuelectenerg-1427	395	6	-	-	VERB
fuelectenerg-1427	395	7	written	write	VERB
fuelectenerg-1427	395	8	in	in	ADP
fuelectenerg-1427	395	9	the	the	DET
fuelectenerg-1427	395	10	following	follow	VERB
fuelectenerg-1427	395	11	matrix	matrix	NOUN
fuelectenerg-1427	395	12	-	-	PUNCT
fuelectenerg-1427	395	13	based	base	VERB
fuelectenerg-1427	395	14	forms	form	NOUN
fuelectenerg-1427	395	15	as	as	SCONJ
fuelectenerg-1427	395	16	shown	show	VERB
fuelectenerg-1427	395	17	in	in	ADP
fuelectenerg-1427	395	18	equations	equation	NOUN
fuelectenerg-1427	395	19	(	(	PUNCT
fuelectenerg-1427	395	20	19	19	NUM
fuelectenerg-1427	395	21	)	)	PUNCT
fuelectenerg-1427	395	22	(	(	PUNCT
fuelectenerg-1427	395	23	22	22	NUM
fuelectenerg-1427	395	24	)	)	PUNCT
fuelectenerg-1427	395	25	.	.	PUNCT
fuelectenerg-1427	396	1	we	we	PRON
fuelectenerg-1427	396	2	observe	observe	VERB
fuelectenerg-1427	396	3	that	that	SCONJ
fuelectenerg-1427	396	4	equations	equation	NOUN
fuelectenerg-1427	396	5	(	(	PUNCT
fuelectenerg-1427	396	6	19	19	NUM
fuelectenerg-1427	396	7	)	)	PUNCT
fuelectenerg-1427	396	8	(	(	PUNCT
fuelectenerg-1427	396	9	22	22	NUM
fuelectenerg-1427	396	10	)	)	PUNCT
fuelectenerg-1427	396	11	are	be	AUX
fuelectenerg-1427	396	12	expansions	expansion	NOUN
fuelectenerg-1427	396	13	for	for	ADP
fuelectenerg-1427	396	14	a	a	DET
fuelectenerg-1427	396	15	single	single	ADJ
fuelectenerg-1427	396	16	variable	variable	NOUN
fuelectenerg-1427	396	17	,	,	PUNCT
fuelectenerg-1427	396	18	but	but	CCONJ
fuelectenerg-1427	396	19	these	these	DET
fuelectenerg-1427	396	20	expansions	expansion	NOUN
fuelectenerg-1427	396	21	can	can	AUX
fuelectenerg-1427	396	22	be	be	AUX
fuelectenerg-1427	396	23	recursively	recursively	ADV
fuelectenerg-1427	396	24	generated	generate	VERB
fuelectenerg-1427	396	25	for	for	ADP
fuelectenerg-1427	396	26	arbitrary	arbitrary	ADJ
fuelectenerg-1427	396	27	number	number	NOUN
fuelectenerg-1427	396	28	of	of	ADP
fuelectenerg-1427	396	29	variables	variable	NOUN
fuelectenerg-1427	396	30	n	n	CCONJ
fuelectenerg-1427	396	31	using	use	VERB
fuelectenerg-1427	396	32	the	the	DET
fuelectenerg-1427	396	33	kronecker	kronecker	NOUN
fuelectenerg-1427	396	34	product	product	NOUN
fuelectenerg-1427	396	35	also	also	ADV
fuelectenerg-1427	396	36	called	call	VERB
fuelectenerg-1427	396	37	the	the	DET
fuelectenerg-1427	396	38	tensor	tensor	NOUN
fuelectenerg-1427	396	39	product	product	NOUN
fuelectenerg-1427	396	40	analogously	analogously	ADV
fuelectenerg-1427	396	41	to	to	ADP
fuelectenerg-1427	396	42	the	the	DET
fuelectenerg-1427	396	43	binary	binary	ADJ
fuelectenerg-1427	396	44	case	case	NOUN
fuelectenerg-1427	397	1	[	[	X
fuelectenerg-1427	397	2	1	1	NUM
fuelectenerg-1427	397	3	,	,	PUNCT
fuelectenerg-1427	397	4	17	17	NUM
fuelectenerg-1427	397	5	]	]	PUNCT
fuelectenerg-1427	397	6	.	.	PUNCT
fuelectenerg-1427	398	1	105	105	NUM
fuelectenerg-1427	398	2	an	an	DET
fuelectenerg-1427	398	3	extended	extend	VERB
fuelectenerg-1427	398	4	green	green	ADJ
fuelectenerg-1427	398	5	sasao	sasao	PROPN
fuelectenerg-1427	398	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	398	7	of	of	ADP
fuelectenerg-1427	398	8	canonical	canonical	ADJ
fuelectenerg-1427	398	9	ternary	ternary	ADJ
fuelectenerg-1427	398	10	galois	galois	NOUN
fuelectenerg-1427	398	11	forms	form	NOUN
fuelectenerg-1427	398	12	...	...	PUNCT
fuelectenerg-1427	398	13	s	s	VERB
fuelectenerg-1427	398	14	a	a	PRON
fuelectenerg-1427	398	15	’	'	PUNCT
fuelectenerg-1427	398	16	a	a	PRON
fuelectenerg-1427	398	17	(	(	PUNCT
fuelectenerg-1427	398	18	)	)	PUNCT
fuelectenerg-1427	398	19	a	a	PRON
fuelectenerg-1427	398	20	pd	pd	PROPN
fuelectenerg-1427	398	21	1	1	NUM
fuelectenerg-1427	398	22	a	a	PRON
fuelectenerg-1427	398	23	(	(	PUNCT
fuelectenerg-1427	398	24	)	)	PUNCT
fuelectenerg-1427	398	25	b	b	NOUN
fuelectenerg-1427	398	26	nd	nd	ADP
fuelectenerg-1427	398	27	1	1	NUM
fuelectenerg-1427	398	28	a	a	PRON
fuelectenerg-1427	398	29	’	'	PUNCT
fuelectenerg-1427	398	30	d	d	ADP
fuelectenerg-1427	398	31	1	1	NUM
fuelectenerg-1427	398	32	a	a	PRON
fuelectenerg-1427	398	33	(	(	PUNCT
fuelectenerg-1427	398	34	)	)	PUNCT
fuelectenerg-1427	398	35	d	d	NOUN
fuelectenerg-1427	398	36	(	(	PUNCT
fuelectenerg-1427	398	37	)	)	PUNCT
fuelectenerg-1427	398	38	c	c	NOUN
fuelectenerg-1427	398	39	figure	figure	VERB
fuelectenerg-1427	398	40	3	3	NUM
fuelectenerg-1427	398	41	:	:	PUNCT
fuelectenerg-1427	398	42	two	two	NUM
fuelectenerg-1427	398	43	-	-	PUNCT
fuelectenerg-1427	398	44	valued	value	VERB
fuelectenerg-1427	398	45	nodes	node	NOUN
fuelectenerg-1427	398	46	:	:	PUNCT
fuelectenerg-1427	398	47	(	(	PUNCT
fuelectenerg-1427	398	48	a	a	X
fuelectenerg-1427	398	49	)	)	PUNCT
fuelectenerg-1427	398	50	shannon	shannon	NOUN
fuelectenerg-1427	398	51	,	,	PUNCT
fuelectenerg-1427	398	52	(	(	PUNCT
fuelectenerg-1427	398	53	b	b	NOUN
fuelectenerg-1427	398	54	)	)	PUNCT
fuelectenerg-1427	398	55	positive	positive	ADJ
fuelectenerg-1427	398	56	davio	davio	NOUN
fuelectenerg-1427	398	57	,	,	PUNCT
fuelectenerg-1427	398	58	(	(	PUNCT
fuelectenerg-1427	398	59	c	c	NOUN
fuelectenerg-1427	398	60	)	)	PUNCT
fuelectenerg-1427	398	61	negative	negative	ADJ
fuelectenerg-1427	398	62	davio	davio	NOUN
fuelectenerg-1427	398	63	,	,	PUNCT
fuelectenerg-1427	398	64	and	and	CCONJ
fuelectenerg-1427	398	65	(	(	PUNCT
fuelectenerg-1427	398	66	d	d	X
fuelectenerg-1427	398	67	)	)	PUNCT
fuelectenerg-1427	398	68	generalized	generalized	ADJ
fuelectenerg-1427	398	69	davio	davio	NOUN
fuelectenerg-1427	398	70	where	where	SCONJ
fuelectenerg-1427	398	71	a	a	DET
fuelectenerg-1427	398	72	∈	∈	NOUN
fuelectenerg-1427	398	73	{	{	PUNCT
fuelectenerg-1427	398	74	a	a	PRON
fuelectenerg-1427	398	75	,	,	PUNCT
fuelectenerg-1427	398	76	a′	a′	PROPN
fuelectenerg-1427	398	77	}	}	PUNCT
fuelectenerg-1427	398	78	.	.	PUNCT
fuelectenerg-1427	399	1	variable	variable	ADJ
fuelectenerg-1427	399	2	,	,	PUNCT
fuelectenerg-1427	399	3	that	that	PRON
fuelectenerg-1427	399	4	is	be	AUX
fuelectenerg-1427	399	5	one	one	NUM
fuelectenerg-1427	399	6	tree	tree	NOUN
fuelectenerg-1427	399	7	level	level	NOUN
fuelectenerg-1427	399	8	,	,	PUNCT
fuelectenerg-1427	399	9	figure	figure	NOUN
fuelectenerg-1427	399	10	4	4	NUM
fuelectenerg-1427	399	11	represents	represent	VERB
fuelectenerg-1427	399	12	the	the	DET
fuelectenerg-1427	399	13	expansion	expansion	NOUN
fuelectenerg-1427	399	14	nodes	node	NOUN
fuelectenerg-1427	399	15	for	for	ADP
fuelectenerg-1427	399	16	ternary	ternary	ADJ
fuelectenerg-1427	399	17	shannon	shannon	NOUN
fuelectenerg-1427	399	18	,	,	PUNCT
fuelectenerg-1427	399	19	davio	davio	NOUN
fuelectenerg-1427	399	20	and	and	CCONJ
fuelectenerg-1427	399	21	generalized	generalized	ADJ
fuelectenerg-1427	399	22	davio	davio	NOUN
fuelectenerg-1427	399	23	(	(	PUNCT
fuelectenerg-1427	399	24	d	d	NOUN
fuelectenerg-1427	399	25	)	)	PUNCT
fuelectenerg-1427	399	26	,	,	PUNCT
fuelectenerg-1427	399	27	respectively	respectively	ADV
fuelectenerg-1427	399	28	.	.	PUNCT
fuelectenerg-1427	400	1	s	s	PART
fuelectenerg-1427	400	2	0	0	NUM
fuelectenerg-1427	400	3	x	x	SYM
fuelectenerg-1427	400	4	1	1	NUM
fuelectenerg-1427	400	5	x	x	SYM
fuelectenerg-1427	400	6	2	2	NUM
fuelectenerg-1427	400	7	x	x	SYM
fuelectenerg-1427	400	8	(	(	PUNCT
fuelectenerg-1427	400	9	a	a	PRON
fuelectenerg-1427	400	10	)	)	PUNCT
fuelectenerg-1427	400	11	d0	d0	NOUN
fuelectenerg-1427	400	12	1	1	NUM
fuelectenerg-1427	400	13	x	x	SYM
fuelectenerg-1427	400	14	2	2	NUM
fuelectenerg-1427	400	15	(	(	PUNCT
fuelectenerg-1427	400	16	b	b	NOUN
fuelectenerg-1427	400	17	)	)	PUNCT
fuelectenerg-1427	400	18	d2	d2	PROPN
fuelectenerg-1427	400	19	1	1	NUM
fuelectenerg-1427	400	20	(	(	PUNCT
fuelectenerg-1427	400	21	d	d	NOUN
fuelectenerg-1427	400	22	)	)	PUNCT
fuelectenerg-1427	401	1	d	d	NOUN
fuelectenerg-1427	401	2	1	1	NUM
fuelectenerg-1427	401	3	(	(	PUNCT
fuelectenerg-1427	401	4	e	e	NOUN
fuelectenerg-1427	401	5	)	)	PUNCT
fuelectenerg-1427	401	6	d1	d1	NOUN
fuelectenerg-1427	401	7	1	1	NUM
fuelectenerg-1427	401	8	(	(	PUNCT
fuelectenerg-1427	401	9	’	'	PUNCT
fuelectenerg-1427	401	10	)	)	PUNCT
fuelectenerg-1427	401	11	x	x	SYM
fuelectenerg-1427	401	12	2	2	NUM
fuelectenerg-1427	401	13	(	(	PUNCT
fuelectenerg-1427	401	14	’’	’'	PUNCT
fuelectenerg-1427	401	15	)	)	PUNCT
fuelectenerg-1427	401	16	x	x	SYM
fuelectenerg-1427	401	17	2	2	NUM
fuelectenerg-1427	401	18	(	(	PUNCT
fuelectenerg-1427	401	19	)	)	PUNCT
fuelectenerg-1427	401	20	x	x	SYM
fuelectenerg-1427	401	21	2	2	NUM
fuelectenerg-1427	401	22	(	(	PUNCT
fuelectenerg-1427	401	23	c	c	NOUN
fuelectenerg-1427	401	24	)	)	PUNCT
fuelectenerg-1427	401	25	x	x	SYM
fuelectenerg-1427	401	26	xx	xx	X
fuelectenerg-1427	401	27	’	'	PUNCT
fuelectenerg-1427	401	28	x	x	NOUN
fuelectenerg-1427	401	29	’’	’'	PUNCT
fuelectenerg-1427	401	30	figure	figure	VERB
fuelectenerg-1427	401	31	4	4	NUM
fuelectenerg-1427	401	32	:	:	PUNCT
fuelectenerg-1427	401	33	ternary	ternary	ADJ
fuelectenerg-1427	401	34	nodes	node	NOUN
fuelectenerg-1427	401	35	for	for	ADP
fuelectenerg-1427	401	36	ternary	ternary	ADJ
fuelectenerg-1427	401	37	decision	decision	NOUN
fuelectenerg-1427	401	38	trees	tree	NOUN
fuelectenerg-1427	401	39	:	:	PUNCT
fuelectenerg-1427	401	40	(	(	PUNCT
fuelectenerg-1427	401	41	a	a	X
fuelectenerg-1427	401	42	)	)	PUNCT
fuelectenerg-1427	401	43	shannon	shannon	NOUN
fuelectenerg-1427	401	44	,	,	PUNCT
fuelectenerg-1427	401	45	(	(	PUNCT
fuelectenerg-1427	401	46	b	b	X
fuelectenerg-1427	401	47	)	)	PUNCT
fuelectenerg-1427	401	48	davio0	davio0	PROPN
fuelectenerg-1427	401	49	,	,	PUNCT
fuelectenerg-1427	401	50	(	(	PUNCT
fuelectenerg-1427	401	51	c	c	X
fuelectenerg-1427	401	52	)	)	PUNCT
fuelectenerg-1427	401	53	davio1	davio1	NOUN
fuelectenerg-1427	401	54	,	,	PUNCT
fuelectenerg-1427	401	55	(	(	PUNCT
fuelectenerg-1427	401	56	d	d	NOUN
fuelectenerg-1427	401	57	)	)	PUNCT
fuelectenerg-1427	401	58	davio2	davio2	PROPN
fuelectenerg-1427	401	59	,	,	PUNCT
fuelectenerg-1427	401	60	and	and	CCONJ
fuelectenerg-1427	401	61	(	(	PUNCT
fuelectenerg-1427	401	62	e	e	NOUN
fuelectenerg-1427	401	63	)	)	PUNCT
fuelectenerg-1427	401	64	generalized	generalized	ADJ
fuelectenerg-1427	401	65	davio	davio	NOUN
fuelectenerg-1427	401	66	(	(	PUNCT
fuelectenerg-1427	401	67	d	d	NOUN
fuelectenerg-1427	401	68	)	)	PUNCT
fuelectenerg-1427	401	69	where	where	SCONJ
fuelectenerg-1427	401	70	x	x	SYM
fuelectenerg-1427	401	71	∈	∈	PROPN
fuelectenerg-1427	401	72	{	{	PUNCT
fuelectenerg-1427	401	73	x	x	NOUN
fuelectenerg-1427	401	74	,	,	PUNCT
fuelectenerg-1427	401	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	401	76	}	}	PUNCT
fuelectenerg-1427	401	77	.	.	PUNCT
fuelectenerg-1427	402	1	in	in	ADP
fuelectenerg-1427	402	2	correspondence	correspondence	NOUN
fuelectenerg-1427	402	3	to	to	ADP
fuelectenerg-1427	402	4	the	the	DET
fuelectenerg-1427	402	5	binary	binary	PROPN
fuelectenerg-1427	402	6	s	s	PROPN
fuelectenerg-1427	402	7	/	/	SYM
fuelectenerg-1427	402	8	d	d	NOUN
fuelectenerg-1427	402	9	trees	tree	NOUN
fuelectenerg-1427	402	10	,	,	PUNCT
fuelectenerg-1427	402	11	one	one	PRON
fuelectenerg-1427	402	12	can	can	AUX
fuelectenerg-1427	402	13	produce	produce	VERB
fuelectenerg-1427	402	14	ternary	ternary	ADJ
fuelectenerg-1427	402	15	s	s	NOUN
fuelectenerg-1427	402	16	/	/	SYM
fuelectenerg-1427	402	17	d	d	NOUN
fuelectenerg-1427	402	18	trees	tree	NOUN
fuelectenerg-1427	402	19	.	.	PUNCT
fuelectenerg-1427	403	1	to	to	PART
fuelectenerg-1427	403	2	define	define	VERB
fuelectenerg-1427	403	3	the	the	DET
fuelectenerg-1427	403	4	ternary	ternary	ADJ
fuelectenerg-1427	403	5	s	s	NOUN
fuelectenerg-1427	403	6	/	/	SYM
fuelectenerg-1427	403	7	d	d	NOUN
fuelectenerg-1427	403	8	trees	tree	NOUN
fuelectenerg-1427	403	9	,	,	PUNCT
fuelectenerg-1427	403	10	we	we	PRON
fuelectenerg-1427	403	11	define	define	VERB
fuelectenerg-1427	403	12	the	the	DET
fuelectenerg-1427	403	13	generalized	generalized	ADJ
fuelectenerg-1427	403	14	davio	davio	NOUN
fuelectenerg-1427	403	15	node	node	NOUN
fuelectenerg-1427	403	16	over	over	ADP
fuelectenerg-1427	403	17	ternary	ternary	ADJ
fuelectenerg-1427	403	18	galois	galois	PROPN
fuelectenerg-1427	403	19	radix	radix	NOUN
fuelectenerg-1427	403	20	as	as	SCONJ
fuelectenerg-1427	403	21	shown	show	VERB
fuelectenerg-1427	403	22	in	in	ADP
fuelectenerg-1427	403	23	figure	figure	NOUN
fuelectenerg-1427	403	24	4(e	4(e	NUM
fuelectenerg-1427	403	25	)	)	PUNCT
fuelectenerg-1427	403	26	.	.	PUNCT
fuelectenerg-1427	404	1	our	our	PRON
fuelectenerg-1427	404	2	notation	notation	NOUN
fuelectenerg-1427	404	3	here	here	ADV
fuelectenerg-1427	404	4	is	be	AUX
fuelectenerg-1427	404	5	that	that	PRON
fuelectenerg-1427	404	6	(	(	PUNCT
fuelectenerg-1427	404	7	x	x	X
fuelectenerg-1427	404	8	)	)	PUNCT
fuelectenerg-1427	404	9	corresponds	correspond	VERB
fuelectenerg-1427	404	10	to	to	ADP
fuelectenerg-1427	404	11	the	the	DET
fuelectenerg-1427	404	12	three	three	NUM
fuelectenerg-1427	404	13	possible	possible	ADJ
fuelectenerg-1427	404	14	shifts	shift	NOUN
fuelectenerg-1427	404	15	of	of	ADP
fuelectenerg-1427	404	16	the	the	DET
fuelectenerg-1427	404	17	variable	variable	NOUN
fuelectenerg-1427	404	18	x	x	NOUN
fuelectenerg-1427	404	19	as	as	SCONJ
fuelectenerg-1427	404	20	follows	follow	VERB
fuelectenerg-1427	404	21	:	:	PUNCT
fuelectenerg-1427	404	22	x	x	SYM
fuelectenerg-1427	404	23	∈	∈	NOUN
fuelectenerg-1427	404	24	{	{	PUNCT
fuelectenerg-1427	404	25	x	x	NOUN
fuelectenerg-1427	404	26	,	,	PUNCT
fuelectenerg-1427	404	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	404	28	}	}	PUNCT
fuelectenerg-1427	404	29	,	,	PUNCT
fuelectenerg-1427	404	30	over	over	ADP
fuelectenerg-1427	404	31	gf(3	gf(3	PROPN
fuelectenerg-1427	404	32	)	)	PUNCT
fuelectenerg-1427	404	33	.	.	PUNCT
fuelectenerg-1427	405	1	(	(	PUNCT
fuelectenerg-1427	405	2	28	28	NUM
fuelectenerg-1427	405	3	)	)	PUNCT
fuelectenerg-1427	405	4	definition	definition	NOUN
fuelectenerg-1427	405	5	1	1	NUM
fuelectenerg-1427	405	6	.	.	PUNCT
fuelectenerg-1427	406	1	the	the	DET
fuelectenerg-1427	406	2	ternary	ternary	ADJ
fuelectenerg-1427	406	3	tree	tree	NOUN
fuelectenerg-1427	406	4	with	with	ADP
fuelectenerg-1427	406	5	ternary	ternary	ADJ
fuelectenerg-1427	406	6	shannon	shannon	NOUN
fuelectenerg-1427	406	7	and	and	CCONJ
fuelectenerg-1427	406	8	ternary	ternary	ADJ
fuelectenerg-1427	406	9	generalized	generalized	ADJ
fuelectenerg-1427	406	10	davio	davio	NOUN
fuelectenerg-1427	406	11	nodes	node	NOUN
fuelectenerg-1427	406	12	,	,	PUNCT
fuelectenerg-1427	406	13	that	that	PRON
fuelectenerg-1427	406	14	generates	generate	VERB
fuelectenerg-1427	406	15	other	other	ADJ
fuelectenerg-1427	406	16	ternary	ternary	ADJ
fuelectenerg-1427	406	17	trees	tree	NOUN
fuelectenerg-1427	406	18	,	,	PUNCT
fuelectenerg-1427	406	19	is	be	AUX
fuelectenerg-1427	406	20	called	call	VERB
fuelectenerg-1427	406	21	ternary	ternary	ADJ
fuelectenerg-1427	406	22	shannon	shannon	NOUN
fuelectenerg-1427	406	23	-	-	PUNCT
fuelectenerg-1427	406	24	davio	davio	NOUN
fuelectenerg-1427	406	25	(	(	PUNCT
fuelectenerg-1427	406	26	s	s	NOUN
fuelectenerg-1427	406	27	/	/	SYM
fuelectenerg-1427	406	28	d	d	NOUN
fuelectenerg-1427	406	29	)	)	PUNCT
fuelectenerg-1427	406	30	tree	tree	NOUN
fuelectenerg-1427	406	31	.	.	PUNCT
fuelectenerg-1427	407	1	utilizing	utilize	VERB
fuelectenerg-1427	407	2	the	the	DET
fuelectenerg-1427	407	3	definition	definition	NOUN
fuelectenerg-1427	407	4	of	of	ADP
fuelectenerg-1427	407	5	ternary	ternary	ADJ
fuelectenerg-1427	407	6	shannon	shannon	NOUN
fuelectenerg-1427	407	7	in	in	ADP
fuelectenerg-1427	407	8	figure	figure	NOUN
fuelectenerg-1427	407	9	4(a	4(a	NUM
fuelectenerg-1427	407	10	)	)	PUNCT
fuelectenerg-1427	407	11	and	and	CCONJ
fuelectenerg-1427	407	12	ternary	ternary	ADJ
fuelectenerg-1427	407	13	generalized	generalized	ADJ
fuelectenerg-1427	407	14	davio	davio	NOUN
fuelectenerg-1427	407	15	in	in	ADP
fuelectenerg-1427	407	16	figure	figure	NOUN
fuelectenerg-1427	407	17	4(e	4(e	NUM
fuelectenerg-1427	407	18	)	)	PUNCT
fuelectenerg-1427	407	19	,	,	PUNCT
fuelectenerg-1427	407	20	we	we	PRON
fuelectenerg-1427	407	21	obtain	obtain	VERB
fuelectenerg-1427	407	22	the	the	DET
fuelectenerg-1427	407	23	ternary	ternary	ADJ
fuelectenerg-1427	407	24	shannon	shannon	NOUN
fuelectenerg-1427	407	25	-	-	PUNCT
fuelectenerg-1427	407	26	davio	davio	NOUN
fuelectenerg-1427	407	27	trees	tree	NOUN
fuelectenerg-1427	407	28	(	(	PUNCT
fuelectenerg-1427	407	29	ternary	ternary	NOUN
fuelectenerg-1427	407	30	s	s	PROPN
fuelectenerg-1427	407	31	/	/	SYM
fuelectenerg-1427	407	32	d	d	NOUN
fuelectenerg-1427	407	33	trees	tree	NOUN
fuelectenerg-1427	407	34	)	)	PUNCT
fuelectenerg-1427	407	35	for	for	ADP
fuelectenerg-1427	407	36	two	two	NUM
fuelectenerg-1427	407	37	variables	variable	NOUN
fuelectenerg-1427	407	38	as	as	SCONJ
fuelectenerg-1427	407	39	shown	show	VERB
fuelectenerg-1427	407	40	in	in	ADP
fuelectenerg-1427	407	41	figure	figure	NOUN
fuelectenerg-1427	407	42	5	5	NUM
fuelectenerg-1427	407	43	.	.	PUNCT
fuelectenerg-1427	407	44	from	from	ADP
fuelectenerg-1427	407	45	the	the	DET
fuelectenerg-1427	407	46	ternary	ternary	ADJ
fuelectenerg-1427	407	47	s	s	PROPN
fuelectenerg-1427	407	48	/	/	SYM
fuelectenerg-1427	407	49	d	d	ADJ
fuelectenerg-1427	407	50	dts	dts	NOUN
fuelectenerg-1427	407	51	shown	show	VERB
fuelectenerg-1427	407	52	in	in	ADP
fuelectenerg-1427	407	53	figure	figure	NOUN
fuelectenerg-1427	407	54	5	5	NUM
fuelectenerg-1427	407	55	,	,	PUNCT
fuelectenerg-1427	407	56	if	if	SCONJ
fuelectenerg-1427	407	57	we	we	PRON
fuelectenerg-1427	407	58	take	take	VERB
fuelectenerg-1427	407	59	any	any	DET
fuelectenerg-1427	407	60	s	s	PROPN
fuelectenerg-1427	407	61	/	/	SYM
fuelectenerg-1427	407	62	d	d	NOUN
fuelectenerg-1427	407	63	tree	tree	NOUN
fuelectenerg-1427	407	64	and	and	CCONJ
fuelectenerg-1427	407	65	multiply	multiply	VERB
fuelectenerg-1427	407	66	the	the	DET
fuelectenerg-1427	407	67	second	second	ADJ
fuelectenerg-1427	407	68	-	-	PUNCT
fuelectenerg-1427	407	69	level	level	NOUN
fuelectenerg-1427	407	70	cofactors	cofactor	NOUN
fuelectenerg-1427	407	71	(	(	PUNCT
fuelectenerg-1427	407	72	which	which	PRON
fuelectenerg-1427	407	73	are	be	AUX
fuelectenerg-1427	407	74	in	in	ADP
fuelectenerg-1427	407	75	the	the	DET
fuelectenerg-1427	407	76	tdt	tdt	PROPN
fuelectenerg-1427	407	77	leaves	leave	NOUN
fuelectenerg-1427	407	78	)	)	PUNCT
fuelectenerg-1427	407	79	each	each	PRON
fuelectenerg-1427	407	80	by	by	ADP
fuelectenerg-1427	407	81	the	the	DET
fuelectenerg-1427	407	82	corresponding	corresponding	ADJ
fuelectenerg-1427	407	83	path	path	NOUN
fuelectenerg-1427	407	84	in	in	ADP
fuelectenerg-1427	407	85	that	that	DET
fuelectenerg-1427	407	86	tdt	tdt	PROPN
fuelectenerg-1427	407	87	,	,	PUNCT
fuelectenerg-1427	407	88	and	and	CCONJ
fuelectenerg-1427	407	89	sum	sum	VERB
fuelectenerg-1427	407	90	all	all	DET
fuelectenerg-1427	407	91	the	the	DET
fuelectenerg-1427	407	92	resulting	result	VERB
fuelectenerg-1427	407	93	cubes	cube	NOUN
fuelectenerg-1427	407	94	(	(	PUNCT
fuelectenerg-1427	407	95	terms	term	NOUN
fuelectenerg-1427	407	96	)	)	PUNCT
fuelectenerg-1427	407	97	over	over	ADP
fuelectenerg-1427	407	98	gf(3	gf(3	PROPN
fuelectenerg-1427	407	99	)	)	PUNCT
fuelectenerg-1427	407	100	,	,	PUNCT
fuelectenerg-1427	407	101	we	we	PRON
fuelectenerg-1427	407	102	obtain	obtain	VERB
fuelectenerg-1427	407	103	the	the	DET
fuelectenerg-1427	407	104	flattened	flatten	VERB
fuelectenerg-1427	407	105	form	form	NOUN
fuelectenerg-1427	407	106	of	of	ADP
fuelectenerg-1427	407	107	the	the	DET
fuelectenerg-1427	407	108	function	function	NOUN
fuelectenerg-1427	407	109	f	f	PROPN
fuelectenerg-1427	407	110	,	,	PUNCT
fuelectenerg-1427	407	111	as	as	ADP
fuelectenerg-1427	407	112	a	a	DET
fuelectenerg-1427	407	113	certain	certain	ADJ
fuelectenerg-1427	407	114	gfsop	gfsop	NOUN
fuelectenerg-1427	407	115	expression	expression	NOUN
fuelectenerg-1427	407	116	.	.	PUNCT
fuelectenerg-1427	408	1	for	for	ADP
fuelectenerg-1427	408	2	each	each	DET
fuelectenerg-1427	408	3	tdt	tdt	PROPN
fuelectenerg-1427	408	4	in	in	ADP
fuelectenerg-1427	408	5	figure	figure	NOUN
fuelectenerg-1427	408	6	5	5	NUM
fuelectenerg-1427	408	7	,	,	PUNCT
fuelectenerg-1427	408	8	there	there	PRON
fuelectenerg-1427	408	9	are	be	VERB
fuelectenerg-1427	408	10	as	as	ADV
fuelectenerg-1427	408	11	many	many	ADJ
fuelectenerg-1427	408	12	forms	form	NOUN
fuelectenerg-1427	408	13	obtained	obtain	VERB
fuelectenerg-1427	408	14	for	for	ADP
fuelectenerg-1427	408	15	the	the	DET
fuelectenerg-1427	408	16	function	function	NOUN
fuelectenerg-1427	408	17	f	f	PROPN
fuelectenerg-1427	408	18	as	as	ADP
fuelectenerg-1427	408	19	the	the	DET
fuelectenerg-1427	408	20	number	number	NOUN
fuelectenerg-1427	408	21	of	of	ADP
fuelectenerg-1427	408	22	possible	possible	ADJ
fuelectenerg-1427	408	23	permutations	permutation	NOUN
fuelectenerg-1427	408	24	of	of	ADP
fuelectenerg-1427	408	25	the	the	DET
fuelectenerg-1427	408	26	polarities	polarity	NOUN
fuelectenerg-1427	408	27	of	of	ADP
fuelectenerg-1427	408	28	the	the	DET
fuelectenerg-1427	408	29	variables	variable	NOUN
fuelectenerg-1427	408	30	in	in	ADP
fuelectenerg-1427	408	31	the	the	DET
fuelectenerg-1427	408	32	second	second	ADJ
fuelectenerg-1427	408	33	-	-	PUNCT
fuelectenerg-1427	408	34	level	level	NOUN
fuelectenerg-1427	408	35	branches	branch	NOUN
fuelectenerg-1427	408	36	of	of	ADP
fuelectenerg-1427	408	37	each	each	DET
fuelectenerg-1427	408	38	tdt	tdt	PROPN
fuelectenerg-1427	408	39	.	.	PUNCT
fuelectenerg-1427	409	1	definition	definition	NOUN
fuelectenerg-1427	409	2	2	2	NUM
fuelectenerg-1427	409	3	.	.	PUNCT
fuelectenerg-1427	410	1	the	the	DET
fuelectenerg-1427	410	2	family	family	NOUN
fuelectenerg-1427	410	3	of	of	ADP
fuelectenerg-1427	410	4	all	all	DET
fuelectenerg-1427	410	5	possible	possible	ADJ
fuelectenerg-1427	410	6	forms	form	NOUN
fuelectenerg-1427	410	7	obtained	obtain	VERB
fuelectenerg-1427	410	8	per	per	ADP
fuelectenerg-1427	410	9	ternary	ternary	NOUN
fuelectenerg-1427	410	10	s	s	PROPN
fuelectenerg-1427	410	11	/	/	SYM
fuelectenerg-1427	410	12	d	d	NOUN
fuelectenerg-1427	410	13	tree	tree	NOUN
fuelectenerg-1427	410	14	is	be	AUX
fuelectenerg-1427	410	15	called	call	VERB
fuelectenerg-1427	410	16	ternary	ternary	ADJ
fuelectenerg-1427	410	17	inclusive	inclusive	ADJ
fuelectenerg-1427	410	18	forms	form	NOUN
fuelectenerg-1427	410	19	(	(	PUNCT
fuelectenerg-1427	410	20	tifs	tifs	PROPN
fuelectenerg-1427	410	21	)	)	PUNCT
fuelectenerg-1427	410	22	.	.	PUNCT
fuelectenerg-1427	411	1	the	the	DET
fuelectenerg-1427	411	2	numbers	number	NOUN
fuelectenerg-1427	411	3	of	of	ADP
fuelectenerg-1427	411	4	these	these	DET
fuelectenerg-1427	411	5	tifs	tif	NOUN
fuelectenerg-1427	411	6	per	per	ADP
fuelectenerg-1427	411	7	tdt	tdt	PROPN
fuelectenerg-1427	411	8	for	for	ADP
fuelectenerg-1427	411	9	two	two	NUM
fuelectenerg-1427	411	10	variables	variable	NOUN
fuelectenerg-1427	411	11	are	be	AUX
fuelectenerg-1427	411	12	shown	show	VERB
fuelectenerg-1427	411	13	on	on	ADP
fuelectenerg-1427	411	14	top	top	NOUN
fuelectenerg-1427	411	15	of	of	ADP
fuelectenerg-1427	411	16	each	each	DET
fuelectenerg-1427	411	17	s	s	PROPN
fuelectenerg-1427	411	18	/	/	SYM
fuelectenerg-1427	411	19	d	d	PROPN
fuelectenerg-1427	411	20	tdt	tdt	PROPN
fuelectenerg-1427	411	21	in	in	ADP
fuelectenerg-1427	411	22	figure	figure	NOUN
fuelectenerg-1427	411	23	5	5	NUM
fuelectenerg-1427	411	24	.	.	PUNCT
fuelectenerg-1427	411	25	by	by	ADP
fuelectenerg-1427	411	26	observing	observe	VERB
fuelectenerg-1427	411	27	figure	figure	NOUN
fuelectenerg-1427	411	28	5	5	NUM
fuelectenerg-1427	411	29	,	,	PUNCT
fuelectenerg-1427	411	30	we	we	PRON
fuelectenerg-1427	411	31	can	can	AUX
fuelectenerg-1427	411	32	generate	generate	VERB
fuelectenerg-1427	411	33	the	the	DET
fuelectenerg-1427	411	34	corresponding	corresponding	ADJ
fuelectenerg-1427	411	35	flattened	flatten	VERB
fuelectenerg-1427	411	36	forms	form	NOUN
fuelectenerg-1427	411	37	by	by	ADP
fuelectenerg-1427	411	38	two	two	NUM
fuelectenerg-1427	411	39	methods	method	NOUN
fuelectenerg-1427	411	40	.	.	PUNCT
fuelectenerg-1427	412	1	a	a	DET
fuelectenerg-1427	412	2	classical	classical	ADJ
fuelectenerg-1427	412	3	method	method	NOUN
fuelectenerg-1427	412	4	,	,	PUNCT
fuelectenerg-1427	412	5	per	per	ADP
fuelectenerg-1427	412	6	analogy	analogy	NOUN
fuelectenerg-1427	412	7	with	with	ADP
fuelectenerg-1427	412	8	well	well	ADV
fuelectenerg-1427	412	9	-	-	PUNCT
fuelectenerg-1427	412	10	known	know	VERB
fuelectenerg-1427	412	11	binary	binary	ADJ
fuelectenerg-1427	412	12	forms	form	NOUN
fuelectenerg-1427	412	13	,	,	PUNCT
fuelectenerg-1427	412	14	would	would	AUX
fuelectenerg-1427	412	15	be	be	AUX
fuelectenerg-1427	412	16	to	to	PART
fuelectenerg-1427	412	17	create	create	VERB
fuelectenerg-1427	412	18	every	every	DET
fuelectenerg-1427	412	19	transform	transform	NOUN
fuelectenerg-1427	412	20	matrix	matrix	NOUN
fuelectenerg-1427	412	21	for	for	ADP
fuelectenerg-1427	412	22	every	every	DET
fuelectenerg-1427	412	23	tif	tif	PROPN
fuelectenerg-1427	412	24	s	s	PROPN
fuelectenerg-1427	412	25	/	/	SYM
fuelectenerg-1427	412	26	d	d	NOUN
fuelectenerg-1427	412	27	tree	tree	NOUN
fuelectenerg-1427	412	28	and	and	CCONJ
fuelectenerg-1427	412	29	then	then	ADV
fuelectenerg-1427	412	30	expand	expand	VERB
fuelectenerg-1427	412	31	using	use	VERB
fuelectenerg-1427	412	32	that	that	DET
fuelectenerg-1427	412	33	transform	transform	NOUN
fuelectenerg-1427	412	34	matrix	matrix	NOUN
fuelectenerg-1427	412	35	.	.	PUNCT
fuelectenerg-1427	413	1	a	a	DET
fuelectenerg-1427	413	2	better	well	ADJ
fuelectenerg-1427	413	3	method	method	NOUN
fuelectenerg-1427	413	4	is	be	AUX
fuelectenerg-1427	413	5	to	to	PART
fuelectenerg-1427	413	6	create	create	VERB
fuelectenerg-1427	413	7	one	one	NUM
fuelectenerg-1427	413	8	flattened	flatten	VERB
fuelectenerg-1427	413	9	108	108	NUM
fuelectenerg-1427	413	10	an	an	DET
fuelectenerg-1427	413	11	extended	extend	VERB
fuelectenerg-1427	413	12	green	green	ADJ
fuelectenerg-1427	413	13	sasao	sasao	PROPN
fuelectenerg-1427	413	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	413	15	of	of	ADP
fuelectenerg-1427	413	16	canonical	canonical	ADJ
fuelectenerg-1427	413	17	ternary	ternary	ADJ
fuelectenerg-1427	413	18	galois	galois	NOUN
fuelectenerg-1427	413	19	forms	form	NOUN
fuelectenerg-1427	413	20	...	...	PUNCT
fuelectenerg-1427	413	21	s	s	VERB
fuelectenerg-1427	413	22	a	a	PRON
fuelectenerg-1427	413	23	’	'	PUNCT
fuelectenerg-1427	413	24	a	a	PRON
fuelectenerg-1427	413	25	(	(	PUNCT
fuelectenerg-1427	413	26	)	)	PUNCT
fuelectenerg-1427	413	27	a	a	PRON
fuelectenerg-1427	413	28	pd	pd	PROPN
fuelectenerg-1427	413	29	1	1	NUM
fuelectenerg-1427	413	30	a	a	PRON
fuelectenerg-1427	413	31	(	(	PUNCT
fuelectenerg-1427	413	32	)	)	PUNCT
fuelectenerg-1427	413	33	b	b	NOUN
fuelectenerg-1427	413	34	nd	nd	ADP
fuelectenerg-1427	413	35	1	1	NUM
fuelectenerg-1427	413	36	a	a	PRON
fuelectenerg-1427	413	37	’	'	PUNCT
fuelectenerg-1427	413	38	d	d	ADP
fuelectenerg-1427	413	39	1	1	NUM
fuelectenerg-1427	413	40	a	a	PRON
fuelectenerg-1427	413	41	(	(	PUNCT
fuelectenerg-1427	413	42	)	)	PUNCT
fuelectenerg-1427	413	43	d	d	NOUN
fuelectenerg-1427	413	44	(	(	PUNCT
fuelectenerg-1427	413	45	)	)	PUNCT
fuelectenerg-1427	413	46	c	c	NOUN
fuelectenerg-1427	413	47	figure	figure	VERB
fuelectenerg-1427	413	48	3	3	NUM
fuelectenerg-1427	413	49	:	:	PUNCT
fuelectenerg-1427	413	50	two	two	NUM
fuelectenerg-1427	413	51	-	-	PUNCT
fuelectenerg-1427	413	52	valued	value	VERB
fuelectenerg-1427	413	53	nodes	node	NOUN
fuelectenerg-1427	413	54	:	:	PUNCT
fuelectenerg-1427	413	55	(	(	PUNCT
fuelectenerg-1427	413	56	a	a	X
fuelectenerg-1427	413	57	)	)	PUNCT
fuelectenerg-1427	413	58	shannon	shannon	NOUN
fuelectenerg-1427	413	59	,	,	PUNCT
fuelectenerg-1427	413	60	(	(	PUNCT
fuelectenerg-1427	413	61	b	b	NOUN
fuelectenerg-1427	413	62	)	)	PUNCT
fuelectenerg-1427	413	63	positive	positive	ADJ
fuelectenerg-1427	413	64	davio	davio	NOUN
fuelectenerg-1427	413	65	,	,	PUNCT
fuelectenerg-1427	413	66	(	(	PUNCT
fuelectenerg-1427	413	67	c	c	NOUN
fuelectenerg-1427	413	68	)	)	PUNCT
fuelectenerg-1427	413	69	negative	negative	ADJ
fuelectenerg-1427	413	70	davio	davio	NOUN
fuelectenerg-1427	413	71	,	,	PUNCT
fuelectenerg-1427	413	72	and	and	CCONJ
fuelectenerg-1427	413	73	(	(	PUNCT
fuelectenerg-1427	413	74	d	d	X
fuelectenerg-1427	413	75	)	)	PUNCT
fuelectenerg-1427	413	76	generalized	generalized	ADJ
fuelectenerg-1427	413	77	davio	davio	NOUN
fuelectenerg-1427	413	78	where	where	SCONJ
fuelectenerg-1427	413	79	a	a	DET
fuelectenerg-1427	413	80	∈	∈	NOUN
fuelectenerg-1427	413	81	{	{	PUNCT
fuelectenerg-1427	413	82	a	a	PRON
fuelectenerg-1427	413	83	,	,	PUNCT
fuelectenerg-1427	413	84	a′	a′	PROPN
fuelectenerg-1427	413	85	}	}	PUNCT
fuelectenerg-1427	413	86	.	.	PUNCT
fuelectenerg-1427	414	1	variable	variable	ADJ
fuelectenerg-1427	414	2	,	,	PUNCT
fuelectenerg-1427	414	3	that	that	PRON
fuelectenerg-1427	414	4	is	be	AUX
fuelectenerg-1427	414	5	one	one	NUM
fuelectenerg-1427	414	6	tree	tree	NOUN
fuelectenerg-1427	414	7	level	level	NOUN
fuelectenerg-1427	414	8	,	,	PUNCT
fuelectenerg-1427	414	9	figure	figure	NOUN
fuelectenerg-1427	414	10	4	4	NUM
fuelectenerg-1427	414	11	represents	represent	VERB
fuelectenerg-1427	414	12	the	the	DET
fuelectenerg-1427	414	13	expansion	expansion	NOUN
fuelectenerg-1427	414	14	nodes	node	NOUN
fuelectenerg-1427	414	15	for	for	ADP
fuelectenerg-1427	414	16	ternary	ternary	ADJ
fuelectenerg-1427	414	17	shannon	shannon	NOUN
fuelectenerg-1427	414	18	,	,	PUNCT
fuelectenerg-1427	414	19	davio	davio	NOUN
fuelectenerg-1427	414	20	and	and	CCONJ
fuelectenerg-1427	414	21	generalized	generalized	ADJ
fuelectenerg-1427	414	22	davio	davio	NOUN
fuelectenerg-1427	414	23	(	(	PUNCT
fuelectenerg-1427	414	24	d	d	NOUN
fuelectenerg-1427	414	25	)	)	PUNCT
fuelectenerg-1427	414	26	,	,	PUNCT
fuelectenerg-1427	414	27	respectively	respectively	ADV
fuelectenerg-1427	414	28	.	.	PUNCT
fuelectenerg-1427	415	1	s	s	PART
fuelectenerg-1427	415	2	0	0	NUM
fuelectenerg-1427	415	3	x	x	SYM
fuelectenerg-1427	415	4	1	1	NUM
fuelectenerg-1427	415	5	x	x	SYM
fuelectenerg-1427	415	6	2	2	NUM
fuelectenerg-1427	415	7	x	x	SYM
fuelectenerg-1427	415	8	(	(	PUNCT
fuelectenerg-1427	415	9	a	a	PRON
fuelectenerg-1427	415	10	)	)	PUNCT
fuelectenerg-1427	415	11	d0	d0	NOUN
fuelectenerg-1427	415	12	1	1	NUM
fuelectenerg-1427	415	13	x	x	SYM
fuelectenerg-1427	415	14	2	2	NUM
fuelectenerg-1427	415	15	(	(	PUNCT
fuelectenerg-1427	415	16	b	b	NOUN
fuelectenerg-1427	415	17	)	)	PUNCT
fuelectenerg-1427	415	18	d2	d2	PROPN
fuelectenerg-1427	415	19	1	1	NUM
fuelectenerg-1427	415	20	(	(	PUNCT
fuelectenerg-1427	415	21	d	d	NOUN
fuelectenerg-1427	415	22	)	)	PUNCT
fuelectenerg-1427	416	1	d	d	NOUN
fuelectenerg-1427	416	2	1	1	NUM
fuelectenerg-1427	416	3	(	(	PUNCT
fuelectenerg-1427	416	4	e	e	NOUN
fuelectenerg-1427	416	5	)	)	PUNCT
fuelectenerg-1427	416	6	d1	d1	NOUN
fuelectenerg-1427	416	7	1	1	NUM
fuelectenerg-1427	416	8	(	(	PUNCT
fuelectenerg-1427	416	9	’	'	PUNCT
fuelectenerg-1427	416	10	)	)	PUNCT
fuelectenerg-1427	416	11	x	x	SYM
fuelectenerg-1427	416	12	2	2	NUM
fuelectenerg-1427	416	13	(	(	PUNCT
fuelectenerg-1427	416	14	’’	’'	PUNCT
fuelectenerg-1427	416	15	)	)	PUNCT
fuelectenerg-1427	416	16	x	x	SYM
fuelectenerg-1427	416	17	2	2	NUM
fuelectenerg-1427	416	18	(	(	PUNCT
fuelectenerg-1427	416	19	)	)	PUNCT
fuelectenerg-1427	416	20	x	x	SYM
fuelectenerg-1427	416	21	2	2	NUM
fuelectenerg-1427	416	22	(	(	PUNCT
fuelectenerg-1427	416	23	c	c	NOUN
fuelectenerg-1427	416	24	)	)	PUNCT
fuelectenerg-1427	416	25	x	x	SYM
fuelectenerg-1427	416	26	xx	xx	X
fuelectenerg-1427	416	27	’	'	PUNCT
fuelectenerg-1427	416	28	x	x	NOUN
fuelectenerg-1427	416	29	’’	’'	PUNCT
fuelectenerg-1427	416	30	figure	figure	VERB
fuelectenerg-1427	416	31	4	4	NUM
fuelectenerg-1427	416	32	:	:	PUNCT
fuelectenerg-1427	416	33	ternary	ternary	ADJ
fuelectenerg-1427	416	34	nodes	node	NOUN
fuelectenerg-1427	416	35	for	for	ADP
fuelectenerg-1427	416	36	ternary	ternary	ADJ
fuelectenerg-1427	416	37	decision	decision	NOUN
fuelectenerg-1427	416	38	trees	tree	NOUN
fuelectenerg-1427	416	39	:	:	PUNCT
fuelectenerg-1427	416	40	(	(	PUNCT
fuelectenerg-1427	416	41	a	a	X
fuelectenerg-1427	416	42	)	)	PUNCT
fuelectenerg-1427	416	43	shannon	shannon	NOUN
fuelectenerg-1427	416	44	,	,	PUNCT
fuelectenerg-1427	416	45	(	(	PUNCT
fuelectenerg-1427	416	46	b	b	X
fuelectenerg-1427	416	47	)	)	PUNCT
fuelectenerg-1427	416	48	davio0	davio0	PROPN
fuelectenerg-1427	416	49	,	,	PUNCT
fuelectenerg-1427	416	50	(	(	PUNCT
fuelectenerg-1427	416	51	c	c	X
fuelectenerg-1427	416	52	)	)	PUNCT
fuelectenerg-1427	416	53	davio1	davio1	NOUN
fuelectenerg-1427	416	54	,	,	PUNCT
fuelectenerg-1427	416	55	(	(	PUNCT
fuelectenerg-1427	416	56	d	d	NOUN
fuelectenerg-1427	416	57	)	)	PUNCT
fuelectenerg-1427	416	58	davio2	davio2	PROPN
fuelectenerg-1427	416	59	,	,	PUNCT
fuelectenerg-1427	416	60	and	and	CCONJ
fuelectenerg-1427	416	61	(	(	PUNCT
fuelectenerg-1427	416	62	e	e	NOUN
fuelectenerg-1427	416	63	)	)	PUNCT
fuelectenerg-1427	416	64	generalized	generalized	ADJ
fuelectenerg-1427	416	65	davio	davio	NOUN
fuelectenerg-1427	416	66	(	(	PUNCT
fuelectenerg-1427	416	67	d	d	NOUN
fuelectenerg-1427	416	68	)	)	PUNCT
fuelectenerg-1427	416	69	where	where	SCONJ
fuelectenerg-1427	416	70	x	x	SYM
fuelectenerg-1427	416	71	∈	∈	PROPN
fuelectenerg-1427	416	72	{	{	PUNCT
fuelectenerg-1427	416	73	x	x	NOUN
fuelectenerg-1427	416	74	,	,	PUNCT
fuelectenerg-1427	416	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	416	76	}	}	PUNCT
fuelectenerg-1427	416	77	.	.	PUNCT
fuelectenerg-1427	417	1	in	in	ADP
fuelectenerg-1427	417	2	correspondence	correspondence	NOUN
fuelectenerg-1427	417	3	to	to	ADP
fuelectenerg-1427	417	4	the	the	DET
fuelectenerg-1427	417	5	binary	binary	PROPN
fuelectenerg-1427	417	6	s	s	PROPN
fuelectenerg-1427	417	7	/	/	SYM
fuelectenerg-1427	417	8	d	d	NOUN
fuelectenerg-1427	417	9	trees	tree	NOUN
fuelectenerg-1427	417	10	,	,	PUNCT
fuelectenerg-1427	417	11	one	one	PRON
fuelectenerg-1427	417	12	can	can	AUX
fuelectenerg-1427	417	13	produce	produce	VERB
fuelectenerg-1427	417	14	ternary	ternary	ADJ
fuelectenerg-1427	417	15	s	s	NOUN
fuelectenerg-1427	417	16	/	/	SYM
fuelectenerg-1427	417	17	d	d	NOUN
fuelectenerg-1427	417	18	trees	tree	NOUN
fuelectenerg-1427	417	19	.	.	PUNCT
fuelectenerg-1427	418	1	to	to	PART
fuelectenerg-1427	418	2	define	define	VERB
fuelectenerg-1427	418	3	the	the	DET
fuelectenerg-1427	418	4	ternary	ternary	ADJ
fuelectenerg-1427	418	5	s	s	NOUN
fuelectenerg-1427	418	6	/	/	SYM
fuelectenerg-1427	418	7	d	d	NOUN
fuelectenerg-1427	418	8	trees	tree	NOUN
fuelectenerg-1427	418	9	,	,	PUNCT
fuelectenerg-1427	418	10	we	we	PRON
fuelectenerg-1427	418	11	define	define	VERB
fuelectenerg-1427	418	12	the	the	DET
fuelectenerg-1427	418	13	generalized	generalized	ADJ
fuelectenerg-1427	418	14	davio	davio	NOUN
fuelectenerg-1427	418	15	node	node	NOUN
fuelectenerg-1427	418	16	over	over	ADP
fuelectenerg-1427	418	17	ternary	ternary	ADJ
fuelectenerg-1427	418	18	galois	galois	PROPN
fuelectenerg-1427	418	19	radix	radix	NOUN
fuelectenerg-1427	418	20	as	as	SCONJ
fuelectenerg-1427	418	21	shown	show	VERB
fuelectenerg-1427	418	22	in	in	ADP
fuelectenerg-1427	418	23	figure	figure	NOUN
fuelectenerg-1427	418	24	4(e	4(e	NUM
fuelectenerg-1427	418	25	)	)	PUNCT
fuelectenerg-1427	418	26	.	.	PUNCT
fuelectenerg-1427	419	1	our	our	PRON
fuelectenerg-1427	419	2	notation	notation	NOUN
fuelectenerg-1427	419	3	here	here	ADV
fuelectenerg-1427	419	4	is	be	AUX
fuelectenerg-1427	419	5	that	that	PRON
fuelectenerg-1427	419	6	(	(	PUNCT
fuelectenerg-1427	419	7	x	x	X
fuelectenerg-1427	419	8	)	)	PUNCT
fuelectenerg-1427	419	9	corresponds	correspond	VERB
fuelectenerg-1427	419	10	to	to	ADP
fuelectenerg-1427	419	11	the	the	DET
fuelectenerg-1427	419	12	three	three	NUM
fuelectenerg-1427	419	13	possible	possible	ADJ
fuelectenerg-1427	419	14	shifts	shift	NOUN
fuelectenerg-1427	419	15	of	of	ADP
fuelectenerg-1427	419	16	the	the	DET
fuelectenerg-1427	419	17	variable	variable	NOUN
fuelectenerg-1427	419	18	x	x	NOUN
fuelectenerg-1427	419	19	as	as	SCONJ
fuelectenerg-1427	419	20	follows	follow	VERB
fuelectenerg-1427	419	21	:	:	PUNCT
fuelectenerg-1427	419	22	x	x	SYM
fuelectenerg-1427	419	23	∈	∈	NOUN
fuelectenerg-1427	419	24	{	{	PUNCT
fuelectenerg-1427	419	25	x	x	NOUN
fuelectenerg-1427	419	26	,	,	PUNCT
fuelectenerg-1427	419	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	419	28	}	}	PUNCT
fuelectenerg-1427	419	29	,	,	PUNCT
fuelectenerg-1427	419	30	over	over	ADP
fuelectenerg-1427	419	31	gf(3	gf(3	PROPN
fuelectenerg-1427	419	32	)	)	PUNCT
fuelectenerg-1427	419	33	.	.	PUNCT
fuelectenerg-1427	420	1	(	(	PUNCT
fuelectenerg-1427	420	2	28	28	NUM
fuelectenerg-1427	420	3	)	)	PUNCT
fuelectenerg-1427	420	4	definition	definition	NOUN
fuelectenerg-1427	420	5	1	1	NUM
fuelectenerg-1427	420	6	.	.	PUNCT
fuelectenerg-1427	421	1	the	the	DET
fuelectenerg-1427	421	2	ternary	ternary	ADJ
fuelectenerg-1427	421	3	tree	tree	NOUN
fuelectenerg-1427	421	4	with	with	ADP
fuelectenerg-1427	421	5	ternary	ternary	ADJ
fuelectenerg-1427	421	6	shannon	shannon	NOUN
fuelectenerg-1427	421	7	and	and	CCONJ
fuelectenerg-1427	421	8	ternary	ternary	ADJ
fuelectenerg-1427	421	9	generalized	generalized	ADJ
fuelectenerg-1427	421	10	davio	davio	NOUN
fuelectenerg-1427	421	11	nodes	node	NOUN
fuelectenerg-1427	421	12	,	,	PUNCT
fuelectenerg-1427	421	13	that	that	PRON
fuelectenerg-1427	421	14	generates	generate	VERB
fuelectenerg-1427	421	15	other	other	ADJ
fuelectenerg-1427	421	16	ternary	ternary	ADJ
fuelectenerg-1427	421	17	trees	tree	NOUN
fuelectenerg-1427	421	18	,	,	PUNCT
fuelectenerg-1427	421	19	is	be	AUX
fuelectenerg-1427	421	20	called	call	VERB
fuelectenerg-1427	421	21	ternary	ternary	ADJ
fuelectenerg-1427	421	22	shannon	shannon	NOUN
fuelectenerg-1427	421	23	-	-	PUNCT
fuelectenerg-1427	421	24	davio	davio	NOUN
fuelectenerg-1427	421	25	(	(	PUNCT
fuelectenerg-1427	421	26	s	s	NOUN
fuelectenerg-1427	421	27	/	/	SYM
fuelectenerg-1427	421	28	d	d	NOUN
fuelectenerg-1427	421	29	)	)	PUNCT
fuelectenerg-1427	421	30	tree	tree	NOUN
fuelectenerg-1427	421	31	.	.	PUNCT
fuelectenerg-1427	422	1	utilizing	utilize	VERB
fuelectenerg-1427	422	2	the	the	DET
fuelectenerg-1427	422	3	definition	definition	NOUN
fuelectenerg-1427	422	4	of	of	ADP
fuelectenerg-1427	422	5	ternary	ternary	ADJ
fuelectenerg-1427	422	6	shannon	shannon	NOUN
fuelectenerg-1427	422	7	in	in	ADP
fuelectenerg-1427	422	8	figure	figure	NOUN
fuelectenerg-1427	422	9	4(a	4(a	NUM
fuelectenerg-1427	422	10	)	)	PUNCT
fuelectenerg-1427	422	11	and	and	CCONJ
fuelectenerg-1427	422	12	ternary	ternary	ADJ
fuelectenerg-1427	422	13	generalized	generalized	ADJ
fuelectenerg-1427	422	14	davio	davio	NOUN
fuelectenerg-1427	422	15	in	in	ADP
fuelectenerg-1427	422	16	figure	figure	NOUN
fuelectenerg-1427	422	17	4(e	4(e	NUM
fuelectenerg-1427	422	18	)	)	PUNCT
fuelectenerg-1427	422	19	,	,	PUNCT
fuelectenerg-1427	422	20	we	we	PRON
fuelectenerg-1427	422	21	obtain	obtain	VERB
fuelectenerg-1427	422	22	the	the	DET
fuelectenerg-1427	422	23	ternary	ternary	ADJ
fuelectenerg-1427	422	24	shannon	shannon	NOUN
fuelectenerg-1427	422	25	-	-	PUNCT
fuelectenerg-1427	422	26	davio	davio	NOUN
fuelectenerg-1427	422	27	trees	tree	NOUN
fuelectenerg-1427	422	28	(	(	PUNCT
fuelectenerg-1427	422	29	ternary	ternary	NOUN
fuelectenerg-1427	422	30	s	s	PROPN
fuelectenerg-1427	422	31	/	/	SYM
fuelectenerg-1427	422	32	d	d	NOUN
fuelectenerg-1427	422	33	trees	tree	NOUN
fuelectenerg-1427	422	34	)	)	PUNCT
fuelectenerg-1427	422	35	for	for	ADP
fuelectenerg-1427	422	36	two	two	NUM
fuelectenerg-1427	422	37	variables	variable	NOUN
fuelectenerg-1427	422	38	as	as	SCONJ
fuelectenerg-1427	422	39	shown	show	VERB
fuelectenerg-1427	422	40	in	in	ADP
fuelectenerg-1427	422	41	figure	figure	NOUN
fuelectenerg-1427	422	42	5	5	NUM
fuelectenerg-1427	422	43	.	.	PUNCT
fuelectenerg-1427	422	44	from	from	ADP
fuelectenerg-1427	422	45	the	the	DET
fuelectenerg-1427	422	46	ternary	ternary	ADJ
fuelectenerg-1427	422	47	s	s	PROPN
fuelectenerg-1427	422	48	/	/	SYM
fuelectenerg-1427	422	49	d	d	ADJ
fuelectenerg-1427	422	50	dts	dts	NOUN
fuelectenerg-1427	422	51	shown	show	VERB
fuelectenerg-1427	422	52	in	in	ADP
fuelectenerg-1427	422	53	figure	figure	NOUN
fuelectenerg-1427	422	54	5	5	NUM
fuelectenerg-1427	422	55	,	,	PUNCT
fuelectenerg-1427	422	56	if	if	SCONJ
fuelectenerg-1427	422	57	we	we	PRON
fuelectenerg-1427	422	58	take	take	VERB
fuelectenerg-1427	422	59	any	any	DET
fuelectenerg-1427	422	60	s	s	PROPN
fuelectenerg-1427	422	61	/	/	SYM
fuelectenerg-1427	422	62	d	d	NOUN
fuelectenerg-1427	422	63	tree	tree	NOUN
fuelectenerg-1427	422	64	and	and	CCONJ
fuelectenerg-1427	422	65	multiply	multiply	VERB
fuelectenerg-1427	422	66	the	the	DET
fuelectenerg-1427	422	67	second	second	ADJ
fuelectenerg-1427	422	68	-	-	PUNCT
fuelectenerg-1427	422	69	level	level	NOUN
fuelectenerg-1427	422	70	cofactors	cofactor	NOUN
fuelectenerg-1427	422	71	(	(	PUNCT
fuelectenerg-1427	422	72	which	which	PRON
fuelectenerg-1427	422	73	are	be	AUX
fuelectenerg-1427	422	74	in	in	ADP
fuelectenerg-1427	422	75	the	the	DET
fuelectenerg-1427	422	76	tdt	tdt	PROPN
fuelectenerg-1427	422	77	leaves	leave	NOUN
fuelectenerg-1427	422	78	)	)	PUNCT
fuelectenerg-1427	422	79	each	each	PRON
fuelectenerg-1427	422	80	by	by	ADP
fuelectenerg-1427	422	81	the	the	DET
fuelectenerg-1427	422	82	corresponding	corresponding	ADJ
fuelectenerg-1427	422	83	path	path	NOUN
fuelectenerg-1427	422	84	in	in	ADP
fuelectenerg-1427	422	85	that	that	DET
fuelectenerg-1427	422	86	tdt	tdt	PROPN
fuelectenerg-1427	422	87	,	,	PUNCT
fuelectenerg-1427	422	88	and	and	CCONJ
fuelectenerg-1427	422	89	sum	sum	VERB
fuelectenerg-1427	422	90	all	all	DET
fuelectenerg-1427	422	91	the	the	DET
fuelectenerg-1427	422	92	resulting	result	VERB
fuelectenerg-1427	422	93	cubes	cube	NOUN
fuelectenerg-1427	422	94	(	(	PUNCT
fuelectenerg-1427	422	95	terms	term	NOUN
fuelectenerg-1427	422	96	)	)	PUNCT
fuelectenerg-1427	422	97	over	over	ADP
fuelectenerg-1427	422	98	gf(3	gf(3	PROPN
fuelectenerg-1427	422	99	)	)	PUNCT
fuelectenerg-1427	422	100	,	,	PUNCT
fuelectenerg-1427	422	101	we	we	PRON
fuelectenerg-1427	422	102	obtain	obtain	VERB
fuelectenerg-1427	422	103	the	the	DET
fuelectenerg-1427	422	104	flattened	flatten	VERB
fuelectenerg-1427	422	105	form	form	NOUN
fuelectenerg-1427	422	106	of	of	ADP
fuelectenerg-1427	422	107	the	the	DET
fuelectenerg-1427	422	108	function	function	NOUN
fuelectenerg-1427	422	109	f	f	PROPN
fuelectenerg-1427	422	110	,	,	PUNCT
fuelectenerg-1427	422	111	as	as	ADP
fuelectenerg-1427	422	112	a	a	DET
fuelectenerg-1427	422	113	certain	certain	ADJ
fuelectenerg-1427	422	114	gfsop	gfsop	NOUN
fuelectenerg-1427	422	115	expression	expression	NOUN
fuelectenerg-1427	422	116	.	.	PUNCT
fuelectenerg-1427	423	1	for	for	ADP
fuelectenerg-1427	423	2	each	each	DET
fuelectenerg-1427	423	3	tdt	tdt	PROPN
fuelectenerg-1427	423	4	in	in	ADP
fuelectenerg-1427	423	5	figure	figure	NOUN
fuelectenerg-1427	423	6	5	5	NUM
fuelectenerg-1427	423	7	,	,	PUNCT
fuelectenerg-1427	423	8	there	there	PRON
fuelectenerg-1427	423	9	are	be	VERB
fuelectenerg-1427	423	10	as	as	ADV
fuelectenerg-1427	423	11	many	many	ADJ
fuelectenerg-1427	423	12	forms	form	NOUN
fuelectenerg-1427	423	13	obtained	obtain	VERB
fuelectenerg-1427	423	14	for	for	ADP
fuelectenerg-1427	423	15	the	the	DET
fuelectenerg-1427	423	16	function	function	NOUN
fuelectenerg-1427	423	17	f	f	PROPN
fuelectenerg-1427	423	18	as	as	ADP
fuelectenerg-1427	423	19	the	the	DET
fuelectenerg-1427	423	20	number	number	NOUN
fuelectenerg-1427	423	21	of	of	ADP
fuelectenerg-1427	423	22	possible	possible	ADJ
fuelectenerg-1427	423	23	permutations	permutation	NOUN
fuelectenerg-1427	423	24	of	of	ADP
fuelectenerg-1427	423	25	the	the	DET
fuelectenerg-1427	423	26	polarities	polarity	NOUN
fuelectenerg-1427	423	27	of	of	ADP
fuelectenerg-1427	423	28	the	the	DET
fuelectenerg-1427	423	29	variables	variable	NOUN
fuelectenerg-1427	423	30	in	in	ADP
fuelectenerg-1427	423	31	the	the	DET
fuelectenerg-1427	423	32	second	second	ADJ
fuelectenerg-1427	423	33	-	-	PUNCT
fuelectenerg-1427	423	34	level	level	NOUN
fuelectenerg-1427	423	35	branches	branch	NOUN
fuelectenerg-1427	423	36	of	of	ADP
fuelectenerg-1427	423	37	each	each	DET
fuelectenerg-1427	423	38	tdt	tdt	PROPN
fuelectenerg-1427	423	39	.	.	PUNCT
fuelectenerg-1427	424	1	definition	definition	NOUN
fuelectenerg-1427	424	2	2	2	NUM
fuelectenerg-1427	424	3	.	.	PUNCT
fuelectenerg-1427	425	1	the	the	DET
fuelectenerg-1427	425	2	family	family	NOUN
fuelectenerg-1427	425	3	of	of	ADP
fuelectenerg-1427	425	4	all	all	DET
fuelectenerg-1427	425	5	possible	possible	ADJ
fuelectenerg-1427	425	6	forms	form	NOUN
fuelectenerg-1427	425	7	obtained	obtain	VERB
fuelectenerg-1427	425	8	per	per	ADP
fuelectenerg-1427	425	9	ternary	ternary	NOUN
fuelectenerg-1427	425	10	s	s	PROPN
fuelectenerg-1427	425	11	/	/	SYM
fuelectenerg-1427	425	12	d	d	NOUN
fuelectenerg-1427	425	13	tree	tree	NOUN
fuelectenerg-1427	425	14	is	be	AUX
fuelectenerg-1427	425	15	called	call	VERB
fuelectenerg-1427	425	16	ternary	ternary	ADJ
fuelectenerg-1427	425	17	inclusive	inclusive	ADJ
fuelectenerg-1427	425	18	forms	form	NOUN
fuelectenerg-1427	425	19	(	(	PUNCT
fuelectenerg-1427	425	20	tifs	tifs	PROPN
fuelectenerg-1427	425	21	)	)	PUNCT
fuelectenerg-1427	425	22	.	.	PUNCT
fuelectenerg-1427	426	1	the	the	DET
fuelectenerg-1427	426	2	numbers	number	NOUN
fuelectenerg-1427	426	3	of	of	ADP
fuelectenerg-1427	426	4	these	these	DET
fuelectenerg-1427	426	5	tifs	tif	NOUN
fuelectenerg-1427	426	6	per	per	ADP
fuelectenerg-1427	426	7	tdt	tdt	PROPN
fuelectenerg-1427	426	8	for	for	ADP
fuelectenerg-1427	426	9	two	two	NUM
fuelectenerg-1427	426	10	variables	variable	NOUN
fuelectenerg-1427	426	11	are	be	AUX
fuelectenerg-1427	426	12	shown	show	VERB
fuelectenerg-1427	426	13	on	on	ADP
fuelectenerg-1427	426	14	top	top	NOUN
fuelectenerg-1427	426	15	of	of	ADP
fuelectenerg-1427	426	16	each	each	DET
fuelectenerg-1427	426	17	s	s	PROPN
fuelectenerg-1427	426	18	/	/	SYM
fuelectenerg-1427	426	19	d	d	PROPN
fuelectenerg-1427	426	20	tdt	tdt	PROPN
fuelectenerg-1427	426	21	in	in	ADP
fuelectenerg-1427	426	22	figure	figure	NOUN
fuelectenerg-1427	426	23	5	5	NUM
fuelectenerg-1427	426	24	.	.	PUNCT
fuelectenerg-1427	426	25	by	by	ADP
fuelectenerg-1427	426	26	observing	observe	VERB
fuelectenerg-1427	426	27	figure	figure	NOUN
fuelectenerg-1427	426	28	5	5	NUM
fuelectenerg-1427	426	29	,	,	PUNCT
fuelectenerg-1427	426	30	we	we	PRON
fuelectenerg-1427	426	31	can	can	AUX
fuelectenerg-1427	426	32	generate	generate	VERB
fuelectenerg-1427	426	33	the	the	DET
fuelectenerg-1427	426	34	corresponding	corresponding	ADJ
fuelectenerg-1427	426	35	flattened	flatten	VERB
fuelectenerg-1427	426	36	forms	form	NOUN
fuelectenerg-1427	426	37	by	by	ADP
fuelectenerg-1427	426	38	two	two	NUM
fuelectenerg-1427	426	39	methods	method	NOUN
fuelectenerg-1427	426	40	.	.	PUNCT
fuelectenerg-1427	427	1	a	a	DET
fuelectenerg-1427	427	2	classical	classical	ADJ
fuelectenerg-1427	427	3	method	method	NOUN
fuelectenerg-1427	427	4	,	,	PUNCT
fuelectenerg-1427	427	5	per	per	ADP
fuelectenerg-1427	427	6	analogy	analogy	NOUN
fuelectenerg-1427	427	7	with	with	ADP
fuelectenerg-1427	427	8	well	well	ADV
fuelectenerg-1427	427	9	-	-	PUNCT
fuelectenerg-1427	427	10	known	know	VERB
fuelectenerg-1427	427	11	binary	binary	ADJ
fuelectenerg-1427	427	12	forms	form	NOUN
fuelectenerg-1427	427	13	,	,	PUNCT
fuelectenerg-1427	427	14	would	would	AUX
fuelectenerg-1427	427	15	be	be	AUX
fuelectenerg-1427	427	16	to	to	PART
fuelectenerg-1427	427	17	create	create	VERB
fuelectenerg-1427	427	18	every	every	DET
fuelectenerg-1427	427	19	transform	transform	NOUN
fuelectenerg-1427	427	20	matrix	matrix	NOUN
fuelectenerg-1427	427	21	for	for	ADP
fuelectenerg-1427	427	22	every	every	DET
fuelectenerg-1427	427	23	tif	tif	PROPN
fuelectenerg-1427	427	24	s	s	PROPN
fuelectenerg-1427	427	25	/	/	SYM
fuelectenerg-1427	427	26	d	d	NOUN
fuelectenerg-1427	427	27	tree	tree	NOUN
fuelectenerg-1427	427	28	and	and	CCONJ
fuelectenerg-1427	427	29	then	then	ADV
fuelectenerg-1427	427	30	expand	expand	VERB
fuelectenerg-1427	427	31	using	use	VERB
fuelectenerg-1427	427	32	that	that	DET
fuelectenerg-1427	427	33	transform	transform	NOUN
fuelectenerg-1427	427	34	matrix	matrix	NOUN
fuelectenerg-1427	427	35	.	.	PUNCT
fuelectenerg-1427	428	1	a	a	DET
fuelectenerg-1427	428	2	better	well	ADJ
fuelectenerg-1427	428	3	method	method	NOUN
fuelectenerg-1427	428	4	is	be	AUX
fuelectenerg-1427	428	5	to	to	PART
fuelectenerg-1427	428	6	create	create	VERB
fuelectenerg-1427	428	7	one	one	NUM
fuelectenerg-1427	428	8	flattened	flatten	VERB
fuelectenerg-1427	428	9	108	108	NUM
fuelectenerg-1427	428	10	an	an	DET
fuelectenerg-1427	428	11	extended	extend	VERB
fuelectenerg-1427	428	12	green	green	ADJ
fuelectenerg-1427	428	13	sasao	sasao	PROPN
fuelectenerg-1427	428	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	428	15	of	of	ADP
fuelectenerg-1427	428	16	canonical	canonical	ADJ
fuelectenerg-1427	428	17	ternary	ternary	ADJ
fuelectenerg-1427	428	18	galois	galois	NOUN
fuelectenerg-1427	428	19	forms	form	NOUN
fuelectenerg-1427	428	20	...	...	PUNCT
fuelectenerg-1427	428	21	s	s	VERB
fuelectenerg-1427	428	22	a	a	PRON
fuelectenerg-1427	428	23	’	'	PUNCT
fuelectenerg-1427	428	24	a	a	PRON
fuelectenerg-1427	428	25	(	(	PUNCT
fuelectenerg-1427	428	26	)	)	PUNCT
fuelectenerg-1427	428	27	a	a	PRON
fuelectenerg-1427	428	28	pd	pd	PROPN
fuelectenerg-1427	428	29	1	1	NUM
fuelectenerg-1427	428	30	a	a	PRON
fuelectenerg-1427	428	31	(	(	PUNCT
fuelectenerg-1427	428	32	)	)	PUNCT
fuelectenerg-1427	428	33	b	b	NOUN
fuelectenerg-1427	428	34	nd	nd	ADP
fuelectenerg-1427	428	35	1	1	NUM
fuelectenerg-1427	428	36	a	a	PRON
fuelectenerg-1427	428	37	’	'	PUNCT
fuelectenerg-1427	428	38	d	d	ADP
fuelectenerg-1427	428	39	1	1	NUM
fuelectenerg-1427	428	40	a	a	PRON
fuelectenerg-1427	428	41	(	(	PUNCT
fuelectenerg-1427	428	42	)	)	PUNCT
fuelectenerg-1427	428	43	d	d	NOUN
fuelectenerg-1427	428	44	(	(	PUNCT
fuelectenerg-1427	428	45	)	)	PUNCT
fuelectenerg-1427	428	46	c	c	NOUN
fuelectenerg-1427	428	47	figure	figure	VERB
fuelectenerg-1427	428	48	3	3	NUM
fuelectenerg-1427	428	49	:	:	PUNCT
fuelectenerg-1427	428	50	two	two	NUM
fuelectenerg-1427	428	51	-	-	PUNCT
fuelectenerg-1427	428	52	valued	value	VERB
fuelectenerg-1427	428	53	nodes	node	NOUN
fuelectenerg-1427	428	54	:	:	PUNCT
fuelectenerg-1427	428	55	(	(	PUNCT
fuelectenerg-1427	428	56	a	a	X
fuelectenerg-1427	428	57	)	)	PUNCT
fuelectenerg-1427	428	58	shannon	shannon	NOUN
fuelectenerg-1427	428	59	,	,	PUNCT
fuelectenerg-1427	428	60	(	(	PUNCT
fuelectenerg-1427	428	61	b	b	NOUN
fuelectenerg-1427	428	62	)	)	PUNCT
fuelectenerg-1427	428	63	positive	positive	ADJ
fuelectenerg-1427	428	64	davio	davio	NOUN
fuelectenerg-1427	428	65	,	,	PUNCT
fuelectenerg-1427	428	66	(	(	PUNCT
fuelectenerg-1427	428	67	c	c	NOUN
fuelectenerg-1427	428	68	)	)	PUNCT
fuelectenerg-1427	428	69	negative	negative	ADJ
fuelectenerg-1427	428	70	davio	davio	NOUN
fuelectenerg-1427	428	71	,	,	PUNCT
fuelectenerg-1427	428	72	and	and	CCONJ
fuelectenerg-1427	428	73	(	(	PUNCT
fuelectenerg-1427	428	74	d	d	X
fuelectenerg-1427	428	75	)	)	PUNCT
fuelectenerg-1427	428	76	generalized	generalized	ADJ
fuelectenerg-1427	428	77	davio	davio	NOUN
fuelectenerg-1427	428	78	where	where	SCONJ
fuelectenerg-1427	428	79	a	a	DET
fuelectenerg-1427	428	80	∈	∈	NOUN
fuelectenerg-1427	428	81	{	{	PUNCT
fuelectenerg-1427	428	82	a	a	PRON
fuelectenerg-1427	428	83	,	,	PUNCT
fuelectenerg-1427	428	84	a′	a′	PROPN
fuelectenerg-1427	428	85	}	}	PUNCT
fuelectenerg-1427	428	86	.	.	PUNCT
fuelectenerg-1427	429	1	variable	variable	ADJ
fuelectenerg-1427	429	2	,	,	PUNCT
fuelectenerg-1427	429	3	that	that	PRON
fuelectenerg-1427	429	4	is	be	AUX
fuelectenerg-1427	429	5	one	one	NUM
fuelectenerg-1427	429	6	tree	tree	NOUN
fuelectenerg-1427	429	7	level	level	NOUN
fuelectenerg-1427	429	8	,	,	PUNCT
fuelectenerg-1427	429	9	figure	figure	NOUN
fuelectenerg-1427	429	10	4	4	NUM
fuelectenerg-1427	429	11	represents	represent	VERB
fuelectenerg-1427	429	12	the	the	DET
fuelectenerg-1427	429	13	expansion	expansion	NOUN
fuelectenerg-1427	429	14	nodes	node	NOUN
fuelectenerg-1427	429	15	for	for	ADP
fuelectenerg-1427	429	16	ternary	ternary	ADJ
fuelectenerg-1427	429	17	shannon	shannon	NOUN
fuelectenerg-1427	429	18	,	,	PUNCT
fuelectenerg-1427	429	19	davio	davio	NOUN
fuelectenerg-1427	429	20	and	and	CCONJ
fuelectenerg-1427	429	21	generalized	generalized	ADJ
fuelectenerg-1427	429	22	davio	davio	NOUN
fuelectenerg-1427	429	23	(	(	PUNCT
fuelectenerg-1427	429	24	d	d	NOUN
fuelectenerg-1427	429	25	)	)	PUNCT
fuelectenerg-1427	429	26	,	,	PUNCT
fuelectenerg-1427	429	27	respectively	respectively	ADV
fuelectenerg-1427	429	28	.	.	PUNCT
fuelectenerg-1427	430	1	s	s	PART
fuelectenerg-1427	430	2	0	0	NUM
fuelectenerg-1427	430	3	x	x	SYM
fuelectenerg-1427	430	4	1	1	NUM
fuelectenerg-1427	430	5	x	x	SYM
fuelectenerg-1427	430	6	2	2	NUM
fuelectenerg-1427	430	7	x	x	SYM
fuelectenerg-1427	430	8	(	(	PUNCT
fuelectenerg-1427	430	9	a	a	PRON
fuelectenerg-1427	430	10	)	)	PUNCT
fuelectenerg-1427	430	11	d0	d0	NOUN
fuelectenerg-1427	430	12	1	1	NUM
fuelectenerg-1427	430	13	x	x	SYM
fuelectenerg-1427	430	14	2	2	NUM
fuelectenerg-1427	430	15	(	(	PUNCT
fuelectenerg-1427	430	16	b	b	NOUN
fuelectenerg-1427	430	17	)	)	PUNCT
fuelectenerg-1427	430	18	d2	d2	PROPN
fuelectenerg-1427	430	19	1	1	NUM
fuelectenerg-1427	430	20	(	(	PUNCT
fuelectenerg-1427	430	21	d	d	NOUN
fuelectenerg-1427	430	22	)	)	PUNCT
fuelectenerg-1427	431	1	d	d	NOUN
fuelectenerg-1427	431	2	1	1	NUM
fuelectenerg-1427	431	3	(	(	PUNCT
fuelectenerg-1427	431	4	e	e	NOUN
fuelectenerg-1427	431	5	)	)	PUNCT
fuelectenerg-1427	431	6	d1	d1	NOUN
fuelectenerg-1427	431	7	1	1	NUM
fuelectenerg-1427	431	8	(	(	PUNCT
fuelectenerg-1427	431	9	’	'	PUNCT
fuelectenerg-1427	431	10	)	)	PUNCT
fuelectenerg-1427	431	11	x	x	SYM
fuelectenerg-1427	431	12	2	2	NUM
fuelectenerg-1427	431	13	(	(	PUNCT
fuelectenerg-1427	431	14	’’	’'	PUNCT
fuelectenerg-1427	431	15	)	)	PUNCT
fuelectenerg-1427	431	16	x	x	SYM
fuelectenerg-1427	431	17	2	2	NUM
fuelectenerg-1427	431	18	(	(	PUNCT
fuelectenerg-1427	431	19	)	)	PUNCT
fuelectenerg-1427	431	20	x	x	SYM
fuelectenerg-1427	431	21	2	2	NUM
fuelectenerg-1427	431	22	(	(	PUNCT
fuelectenerg-1427	431	23	c	c	NOUN
fuelectenerg-1427	431	24	)	)	PUNCT
fuelectenerg-1427	431	25	x	x	SYM
fuelectenerg-1427	431	26	xx	xx	X
fuelectenerg-1427	431	27	’	'	PUNCT
fuelectenerg-1427	431	28	x	x	NOUN
fuelectenerg-1427	431	29	’’	’'	PUNCT
fuelectenerg-1427	431	30	figure	figure	VERB
fuelectenerg-1427	431	31	4	4	NUM
fuelectenerg-1427	431	32	:	:	PUNCT
fuelectenerg-1427	431	33	ternary	ternary	ADJ
fuelectenerg-1427	431	34	nodes	node	NOUN
fuelectenerg-1427	431	35	for	for	ADP
fuelectenerg-1427	431	36	ternary	ternary	ADJ
fuelectenerg-1427	431	37	decision	decision	NOUN
fuelectenerg-1427	431	38	trees	tree	NOUN
fuelectenerg-1427	431	39	:	:	PUNCT
fuelectenerg-1427	431	40	(	(	PUNCT
fuelectenerg-1427	431	41	a	a	X
fuelectenerg-1427	431	42	)	)	PUNCT
fuelectenerg-1427	431	43	shannon	shannon	NOUN
fuelectenerg-1427	431	44	,	,	PUNCT
fuelectenerg-1427	431	45	(	(	PUNCT
fuelectenerg-1427	431	46	b	b	X
fuelectenerg-1427	431	47	)	)	PUNCT
fuelectenerg-1427	431	48	davio0	davio0	PROPN
fuelectenerg-1427	431	49	,	,	PUNCT
fuelectenerg-1427	431	50	(	(	PUNCT
fuelectenerg-1427	431	51	c	c	X
fuelectenerg-1427	431	52	)	)	PUNCT
fuelectenerg-1427	431	53	davio1	davio1	NOUN
fuelectenerg-1427	431	54	,	,	PUNCT
fuelectenerg-1427	431	55	(	(	PUNCT
fuelectenerg-1427	431	56	d	d	NOUN
fuelectenerg-1427	431	57	)	)	PUNCT
fuelectenerg-1427	431	58	davio2	davio2	PROPN
fuelectenerg-1427	431	59	,	,	PUNCT
fuelectenerg-1427	431	60	and	and	CCONJ
fuelectenerg-1427	431	61	(	(	PUNCT
fuelectenerg-1427	431	62	e	e	NOUN
fuelectenerg-1427	431	63	)	)	PUNCT
fuelectenerg-1427	431	64	generalized	generalized	ADJ
fuelectenerg-1427	431	65	davio	davio	NOUN
fuelectenerg-1427	431	66	(	(	PUNCT
fuelectenerg-1427	431	67	d	d	NOUN
fuelectenerg-1427	431	68	)	)	PUNCT
fuelectenerg-1427	431	69	where	where	SCONJ
fuelectenerg-1427	431	70	x	x	SYM
fuelectenerg-1427	431	71	∈	∈	PROPN
fuelectenerg-1427	431	72	{	{	PUNCT
fuelectenerg-1427	431	73	x	x	NOUN
fuelectenerg-1427	431	74	,	,	PUNCT
fuelectenerg-1427	431	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	431	76	}	}	PUNCT
fuelectenerg-1427	431	77	.	.	PUNCT
fuelectenerg-1427	432	1	in	in	ADP
fuelectenerg-1427	432	2	correspondence	correspondence	NOUN
fuelectenerg-1427	432	3	to	to	ADP
fuelectenerg-1427	432	4	the	the	DET
fuelectenerg-1427	432	5	binary	binary	PROPN
fuelectenerg-1427	432	6	s	s	PROPN
fuelectenerg-1427	432	7	/	/	SYM
fuelectenerg-1427	432	8	d	d	NOUN
fuelectenerg-1427	432	9	trees	tree	NOUN
fuelectenerg-1427	432	10	,	,	PUNCT
fuelectenerg-1427	432	11	one	one	PRON
fuelectenerg-1427	432	12	can	can	AUX
fuelectenerg-1427	432	13	produce	produce	VERB
fuelectenerg-1427	432	14	ternary	ternary	ADJ
fuelectenerg-1427	432	15	s	s	NOUN
fuelectenerg-1427	432	16	/	/	SYM
fuelectenerg-1427	432	17	d	d	NOUN
fuelectenerg-1427	432	18	trees	tree	NOUN
fuelectenerg-1427	432	19	.	.	PUNCT
fuelectenerg-1427	433	1	to	to	PART
fuelectenerg-1427	433	2	define	define	VERB
fuelectenerg-1427	433	3	the	the	DET
fuelectenerg-1427	433	4	ternary	ternary	ADJ
fuelectenerg-1427	433	5	s	s	NOUN
fuelectenerg-1427	433	6	/	/	SYM
fuelectenerg-1427	433	7	d	d	NOUN
fuelectenerg-1427	433	8	trees	tree	NOUN
fuelectenerg-1427	433	9	,	,	PUNCT
fuelectenerg-1427	433	10	we	we	PRON
fuelectenerg-1427	433	11	define	define	VERB
fuelectenerg-1427	433	12	the	the	DET
fuelectenerg-1427	433	13	generalized	generalized	ADJ
fuelectenerg-1427	433	14	davio	davio	NOUN
fuelectenerg-1427	433	15	node	node	NOUN
fuelectenerg-1427	433	16	over	over	ADP
fuelectenerg-1427	433	17	ternary	ternary	ADJ
fuelectenerg-1427	433	18	galois	galois	PROPN
fuelectenerg-1427	433	19	radix	radix	NOUN
fuelectenerg-1427	433	20	as	as	SCONJ
fuelectenerg-1427	433	21	shown	show	VERB
fuelectenerg-1427	433	22	in	in	ADP
fuelectenerg-1427	433	23	figure	figure	NOUN
fuelectenerg-1427	433	24	4(e	4(e	NUM
fuelectenerg-1427	433	25	)	)	PUNCT
fuelectenerg-1427	433	26	.	.	PUNCT
fuelectenerg-1427	434	1	our	our	PRON
fuelectenerg-1427	434	2	notation	notation	NOUN
fuelectenerg-1427	434	3	here	here	ADV
fuelectenerg-1427	434	4	is	be	AUX
fuelectenerg-1427	434	5	that	that	PRON
fuelectenerg-1427	434	6	(	(	PUNCT
fuelectenerg-1427	434	7	x	x	X
fuelectenerg-1427	434	8	)	)	PUNCT
fuelectenerg-1427	434	9	corresponds	correspond	VERB
fuelectenerg-1427	434	10	to	to	ADP
fuelectenerg-1427	434	11	the	the	DET
fuelectenerg-1427	434	12	three	three	NUM
fuelectenerg-1427	434	13	possible	possible	ADJ
fuelectenerg-1427	434	14	shifts	shift	NOUN
fuelectenerg-1427	434	15	of	of	ADP
fuelectenerg-1427	434	16	the	the	DET
fuelectenerg-1427	434	17	variable	variable	NOUN
fuelectenerg-1427	434	18	x	x	NOUN
fuelectenerg-1427	434	19	as	as	SCONJ
fuelectenerg-1427	434	20	follows	follow	VERB
fuelectenerg-1427	434	21	:	:	PUNCT
fuelectenerg-1427	434	22	x	x	SYM
fuelectenerg-1427	434	23	∈	∈	NOUN
fuelectenerg-1427	434	24	{	{	PUNCT
fuelectenerg-1427	434	25	x	x	NOUN
fuelectenerg-1427	434	26	,	,	PUNCT
fuelectenerg-1427	434	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	434	28	}	}	PUNCT
fuelectenerg-1427	434	29	,	,	PUNCT
fuelectenerg-1427	434	30	over	over	ADP
fuelectenerg-1427	434	31	gf(3	gf(3	PROPN
fuelectenerg-1427	434	32	)	)	PUNCT
fuelectenerg-1427	434	33	.	.	PUNCT
fuelectenerg-1427	435	1	(	(	PUNCT
fuelectenerg-1427	435	2	28	28	NUM
fuelectenerg-1427	435	3	)	)	PUNCT
fuelectenerg-1427	435	4	definition	definition	NOUN
fuelectenerg-1427	435	5	1	1	NUM
fuelectenerg-1427	435	6	.	.	PUNCT
fuelectenerg-1427	436	1	the	the	DET
fuelectenerg-1427	436	2	ternary	ternary	ADJ
fuelectenerg-1427	436	3	tree	tree	NOUN
fuelectenerg-1427	436	4	with	with	ADP
fuelectenerg-1427	436	5	ternary	ternary	ADJ
fuelectenerg-1427	436	6	shannon	shannon	NOUN
fuelectenerg-1427	436	7	and	and	CCONJ
fuelectenerg-1427	436	8	ternary	ternary	ADJ
fuelectenerg-1427	436	9	generalized	generalized	ADJ
fuelectenerg-1427	436	10	davio	davio	NOUN
fuelectenerg-1427	436	11	nodes	node	NOUN
fuelectenerg-1427	436	12	,	,	PUNCT
fuelectenerg-1427	436	13	that	that	PRON
fuelectenerg-1427	436	14	generates	generate	VERB
fuelectenerg-1427	436	15	other	other	ADJ
fuelectenerg-1427	436	16	ternary	ternary	ADJ
fuelectenerg-1427	436	17	trees	tree	NOUN
fuelectenerg-1427	436	18	,	,	PUNCT
fuelectenerg-1427	436	19	is	be	AUX
fuelectenerg-1427	436	20	called	call	VERB
fuelectenerg-1427	436	21	ternary	ternary	ADJ
fuelectenerg-1427	436	22	shannon	shannon	NOUN
fuelectenerg-1427	436	23	-	-	PUNCT
fuelectenerg-1427	436	24	davio	davio	NOUN
fuelectenerg-1427	436	25	(	(	PUNCT
fuelectenerg-1427	436	26	s	s	NOUN
fuelectenerg-1427	436	27	/	/	SYM
fuelectenerg-1427	436	28	d	d	NOUN
fuelectenerg-1427	436	29	)	)	PUNCT
fuelectenerg-1427	436	30	tree	tree	NOUN
fuelectenerg-1427	436	31	.	.	PUNCT
fuelectenerg-1427	437	1	utilizing	utilize	VERB
fuelectenerg-1427	437	2	the	the	DET
fuelectenerg-1427	437	3	definition	definition	NOUN
fuelectenerg-1427	437	4	of	of	ADP
fuelectenerg-1427	437	5	ternary	ternary	ADJ
fuelectenerg-1427	437	6	shannon	shannon	NOUN
fuelectenerg-1427	437	7	in	in	ADP
fuelectenerg-1427	437	8	figure	figure	NOUN
fuelectenerg-1427	437	9	4(a	4(a	NUM
fuelectenerg-1427	437	10	)	)	PUNCT
fuelectenerg-1427	437	11	and	and	CCONJ
fuelectenerg-1427	437	12	ternary	ternary	ADJ
fuelectenerg-1427	437	13	generalized	generalized	ADJ
fuelectenerg-1427	437	14	davio	davio	NOUN
fuelectenerg-1427	437	15	in	in	ADP
fuelectenerg-1427	437	16	figure	figure	NOUN
fuelectenerg-1427	437	17	4(e	4(e	NUM
fuelectenerg-1427	437	18	)	)	PUNCT
fuelectenerg-1427	437	19	,	,	PUNCT
fuelectenerg-1427	437	20	we	we	PRON
fuelectenerg-1427	437	21	obtain	obtain	VERB
fuelectenerg-1427	437	22	the	the	DET
fuelectenerg-1427	437	23	ternary	ternary	ADJ
fuelectenerg-1427	437	24	shannon	shannon	NOUN
fuelectenerg-1427	437	25	-	-	PUNCT
fuelectenerg-1427	437	26	davio	davio	NOUN
fuelectenerg-1427	437	27	trees	tree	NOUN
fuelectenerg-1427	437	28	(	(	PUNCT
fuelectenerg-1427	437	29	ternary	ternary	NOUN
fuelectenerg-1427	437	30	s	s	PROPN
fuelectenerg-1427	437	31	/	/	SYM
fuelectenerg-1427	437	32	d	d	NOUN
fuelectenerg-1427	437	33	trees	tree	NOUN
fuelectenerg-1427	437	34	)	)	PUNCT
fuelectenerg-1427	437	35	for	for	ADP
fuelectenerg-1427	437	36	two	two	NUM
fuelectenerg-1427	437	37	variables	variable	NOUN
fuelectenerg-1427	437	38	as	as	SCONJ
fuelectenerg-1427	437	39	shown	show	VERB
fuelectenerg-1427	437	40	in	in	ADP
fuelectenerg-1427	437	41	figure	figure	NOUN
fuelectenerg-1427	437	42	5	5	NUM
fuelectenerg-1427	437	43	.	.	PUNCT
fuelectenerg-1427	437	44	from	from	ADP
fuelectenerg-1427	437	45	the	the	DET
fuelectenerg-1427	437	46	ternary	ternary	ADJ
fuelectenerg-1427	437	47	s	s	PROPN
fuelectenerg-1427	437	48	/	/	SYM
fuelectenerg-1427	437	49	d	d	ADJ
fuelectenerg-1427	437	50	dts	dts	NOUN
fuelectenerg-1427	437	51	shown	show	VERB
fuelectenerg-1427	437	52	in	in	ADP
fuelectenerg-1427	437	53	figure	figure	NOUN
fuelectenerg-1427	437	54	5	5	NUM
fuelectenerg-1427	437	55	,	,	PUNCT
fuelectenerg-1427	437	56	if	if	SCONJ
fuelectenerg-1427	437	57	we	we	PRON
fuelectenerg-1427	437	58	take	take	VERB
fuelectenerg-1427	437	59	any	any	DET
fuelectenerg-1427	437	60	s	s	PROPN
fuelectenerg-1427	437	61	/	/	SYM
fuelectenerg-1427	437	62	d	d	NOUN
fuelectenerg-1427	437	63	tree	tree	NOUN
fuelectenerg-1427	437	64	and	and	CCONJ
fuelectenerg-1427	437	65	multiply	multiply	VERB
fuelectenerg-1427	437	66	the	the	DET
fuelectenerg-1427	437	67	second	second	ADJ
fuelectenerg-1427	437	68	-	-	PUNCT
fuelectenerg-1427	437	69	level	level	NOUN
fuelectenerg-1427	437	70	cofactors	cofactor	NOUN
fuelectenerg-1427	437	71	(	(	PUNCT
fuelectenerg-1427	437	72	which	which	PRON
fuelectenerg-1427	437	73	are	be	AUX
fuelectenerg-1427	437	74	in	in	ADP
fuelectenerg-1427	437	75	the	the	DET
fuelectenerg-1427	437	76	tdt	tdt	PROPN
fuelectenerg-1427	437	77	leaves	leave	NOUN
fuelectenerg-1427	437	78	)	)	PUNCT
fuelectenerg-1427	437	79	each	each	PRON
fuelectenerg-1427	437	80	by	by	ADP
fuelectenerg-1427	437	81	the	the	DET
fuelectenerg-1427	437	82	corresponding	corresponding	ADJ
fuelectenerg-1427	437	83	path	path	NOUN
fuelectenerg-1427	437	84	in	in	ADP
fuelectenerg-1427	437	85	that	that	DET
fuelectenerg-1427	437	86	tdt	tdt	PROPN
fuelectenerg-1427	437	87	,	,	PUNCT
fuelectenerg-1427	437	88	and	and	CCONJ
fuelectenerg-1427	437	89	sum	sum	VERB
fuelectenerg-1427	437	90	all	all	DET
fuelectenerg-1427	437	91	the	the	DET
fuelectenerg-1427	437	92	resulting	result	VERB
fuelectenerg-1427	437	93	cubes	cube	NOUN
fuelectenerg-1427	437	94	(	(	PUNCT
fuelectenerg-1427	437	95	terms	term	NOUN
fuelectenerg-1427	437	96	)	)	PUNCT
fuelectenerg-1427	437	97	over	over	ADP
fuelectenerg-1427	437	98	gf(3	gf(3	PROPN
fuelectenerg-1427	437	99	)	)	PUNCT
fuelectenerg-1427	437	100	,	,	PUNCT
fuelectenerg-1427	437	101	we	we	PRON
fuelectenerg-1427	437	102	obtain	obtain	VERB
fuelectenerg-1427	437	103	the	the	DET
fuelectenerg-1427	437	104	flattened	flatten	VERB
fuelectenerg-1427	437	105	form	form	NOUN
fuelectenerg-1427	437	106	of	of	ADP
fuelectenerg-1427	437	107	the	the	DET
fuelectenerg-1427	437	108	function	function	NOUN
fuelectenerg-1427	437	109	f	f	PROPN
fuelectenerg-1427	437	110	,	,	PUNCT
fuelectenerg-1427	437	111	as	as	ADP
fuelectenerg-1427	437	112	a	a	DET
fuelectenerg-1427	437	113	certain	certain	ADJ
fuelectenerg-1427	437	114	gfsop	gfsop	NOUN
fuelectenerg-1427	437	115	expression	expression	NOUN
fuelectenerg-1427	437	116	.	.	PUNCT
fuelectenerg-1427	438	1	for	for	ADP
fuelectenerg-1427	438	2	each	each	DET
fuelectenerg-1427	438	3	tdt	tdt	PROPN
fuelectenerg-1427	438	4	in	in	ADP
fuelectenerg-1427	438	5	figure	figure	NOUN
fuelectenerg-1427	438	6	5	5	NUM
fuelectenerg-1427	438	7	,	,	PUNCT
fuelectenerg-1427	438	8	there	there	PRON
fuelectenerg-1427	438	9	are	be	VERB
fuelectenerg-1427	438	10	as	as	ADV
fuelectenerg-1427	438	11	many	many	ADJ
fuelectenerg-1427	438	12	forms	form	NOUN
fuelectenerg-1427	438	13	obtained	obtain	VERB
fuelectenerg-1427	438	14	for	for	ADP
fuelectenerg-1427	438	15	the	the	DET
fuelectenerg-1427	438	16	function	function	NOUN
fuelectenerg-1427	438	17	f	f	PROPN
fuelectenerg-1427	438	18	as	as	ADP
fuelectenerg-1427	438	19	the	the	DET
fuelectenerg-1427	438	20	number	number	NOUN
fuelectenerg-1427	438	21	of	of	ADP
fuelectenerg-1427	438	22	possible	possible	ADJ
fuelectenerg-1427	438	23	permutations	permutation	NOUN
fuelectenerg-1427	438	24	of	of	ADP
fuelectenerg-1427	438	25	the	the	DET
fuelectenerg-1427	438	26	polarities	polarity	NOUN
fuelectenerg-1427	438	27	of	of	ADP
fuelectenerg-1427	438	28	the	the	DET
fuelectenerg-1427	438	29	variables	variable	NOUN
fuelectenerg-1427	438	30	in	in	ADP
fuelectenerg-1427	438	31	the	the	DET
fuelectenerg-1427	438	32	second	second	ADJ
fuelectenerg-1427	438	33	-	-	PUNCT
fuelectenerg-1427	438	34	level	level	NOUN
fuelectenerg-1427	438	35	branches	branch	NOUN
fuelectenerg-1427	438	36	of	of	ADP
fuelectenerg-1427	438	37	each	each	DET
fuelectenerg-1427	438	38	tdt	tdt	PROPN
fuelectenerg-1427	438	39	.	.	PUNCT
fuelectenerg-1427	439	1	definition	definition	NOUN
fuelectenerg-1427	439	2	2	2	NUM
fuelectenerg-1427	439	3	.	.	PUNCT
fuelectenerg-1427	440	1	the	the	DET
fuelectenerg-1427	440	2	family	family	NOUN
fuelectenerg-1427	440	3	of	of	ADP
fuelectenerg-1427	440	4	all	all	DET
fuelectenerg-1427	440	5	possible	possible	ADJ
fuelectenerg-1427	440	6	forms	form	NOUN
fuelectenerg-1427	440	7	obtained	obtain	VERB
fuelectenerg-1427	440	8	per	per	ADP
fuelectenerg-1427	440	9	ternary	ternary	NOUN
fuelectenerg-1427	440	10	s	s	PROPN
fuelectenerg-1427	440	11	/	/	SYM
fuelectenerg-1427	440	12	d	d	NOUN
fuelectenerg-1427	440	13	tree	tree	NOUN
fuelectenerg-1427	440	14	is	be	AUX
fuelectenerg-1427	440	15	called	call	VERB
fuelectenerg-1427	440	16	ternary	ternary	ADJ
fuelectenerg-1427	440	17	inclusive	inclusive	ADJ
fuelectenerg-1427	440	18	forms	form	NOUN
fuelectenerg-1427	440	19	(	(	PUNCT
fuelectenerg-1427	440	20	tifs	tifs	PROPN
fuelectenerg-1427	440	21	)	)	PUNCT
fuelectenerg-1427	440	22	.	.	PUNCT
fuelectenerg-1427	441	1	the	the	DET
fuelectenerg-1427	441	2	numbers	number	NOUN
fuelectenerg-1427	441	3	of	of	ADP
fuelectenerg-1427	441	4	these	these	DET
fuelectenerg-1427	441	5	tifs	tif	NOUN
fuelectenerg-1427	441	6	per	per	ADP
fuelectenerg-1427	441	7	tdt	tdt	PROPN
fuelectenerg-1427	441	8	for	for	ADP
fuelectenerg-1427	441	9	two	two	NUM
fuelectenerg-1427	441	10	variables	variable	NOUN
fuelectenerg-1427	441	11	are	be	AUX
fuelectenerg-1427	441	12	shown	show	VERB
fuelectenerg-1427	441	13	on	on	ADP
fuelectenerg-1427	441	14	top	top	NOUN
fuelectenerg-1427	441	15	of	of	ADP
fuelectenerg-1427	441	16	each	each	DET
fuelectenerg-1427	441	17	s	s	PROPN
fuelectenerg-1427	441	18	/	/	SYM
fuelectenerg-1427	441	19	d	d	PROPN
fuelectenerg-1427	441	20	tdt	tdt	PROPN
fuelectenerg-1427	441	21	in	in	ADP
fuelectenerg-1427	441	22	figure	figure	NOUN
fuelectenerg-1427	441	23	5	5	NUM
fuelectenerg-1427	441	24	.	.	PUNCT
fuelectenerg-1427	441	25	by	by	ADP
fuelectenerg-1427	441	26	observing	observe	VERB
fuelectenerg-1427	441	27	figure	figure	NOUN
fuelectenerg-1427	441	28	5	5	NUM
fuelectenerg-1427	441	29	,	,	PUNCT
fuelectenerg-1427	441	30	we	we	PRON
fuelectenerg-1427	441	31	can	can	AUX
fuelectenerg-1427	441	32	generate	generate	VERB
fuelectenerg-1427	441	33	the	the	DET
fuelectenerg-1427	441	34	corresponding	corresponding	ADJ
fuelectenerg-1427	441	35	flattened	flatten	VERB
fuelectenerg-1427	441	36	forms	form	NOUN
fuelectenerg-1427	441	37	by	by	ADP
fuelectenerg-1427	441	38	two	two	NUM
fuelectenerg-1427	441	39	methods	method	NOUN
fuelectenerg-1427	441	40	.	.	PUNCT
fuelectenerg-1427	442	1	a	a	DET
fuelectenerg-1427	442	2	classical	classical	ADJ
fuelectenerg-1427	442	3	method	method	NOUN
fuelectenerg-1427	442	4	,	,	PUNCT
fuelectenerg-1427	442	5	per	per	ADP
fuelectenerg-1427	442	6	analogy	analogy	NOUN
fuelectenerg-1427	442	7	with	with	ADP
fuelectenerg-1427	442	8	well	well	ADV
fuelectenerg-1427	442	9	-	-	PUNCT
fuelectenerg-1427	442	10	known	know	VERB
fuelectenerg-1427	442	11	binary	binary	ADJ
fuelectenerg-1427	442	12	forms	form	NOUN
fuelectenerg-1427	442	13	,	,	PUNCT
fuelectenerg-1427	442	14	would	would	AUX
fuelectenerg-1427	442	15	be	be	AUX
fuelectenerg-1427	442	16	to	to	PART
fuelectenerg-1427	442	17	create	create	VERB
fuelectenerg-1427	442	18	every	every	DET
fuelectenerg-1427	442	19	transform	transform	NOUN
fuelectenerg-1427	442	20	matrix	matrix	NOUN
fuelectenerg-1427	442	21	for	for	ADP
fuelectenerg-1427	442	22	every	every	DET
fuelectenerg-1427	442	23	tif	tif	PROPN
fuelectenerg-1427	442	24	s	s	PROPN
fuelectenerg-1427	442	25	/	/	SYM
fuelectenerg-1427	442	26	d	d	NOUN
fuelectenerg-1427	442	27	tree	tree	NOUN
fuelectenerg-1427	442	28	and	and	CCONJ
fuelectenerg-1427	442	29	then	then	ADV
fuelectenerg-1427	442	30	expand	expand	VERB
fuelectenerg-1427	442	31	using	use	VERB
fuelectenerg-1427	442	32	that	that	DET
fuelectenerg-1427	442	33	transform	transform	NOUN
fuelectenerg-1427	442	34	matrix	matrix	NOUN
fuelectenerg-1427	442	35	.	.	PUNCT
fuelectenerg-1427	443	1	a	a	DET
fuelectenerg-1427	443	2	better	well	ADJ
fuelectenerg-1427	443	3	method	method	NOUN
fuelectenerg-1427	443	4	is	be	AUX
fuelectenerg-1427	443	5	to	to	PART
fuelectenerg-1427	443	6	create	create	VERB
fuelectenerg-1427	443	7	one	one	NUM
fuelectenerg-1427	443	8	flattened	flatten	VERB
fuelectenerg-1427	443	9	108	108	NUM
fuelectenerg-1427	443	10	52	52	NUM
fuelectenerg-1427	443	11	a.	a.	NOUN
fuelectenerg-1427	443	12	n.	n.	PROPN
fuelectenerg-1427	443	13	al	al	PROPN
fuelectenerg-1427	443	14	-	-	PUNCT
fuelectenerg-1427	443	15	rabadi	rabadi	VERB
fuelectenerg-1427	443	16	an	an	DET
fuelectenerg-1427	443	17	extended	extended	ADJ
fuelectenerg-1427	443	18	green	green	ADJ
fuelectenerg-1427	443	19	sasao	sasao	PROPN
fuelectenerg-1427	443	20	hierarchy	hierarchy	NOUN
fuelectenerg-1427	443	21	of	of	ADP
fuelectenerg-1427	443	22	canonical	canonical	ADJ
fuelectenerg-1427	443	23	ternary	ternary	ADJ
fuelectenerg-1427	443	24	galois	galois	NOUN
fuelectenerg-1427	443	25	forms	form	NOUN
fuelectenerg-1427	443	26	and	and	CCONJ
fuelectenerg-1427	443	27	universal	universal	ADJ
fuelectenerg-1427	443	28	logic	logic	NOUN
fuelectenerg-1427	443	29	modules	module	NOUN
fuelectenerg-1427	443	30	53	53	NUM
fuelectenerg-1427	443	31	an	an	DET
fuelectenerg-1427	443	32	extended	extend	VERB
fuelectenerg-1427	443	33	green	green	ADJ
fuelectenerg-1427	443	34	sasao	sasao	PROPN
fuelectenerg-1427	443	35	hierarchy	hierarchy	NOUN
fuelectenerg-1427	443	36	of	of	ADP
fuelectenerg-1427	443	37	canonical	canonical	ADJ
fuelectenerg-1427	443	38	ternary	ternary	ADJ
fuelectenerg-1427	443	39	galois	galois	NOUN
fuelectenerg-1427	443	40	forms	form	NOUN
fuelectenerg-1427	443	41	...	...	PUNCT
fuelectenerg-1427	443	42	proof	proof	NOUN
fuelectenerg-1427	443	43	.	.	PUNCT
fuelectenerg-1427	444	1	from	from	ADP
fuelectenerg-1427	444	2	equation	equation	NOUN
fuelectenerg-1427	444	3	(	(	PUNCT
fuelectenerg-1427	444	4	5	5	NUM
fuelectenerg-1427	444	5	)	)	PUNCT
fuelectenerg-1427	444	6	,	,	PUNCT
fuelectenerg-1427	444	7	if	if	SCONJ
fuelectenerg-1427	444	8	we	we	PRON
fuelectenerg-1427	444	9	substitute	substitute	VERB
fuelectenerg-1427	444	10	the	the	DET
fuelectenerg-1427	444	11	values	value	NOUN
fuelectenerg-1427	444	12	of	of	ADP
fuelectenerg-1427	444	13	the	the	DET
fuelectenerg-1427	444	14	1	1	NUM
fuelectenerg-1427	444	15	-	-	PUNCT
fuelectenerg-1427	444	16	rpl	rpl	NOUN
fuelectenerg-1427	444	17	in	in	ADP
fuelectenerg-1427	444	18	equation	equation	NOUN
fuelectenerg-1427	444	19	(	(	PUNCT
fuelectenerg-1427	444	20	6	6	NUM
fuelectenerg-1427	444	21	)	)	PUNCT
fuelectenerg-1427	444	22	,	,	PUNCT
fuelectenerg-1427	444	23	we	we	PRON
fuelectenerg-1427	444	24	obtain	obtain	VERB
fuelectenerg-1427	444	25	the	the	DET
fuelectenerg-1427	444	26	following	follow	VERB
fuelectenerg-1427	444	27	{	{	PUNCT
fuelectenerg-1427	444	28	x	x	SYM
fuelectenerg-1427	444	29	=	=	SYM
fuelectenerg-1427	444	30	0	0	NUM
fuelectenerg-1427	444	31	⇒	⇒	NOUN
fuelectenerg-1427	444	32	fx=0	fx=0	ADV
fuelectenerg-1427	444	33	=	=	SYM
fuelectenerg-1427	444	34	f0,x	f0,x	NOUN
fuelectenerg-1427	444	35	=	=	SYM
fuelectenerg-1427	444	36	1	1	NUM
fuelectenerg-1427	444	37	⇒	⇒	X
fuelectenerg-1427	444	38	fx=1	fx=1	ADJ
fuelectenerg-1427	444	39	=	=	SYM
fuelectenerg-1427	444	40	f1,x	f1,x	NOUN
fuelectenerg-1427	444	41	=	=	SYM
fuelectenerg-1427	444	42	2	2	NUM
fuelectenerg-1427	444	43	⇒	⇒	NOUN
fuelectenerg-1427	444	44	fx=2	fx=2	NOUN
fuelectenerg-1427	444	45	=	=	PUNCT
fuelectenerg-1427	444	46	f2	f2	PROPN
fuelectenerg-1427	444	47	}	}	PUNCT
fuelectenerg-1427	444	48	which	which	PRON
fuelectenerg-1427	444	49	are	be	AUX
fuelectenerg-1427	444	50	the	the	DET
fuelectenerg-1427	444	51	cofactors	cofactor	NOUN
fuelectenerg-1427	444	52	of	of	ADP
fuelectenerg-1427	444	53	variable	variable	ADJ
fuelectenerg-1427	444	54	x	x	X
fuelectenerg-1427	444	55	of	of	ADP
fuelectenerg-1427	444	56	values	value	NOUN
fuelectenerg-1427	444	57	{	{	PUNCT
fuelectenerg-1427	444	58	0,1,2	0,1,2	NUM
fuelectenerg-1427	444	59	}	}	PUNCT
fuelectenerg-1427	444	60	,	,	PUNCT
fuelectenerg-1427	444	61	respectively	respectively	ADV
fuelectenerg-1427	444	62	.	.	PUNCT
fuelectenerg-1427	444	63	example	example	NOUN
fuelectenerg-1427	445	1	2	2	NUM
fuelectenerg-1427	445	2	.	.	PUNCT
fuelectenerg-1427	445	3	let	let	VERB
fuelectenerg-1427	445	4	f	f	PROPN
fuelectenerg-1427	445	5	(	(	PUNCT
fuelectenerg-1427	445	6	x1,x2	x1,x2	PROPN
fuelectenerg-1427	445	7	)	)	PUNCT
fuelectenerg-1427	446	1	=	=	SYM
fuelectenerg-1427	446	2	x′1x2	x′1x2	X
fuelectenerg-1427	447	1	+	+	SYM
fuelectenerg-1427	448	1	x′′2x1	x′′2x1	PROPN
fuelectenerg-1427	448	2	.	.	PUNCT
fuelectenerg-1427	449	1	then	then	ADV
fuelectenerg-1427	449	2	,	,	PUNCT
fuelectenerg-1427	449	3	using	use	VERB
fuelectenerg-1427	449	4	figure	figure	NOUN
fuelectenerg-1427	449	5	1	1	NUM
fuelectenerg-1427	449	6	,	,	PUNCT
fuelectenerg-1427	449	7	the	the	DET
fuelectenerg-1427	449	8	ternary	ternary	ADJ
fuelectenerg-1427	449	9	truth	truth	NOUN
fuelectenerg-1427	449	10	vector	vector	NOUN
fuelectenerg-1427	449	11	with	with	ADP
fuelectenerg-1427	449	12	the	the	DET
fuelectenerg-1427	449	13	variable	variable	ADJ
fuelectenerg-1427	449	14	order	order	NOUN
fuelectenerg-1427	449	15	{	{	PUNCT
fuelectenerg-1427	449	16	x1,x2	x1,x2	PROPN
fuelectenerg-1427	449	17	}	}	PUNCT
fuelectenerg-1427	449	18	is	be	AUX
fuelectenerg-1427	449	19	f	f	X
fuelectenerg-1427	449	20	=	=	PUNCT
fuelectenerg-1427	450	1	[	[	PUNCT
fuelectenerg-1427	450	2	0,2,1,1,2,0,2,2,2]t	0,2,1,1,2,0,2,2,2]t	PROPN
fuelectenerg-1427	450	3	.	.	PUNCT
fuelectenerg-1427	451	1	using	use	VERB
fuelectenerg-1427	451	2	equation	equation	NOUN
fuelectenerg-1427	451	3	(	(	PUNCT
fuelectenerg-1427	451	4	6	6	NUM
fuelectenerg-1427	451	5	)	)	PUNCT
fuelectenerg-1427	451	6	,	,	PUNCT
fuelectenerg-1427	451	7	we	we	PRON
fuelectenerg-1427	451	8	obtain	obtain	VERB
fuelectenerg-1427	451	9	the	the	DET
fuelectenerg-1427	451	10	following	following	ADJ
fuelectenerg-1427	451	11	gf(3	gf(3	PROPN
fuelectenerg-1427	451	12	)	)	PUNCT
fuelectenerg-1427	451	13	shannon	shannon	PROPN
fuelectenerg-1427	451	14	expansion	expansion	NOUN
fuelectenerg-1427	451	15	f	f	PROPN
fuelectenerg-1427	451	16	(	(	PUNCT
fuelectenerg-1427	451	17	x1,x2	x1,x2	PROPN
fuelectenerg-1427	451	18	)	)	PUNCT
fuelectenerg-1427	452	1	=	=	PUNCT
fuelectenerg-1427	452	2	0x1	0x1	NOUN
fuelectenerg-1427	452	3	1x2	1x2	NUM
fuelectenerg-1427	453	1	+	+	CCONJ
fuelectenerg-1427	453	2	2	2	NUM
fuelectenerg-1427	453	3	·	·	PUNCT
fuelectenerg-1427	453	4	0x1	0x1	NOUN
fuelectenerg-1427	453	5	2x2	2x2	NUM
fuelectenerg-1427	454	1	+	+	CCONJ
fuelectenerg-1427	454	2	2	2	NUM
fuelectenerg-1427	454	3	·	·	SYM
fuelectenerg-1427	454	4	1x1	1x1	NUM
fuelectenerg-1427	454	5	0x2	0x2	NOUN
fuelectenerg-1427	454	6	+	+	CCONJ
fuelectenerg-1427	454	7	2	2	NUM
fuelectenerg-1427	454	8	·	·	SYM
fuelectenerg-1427	454	9	1x1	1x1	NUM
fuelectenerg-1427	454	10	1x2	1x2	NUM
fuelectenerg-1427	454	11	+	+	CCONJ
fuelectenerg-1427	455	1	2	2	NUM
fuelectenerg-1427	455	2	·	·	SYM
fuelectenerg-1427	455	3	1x1	1x1	NUM
fuelectenerg-1427	455	4	2x2	2x2	NUM
fuelectenerg-1427	455	5	+	+	SYM
fuelectenerg-1427	455	6	2x1	2x1	NUM
fuelectenerg-1427	455	7	0x2	0x2	NOUN
fuelectenerg-1427	455	8	+2	+2	PROPN
fuelectenerg-1427	455	9	·	·	PUNCT
fuelectenerg-1427	456	1	2x1	2x1	NUM
fuelectenerg-1427	456	2	2x2	2x2	NUM
fuelectenerg-1427	456	3	.	.	PUNCT
fuelectenerg-1427	457	1	by	by	ADP
fuelectenerg-1427	457	2	using	use	VERB
fuelectenerg-1427	457	3	the	the	DET
fuelectenerg-1427	457	4	addition	addition	NOUN
fuelectenerg-1427	457	5	and	and	CCONJ
fuelectenerg-1427	457	6	multiplication	multiplication	NOUN
fuelectenerg-1427	457	7	over	over	ADP
fuelectenerg-1427	457	8	gf(3	gf(3	PROPN
fuelectenerg-1427	457	9	)	)	PUNCT
fuelectenerg-1427	457	10	utilizing	utilize	VERB
fuelectenerg-1427	457	11	figure	figure	NOUN
fuelectenerg-1427	457	12	1	1	NUM
fuelectenerg-1427	457	13	,	,	PUNCT
fuelectenerg-1427	457	14	the	the	DET
fuelectenerg-1427	457	15	1	1	NUM
fuelectenerg-1427	457	16	-	-	PUNCT
fuelectenerg-1427	457	17	rpl	rpl	NOUN
fuelectenerg-1427	457	18	which	which	PRON
fuelectenerg-1427	457	19	is	be	AUX
fuelectenerg-1427	457	20	defined	define	VERB
fuelectenerg-1427	457	21	in	in	ADP
fuelectenerg-1427	457	22	equation	equation	NOUN
fuelectenerg-1427	457	23	(	(	PUNCT
fuelectenerg-1427	457	24	5	5	NUM
fuelectenerg-1427	457	25	)	)	PUNCT
fuelectenerg-1427	457	26	is	be	AUX
fuelectenerg-1427	457	27	related	relate	VERB
fuelectenerg-1427	457	28	to	to	ADP
fuelectenerg-1427	457	29	the	the	DET
fuelectenerg-1427	457	30	shifts	shift	NOUN
fuelectenerg-1427	457	31	of	of	ADP
fuelectenerg-1427	457	32	variables	variable	NOUN
fuelectenerg-1427	457	33	over	over	ADP
fuelectenerg-1427	457	34	gf(3	gf(3	PROPN
fuelectenerg-1427	457	35	)	)	PUNCT
fuelectenerg-1427	457	36	in	in	ADP
fuelectenerg-1427	457	37	terms	term	NOUN
fuelectenerg-1427	457	38	of	of	ADP
fuelectenerg-1427	457	39	powers	power	NOUN
fuelectenerg-1427	457	40	as	as	SCONJ
fuelectenerg-1427	457	41	follows	follow	VERB
fuelectenerg-1427	457	42	:	:	PUNCT
fuelectenerg-1427	458	1	0x	0x	NUM
fuelectenerg-1427	458	2	=	=	NOUN
fuelectenerg-1427	458	3	2(x)2	2(x)2	NOUN
fuelectenerg-1427	458	4	+1	+1	X
fuelectenerg-1427	458	5	,	,	PUNCT
fuelectenerg-1427	458	6	(	(	PUNCT
fuelectenerg-1427	458	7	7	7	X
fuelectenerg-1427	458	8	)	)	PUNCT
fuelectenerg-1427	458	9	0x	0x	NOUN
fuelectenerg-1427	458	10	=	=	NOUN
fuelectenerg-1427	458	11	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	458	12	+2(x′	+2(x′	NUM
fuelectenerg-1427	458	13	)	)	PUNCT
fuelectenerg-1427	458	14	,	,	PUNCT
fuelectenerg-1427	458	15	(	(	PUNCT
fuelectenerg-1427	458	16	8)	8)	NUM
fuelectenerg-1427	458	17	0x	0x	NUM
fuelectenerg-1427	458	18	=	=	SYM
fuelectenerg-1427	458	19	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	458	20	+	+	CCONJ
fuelectenerg-1427	458	21	x′′	x′′	PROPN
fuelectenerg-1427	458	22	,	,	PUNCT
fuelectenerg-1427	458	23	(	(	PUNCT
fuelectenerg-1427	458	24	9	9	NUM
fuelectenerg-1427	458	25	)	)	PUNCT
fuelectenerg-1427	458	26	1x	1x	NOUN
fuelectenerg-1427	459	1	=	=	NOUN
fuelectenerg-1427	459	2	2(x)2	2(x)2	NOUN
fuelectenerg-1427	459	3	+2(x	+2(x	NOUN
fuelectenerg-1427	459	4	)	)	PUNCT
fuelectenerg-1427	459	5	,	,	PUNCT
fuelectenerg-1427	459	6	(	(	PUNCT
fuelectenerg-1427	459	7	10	10	NUM
fuelectenerg-1427	459	8	)	)	PUNCT
fuelectenerg-1427	459	9	1x	1x	NOUN
fuelectenerg-1427	460	1	=	=	NOUN
fuelectenerg-1427	460	2	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	460	3	+	+	X
fuelectenerg-1427	460	4	x′	x′	NUM
fuelectenerg-1427	460	5	,	,	PUNCT
fuelectenerg-1427	460	6	(	(	PUNCT
fuelectenerg-1427	460	7	11	11	NUM
fuelectenerg-1427	460	8	)	)	PUNCT
fuelectenerg-1427	460	9	1x	1x	NOUN
fuelectenerg-1427	461	1	=	=	SYM
fuelectenerg-1427	461	2	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	461	3	+1	+1	PROPN
fuelectenerg-1427	461	4	,	,	PUNCT
fuelectenerg-1427	461	5	(	(	PUNCT
fuelectenerg-1427	461	6	12	12	NUM
fuelectenerg-1427	461	7	)	)	PUNCT
fuelectenerg-1427	461	8	2x	2x	NOUN
fuelectenerg-1427	462	1	=	=	NOUN
fuelectenerg-1427	462	2	2(x)2	2(x)2	NOUN
fuelectenerg-1427	462	3	+	+	CCONJ
fuelectenerg-1427	462	4	x	x	X
fuelectenerg-1427	462	5	,	,	PUNCT
fuelectenerg-1427	462	6	(	(	PUNCT
fuelectenerg-1427	462	7	13	13	NUM
fuelectenerg-1427	462	8	)	)	PUNCT
fuelectenerg-1427	462	9	2x	2x	NOUN
fuelectenerg-1427	463	1	=	=	NOUN
fuelectenerg-1427	463	2	2(x′)2	2(x′)2	NUM
fuelectenerg-1427	463	3	+1	+1	PROPN
fuelectenerg-1427	463	4	,	,	PUNCT
fuelectenerg-1427	463	5	(	(	PUNCT
fuelectenerg-1427	463	6	14	14	NUM
fuelectenerg-1427	463	7	)	)	PUNCT
fuelectenerg-1427	463	8	2x	2x	NUM
fuelectenerg-1427	463	9	=	=	NOUN
fuelectenerg-1427	463	10	2(x′′)2	2(x′′)2	NUM
fuelectenerg-1427	463	11	+2(x′′	+2(x′′	NUM
fuelectenerg-1427	463	12	)	)	PUNCT
fuelectenerg-1427	463	13	.	.	PUNCT
fuelectenerg-1427	464	1	(	(	PUNCT
fuelectenerg-1427	464	2	15	15	NUM
fuelectenerg-1427	464	3	)	)	PUNCT
fuelectenerg-1427	464	4	after	after	ADP
fuelectenerg-1427	464	5	the	the	DET
fuelectenerg-1427	464	6	substitution	substitution	NOUN
fuelectenerg-1427	464	7	of	of	ADP
fuelectenerg-1427	464	8	equations	equation	NOUN
fuelectenerg-1427	464	9	(	(	PUNCT
fuelectenerg-1427	464	10	7	7	NUM
fuelectenerg-1427	464	11	)	)	PUNCT
fuelectenerg-1427	464	12	(	(	PUNCT
fuelectenerg-1427	464	13	15	15	NUM
fuelectenerg-1427	464	14	)	)	PUNCT
fuelectenerg-1427	464	15	in	in	ADP
fuelectenerg-1427	464	16	equation	equation	NOUN
fuelectenerg-1427	464	17	(	(	PUNCT
fuelectenerg-1427	464	18	6	6	NUM
fuelectenerg-1427	464	19	)	)	PUNCT
fuelectenerg-1427	464	20	,	,	PUNCT
fuelectenerg-1427	464	21	and	and	CCONJ
fuelectenerg-1427	464	22	after	after	ADP
fuelectenerg-1427	464	23	the	the	DET
fuelectenerg-1427	464	24	minimization	minimization	NOUN
fuelectenerg-1427	464	25	of	of	ADP
fuelectenerg-1427	464	26	the	the	DET
fuelectenerg-1427	464	27	terms	term	NOUN
fuelectenerg-1427	464	28	according	accord	VERB
fuelectenerg-1427	464	29	to	to	ADP
fuelectenerg-1427	464	30	the	the	DET
fuelectenerg-1427	464	31	gf	gf	PROPN
fuelectenerg-1427	464	32	operations	operation	NOUN
fuelectenerg-1427	464	33	in	in	ADP
fuelectenerg-1427	464	34	figure	figure	NOUN
fuelectenerg-1427	464	35	1	1	NUM
fuelectenerg-1427	464	36	,	,	PUNCT
fuelectenerg-1427	464	37	one	one	NOUN
fuelectenerg-1427	464	38	obtains	obtain	VERB
fuelectenerg-1427	464	39	the	the	DET
fuelectenerg-1427	464	40	following	follow	VERB
fuelectenerg-1427	464	41	equations	equation	NOUN
fuelectenerg-1427	464	42	:	:	PUNCT
fuelectenerg-1427	464	43	f	f	PROPN
fuelectenerg-1427	464	44	=	=	SYM
fuelectenerg-1427	464	45	1	1	NUM
fuelectenerg-1427	464	46	·	·	PUNCT
fuelectenerg-1427	464	47	f0	f0	PROPN
fuelectenerg-1427	464	48	+	+	CCONJ
fuelectenerg-1427	464	49	x	x	X
fuelectenerg-1427	464	50	·	·	PUNCT
fuelectenerg-1427	464	51	(	(	PUNCT
fuelectenerg-1427	464	52	2	2	NUM
fuelectenerg-1427	464	53	f1	f1	NOUN
fuelectenerg-1427	464	54	+	+	X
fuelectenerg-1427	464	55	f2)+2(x)2	f2)+2(x)2	PROPN
fuelectenerg-1427	464	56	(	(	PUNCT
fuelectenerg-1427	464	57	f0	f0	PROPN
fuelectenerg-1427	464	58	+	+	CCONJ
fuelectenerg-1427	464	59	f1	f1	NOUN
fuelectenerg-1427	464	60	+	+	CCONJ
fuelectenerg-1427	464	61	f2	f2	PROPN
fuelectenerg-1427	464	62	)	)	PUNCT
fuelectenerg-1427	464	63	,	,	PUNCT
fuelectenerg-1427	464	64	(	(	PUNCT
fuelectenerg-1427	464	65	16	16	NUM
fuelectenerg-1427	464	66	)	)	PUNCT
fuelectenerg-1427	464	67	f	f	NOUN
fuelectenerg-1427	465	1	=	=	SYM
fuelectenerg-1427	465	2	1	1	X
fuelectenerg-1427	465	3	·	·	PUNCT
fuelectenerg-1427	465	4	f2	f2	PROPN
fuelectenerg-1427	465	5	+	+	NOUN
fuelectenerg-1427	465	6	x′	x′	PROPN
fuelectenerg-1427	465	7	·	·	PUNCT
fuelectenerg-1427	465	8	(	(	PUNCT
fuelectenerg-1427	465	9	2	2	NUM
fuelectenerg-1427	465	10	f0	f0	PROPN
fuelectenerg-1427	465	11	+	+	CCONJ
fuelectenerg-1427	465	12	f1)+2(x′)2	f1)+2(x′)2	PROPN
fuelectenerg-1427	465	13	(	(	PUNCT
fuelectenerg-1427	465	14	f0	f0	PROPN
fuelectenerg-1427	465	15	+	+	CCONJ
fuelectenerg-1427	465	16	f1	f1	NOUN
fuelectenerg-1427	465	17	+	+	CCONJ
fuelectenerg-1427	465	18	f2	f2	PROPN
fuelectenerg-1427	465	19	)	)	PUNCT
fuelectenerg-1427	465	20	,	,	PUNCT
fuelectenerg-1427	465	21	(	(	PUNCT
fuelectenerg-1427	465	22	17	17	NUM
fuelectenerg-1427	465	23	)	)	PUNCT
fuelectenerg-1427	465	24	f	f	NOUN
fuelectenerg-1427	466	1	=	=	SYM
fuelectenerg-1427	466	2	1	1	NUM
fuelectenerg-1427	466	3	·	·	PUNCT
fuelectenerg-1427	466	4	f1	f1	NOUN
fuelectenerg-1427	466	5	+	+	CCONJ
fuelectenerg-1427	466	6	x	x	X
fuelectenerg-1427	466	7	”	"	PUNCT
fuelectenerg-1427	466	8	·	·	PUNCT
fuelectenerg-1427	466	9	(	(	PUNCT
fuelectenerg-1427	466	10	2	2	NUM
fuelectenerg-1427	466	11	f2	f2	NOUN
fuelectenerg-1427	466	12	+	+	CCONJ
fuelectenerg-1427	466	13	f0)+2(x′′)2	f0)+2(x′′)2	PROPN
fuelectenerg-1427	466	14	(	(	PUNCT
fuelectenerg-1427	466	15	f0	f0	PROPN
fuelectenerg-1427	466	16	+	+	CCONJ
fuelectenerg-1427	466	17	f1	f1	NOUN
fuelectenerg-1427	466	18	+	+	CCONJ
fuelectenerg-1427	466	19	f2	f2	PROPN
fuelectenerg-1427	466	20	)	)	PUNCT
fuelectenerg-1427	466	21	.	.	PUNCT
fuelectenerg-1427	467	1	(	(	PUNCT
fuelectenerg-1427	467	2	18	18	NUM
fuelectenerg-1427	467	3	)	)	PUNCT
fuelectenerg-1427	467	4	equations	equation	NOUN
fuelectenerg-1427	467	5	(	(	PUNCT
fuelectenerg-1427	467	6	6	6	NUM
fuelectenerg-1427	467	7	)	)	PUNCT
fuelectenerg-1427	467	8	and	and	CCONJ
fuelectenerg-1427	467	9	(	(	PUNCT
fuelectenerg-1427	467	10	16	16	NUM
fuelectenerg-1427	467	11	)	)	PUNCT
fuelectenerg-1427	467	12	(	(	PUNCT
fuelectenerg-1427	467	13	18	18	NUM
fuelectenerg-1427	467	14	)	)	PUNCT
fuelectenerg-1427	467	15	are	be	AUX
fuelectenerg-1427	467	16	the	the	DET
fuelectenerg-1427	467	17	ternary	ternary	ADJ
fuelectenerg-1427	467	18	fundamental	fundamental	ADJ
fuelectenerg-1427	467	19	shannon	shannon	NOUN
fuelectenerg-1427	467	20	and	and	CCONJ
fuelectenerg-1427	467	21	davio	davio	NOUN
fuelectenerg-1427	467	22	expansions	expansion	NOUN
fuelectenerg-1427	467	23	for	for	ADP
fuelectenerg-1427	467	24	a	a	DET
fuelectenerg-1427	467	25	single	single	ADJ
fuelectenerg-1427	467	26	variable	variable	NOUN
fuelectenerg-1427	467	27	,	,	PUNCT
fuelectenerg-1427	467	28	respectively	respectively	ADV
fuelectenerg-1427	467	29	.	.	PUNCT
fuelectenerg-1427	468	1	these	these	DET
fuelectenerg-1427	468	2	equations	equation	NOUN
fuelectenerg-1427	468	3	can	can	AUX
fuelectenerg-1427	468	4	be	be	AUX
fuelectenerg-1427	468	5	re	re	VERB
fuelectenerg-1427	468	6	-	-	VERB
fuelectenerg-1427	468	7	written	write	VERB
fuelectenerg-1427	468	8	in	in	ADP
fuelectenerg-1427	468	9	the	the	DET
fuelectenerg-1427	468	10	following	follow	VERB
fuelectenerg-1427	468	11	matrix	matrix	NOUN
fuelectenerg-1427	468	12	-	-	PUNCT
fuelectenerg-1427	468	13	based	base	VERB
fuelectenerg-1427	468	14	forms	form	NOUN
fuelectenerg-1427	468	15	as	as	SCONJ
fuelectenerg-1427	468	16	shown	show	VERB
fuelectenerg-1427	468	17	in	in	ADP
fuelectenerg-1427	468	18	equations	equation	NOUN
fuelectenerg-1427	468	19	(	(	PUNCT
fuelectenerg-1427	468	20	19	19	NUM
fuelectenerg-1427	468	21	)	)	PUNCT
fuelectenerg-1427	468	22	(	(	PUNCT
fuelectenerg-1427	468	23	22	22	NUM
fuelectenerg-1427	468	24	)	)	PUNCT
fuelectenerg-1427	468	25	.	.	PUNCT
fuelectenerg-1427	469	1	we	we	PRON
fuelectenerg-1427	469	2	observe	observe	VERB
fuelectenerg-1427	469	3	that	that	SCONJ
fuelectenerg-1427	469	4	equations	equation	NOUN
fuelectenerg-1427	469	5	(	(	PUNCT
fuelectenerg-1427	469	6	19	19	NUM
fuelectenerg-1427	469	7	)	)	PUNCT
fuelectenerg-1427	469	8	(	(	PUNCT
fuelectenerg-1427	469	9	22	22	NUM
fuelectenerg-1427	469	10	)	)	PUNCT
fuelectenerg-1427	469	11	are	be	AUX
fuelectenerg-1427	469	12	expansions	expansion	NOUN
fuelectenerg-1427	469	13	for	for	ADP
fuelectenerg-1427	469	14	a	a	DET
fuelectenerg-1427	469	15	single	single	ADJ
fuelectenerg-1427	469	16	variable	variable	NOUN
fuelectenerg-1427	469	17	,	,	PUNCT
fuelectenerg-1427	469	18	but	but	CCONJ
fuelectenerg-1427	469	19	these	these	DET
fuelectenerg-1427	469	20	expansions	expansion	NOUN
fuelectenerg-1427	469	21	can	can	AUX
fuelectenerg-1427	469	22	be	be	AUX
fuelectenerg-1427	469	23	recursively	recursively	ADV
fuelectenerg-1427	469	24	generated	generate	VERB
fuelectenerg-1427	469	25	for	for	ADP
fuelectenerg-1427	469	26	arbitrary	arbitrary	ADJ
fuelectenerg-1427	469	27	number	number	NOUN
fuelectenerg-1427	469	28	of	of	ADP
fuelectenerg-1427	469	29	variables	variable	NOUN
fuelectenerg-1427	469	30	n	n	CCONJ
fuelectenerg-1427	469	31	using	use	VERB
fuelectenerg-1427	469	32	the	the	DET
fuelectenerg-1427	469	33	kronecker	kronecker	NOUN
fuelectenerg-1427	469	34	product	product	NOUN
fuelectenerg-1427	469	35	also	also	ADV
fuelectenerg-1427	469	36	called	call	VERB
fuelectenerg-1427	469	37	the	the	DET
fuelectenerg-1427	469	38	tensor	tensor	NOUN
fuelectenerg-1427	469	39	product	product	NOUN
fuelectenerg-1427	469	40	analogously	analogously	ADV
fuelectenerg-1427	469	41	to	to	ADP
fuelectenerg-1427	469	42	the	the	DET
fuelectenerg-1427	469	43	binary	binary	ADJ
fuelectenerg-1427	469	44	case	case	NOUN
fuelectenerg-1427	470	1	[	[	X
fuelectenerg-1427	470	2	1	1	NUM
fuelectenerg-1427	470	3	,	,	PUNCT
fuelectenerg-1427	470	4	17	17	NUM
fuelectenerg-1427	470	5	]	]	PUNCT
fuelectenerg-1427	470	6	.	.	PUNCT
fuelectenerg-1427	471	1	105	105	NUM
fuelectenerg-1427	471	2	54	54	NUM
fuelectenerg-1427	471	3	a.	a.	NOUN
fuelectenerg-1427	471	4	n.	n.	PROPN
fuelectenerg-1427	471	5	al	al	PROPN
fuelectenerg-1427	471	6	-	-	PUNCT
fuelectenerg-1427	471	7	rabadi	rabadi	VERB
fuelectenerg-1427	471	8	an	an	DET
fuelectenerg-1427	471	9	extended	extended	ADJ
fuelectenerg-1427	471	10	green	green	ADJ
fuelectenerg-1427	471	11	sasao	sasao	PROPN
fuelectenerg-1427	471	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	471	13	of	of	ADP
fuelectenerg-1427	471	14	canonical	canonical	ADJ
fuelectenerg-1427	471	15	ternary	ternary	ADJ
fuelectenerg-1427	471	16	galois	galois	NOUN
fuelectenerg-1427	471	17	forms	form	NOUN
fuelectenerg-1427	471	18	and	and	CCONJ
fuelectenerg-1427	471	19	universal	universal	ADJ
fuelectenerg-1427	471	20	logic	logic	NOUN
fuelectenerg-1427	471	21	modules	module	VERB
fuelectenerg-1427	471	22	55	55	NUM
fuelectenerg-1427	471	23	an	an	DET
fuelectenerg-1427	471	24	extended	extended	ADJ
fuelectenerg-1427	471	25	green	green	ADJ
fuelectenerg-1427	471	26	sasao	sasao	PROPN
fuelectenerg-1427	471	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	471	28	of	of	ADP
fuelectenerg-1427	471	29	canonical	canonical	ADJ
fuelectenerg-1427	471	30	ternary	ternary	ADJ
fuelectenerg-1427	471	31	galois	galois	NOUN
fuelectenerg-1427	471	32	forms	form	NOUN
fuelectenerg-1427	471	33	...	...	PUNCT
fuelectenerg-1427	472	1	f	f	X
fuelectenerg-1427	472	2	=	=	SYM
fuelectenerg-1427	472	3	�	�	PROPN
fuelectenerg-1427	472	4	0x	0x	PROPN
fuelectenerg-1427	472	5	1x	1x	NUM
fuelectenerg-1427	472	6	2x	2x	NUM
fuelectenerg-1427	472	7	�	�	PROPN
fuelectenerg-1427	472	8			PROPN
fuelectenerg-1427	472	9			NOUN
fuelectenerg-1427	472	10	1	1	NUM
fuelectenerg-1427	472	11	0	0	NUM
fuelectenerg-1427	472	12	0	0	NUM
fuelectenerg-1427	472	13	0	0	NUM
fuelectenerg-1427	472	14	1	1	NUM
fuelectenerg-1427	472	15	0	0	NUM
fuelectenerg-1427	472	16	0	0	NUM
fuelectenerg-1427	472	17	0	0	NUM
fuelectenerg-1427	472	18	1	1	NUM
fuelectenerg-1427	472	19			PROPN
fuelectenerg-1427	472	20			PROPN
fuelectenerg-1427	472	21			NOUN
fuelectenerg-1427	472	22			NUM
fuelectenerg-1427	472	23	f0	f0	PROPN
fuelectenerg-1427	472	24	f1	f1	PROPN
fuelectenerg-1427	472	25	f2	f2	PROPN
fuelectenerg-1427	472	26			PROPN
fuelectenerg-1427	472	27			PROPN
fuelectenerg-1427	472	28	,	,	PUNCT
fuelectenerg-1427	472	29	(	(	PUNCT
fuelectenerg-1427	472	30	19	19	NUM
fuelectenerg-1427	472	31	)	)	PUNCT
fuelectenerg-1427	472	32	f	f	NOUN
fuelectenerg-1427	472	33	=	=	SYM
fuelectenerg-1427	472	34	�	�	PROPN
fuelectenerg-1427	472	35	1	1	NUM
fuelectenerg-1427	472	36	x	x	SYM
fuelectenerg-1427	472	37	x2	x2	PROPN
fuelectenerg-1427	472	38	�	�	PROPN
fuelectenerg-1427	472	39			PROPN
fuelectenerg-1427	472	40			VERB
fuelectenerg-1427	472	41	1	1	NUM
fuelectenerg-1427	472	42	0	0	NUM
fuelectenerg-1427	472	43	0	0	NUM
fuelectenerg-1427	472	44	0	0	NUM
fuelectenerg-1427	472	45	2	2	NUM
fuelectenerg-1427	472	46	1	1	NUM
fuelectenerg-1427	472	47	2	2	NUM
fuelectenerg-1427	472	48	2	2	NUM
fuelectenerg-1427	472	49	2	2	NUM
fuelectenerg-1427	472	50			PROPN
fuelectenerg-1427	472	51			PROPN
fuelectenerg-1427	472	52			NOUN
fuelectenerg-1427	472	53			NUM
fuelectenerg-1427	472	54	f0	f0	PROPN
fuelectenerg-1427	472	55	f1	f1	PROPN
fuelectenerg-1427	472	56	f2	f2	PROPN
fuelectenerg-1427	472	57			PROPN
fuelectenerg-1427	472	58			PROPN
fuelectenerg-1427	472	59	,	,	PUNCT
fuelectenerg-1427	472	60	(	(	PUNCT
fuelectenerg-1427	472	61	20	20	NUM
fuelectenerg-1427	472	62	)	)	PUNCT
fuelectenerg-1427	472	63	f	f	NOUN
fuelectenerg-1427	472	64	=	=	SYM
fuelectenerg-1427	472	65	�	�	PROPN
fuelectenerg-1427	472	66	1	1	NUM
fuelectenerg-1427	472	67	x′	x′	PROPN
fuelectenerg-1427	472	68	(	(	PUNCT
fuelectenerg-1427	472	69	x′)2	x′)2	PROPN
fuelectenerg-1427	472	70	�	�	PROPN
fuelectenerg-1427	472	71			PROPN
fuelectenerg-1427	472	72			NOUN
fuelectenerg-1427	472	73	0	0	NUM
fuelectenerg-1427	472	74	0	0	NUM
fuelectenerg-1427	472	75	1	1	NUM
fuelectenerg-1427	472	76	2	2	NUM
fuelectenerg-1427	472	77	1	1	NUM
fuelectenerg-1427	472	78	0	0	NUM
fuelectenerg-1427	472	79	2	2	NUM
fuelectenerg-1427	472	80	2	2	NUM
fuelectenerg-1427	472	81	2	2	NUM
fuelectenerg-1427	472	82			PROPN
fuelectenerg-1427	472	83			PROPN
fuelectenerg-1427	472	84			NOUN
fuelectenerg-1427	472	85			NUM
fuelectenerg-1427	472	86	f0	f0	PROPN
fuelectenerg-1427	472	87	f1	f1	PROPN
fuelectenerg-1427	472	88	f2	f2	PROPN
fuelectenerg-1427	472	89			PROPN
fuelectenerg-1427	472	90			PROPN
fuelectenerg-1427	472	91	,	,	PUNCT
fuelectenerg-1427	472	92	(	(	PUNCT
fuelectenerg-1427	472	93	21	21	NUM
fuelectenerg-1427	472	94	)	)	PUNCT
fuelectenerg-1427	472	95	f	f	NOUN
fuelectenerg-1427	472	96	=	=	SYM
fuelectenerg-1427	472	97	�	�	PROPN
fuelectenerg-1427	472	98	1	1	NUM
fuelectenerg-1427	472	99	x′′	x′′	PROPN
fuelectenerg-1427	472	100	(	(	PUNCT
fuelectenerg-1427	472	101	x′′)2	x′′)2	PROPN
fuelectenerg-1427	472	102	�	�	PROPN
fuelectenerg-1427	472	103			PROPN
fuelectenerg-1427	472	104			NOUN
fuelectenerg-1427	472	105	0	0	NUM
fuelectenerg-1427	472	106	1	1	NUM
fuelectenerg-1427	472	107	0	0	NUM
fuelectenerg-1427	472	108	1	1	NUM
fuelectenerg-1427	472	109	0	0	NUM
fuelectenerg-1427	472	110	2	2	NUM
fuelectenerg-1427	472	111	2	2	NUM
fuelectenerg-1427	472	112	2	2	NUM
fuelectenerg-1427	472	113	2	2	NUM
fuelectenerg-1427	472	114			PROPN
fuelectenerg-1427	472	115			PROPN
fuelectenerg-1427	472	116			NOUN
fuelectenerg-1427	472	117			NUM
fuelectenerg-1427	472	118	f0	f0	PROPN
fuelectenerg-1427	472	119	f1	f1	PROPN
fuelectenerg-1427	472	120	f2	f2	PROPN
fuelectenerg-1427	472	121			PROPN
fuelectenerg-1427	472	122			PROPN
fuelectenerg-1427	472	123	.	.	PUNCT
fuelectenerg-1427	473	1	(	(	PUNCT
fuelectenerg-1427	473	2	22	22	NUM
fuelectenerg-1427	473	3	)	)	PUNCT
fuelectenerg-1427	473	4	the	the	DET
fuelectenerg-1427	473	5	recursive	recursive	ADJ
fuelectenerg-1427	473	6	generation	generation	NOUN
fuelectenerg-1427	473	7	using	use	VERB
fuelectenerg-1427	473	8	the	the	DET
fuelectenerg-1427	473	9	kronecker	kronecker	NOUN
fuelectenerg-1427	473	10	product	product	NOUN
fuelectenerg-1427	473	11	for	for	ADP
fuelectenerg-1427	473	12	arbitrary	arbitrary	ADJ
fuelectenerg-1427	473	13	number	number	NOUN
fuelectenerg-1427	473	14	of	of	ADP
fuelectenerg-1427	473	15	variables	variable	NOUN
fuelectenerg-1427	473	16	can	can	AUX
fuelectenerg-1427	473	17	be	be	AUX
fuelectenerg-1427	473	18	expressed	express	VERB
fuelectenerg-1427	473	19	formally	formally	ADV
fuelectenerg-1427	473	20	as	as	ADP
fuelectenerg-1427	473	21	in	in	ADP
fuelectenerg-1427	473	22	the	the	DET
fuelectenerg-1427	473	23	following	follow	VERB
fuelectenerg-1427	473	24	forms	form	NOUN
fuelectenerg-1427	473	25	for	for	ADP
fuelectenerg-1427	473	26	ternary	ternary	ADJ
fuelectenerg-1427	473	27	shannon	shannon	NOUN
fuelectenerg-1427	473	28	(	(	PUNCT
fuelectenerg-1427	473	29	s	s	NOUN
fuelectenerg-1427	473	30	)	)	PUNCT
fuelectenerg-1427	473	31	and	and	CCONJ
fuelectenerg-1427	473	32	davio	davio	NOUN
fuelectenerg-1427	473	33	(	(	PUNCT
fuelectenerg-1427	473	34	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	473	35	)	)	PUNCT
fuelectenerg-1427	473	36	expansions	expansion	NOUN
fuelectenerg-1427	473	37	,	,	PUNCT
fuelectenerg-1427	473	38	respectively	respectively	ADV
fuelectenerg-1427	473	39	:	:	PUNCT
fuelectenerg-1427	474	1	f	f	X
fuelectenerg-1427	474	2	=	=	SYM
fuelectenerg-1427	474	3	n	n	PRON
fuelectenerg-1427	474	4	�	�	PROPN
fuelectenerg-1427	474	5	i=1	i=1	PROPN
fuelectenerg-1427	474	6	�	�	PROPN
fuelectenerg-1427	474	7	0xi	0xi	PROPN
fuelectenerg-1427	474	8	1xi	1xi	PROPN
fuelectenerg-1427	474	9	2xi	2xi	ADJ
fuelectenerg-1427	474	10	�	�	PROPN
fuelectenerg-1427	474	11	n	n	CCONJ
fuelectenerg-1427	474	12	�	�	PROPN
fuelectenerg-1427	474	13	i=1	i=1	PROPN
fuelectenerg-1427	475	1	[	[	X
fuelectenerg-1427	475	2	s][	s][	PROPN
fuelectenerg-1427	475	3	�	�	PROPN
fuelectenerg-1427	475	4	f	f	X
fuelectenerg-1427	475	5	]	]	X
fuelectenerg-1427	475	6	,	,	PUNCT
fuelectenerg-1427	475	7	(	(	PUNCT
fuelectenerg-1427	475	8	23	23	NUM
fuelectenerg-1427	475	9	)	)	PUNCT
fuelectenerg-1427	475	10	f	f	NOUN
fuelectenerg-1427	476	1	=	=	SYM
fuelectenerg-1427	476	2	n	n	PRON
fuelectenerg-1427	476	3	�	�	PROPN
fuelectenerg-1427	476	4	i=1	i=1	PROPN
fuelectenerg-1427	476	5	�	�	PROPN
fuelectenerg-1427	476	6	1	1	NUM
fuelectenerg-1427	476	7	xi	xi	ADP
fuelectenerg-1427	476	8	x2	x2	INTJ
fuelectenerg-1427	476	9	i	i	PRON
fuelectenerg-1427	476	10	�	�	PROPN
fuelectenerg-1427	476	11	n	n	CCONJ
fuelectenerg-1427	476	12	�	�	PROPN
fuelectenerg-1427	476	13	i=1	i=1	X
fuelectenerg-1427	477	1	[	[	X
fuelectenerg-1427	477	2	d0][	d0][	NOUN
fuelectenerg-1427	477	3	�	�	X
fuelectenerg-1427	477	4	f	f	X
fuelectenerg-1427	477	5	]	]	X
fuelectenerg-1427	477	6	,	,	PUNCT
fuelectenerg-1427	477	7	(	(	PUNCT
fuelectenerg-1427	477	8	24	24	NUM
fuelectenerg-1427	477	9	)	)	PUNCT
fuelectenerg-1427	477	10	f	f	NOUN
fuelectenerg-1427	478	1	=	=	SYM
fuelectenerg-1427	478	2	n	n	PRON
fuelectenerg-1427	478	3	�	�	PROPN
fuelectenerg-1427	478	4	i=1	i=1	PROPN
fuelectenerg-1427	478	5	�	�	PROPN
fuelectenerg-1427	478	6	1	1	NUM
fuelectenerg-1427	478	7	x′i	x′i	PROPN
fuelectenerg-1427	478	8	(	(	PUNCT
fuelectenerg-1427	478	9	x′i	x′i	NOUN
fuelectenerg-1427	478	10	)	)	PUNCT
fuelectenerg-1427	478	11	2	2	NUM
fuelectenerg-1427	478	12	�	�	PROPN
fuelectenerg-1427	478	13	n	n	PRON
fuelectenerg-1427	478	14	�	�	PROPN
fuelectenerg-1427	478	15	i=1	i=1	PART
fuelectenerg-1427	479	1	[	[	X
fuelectenerg-1427	479	2	d1][	d1][	X
fuelectenerg-1427	479	3	�	�	NOUN
fuelectenerg-1427	479	4	f	f	X
fuelectenerg-1427	479	5	]	]	X
fuelectenerg-1427	479	6	,	,	PUNCT
fuelectenerg-1427	479	7	(	(	PUNCT
fuelectenerg-1427	479	8	25	25	NUM
fuelectenerg-1427	479	9	)	)	PUNCT
fuelectenerg-1427	479	10	f	f	NOUN
fuelectenerg-1427	480	1	=	=	SYM
fuelectenerg-1427	480	2	n	n	PRON
fuelectenerg-1427	480	3	�	�	PROPN
fuelectenerg-1427	480	4	i=1	i=1	PROPN
fuelectenerg-1427	480	5	�	�	PROPN
fuelectenerg-1427	480	6	1	1	NUM
fuelectenerg-1427	480	7	x′′i	x′′i	PROPN
fuelectenerg-1427	480	8	(	(	PUNCT
fuelectenerg-1427	480	9	x′′i	x′′i	PROPN
fuelectenerg-1427	480	10	)	)	PUNCT
fuelectenerg-1427	480	11	2	2	NUM
fuelectenerg-1427	480	12	�	�	PROPN
fuelectenerg-1427	480	13	n	n	CCONJ
fuelectenerg-1427	480	14	�	�	PROPN
fuelectenerg-1427	480	15	i=1	i=1	PROPN
fuelectenerg-1427	481	1	[	[	AUX
fuelectenerg-1427	481	2	d2][	d2][	PROPN
fuelectenerg-1427	481	3	�	�	PROPN
fuelectenerg-1427	481	4	f	f	PROPN
fuelectenerg-1427	481	5	]	]	PUNCT
fuelectenerg-1427	481	6	.	.	PUNCT
fuelectenerg-1427	482	1	(	(	PUNCT
fuelectenerg-1427	482	2	26	26	NUM
fuelectenerg-1427	482	3	)	)	PUNCT
fuelectenerg-1427	482	4	analogously	analogously	ADV
fuelectenerg-1427	482	5	to	to	ADP
fuelectenerg-1427	482	6	the	the	DET
fuelectenerg-1427	482	7	binary	binary	ADJ
fuelectenerg-1427	482	8	case	case	NOUN
fuelectenerg-1427	482	9	,	,	PUNCT
fuelectenerg-1427	482	10	we	we	PRON
fuelectenerg-1427	482	11	can	can	AUX
fuelectenerg-1427	482	12	have	have	VERB
fuelectenerg-1427	482	13	expansions	expansion	NOUN
fuelectenerg-1427	482	14	that	that	PRON
fuelectenerg-1427	482	15	are	be	AUX
fuelectenerg-1427	482	16	mixed	mix	VERB
fuelectenerg-1427	482	17	of	of	ADP
fuelectenerg-1427	482	18	shannon	shannon	PROPN
fuelectenerg-1427	482	19	(	(	PUNCT
fuelectenerg-1427	482	20	s	s	PROPN
fuelectenerg-1427	482	21	)	)	PUNCT
fuelectenerg-1427	482	22	for	for	ADP
fuelectenerg-1427	482	23	certain	certain	ADJ
fuelectenerg-1427	482	24	variables	variable	NOUN
fuelectenerg-1427	482	25	and	and	CCONJ
fuelectenerg-1427	482	26	davio	davio	NOUN
fuelectenerg-1427	482	27	(	(	PUNCT
fuelectenerg-1427	482	28	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	482	29	)	)	PUNCT
fuelectenerg-1427	482	30	for	for	ADP
fuelectenerg-1427	482	31	the	the	DET
fuelectenerg-1427	482	32	other	other	ADJ
fuelectenerg-1427	482	33	variables	variable	NOUN
fuelectenerg-1427	482	34	.	.	PUNCT
fuelectenerg-1427	483	1	this	this	PRON
fuelectenerg-1427	483	2	will	will	AUX
fuelectenerg-1427	483	3	lead	lead	VERB
fuelectenerg-1427	483	4	,	,	PUNCT
fuelectenerg-1427	483	5	analogously	analogously	ADV
fuelectenerg-1427	483	6	to	to	ADP
fuelectenerg-1427	483	7	the	the	DET
fuelectenerg-1427	483	8	binary	binary	ADJ
fuelectenerg-1427	483	9	case	case	NOUN
fuelectenerg-1427	483	10	,	,	PUNCT
fuelectenerg-1427	483	11	to	to	ADP
fuelectenerg-1427	483	12	the	the	DET
fuelectenerg-1427	483	13	kronecker	kronecker	NOUN
fuelectenerg-1427	483	14	ternary	ternary	ADJ
fuelectenerg-1427	483	15	decision	decision	NOUN
fuelectenerg-1427	483	16	trees	tree	NOUN
fuelectenerg-1427	483	17	(	(	PUNCT
fuelectenerg-1427	483	18	tdts	tdts	ADJ
fuelectenerg-1427	483	19	)	)	PUNCT
fuelectenerg-1427	483	20	.	.	PUNCT
fuelectenerg-1427	484	1	moreover	moreover	ADV
fuelectenerg-1427	484	2	,	,	PUNCT
fuelectenerg-1427	484	3	mixed	mixed	ADJ
fuelectenerg-1427	484	4	expansions	expansion	NOUN
fuelectenerg-1427	484	5	can	can	AUX
fuelectenerg-1427	484	6	be	be	AUX
fuelectenerg-1427	484	7	extended	extend	VERB
fuelectenerg-1427	484	8	to	to	PART
fuelectenerg-1427	484	9	include	include	VERB
fuelectenerg-1427	484	10	the	the	DET
fuelectenerg-1427	484	11	case	case	NOUN
fuelectenerg-1427	484	12	of	of	ADP
fuelectenerg-1427	484	13	pseudo	pseudo	NOUN
fuelectenerg-1427	484	14	kronecker	kronecker	NOUN
fuelectenerg-1427	484	15	tdts	tdts	NOUN
fuelectenerg-1427	485	1	[	[	X
fuelectenerg-1427	485	2	17	17	NUM
fuelectenerg-1427	485	3	]	]	SYM
fuelectenerg-1427	485	4	.	.	PUNCT
fuelectenerg-1427	486	1	2	2	NUM
fuelectenerg-1427	486	2	new	new	ADJ
fuelectenerg-1427	486	3	multiple	multiple	ADV
fuelectenerg-1427	486	4	-	-	PUNCT
fuelectenerg-1427	486	5	valued	value	VERB
fuelectenerg-1427	486	6	s	s	PROPN
fuelectenerg-1427	486	7	/	/	SYM
fuelectenerg-1427	486	8	d	d	NOUN
fuelectenerg-1427	486	9	trees	tree	NOUN
fuelectenerg-1427	486	10	and	and	CCONJ
fuelectenerg-1427	486	11	their	their	PRON
fuelectenerg-1427	486	12	canonical	canonical	ADJ
fuelectenerg-1427	486	13	galois	galois	PROPN
fuelectenerg-1427	486	14	sop	sop	NOUN
fuelectenerg-1427	486	15	forms	form	NOUN
fuelectenerg-1427	486	16	economical	economical	ADJ
fuelectenerg-1427	486	17	and	and	CCONJ
fuelectenerg-1427	486	18	highly	highly	ADV
fuelectenerg-1427	486	19	testable	testable	ADJ
fuelectenerg-1427	486	20	implementations	implementation	NOUN
fuelectenerg-1427	486	21	of	of	ADP
fuelectenerg-1427	486	22	boolean	boolean	ADJ
fuelectenerg-1427	486	23	functions	function	NOUN
fuelectenerg-1427	486	24	,	,	PUNCT
fuelectenerg-1427	486	25	based	base	VERB
fuelectenerg-1427	486	26	on	on	ADP
fuelectenerg-1427	486	27	reedmuller	reedmuller	NOUN
fuelectenerg-1427	486	28	(	(	PUNCT
fuelectenerg-1427	486	29	and	and	CCONJ
fuelectenerg-1427	486	30	-	-	PUNCT
fuelectenerg-1427	486	31	exor	exor	VERB
fuelectenerg-1427	486	32	)	)	PUNCT
fuelectenerg-1427	486	33	logic	logic	NOUN
fuelectenerg-1427	486	34	,	,	PUNCT
fuelectenerg-1427	486	35	play	play	VERB
fuelectenerg-1427	486	36	an	an	DET
fuelectenerg-1427	486	37	important	important	ADJ
fuelectenerg-1427	486	38	role	role	NOUN
fuelectenerg-1427	486	39	in	in	ADP
fuelectenerg-1427	486	40	logic	logic	ADJ
fuelectenerg-1427	486	41	synthesis	synthesis	NOUN
fuelectenerg-1427	486	42	and	and	CCONJ
fuelectenerg-1427	486	43	circuit	circuit	NOUN
fuelectenerg-1427	486	44	design	design	NOUN
fuelectenerg-1427	486	45	.	.	PUNCT
fuelectenerg-1427	487	1	the	the	DET
fuelectenerg-1427	487	2	and	and	CCONJ
fuelectenerg-1427	487	3	-	-	PUNCT
fuelectenerg-1427	487	4	exor	exor	PROPN
fuelectenerg-1427	487	5	circuits	circuit	NOUN
fuelectenerg-1427	487	6	include	include	VERB
fuelectenerg-1427	487	7	canonical	canonical	ADJ
fuelectenerg-1427	487	8	forms	form	NOUN
fuelectenerg-1427	487	9	which	which	PRON
fuelectenerg-1427	487	10	are	be	AUX
fuelectenerg-1427	487	11	expansions	expansion	NOUN
fuelectenerg-1427	487	12	that	that	PRON
fuelectenerg-1427	487	13	are	be	AUX
fuelectenerg-1427	487	14	unique	unique	ADJ
fuelectenerg-1427	487	15	representations	representation	NOUN
fuelectenerg-1427	487	16	of	of	ADP
fuelectenerg-1427	487	17	a	a	DET
fuelectenerg-1427	487	18	boolean	boolean	ADJ
fuelectenerg-1427	487	19	function	function	NOUN
fuelectenerg-1427	487	20	.	.	PUNCT
fuelectenerg-1427	488	1	several	several	ADJ
fuelectenerg-1427	488	2	large	large	ADJ
fuelectenerg-1427	488	3	families	family	NOUN
fuelectenerg-1427	488	4	of	of	ADP
fuelectenerg-1427	488	5	canonical	canonical	ADJ
fuelectenerg-1427	488	6	forms	form	NOUN
fuelectenerg-1427	488	7	:	:	PUNCT
fuelectenerg-1427	488	8	fixed	fix	VERB
fuelectenerg-1427	488	9	polarity	polarity	NOUN
fuelectenerg-1427	488	10	reed	reed	NOUN
fuelectenerg-1427	488	11	-	-	PUNCT
fuelectenerg-1427	488	12	muller	muller	NOUN
fuelectenerg-1427	488	13	(	(	PUNCT
fuelectenerg-1427	488	14	fprm	fprm	PROPN
fuelectenerg-1427	488	15	)	)	PUNCT
fuelectenerg-1427	488	16	forms	form	NOUN
fuelectenerg-1427	488	17	,	,	PUNCT
fuelectenerg-1427	488	18	generalized	generalized	ADJ
fuelectenerg-1427	488	19	reed	reed	NOUN
fuelectenerg-1427	488	20	-	-	PUNCT
fuelectenerg-1427	488	21	muller	muller	NOUN
fuelectenerg-1427	488	22	(	(	PUNCT
fuelectenerg-1427	488	23	grm	grm	NOUN
fuelectenerg-1427	488	24	)	)	PUNCT
fuelectenerg-1427	488	25	forms	form	NOUN
fuelectenerg-1427	488	26	,	,	PUNCT
fuelectenerg-1427	488	27	kronecker	kronecker	NOUN
fuelectenerg-1427	488	28	(	(	PUNCT
fuelectenerg-1427	488	29	kro	kro	PROPN
fuelectenerg-1427	488	30	)	)	PUNCT
fuelectenerg-1427	488	31	forms	form	NOUN
fuelectenerg-1427	488	32	and	and	CCONJ
fuelectenerg-1427	488	33	pseudo	pseudo	NOUN
fuelectenerg-1427	488	34	-	-	NOUN
fuelectenerg-1427	488	35	kronecker	kronecker	NOUN
fuelectenerg-1427	488	36	(	(	PUNCT
fuelectenerg-1427	488	37	psdkro	psdkro	NOUN
fuelectenerg-1427	488	38	)	)	PUNCT
fuelectenerg-1427	488	39	forms	form	NOUN
fuelectenerg-1427	488	40	,	,	PUNCT
fuelectenerg-1427	488	41	referred	refer	VERB
fuelectenerg-1427	488	42	to	to	ADP
fuelectenerg-1427	488	43	106	106	NUM
fuelectenerg-1427	488	44	an	an	DET
fuelectenerg-1427	488	45	extended	extend	VERB
fuelectenerg-1427	488	46	green	green	ADJ
fuelectenerg-1427	488	47	sasao	sasao	PROPN
fuelectenerg-1427	488	48	hierarchy	hierarchy	NOUN
fuelectenerg-1427	488	49	of	of	ADP
fuelectenerg-1427	488	50	canonical	canonical	ADJ
fuelectenerg-1427	488	51	ternary	ternary	ADJ
fuelectenerg-1427	488	52	galois	galois	NOUN
fuelectenerg-1427	488	53	forms	form	NOUN
fuelectenerg-1427	488	54	...	...	PUNCT
fuelectenerg-1427	489	1	f	f	X
fuelectenerg-1427	489	2	=	=	SYM
fuelectenerg-1427	489	3	�	�	PROPN
fuelectenerg-1427	489	4	0x	0x	PROPN
fuelectenerg-1427	489	5	1x	1x	NUM
fuelectenerg-1427	489	6	2x	2x	NUM
fuelectenerg-1427	489	7	�	�	PROPN
fuelectenerg-1427	489	8			PROPN
fuelectenerg-1427	489	9			NOUN
fuelectenerg-1427	489	10	1	1	NUM
fuelectenerg-1427	489	11	0	0	NUM
fuelectenerg-1427	489	12	0	0	NUM
fuelectenerg-1427	489	13	0	0	NUM
fuelectenerg-1427	489	14	1	1	NUM
fuelectenerg-1427	489	15	0	0	NUM
fuelectenerg-1427	489	16	0	0	NUM
fuelectenerg-1427	489	17	0	0	NUM
fuelectenerg-1427	489	18	1	1	NUM
fuelectenerg-1427	489	19			PROPN
fuelectenerg-1427	489	20			PROPN
fuelectenerg-1427	489	21			NOUN
fuelectenerg-1427	489	22			NUM
fuelectenerg-1427	489	23	f0	f0	PROPN
fuelectenerg-1427	489	24	f1	f1	PROPN
fuelectenerg-1427	489	25	f2	f2	PROPN
fuelectenerg-1427	489	26			PROPN
fuelectenerg-1427	489	27			PROPN
fuelectenerg-1427	489	28	,	,	PUNCT
fuelectenerg-1427	489	29	(	(	PUNCT
fuelectenerg-1427	489	30	19	19	NUM
fuelectenerg-1427	489	31	)	)	PUNCT
fuelectenerg-1427	489	32	f	f	NOUN
fuelectenerg-1427	489	33	=	=	SYM
fuelectenerg-1427	489	34	�	�	PROPN
fuelectenerg-1427	489	35	1	1	NUM
fuelectenerg-1427	489	36	x	x	SYM
fuelectenerg-1427	489	37	x2	x2	PROPN
fuelectenerg-1427	489	38	�	�	PROPN
fuelectenerg-1427	489	39			PROPN
fuelectenerg-1427	489	40			VERB
fuelectenerg-1427	489	41	1	1	NUM
fuelectenerg-1427	489	42	0	0	NUM
fuelectenerg-1427	489	43	0	0	NUM
fuelectenerg-1427	489	44	0	0	NUM
fuelectenerg-1427	489	45	2	2	NUM
fuelectenerg-1427	489	46	1	1	NUM
fuelectenerg-1427	489	47	2	2	NUM
fuelectenerg-1427	489	48	2	2	NUM
fuelectenerg-1427	489	49	2	2	NUM
fuelectenerg-1427	489	50			PROPN
fuelectenerg-1427	489	51			PROPN
fuelectenerg-1427	489	52			NOUN
fuelectenerg-1427	489	53			NUM
fuelectenerg-1427	489	54	f0	f0	PROPN
fuelectenerg-1427	489	55	f1	f1	PROPN
fuelectenerg-1427	489	56	f2	f2	PROPN
fuelectenerg-1427	489	57			PROPN
fuelectenerg-1427	489	58			PROPN
fuelectenerg-1427	489	59	,	,	PUNCT
fuelectenerg-1427	489	60	(	(	PUNCT
fuelectenerg-1427	489	61	20	20	NUM
fuelectenerg-1427	489	62	)	)	PUNCT
fuelectenerg-1427	489	63	f	f	NOUN
fuelectenerg-1427	489	64	=	=	SYM
fuelectenerg-1427	489	65	�	�	PROPN
fuelectenerg-1427	489	66	1	1	NUM
fuelectenerg-1427	489	67	x′	x′	PROPN
fuelectenerg-1427	489	68	(	(	PUNCT
fuelectenerg-1427	489	69	x′)2	x′)2	PROPN
fuelectenerg-1427	489	70	�	�	PROPN
fuelectenerg-1427	489	71			PROPN
fuelectenerg-1427	489	72			NOUN
fuelectenerg-1427	489	73	0	0	NUM
fuelectenerg-1427	489	74	0	0	NUM
fuelectenerg-1427	489	75	1	1	NUM
fuelectenerg-1427	489	76	2	2	NUM
fuelectenerg-1427	489	77	1	1	NUM
fuelectenerg-1427	489	78	0	0	NUM
fuelectenerg-1427	489	79	2	2	NUM
fuelectenerg-1427	489	80	2	2	NUM
fuelectenerg-1427	489	81	2	2	NUM
fuelectenerg-1427	489	82			PROPN
fuelectenerg-1427	489	83			PROPN
fuelectenerg-1427	489	84			NOUN
fuelectenerg-1427	489	85			NUM
fuelectenerg-1427	489	86	f0	f0	PROPN
fuelectenerg-1427	489	87	f1	f1	PROPN
fuelectenerg-1427	489	88	f2	f2	PROPN
fuelectenerg-1427	489	89			PROPN
fuelectenerg-1427	489	90			PROPN
fuelectenerg-1427	489	91	,	,	PUNCT
fuelectenerg-1427	489	92	(	(	PUNCT
fuelectenerg-1427	489	93	21	21	NUM
fuelectenerg-1427	489	94	)	)	PUNCT
fuelectenerg-1427	489	95	f	f	NOUN
fuelectenerg-1427	489	96	=	=	SYM
fuelectenerg-1427	489	97	�	�	PROPN
fuelectenerg-1427	489	98	1	1	NUM
fuelectenerg-1427	489	99	x′′	x′′	PROPN
fuelectenerg-1427	489	100	(	(	PUNCT
fuelectenerg-1427	489	101	x′′)2	x′′)2	PROPN
fuelectenerg-1427	489	102	�	�	PROPN
fuelectenerg-1427	489	103			PROPN
fuelectenerg-1427	489	104			NOUN
fuelectenerg-1427	489	105	0	0	NUM
fuelectenerg-1427	489	106	1	1	NUM
fuelectenerg-1427	489	107	0	0	NUM
fuelectenerg-1427	489	108	1	1	NUM
fuelectenerg-1427	489	109	0	0	NUM
fuelectenerg-1427	489	110	2	2	NUM
fuelectenerg-1427	489	111	2	2	NUM
fuelectenerg-1427	489	112	2	2	NUM
fuelectenerg-1427	489	113	2	2	NUM
fuelectenerg-1427	489	114			PROPN
fuelectenerg-1427	489	115			PROPN
fuelectenerg-1427	489	116			NOUN
fuelectenerg-1427	489	117			NUM
fuelectenerg-1427	489	118	f0	f0	PROPN
fuelectenerg-1427	489	119	f1	f1	PROPN
fuelectenerg-1427	489	120	f2	f2	PROPN
fuelectenerg-1427	489	121			PROPN
fuelectenerg-1427	489	122			PROPN
fuelectenerg-1427	489	123	.	.	PUNCT
fuelectenerg-1427	490	1	(	(	PUNCT
fuelectenerg-1427	490	2	22	22	NUM
fuelectenerg-1427	490	3	)	)	PUNCT
fuelectenerg-1427	490	4	the	the	DET
fuelectenerg-1427	490	5	recursive	recursive	ADJ
fuelectenerg-1427	490	6	generation	generation	NOUN
fuelectenerg-1427	490	7	using	use	VERB
fuelectenerg-1427	490	8	the	the	DET
fuelectenerg-1427	490	9	kronecker	kronecker	NOUN
fuelectenerg-1427	490	10	product	product	NOUN
fuelectenerg-1427	490	11	for	for	ADP
fuelectenerg-1427	490	12	arbitrary	arbitrary	ADJ
fuelectenerg-1427	490	13	number	number	NOUN
fuelectenerg-1427	490	14	of	of	ADP
fuelectenerg-1427	490	15	variables	variable	NOUN
fuelectenerg-1427	490	16	can	can	AUX
fuelectenerg-1427	490	17	be	be	AUX
fuelectenerg-1427	490	18	expressed	express	VERB
fuelectenerg-1427	490	19	formally	formally	ADV
fuelectenerg-1427	490	20	as	as	ADP
fuelectenerg-1427	490	21	in	in	ADP
fuelectenerg-1427	490	22	the	the	DET
fuelectenerg-1427	490	23	following	follow	VERB
fuelectenerg-1427	490	24	forms	form	NOUN
fuelectenerg-1427	490	25	for	for	ADP
fuelectenerg-1427	490	26	ternary	ternary	ADJ
fuelectenerg-1427	490	27	shannon	shannon	NOUN
fuelectenerg-1427	490	28	(	(	PUNCT
fuelectenerg-1427	490	29	s	s	NOUN
fuelectenerg-1427	490	30	)	)	PUNCT
fuelectenerg-1427	490	31	and	and	CCONJ
fuelectenerg-1427	490	32	davio	davio	NOUN
fuelectenerg-1427	490	33	(	(	PUNCT
fuelectenerg-1427	490	34	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	490	35	)	)	PUNCT
fuelectenerg-1427	490	36	expansions	expansion	NOUN
fuelectenerg-1427	490	37	,	,	PUNCT
fuelectenerg-1427	490	38	respectively	respectively	ADV
fuelectenerg-1427	490	39	:	:	PUNCT
fuelectenerg-1427	491	1	f	f	X
fuelectenerg-1427	491	2	=	=	SYM
fuelectenerg-1427	491	3	n	n	PRON
fuelectenerg-1427	491	4	�	�	PROPN
fuelectenerg-1427	491	5	i=1	i=1	PROPN
fuelectenerg-1427	491	6	�	�	PROPN
fuelectenerg-1427	491	7	0xi	0xi	PROPN
fuelectenerg-1427	491	8	1xi	1xi	PROPN
fuelectenerg-1427	491	9	2xi	2xi	ADJ
fuelectenerg-1427	491	10	�	�	PROPN
fuelectenerg-1427	491	11	n	n	CCONJ
fuelectenerg-1427	491	12	�	�	PROPN
fuelectenerg-1427	491	13	i=1	i=1	PROPN
fuelectenerg-1427	492	1	[	[	X
fuelectenerg-1427	492	2	s][	s][	PROPN
fuelectenerg-1427	492	3	�	�	PROPN
fuelectenerg-1427	492	4	f	f	X
fuelectenerg-1427	492	5	]	]	X
fuelectenerg-1427	492	6	,	,	PUNCT
fuelectenerg-1427	492	7	(	(	PUNCT
fuelectenerg-1427	492	8	23	23	NUM
fuelectenerg-1427	492	9	)	)	PUNCT
fuelectenerg-1427	492	10	f	f	NOUN
fuelectenerg-1427	493	1	=	=	SYM
fuelectenerg-1427	493	2	n	n	PRON
fuelectenerg-1427	493	3	�	�	PROPN
fuelectenerg-1427	493	4	i=1	i=1	PROPN
fuelectenerg-1427	493	5	�	�	PROPN
fuelectenerg-1427	493	6	1	1	NUM
fuelectenerg-1427	493	7	xi	xi	ADP
fuelectenerg-1427	493	8	x2	x2	INTJ
fuelectenerg-1427	493	9	i	i	PRON
fuelectenerg-1427	493	10	�	�	PROPN
fuelectenerg-1427	493	11	n	n	CCONJ
fuelectenerg-1427	493	12	�	�	PROPN
fuelectenerg-1427	493	13	i=1	i=1	X
fuelectenerg-1427	494	1	[	[	X
fuelectenerg-1427	494	2	d0][	d0][	NOUN
fuelectenerg-1427	494	3	�	�	X
fuelectenerg-1427	494	4	f	f	X
fuelectenerg-1427	494	5	]	]	X
fuelectenerg-1427	494	6	,	,	PUNCT
fuelectenerg-1427	494	7	(	(	PUNCT
fuelectenerg-1427	494	8	24	24	NUM
fuelectenerg-1427	494	9	)	)	PUNCT
fuelectenerg-1427	494	10	f	f	NOUN
fuelectenerg-1427	495	1	=	=	SYM
fuelectenerg-1427	495	2	n	n	PRON
fuelectenerg-1427	495	3	�	�	PROPN
fuelectenerg-1427	495	4	i=1	i=1	PROPN
fuelectenerg-1427	495	5	�	�	PROPN
fuelectenerg-1427	495	6	1	1	NUM
fuelectenerg-1427	495	7	x′i	x′i	PROPN
fuelectenerg-1427	495	8	(	(	PUNCT
fuelectenerg-1427	495	9	x′i	x′i	NOUN
fuelectenerg-1427	495	10	)	)	PUNCT
fuelectenerg-1427	495	11	2	2	NUM
fuelectenerg-1427	495	12	�	�	PROPN
fuelectenerg-1427	495	13	n	n	PRON
fuelectenerg-1427	495	14	�	�	PROPN
fuelectenerg-1427	495	15	i=1	i=1	PART
fuelectenerg-1427	496	1	[	[	X
fuelectenerg-1427	496	2	d1][	d1][	X
fuelectenerg-1427	496	3	�	�	NOUN
fuelectenerg-1427	496	4	f	f	X
fuelectenerg-1427	496	5	]	]	X
fuelectenerg-1427	496	6	,	,	PUNCT
fuelectenerg-1427	496	7	(	(	PUNCT
fuelectenerg-1427	496	8	25	25	NUM
fuelectenerg-1427	496	9	)	)	PUNCT
fuelectenerg-1427	496	10	f	f	NOUN
fuelectenerg-1427	497	1	=	=	SYM
fuelectenerg-1427	497	2	n	n	PRON
fuelectenerg-1427	497	3	�	�	PROPN
fuelectenerg-1427	497	4	i=1	i=1	PROPN
fuelectenerg-1427	497	5	�	�	PROPN
fuelectenerg-1427	497	6	1	1	NUM
fuelectenerg-1427	497	7	x′′i	x′′i	PROPN
fuelectenerg-1427	497	8	(	(	PUNCT
fuelectenerg-1427	497	9	x′′i	x′′i	PROPN
fuelectenerg-1427	497	10	)	)	PUNCT
fuelectenerg-1427	497	11	2	2	NUM
fuelectenerg-1427	497	12	�	�	PROPN
fuelectenerg-1427	497	13	n	n	CCONJ
fuelectenerg-1427	497	14	�	�	PROPN
fuelectenerg-1427	497	15	i=1	i=1	PROPN
fuelectenerg-1427	498	1	[	[	AUX
fuelectenerg-1427	498	2	d2][	d2][	PROPN
fuelectenerg-1427	498	3	�	�	PROPN
fuelectenerg-1427	498	4	f	f	PROPN
fuelectenerg-1427	498	5	]	]	PUNCT
fuelectenerg-1427	498	6	.	.	PUNCT
fuelectenerg-1427	499	1	(	(	PUNCT
fuelectenerg-1427	499	2	26	26	NUM
fuelectenerg-1427	499	3	)	)	PUNCT
fuelectenerg-1427	499	4	analogously	analogously	ADV
fuelectenerg-1427	499	5	to	to	ADP
fuelectenerg-1427	499	6	the	the	DET
fuelectenerg-1427	499	7	binary	binary	ADJ
fuelectenerg-1427	499	8	case	case	NOUN
fuelectenerg-1427	499	9	,	,	PUNCT
fuelectenerg-1427	499	10	we	we	PRON
fuelectenerg-1427	499	11	can	can	AUX
fuelectenerg-1427	499	12	have	have	VERB
fuelectenerg-1427	499	13	expansions	expansion	NOUN
fuelectenerg-1427	499	14	that	that	PRON
fuelectenerg-1427	499	15	are	be	AUX
fuelectenerg-1427	499	16	mixed	mix	VERB
fuelectenerg-1427	499	17	of	of	ADP
fuelectenerg-1427	499	18	shannon	shannon	PROPN
fuelectenerg-1427	499	19	(	(	PUNCT
fuelectenerg-1427	499	20	s	s	PROPN
fuelectenerg-1427	499	21	)	)	PUNCT
fuelectenerg-1427	499	22	for	for	ADP
fuelectenerg-1427	499	23	certain	certain	ADJ
fuelectenerg-1427	499	24	variables	variable	NOUN
fuelectenerg-1427	499	25	and	and	CCONJ
fuelectenerg-1427	499	26	davio	davio	NOUN
fuelectenerg-1427	499	27	(	(	PUNCT
fuelectenerg-1427	499	28	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	499	29	)	)	PUNCT
fuelectenerg-1427	499	30	for	for	ADP
fuelectenerg-1427	499	31	the	the	DET
fuelectenerg-1427	499	32	other	other	ADJ
fuelectenerg-1427	499	33	variables	variable	NOUN
fuelectenerg-1427	499	34	.	.	PUNCT
fuelectenerg-1427	500	1	this	this	PRON
fuelectenerg-1427	500	2	will	will	AUX
fuelectenerg-1427	500	3	lead	lead	VERB
fuelectenerg-1427	500	4	,	,	PUNCT
fuelectenerg-1427	500	5	analogously	analogously	ADV
fuelectenerg-1427	500	6	to	to	ADP
fuelectenerg-1427	500	7	the	the	DET
fuelectenerg-1427	500	8	binary	binary	ADJ
fuelectenerg-1427	500	9	case	case	NOUN
fuelectenerg-1427	500	10	,	,	PUNCT
fuelectenerg-1427	500	11	to	to	ADP
fuelectenerg-1427	500	12	the	the	DET
fuelectenerg-1427	500	13	kronecker	kronecker	NOUN
fuelectenerg-1427	500	14	ternary	ternary	ADJ
fuelectenerg-1427	500	15	decision	decision	NOUN
fuelectenerg-1427	500	16	trees	tree	NOUN
fuelectenerg-1427	500	17	(	(	PUNCT
fuelectenerg-1427	500	18	tdts	tdts	ADJ
fuelectenerg-1427	500	19	)	)	PUNCT
fuelectenerg-1427	500	20	.	.	PUNCT
fuelectenerg-1427	501	1	moreover	moreover	ADV
fuelectenerg-1427	501	2	,	,	PUNCT
fuelectenerg-1427	501	3	mixed	mixed	ADJ
fuelectenerg-1427	501	4	expansions	expansion	NOUN
fuelectenerg-1427	501	5	can	can	AUX
fuelectenerg-1427	501	6	be	be	AUX
fuelectenerg-1427	501	7	extended	extend	VERB
fuelectenerg-1427	501	8	to	to	PART
fuelectenerg-1427	501	9	include	include	VERB
fuelectenerg-1427	501	10	the	the	DET
fuelectenerg-1427	501	11	case	case	NOUN
fuelectenerg-1427	501	12	of	of	ADP
fuelectenerg-1427	501	13	pseudo	pseudo	NOUN
fuelectenerg-1427	501	14	kronecker	kronecker	NOUN
fuelectenerg-1427	501	15	tdts	tdts	NOUN
fuelectenerg-1427	502	1	[	[	X
fuelectenerg-1427	502	2	17	17	NUM
fuelectenerg-1427	502	3	]	]	SYM
fuelectenerg-1427	502	4	.	.	PUNCT
fuelectenerg-1427	503	1	2	2	NUM
fuelectenerg-1427	503	2	new	new	ADJ
fuelectenerg-1427	503	3	multiple	multiple	ADV
fuelectenerg-1427	503	4	-	-	PUNCT
fuelectenerg-1427	503	5	valued	value	VERB
fuelectenerg-1427	503	6	s	s	PROPN
fuelectenerg-1427	503	7	/	/	SYM
fuelectenerg-1427	503	8	d	d	NOUN
fuelectenerg-1427	503	9	trees	tree	NOUN
fuelectenerg-1427	503	10	and	and	CCONJ
fuelectenerg-1427	503	11	their	their	PRON
fuelectenerg-1427	503	12	canonical	canonical	ADJ
fuelectenerg-1427	503	13	galois	galois	PROPN
fuelectenerg-1427	503	14	sop	sop	NOUN
fuelectenerg-1427	503	15	forms	form	NOUN
fuelectenerg-1427	503	16	economical	economical	ADJ
fuelectenerg-1427	503	17	and	and	CCONJ
fuelectenerg-1427	503	18	highly	highly	ADV
fuelectenerg-1427	503	19	testable	testable	ADJ
fuelectenerg-1427	503	20	implementations	implementation	NOUN
fuelectenerg-1427	503	21	of	of	ADP
fuelectenerg-1427	503	22	boolean	boolean	ADJ
fuelectenerg-1427	503	23	functions	function	NOUN
fuelectenerg-1427	503	24	,	,	PUNCT
fuelectenerg-1427	503	25	based	base	VERB
fuelectenerg-1427	503	26	on	on	ADP
fuelectenerg-1427	503	27	reedmuller	reedmuller	NOUN
fuelectenerg-1427	503	28	(	(	PUNCT
fuelectenerg-1427	503	29	and	and	CCONJ
fuelectenerg-1427	503	30	-	-	PUNCT
fuelectenerg-1427	503	31	exor	exor	VERB
fuelectenerg-1427	503	32	)	)	PUNCT
fuelectenerg-1427	503	33	logic	logic	NOUN
fuelectenerg-1427	503	34	,	,	PUNCT
fuelectenerg-1427	503	35	play	play	VERB
fuelectenerg-1427	503	36	an	an	DET
fuelectenerg-1427	503	37	important	important	ADJ
fuelectenerg-1427	503	38	role	role	NOUN
fuelectenerg-1427	503	39	in	in	ADP
fuelectenerg-1427	503	40	logic	logic	ADJ
fuelectenerg-1427	503	41	synthesis	synthesis	NOUN
fuelectenerg-1427	503	42	and	and	CCONJ
fuelectenerg-1427	503	43	circuit	circuit	NOUN
fuelectenerg-1427	503	44	design	design	NOUN
fuelectenerg-1427	503	45	.	.	PUNCT
fuelectenerg-1427	504	1	the	the	DET
fuelectenerg-1427	504	2	and	and	CCONJ
fuelectenerg-1427	504	3	-	-	PUNCT
fuelectenerg-1427	504	4	exor	exor	PROPN
fuelectenerg-1427	504	5	circuits	circuit	NOUN
fuelectenerg-1427	504	6	include	include	VERB
fuelectenerg-1427	504	7	canonical	canonical	ADJ
fuelectenerg-1427	504	8	forms	form	NOUN
fuelectenerg-1427	504	9	which	which	PRON
fuelectenerg-1427	504	10	are	be	AUX
fuelectenerg-1427	504	11	expansions	expansion	NOUN
fuelectenerg-1427	504	12	that	that	PRON
fuelectenerg-1427	504	13	are	be	AUX
fuelectenerg-1427	504	14	unique	unique	ADJ
fuelectenerg-1427	504	15	representations	representation	NOUN
fuelectenerg-1427	504	16	of	of	ADP
fuelectenerg-1427	504	17	a	a	DET
fuelectenerg-1427	504	18	boolean	boolean	ADJ
fuelectenerg-1427	504	19	function	function	NOUN
fuelectenerg-1427	504	20	.	.	PUNCT
fuelectenerg-1427	505	1	several	several	ADJ
fuelectenerg-1427	505	2	large	large	ADJ
fuelectenerg-1427	505	3	families	family	NOUN
fuelectenerg-1427	505	4	of	of	ADP
fuelectenerg-1427	505	5	canonical	canonical	ADJ
fuelectenerg-1427	505	6	forms	form	NOUN
fuelectenerg-1427	505	7	:	:	PUNCT
fuelectenerg-1427	505	8	fixed	fix	VERB
fuelectenerg-1427	505	9	polarity	polarity	NOUN
fuelectenerg-1427	505	10	reed	reed	NOUN
fuelectenerg-1427	505	11	-	-	PUNCT
fuelectenerg-1427	505	12	muller	muller	NOUN
fuelectenerg-1427	505	13	(	(	PUNCT
fuelectenerg-1427	505	14	fprm	fprm	PROPN
fuelectenerg-1427	505	15	)	)	PUNCT
fuelectenerg-1427	505	16	forms	form	NOUN
fuelectenerg-1427	505	17	,	,	PUNCT
fuelectenerg-1427	505	18	generalized	generalized	ADJ
fuelectenerg-1427	505	19	reed	reed	NOUN
fuelectenerg-1427	505	20	-	-	PUNCT
fuelectenerg-1427	505	21	muller	muller	NOUN
fuelectenerg-1427	505	22	(	(	PUNCT
fuelectenerg-1427	505	23	grm	grm	NOUN
fuelectenerg-1427	505	24	)	)	PUNCT
fuelectenerg-1427	505	25	forms	form	NOUN
fuelectenerg-1427	505	26	,	,	PUNCT
fuelectenerg-1427	505	27	kronecker	kronecker	NOUN
fuelectenerg-1427	505	28	(	(	PUNCT
fuelectenerg-1427	505	29	kro	kro	PROPN
fuelectenerg-1427	505	30	)	)	PUNCT
fuelectenerg-1427	505	31	forms	form	NOUN
fuelectenerg-1427	505	32	and	and	CCONJ
fuelectenerg-1427	505	33	pseudo	pseudo	NOUN
fuelectenerg-1427	505	34	-	-	NOUN
fuelectenerg-1427	505	35	kronecker	kronecker	NOUN
fuelectenerg-1427	505	36	(	(	PUNCT
fuelectenerg-1427	505	37	psdkro	psdkro	NOUN
fuelectenerg-1427	505	38	)	)	PUNCT
fuelectenerg-1427	505	39	forms	form	NOUN
fuelectenerg-1427	505	40	,	,	PUNCT
fuelectenerg-1427	505	41	referred	refer	VERB
fuelectenerg-1427	505	42	to	to	ADP
fuelectenerg-1427	505	43	106	106	NUM
fuelectenerg-1427	505	44	an	an	DET
fuelectenerg-1427	505	45	extended	extend	VERB
fuelectenerg-1427	505	46	green	green	ADJ
fuelectenerg-1427	505	47	sasao	sasao	PROPN
fuelectenerg-1427	505	48	hierarchy	hierarchy	NOUN
fuelectenerg-1427	505	49	of	of	ADP
fuelectenerg-1427	505	50	canonical	canonical	ADJ
fuelectenerg-1427	505	51	ternary	ternary	ADJ
fuelectenerg-1427	505	52	galois	galois	NOUN
fuelectenerg-1427	505	53	forms	form	NOUN
fuelectenerg-1427	505	54	...	...	PUNCT
fuelectenerg-1427	506	1	f	f	X
fuelectenerg-1427	506	2	=	=	SYM
fuelectenerg-1427	506	3	�	�	PROPN
fuelectenerg-1427	506	4	0x	0x	PROPN
fuelectenerg-1427	506	5	1x	1x	NUM
fuelectenerg-1427	506	6	2x	2x	NUM
fuelectenerg-1427	506	7	�	�	PROPN
fuelectenerg-1427	506	8			PROPN
fuelectenerg-1427	506	9			NOUN
fuelectenerg-1427	506	10	1	1	NUM
fuelectenerg-1427	506	11	0	0	NUM
fuelectenerg-1427	506	12	0	0	NUM
fuelectenerg-1427	506	13	0	0	NUM
fuelectenerg-1427	506	14	1	1	NUM
fuelectenerg-1427	506	15	0	0	NUM
fuelectenerg-1427	506	16	0	0	NUM
fuelectenerg-1427	506	17	0	0	NUM
fuelectenerg-1427	506	18	1	1	NUM
fuelectenerg-1427	506	19			PROPN
fuelectenerg-1427	506	20			PROPN
fuelectenerg-1427	506	21			NOUN
fuelectenerg-1427	506	22			NUM
fuelectenerg-1427	506	23	f0	f0	PROPN
fuelectenerg-1427	506	24	f1	f1	PROPN
fuelectenerg-1427	506	25	f2	f2	PROPN
fuelectenerg-1427	506	26			PROPN
fuelectenerg-1427	506	27			PROPN
fuelectenerg-1427	506	28	,	,	PUNCT
fuelectenerg-1427	506	29	(	(	PUNCT
fuelectenerg-1427	506	30	19	19	NUM
fuelectenerg-1427	506	31	)	)	PUNCT
fuelectenerg-1427	506	32	f	f	NOUN
fuelectenerg-1427	506	33	=	=	SYM
fuelectenerg-1427	506	34	�	�	PROPN
fuelectenerg-1427	506	35	1	1	NUM
fuelectenerg-1427	506	36	x	x	SYM
fuelectenerg-1427	506	37	x2	x2	PROPN
fuelectenerg-1427	506	38	�	�	PROPN
fuelectenerg-1427	506	39			PROPN
fuelectenerg-1427	506	40			VERB
fuelectenerg-1427	506	41	1	1	NUM
fuelectenerg-1427	506	42	0	0	NUM
fuelectenerg-1427	506	43	0	0	NUM
fuelectenerg-1427	506	44	0	0	NUM
fuelectenerg-1427	506	45	2	2	NUM
fuelectenerg-1427	506	46	1	1	NUM
fuelectenerg-1427	506	47	2	2	NUM
fuelectenerg-1427	506	48	2	2	NUM
fuelectenerg-1427	506	49	2	2	NUM
fuelectenerg-1427	506	50			PROPN
fuelectenerg-1427	506	51			PROPN
fuelectenerg-1427	506	52			NOUN
fuelectenerg-1427	506	53			NUM
fuelectenerg-1427	506	54	f0	f0	PROPN
fuelectenerg-1427	506	55	f1	f1	PROPN
fuelectenerg-1427	506	56	f2	f2	PROPN
fuelectenerg-1427	506	57			PROPN
fuelectenerg-1427	506	58			PROPN
fuelectenerg-1427	506	59	,	,	PUNCT
fuelectenerg-1427	506	60	(	(	PUNCT
fuelectenerg-1427	506	61	20	20	NUM
fuelectenerg-1427	506	62	)	)	PUNCT
fuelectenerg-1427	506	63	f	f	NOUN
fuelectenerg-1427	506	64	=	=	SYM
fuelectenerg-1427	506	65	�	�	PROPN
fuelectenerg-1427	506	66	1	1	NUM
fuelectenerg-1427	506	67	x′	x′	PROPN
fuelectenerg-1427	506	68	(	(	PUNCT
fuelectenerg-1427	506	69	x′)2	x′)2	PROPN
fuelectenerg-1427	506	70	�	�	PROPN
fuelectenerg-1427	506	71			PROPN
fuelectenerg-1427	506	72			NOUN
fuelectenerg-1427	506	73	0	0	NUM
fuelectenerg-1427	506	74	0	0	NUM
fuelectenerg-1427	506	75	1	1	NUM
fuelectenerg-1427	506	76	2	2	NUM
fuelectenerg-1427	506	77	1	1	NUM
fuelectenerg-1427	506	78	0	0	NUM
fuelectenerg-1427	506	79	2	2	NUM
fuelectenerg-1427	506	80	2	2	NUM
fuelectenerg-1427	506	81	2	2	NUM
fuelectenerg-1427	506	82			PROPN
fuelectenerg-1427	506	83			PROPN
fuelectenerg-1427	506	84			NOUN
fuelectenerg-1427	506	85			NUM
fuelectenerg-1427	506	86	f0	f0	PROPN
fuelectenerg-1427	506	87	f1	f1	PROPN
fuelectenerg-1427	506	88	f2	f2	PROPN
fuelectenerg-1427	506	89			PROPN
fuelectenerg-1427	506	90			PROPN
fuelectenerg-1427	506	91	,	,	PUNCT
fuelectenerg-1427	506	92	(	(	PUNCT
fuelectenerg-1427	506	93	21	21	NUM
fuelectenerg-1427	506	94	)	)	PUNCT
fuelectenerg-1427	506	95	f	f	NOUN
fuelectenerg-1427	506	96	=	=	SYM
fuelectenerg-1427	506	97	�	�	PROPN
fuelectenerg-1427	506	98	1	1	NUM
fuelectenerg-1427	506	99	x′′	x′′	PROPN
fuelectenerg-1427	506	100	(	(	PUNCT
fuelectenerg-1427	506	101	x′′)2	x′′)2	PROPN
fuelectenerg-1427	506	102	�	�	PROPN
fuelectenerg-1427	506	103			PROPN
fuelectenerg-1427	506	104			NOUN
fuelectenerg-1427	506	105	0	0	NUM
fuelectenerg-1427	506	106	1	1	NUM
fuelectenerg-1427	506	107	0	0	NUM
fuelectenerg-1427	506	108	1	1	NUM
fuelectenerg-1427	506	109	0	0	NUM
fuelectenerg-1427	506	110	2	2	NUM
fuelectenerg-1427	506	111	2	2	NUM
fuelectenerg-1427	506	112	2	2	NUM
fuelectenerg-1427	506	113	2	2	NUM
fuelectenerg-1427	506	114			PROPN
fuelectenerg-1427	506	115			PROPN
fuelectenerg-1427	506	116			NOUN
fuelectenerg-1427	506	117			NUM
fuelectenerg-1427	506	118	f0	f0	PROPN
fuelectenerg-1427	506	119	f1	f1	PROPN
fuelectenerg-1427	506	120	f2	f2	PROPN
fuelectenerg-1427	506	121			PROPN
fuelectenerg-1427	506	122			PROPN
fuelectenerg-1427	506	123	.	.	PUNCT
fuelectenerg-1427	507	1	(	(	PUNCT
fuelectenerg-1427	507	2	22	22	NUM
fuelectenerg-1427	507	3	)	)	PUNCT
fuelectenerg-1427	507	4	the	the	DET
fuelectenerg-1427	507	5	recursive	recursive	ADJ
fuelectenerg-1427	507	6	generation	generation	NOUN
fuelectenerg-1427	507	7	using	use	VERB
fuelectenerg-1427	507	8	the	the	DET
fuelectenerg-1427	507	9	kronecker	kronecker	NOUN
fuelectenerg-1427	507	10	product	product	NOUN
fuelectenerg-1427	507	11	for	for	ADP
fuelectenerg-1427	507	12	arbitrary	arbitrary	ADJ
fuelectenerg-1427	507	13	number	number	NOUN
fuelectenerg-1427	507	14	of	of	ADP
fuelectenerg-1427	507	15	variables	variable	NOUN
fuelectenerg-1427	507	16	can	can	AUX
fuelectenerg-1427	507	17	be	be	AUX
fuelectenerg-1427	507	18	expressed	express	VERB
fuelectenerg-1427	507	19	formally	formally	ADV
fuelectenerg-1427	507	20	as	as	ADP
fuelectenerg-1427	507	21	in	in	ADP
fuelectenerg-1427	507	22	the	the	DET
fuelectenerg-1427	507	23	following	follow	VERB
fuelectenerg-1427	507	24	forms	form	NOUN
fuelectenerg-1427	507	25	for	for	ADP
fuelectenerg-1427	507	26	ternary	ternary	ADJ
fuelectenerg-1427	507	27	shannon	shannon	NOUN
fuelectenerg-1427	507	28	(	(	PUNCT
fuelectenerg-1427	507	29	s	s	NOUN
fuelectenerg-1427	507	30	)	)	PUNCT
fuelectenerg-1427	507	31	and	and	CCONJ
fuelectenerg-1427	507	32	davio	davio	NOUN
fuelectenerg-1427	507	33	(	(	PUNCT
fuelectenerg-1427	507	34	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	507	35	)	)	PUNCT
fuelectenerg-1427	507	36	expansions	expansion	NOUN
fuelectenerg-1427	507	37	,	,	PUNCT
fuelectenerg-1427	507	38	respectively	respectively	ADV
fuelectenerg-1427	507	39	:	:	PUNCT
fuelectenerg-1427	508	1	f	f	X
fuelectenerg-1427	508	2	=	=	SYM
fuelectenerg-1427	508	3	n	n	PRON
fuelectenerg-1427	508	4	�	�	PROPN
fuelectenerg-1427	508	5	i=1	i=1	PROPN
fuelectenerg-1427	508	6	�	�	PROPN
fuelectenerg-1427	508	7	0xi	0xi	PROPN
fuelectenerg-1427	508	8	1xi	1xi	PROPN
fuelectenerg-1427	508	9	2xi	2xi	ADJ
fuelectenerg-1427	508	10	�	�	PROPN
fuelectenerg-1427	508	11	n	n	CCONJ
fuelectenerg-1427	508	12	�	�	PROPN
fuelectenerg-1427	508	13	i=1	i=1	PROPN
fuelectenerg-1427	509	1	[	[	X
fuelectenerg-1427	509	2	s][	s][	PROPN
fuelectenerg-1427	509	3	�	�	PROPN
fuelectenerg-1427	509	4	f	f	X
fuelectenerg-1427	509	5	]	]	X
fuelectenerg-1427	509	6	,	,	PUNCT
fuelectenerg-1427	509	7	(	(	PUNCT
fuelectenerg-1427	509	8	23	23	NUM
fuelectenerg-1427	509	9	)	)	PUNCT
fuelectenerg-1427	509	10	f	f	NOUN
fuelectenerg-1427	510	1	=	=	SYM
fuelectenerg-1427	510	2	n	n	PRON
fuelectenerg-1427	510	3	�	�	PROPN
fuelectenerg-1427	510	4	i=1	i=1	PROPN
fuelectenerg-1427	510	5	�	�	PROPN
fuelectenerg-1427	510	6	1	1	NUM
fuelectenerg-1427	510	7	xi	xi	ADP
fuelectenerg-1427	510	8	x2	x2	INTJ
fuelectenerg-1427	510	9	i	i	PRON
fuelectenerg-1427	510	10	�	�	PROPN
fuelectenerg-1427	510	11	n	n	CCONJ
fuelectenerg-1427	510	12	�	�	PROPN
fuelectenerg-1427	510	13	i=1	i=1	X
fuelectenerg-1427	511	1	[	[	X
fuelectenerg-1427	511	2	d0][	d0][	NOUN
fuelectenerg-1427	511	3	�	�	X
fuelectenerg-1427	511	4	f	f	X
fuelectenerg-1427	511	5	]	]	X
fuelectenerg-1427	511	6	,	,	PUNCT
fuelectenerg-1427	511	7	(	(	PUNCT
fuelectenerg-1427	511	8	24	24	NUM
fuelectenerg-1427	511	9	)	)	PUNCT
fuelectenerg-1427	511	10	f	f	NOUN
fuelectenerg-1427	512	1	=	=	SYM
fuelectenerg-1427	512	2	n	n	PRON
fuelectenerg-1427	512	3	�	�	PROPN
fuelectenerg-1427	512	4	i=1	i=1	PROPN
fuelectenerg-1427	512	5	�	�	PROPN
fuelectenerg-1427	512	6	1	1	NUM
fuelectenerg-1427	512	7	x′i	x′i	PROPN
fuelectenerg-1427	512	8	(	(	PUNCT
fuelectenerg-1427	512	9	x′i	x′i	NOUN
fuelectenerg-1427	512	10	)	)	PUNCT
fuelectenerg-1427	512	11	2	2	NUM
fuelectenerg-1427	512	12	�	�	PROPN
fuelectenerg-1427	512	13	n	n	PRON
fuelectenerg-1427	512	14	�	�	PROPN
fuelectenerg-1427	512	15	i=1	i=1	PART
fuelectenerg-1427	513	1	[	[	X
fuelectenerg-1427	513	2	d1][	d1][	X
fuelectenerg-1427	513	3	�	�	NOUN
fuelectenerg-1427	513	4	f	f	X
fuelectenerg-1427	513	5	]	]	X
fuelectenerg-1427	513	6	,	,	PUNCT
fuelectenerg-1427	513	7	(	(	PUNCT
fuelectenerg-1427	513	8	25	25	NUM
fuelectenerg-1427	513	9	)	)	PUNCT
fuelectenerg-1427	513	10	f	f	NOUN
fuelectenerg-1427	514	1	=	=	SYM
fuelectenerg-1427	514	2	n	n	PRON
fuelectenerg-1427	514	3	�	�	PROPN
fuelectenerg-1427	514	4	i=1	i=1	PROPN
fuelectenerg-1427	514	5	�	�	PROPN
fuelectenerg-1427	514	6	1	1	NUM
fuelectenerg-1427	514	7	x′′i	x′′i	PROPN
fuelectenerg-1427	514	8	(	(	PUNCT
fuelectenerg-1427	514	9	x′′i	x′′i	PROPN
fuelectenerg-1427	514	10	)	)	PUNCT
fuelectenerg-1427	514	11	2	2	NUM
fuelectenerg-1427	514	12	�	�	PROPN
fuelectenerg-1427	514	13	n	n	CCONJ
fuelectenerg-1427	514	14	�	�	PROPN
fuelectenerg-1427	514	15	i=1	i=1	PROPN
fuelectenerg-1427	515	1	[	[	AUX
fuelectenerg-1427	515	2	d2][	d2][	PROPN
fuelectenerg-1427	515	3	�	�	PROPN
fuelectenerg-1427	515	4	f	f	PROPN
fuelectenerg-1427	515	5	]	]	PUNCT
fuelectenerg-1427	515	6	.	.	PUNCT
fuelectenerg-1427	516	1	(	(	PUNCT
fuelectenerg-1427	516	2	26	26	NUM
fuelectenerg-1427	516	3	)	)	PUNCT
fuelectenerg-1427	516	4	analogously	analogously	ADV
fuelectenerg-1427	516	5	to	to	ADP
fuelectenerg-1427	516	6	the	the	DET
fuelectenerg-1427	516	7	binary	binary	ADJ
fuelectenerg-1427	516	8	case	case	NOUN
fuelectenerg-1427	516	9	,	,	PUNCT
fuelectenerg-1427	516	10	we	we	PRON
fuelectenerg-1427	516	11	can	can	AUX
fuelectenerg-1427	516	12	have	have	VERB
fuelectenerg-1427	516	13	expansions	expansion	NOUN
fuelectenerg-1427	516	14	that	that	PRON
fuelectenerg-1427	516	15	are	be	AUX
fuelectenerg-1427	516	16	mixed	mix	VERB
fuelectenerg-1427	516	17	of	of	ADP
fuelectenerg-1427	516	18	shannon	shannon	PROPN
fuelectenerg-1427	516	19	(	(	PUNCT
fuelectenerg-1427	516	20	s	s	PROPN
fuelectenerg-1427	516	21	)	)	PUNCT
fuelectenerg-1427	516	22	for	for	ADP
fuelectenerg-1427	516	23	certain	certain	ADJ
fuelectenerg-1427	516	24	variables	variable	NOUN
fuelectenerg-1427	516	25	and	and	CCONJ
fuelectenerg-1427	516	26	davio	davio	NOUN
fuelectenerg-1427	516	27	(	(	PUNCT
fuelectenerg-1427	516	28	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	516	29	)	)	PUNCT
fuelectenerg-1427	516	30	for	for	ADP
fuelectenerg-1427	516	31	the	the	DET
fuelectenerg-1427	516	32	other	other	ADJ
fuelectenerg-1427	516	33	variables	variable	NOUN
fuelectenerg-1427	516	34	.	.	PUNCT
fuelectenerg-1427	517	1	this	this	PRON
fuelectenerg-1427	517	2	will	will	AUX
fuelectenerg-1427	517	3	lead	lead	VERB
fuelectenerg-1427	517	4	,	,	PUNCT
fuelectenerg-1427	517	5	analogously	analogously	ADV
fuelectenerg-1427	517	6	to	to	ADP
fuelectenerg-1427	517	7	the	the	DET
fuelectenerg-1427	517	8	binary	binary	ADJ
fuelectenerg-1427	517	9	case	case	NOUN
fuelectenerg-1427	517	10	,	,	PUNCT
fuelectenerg-1427	517	11	to	to	ADP
fuelectenerg-1427	517	12	the	the	DET
fuelectenerg-1427	517	13	kronecker	kronecker	NOUN
fuelectenerg-1427	517	14	ternary	ternary	ADJ
fuelectenerg-1427	517	15	decision	decision	NOUN
fuelectenerg-1427	517	16	trees	tree	NOUN
fuelectenerg-1427	517	17	(	(	PUNCT
fuelectenerg-1427	517	18	tdts	tdts	ADJ
fuelectenerg-1427	517	19	)	)	PUNCT
fuelectenerg-1427	517	20	.	.	PUNCT
fuelectenerg-1427	518	1	moreover	moreover	ADV
fuelectenerg-1427	518	2	,	,	PUNCT
fuelectenerg-1427	518	3	mixed	mixed	ADJ
fuelectenerg-1427	518	4	expansions	expansion	NOUN
fuelectenerg-1427	518	5	can	can	AUX
fuelectenerg-1427	518	6	be	be	AUX
fuelectenerg-1427	518	7	extended	extend	VERB
fuelectenerg-1427	518	8	to	to	PART
fuelectenerg-1427	518	9	include	include	VERB
fuelectenerg-1427	518	10	the	the	DET
fuelectenerg-1427	518	11	case	case	NOUN
fuelectenerg-1427	518	12	of	of	ADP
fuelectenerg-1427	518	13	pseudo	pseudo	NOUN
fuelectenerg-1427	518	14	kronecker	kronecker	NOUN
fuelectenerg-1427	518	15	tdts	tdts	NOUN
fuelectenerg-1427	519	1	[	[	X
fuelectenerg-1427	519	2	17	17	NUM
fuelectenerg-1427	519	3	]	]	SYM
fuelectenerg-1427	519	4	.	.	PUNCT
fuelectenerg-1427	520	1	2	2	NUM
fuelectenerg-1427	520	2	new	new	ADJ
fuelectenerg-1427	520	3	multiple	multiple	ADV
fuelectenerg-1427	520	4	-	-	PUNCT
fuelectenerg-1427	520	5	valued	value	VERB
fuelectenerg-1427	520	6	s	s	PROPN
fuelectenerg-1427	520	7	/	/	SYM
fuelectenerg-1427	520	8	d	d	NOUN
fuelectenerg-1427	520	9	trees	tree	NOUN
fuelectenerg-1427	520	10	and	and	CCONJ
fuelectenerg-1427	520	11	their	their	PRON
fuelectenerg-1427	520	12	canonical	canonical	ADJ
fuelectenerg-1427	520	13	galois	galois	PROPN
fuelectenerg-1427	520	14	sop	sop	NOUN
fuelectenerg-1427	520	15	forms	form	NOUN
fuelectenerg-1427	520	16	economical	economical	ADJ
fuelectenerg-1427	520	17	and	and	CCONJ
fuelectenerg-1427	520	18	highly	highly	ADV
fuelectenerg-1427	520	19	testable	testable	ADJ
fuelectenerg-1427	520	20	implementations	implementation	NOUN
fuelectenerg-1427	520	21	of	of	ADP
fuelectenerg-1427	520	22	boolean	boolean	ADJ
fuelectenerg-1427	520	23	functions	function	NOUN
fuelectenerg-1427	520	24	,	,	PUNCT
fuelectenerg-1427	520	25	based	base	VERB
fuelectenerg-1427	520	26	on	on	ADP
fuelectenerg-1427	520	27	reedmuller	reedmuller	NOUN
fuelectenerg-1427	520	28	(	(	PUNCT
fuelectenerg-1427	520	29	and	and	CCONJ
fuelectenerg-1427	520	30	-	-	PUNCT
fuelectenerg-1427	520	31	exor	exor	VERB
fuelectenerg-1427	520	32	)	)	PUNCT
fuelectenerg-1427	520	33	logic	logic	NOUN
fuelectenerg-1427	520	34	,	,	PUNCT
fuelectenerg-1427	520	35	play	play	VERB
fuelectenerg-1427	520	36	an	an	DET
fuelectenerg-1427	520	37	important	important	ADJ
fuelectenerg-1427	520	38	role	role	NOUN
fuelectenerg-1427	520	39	in	in	ADP
fuelectenerg-1427	520	40	logic	logic	ADJ
fuelectenerg-1427	520	41	synthesis	synthesis	NOUN
fuelectenerg-1427	520	42	and	and	CCONJ
fuelectenerg-1427	520	43	circuit	circuit	NOUN
fuelectenerg-1427	520	44	design	design	NOUN
fuelectenerg-1427	520	45	.	.	PUNCT
fuelectenerg-1427	521	1	the	the	DET
fuelectenerg-1427	521	2	and	and	CCONJ
fuelectenerg-1427	521	3	-	-	PUNCT
fuelectenerg-1427	521	4	exor	exor	PROPN
fuelectenerg-1427	521	5	circuits	circuit	NOUN
fuelectenerg-1427	521	6	include	include	VERB
fuelectenerg-1427	521	7	canonical	canonical	ADJ
fuelectenerg-1427	521	8	forms	form	NOUN
fuelectenerg-1427	521	9	which	which	PRON
fuelectenerg-1427	521	10	are	be	AUX
fuelectenerg-1427	521	11	expansions	expansion	NOUN
fuelectenerg-1427	521	12	that	that	PRON
fuelectenerg-1427	521	13	are	be	AUX
fuelectenerg-1427	521	14	unique	unique	ADJ
fuelectenerg-1427	521	15	representations	representation	NOUN
fuelectenerg-1427	521	16	of	of	ADP
fuelectenerg-1427	521	17	a	a	DET
fuelectenerg-1427	521	18	boolean	boolean	ADJ
fuelectenerg-1427	521	19	function	function	NOUN
fuelectenerg-1427	521	20	.	.	PUNCT
fuelectenerg-1427	522	1	several	several	ADJ
fuelectenerg-1427	522	2	large	large	ADJ
fuelectenerg-1427	522	3	families	family	NOUN
fuelectenerg-1427	522	4	of	of	ADP
fuelectenerg-1427	522	5	canonical	canonical	ADJ
fuelectenerg-1427	522	6	forms	form	NOUN
fuelectenerg-1427	522	7	:	:	PUNCT
fuelectenerg-1427	522	8	fixed	fix	VERB
fuelectenerg-1427	522	9	polarity	polarity	NOUN
fuelectenerg-1427	522	10	reed	reed	NOUN
fuelectenerg-1427	522	11	-	-	PUNCT
fuelectenerg-1427	522	12	muller	muller	NOUN
fuelectenerg-1427	522	13	(	(	PUNCT
fuelectenerg-1427	522	14	fprm	fprm	PROPN
fuelectenerg-1427	522	15	)	)	PUNCT
fuelectenerg-1427	522	16	forms	form	NOUN
fuelectenerg-1427	522	17	,	,	PUNCT
fuelectenerg-1427	522	18	generalized	generalized	ADJ
fuelectenerg-1427	522	19	reed	reed	NOUN
fuelectenerg-1427	522	20	-	-	PUNCT
fuelectenerg-1427	522	21	muller	muller	NOUN
fuelectenerg-1427	522	22	(	(	PUNCT
fuelectenerg-1427	522	23	grm	grm	NOUN
fuelectenerg-1427	522	24	)	)	PUNCT
fuelectenerg-1427	522	25	forms	form	NOUN
fuelectenerg-1427	522	26	,	,	PUNCT
fuelectenerg-1427	522	27	kronecker	kronecker	NOUN
fuelectenerg-1427	522	28	(	(	PUNCT
fuelectenerg-1427	522	29	kro	kro	PROPN
fuelectenerg-1427	522	30	)	)	PUNCT
fuelectenerg-1427	522	31	forms	form	NOUN
fuelectenerg-1427	522	32	and	and	CCONJ
fuelectenerg-1427	522	33	pseudo	pseudo	NOUN
fuelectenerg-1427	522	34	-	-	NOUN
fuelectenerg-1427	522	35	kronecker	kronecker	NOUN
fuelectenerg-1427	522	36	(	(	PUNCT
fuelectenerg-1427	522	37	psdkro	psdkro	NOUN
fuelectenerg-1427	522	38	)	)	PUNCT
fuelectenerg-1427	522	39	forms	form	NOUN
fuelectenerg-1427	522	40	,	,	PUNCT
fuelectenerg-1427	522	41	referred	refer	VERB
fuelectenerg-1427	522	42	to	to	ADP
fuelectenerg-1427	522	43	106	106	NUM
fuelectenerg-1427	522	44	54	54	NUM
fuelectenerg-1427	522	45	a.	a.	NOUN
fuelectenerg-1427	522	46	n.	n.	PROPN
fuelectenerg-1427	522	47	al	al	PROPN
fuelectenerg-1427	522	48	-	-	PUNCT
fuelectenerg-1427	522	49	rabadi	rabadi	VERB
fuelectenerg-1427	522	50	an	an	DET
fuelectenerg-1427	522	51	extended	extended	ADJ
fuelectenerg-1427	522	52	green	green	ADJ
fuelectenerg-1427	522	53	sasao	sasao	PROPN
fuelectenerg-1427	522	54	hierarchy	hierarchy	NOUN
fuelectenerg-1427	522	55	of	of	ADP
fuelectenerg-1427	522	56	canonical	canonical	ADJ
fuelectenerg-1427	522	57	ternary	ternary	ADJ
fuelectenerg-1427	522	58	galois	galois	NOUN
fuelectenerg-1427	522	59	forms	form	NOUN
fuelectenerg-1427	522	60	and	and	CCONJ
fuelectenerg-1427	522	61	universal	universal	ADJ
fuelectenerg-1427	522	62	logic	logic	NOUN
fuelectenerg-1427	522	63	modules	module	VERB
fuelectenerg-1427	522	64	55	55	NUM
fuelectenerg-1427	522	65	an	an	DET
fuelectenerg-1427	522	66	extended	extended	ADJ
fuelectenerg-1427	522	67	green	green	ADJ
fuelectenerg-1427	522	68	sasao	sasao	PROPN
fuelectenerg-1427	522	69	hierarchy	hierarchy	NOUN
fuelectenerg-1427	522	70	of	of	ADP
fuelectenerg-1427	522	71	canonical	canonical	ADJ
fuelectenerg-1427	522	72	ternary	ternary	ADJ
fuelectenerg-1427	522	73	galois	galois	NOUN
fuelectenerg-1427	522	74	forms	form	NOUN
fuelectenerg-1427	522	75	...	...	PUNCT
fuelectenerg-1427	522	76	as	as	ADP
fuelectenerg-1427	522	77	the	the	DET
fuelectenerg-1427	522	78	green	green	PROPN
fuelectenerg-1427	522	79	-	-	PUNCT
fuelectenerg-1427	522	80	sasao	sasao	PROPN
fuelectenerg-1427	522	81	hierarchy	hierarchy	NOUN
fuelectenerg-1427	522	82	,	,	PUNCT
fuelectenerg-1427	522	83	have	have	AUX
fuelectenerg-1427	522	84	been	be	AUX
fuelectenerg-1427	522	85	described	describe	VERB
fuelectenerg-1427	522	86	[	[	X
fuelectenerg-1427	522	87	1	1	NUM
fuelectenerg-1427	522	88	,	,	PUNCT
fuelectenerg-1427	522	89	10	10	NUM
fuelectenerg-1427	522	90	,	,	PUNCT
fuelectenerg-1427	522	91	17	17	NUM
fuelectenerg-1427	522	92	]	]	PUNCT
fuelectenerg-1427	522	93	.	.	PUNCT
fuelectenerg-1427	523	1	because	because	SCONJ
fuelectenerg-1427	523	2	canonical	canonical	ADJ
fuelectenerg-1427	523	3	families	family	NOUN
fuelectenerg-1427	523	4	have	have	VERB
fuelectenerg-1427	523	5	higher	high	ADJ
fuelectenerg-1427	523	6	testability	testability	NOUN
fuelectenerg-1427	523	7	and	and	CCONJ
fuelectenerg-1427	523	8	some	some	DET
fuelectenerg-1427	523	9	other	other	ADJ
fuelectenerg-1427	523	10	properties	property	NOUN
fuelectenerg-1427	523	11	desirable	desirable	ADJ
fuelectenerg-1427	523	12	for	for	ADP
fuelectenerg-1427	523	13	efficient	efficient	ADJ
fuelectenerg-1427	523	14	synthesis	synthesis	NOUN
fuelectenerg-1427	523	15	,	,	PUNCT
fuelectenerg-1427	523	16	especially	especially	ADV
fuelectenerg-1427	523	17	of	of	ADP
fuelectenerg-1427	523	18	some	some	DET
fuelectenerg-1427	523	19	classes	class	NOUN
fuelectenerg-1427	523	20	of	of	ADP
fuelectenerg-1427	523	21	functions	function	NOUN
fuelectenerg-1427	523	22	,	,	PUNCT
fuelectenerg-1427	523	23	they	they	PRON
fuelectenerg-1427	523	24	are	be	AUX
fuelectenerg-1427	523	25	widely	widely	ADV
fuelectenerg-1427	523	26	investigated	investigate	VERB
fuelectenerg-1427	523	27	.	.	PUNCT
fuelectenerg-1427	524	1	a	a	DET
fuelectenerg-1427	524	2	similar	similar	ADJ
fuelectenerg-1427	524	3	ternary	ternary	ADJ
fuelectenerg-1427	524	4	version	version	NOUN
fuelectenerg-1427	524	5	of	of	ADP
fuelectenerg-1427	524	6	the	the	DET
fuelectenerg-1427	524	7	binary	binary	ADJ
fuelectenerg-1427	524	8	green	green	PROPN
fuelectenerg-1427	524	9	-	-	PUNCT
fuelectenerg-1427	524	10	sasao	sasao	PROPN
fuelectenerg-1427	524	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	524	12	can	can	AUX
fuelectenerg-1427	524	13	be	be	AUX
fuelectenerg-1427	524	14	developed	develop	VERB
fuelectenerg-1427	524	15	,	,	PUNCT
fuelectenerg-1427	524	16	where	where	SCONJ
fuelectenerg-1427	524	17	this	this	DET
fuelectenerg-1427	524	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	524	19	can	can	AUX
fuelectenerg-1427	524	20	find	find	VERB
fuelectenerg-1427	524	21	applications	application	NOUN
fuelectenerg-1427	524	22	in	in	ADP
fuelectenerg-1427	524	23	minimizing	minimize	VERB
fuelectenerg-1427	524	24	galois	galois	PROPN
fuelectenerg-1427	524	25	field	field	NOUN
fuelectenerg-1427	524	26	sum	sum	NOUN
fuelectenerg-1427	524	27	-	-	PUNCT
fuelectenerg-1427	524	28	of	of	ADP
fuelectenerg-1427	524	29	-	-	PUNCT
fuelectenerg-1427	524	30	product	product	NOUN
fuelectenerg-1427	524	31	(	(	PUNCT
fuelectenerg-1427	524	32	gfsop	gfsop	NOUN
fuelectenerg-1427	524	33	)	)	PUNCT
fuelectenerg-1427	524	34	expressions	expression	NOUN
fuelectenerg-1427	524	35	which	which	PRON
fuelectenerg-1427	524	36	are	be	AUX
fuelectenerg-1427	524	37	expressions	expression	NOUN
fuelectenerg-1427	524	38	in	in	ADP
fuelectenerg-1427	524	39	the	the	DET
fuelectenerg-1427	524	40	sum	sum	NOUN
fuelectenerg-1427	524	41	-	-	PUNCT
fuelectenerg-1427	524	42	of	of	ADP
fuelectenerg-1427	524	43	-	-	PUNCT
fuelectenerg-1427	524	44	product	product	NOUN
fuelectenerg-1427	524	45	form	form	NOUN
fuelectenerg-1427	524	46	that	that	PRON
fuelectenerg-1427	524	47	uses	use	VERB
fuelectenerg-1427	524	48	the	the	DET
fuelectenerg-1427	524	49	additions	addition	NOUN
fuelectenerg-1427	524	50	and	and	CCONJ
fuelectenerg-1427	524	51	multiplications	multiplication	NOUN
fuelectenerg-1427	524	52	of	of	ADP
fuelectenerg-1427	524	53	arbitrary	arbitrary	ADJ
fuelectenerg-1427	524	54	radix	radix	PROPN
fuelectenerg-1427	524	55	galois	galois	PROPN
fuelectenerg-1427	524	56	field	field	NOUN
fuelectenerg-1427	524	57	,	,	PUNCT
fuelectenerg-1427	524	58	and	and	CCONJ
fuelectenerg-1427	524	59	can	can	AUX
fuelectenerg-1427	524	60	be	be	AUX
fuelectenerg-1427	524	61	used	use	VERB
fuelectenerg-1427	524	62	for	for	ADP
fuelectenerg-1427	524	63	the	the	DET
fuelectenerg-1427	524	64	creation	creation	NOUN
fuelectenerg-1427	524	65	of	of	ADP
fuelectenerg-1427	524	66	new	new	ADJ
fuelectenerg-1427	524	67	forms	form	NOUN
fuelectenerg-1427	524	68	,	,	PUNCT
fuelectenerg-1427	524	69	decision	decision	NOUN
fuelectenerg-1427	524	70	diagrams	diagram	NOUN
fuelectenerg-1427	524	71	and	and	CCONJ
fuelectenerg-1427	524	72	regular	regular	ADJ
fuelectenerg-1427	524	73	structures	structure	NOUN
fuelectenerg-1427	524	74	.	.	PUNCT
fuelectenerg-1427	525	1	the	the	DET
fuelectenerg-1427	525	2	current	current	ADJ
fuelectenerg-1427	525	3	state	state	NOUN
fuelectenerg-1427	525	4	-	-	PUNCT
fuelectenerg-1427	525	5	of	of	ADP
fuelectenerg-1427	525	6	-	-	PUNCT
fuelectenerg-1427	525	7	the	the	DET
fuelectenerg-1427	525	8	-	-	PUNCT
fuelectenerg-1427	525	9	art	art	NOUN
fuelectenerg-1427	525	10	minimizers	minimizer	NOUN
fuelectenerg-1427	525	11	of	of	ADP
fuelectenerg-1427	525	12	exclusive	exclusive	ADJ
fuelectenerg-1427	525	13	sum	sum	NOUN
fuelectenerg-1427	525	14	-	-	PUNCT
fuelectenerg-1427	525	15	of	of	ADP
fuelectenerg-1427	525	16	-	-	PUNCT
fuelectenerg-1427	525	17	product	product	NOUN
fuelectenerg-1427	525	18	(	(	PUNCT
fuelectenerg-1427	525	19	esop	esop	PROPN
fuelectenerg-1427	525	20	)	)	PUNCT
fuelectenerg-1427	525	21	expressions	expression	NOUN
fuelectenerg-1427	525	22	are	be	AUX
fuelectenerg-1427	525	23	based	base	VERB
fuelectenerg-1427	525	24	on	on	ADP
fuelectenerg-1427	525	25	heuristics	heuristic	NOUN
fuelectenerg-1427	525	26	and	and	CCONJ
fuelectenerg-1427	525	27	give	give	VERB
fuelectenerg-1427	525	28	the	the	DET
fuelectenerg-1427	525	29	exact	exact	ADJ
fuelectenerg-1427	525	30	solution	solution	NOUN
fuelectenerg-1427	525	31	only	only	ADV
fuelectenerg-1427	525	32	for	for	ADP
fuelectenerg-1427	525	33	functions	function	NOUN
fuelectenerg-1427	525	34	with	with	ADP
fuelectenerg-1427	525	35	a	a	DET
fuelectenerg-1427	525	36	small	small	ADJ
fuelectenerg-1427	525	37	number	number	NOUN
fuelectenerg-1427	525	38	of	of	ADP
fuelectenerg-1427	525	39	variables	variable	NOUN
fuelectenerg-1427	525	40	.	.	PUNCT
fuelectenerg-1427	526	1	for	for	ADP
fuelectenerg-1427	526	2	example	example	NOUN
fuelectenerg-1427	526	3	,	,	PUNCT
fuelectenerg-1427	526	4	a	a	DET
fuelectenerg-1427	526	5	formulation	formulation	NOUN
fuelectenerg-1427	526	6	for	for	ADP
fuelectenerg-1427	526	7	finding	find	VERB
fuelectenerg-1427	526	8	exact	exact	ADJ
fuelectenerg-1427	526	9	esop	esop	PROPN
fuelectenerg-1427	526	10	was	be	AUX
fuelectenerg-1427	526	11	given	give	VERB
fuelectenerg-1427	526	12	[	[	X
fuelectenerg-1427	526	13	11	11	NUM
fuelectenerg-1427	526	14	]	]	PUNCT
fuelectenerg-1427	526	15	,	,	PUNCT
fuelectenerg-1427	526	16	and	and	CCONJ
fuelectenerg-1427	526	17	an	an	DET
fuelectenerg-1427	526	18	algorithm	algorithm	NOUN
fuelectenerg-1427	526	19	to	to	PART
fuelectenerg-1427	526	20	derive	derive	VERB
fuelectenerg-1427	526	21	minimum	minimum	ADJ
fuelectenerg-1427	526	22	esop	esop	NOUN
fuelectenerg-1427	526	23	for	for	ADP
fuelectenerg-1427	526	24	6	6	NUM
fuelectenerg-1427	526	25	-	-	PUNCT
fuelectenerg-1427	526	26	variable	variable	ADJ
fuelectenerg-1427	526	27	function	function	NOUN
fuelectenerg-1427	526	28	was	be	AUX
fuelectenerg-1427	526	29	provided	provide	VERB
fuelectenerg-1427	526	30	[	[	X
fuelectenerg-1427	526	31	25	25	NUM
fuelectenerg-1427	526	32	]	]	PUNCT
fuelectenerg-1427	526	33	.	.	PUNCT
fuelectenerg-1427	527	1	because	because	SCONJ
fuelectenerg-1427	527	2	gfsop	gfsop	PROPN
fuelectenerg-1427	527	3	minimization	minimization	NOUN
fuelectenerg-1427	527	4	is	be	AUX
fuelectenerg-1427	527	5	even	even	ADV
fuelectenerg-1427	527	6	more	more	ADV
fuelectenerg-1427	527	7	difficult	difficult	ADJ
fuelectenerg-1427	527	8	,	,	PUNCT
fuelectenerg-1427	527	9	it	it	PRON
fuelectenerg-1427	527	10	is	be	AUX
fuelectenerg-1427	527	11	important	important	ADJ
fuelectenerg-1427	527	12	to	to	PART
fuelectenerg-1427	527	13	investigate	investigate	VERB
fuelectenerg-1427	527	14	the	the	DET
fuelectenerg-1427	527	15	structural	structural	ADJ
fuelectenerg-1427	527	16	properties	property	NOUN
fuelectenerg-1427	527	17	and	and	CCONJ
fuelectenerg-1427	527	18	the	the	DET
fuelectenerg-1427	527	19	counts	count	NOUN
fuelectenerg-1427	527	20	of	of	ADP
fuelectenerg-1427	527	21	their	their	PRON
fuelectenerg-1427	527	22	canonical	canonical	ADJ
fuelectenerg-1427	527	23	sub	sub	NOUN
fuelectenerg-1427	527	24	-	-	NOUN
fuelectenerg-1427	527	25	families	family	NOUN
fuelectenerg-1427	527	26	.	.	PUNCT
fuelectenerg-1427	528	1	two	two	NUM
fuelectenerg-1427	528	2	families	family	NOUN
fuelectenerg-1427	528	3	of	of	ADP
fuelectenerg-1427	528	4	binary	binary	ADJ
fuelectenerg-1427	528	5	canonical	canonical	ADJ
fuelectenerg-1427	528	6	reed	reed	NOUN
fuelectenerg-1427	528	7	-	-	PUNCT
fuelectenerg-1427	528	8	muller	muller	NOUN
fuelectenerg-1427	528	9	forms	form	NOUN
fuelectenerg-1427	528	10	,	,	PUNCT
fuelectenerg-1427	528	11	called	call	VERB
fuelectenerg-1427	528	12	inclusive	inclusive	ADJ
fuelectenerg-1427	528	13	forms	form	NOUN
fuelectenerg-1427	528	14	(	(	PUNCT
fuelectenerg-1427	528	15	ifs	ifs	PROPN
fuelectenerg-1427	528	16	)	)	PUNCT
fuelectenerg-1427	528	17	and	and	CCONJ
fuelectenerg-1427	528	18	generalized	generalized	ADJ
fuelectenerg-1427	528	19	inclusive	inclusive	ADJ
fuelectenerg-1427	528	20	forms	form	NOUN
fuelectenerg-1427	528	21	(	(	PUNCT
fuelectenerg-1427	528	22	gifs	gifs	PROPN
fuelectenerg-1427	528	23	)	)	PUNCT
fuelectenerg-1427	528	24	were	be	AUX
fuelectenerg-1427	528	25	presented	present	VERB
fuelectenerg-1427	528	26	[	[	X
fuelectenerg-1427	528	27	1	1	NUM
fuelectenerg-1427	528	28	]	]	PUNCT
fuelectenerg-1427	528	29	,	,	PUNCT
fuelectenerg-1427	528	30	where	where	SCONJ
fuelectenerg-1427	528	31	the	the	DET
fuelectenerg-1427	528	32	second	second	ADJ
fuelectenerg-1427	528	33	family	family	NOUN
fuelectenerg-1427	528	34	was	be	AUX
fuelectenerg-1427	528	35	the	the	DET
fuelectenerg-1427	528	36	first	first	ADJ
fuelectenerg-1427	528	37	to	to	PART
fuelectenerg-1427	528	38	include	include	VERB
fuelectenerg-1427	528	39	all	all	DET
fuelectenerg-1427	528	40	minimum	minimum	ADJ
fuelectenerg-1427	528	41	esops	esop	NOUN
fuelectenerg-1427	528	42	(	(	PUNCT
fuelectenerg-1427	528	43	binary	binary	ADJ
fuelectenerg-1427	528	44	gfsops	gfsop	NOUN
fuelectenerg-1427	528	45	)	)	PUNCT
fuelectenerg-1427	528	46	.	.	PUNCT
fuelectenerg-1427	529	1	in	in	ADP
fuelectenerg-1427	529	2	these	these	DET
fuelectenerg-1427	529	3	forms	form	NOUN
fuelectenerg-1427	529	4	,	,	PUNCT
fuelectenerg-1427	529	5	if	if	SCONJ
fuelectenerg-1427	529	6	is	be	AUX
fuelectenerg-1427	529	7	the	the	DET
fuelectenerg-1427	529	8	form	form	NOUN
fuelectenerg-1427	529	9	generated	generate	VERB
fuelectenerg-1427	529	10	by	by	ADP
fuelectenerg-1427	529	11	the	the	DET
fuelectenerg-1427	529	12	corresponding	correspond	VERB
fuelectenerg-1427	529	13	s	s	PROPN
fuelectenerg-1427	529	14	/	/	SYM
fuelectenerg-1427	529	15	d	d	NOUN
fuelectenerg-1427	529	16	tree	tree	NOUN
fuelectenerg-1427	529	17	and	and	CCONJ
fuelectenerg-1427	529	18	gif	gif	NOUN
fuelectenerg-1427	529	19	is	be	AUX
fuelectenerg-1427	529	20	the	the	DET
fuelectenerg-1427	529	21	form	form	NOUN
fuelectenerg-1427	529	22	which	which	PRON
fuelectenerg-1427	529	23	is	be	AUX
fuelectenerg-1427	529	24	the	the	DET
fuelectenerg-1427	529	25	union	union	NOUN
fuelectenerg-1427	529	26	of	of	ADP
fuelectenerg-1427	529	27	the	the	DET
fuelectenerg-1427	529	28	various	various	ADJ
fuelectenerg-1427	529	29	variable	variable	NOUN
fuelectenerg-1427	529	30	-	-	PUNCT
fuelectenerg-1427	529	31	based	base	VERB
fuelectenerg-1427	529	32	ordering	order	VERB
fuelectenerg-1427	529	33	ifs	ifs	PROPN
fuelectenerg-1427	529	34	(	(	PUNCT
fuelectenerg-1427	529	35	cf	cf	NOUN
fuelectenerg-1427	529	36	.	.	PUNCT
fuelectenerg-1427	530	1	definitions	definition	NOUN
fuelectenerg-1427	530	2	and	and	CCONJ
fuelectenerg-1427	530	3	theorems	theorem	NOUN
fuelectenerg-1427	530	4	of	of	ADP
fuelectenerg-1427	530	5	these	these	DET
fuelectenerg-1427	530	6	forms	form	NOUN
fuelectenerg-1427	530	7	in	in	ADP
fuelectenerg-1427	530	8	the	the	DET
fuelectenerg-1427	530	9	next	next	ADJ
fuelectenerg-1427	530	10	subsection	subsection	NOUN
fuelectenerg-1427	530	11	)	)	PUNCT
fuelectenerg-1427	530	12	.	.	PUNCT
fuelectenerg-1427	531	1	in	in	ADP
fuelectenerg-1427	531	2	this	this	DET
fuelectenerg-1427	531	3	paper	paper	NOUN
fuelectenerg-1427	531	4	,	,	PUNCT
fuelectenerg-1427	531	5	we	we	PRON
fuelectenerg-1427	531	6	propose	propose	VERB
fuelectenerg-1427	531	7	,	,	PUNCT
fuelectenerg-1427	531	8	as	as	SCONJ
fuelectenerg-1427	531	9	analogous	analogous	ADJ
fuelectenerg-1427	531	10	to	to	ADP
fuelectenerg-1427	531	11	the	the	DET
fuelectenerg-1427	531	12	binary	binary	ADJ
fuelectenerg-1427	531	13	case	case	NOUN
fuelectenerg-1427	531	14	,	,	PUNCT
fuelectenerg-1427	531	15	two	two	NUM
fuelectenerg-1427	531	16	general	general	ADJ
fuelectenerg-1427	531	17	families	family	NOUN
fuelectenerg-1427	531	18	of	of	ADP
fuelectenerg-1427	531	19	canonical	canonical	ADJ
fuelectenerg-1427	531	20	ternary	ternary	ADJ
fuelectenerg-1427	531	21	reed	reed	NOUN
fuelectenerg-1427	531	22	-	-	PUNCT
fuelectenerg-1427	531	23	muller	muller	NOUN
fuelectenerg-1427	531	24	forms	form	NOUN
fuelectenerg-1427	531	25	,	,	PUNCT
fuelectenerg-1427	531	26	called	call	VERB
fuelectenerg-1427	531	27	ternary	ternary	ADJ
fuelectenerg-1427	531	28	inclusive	inclusive	ADJ
fuelectenerg-1427	531	29	forms	form	NOUN
fuelectenerg-1427	531	30	(	(	PUNCT
fuelectenerg-1427	531	31	tifs	tifs	PROPN
fuelectenerg-1427	531	32	)	)	PUNCT
fuelectenerg-1427	531	33	and	and	CCONJ
fuelectenerg-1427	531	34	their	their	PRON
fuelectenerg-1427	531	35	generalization	generalization	NOUN
fuelectenerg-1427	531	36	of	of	ADP
fuelectenerg-1427	531	37	ternary	ternary	ADJ
fuelectenerg-1427	531	38	generalized	generalize	VERB
fuelectenerg-1427	531	39	inclusive	inclusive	ADJ
fuelectenerg-1427	531	40	forms	form	NOUN
fuelectenerg-1427	531	41	(	(	PUNCT
fuelectenerg-1427	531	42	tgifs	tgif	NOUN
fuelectenerg-1427	531	43	)	)	PUNCT
fuelectenerg-1427	531	44	,	,	PUNCT
fuelectenerg-1427	531	45	where	where	SCONJ
fuelectenerg-1427	531	46	gfsop	gfsop	NOUN
fuelectenerg-1427	531	47	minimizer	minimizer	NOUN
fuelectenerg-1427	531	48	based	base	VERB
fuelectenerg-1427	531	49	on	on	ADP
fuelectenerg-1427	531	50	these	these	DET
fuelectenerg-1427	531	51	new	new	ADJ
fuelectenerg-1427	531	52	forms	form	NOUN
fuelectenerg-1427	531	53	can	can	AUX
fuelectenerg-1427	531	54	be	be	AUX
fuelectenerg-1427	531	55	used	use	VERB
fuelectenerg-1427	531	56	to	to	PART
fuelectenerg-1427	531	57	minimize	minimize	VERB
fuelectenerg-1427	531	58	functional	functional	ADJ
fuelectenerg-1427	531	59	gfsop	gfsop	NOUN
fuelectenerg-1427	531	60	expressions	expression	NOUN
fuelectenerg-1427	531	61	and	and	CCONJ
fuelectenerg-1427	531	62	the	the	DET
fuelectenerg-1427	531	63	second	second	ADJ
fuelectenerg-1427	531	64	family	family	NOUN
fuelectenerg-1427	531	65	of	of	ADP
fuelectenerg-1427	531	66	tgifs	tgif	NOUN
fuelectenerg-1427	531	67	includes	include	VERB
fuelectenerg-1427	531	68	minimum	minimum	ADJ
fuelectenerg-1427	531	69	gfsops	gfsop	NOUN
fuelectenerg-1427	531	70	over	over	ADP
fuelectenerg-1427	531	71	ternary	ternary	ADJ
fuelectenerg-1427	531	72	galois	galois	PROPN
fuelectenerg-1427	531	73	field	field	NOUN
fuelectenerg-1427	531	74	.	.	PUNCT
fuelectenerg-1427	532	1	one	one	NUM
fuelectenerg-1427	532	2	of	of	ADP
fuelectenerg-1427	532	3	the	the	DET
fuelectenerg-1427	532	4	motivations	motivation	NOUN
fuelectenerg-1427	532	5	for	for	ADP
fuelectenerg-1427	532	6	this	this	DET
fuelectenerg-1427	532	7	work	work	NOUN
fuelectenerg-1427	532	8	is	be	AUX
fuelectenerg-1427	532	9	the	the	DET
fuelectenerg-1427	532	10	application	application	NOUN
fuelectenerg-1427	532	11	of	of	ADP
fuelectenerg-1427	532	12	these	these	DET
fuelectenerg-1427	532	13	tifs	tif	NOUN
fuelectenerg-1427	532	14	and	and	CCONJ
fuelectenerg-1427	532	15	tgifs	tgif	NOUN
fuelectenerg-1427	532	16	to	to	PART
fuelectenerg-1427	532	17	find	find	VERB
fuelectenerg-1427	532	18	minimum	minimum	ADJ
fuelectenerg-1427	532	19	gfsop	gfsop	NOUN
fuelectenerg-1427	532	20	for	for	ADP
fuelectenerg-1427	532	21	multiple	multiple	ADV
fuelectenerg-1427	532	22	-	-	PUNCT
fuelectenerg-1427	532	23	valued	value	VERB
fuelectenerg-1427	532	24	inputs	input	NOUN
fuelectenerg-1427	532	25	multiple	multiple	ADV
fuelectenerg-1427	532	26	-	-	PUNCT
fuelectenerg-1427	532	27	valued	value	VERB
fuelectenerg-1427	532	28	outputs	output	NOUN
fuelectenerg-1427	532	29	within	within	ADP
fuelectenerg-1427	532	30	logic	logic	ADJ
fuelectenerg-1427	532	31	synthesis	synthesis	NOUN
fuelectenerg-1427	532	32	,	,	PUNCT
fuelectenerg-1427	532	33	where	where	SCONJ
fuelectenerg-1427	532	34	the	the	DET
fuelectenerg-1427	532	35	corresponding	correspond	VERB
fuelectenerg-1427	532	36	s	s	PROPN
fuelectenerg-1427	532	37	/	/	SYM
fuelectenerg-1427	532	38	d	d	NOUN
fuelectenerg-1427	532	39	trees	tree	NOUN
fuelectenerg-1427	532	40	provide	provide	VERB
fuelectenerg-1427	532	41	more	more	ADJ
fuelectenerg-1427	532	42	general	general	ADJ
fuelectenerg-1427	532	43	polarity	polarity	NOUN
fuelectenerg-1427	532	44	that	that	PRON
fuelectenerg-1427	532	45	contains	contain	VERB
fuelectenerg-1427	532	46	grm	grm	NOUN
fuelectenerg-1427	532	47	forms	form	NOUN
fuelectenerg-1427	532	48	as	as	ADP
fuelectenerg-1427	532	49	a	a	DET
fuelectenerg-1427	532	50	special	special	ADJ
fuelectenerg-1427	532	51	case	case	NOUN
fuelectenerg-1427	532	52	.	.	PUNCT
fuelectenerg-1427	533	1	2.1	2.1	NUM
fuelectenerg-1427	533	2	s	s	NOUN
fuelectenerg-1427	533	3	/	/	SYM
fuelectenerg-1427	533	4	d	d	NOUN
fuelectenerg-1427	533	5	trees	tree	NOUN
fuelectenerg-1427	533	6	and	and	CCONJ
fuelectenerg-1427	533	7	their	their	PRON
fuelectenerg-1427	533	8	inclusive	inclusive	ADJ
fuelectenerg-1427	533	9	forms	form	NOUN
fuelectenerg-1427	533	10	and	and	CCONJ
fuelectenerg-1427	533	11	generalized	generalized	ADJ
fuelectenerg-1427	533	12	inclusive	inclusive	ADJ
fuelectenerg-1427	533	13	forms	form	NOUN
fuelectenerg-1427	533	14	two	two	NUM
fuelectenerg-1427	533	15	general	general	ADJ
fuelectenerg-1427	533	16	families	family	NOUN
fuelectenerg-1427	533	17	based	base	VERB
fuelectenerg-1427	533	18	on	on	ADP
fuelectenerg-1427	533	19	the	the	DET
fuelectenerg-1427	533	20	shannon	shannon	PROPN
fuelectenerg-1427	533	21	expansion	expansion	NOUN
fuelectenerg-1427	533	22	and	and	CCONJ
fuelectenerg-1427	533	23	the	the	DET
fuelectenerg-1427	533	24	generalized	generalized	ADJ
fuelectenerg-1427	533	25	davio	davio	NOUN
fuelectenerg-1427	533	26	expansion	expansion	NOUN
fuelectenerg-1427	533	27	which	which	PRON
fuelectenerg-1427	533	28	are	be	AUX
fuelectenerg-1427	533	29	produced	produce	VERB
fuelectenerg-1427	533	30	using	use	VERB
fuelectenerg-1427	533	31	the	the	DET
fuelectenerg-1427	533	32	corresponding	correspond	VERB
fuelectenerg-1427	533	33	s	s	PROPN
fuelectenerg-1427	533	34	/	/	SYM
fuelectenerg-1427	533	35	d	d	NOUN
fuelectenerg-1427	533	36	trees	tree	NOUN
fuelectenerg-1427	533	37	are	be	AUX
fuelectenerg-1427	533	38	presented	present	VERB
fuelectenerg-1427	533	39	in	in	ADP
fuelectenerg-1427	533	40	this	this	DET
fuelectenerg-1427	533	41	subsection	subsection	NOUN
fuelectenerg-1427	533	42	.	.	PUNCT
fuelectenerg-1427	534	1	these	these	DET
fuelectenerg-1427	534	2	families	family	NOUN
fuelectenerg-1427	534	3	are	be	AUX
fuelectenerg-1427	534	4	called	call	VERB
fuelectenerg-1427	534	5	the	the	DET
fuelectenerg-1427	534	6	inclusive	inclusive	ADJ
fuelectenerg-1427	534	7	forms	form	NOUN
fuelectenerg-1427	534	8	(	(	PUNCT
fuelectenerg-1427	534	9	ifs	ifs	PROPN
fuelectenerg-1427	534	10	)	)	PUNCT
fuelectenerg-1427	534	11	and	and	CCONJ
fuelectenerg-1427	534	12	the	the	DET
fuelectenerg-1427	534	13	generalized	generalized	ADJ
fuelectenerg-1427	534	14	inclusive	inclusive	ADJ
fuelectenerg-1427	534	15	forms	form	NOUN
fuelectenerg-1427	534	16	(	(	PUNCT
fuelectenerg-1427	534	17	gifs	gifs	PROPN
fuelectenerg-1427	534	18	)	)	PUNCT
fuelectenerg-1427	534	19	.	.	PUNCT
fuelectenerg-1427	535	1	the	the	DET
fuelectenerg-1427	535	2	corresponding	corresponding	ADJ
fuelectenerg-1427	535	3	expansions	expansion	NOUN
fuelectenerg-1427	535	4	over	over	ADP
fuelectenerg-1427	535	5	gf(2	gf(2	PROPN
fuelectenerg-1427	535	6	)	)	PUNCT
fuelectenerg-1427	535	7	are	be	AUX
fuelectenerg-1427	535	8	shown	show	VERB
fuelectenerg-1427	535	9	in	in	ADP
fuelectenerg-1427	535	10	figure	figure	NOUN
fuelectenerg-1427	535	11	3	3	NUM
fuelectenerg-1427	535	12	,	,	PUNCT
fuelectenerg-1427	535	13	where	where	SCONJ
fuelectenerg-1427	535	14	figure	figure	NOUN
fuelectenerg-1427	535	15	3(d	3(d	NOUN
fuelectenerg-1427	535	16	)	)	PUNCT
fuelectenerg-1427	535	17	shows	show	VERB
fuelectenerg-1427	535	18	the	the	DET
fuelectenerg-1427	535	19	new	new	ADJ
fuelectenerg-1427	535	20	node	node	NOUN
fuelectenerg-1427	535	21	which	which	PRON
fuelectenerg-1427	535	22	is	be	AUX
fuelectenerg-1427	535	23	based	base	VERB
fuelectenerg-1427	535	24	on	on	ADP
fuelectenerg-1427	535	25	binary	binary	ADJ
fuelectenerg-1427	535	26	davio	davio	NOUN
fuelectenerg-1427	535	27	expansions	expansion	NOUN
fuelectenerg-1427	535	28	called	call	VERB
fuelectenerg-1427	535	29	the	the	DET
fuelectenerg-1427	535	30	generalized	generalized	ADJ
fuelectenerg-1427	535	31	davio	davio	NOUN
fuelectenerg-1427	535	32	(	(	PUNCT
fuelectenerg-1427	535	33	d	d	NOUN
fuelectenerg-1427	535	34	)	)	PUNCT
fuelectenerg-1427	535	35	expansion	expansion	NOUN
fuelectenerg-1427	535	36	(	(	PUNCT
fuelectenerg-1427	535	37	cf	cf	NOUN
fuelectenerg-1427	535	38	.	.	PUNCT
fuelectenerg-1427	536	1	equation	equation	NOUN
fuelectenerg-1427	536	2	(	(	PUNCT
fuelectenerg-1427	536	3	28	28	NUM
fuelectenerg-1427	536	4	)	)	PUNCT
fuelectenerg-1427	536	5	for	for	ADP
fuelectenerg-1427	536	6	the	the	DET
fuelectenerg-1427	536	7	more	more	ADV
fuelectenerg-1427	536	8	general	general	ADJ
fuelectenerg-1427	536	9	ternary	ternary	ADJ
fuelectenerg-1427	536	10	case	case	NOUN
fuelectenerg-1427	536	11	)	)	PUNCT
fuelectenerg-1427	536	12	that	that	PRON
fuelectenerg-1427	536	13	generates	generate	VERB
fuelectenerg-1427	536	14	the	the	DET
fuelectenerg-1427	536	15	negative	negative	ADJ
fuelectenerg-1427	536	16	and	and	CCONJ
fuelectenerg-1427	536	17	positive	positive	ADJ
fuelectenerg-1427	536	18	davio	davio	NOUN
fuelectenerg-1427	536	19	expansions	expansion	NOUN
fuelectenerg-1427	536	20	as	as	ADP
fuelectenerg-1427	536	21	special	special	ADJ
fuelectenerg-1427	536	22	cases	case	NOUN
fuelectenerg-1427	536	23	.	.	PUNCT
fuelectenerg-1427	537	1	the	the	DET
fuelectenerg-1427	537	2	s	s	PROPN
fuelectenerg-1427	537	3	/	/	SYM
fuelectenerg-1427	537	4	d	d	NOUN
fuelectenerg-1427	537	5	trees	tree	NOUN
fuelectenerg-1427	537	6	for	for	ADP
fuelectenerg-1427	537	7	ifs	ifs	PROPN
fuelectenerg-1427	537	8	of	of	ADP
fuelectenerg-1427	537	9	two	two	NUM
fuelectenerg-1427	537	10	variables	variable	NOUN
fuelectenerg-1427	537	11	can	can	AUX
fuelectenerg-1427	537	12	be	be	AUX
fuelectenerg-1427	537	13	generated	generate	VERB
fuelectenerg-1427	537	14	for	for	ADP
fuelectenerg-1427	537	15	variable	variable	ADJ
fuelectenerg-1427	537	16	order	order	NOUN
fuelectenerg-1427	537	17	{	{	PUNCT
fuelectenerg-1427	537	18	a	a	DET
fuelectenerg-1427	537	19	,	,	PUNCT
fuelectenerg-1427	537	20	b	b	NOUN
fuelectenerg-1427	537	21	}	}	PUNCT
fuelectenerg-1427	537	22	and	and	CCONJ
fuelectenerg-1427	537	23	for	for	ADP
fuelectenerg-1427	537	24	variable	variable	ADJ
fuelectenerg-1427	537	25	order	order	NOUN
fuelectenerg-1427	537	26	{	{	PUNCT
fuelectenerg-1427	537	27	b	b	NOUN
fuelectenerg-1427	537	28	,	,	PUNCT
fuelectenerg-1427	537	29	a	a	PRON
fuelectenerg-1427	537	30	}	}	PUNCT
fuelectenerg-1427	537	31	as	as	ADV
fuelectenerg-1427	537	32	well	well	ADV
fuelectenerg-1427	537	33	.	.	PUNCT
fuelectenerg-1427	538	1	the	the	DET
fuelectenerg-1427	538	2	set	set	NOUN
fuelectenerg-1427	538	3	of	of	ADP
fuelectenerg-1427	538	4	gifs	gifs	PROPN
fuelectenerg-1427	538	5	for	for	ADP
fuelectenerg-1427	538	6	two	two	NUM
fuelectenerg-1427	538	7	variables	variable	NOUN
fuelectenerg-1427	538	8	is	be	AUX
fuelectenerg-1427	538	9	the	the	DET
fuelectenerg-1427	538	10	union	union	NOUN
fuelectenerg-1427	538	11	of	of	ADP
fuelectenerg-1427	538	12	these	these	DET
fuelectenerg-1427	538	13	two	two	NUM
fuelectenerg-1427	538	14	order	order	NOUN
fuelectenerg-1427	538	15	-	-	PUNCT
fuelectenerg-1427	538	16	based	base	VERB
fuelectenerg-1427	538	17	ifs	ifs	PROPN
fuelectenerg-1427	538	18	,	,	PUNCT
fuelectenerg-1427	538	19	where	where	SCONJ
fuelectenerg-1427	538	20	the	the	DET
fuelectenerg-1427	538	21	total	total	ADJ
fuelectenerg-1427	538	22	number	number	NOUN
fuelectenerg-1427	538	23	of	of	ADP
fuelectenerg-1427	538	24	the	the	DET
fuelectenerg-1427	538	25	resulting	result	VERB
fuelectenerg-1427	538	26	gifs	gifs	NOUN
fuelectenerg-1427	538	27	is	be	AUX
fuelectenerg-1427	538	28	equal	equal	ADJ
fuelectenerg-1427	538	29	to	to	ADP
fuelectenerg-1427	538	30	:	:	PUNCT
fuelectenerg-1427	538	31	#	#	SYM
fuelectenerg-1427	538	32	gif	gif	NOUN
fuelectenerg-1427	538	33	=	=	NOUN
fuelectenerg-1427	538	34	2	2	NUM
fuelectenerg-1427	538	35	·	·	PUNCT
fuelectenerg-1427	538	36	(	(	PUNCT
fuelectenerg-1427	538	37	#	#	SYM
fuelectenerg-1427	538	38	ifa	ifa	PROPN
fuelectenerg-1427	538	39	,	,	PUNCT
fuelectenerg-1427	538	40	b)−#(ifa	b)−#(ifa	PROPN
fuelectenerg-1427	538	41	,	,	PUNCT
fuelectenerg-1427	538	42	b	b	PROPN
fuelectenerg-1427	538	43	⋂	⋂	PROPN
fuelectenerg-1427	538	44	ifb	ifb	PROPN
fuelectenerg-1427	538	45	,	,	PUNCT
fuelectenerg-1427	538	46	a	a	PRON
fuelectenerg-1427	538	47	)	)	PUNCT
fuelectenerg-1427	538	48	.	.	PUNCT
fuelectenerg-1427	539	1	(	(	PUNCT
fuelectenerg-1427	539	2	27	27	NUM
fuelectenerg-1427	539	3	)	)	PUNCT
fuelectenerg-1427	539	4	the	the	DET
fuelectenerg-1427	539	5	galois	galois	PROPN
fuelectenerg-1427	539	6	-	-	PUNCT
fuelectenerg-1427	539	7	based	base	VERB
fuelectenerg-1427	539	8	shannon	shannon	NOUN
fuelectenerg-1427	539	9	and	and	CCONJ
fuelectenerg-1427	539	10	davio	davio	NOUN
fuelectenerg-1427	539	11	ternary	ternary	ADJ
fuelectenerg-1427	539	12	expansions	expansion	NOUN
fuelectenerg-1427	539	13	(	(	PUNCT
fuelectenerg-1427	539	14	i.e.	i.e.	X
fuelectenerg-1427	539	15	,	,	PUNCT
fuelectenerg-1427	539	16	flattened	flatten	VERB
fuelectenerg-1427	539	17	forms	form	NOUN
fuelectenerg-1427	539	18	)	)	PUNCT
fuelectenerg-1427	539	19	can	can	AUX
fuelectenerg-1427	539	20	be	be	AUX
fuelectenerg-1427	539	21	represented	represent	VERB
fuelectenerg-1427	539	22	in	in	ADP
fuelectenerg-1427	539	23	ternary	ternary	ADJ
fuelectenerg-1427	539	24	dts	dts	NOUN
fuelectenerg-1427	539	25	(	(	PUNCT
fuelectenerg-1427	539	26	tdts	tdts	ADJ
fuelectenerg-1427	539	27	)	)	PUNCT
fuelectenerg-1427	539	28	and	and	CCONJ
fuelectenerg-1427	539	29	the	the	DET
fuelectenerg-1427	539	30	corresponding	corresponding	ADJ
fuelectenerg-1427	539	31	varieties	variety	NOUN
fuelectenerg-1427	539	32	of	of	ADP
fuelectenerg-1427	539	33	ternary	ternary	ADJ
fuelectenerg-1427	539	34	dds	dds	PROPN
fuelectenerg-1427	539	35	(	(	PUNCT
fuelectenerg-1427	539	36	tdds	tdds	PROPN
fuelectenerg-1427	539	37	)	)	PUNCT
fuelectenerg-1427	539	38	according	accord	VERB
fuelectenerg-1427	539	39	to	to	ADP
fuelectenerg-1427	539	40	the	the	DET
fuelectenerg-1427	539	41	corresponding	corresponding	ADJ
fuelectenerg-1427	539	42	reduction	reduction	NOUN
fuelectenerg-1427	539	43	rules	rule	NOUN
fuelectenerg-1427	539	44	that	that	PRON
fuelectenerg-1427	539	45	are	be	AUX
fuelectenerg-1427	539	46	used	use	VERB
fuelectenerg-1427	539	47	[	[	PUNCT
fuelectenerg-1427	539	48	1	1	NUM
fuelectenerg-1427	539	49	,	,	PUNCT
fuelectenerg-1427	539	50	17	17	NUM
fuelectenerg-1427	539	51	]	]	PUNCT
fuelectenerg-1427	539	52	.	.	PUNCT
fuelectenerg-1427	540	1	for	for	ADP
fuelectenerg-1427	540	2	one	one	NUM
fuelectenerg-1427	540	3	107	107	NUM
fuelectenerg-1427	540	4	an	an	DET
fuelectenerg-1427	540	5	extended	extended	ADJ
fuelectenerg-1427	540	6	green	green	ADJ
fuelectenerg-1427	540	7	sasao	sasao	PROPN
fuelectenerg-1427	540	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	540	9	of	of	ADP
fuelectenerg-1427	540	10	canonical	canonical	ADJ
fuelectenerg-1427	540	11	ternary	ternary	ADJ
fuelectenerg-1427	540	12	galois	galois	NOUN
fuelectenerg-1427	540	13	forms	form	NOUN
fuelectenerg-1427	540	14	...	...	PUNCT
fuelectenerg-1427	540	15	as	as	ADP
fuelectenerg-1427	540	16	the	the	DET
fuelectenerg-1427	540	17	green	green	PROPN
fuelectenerg-1427	540	18	-	-	PUNCT
fuelectenerg-1427	540	19	sasao	sasao	PROPN
fuelectenerg-1427	540	20	hierarchy	hierarchy	NOUN
fuelectenerg-1427	540	21	,	,	PUNCT
fuelectenerg-1427	540	22	have	have	AUX
fuelectenerg-1427	540	23	been	be	AUX
fuelectenerg-1427	540	24	described	describe	VERB
fuelectenerg-1427	540	25	[	[	X
fuelectenerg-1427	540	26	1	1	NUM
fuelectenerg-1427	540	27	,	,	PUNCT
fuelectenerg-1427	540	28	10	10	NUM
fuelectenerg-1427	540	29	,	,	PUNCT
fuelectenerg-1427	540	30	17	17	NUM
fuelectenerg-1427	540	31	]	]	PUNCT
fuelectenerg-1427	540	32	.	.	PUNCT
fuelectenerg-1427	541	1	because	because	SCONJ
fuelectenerg-1427	541	2	canonical	canonical	ADJ
fuelectenerg-1427	541	3	families	family	NOUN
fuelectenerg-1427	541	4	have	have	VERB
fuelectenerg-1427	541	5	higher	high	ADJ
fuelectenerg-1427	541	6	testability	testability	NOUN
fuelectenerg-1427	541	7	and	and	CCONJ
fuelectenerg-1427	541	8	some	some	DET
fuelectenerg-1427	541	9	other	other	ADJ
fuelectenerg-1427	541	10	properties	property	NOUN
fuelectenerg-1427	541	11	desirable	desirable	ADJ
fuelectenerg-1427	541	12	for	for	ADP
fuelectenerg-1427	541	13	efficient	efficient	ADJ
fuelectenerg-1427	541	14	synthesis	synthesis	NOUN
fuelectenerg-1427	541	15	,	,	PUNCT
fuelectenerg-1427	541	16	especially	especially	ADV
fuelectenerg-1427	541	17	of	of	ADP
fuelectenerg-1427	541	18	some	some	DET
fuelectenerg-1427	541	19	classes	class	NOUN
fuelectenerg-1427	541	20	of	of	ADP
fuelectenerg-1427	541	21	functions	function	NOUN
fuelectenerg-1427	541	22	,	,	PUNCT
fuelectenerg-1427	541	23	they	they	PRON
fuelectenerg-1427	541	24	are	be	AUX
fuelectenerg-1427	541	25	widely	widely	ADV
fuelectenerg-1427	541	26	investigated	investigate	VERB
fuelectenerg-1427	541	27	.	.	PUNCT
fuelectenerg-1427	542	1	a	a	DET
fuelectenerg-1427	542	2	similar	similar	ADJ
fuelectenerg-1427	542	3	ternary	ternary	ADJ
fuelectenerg-1427	542	4	version	version	NOUN
fuelectenerg-1427	542	5	of	of	ADP
fuelectenerg-1427	542	6	the	the	DET
fuelectenerg-1427	542	7	binary	binary	ADJ
fuelectenerg-1427	542	8	green	green	PROPN
fuelectenerg-1427	542	9	-	-	PUNCT
fuelectenerg-1427	542	10	sasao	sasao	PROPN
fuelectenerg-1427	542	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	542	12	can	can	AUX
fuelectenerg-1427	542	13	be	be	AUX
fuelectenerg-1427	542	14	developed	develop	VERB
fuelectenerg-1427	542	15	,	,	PUNCT
fuelectenerg-1427	542	16	where	where	SCONJ
fuelectenerg-1427	542	17	this	this	DET
fuelectenerg-1427	542	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	542	19	can	can	AUX
fuelectenerg-1427	542	20	find	find	VERB
fuelectenerg-1427	542	21	applications	application	NOUN
fuelectenerg-1427	542	22	in	in	ADP
fuelectenerg-1427	542	23	minimizing	minimize	VERB
fuelectenerg-1427	542	24	galois	galois	PROPN
fuelectenerg-1427	542	25	field	field	NOUN
fuelectenerg-1427	542	26	sum	sum	NOUN
fuelectenerg-1427	542	27	-	-	PUNCT
fuelectenerg-1427	542	28	of	of	ADP
fuelectenerg-1427	542	29	-	-	PUNCT
fuelectenerg-1427	542	30	product	product	NOUN
fuelectenerg-1427	542	31	(	(	PUNCT
fuelectenerg-1427	542	32	gfsop	gfsop	NOUN
fuelectenerg-1427	542	33	)	)	PUNCT
fuelectenerg-1427	542	34	expressions	expression	NOUN
fuelectenerg-1427	542	35	which	which	PRON
fuelectenerg-1427	542	36	are	be	AUX
fuelectenerg-1427	542	37	expressions	expression	NOUN
fuelectenerg-1427	542	38	in	in	ADP
fuelectenerg-1427	542	39	the	the	DET
fuelectenerg-1427	542	40	sum	sum	NOUN
fuelectenerg-1427	542	41	-	-	PUNCT
fuelectenerg-1427	542	42	of	of	ADP
fuelectenerg-1427	542	43	-	-	PUNCT
fuelectenerg-1427	542	44	product	product	NOUN
fuelectenerg-1427	542	45	form	form	NOUN
fuelectenerg-1427	542	46	that	that	PRON
fuelectenerg-1427	542	47	uses	use	VERB
fuelectenerg-1427	542	48	the	the	DET
fuelectenerg-1427	542	49	additions	addition	NOUN
fuelectenerg-1427	542	50	and	and	CCONJ
fuelectenerg-1427	542	51	multiplications	multiplication	NOUN
fuelectenerg-1427	542	52	of	of	ADP
fuelectenerg-1427	542	53	arbitrary	arbitrary	ADJ
fuelectenerg-1427	542	54	radix	radix	PROPN
fuelectenerg-1427	542	55	galois	galois	PROPN
fuelectenerg-1427	542	56	field	field	NOUN
fuelectenerg-1427	542	57	,	,	PUNCT
fuelectenerg-1427	542	58	and	and	CCONJ
fuelectenerg-1427	542	59	can	can	AUX
fuelectenerg-1427	542	60	be	be	AUX
fuelectenerg-1427	542	61	used	use	VERB
fuelectenerg-1427	542	62	for	for	ADP
fuelectenerg-1427	542	63	the	the	DET
fuelectenerg-1427	542	64	creation	creation	NOUN
fuelectenerg-1427	542	65	of	of	ADP
fuelectenerg-1427	542	66	new	new	ADJ
fuelectenerg-1427	542	67	forms	form	NOUN
fuelectenerg-1427	542	68	,	,	PUNCT
fuelectenerg-1427	542	69	decision	decision	NOUN
fuelectenerg-1427	542	70	diagrams	diagram	NOUN
fuelectenerg-1427	542	71	and	and	CCONJ
fuelectenerg-1427	542	72	regular	regular	ADJ
fuelectenerg-1427	542	73	structures	structure	NOUN
fuelectenerg-1427	542	74	.	.	PUNCT
fuelectenerg-1427	543	1	the	the	DET
fuelectenerg-1427	543	2	current	current	ADJ
fuelectenerg-1427	543	3	state	state	NOUN
fuelectenerg-1427	543	4	-	-	PUNCT
fuelectenerg-1427	543	5	of	of	ADP
fuelectenerg-1427	543	6	-	-	PUNCT
fuelectenerg-1427	543	7	the	the	DET
fuelectenerg-1427	543	8	-	-	PUNCT
fuelectenerg-1427	543	9	art	art	NOUN
fuelectenerg-1427	543	10	minimizers	minimizer	NOUN
fuelectenerg-1427	543	11	of	of	ADP
fuelectenerg-1427	543	12	exclusive	exclusive	ADJ
fuelectenerg-1427	543	13	sum	sum	NOUN
fuelectenerg-1427	543	14	-	-	PUNCT
fuelectenerg-1427	543	15	of	of	ADP
fuelectenerg-1427	543	16	-	-	PUNCT
fuelectenerg-1427	543	17	product	product	NOUN
fuelectenerg-1427	543	18	(	(	PUNCT
fuelectenerg-1427	543	19	esop	esop	PROPN
fuelectenerg-1427	543	20	)	)	PUNCT
fuelectenerg-1427	543	21	expressions	expression	NOUN
fuelectenerg-1427	543	22	are	be	AUX
fuelectenerg-1427	543	23	based	base	VERB
fuelectenerg-1427	543	24	on	on	ADP
fuelectenerg-1427	543	25	heuristics	heuristic	NOUN
fuelectenerg-1427	543	26	and	and	CCONJ
fuelectenerg-1427	543	27	give	give	VERB
fuelectenerg-1427	543	28	the	the	DET
fuelectenerg-1427	543	29	exact	exact	ADJ
fuelectenerg-1427	543	30	solution	solution	NOUN
fuelectenerg-1427	543	31	only	only	ADV
fuelectenerg-1427	543	32	for	for	ADP
fuelectenerg-1427	543	33	functions	function	NOUN
fuelectenerg-1427	543	34	with	with	ADP
fuelectenerg-1427	543	35	a	a	DET
fuelectenerg-1427	543	36	small	small	ADJ
fuelectenerg-1427	543	37	number	number	NOUN
fuelectenerg-1427	543	38	of	of	ADP
fuelectenerg-1427	543	39	variables	variable	NOUN
fuelectenerg-1427	543	40	.	.	PUNCT
fuelectenerg-1427	544	1	for	for	ADP
fuelectenerg-1427	544	2	example	example	NOUN
fuelectenerg-1427	544	3	,	,	PUNCT
fuelectenerg-1427	544	4	a	a	DET
fuelectenerg-1427	544	5	formulation	formulation	NOUN
fuelectenerg-1427	544	6	for	for	ADP
fuelectenerg-1427	544	7	finding	find	VERB
fuelectenerg-1427	544	8	exact	exact	ADJ
fuelectenerg-1427	544	9	esop	esop	PROPN
fuelectenerg-1427	544	10	was	be	AUX
fuelectenerg-1427	544	11	given	give	VERB
fuelectenerg-1427	544	12	[	[	X
fuelectenerg-1427	544	13	11	11	NUM
fuelectenerg-1427	544	14	]	]	PUNCT
fuelectenerg-1427	544	15	,	,	PUNCT
fuelectenerg-1427	544	16	and	and	CCONJ
fuelectenerg-1427	544	17	an	an	DET
fuelectenerg-1427	544	18	algorithm	algorithm	NOUN
fuelectenerg-1427	544	19	to	to	PART
fuelectenerg-1427	544	20	derive	derive	VERB
fuelectenerg-1427	544	21	minimum	minimum	ADJ
fuelectenerg-1427	544	22	esop	esop	NOUN
fuelectenerg-1427	544	23	for	for	ADP
fuelectenerg-1427	544	24	6	6	NUM
fuelectenerg-1427	544	25	-	-	PUNCT
fuelectenerg-1427	544	26	variable	variable	ADJ
fuelectenerg-1427	544	27	function	function	NOUN
fuelectenerg-1427	544	28	was	be	AUX
fuelectenerg-1427	544	29	provided	provide	VERB
fuelectenerg-1427	544	30	[	[	X
fuelectenerg-1427	544	31	25	25	NUM
fuelectenerg-1427	544	32	]	]	PUNCT
fuelectenerg-1427	544	33	.	.	PUNCT
fuelectenerg-1427	545	1	because	because	SCONJ
fuelectenerg-1427	545	2	gfsop	gfsop	PROPN
fuelectenerg-1427	545	3	minimization	minimization	NOUN
fuelectenerg-1427	545	4	is	be	AUX
fuelectenerg-1427	545	5	even	even	ADV
fuelectenerg-1427	545	6	more	more	ADV
fuelectenerg-1427	545	7	difficult	difficult	ADJ
fuelectenerg-1427	545	8	,	,	PUNCT
fuelectenerg-1427	545	9	it	it	PRON
fuelectenerg-1427	545	10	is	be	AUX
fuelectenerg-1427	545	11	important	important	ADJ
fuelectenerg-1427	545	12	to	to	PART
fuelectenerg-1427	545	13	investigate	investigate	VERB
fuelectenerg-1427	545	14	the	the	DET
fuelectenerg-1427	545	15	structural	structural	ADJ
fuelectenerg-1427	545	16	properties	property	NOUN
fuelectenerg-1427	545	17	and	and	CCONJ
fuelectenerg-1427	545	18	the	the	DET
fuelectenerg-1427	545	19	counts	count	NOUN
fuelectenerg-1427	545	20	of	of	ADP
fuelectenerg-1427	545	21	their	their	PRON
fuelectenerg-1427	545	22	canonical	canonical	ADJ
fuelectenerg-1427	545	23	sub	sub	NOUN
fuelectenerg-1427	545	24	-	-	NOUN
fuelectenerg-1427	545	25	families	family	NOUN
fuelectenerg-1427	545	26	.	.	PUNCT
fuelectenerg-1427	546	1	two	two	NUM
fuelectenerg-1427	546	2	families	family	NOUN
fuelectenerg-1427	546	3	of	of	ADP
fuelectenerg-1427	546	4	binary	binary	ADJ
fuelectenerg-1427	546	5	canonical	canonical	ADJ
fuelectenerg-1427	546	6	reed	reed	NOUN
fuelectenerg-1427	546	7	-	-	PUNCT
fuelectenerg-1427	546	8	muller	muller	NOUN
fuelectenerg-1427	546	9	forms	form	NOUN
fuelectenerg-1427	546	10	,	,	PUNCT
fuelectenerg-1427	546	11	called	call	VERB
fuelectenerg-1427	546	12	inclusive	inclusive	ADJ
fuelectenerg-1427	546	13	forms	form	NOUN
fuelectenerg-1427	546	14	(	(	PUNCT
fuelectenerg-1427	546	15	ifs	ifs	PROPN
fuelectenerg-1427	546	16	)	)	PUNCT
fuelectenerg-1427	546	17	and	and	CCONJ
fuelectenerg-1427	546	18	generalized	generalized	ADJ
fuelectenerg-1427	546	19	inclusive	inclusive	ADJ
fuelectenerg-1427	546	20	forms	form	NOUN
fuelectenerg-1427	546	21	(	(	PUNCT
fuelectenerg-1427	546	22	gifs	gifs	PROPN
fuelectenerg-1427	546	23	)	)	PUNCT
fuelectenerg-1427	546	24	were	be	AUX
fuelectenerg-1427	546	25	presented	present	VERB
fuelectenerg-1427	546	26	[	[	X
fuelectenerg-1427	546	27	1	1	NUM
fuelectenerg-1427	546	28	]	]	PUNCT
fuelectenerg-1427	546	29	,	,	PUNCT
fuelectenerg-1427	546	30	where	where	SCONJ
fuelectenerg-1427	546	31	the	the	DET
fuelectenerg-1427	546	32	second	second	ADJ
fuelectenerg-1427	546	33	family	family	NOUN
fuelectenerg-1427	546	34	was	be	AUX
fuelectenerg-1427	546	35	the	the	DET
fuelectenerg-1427	546	36	first	first	ADJ
fuelectenerg-1427	546	37	to	to	PART
fuelectenerg-1427	546	38	include	include	VERB
fuelectenerg-1427	546	39	all	all	DET
fuelectenerg-1427	546	40	minimum	minimum	ADJ
fuelectenerg-1427	546	41	esops	esop	NOUN
fuelectenerg-1427	546	42	(	(	PUNCT
fuelectenerg-1427	546	43	binary	binary	ADJ
fuelectenerg-1427	546	44	gfsops	gfsop	NOUN
fuelectenerg-1427	546	45	)	)	PUNCT
fuelectenerg-1427	546	46	.	.	PUNCT
fuelectenerg-1427	547	1	in	in	ADP
fuelectenerg-1427	547	2	these	these	DET
fuelectenerg-1427	547	3	forms	form	NOUN
fuelectenerg-1427	547	4	,	,	PUNCT
fuelectenerg-1427	547	5	if	if	SCONJ
fuelectenerg-1427	547	6	is	be	AUX
fuelectenerg-1427	547	7	the	the	DET
fuelectenerg-1427	547	8	form	form	NOUN
fuelectenerg-1427	547	9	generated	generate	VERB
fuelectenerg-1427	547	10	by	by	ADP
fuelectenerg-1427	547	11	the	the	DET
fuelectenerg-1427	547	12	corresponding	correspond	VERB
fuelectenerg-1427	547	13	s	s	PROPN
fuelectenerg-1427	547	14	/	/	SYM
fuelectenerg-1427	547	15	d	d	NOUN
fuelectenerg-1427	547	16	tree	tree	NOUN
fuelectenerg-1427	547	17	and	and	CCONJ
fuelectenerg-1427	547	18	gif	gif	NOUN
fuelectenerg-1427	547	19	is	be	AUX
fuelectenerg-1427	547	20	the	the	DET
fuelectenerg-1427	547	21	form	form	NOUN
fuelectenerg-1427	547	22	which	which	PRON
fuelectenerg-1427	547	23	is	be	AUX
fuelectenerg-1427	547	24	the	the	DET
fuelectenerg-1427	547	25	union	union	NOUN
fuelectenerg-1427	547	26	of	of	ADP
fuelectenerg-1427	547	27	the	the	DET
fuelectenerg-1427	547	28	various	various	ADJ
fuelectenerg-1427	547	29	variable	variable	NOUN
fuelectenerg-1427	547	30	-	-	PUNCT
fuelectenerg-1427	547	31	based	base	VERB
fuelectenerg-1427	547	32	ordering	order	VERB
fuelectenerg-1427	547	33	ifs	ifs	PROPN
fuelectenerg-1427	547	34	(	(	PUNCT
fuelectenerg-1427	547	35	cf	cf	NOUN
fuelectenerg-1427	547	36	.	.	PUNCT
fuelectenerg-1427	548	1	definitions	definition	NOUN
fuelectenerg-1427	548	2	and	and	CCONJ
fuelectenerg-1427	548	3	theorems	theorem	NOUN
fuelectenerg-1427	548	4	of	of	ADP
fuelectenerg-1427	548	5	these	these	DET
fuelectenerg-1427	548	6	forms	form	NOUN
fuelectenerg-1427	548	7	in	in	ADP
fuelectenerg-1427	548	8	the	the	DET
fuelectenerg-1427	548	9	next	next	ADJ
fuelectenerg-1427	548	10	subsection	subsection	NOUN
fuelectenerg-1427	548	11	)	)	PUNCT
fuelectenerg-1427	548	12	.	.	PUNCT
fuelectenerg-1427	549	1	in	in	ADP
fuelectenerg-1427	549	2	this	this	DET
fuelectenerg-1427	549	3	paper	paper	NOUN
fuelectenerg-1427	549	4	,	,	PUNCT
fuelectenerg-1427	549	5	we	we	PRON
fuelectenerg-1427	549	6	propose	propose	VERB
fuelectenerg-1427	549	7	,	,	PUNCT
fuelectenerg-1427	549	8	as	as	SCONJ
fuelectenerg-1427	549	9	analogous	analogous	ADJ
fuelectenerg-1427	549	10	to	to	ADP
fuelectenerg-1427	549	11	the	the	DET
fuelectenerg-1427	549	12	binary	binary	ADJ
fuelectenerg-1427	549	13	case	case	NOUN
fuelectenerg-1427	549	14	,	,	PUNCT
fuelectenerg-1427	549	15	two	two	NUM
fuelectenerg-1427	549	16	general	general	ADJ
fuelectenerg-1427	549	17	families	family	NOUN
fuelectenerg-1427	549	18	of	of	ADP
fuelectenerg-1427	549	19	canonical	canonical	ADJ
fuelectenerg-1427	549	20	ternary	ternary	ADJ
fuelectenerg-1427	549	21	reed	reed	NOUN
fuelectenerg-1427	549	22	-	-	PUNCT
fuelectenerg-1427	549	23	muller	muller	NOUN
fuelectenerg-1427	549	24	forms	form	NOUN
fuelectenerg-1427	549	25	,	,	PUNCT
fuelectenerg-1427	549	26	called	call	VERB
fuelectenerg-1427	549	27	ternary	ternary	ADJ
fuelectenerg-1427	549	28	inclusive	inclusive	ADJ
fuelectenerg-1427	549	29	forms	form	NOUN
fuelectenerg-1427	549	30	(	(	PUNCT
fuelectenerg-1427	549	31	tifs	tifs	PROPN
fuelectenerg-1427	549	32	)	)	PUNCT
fuelectenerg-1427	549	33	and	and	CCONJ
fuelectenerg-1427	549	34	their	their	PRON
fuelectenerg-1427	549	35	generalization	generalization	NOUN
fuelectenerg-1427	549	36	of	of	ADP
fuelectenerg-1427	549	37	ternary	ternary	ADJ
fuelectenerg-1427	549	38	generalized	generalize	VERB
fuelectenerg-1427	549	39	inclusive	inclusive	ADJ
fuelectenerg-1427	549	40	forms	form	NOUN
fuelectenerg-1427	549	41	(	(	PUNCT
fuelectenerg-1427	549	42	tgifs	tgif	NOUN
fuelectenerg-1427	549	43	)	)	PUNCT
fuelectenerg-1427	549	44	,	,	PUNCT
fuelectenerg-1427	549	45	where	where	SCONJ
fuelectenerg-1427	549	46	gfsop	gfsop	NOUN
fuelectenerg-1427	549	47	minimizer	minimizer	NOUN
fuelectenerg-1427	549	48	based	base	VERB
fuelectenerg-1427	549	49	on	on	ADP
fuelectenerg-1427	549	50	these	these	DET
fuelectenerg-1427	549	51	new	new	ADJ
fuelectenerg-1427	549	52	forms	form	NOUN
fuelectenerg-1427	549	53	can	can	AUX
fuelectenerg-1427	549	54	be	be	AUX
fuelectenerg-1427	549	55	used	use	VERB
fuelectenerg-1427	549	56	to	to	PART
fuelectenerg-1427	549	57	minimize	minimize	VERB
fuelectenerg-1427	549	58	functional	functional	ADJ
fuelectenerg-1427	549	59	gfsop	gfsop	NOUN
fuelectenerg-1427	549	60	expressions	expression	NOUN
fuelectenerg-1427	549	61	and	and	CCONJ
fuelectenerg-1427	549	62	the	the	DET
fuelectenerg-1427	549	63	second	second	ADJ
fuelectenerg-1427	549	64	family	family	NOUN
fuelectenerg-1427	549	65	of	of	ADP
fuelectenerg-1427	549	66	tgifs	tgif	NOUN
fuelectenerg-1427	549	67	includes	include	VERB
fuelectenerg-1427	549	68	minimum	minimum	ADJ
fuelectenerg-1427	549	69	gfsops	gfsop	NOUN
fuelectenerg-1427	549	70	over	over	ADP
fuelectenerg-1427	549	71	ternary	ternary	ADJ
fuelectenerg-1427	549	72	galois	galois	PROPN
fuelectenerg-1427	549	73	field	field	NOUN
fuelectenerg-1427	549	74	.	.	PUNCT
fuelectenerg-1427	550	1	one	one	NUM
fuelectenerg-1427	550	2	of	of	ADP
fuelectenerg-1427	550	3	the	the	DET
fuelectenerg-1427	550	4	motivations	motivation	NOUN
fuelectenerg-1427	550	5	for	for	ADP
fuelectenerg-1427	550	6	this	this	DET
fuelectenerg-1427	550	7	work	work	NOUN
fuelectenerg-1427	550	8	is	be	AUX
fuelectenerg-1427	550	9	the	the	DET
fuelectenerg-1427	550	10	application	application	NOUN
fuelectenerg-1427	550	11	of	of	ADP
fuelectenerg-1427	550	12	these	these	DET
fuelectenerg-1427	550	13	tifs	tif	NOUN
fuelectenerg-1427	550	14	and	and	CCONJ
fuelectenerg-1427	550	15	tgifs	tgif	NOUN
fuelectenerg-1427	550	16	to	to	PART
fuelectenerg-1427	550	17	find	find	VERB
fuelectenerg-1427	550	18	minimum	minimum	ADJ
fuelectenerg-1427	550	19	gfsop	gfsop	NOUN
fuelectenerg-1427	550	20	for	for	ADP
fuelectenerg-1427	550	21	multiple	multiple	ADV
fuelectenerg-1427	550	22	-	-	PUNCT
fuelectenerg-1427	550	23	valued	value	VERB
fuelectenerg-1427	550	24	inputs	input	NOUN
fuelectenerg-1427	550	25	multiple	multiple	ADV
fuelectenerg-1427	550	26	-	-	PUNCT
fuelectenerg-1427	550	27	valued	value	VERB
fuelectenerg-1427	550	28	outputs	output	NOUN
fuelectenerg-1427	550	29	within	within	ADP
fuelectenerg-1427	550	30	logic	logic	ADJ
fuelectenerg-1427	550	31	synthesis	synthesis	NOUN
fuelectenerg-1427	550	32	,	,	PUNCT
fuelectenerg-1427	550	33	where	where	SCONJ
fuelectenerg-1427	550	34	the	the	DET
fuelectenerg-1427	550	35	corresponding	correspond	VERB
fuelectenerg-1427	550	36	s	s	PROPN
fuelectenerg-1427	550	37	/	/	SYM
fuelectenerg-1427	550	38	d	d	NOUN
fuelectenerg-1427	550	39	trees	tree	NOUN
fuelectenerg-1427	550	40	provide	provide	VERB
fuelectenerg-1427	550	41	more	more	ADJ
fuelectenerg-1427	550	42	general	general	ADJ
fuelectenerg-1427	550	43	polarity	polarity	NOUN
fuelectenerg-1427	550	44	that	that	PRON
fuelectenerg-1427	550	45	contains	contain	VERB
fuelectenerg-1427	550	46	grm	grm	NOUN
fuelectenerg-1427	550	47	forms	form	NOUN
fuelectenerg-1427	550	48	as	as	ADP
fuelectenerg-1427	550	49	a	a	DET
fuelectenerg-1427	550	50	special	special	ADJ
fuelectenerg-1427	550	51	case	case	NOUN
fuelectenerg-1427	550	52	.	.	PUNCT
fuelectenerg-1427	551	1	2.1	2.1	NUM
fuelectenerg-1427	551	2	s	s	NOUN
fuelectenerg-1427	551	3	/	/	SYM
fuelectenerg-1427	551	4	d	d	NOUN
fuelectenerg-1427	551	5	trees	tree	NOUN
fuelectenerg-1427	551	6	and	and	CCONJ
fuelectenerg-1427	551	7	their	their	PRON
fuelectenerg-1427	551	8	inclusive	inclusive	ADJ
fuelectenerg-1427	551	9	forms	form	NOUN
fuelectenerg-1427	551	10	and	and	CCONJ
fuelectenerg-1427	551	11	generalized	generalized	ADJ
fuelectenerg-1427	551	12	inclusive	inclusive	ADJ
fuelectenerg-1427	551	13	forms	form	NOUN
fuelectenerg-1427	551	14	two	two	NUM
fuelectenerg-1427	551	15	general	general	ADJ
fuelectenerg-1427	551	16	families	family	NOUN
fuelectenerg-1427	551	17	based	base	VERB
fuelectenerg-1427	551	18	on	on	ADP
fuelectenerg-1427	551	19	the	the	DET
fuelectenerg-1427	551	20	shannon	shannon	PROPN
fuelectenerg-1427	551	21	expansion	expansion	NOUN
fuelectenerg-1427	551	22	and	and	CCONJ
fuelectenerg-1427	551	23	the	the	DET
fuelectenerg-1427	551	24	generalized	generalized	ADJ
fuelectenerg-1427	551	25	davio	davio	NOUN
fuelectenerg-1427	551	26	expansion	expansion	NOUN
fuelectenerg-1427	551	27	which	which	PRON
fuelectenerg-1427	551	28	are	be	AUX
fuelectenerg-1427	551	29	produced	produce	VERB
fuelectenerg-1427	551	30	using	use	VERB
fuelectenerg-1427	551	31	the	the	DET
fuelectenerg-1427	551	32	corresponding	correspond	VERB
fuelectenerg-1427	551	33	s	s	PROPN
fuelectenerg-1427	551	34	/	/	SYM
fuelectenerg-1427	551	35	d	d	NOUN
fuelectenerg-1427	551	36	trees	tree	NOUN
fuelectenerg-1427	551	37	are	be	AUX
fuelectenerg-1427	551	38	presented	present	VERB
fuelectenerg-1427	551	39	in	in	ADP
fuelectenerg-1427	551	40	this	this	DET
fuelectenerg-1427	551	41	subsection	subsection	NOUN
fuelectenerg-1427	551	42	.	.	PUNCT
fuelectenerg-1427	552	1	these	these	DET
fuelectenerg-1427	552	2	families	family	NOUN
fuelectenerg-1427	552	3	are	be	AUX
fuelectenerg-1427	552	4	called	call	VERB
fuelectenerg-1427	552	5	the	the	DET
fuelectenerg-1427	552	6	inclusive	inclusive	ADJ
fuelectenerg-1427	552	7	forms	form	NOUN
fuelectenerg-1427	552	8	(	(	PUNCT
fuelectenerg-1427	552	9	ifs	ifs	PROPN
fuelectenerg-1427	552	10	)	)	PUNCT
fuelectenerg-1427	552	11	and	and	CCONJ
fuelectenerg-1427	552	12	the	the	DET
fuelectenerg-1427	552	13	generalized	generalized	ADJ
fuelectenerg-1427	552	14	inclusive	inclusive	ADJ
fuelectenerg-1427	552	15	forms	form	NOUN
fuelectenerg-1427	552	16	(	(	PUNCT
fuelectenerg-1427	552	17	gifs	gifs	PROPN
fuelectenerg-1427	552	18	)	)	PUNCT
fuelectenerg-1427	552	19	.	.	PUNCT
fuelectenerg-1427	553	1	the	the	DET
fuelectenerg-1427	553	2	corresponding	corresponding	ADJ
fuelectenerg-1427	553	3	expansions	expansion	NOUN
fuelectenerg-1427	553	4	over	over	ADP
fuelectenerg-1427	553	5	gf(2	gf(2	PROPN
fuelectenerg-1427	553	6	)	)	PUNCT
fuelectenerg-1427	553	7	are	be	AUX
fuelectenerg-1427	553	8	shown	show	VERB
fuelectenerg-1427	553	9	in	in	ADP
fuelectenerg-1427	553	10	figure	figure	NOUN
fuelectenerg-1427	553	11	3	3	NUM
fuelectenerg-1427	553	12	,	,	PUNCT
fuelectenerg-1427	553	13	where	where	SCONJ
fuelectenerg-1427	553	14	figure	figure	NOUN
fuelectenerg-1427	553	15	3(d	3(d	NOUN
fuelectenerg-1427	553	16	)	)	PUNCT
fuelectenerg-1427	553	17	shows	show	VERB
fuelectenerg-1427	553	18	the	the	DET
fuelectenerg-1427	553	19	new	new	ADJ
fuelectenerg-1427	553	20	node	node	NOUN
fuelectenerg-1427	553	21	which	which	PRON
fuelectenerg-1427	553	22	is	be	AUX
fuelectenerg-1427	553	23	based	base	VERB
fuelectenerg-1427	553	24	on	on	ADP
fuelectenerg-1427	553	25	binary	binary	ADJ
fuelectenerg-1427	553	26	davio	davio	NOUN
fuelectenerg-1427	553	27	expansions	expansion	NOUN
fuelectenerg-1427	553	28	called	call	VERB
fuelectenerg-1427	553	29	the	the	DET
fuelectenerg-1427	553	30	generalized	generalized	ADJ
fuelectenerg-1427	553	31	davio	davio	NOUN
fuelectenerg-1427	553	32	(	(	PUNCT
fuelectenerg-1427	553	33	d	d	NOUN
fuelectenerg-1427	553	34	)	)	PUNCT
fuelectenerg-1427	553	35	expansion	expansion	NOUN
fuelectenerg-1427	553	36	(	(	PUNCT
fuelectenerg-1427	553	37	cf	cf	NOUN
fuelectenerg-1427	553	38	.	.	PUNCT
fuelectenerg-1427	554	1	equation	equation	NOUN
fuelectenerg-1427	554	2	(	(	PUNCT
fuelectenerg-1427	554	3	28	28	NUM
fuelectenerg-1427	554	4	)	)	PUNCT
fuelectenerg-1427	554	5	for	for	ADP
fuelectenerg-1427	554	6	the	the	DET
fuelectenerg-1427	554	7	more	more	ADV
fuelectenerg-1427	554	8	general	general	ADJ
fuelectenerg-1427	554	9	ternary	ternary	ADJ
fuelectenerg-1427	554	10	case	case	NOUN
fuelectenerg-1427	554	11	)	)	PUNCT
fuelectenerg-1427	554	12	that	that	PRON
fuelectenerg-1427	554	13	generates	generate	VERB
fuelectenerg-1427	554	14	the	the	DET
fuelectenerg-1427	554	15	negative	negative	ADJ
fuelectenerg-1427	554	16	and	and	CCONJ
fuelectenerg-1427	554	17	positive	positive	ADJ
fuelectenerg-1427	554	18	davio	davio	NOUN
fuelectenerg-1427	554	19	expansions	expansion	NOUN
fuelectenerg-1427	554	20	as	as	ADP
fuelectenerg-1427	554	21	special	special	ADJ
fuelectenerg-1427	554	22	cases	case	NOUN
fuelectenerg-1427	554	23	.	.	PUNCT
fuelectenerg-1427	555	1	the	the	DET
fuelectenerg-1427	555	2	s	s	PROPN
fuelectenerg-1427	555	3	/	/	SYM
fuelectenerg-1427	555	4	d	d	NOUN
fuelectenerg-1427	555	5	trees	tree	NOUN
fuelectenerg-1427	555	6	for	for	ADP
fuelectenerg-1427	555	7	ifs	ifs	PROPN
fuelectenerg-1427	555	8	of	of	ADP
fuelectenerg-1427	555	9	two	two	NUM
fuelectenerg-1427	555	10	variables	variable	NOUN
fuelectenerg-1427	555	11	can	can	AUX
fuelectenerg-1427	555	12	be	be	AUX
fuelectenerg-1427	555	13	generated	generate	VERB
fuelectenerg-1427	555	14	for	for	ADP
fuelectenerg-1427	555	15	variable	variable	ADJ
fuelectenerg-1427	555	16	order	order	NOUN
fuelectenerg-1427	555	17	{	{	PUNCT
fuelectenerg-1427	555	18	a	a	DET
fuelectenerg-1427	555	19	,	,	PUNCT
fuelectenerg-1427	555	20	b	b	NOUN
fuelectenerg-1427	555	21	}	}	PUNCT
fuelectenerg-1427	555	22	and	and	CCONJ
fuelectenerg-1427	555	23	for	for	ADP
fuelectenerg-1427	555	24	variable	variable	ADJ
fuelectenerg-1427	555	25	order	order	NOUN
fuelectenerg-1427	555	26	{	{	PUNCT
fuelectenerg-1427	555	27	b	b	NOUN
fuelectenerg-1427	555	28	,	,	PUNCT
fuelectenerg-1427	555	29	a	a	PRON
fuelectenerg-1427	555	30	}	}	PUNCT
fuelectenerg-1427	555	31	as	as	ADV
fuelectenerg-1427	555	32	well	well	ADV
fuelectenerg-1427	555	33	.	.	PUNCT
fuelectenerg-1427	556	1	the	the	DET
fuelectenerg-1427	556	2	set	set	NOUN
fuelectenerg-1427	556	3	of	of	ADP
fuelectenerg-1427	556	4	gifs	gifs	PROPN
fuelectenerg-1427	556	5	for	for	ADP
fuelectenerg-1427	556	6	two	two	NUM
fuelectenerg-1427	556	7	variables	variable	NOUN
fuelectenerg-1427	556	8	is	be	AUX
fuelectenerg-1427	556	9	the	the	DET
fuelectenerg-1427	556	10	union	union	NOUN
fuelectenerg-1427	556	11	of	of	ADP
fuelectenerg-1427	556	12	these	these	DET
fuelectenerg-1427	556	13	two	two	NUM
fuelectenerg-1427	556	14	order	order	NOUN
fuelectenerg-1427	556	15	-	-	PUNCT
fuelectenerg-1427	556	16	based	base	VERB
fuelectenerg-1427	556	17	ifs	ifs	PROPN
fuelectenerg-1427	556	18	,	,	PUNCT
fuelectenerg-1427	556	19	where	where	SCONJ
fuelectenerg-1427	556	20	the	the	DET
fuelectenerg-1427	556	21	total	total	ADJ
fuelectenerg-1427	556	22	number	number	NOUN
fuelectenerg-1427	556	23	of	of	ADP
fuelectenerg-1427	556	24	the	the	DET
fuelectenerg-1427	556	25	resulting	result	VERB
fuelectenerg-1427	556	26	gifs	gifs	NOUN
fuelectenerg-1427	556	27	is	be	AUX
fuelectenerg-1427	556	28	equal	equal	ADJ
fuelectenerg-1427	556	29	to	to	ADP
fuelectenerg-1427	556	30	:	:	PUNCT
fuelectenerg-1427	556	31	#	#	SYM
fuelectenerg-1427	556	32	gif	gif	NOUN
fuelectenerg-1427	556	33	=	=	NOUN
fuelectenerg-1427	556	34	2	2	NUM
fuelectenerg-1427	556	35	·	·	PUNCT
fuelectenerg-1427	556	36	(	(	PUNCT
fuelectenerg-1427	556	37	#	#	SYM
fuelectenerg-1427	556	38	ifa	ifa	PROPN
fuelectenerg-1427	556	39	,	,	PUNCT
fuelectenerg-1427	556	40	b)−#(ifa	b)−#(ifa	PROPN
fuelectenerg-1427	556	41	,	,	PUNCT
fuelectenerg-1427	556	42	b	b	PROPN
fuelectenerg-1427	556	43	⋂	⋂	PROPN
fuelectenerg-1427	556	44	ifb	ifb	PROPN
fuelectenerg-1427	556	45	,	,	PUNCT
fuelectenerg-1427	556	46	a	a	PRON
fuelectenerg-1427	556	47	)	)	PUNCT
fuelectenerg-1427	556	48	.	.	PUNCT
fuelectenerg-1427	557	1	(	(	PUNCT
fuelectenerg-1427	557	2	27	27	NUM
fuelectenerg-1427	557	3	)	)	PUNCT
fuelectenerg-1427	557	4	the	the	DET
fuelectenerg-1427	557	5	galois	galois	PROPN
fuelectenerg-1427	557	6	-	-	PUNCT
fuelectenerg-1427	557	7	based	base	VERB
fuelectenerg-1427	557	8	shannon	shannon	NOUN
fuelectenerg-1427	557	9	and	and	CCONJ
fuelectenerg-1427	557	10	davio	davio	NOUN
fuelectenerg-1427	557	11	ternary	ternary	ADJ
fuelectenerg-1427	557	12	expansions	expansion	NOUN
fuelectenerg-1427	557	13	(	(	PUNCT
fuelectenerg-1427	557	14	i.e.	i.e.	X
fuelectenerg-1427	557	15	,	,	PUNCT
fuelectenerg-1427	557	16	flattened	flatten	VERB
fuelectenerg-1427	557	17	forms	form	NOUN
fuelectenerg-1427	557	18	)	)	PUNCT
fuelectenerg-1427	557	19	can	can	AUX
fuelectenerg-1427	557	20	be	be	AUX
fuelectenerg-1427	557	21	represented	represent	VERB
fuelectenerg-1427	557	22	in	in	ADP
fuelectenerg-1427	557	23	ternary	ternary	ADJ
fuelectenerg-1427	557	24	dts	dts	NOUN
fuelectenerg-1427	557	25	(	(	PUNCT
fuelectenerg-1427	557	26	tdts	tdts	ADJ
fuelectenerg-1427	557	27	)	)	PUNCT
fuelectenerg-1427	557	28	and	and	CCONJ
fuelectenerg-1427	557	29	the	the	DET
fuelectenerg-1427	557	30	corresponding	corresponding	ADJ
fuelectenerg-1427	557	31	varieties	variety	NOUN
fuelectenerg-1427	557	32	of	of	ADP
fuelectenerg-1427	557	33	ternary	ternary	ADJ
fuelectenerg-1427	557	34	dds	dds	PROPN
fuelectenerg-1427	557	35	(	(	PUNCT
fuelectenerg-1427	557	36	tdds	tdds	PROPN
fuelectenerg-1427	557	37	)	)	PUNCT
fuelectenerg-1427	557	38	according	accord	VERB
fuelectenerg-1427	557	39	to	to	ADP
fuelectenerg-1427	557	40	the	the	DET
fuelectenerg-1427	557	41	corresponding	corresponding	ADJ
fuelectenerg-1427	557	42	reduction	reduction	NOUN
fuelectenerg-1427	557	43	rules	rule	NOUN
fuelectenerg-1427	557	44	that	that	PRON
fuelectenerg-1427	557	45	are	be	AUX
fuelectenerg-1427	557	46	used	use	VERB
fuelectenerg-1427	557	47	[	[	PUNCT
fuelectenerg-1427	557	48	1	1	NUM
fuelectenerg-1427	557	49	,	,	PUNCT
fuelectenerg-1427	557	50	17	17	NUM
fuelectenerg-1427	557	51	]	]	PUNCT
fuelectenerg-1427	557	52	.	.	PUNCT
fuelectenerg-1427	558	1	for	for	ADP
fuelectenerg-1427	558	2	one	one	NUM
fuelectenerg-1427	558	3	107	107	NUM
fuelectenerg-1427	558	4	an	an	DET
fuelectenerg-1427	558	5	extended	extended	ADJ
fuelectenerg-1427	558	6	green	green	ADJ
fuelectenerg-1427	558	7	sasao	sasao	PROPN
fuelectenerg-1427	558	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	558	9	of	of	ADP
fuelectenerg-1427	558	10	canonical	canonical	ADJ
fuelectenerg-1427	558	11	ternary	ternary	ADJ
fuelectenerg-1427	558	12	galois	galois	NOUN
fuelectenerg-1427	558	13	forms	form	NOUN
fuelectenerg-1427	558	14	...	...	PUNCT
fuelectenerg-1427	558	15	as	as	ADP
fuelectenerg-1427	558	16	the	the	DET
fuelectenerg-1427	558	17	green	green	PROPN
fuelectenerg-1427	558	18	-	-	PUNCT
fuelectenerg-1427	558	19	sasao	sasao	PROPN
fuelectenerg-1427	558	20	hierarchy	hierarchy	NOUN
fuelectenerg-1427	558	21	,	,	PUNCT
fuelectenerg-1427	558	22	have	have	AUX
fuelectenerg-1427	558	23	been	be	AUX
fuelectenerg-1427	558	24	described	describe	VERB
fuelectenerg-1427	558	25	[	[	X
fuelectenerg-1427	558	26	1	1	NUM
fuelectenerg-1427	558	27	,	,	PUNCT
fuelectenerg-1427	558	28	10	10	NUM
fuelectenerg-1427	558	29	,	,	PUNCT
fuelectenerg-1427	558	30	17	17	NUM
fuelectenerg-1427	558	31	]	]	PUNCT
fuelectenerg-1427	558	32	.	.	PUNCT
fuelectenerg-1427	559	1	because	because	SCONJ
fuelectenerg-1427	559	2	canonical	canonical	ADJ
fuelectenerg-1427	559	3	families	family	NOUN
fuelectenerg-1427	559	4	have	have	VERB
fuelectenerg-1427	559	5	higher	high	ADJ
fuelectenerg-1427	559	6	testability	testability	NOUN
fuelectenerg-1427	559	7	and	and	CCONJ
fuelectenerg-1427	559	8	some	some	DET
fuelectenerg-1427	559	9	other	other	ADJ
fuelectenerg-1427	559	10	properties	property	NOUN
fuelectenerg-1427	559	11	desirable	desirable	ADJ
fuelectenerg-1427	559	12	for	for	ADP
fuelectenerg-1427	559	13	efficient	efficient	ADJ
fuelectenerg-1427	559	14	synthesis	synthesis	NOUN
fuelectenerg-1427	559	15	,	,	PUNCT
fuelectenerg-1427	559	16	especially	especially	ADV
fuelectenerg-1427	559	17	of	of	ADP
fuelectenerg-1427	559	18	some	some	DET
fuelectenerg-1427	559	19	classes	class	NOUN
fuelectenerg-1427	559	20	of	of	ADP
fuelectenerg-1427	559	21	functions	function	NOUN
fuelectenerg-1427	559	22	,	,	PUNCT
fuelectenerg-1427	559	23	they	they	PRON
fuelectenerg-1427	559	24	are	be	AUX
fuelectenerg-1427	559	25	widely	widely	ADV
fuelectenerg-1427	559	26	investigated	investigate	VERB
fuelectenerg-1427	559	27	.	.	PUNCT
fuelectenerg-1427	560	1	a	a	DET
fuelectenerg-1427	560	2	similar	similar	ADJ
fuelectenerg-1427	560	3	ternary	ternary	ADJ
fuelectenerg-1427	560	4	version	version	NOUN
fuelectenerg-1427	560	5	of	of	ADP
fuelectenerg-1427	560	6	the	the	DET
fuelectenerg-1427	560	7	binary	binary	ADJ
fuelectenerg-1427	560	8	green	green	PROPN
fuelectenerg-1427	560	9	-	-	PUNCT
fuelectenerg-1427	560	10	sasao	sasao	PROPN
fuelectenerg-1427	560	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	560	12	can	can	AUX
fuelectenerg-1427	560	13	be	be	AUX
fuelectenerg-1427	560	14	developed	develop	VERB
fuelectenerg-1427	560	15	,	,	PUNCT
fuelectenerg-1427	560	16	where	where	SCONJ
fuelectenerg-1427	560	17	this	this	DET
fuelectenerg-1427	560	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	560	19	can	can	AUX
fuelectenerg-1427	560	20	find	find	VERB
fuelectenerg-1427	560	21	applications	application	NOUN
fuelectenerg-1427	560	22	in	in	ADP
fuelectenerg-1427	560	23	minimizing	minimize	VERB
fuelectenerg-1427	560	24	galois	galois	PROPN
fuelectenerg-1427	560	25	field	field	NOUN
fuelectenerg-1427	560	26	sum	sum	NOUN
fuelectenerg-1427	560	27	-	-	PUNCT
fuelectenerg-1427	560	28	of	of	ADP
fuelectenerg-1427	560	29	-	-	PUNCT
fuelectenerg-1427	560	30	product	product	NOUN
fuelectenerg-1427	560	31	(	(	PUNCT
fuelectenerg-1427	560	32	gfsop	gfsop	NOUN
fuelectenerg-1427	560	33	)	)	PUNCT
fuelectenerg-1427	560	34	expressions	expression	NOUN
fuelectenerg-1427	560	35	which	which	PRON
fuelectenerg-1427	560	36	are	be	AUX
fuelectenerg-1427	560	37	expressions	expression	NOUN
fuelectenerg-1427	560	38	in	in	ADP
fuelectenerg-1427	560	39	the	the	DET
fuelectenerg-1427	560	40	sum	sum	NOUN
fuelectenerg-1427	560	41	-	-	PUNCT
fuelectenerg-1427	560	42	of	of	ADP
fuelectenerg-1427	560	43	-	-	PUNCT
fuelectenerg-1427	560	44	product	product	NOUN
fuelectenerg-1427	560	45	form	form	NOUN
fuelectenerg-1427	560	46	that	that	PRON
fuelectenerg-1427	560	47	uses	use	VERB
fuelectenerg-1427	560	48	the	the	DET
fuelectenerg-1427	560	49	additions	addition	NOUN
fuelectenerg-1427	560	50	and	and	CCONJ
fuelectenerg-1427	560	51	multiplications	multiplication	NOUN
fuelectenerg-1427	560	52	of	of	ADP
fuelectenerg-1427	560	53	arbitrary	arbitrary	ADJ
fuelectenerg-1427	560	54	radix	radix	PROPN
fuelectenerg-1427	560	55	galois	galois	PROPN
fuelectenerg-1427	560	56	field	field	NOUN
fuelectenerg-1427	560	57	,	,	PUNCT
fuelectenerg-1427	560	58	and	and	CCONJ
fuelectenerg-1427	560	59	can	can	AUX
fuelectenerg-1427	560	60	be	be	AUX
fuelectenerg-1427	560	61	used	use	VERB
fuelectenerg-1427	560	62	for	for	ADP
fuelectenerg-1427	560	63	the	the	DET
fuelectenerg-1427	560	64	creation	creation	NOUN
fuelectenerg-1427	560	65	of	of	ADP
fuelectenerg-1427	560	66	new	new	ADJ
fuelectenerg-1427	560	67	forms	form	NOUN
fuelectenerg-1427	560	68	,	,	PUNCT
fuelectenerg-1427	560	69	decision	decision	NOUN
fuelectenerg-1427	560	70	diagrams	diagram	NOUN
fuelectenerg-1427	560	71	and	and	CCONJ
fuelectenerg-1427	560	72	regular	regular	ADJ
fuelectenerg-1427	560	73	structures	structure	NOUN
fuelectenerg-1427	560	74	.	.	PUNCT
fuelectenerg-1427	561	1	the	the	DET
fuelectenerg-1427	561	2	current	current	ADJ
fuelectenerg-1427	561	3	state	state	NOUN
fuelectenerg-1427	561	4	-	-	PUNCT
fuelectenerg-1427	561	5	of	of	ADP
fuelectenerg-1427	561	6	-	-	PUNCT
fuelectenerg-1427	561	7	the	the	DET
fuelectenerg-1427	561	8	-	-	PUNCT
fuelectenerg-1427	561	9	art	art	NOUN
fuelectenerg-1427	561	10	minimizers	minimizer	NOUN
fuelectenerg-1427	561	11	of	of	ADP
fuelectenerg-1427	561	12	exclusive	exclusive	ADJ
fuelectenerg-1427	561	13	sum	sum	NOUN
fuelectenerg-1427	561	14	-	-	PUNCT
fuelectenerg-1427	561	15	of	of	ADP
fuelectenerg-1427	561	16	-	-	PUNCT
fuelectenerg-1427	561	17	product	product	NOUN
fuelectenerg-1427	561	18	(	(	PUNCT
fuelectenerg-1427	561	19	esop	esop	PROPN
fuelectenerg-1427	561	20	)	)	PUNCT
fuelectenerg-1427	561	21	expressions	expression	NOUN
fuelectenerg-1427	561	22	are	be	AUX
fuelectenerg-1427	561	23	based	base	VERB
fuelectenerg-1427	561	24	on	on	ADP
fuelectenerg-1427	561	25	heuristics	heuristic	NOUN
fuelectenerg-1427	561	26	and	and	CCONJ
fuelectenerg-1427	561	27	give	give	VERB
fuelectenerg-1427	561	28	the	the	DET
fuelectenerg-1427	561	29	exact	exact	ADJ
fuelectenerg-1427	561	30	solution	solution	NOUN
fuelectenerg-1427	561	31	only	only	ADV
fuelectenerg-1427	561	32	for	for	ADP
fuelectenerg-1427	561	33	functions	function	NOUN
fuelectenerg-1427	561	34	with	with	ADP
fuelectenerg-1427	561	35	a	a	DET
fuelectenerg-1427	561	36	small	small	ADJ
fuelectenerg-1427	561	37	number	number	NOUN
fuelectenerg-1427	561	38	of	of	ADP
fuelectenerg-1427	561	39	variables	variable	NOUN
fuelectenerg-1427	561	40	.	.	PUNCT
fuelectenerg-1427	562	1	for	for	ADP
fuelectenerg-1427	562	2	example	example	NOUN
fuelectenerg-1427	562	3	,	,	PUNCT
fuelectenerg-1427	562	4	a	a	DET
fuelectenerg-1427	562	5	formulation	formulation	NOUN
fuelectenerg-1427	562	6	for	for	ADP
fuelectenerg-1427	562	7	finding	find	VERB
fuelectenerg-1427	562	8	exact	exact	ADJ
fuelectenerg-1427	562	9	esop	esop	PROPN
fuelectenerg-1427	562	10	was	be	AUX
fuelectenerg-1427	562	11	given	give	VERB
fuelectenerg-1427	562	12	[	[	X
fuelectenerg-1427	562	13	11	11	NUM
fuelectenerg-1427	562	14	]	]	PUNCT
fuelectenerg-1427	562	15	,	,	PUNCT
fuelectenerg-1427	562	16	and	and	CCONJ
fuelectenerg-1427	562	17	an	an	DET
fuelectenerg-1427	562	18	algorithm	algorithm	NOUN
fuelectenerg-1427	562	19	to	to	PART
fuelectenerg-1427	562	20	derive	derive	VERB
fuelectenerg-1427	562	21	minimum	minimum	ADJ
fuelectenerg-1427	562	22	esop	esop	NOUN
fuelectenerg-1427	562	23	for	for	ADP
fuelectenerg-1427	562	24	6	6	NUM
fuelectenerg-1427	562	25	-	-	PUNCT
fuelectenerg-1427	562	26	variable	variable	ADJ
fuelectenerg-1427	562	27	function	function	NOUN
fuelectenerg-1427	562	28	was	be	AUX
fuelectenerg-1427	562	29	provided	provide	VERB
fuelectenerg-1427	562	30	[	[	X
fuelectenerg-1427	562	31	25	25	NUM
fuelectenerg-1427	562	32	]	]	PUNCT
fuelectenerg-1427	562	33	.	.	PUNCT
fuelectenerg-1427	563	1	because	because	SCONJ
fuelectenerg-1427	563	2	gfsop	gfsop	PROPN
fuelectenerg-1427	563	3	minimization	minimization	NOUN
fuelectenerg-1427	563	4	is	be	AUX
fuelectenerg-1427	563	5	even	even	ADV
fuelectenerg-1427	563	6	more	more	ADV
fuelectenerg-1427	563	7	difficult	difficult	ADJ
fuelectenerg-1427	563	8	,	,	PUNCT
fuelectenerg-1427	563	9	it	it	PRON
fuelectenerg-1427	563	10	is	be	AUX
fuelectenerg-1427	563	11	important	important	ADJ
fuelectenerg-1427	563	12	to	to	PART
fuelectenerg-1427	563	13	investigate	investigate	VERB
fuelectenerg-1427	563	14	the	the	DET
fuelectenerg-1427	563	15	structural	structural	ADJ
fuelectenerg-1427	563	16	properties	property	NOUN
fuelectenerg-1427	563	17	and	and	CCONJ
fuelectenerg-1427	563	18	the	the	DET
fuelectenerg-1427	563	19	counts	count	NOUN
fuelectenerg-1427	563	20	of	of	ADP
fuelectenerg-1427	563	21	their	their	PRON
fuelectenerg-1427	563	22	canonical	canonical	ADJ
fuelectenerg-1427	563	23	sub	sub	NOUN
fuelectenerg-1427	563	24	-	-	NOUN
fuelectenerg-1427	563	25	families	family	NOUN
fuelectenerg-1427	563	26	.	.	PUNCT
fuelectenerg-1427	564	1	two	two	NUM
fuelectenerg-1427	564	2	families	family	NOUN
fuelectenerg-1427	564	3	of	of	ADP
fuelectenerg-1427	564	4	binary	binary	ADJ
fuelectenerg-1427	564	5	canonical	canonical	ADJ
fuelectenerg-1427	564	6	reed	reed	NOUN
fuelectenerg-1427	564	7	-	-	PUNCT
fuelectenerg-1427	564	8	muller	muller	NOUN
fuelectenerg-1427	564	9	forms	form	NOUN
fuelectenerg-1427	564	10	,	,	PUNCT
fuelectenerg-1427	564	11	called	call	VERB
fuelectenerg-1427	564	12	inclusive	inclusive	ADJ
fuelectenerg-1427	564	13	forms	form	NOUN
fuelectenerg-1427	564	14	(	(	PUNCT
fuelectenerg-1427	564	15	ifs	ifs	PROPN
fuelectenerg-1427	564	16	)	)	PUNCT
fuelectenerg-1427	564	17	and	and	CCONJ
fuelectenerg-1427	564	18	generalized	generalized	ADJ
fuelectenerg-1427	564	19	inclusive	inclusive	ADJ
fuelectenerg-1427	564	20	forms	form	NOUN
fuelectenerg-1427	564	21	(	(	PUNCT
fuelectenerg-1427	564	22	gifs	gifs	PROPN
fuelectenerg-1427	564	23	)	)	PUNCT
fuelectenerg-1427	564	24	were	be	AUX
fuelectenerg-1427	564	25	presented	present	VERB
fuelectenerg-1427	564	26	[	[	X
fuelectenerg-1427	564	27	1	1	NUM
fuelectenerg-1427	564	28	]	]	PUNCT
fuelectenerg-1427	564	29	,	,	PUNCT
fuelectenerg-1427	564	30	where	where	SCONJ
fuelectenerg-1427	564	31	the	the	DET
fuelectenerg-1427	564	32	second	second	ADJ
fuelectenerg-1427	564	33	family	family	NOUN
fuelectenerg-1427	564	34	was	be	AUX
fuelectenerg-1427	564	35	the	the	DET
fuelectenerg-1427	564	36	first	first	ADJ
fuelectenerg-1427	564	37	to	to	PART
fuelectenerg-1427	564	38	include	include	VERB
fuelectenerg-1427	564	39	all	all	DET
fuelectenerg-1427	564	40	minimum	minimum	ADJ
fuelectenerg-1427	564	41	esops	esop	NOUN
fuelectenerg-1427	564	42	(	(	PUNCT
fuelectenerg-1427	564	43	binary	binary	ADJ
fuelectenerg-1427	564	44	gfsops	gfsop	NOUN
fuelectenerg-1427	564	45	)	)	PUNCT
fuelectenerg-1427	564	46	.	.	PUNCT
fuelectenerg-1427	565	1	in	in	ADP
fuelectenerg-1427	565	2	these	these	DET
fuelectenerg-1427	565	3	forms	form	NOUN
fuelectenerg-1427	565	4	,	,	PUNCT
fuelectenerg-1427	565	5	if	if	SCONJ
fuelectenerg-1427	565	6	is	be	AUX
fuelectenerg-1427	565	7	the	the	DET
fuelectenerg-1427	565	8	form	form	NOUN
fuelectenerg-1427	565	9	generated	generate	VERB
fuelectenerg-1427	565	10	by	by	ADP
fuelectenerg-1427	565	11	the	the	DET
fuelectenerg-1427	565	12	corresponding	correspond	VERB
fuelectenerg-1427	565	13	s	s	PROPN
fuelectenerg-1427	565	14	/	/	SYM
fuelectenerg-1427	565	15	d	d	NOUN
fuelectenerg-1427	565	16	tree	tree	NOUN
fuelectenerg-1427	565	17	and	and	CCONJ
fuelectenerg-1427	565	18	gif	gif	NOUN
fuelectenerg-1427	565	19	is	be	AUX
fuelectenerg-1427	565	20	the	the	DET
fuelectenerg-1427	565	21	form	form	NOUN
fuelectenerg-1427	565	22	which	which	PRON
fuelectenerg-1427	565	23	is	be	AUX
fuelectenerg-1427	565	24	the	the	DET
fuelectenerg-1427	565	25	union	union	NOUN
fuelectenerg-1427	565	26	of	of	ADP
fuelectenerg-1427	565	27	the	the	DET
fuelectenerg-1427	565	28	various	various	ADJ
fuelectenerg-1427	565	29	variable	variable	NOUN
fuelectenerg-1427	565	30	-	-	PUNCT
fuelectenerg-1427	565	31	based	base	VERB
fuelectenerg-1427	565	32	ordering	order	VERB
fuelectenerg-1427	565	33	ifs	ifs	PROPN
fuelectenerg-1427	565	34	(	(	PUNCT
fuelectenerg-1427	565	35	cf	cf	NOUN
fuelectenerg-1427	565	36	.	.	PUNCT
fuelectenerg-1427	566	1	definitions	definition	NOUN
fuelectenerg-1427	566	2	and	and	CCONJ
fuelectenerg-1427	566	3	theorems	theorem	NOUN
fuelectenerg-1427	566	4	of	of	ADP
fuelectenerg-1427	566	5	these	these	DET
fuelectenerg-1427	566	6	forms	form	NOUN
fuelectenerg-1427	566	7	in	in	ADP
fuelectenerg-1427	566	8	the	the	DET
fuelectenerg-1427	566	9	next	next	ADJ
fuelectenerg-1427	566	10	subsection	subsection	NOUN
fuelectenerg-1427	566	11	)	)	PUNCT
fuelectenerg-1427	566	12	.	.	PUNCT
fuelectenerg-1427	567	1	in	in	ADP
fuelectenerg-1427	567	2	this	this	DET
fuelectenerg-1427	567	3	paper	paper	NOUN
fuelectenerg-1427	567	4	,	,	PUNCT
fuelectenerg-1427	567	5	we	we	PRON
fuelectenerg-1427	567	6	propose	propose	VERB
fuelectenerg-1427	567	7	,	,	PUNCT
fuelectenerg-1427	567	8	as	as	SCONJ
fuelectenerg-1427	567	9	analogous	analogous	ADJ
fuelectenerg-1427	567	10	to	to	ADP
fuelectenerg-1427	567	11	the	the	DET
fuelectenerg-1427	567	12	binary	binary	ADJ
fuelectenerg-1427	567	13	case	case	NOUN
fuelectenerg-1427	567	14	,	,	PUNCT
fuelectenerg-1427	567	15	two	two	NUM
fuelectenerg-1427	567	16	general	general	ADJ
fuelectenerg-1427	567	17	families	family	NOUN
fuelectenerg-1427	567	18	of	of	ADP
fuelectenerg-1427	567	19	canonical	canonical	ADJ
fuelectenerg-1427	567	20	ternary	ternary	ADJ
fuelectenerg-1427	567	21	reed	reed	NOUN
fuelectenerg-1427	567	22	-	-	PUNCT
fuelectenerg-1427	567	23	muller	muller	NOUN
fuelectenerg-1427	567	24	forms	form	NOUN
fuelectenerg-1427	567	25	,	,	PUNCT
fuelectenerg-1427	567	26	called	call	VERB
fuelectenerg-1427	567	27	ternary	ternary	ADJ
fuelectenerg-1427	567	28	inclusive	inclusive	ADJ
fuelectenerg-1427	567	29	forms	form	NOUN
fuelectenerg-1427	567	30	(	(	PUNCT
fuelectenerg-1427	567	31	tifs	tifs	PROPN
fuelectenerg-1427	567	32	)	)	PUNCT
fuelectenerg-1427	567	33	and	and	CCONJ
fuelectenerg-1427	567	34	their	their	PRON
fuelectenerg-1427	567	35	generalization	generalization	NOUN
fuelectenerg-1427	567	36	of	of	ADP
fuelectenerg-1427	567	37	ternary	ternary	ADJ
fuelectenerg-1427	567	38	generalized	generalize	VERB
fuelectenerg-1427	567	39	inclusive	inclusive	ADJ
fuelectenerg-1427	567	40	forms	form	NOUN
fuelectenerg-1427	567	41	(	(	PUNCT
fuelectenerg-1427	567	42	tgifs	tgif	NOUN
fuelectenerg-1427	567	43	)	)	PUNCT
fuelectenerg-1427	567	44	,	,	PUNCT
fuelectenerg-1427	567	45	where	where	SCONJ
fuelectenerg-1427	567	46	gfsop	gfsop	NOUN
fuelectenerg-1427	567	47	minimizer	minimizer	NOUN
fuelectenerg-1427	567	48	based	base	VERB
fuelectenerg-1427	567	49	on	on	ADP
fuelectenerg-1427	567	50	these	these	DET
fuelectenerg-1427	567	51	new	new	ADJ
fuelectenerg-1427	567	52	forms	form	NOUN
fuelectenerg-1427	567	53	can	can	AUX
fuelectenerg-1427	567	54	be	be	AUX
fuelectenerg-1427	567	55	used	use	VERB
fuelectenerg-1427	567	56	to	to	PART
fuelectenerg-1427	567	57	minimize	minimize	VERB
fuelectenerg-1427	567	58	functional	functional	ADJ
fuelectenerg-1427	567	59	gfsop	gfsop	NOUN
fuelectenerg-1427	567	60	expressions	expression	NOUN
fuelectenerg-1427	567	61	and	and	CCONJ
fuelectenerg-1427	567	62	the	the	DET
fuelectenerg-1427	567	63	second	second	ADJ
fuelectenerg-1427	567	64	family	family	NOUN
fuelectenerg-1427	567	65	of	of	ADP
fuelectenerg-1427	567	66	tgifs	tgif	NOUN
fuelectenerg-1427	567	67	includes	include	VERB
fuelectenerg-1427	567	68	minimum	minimum	ADJ
fuelectenerg-1427	567	69	gfsops	gfsop	NOUN
fuelectenerg-1427	567	70	over	over	ADP
fuelectenerg-1427	567	71	ternary	ternary	ADJ
fuelectenerg-1427	567	72	galois	galois	PROPN
fuelectenerg-1427	567	73	field	field	NOUN
fuelectenerg-1427	567	74	.	.	PUNCT
fuelectenerg-1427	568	1	one	one	NUM
fuelectenerg-1427	568	2	of	of	ADP
fuelectenerg-1427	568	3	the	the	DET
fuelectenerg-1427	568	4	motivations	motivation	NOUN
fuelectenerg-1427	568	5	for	for	ADP
fuelectenerg-1427	568	6	this	this	DET
fuelectenerg-1427	568	7	work	work	NOUN
fuelectenerg-1427	568	8	is	be	AUX
fuelectenerg-1427	568	9	the	the	DET
fuelectenerg-1427	568	10	application	application	NOUN
fuelectenerg-1427	568	11	of	of	ADP
fuelectenerg-1427	568	12	these	these	DET
fuelectenerg-1427	568	13	tifs	tif	NOUN
fuelectenerg-1427	568	14	and	and	CCONJ
fuelectenerg-1427	568	15	tgifs	tgif	NOUN
fuelectenerg-1427	568	16	to	to	PART
fuelectenerg-1427	568	17	find	find	VERB
fuelectenerg-1427	568	18	minimum	minimum	ADJ
fuelectenerg-1427	568	19	gfsop	gfsop	NOUN
fuelectenerg-1427	568	20	for	for	ADP
fuelectenerg-1427	568	21	multiple	multiple	ADV
fuelectenerg-1427	568	22	-	-	PUNCT
fuelectenerg-1427	568	23	valued	value	VERB
fuelectenerg-1427	568	24	inputs	input	NOUN
fuelectenerg-1427	568	25	multiple	multiple	ADV
fuelectenerg-1427	568	26	-	-	PUNCT
fuelectenerg-1427	568	27	valued	value	VERB
fuelectenerg-1427	568	28	outputs	output	NOUN
fuelectenerg-1427	568	29	within	within	ADP
fuelectenerg-1427	568	30	logic	logic	ADJ
fuelectenerg-1427	568	31	synthesis	synthesis	NOUN
fuelectenerg-1427	568	32	,	,	PUNCT
fuelectenerg-1427	568	33	where	where	SCONJ
fuelectenerg-1427	568	34	the	the	DET
fuelectenerg-1427	568	35	corresponding	correspond	VERB
fuelectenerg-1427	568	36	s	s	PROPN
fuelectenerg-1427	568	37	/	/	SYM
fuelectenerg-1427	568	38	d	d	NOUN
fuelectenerg-1427	568	39	trees	tree	NOUN
fuelectenerg-1427	568	40	provide	provide	VERB
fuelectenerg-1427	568	41	more	more	ADJ
fuelectenerg-1427	568	42	general	general	ADJ
fuelectenerg-1427	568	43	polarity	polarity	NOUN
fuelectenerg-1427	568	44	that	that	PRON
fuelectenerg-1427	568	45	contains	contain	VERB
fuelectenerg-1427	568	46	grm	grm	NOUN
fuelectenerg-1427	568	47	forms	form	NOUN
fuelectenerg-1427	568	48	as	as	ADP
fuelectenerg-1427	568	49	a	a	DET
fuelectenerg-1427	568	50	special	special	ADJ
fuelectenerg-1427	568	51	case	case	NOUN
fuelectenerg-1427	568	52	.	.	PUNCT
fuelectenerg-1427	569	1	2.1	2.1	NUM
fuelectenerg-1427	569	2	s	s	NOUN
fuelectenerg-1427	569	3	/	/	SYM
fuelectenerg-1427	569	4	d	d	NOUN
fuelectenerg-1427	569	5	trees	tree	NOUN
fuelectenerg-1427	569	6	and	and	CCONJ
fuelectenerg-1427	569	7	their	their	PRON
fuelectenerg-1427	569	8	inclusive	inclusive	ADJ
fuelectenerg-1427	569	9	forms	form	NOUN
fuelectenerg-1427	569	10	and	and	CCONJ
fuelectenerg-1427	569	11	generalized	generalized	ADJ
fuelectenerg-1427	569	12	inclusive	inclusive	ADJ
fuelectenerg-1427	569	13	forms	form	NOUN
fuelectenerg-1427	569	14	two	two	NUM
fuelectenerg-1427	569	15	general	general	ADJ
fuelectenerg-1427	569	16	families	family	NOUN
fuelectenerg-1427	569	17	based	base	VERB
fuelectenerg-1427	569	18	on	on	ADP
fuelectenerg-1427	569	19	the	the	DET
fuelectenerg-1427	569	20	shannon	shannon	PROPN
fuelectenerg-1427	569	21	expansion	expansion	NOUN
fuelectenerg-1427	569	22	and	and	CCONJ
fuelectenerg-1427	569	23	the	the	DET
fuelectenerg-1427	569	24	generalized	generalized	ADJ
fuelectenerg-1427	569	25	davio	davio	NOUN
fuelectenerg-1427	569	26	expansion	expansion	NOUN
fuelectenerg-1427	569	27	which	which	PRON
fuelectenerg-1427	569	28	are	be	AUX
fuelectenerg-1427	569	29	produced	produce	VERB
fuelectenerg-1427	569	30	using	use	VERB
fuelectenerg-1427	569	31	the	the	DET
fuelectenerg-1427	569	32	corresponding	correspond	VERB
fuelectenerg-1427	569	33	s	s	PROPN
fuelectenerg-1427	569	34	/	/	SYM
fuelectenerg-1427	569	35	d	d	NOUN
fuelectenerg-1427	569	36	trees	tree	NOUN
fuelectenerg-1427	569	37	are	be	AUX
fuelectenerg-1427	569	38	presented	present	VERB
fuelectenerg-1427	569	39	in	in	ADP
fuelectenerg-1427	569	40	this	this	DET
fuelectenerg-1427	569	41	subsection	subsection	NOUN
fuelectenerg-1427	569	42	.	.	PUNCT
fuelectenerg-1427	570	1	these	these	DET
fuelectenerg-1427	570	2	families	family	NOUN
fuelectenerg-1427	570	3	are	be	AUX
fuelectenerg-1427	570	4	called	call	VERB
fuelectenerg-1427	570	5	the	the	DET
fuelectenerg-1427	570	6	inclusive	inclusive	ADJ
fuelectenerg-1427	570	7	forms	form	NOUN
fuelectenerg-1427	570	8	(	(	PUNCT
fuelectenerg-1427	570	9	ifs	ifs	PROPN
fuelectenerg-1427	570	10	)	)	PUNCT
fuelectenerg-1427	570	11	and	and	CCONJ
fuelectenerg-1427	570	12	the	the	DET
fuelectenerg-1427	570	13	generalized	generalized	ADJ
fuelectenerg-1427	570	14	inclusive	inclusive	ADJ
fuelectenerg-1427	570	15	forms	form	NOUN
fuelectenerg-1427	570	16	(	(	PUNCT
fuelectenerg-1427	570	17	gifs	gifs	PROPN
fuelectenerg-1427	570	18	)	)	PUNCT
fuelectenerg-1427	570	19	.	.	PUNCT
fuelectenerg-1427	571	1	the	the	DET
fuelectenerg-1427	571	2	corresponding	corresponding	ADJ
fuelectenerg-1427	571	3	expansions	expansion	NOUN
fuelectenerg-1427	571	4	over	over	ADP
fuelectenerg-1427	571	5	gf(2	gf(2	PROPN
fuelectenerg-1427	571	6	)	)	PUNCT
fuelectenerg-1427	571	7	are	be	AUX
fuelectenerg-1427	571	8	shown	show	VERB
fuelectenerg-1427	571	9	in	in	ADP
fuelectenerg-1427	571	10	figure	figure	NOUN
fuelectenerg-1427	571	11	3	3	NUM
fuelectenerg-1427	571	12	,	,	PUNCT
fuelectenerg-1427	571	13	where	where	SCONJ
fuelectenerg-1427	571	14	figure	figure	NOUN
fuelectenerg-1427	571	15	3(d	3(d	NOUN
fuelectenerg-1427	571	16	)	)	PUNCT
fuelectenerg-1427	571	17	shows	show	VERB
fuelectenerg-1427	571	18	the	the	DET
fuelectenerg-1427	571	19	new	new	ADJ
fuelectenerg-1427	571	20	node	node	NOUN
fuelectenerg-1427	571	21	which	which	PRON
fuelectenerg-1427	571	22	is	be	AUX
fuelectenerg-1427	571	23	based	base	VERB
fuelectenerg-1427	571	24	on	on	ADP
fuelectenerg-1427	571	25	binary	binary	ADJ
fuelectenerg-1427	571	26	davio	davio	NOUN
fuelectenerg-1427	571	27	expansions	expansion	NOUN
fuelectenerg-1427	571	28	called	call	VERB
fuelectenerg-1427	571	29	the	the	DET
fuelectenerg-1427	571	30	generalized	generalized	ADJ
fuelectenerg-1427	571	31	davio	davio	NOUN
fuelectenerg-1427	571	32	(	(	PUNCT
fuelectenerg-1427	571	33	d	d	NOUN
fuelectenerg-1427	571	34	)	)	PUNCT
fuelectenerg-1427	571	35	expansion	expansion	NOUN
fuelectenerg-1427	571	36	(	(	PUNCT
fuelectenerg-1427	571	37	cf	cf	NOUN
fuelectenerg-1427	571	38	.	.	PUNCT
fuelectenerg-1427	572	1	equation	equation	NOUN
fuelectenerg-1427	572	2	(	(	PUNCT
fuelectenerg-1427	572	3	28	28	NUM
fuelectenerg-1427	572	4	)	)	PUNCT
fuelectenerg-1427	572	5	for	for	ADP
fuelectenerg-1427	572	6	the	the	DET
fuelectenerg-1427	572	7	more	more	ADV
fuelectenerg-1427	572	8	general	general	ADJ
fuelectenerg-1427	572	9	ternary	ternary	ADJ
fuelectenerg-1427	572	10	case	case	NOUN
fuelectenerg-1427	572	11	)	)	PUNCT
fuelectenerg-1427	572	12	that	that	PRON
fuelectenerg-1427	572	13	generates	generate	VERB
fuelectenerg-1427	572	14	the	the	DET
fuelectenerg-1427	572	15	negative	negative	ADJ
fuelectenerg-1427	572	16	and	and	CCONJ
fuelectenerg-1427	572	17	positive	positive	ADJ
fuelectenerg-1427	572	18	davio	davio	NOUN
fuelectenerg-1427	572	19	expansions	expansion	NOUN
fuelectenerg-1427	572	20	as	as	ADP
fuelectenerg-1427	572	21	special	special	ADJ
fuelectenerg-1427	572	22	cases	case	NOUN
fuelectenerg-1427	572	23	.	.	PUNCT
fuelectenerg-1427	573	1	the	the	DET
fuelectenerg-1427	573	2	s	s	PROPN
fuelectenerg-1427	573	3	/	/	SYM
fuelectenerg-1427	573	4	d	d	NOUN
fuelectenerg-1427	573	5	trees	tree	NOUN
fuelectenerg-1427	573	6	for	for	ADP
fuelectenerg-1427	573	7	ifs	ifs	PROPN
fuelectenerg-1427	573	8	of	of	ADP
fuelectenerg-1427	573	9	two	two	NUM
fuelectenerg-1427	573	10	variables	variable	NOUN
fuelectenerg-1427	573	11	can	can	AUX
fuelectenerg-1427	573	12	be	be	AUX
fuelectenerg-1427	573	13	generated	generate	VERB
fuelectenerg-1427	573	14	for	for	ADP
fuelectenerg-1427	573	15	variable	variable	ADJ
fuelectenerg-1427	573	16	order	order	NOUN
fuelectenerg-1427	573	17	{	{	PUNCT
fuelectenerg-1427	573	18	a	a	DET
fuelectenerg-1427	573	19	,	,	PUNCT
fuelectenerg-1427	573	20	b	b	NOUN
fuelectenerg-1427	573	21	}	}	PUNCT
fuelectenerg-1427	573	22	and	and	CCONJ
fuelectenerg-1427	573	23	for	for	ADP
fuelectenerg-1427	573	24	variable	variable	ADJ
fuelectenerg-1427	573	25	order	order	NOUN
fuelectenerg-1427	573	26	{	{	PUNCT
fuelectenerg-1427	573	27	b	b	NOUN
fuelectenerg-1427	573	28	,	,	PUNCT
fuelectenerg-1427	573	29	a	a	PRON
fuelectenerg-1427	573	30	}	}	PUNCT
fuelectenerg-1427	573	31	as	as	ADV
fuelectenerg-1427	573	32	well	well	ADV
fuelectenerg-1427	573	33	.	.	PUNCT
fuelectenerg-1427	574	1	the	the	DET
fuelectenerg-1427	574	2	set	set	NOUN
fuelectenerg-1427	574	3	of	of	ADP
fuelectenerg-1427	574	4	gifs	gifs	PROPN
fuelectenerg-1427	574	5	for	for	ADP
fuelectenerg-1427	574	6	two	two	NUM
fuelectenerg-1427	574	7	variables	variable	NOUN
fuelectenerg-1427	574	8	is	be	AUX
fuelectenerg-1427	574	9	the	the	DET
fuelectenerg-1427	574	10	union	union	NOUN
fuelectenerg-1427	574	11	of	of	ADP
fuelectenerg-1427	574	12	these	these	DET
fuelectenerg-1427	574	13	two	two	NUM
fuelectenerg-1427	574	14	order	order	NOUN
fuelectenerg-1427	574	15	-	-	PUNCT
fuelectenerg-1427	574	16	based	base	VERB
fuelectenerg-1427	574	17	ifs	ifs	PROPN
fuelectenerg-1427	574	18	,	,	PUNCT
fuelectenerg-1427	574	19	where	where	SCONJ
fuelectenerg-1427	574	20	the	the	DET
fuelectenerg-1427	574	21	total	total	ADJ
fuelectenerg-1427	574	22	number	number	NOUN
fuelectenerg-1427	574	23	of	of	ADP
fuelectenerg-1427	574	24	the	the	DET
fuelectenerg-1427	574	25	resulting	result	VERB
fuelectenerg-1427	574	26	gifs	gifs	NOUN
fuelectenerg-1427	574	27	is	be	AUX
fuelectenerg-1427	574	28	equal	equal	ADJ
fuelectenerg-1427	574	29	to	to	ADP
fuelectenerg-1427	574	30	:	:	PUNCT
fuelectenerg-1427	574	31	#	#	SYM
fuelectenerg-1427	574	32	gif	gif	NOUN
fuelectenerg-1427	574	33	=	=	NOUN
fuelectenerg-1427	574	34	2	2	NUM
fuelectenerg-1427	574	35	·	·	PUNCT
fuelectenerg-1427	574	36	(	(	PUNCT
fuelectenerg-1427	574	37	#	#	SYM
fuelectenerg-1427	574	38	ifa	ifa	PROPN
fuelectenerg-1427	574	39	,	,	PUNCT
fuelectenerg-1427	574	40	b)−#(ifa	b)−#(ifa	PROPN
fuelectenerg-1427	574	41	,	,	PUNCT
fuelectenerg-1427	574	42	b	b	PROPN
fuelectenerg-1427	574	43	⋂	⋂	PROPN
fuelectenerg-1427	574	44	ifb	ifb	PROPN
fuelectenerg-1427	574	45	,	,	PUNCT
fuelectenerg-1427	574	46	a	a	PRON
fuelectenerg-1427	574	47	)	)	PUNCT
fuelectenerg-1427	574	48	.	.	PUNCT
fuelectenerg-1427	575	1	(	(	PUNCT
fuelectenerg-1427	575	2	27	27	NUM
fuelectenerg-1427	575	3	)	)	PUNCT
fuelectenerg-1427	575	4	the	the	DET
fuelectenerg-1427	575	5	galois	galois	PROPN
fuelectenerg-1427	575	6	-	-	PUNCT
fuelectenerg-1427	575	7	based	base	VERB
fuelectenerg-1427	575	8	shannon	shannon	NOUN
fuelectenerg-1427	575	9	and	and	CCONJ
fuelectenerg-1427	575	10	davio	davio	NOUN
fuelectenerg-1427	575	11	ternary	ternary	ADJ
fuelectenerg-1427	575	12	expansions	expansion	NOUN
fuelectenerg-1427	575	13	(	(	PUNCT
fuelectenerg-1427	575	14	i.e.	i.e.	X
fuelectenerg-1427	575	15	,	,	PUNCT
fuelectenerg-1427	575	16	flattened	flatten	VERB
fuelectenerg-1427	575	17	forms	form	NOUN
fuelectenerg-1427	575	18	)	)	PUNCT
fuelectenerg-1427	575	19	can	can	AUX
fuelectenerg-1427	575	20	be	be	AUX
fuelectenerg-1427	575	21	represented	represent	VERB
fuelectenerg-1427	575	22	in	in	ADP
fuelectenerg-1427	575	23	ternary	ternary	ADJ
fuelectenerg-1427	575	24	dts	dts	NOUN
fuelectenerg-1427	575	25	(	(	PUNCT
fuelectenerg-1427	575	26	tdts	tdts	ADJ
fuelectenerg-1427	575	27	)	)	PUNCT
fuelectenerg-1427	575	28	and	and	CCONJ
fuelectenerg-1427	575	29	the	the	DET
fuelectenerg-1427	575	30	corresponding	corresponding	ADJ
fuelectenerg-1427	575	31	varieties	variety	NOUN
fuelectenerg-1427	575	32	of	of	ADP
fuelectenerg-1427	575	33	ternary	ternary	ADJ
fuelectenerg-1427	575	34	dds	dds	PROPN
fuelectenerg-1427	575	35	(	(	PUNCT
fuelectenerg-1427	575	36	tdds	tdds	PROPN
fuelectenerg-1427	575	37	)	)	PUNCT
fuelectenerg-1427	575	38	according	accord	VERB
fuelectenerg-1427	575	39	to	to	ADP
fuelectenerg-1427	575	40	the	the	DET
fuelectenerg-1427	575	41	corresponding	corresponding	ADJ
fuelectenerg-1427	575	42	reduction	reduction	NOUN
fuelectenerg-1427	575	43	rules	rule	NOUN
fuelectenerg-1427	575	44	that	that	PRON
fuelectenerg-1427	575	45	are	be	AUX
fuelectenerg-1427	575	46	used	use	VERB
fuelectenerg-1427	575	47	[	[	PUNCT
fuelectenerg-1427	575	48	1	1	NUM
fuelectenerg-1427	575	49	,	,	PUNCT
fuelectenerg-1427	575	50	17	17	NUM
fuelectenerg-1427	575	51	]	]	PUNCT
fuelectenerg-1427	575	52	.	.	PUNCT
fuelectenerg-1427	576	1	for	for	ADP
fuelectenerg-1427	576	2	one	one	NUM
fuelectenerg-1427	576	3	107	107	NUM
fuelectenerg-1427	576	4	an	an	DET
fuelectenerg-1427	576	5	extended	extended	ADJ
fuelectenerg-1427	576	6	green	green	ADJ
fuelectenerg-1427	576	7	sasao	sasao	PROPN
fuelectenerg-1427	576	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	576	9	of	of	ADP
fuelectenerg-1427	576	10	canonical	canonical	ADJ
fuelectenerg-1427	576	11	ternary	ternary	ADJ
fuelectenerg-1427	576	12	galois	galois	NOUN
fuelectenerg-1427	576	13	forms	form	NOUN
fuelectenerg-1427	576	14	...	...	PUNCT
fuelectenerg-1427	576	15	as	as	ADP
fuelectenerg-1427	576	16	the	the	DET
fuelectenerg-1427	576	17	green	green	PROPN
fuelectenerg-1427	576	18	-	-	PUNCT
fuelectenerg-1427	576	19	sasao	sasao	PROPN
fuelectenerg-1427	576	20	hierarchy	hierarchy	NOUN
fuelectenerg-1427	576	21	,	,	PUNCT
fuelectenerg-1427	576	22	have	have	AUX
fuelectenerg-1427	576	23	been	be	AUX
fuelectenerg-1427	576	24	described	describe	VERB
fuelectenerg-1427	576	25	[	[	X
fuelectenerg-1427	576	26	1	1	NUM
fuelectenerg-1427	576	27	,	,	PUNCT
fuelectenerg-1427	576	28	10	10	NUM
fuelectenerg-1427	576	29	,	,	PUNCT
fuelectenerg-1427	576	30	17	17	NUM
fuelectenerg-1427	576	31	]	]	PUNCT
fuelectenerg-1427	576	32	.	.	PUNCT
fuelectenerg-1427	577	1	because	because	SCONJ
fuelectenerg-1427	577	2	canonical	canonical	ADJ
fuelectenerg-1427	577	3	families	family	NOUN
fuelectenerg-1427	577	4	have	have	VERB
fuelectenerg-1427	577	5	higher	high	ADJ
fuelectenerg-1427	577	6	testability	testability	NOUN
fuelectenerg-1427	577	7	and	and	CCONJ
fuelectenerg-1427	577	8	some	some	DET
fuelectenerg-1427	577	9	other	other	ADJ
fuelectenerg-1427	577	10	properties	property	NOUN
fuelectenerg-1427	577	11	desirable	desirable	ADJ
fuelectenerg-1427	577	12	for	for	ADP
fuelectenerg-1427	577	13	efficient	efficient	ADJ
fuelectenerg-1427	577	14	synthesis	synthesis	NOUN
fuelectenerg-1427	577	15	,	,	PUNCT
fuelectenerg-1427	577	16	especially	especially	ADV
fuelectenerg-1427	577	17	of	of	ADP
fuelectenerg-1427	577	18	some	some	DET
fuelectenerg-1427	577	19	classes	class	NOUN
fuelectenerg-1427	577	20	of	of	ADP
fuelectenerg-1427	577	21	functions	function	NOUN
fuelectenerg-1427	577	22	,	,	PUNCT
fuelectenerg-1427	577	23	they	they	PRON
fuelectenerg-1427	577	24	are	be	AUX
fuelectenerg-1427	577	25	widely	widely	ADV
fuelectenerg-1427	577	26	investigated	investigate	VERB
fuelectenerg-1427	577	27	.	.	PUNCT
fuelectenerg-1427	578	1	a	a	DET
fuelectenerg-1427	578	2	similar	similar	ADJ
fuelectenerg-1427	578	3	ternary	ternary	ADJ
fuelectenerg-1427	578	4	version	version	NOUN
fuelectenerg-1427	578	5	of	of	ADP
fuelectenerg-1427	578	6	the	the	DET
fuelectenerg-1427	578	7	binary	binary	ADJ
fuelectenerg-1427	578	8	green	green	PROPN
fuelectenerg-1427	578	9	-	-	PUNCT
fuelectenerg-1427	578	10	sasao	sasao	PROPN
fuelectenerg-1427	578	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	578	12	can	can	AUX
fuelectenerg-1427	578	13	be	be	AUX
fuelectenerg-1427	578	14	developed	develop	VERB
fuelectenerg-1427	578	15	,	,	PUNCT
fuelectenerg-1427	578	16	where	where	SCONJ
fuelectenerg-1427	578	17	this	this	DET
fuelectenerg-1427	578	18	hierarchy	hierarchy	NOUN
fuelectenerg-1427	578	19	can	can	AUX
fuelectenerg-1427	578	20	find	find	VERB
fuelectenerg-1427	578	21	applications	application	NOUN
fuelectenerg-1427	578	22	in	in	ADP
fuelectenerg-1427	578	23	minimizing	minimize	VERB
fuelectenerg-1427	578	24	galois	galois	PROPN
fuelectenerg-1427	578	25	field	field	NOUN
fuelectenerg-1427	578	26	sum	sum	NOUN
fuelectenerg-1427	578	27	-	-	PUNCT
fuelectenerg-1427	578	28	of	of	ADP
fuelectenerg-1427	578	29	-	-	PUNCT
fuelectenerg-1427	578	30	product	product	NOUN
fuelectenerg-1427	578	31	(	(	PUNCT
fuelectenerg-1427	578	32	gfsop	gfsop	NOUN
fuelectenerg-1427	578	33	)	)	PUNCT
fuelectenerg-1427	578	34	expressions	expression	NOUN
fuelectenerg-1427	578	35	which	which	PRON
fuelectenerg-1427	578	36	are	be	AUX
fuelectenerg-1427	578	37	expressions	expression	NOUN
fuelectenerg-1427	578	38	in	in	ADP
fuelectenerg-1427	578	39	the	the	DET
fuelectenerg-1427	578	40	sum	sum	NOUN
fuelectenerg-1427	578	41	-	-	PUNCT
fuelectenerg-1427	578	42	of	of	ADP
fuelectenerg-1427	578	43	-	-	PUNCT
fuelectenerg-1427	578	44	product	product	NOUN
fuelectenerg-1427	578	45	form	form	NOUN
fuelectenerg-1427	578	46	that	that	PRON
fuelectenerg-1427	578	47	uses	use	VERB
fuelectenerg-1427	578	48	the	the	DET
fuelectenerg-1427	578	49	additions	addition	NOUN
fuelectenerg-1427	578	50	and	and	CCONJ
fuelectenerg-1427	578	51	multiplications	multiplication	NOUN
fuelectenerg-1427	578	52	of	of	ADP
fuelectenerg-1427	578	53	arbitrary	arbitrary	ADJ
fuelectenerg-1427	578	54	radix	radix	PROPN
fuelectenerg-1427	578	55	galois	galois	PROPN
fuelectenerg-1427	578	56	field	field	NOUN
fuelectenerg-1427	578	57	,	,	PUNCT
fuelectenerg-1427	578	58	and	and	CCONJ
fuelectenerg-1427	578	59	can	can	AUX
fuelectenerg-1427	578	60	be	be	AUX
fuelectenerg-1427	578	61	used	use	VERB
fuelectenerg-1427	578	62	for	for	ADP
fuelectenerg-1427	578	63	the	the	DET
fuelectenerg-1427	578	64	creation	creation	NOUN
fuelectenerg-1427	578	65	of	of	ADP
fuelectenerg-1427	578	66	new	new	ADJ
fuelectenerg-1427	578	67	forms	form	NOUN
fuelectenerg-1427	578	68	,	,	PUNCT
fuelectenerg-1427	578	69	decision	decision	NOUN
fuelectenerg-1427	578	70	diagrams	diagram	NOUN
fuelectenerg-1427	578	71	and	and	CCONJ
fuelectenerg-1427	578	72	regular	regular	ADJ
fuelectenerg-1427	578	73	structures	structure	NOUN
fuelectenerg-1427	578	74	.	.	PUNCT
fuelectenerg-1427	579	1	the	the	DET
fuelectenerg-1427	579	2	current	current	ADJ
fuelectenerg-1427	579	3	state	state	NOUN
fuelectenerg-1427	579	4	-	-	PUNCT
fuelectenerg-1427	579	5	of	of	ADP
fuelectenerg-1427	579	6	-	-	PUNCT
fuelectenerg-1427	579	7	the	the	DET
fuelectenerg-1427	579	8	-	-	PUNCT
fuelectenerg-1427	579	9	art	art	NOUN
fuelectenerg-1427	579	10	minimizers	minimizer	NOUN
fuelectenerg-1427	579	11	of	of	ADP
fuelectenerg-1427	579	12	exclusive	exclusive	ADJ
fuelectenerg-1427	579	13	sum	sum	NOUN
fuelectenerg-1427	579	14	-	-	PUNCT
fuelectenerg-1427	579	15	of	of	ADP
fuelectenerg-1427	579	16	-	-	PUNCT
fuelectenerg-1427	579	17	product	product	NOUN
fuelectenerg-1427	579	18	(	(	PUNCT
fuelectenerg-1427	579	19	esop	esop	PROPN
fuelectenerg-1427	579	20	)	)	PUNCT
fuelectenerg-1427	579	21	expressions	expression	NOUN
fuelectenerg-1427	579	22	are	be	AUX
fuelectenerg-1427	579	23	based	base	VERB
fuelectenerg-1427	579	24	on	on	ADP
fuelectenerg-1427	579	25	heuristics	heuristic	NOUN
fuelectenerg-1427	579	26	and	and	CCONJ
fuelectenerg-1427	579	27	give	give	VERB
fuelectenerg-1427	579	28	the	the	DET
fuelectenerg-1427	579	29	exact	exact	ADJ
fuelectenerg-1427	579	30	solution	solution	NOUN
fuelectenerg-1427	579	31	only	only	ADV
fuelectenerg-1427	579	32	for	for	ADP
fuelectenerg-1427	579	33	functions	function	NOUN
fuelectenerg-1427	579	34	with	with	ADP
fuelectenerg-1427	579	35	a	a	DET
fuelectenerg-1427	579	36	small	small	ADJ
fuelectenerg-1427	579	37	number	number	NOUN
fuelectenerg-1427	579	38	of	of	ADP
fuelectenerg-1427	579	39	variables	variable	NOUN
fuelectenerg-1427	579	40	.	.	PUNCT
fuelectenerg-1427	580	1	for	for	ADP
fuelectenerg-1427	580	2	example	example	NOUN
fuelectenerg-1427	580	3	,	,	PUNCT
fuelectenerg-1427	580	4	a	a	DET
fuelectenerg-1427	580	5	formulation	formulation	NOUN
fuelectenerg-1427	580	6	for	for	ADP
fuelectenerg-1427	580	7	finding	find	VERB
fuelectenerg-1427	580	8	exact	exact	ADJ
fuelectenerg-1427	580	9	esop	esop	PROPN
fuelectenerg-1427	580	10	was	be	AUX
fuelectenerg-1427	580	11	given	give	VERB
fuelectenerg-1427	580	12	[	[	X
fuelectenerg-1427	580	13	11	11	NUM
fuelectenerg-1427	580	14	]	]	PUNCT
fuelectenerg-1427	580	15	,	,	PUNCT
fuelectenerg-1427	580	16	and	and	CCONJ
fuelectenerg-1427	580	17	an	an	DET
fuelectenerg-1427	580	18	algorithm	algorithm	NOUN
fuelectenerg-1427	580	19	to	to	PART
fuelectenerg-1427	580	20	derive	derive	VERB
fuelectenerg-1427	580	21	minimum	minimum	ADJ
fuelectenerg-1427	580	22	esop	esop	NOUN
fuelectenerg-1427	580	23	for	for	ADP
fuelectenerg-1427	580	24	6	6	NUM
fuelectenerg-1427	580	25	-	-	PUNCT
fuelectenerg-1427	580	26	variable	variable	ADJ
fuelectenerg-1427	580	27	function	function	NOUN
fuelectenerg-1427	580	28	was	be	AUX
fuelectenerg-1427	580	29	provided	provide	VERB
fuelectenerg-1427	580	30	[	[	X
fuelectenerg-1427	580	31	25	25	NUM
fuelectenerg-1427	580	32	]	]	PUNCT
fuelectenerg-1427	580	33	.	.	PUNCT
fuelectenerg-1427	581	1	because	because	SCONJ
fuelectenerg-1427	581	2	gfsop	gfsop	PROPN
fuelectenerg-1427	581	3	minimization	minimization	NOUN
fuelectenerg-1427	581	4	is	be	AUX
fuelectenerg-1427	581	5	even	even	ADV
fuelectenerg-1427	581	6	more	more	ADV
fuelectenerg-1427	581	7	difficult	difficult	ADJ
fuelectenerg-1427	581	8	,	,	PUNCT
fuelectenerg-1427	581	9	it	it	PRON
fuelectenerg-1427	581	10	is	be	AUX
fuelectenerg-1427	581	11	important	important	ADJ
fuelectenerg-1427	581	12	to	to	PART
fuelectenerg-1427	581	13	investigate	investigate	VERB
fuelectenerg-1427	581	14	the	the	DET
fuelectenerg-1427	581	15	structural	structural	ADJ
fuelectenerg-1427	581	16	properties	property	NOUN
fuelectenerg-1427	581	17	and	and	CCONJ
fuelectenerg-1427	581	18	the	the	DET
fuelectenerg-1427	581	19	counts	count	NOUN
fuelectenerg-1427	581	20	of	of	ADP
fuelectenerg-1427	581	21	their	their	PRON
fuelectenerg-1427	581	22	canonical	canonical	ADJ
fuelectenerg-1427	581	23	sub	sub	NOUN
fuelectenerg-1427	581	24	-	-	NOUN
fuelectenerg-1427	581	25	families	family	NOUN
fuelectenerg-1427	581	26	.	.	PUNCT
fuelectenerg-1427	582	1	two	two	NUM
fuelectenerg-1427	582	2	families	family	NOUN
fuelectenerg-1427	582	3	of	of	ADP
fuelectenerg-1427	582	4	binary	binary	ADJ
fuelectenerg-1427	582	5	canonical	canonical	ADJ
fuelectenerg-1427	582	6	reed	reed	NOUN
fuelectenerg-1427	582	7	-	-	PUNCT
fuelectenerg-1427	582	8	muller	muller	NOUN
fuelectenerg-1427	582	9	forms	form	NOUN
fuelectenerg-1427	582	10	,	,	PUNCT
fuelectenerg-1427	582	11	called	call	VERB
fuelectenerg-1427	582	12	inclusive	inclusive	ADJ
fuelectenerg-1427	582	13	forms	form	NOUN
fuelectenerg-1427	582	14	(	(	PUNCT
fuelectenerg-1427	582	15	ifs	ifs	PROPN
fuelectenerg-1427	582	16	)	)	PUNCT
fuelectenerg-1427	582	17	and	and	CCONJ
fuelectenerg-1427	582	18	generalized	generalized	ADJ
fuelectenerg-1427	582	19	inclusive	inclusive	ADJ
fuelectenerg-1427	582	20	forms	form	NOUN
fuelectenerg-1427	582	21	(	(	PUNCT
fuelectenerg-1427	582	22	gifs	gifs	PROPN
fuelectenerg-1427	582	23	)	)	PUNCT
fuelectenerg-1427	582	24	were	be	AUX
fuelectenerg-1427	582	25	presented	present	VERB
fuelectenerg-1427	582	26	[	[	X
fuelectenerg-1427	582	27	1	1	NUM
fuelectenerg-1427	582	28	]	]	PUNCT
fuelectenerg-1427	582	29	,	,	PUNCT
fuelectenerg-1427	582	30	where	where	SCONJ
fuelectenerg-1427	582	31	the	the	DET
fuelectenerg-1427	582	32	second	second	ADJ
fuelectenerg-1427	582	33	family	family	NOUN
fuelectenerg-1427	582	34	was	be	AUX
fuelectenerg-1427	582	35	the	the	DET
fuelectenerg-1427	582	36	first	first	ADJ
fuelectenerg-1427	582	37	to	to	PART
fuelectenerg-1427	582	38	include	include	VERB
fuelectenerg-1427	582	39	all	all	DET
fuelectenerg-1427	582	40	minimum	minimum	ADJ
fuelectenerg-1427	582	41	esops	esop	NOUN
fuelectenerg-1427	582	42	(	(	PUNCT
fuelectenerg-1427	582	43	binary	binary	ADJ
fuelectenerg-1427	582	44	gfsops	gfsop	NOUN
fuelectenerg-1427	582	45	)	)	PUNCT
fuelectenerg-1427	582	46	.	.	PUNCT
fuelectenerg-1427	583	1	in	in	ADP
fuelectenerg-1427	583	2	these	these	DET
fuelectenerg-1427	583	3	forms	form	NOUN
fuelectenerg-1427	583	4	,	,	PUNCT
fuelectenerg-1427	583	5	if	if	SCONJ
fuelectenerg-1427	583	6	is	be	AUX
fuelectenerg-1427	583	7	the	the	DET
fuelectenerg-1427	583	8	form	form	NOUN
fuelectenerg-1427	583	9	generated	generate	VERB
fuelectenerg-1427	583	10	by	by	ADP
fuelectenerg-1427	583	11	the	the	DET
fuelectenerg-1427	583	12	corresponding	correspond	VERB
fuelectenerg-1427	583	13	s	s	PROPN
fuelectenerg-1427	583	14	/	/	SYM
fuelectenerg-1427	583	15	d	d	NOUN
fuelectenerg-1427	583	16	tree	tree	NOUN
fuelectenerg-1427	583	17	and	and	CCONJ
fuelectenerg-1427	583	18	gif	gif	NOUN
fuelectenerg-1427	583	19	is	be	AUX
fuelectenerg-1427	583	20	the	the	DET
fuelectenerg-1427	583	21	form	form	NOUN
fuelectenerg-1427	583	22	which	which	PRON
fuelectenerg-1427	583	23	is	be	AUX
fuelectenerg-1427	583	24	the	the	DET
fuelectenerg-1427	583	25	union	union	NOUN
fuelectenerg-1427	583	26	of	of	ADP
fuelectenerg-1427	583	27	the	the	DET
fuelectenerg-1427	583	28	various	various	ADJ
fuelectenerg-1427	583	29	variable	variable	NOUN
fuelectenerg-1427	583	30	-	-	PUNCT
fuelectenerg-1427	583	31	based	base	VERB
fuelectenerg-1427	583	32	ordering	order	VERB
fuelectenerg-1427	583	33	ifs	ifs	PROPN
fuelectenerg-1427	583	34	(	(	PUNCT
fuelectenerg-1427	583	35	cf	cf	NOUN
fuelectenerg-1427	583	36	.	.	PUNCT
fuelectenerg-1427	584	1	definitions	definition	NOUN
fuelectenerg-1427	584	2	and	and	CCONJ
fuelectenerg-1427	584	3	theorems	theorem	NOUN
fuelectenerg-1427	584	4	of	of	ADP
fuelectenerg-1427	584	5	these	these	DET
fuelectenerg-1427	584	6	forms	form	NOUN
fuelectenerg-1427	584	7	in	in	ADP
fuelectenerg-1427	584	8	the	the	DET
fuelectenerg-1427	584	9	next	next	ADJ
fuelectenerg-1427	584	10	subsection	subsection	NOUN
fuelectenerg-1427	584	11	)	)	PUNCT
fuelectenerg-1427	584	12	.	.	PUNCT
fuelectenerg-1427	585	1	in	in	ADP
fuelectenerg-1427	585	2	this	this	DET
fuelectenerg-1427	585	3	paper	paper	NOUN
fuelectenerg-1427	585	4	,	,	PUNCT
fuelectenerg-1427	585	5	we	we	PRON
fuelectenerg-1427	585	6	propose	propose	VERB
fuelectenerg-1427	585	7	,	,	PUNCT
fuelectenerg-1427	585	8	as	as	SCONJ
fuelectenerg-1427	585	9	analogous	analogous	ADJ
fuelectenerg-1427	585	10	to	to	ADP
fuelectenerg-1427	585	11	the	the	DET
fuelectenerg-1427	585	12	binary	binary	ADJ
fuelectenerg-1427	585	13	case	case	NOUN
fuelectenerg-1427	585	14	,	,	PUNCT
fuelectenerg-1427	585	15	two	two	NUM
fuelectenerg-1427	585	16	general	general	ADJ
fuelectenerg-1427	585	17	families	family	NOUN
fuelectenerg-1427	585	18	of	of	ADP
fuelectenerg-1427	585	19	canonical	canonical	ADJ
fuelectenerg-1427	585	20	ternary	ternary	ADJ
fuelectenerg-1427	585	21	reed	reed	NOUN
fuelectenerg-1427	585	22	-	-	PUNCT
fuelectenerg-1427	585	23	muller	muller	NOUN
fuelectenerg-1427	585	24	forms	form	NOUN
fuelectenerg-1427	585	25	,	,	PUNCT
fuelectenerg-1427	585	26	called	call	VERB
fuelectenerg-1427	585	27	ternary	ternary	ADJ
fuelectenerg-1427	585	28	inclusive	inclusive	ADJ
fuelectenerg-1427	585	29	forms	form	NOUN
fuelectenerg-1427	585	30	(	(	PUNCT
fuelectenerg-1427	585	31	tifs	tifs	PROPN
fuelectenerg-1427	585	32	)	)	PUNCT
fuelectenerg-1427	585	33	and	and	CCONJ
fuelectenerg-1427	585	34	their	their	PRON
fuelectenerg-1427	585	35	generalization	generalization	NOUN
fuelectenerg-1427	585	36	of	of	ADP
fuelectenerg-1427	585	37	ternary	ternary	ADJ
fuelectenerg-1427	585	38	generalized	generalize	VERB
fuelectenerg-1427	585	39	inclusive	inclusive	ADJ
fuelectenerg-1427	585	40	forms	form	NOUN
fuelectenerg-1427	585	41	(	(	PUNCT
fuelectenerg-1427	585	42	tgifs	tgif	NOUN
fuelectenerg-1427	585	43	)	)	PUNCT
fuelectenerg-1427	585	44	,	,	PUNCT
fuelectenerg-1427	585	45	where	where	SCONJ
fuelectenerg-1427	585	46	gfsop	gfsop	NOUN
fuelectenerg-1427	585	47	minimizer	minimizer	NOUN
fuelectenerg-1427	585	48	based	base	VERB
fuelectenerg-1427	585	49	on	on	ADP
fuelectenerg-1427	585	50	these	these	DET
fuelectenerg-1427	585	51	new	new	ADJ
fuelectenerg-1427	585	52	forms	form	NOUN
fuelectenerg-1427	585	53	can	can	AUX
fuelectenerg-1427	585	54	be	be	AUX
fuelectenerg-1427	585	55	used	use	VERB
fuelectenerg-1427	585	56	to	to	PART
fuelectenerg-1427	585	57	minimize	minimize	VERB
fuelectenerg-1427	585	58	functional	functional	ADJ
fuelectenerg-1427	585	59	gfsop	gfsop	NOUN
fuelectenerg-1427	585	60	expressions	expression	NOUN
fuelectenerg-1427	585	61	and	and	CCONJ
fuelectenerg-1427	585	62	the	the	DET
fuelectenerg-1427	585	63	second	second	ADJ
fuelectenerg-1427	585	64	family	family	NOUN
fuelectenerg-1427	585	65	of	of	ADP
fuelectenerg-1427	585	66	tgifs	tgif	NOUN
fuelectenerg-1427	585	67	includes	include	VERB
fuelectenerg-1427	585	68	minimum	minimum	ADJ
fuelectenerg-1427	585	69	gfsops	gfsop	NOUN
fuelectenerg-1427	585	70	over	over	ADP
fuelectenerg-1427	585	71	ternary	ternary	ADJ
fuelectenerg-1427	585	72	galois	galois	PROPN
fuelectenerg-1427	585	73	field	field	NOUN
fuelectenerg-1427	585	74	.	.	PUNCT
fuelectenerg-1427	586	1	one	one	NUM
fuelectenerg-1427	586	2	of	of	ADP
fuelectenerg-1427	586	3	the	the	DET
fuelectenerg-1427	586	4	motivations	motivation	NOUN
fuelectenerg-1427	586	5	for	for	ADP
fuelectenerg-1427	586	6	this	this	DET
fuelectenerg-1427	586	7	work	work	NOUN
fuelectenerg-1427	586	8	is	be	AUX
fuelectenerg-1427	586	9	the	the	DET
fuelectenerg-1427	586	10	application	application	NOUN
fuelectenerg-1427	586	11	of	of	ADP
fuelectenerg-1427	586	12	these	these	DET
fuelectenerg-1427	586	13	tifs	tif	NOUN
fuelectenerg-1427	586	14	and	and	CCONJ
fuelectenerg-1427	586	15	tgifs	tgif	NOUN
fuelectenerg-1427	586	16	to	to	PART
fuelectenerg-1427	586	17	find	find	VERB
fuelectenerg-1427	586	18	minimum	minimum	ADJ
fuelectenerg-1427	586	19	gfsop	gfsop	NOUN
fuelectenerg-1427	586	20	for	for	ADP
fuelectenerg-1427	586	21	multiple	multiple	ADV
fuelectenerg-1427	586	22	-	-	PUNCT
fuelectenerg-1427	586	23	valued	value	VERB
fuelectenerg-1427	586	24	inputs	input	NOUN
fuelectenerg-1427	586	25	multiple	multiple	ADV
fuelectenerg-1427	586	26	-	-	PUNCT
fuelectenerg-1427	586	27	valued	value	VERB
fuelectenerg-1427	586	28	outputs	output	NOUN
fuelectenerg-1427	586	29	within	within	ADP
fuelectenerg-1427	586	30	logic	logic	ADJ
fuelectenerg-1427	586	31	synthesis	synthesis	NOUN
fuelectenerg-1427	586	32	,	,	PUNCT
fuelectenerg-1427	586	33	where	where	SCONJ
fuelectenerg-1427	586	34	the	the	DET
fuelectenerg-1427	586	35	corresponding	correspond	VERB
fuelectenerg-1427	586	36	s	s	PROPN
fuelectenerg-1427	586	37	/	/	SYM
fuelectenerg-1427	586	38	d	d	NOUN
fuelectenerg-1427	586	39	trees	tree	NOUN
fuelectenerg-1427	586	40	provide	provide	VERB
fuelectenerg-1427	586	41	more	more	ADJ
fuelectenerg-1427	586	42	general	general	ADJ
fuelectenerg-1427	586	43	polarity	polarity	NOUN
fuelectenerg-1427	586	44	that	that	PRON
fuelectenerg-1427	586	45	contains	contain	VERB
fuelectenerg-1427	586	46	grm	grm	NOUN
fuelectenerg-1427	586	47	forms	form	NOUN
fuelectenerg-1427	586	48	as	as	ADP
fuelectenerg-1427	586	49	a	a	DET
fuelectenerg-1427	586	50	special	special	ADJ
fuelectenerg-1427	586	51	case	case	NOUN
fuelectenerg-1427	586	52	.	.	PUNCT
fuelectenerg-1427	587	1	2.1	2.1	NUM
fuelectenerg-1427	587	2	s	s	NOUN
fuelectenerg-1427	587	3	/	/	SYM
fuelectenerg-1427	587	4	d	d	NOUN
fuelectenerg-1427	587	5	trees	tree	NOUN
fuelectenerg-1427	587	6	and	and	CCONJ
fuelectenerg-1427	587	7	their	their	PRON
fuelectenerg-1427	587	8	inclusive	inclusive	ADJ
fuelectenerg-1427	587	9	forms	form	NOUN
fuelectenerg-1427	587	10	and	and	CCONJ
fuelectenerg-1427	587	11	generalized	generalized	ADJ
fuelectenerg-1427	587	12	inclusive	inclusive	ADJ
fuelectenerg-1427	587	13	forms	form	NOUN
fuelectenerg-1427	587	14	two	two	NUM
fuelectenerg-1427	587	15	general	general	ADJ
fuelectenerg-1427	587	16	families	family	NOUN
fuelectenerg-1427	587	17	based	base	VERB
fuelectenerg-1427	587	18	on	on	ADP
fuelectenerg-1427	587	19	the	the	DET
fuelectenerg-1427	587	20	shannon	shannon	PROPN
fuelectenerg-1427	587	21	expansion	expansion	NOUN
fuelectenerg-1427	587	22	and	and	CCONJ
fuelectenerg-1427	587	23	the	the	DET
fuelectenerg-1427	587	24	generalized	generalized	ADJ
fuelectenerg-1427	587	25	davio	davio	NOUN
fuelectenerg-1427	587	26	expansion	expansion	NOUN
fuelectenerg-1427	587	27	which	which	PRON
fuelectenerg-1427	587	28	are	be	AUX
fuelectenerg-1427	587	29	produced	produce	VERB
fuelectenerg-1427	587	30	using	use	VERB
fuelectenerg-1427	587	31	the	the	DET
fuelectenerg-1427	587	32	corresponding	correspond	VERB
fuelectenerg-1427	587	33	s	s	PROPN
fuelectenerg-1427	587	34	/	/	SYM
fuelectenerg-1427	587	35	d	d	NOUN
fuelectenerg-1427	587	36	trees	tree	NOUN
fuelectenerg-1427	587	37	are	be	AUX
fuelectenerg-1427	587	38	presented	present	VERB
fuelectenerg-1427	587	39	in	in	ADP
fuelectenerg-1427	587	40	this	this	DET
fuelectenerg-1427	587	41	subsection	subsection	NOUN
fuelectenerg-1427	587	42	.	.	PUNCT
fuelectenerg-1427	588	1	these	these	DET
fuelectenerg-1427	588	2	families	family	NOUN
fuelectenerg-1427	588	3	are	be	AUX
fuelectenerg-1427	588	4	called	call	VERB
fuelectenerg-1427	588	5	the	the	DET
fuelectenerg-1427	588	6	inclusive	inclusive	ADJ
fuelectenerg-1427	588	7	forms	form	NOUN
fuelectenerg-1427	588	8	(	(	PUNCT
fuelectenerg-1427	588	9	ifs	ifs	PROPN
fuelectenerg-1427	588	10	)	)	PUNCT
fuelectenerg-1427	588	11	and	and	CCONJ
fuelectenerg-1427	588	12	the	the	DET
fuelectenerg-1427	588	13	generalized	generalized	ADJ
fuelectenerg-1427	588	14	inclusive	inclusive	ADJ
fuelectenerg-1427	588	15	forms	form	NOUN
fuelectenerg-1427	588	16	(	(	PUNCT
fuelectenerg-1427	588	17	gifs	gifs	PROPN
fuelectenerg-1427	588	18	)	)	PUNCT
fuelectenerg-1427	588	19	.	.	PUNCT
fuelectenerg-1427	589	1	the	the	DET
fuelectenerg-1427	589	2	corresponding	corresponding	ADJ
fuelectenerg-1427	589	3	expansions	expansion	NOUN
fuelectenerg-1427	589	4	over	over	ADP
fuelectenerg-1427	589	5	gf(2	gf(2	PROPN
fuelectenerg-1427	589	6	)	)	PUNCT
fuelectenerg-1427	589	7	are	be	AUX
fuelectenerg-1427	589	8	shown	show	VERB
fuelectenerg-1427	589	9	in	in	ADP
fuelectenerg-1427	589	10	figure	figure	NOUN
fuelectenerg-1427	589	11	3	3	NUM
fuelectenerg-1427	589	12	,	,	PUNCT
fuelectenerg-1427	589	13	where	where	SCONJ
fuelectenerg-1427	589	14	figure	figure	NOUN
fuelectenerg-1427	589	15	3(d	3(d	NOUN
fuelectenerg-1427	589	16	)	)	PUNCT
fuelectenerg-1427	589	17	shows	show	VERB
fuelectenerg-1427	589	18	the	the	DET
fuelectenerg-1427	589	19	new	new	ADJ
fuelectenerg-1427	589	20	node	node	NOUN
fuelectenerg-1427	589	21	which	which	PRON
fuelectenerg-1427	589	22	is	be	AUX
fuelectenerg-1427	589	23	based	base	VERB
fuelectenerg-1427	589	24	on	on	ADP
fuelectenerg-1427	589	25	binary	binary	ADJ
fuelectenerg-1427	589	26	davio	davio	NOUN
fuelectenerg-1427	589	27	expansions	expansion	NOUN
fuelectenerg-1427	589	28	called	call	VERB
fuelectenerg-1427	589	29	the	the	DET
fuelectenerg-1427	589	30	generalized	generalized	ADJ
fuelectenerg-1427	589	31	davio	davio	NOUN
fuelectenerg-1427	589	32	(	(	PUNCT
fuelectenerg-1427	589	33	d	d	NOUN
fuelectenerg-1427	589	34	)	)	PUNCT
fuelectenerg-1427	589	35	expansion	expansion	NOUN
fuelectenerg-1427	589	36	(	(	PUNCT
fuelectenerg-1427	589	37	cf	cf	NOUN
fuelectenerg-1427	589	38	.	.	PUNCT
fuelectenerg-1427	590	1	equation	equation	NOUN
fuelectenerg-1427	590	2	(	(	PUNCT
fuelectenerg-1427	590	3	28	28	NUM
fuelectenerg-1427	590	4	)	)	PUNCT
fuelectenerg-1427	590	5	for	for	ADP
fuelectenerg-1427	590	6	the	the	DET
fuelectenerg-1427	590	7	more	more	ADV
fuelectenerg-1427	590	8	general	general	ADJ
fuelectenerg-1427	590	9	ternary	ternary	ADJ
fuelectenerg-1427	590	10	case	case	NOUN
fuelectenerg-1427	590	11	)	)	PUNCT
fuelectenerg-1427	590	12	that	that	PRON
fuelectenerg-1427	590	13	generates	generate	VERB
fuelectenerg-1427	590	14	the	the	DET
fuelectenerg-1427	590	15	negative	negative	ADJ
fuelectenerg-1427	590	16	and	and	CCONJ
fuelectenerg-1427	590	17	positive	positive	ADJ
fuelectenerg-1427	590	18	davio	davio	NOUN
fuelectenerg-1427	590	19	expansions	expansion	NOUN
fuelectenerg-1427	590	20	as	as	ADP
fuelectenerg-1427	590	21	special	special	ADJ
fuelectenerg-1427	590	22	cases	case	NOUN
fuelectenerg-1427	590	23	.	.	PUNCT
fuelectenerg-1427	591	1	the	the	DET
fuelectenerg-1427	591	2	s	s	PROPN
fuelectenerg-1427	591	3	/	/	SYM
fuelectenerg-1427	591	4	d	d	NOUN
fuelectenerg-1427	591	5	trees	tree	NOUN
fuelectenerg-1427	591	6	for	for	ADP
fuelectenerg-1427	591	7	ifs	ifs	PROPN
fuelectenerg-1427	591	8	of	of	ADP
fuelectenerg-1427	591	9	two	two	NUM
fuelectenerg-1427	591	10	variables	variable	NOUN
fuelectenerg-1427	591	11	can	can	AUX
fuelectenerg-1427	591	12	be	be	AUX
fuelectenerg-1427	591	13	generated	generate	VERB
fuelectenerg-1427	591	14	for	for	ADP
fuelectenerg-1427	591	15	variable	variable	ADJ
fuelectenerg-1427	591	16	order	order	NOUN
fuelectenerg-1427	591	17	{	{	PUNCT
fuelectenerg-1427	591	18	a	a	DET
fuelectenerg-1427	591	19	,	,	PUNCT
fuelectenerg-1427	591	20	b	b	NOUN
fuelectenerg-1427	591	21	}	}	PUNCT
fuelectenerg-1427	591	22	and	and	CCONJ
fuelectenerg-1427	591	23	for	for	ADP
fuelectenerg-1427	591	24	variable	variable	ADJ
fuelectenerg-1427	591	25	order	order	NOUN
fuelectenerg-1427	591	26	{	{	PUNCT
fuelectenerg-1427	591	27	b	b	NOUN
fuelectenerg-1427	591	28	,	,	PUNCT
fuelectenerg-1427	591	29	a	a	PRON
fuelectenerg-1427	591	30	}	}	PUNCT
fuelectenerg-1427	591	31	as	as	ADV
fuelectenerg-1427	591	32	well	well	ADV
fuelectenerg-1427	591	33	.	.	PUNCT
fuelectenerg-1427	592	1	the	the	DET
fuelectenerg-1427	592	2	set	set	NOUN
fuelectenerg-1427	592	3	of	of	ADP
fuelectenerg-1427	592	4	gifs	gifs	PROPN
fuelectenerg-1427	592	5	for	for	ADP
fuelectenerg-1427	592	6	two	two	NUM
fuelectenerg-1427	592	7	variables	variable	NOUN
fuelectenerg-1427	592	8	is	be	AUX
fuelectenerg-1427	592	9	the	the	DET
fuelectenerg-1427	592	10	union	union	NOUN
fuelectenerg-1427	592	11	of	of	ADP
fuelectenerg-1427	592	12	these	these	DET
fuelectenerg-1427	592	13	two	two	NUM
fuelectenerg-1427	592	14	order	order	NOUN
fuelectenerg-1427	592	15	-	-	PUNCT
fuelectenerg-1427	592	16	based	base	VERB
fuelectenerg-1427	592	17	ifs	ifs	PROPN
fuelectenerg-1427	592	18	,	,	PUNCT
fuelectenerg-1427	592	19	where	where	SCONJ
fuelectenerg-1427	592	20	the	the	DET
fuelectenerg-1427	592	21	total	total	ADJ
fuelectenerg-1427	592	22	number	number	NOUN
fuelectenerg-1427	592	23	of	of	ADP
fuelectenerg-1427	592	24	the	the	DET
fuelectenerg-1427	592	25	resulting	result	VERB
fuelectenerg-1427	592	26	gifs	gifs	NOUN
fuelectenerg-1427	592	27	is	be	AUX
fuelectenerg-1427	592	28	equal	equal	ADJ
fuelectenerg-1427	592	29	to	to	ADP
fuelectenerg-1427	592	30	:	:	PUNCT
fuelectenerg-1427	592	31	#	#	SYM
fuelectenerg-1427	592	32	gif	gif	NOUN
fuelectenerg-1427	592	33	=	=	NOUN
fuelectenerg-1427	592	34	2	2	NUM
fuelectenerg-1427	592	35	·	·	PUNCT
fuelectenerg-1427	592	36	(	(	PUNCT
fuelectenerg-1427	592	37	#	#	SYM
fuelectenerg-1427	592	38	ifa	ifa	PROPN
fuelectenerg-1427	592	39	,	,	PUNCT
fuelectenerg-1427	592	40	b)−#(ifa	b)−#(ifa	PROPN
fuelectenerg-1427	592	41	,	,	PUNCT
fuelectenerg-1427	592	42	b	b	PROPN
fuelectenerg-1427	592	43	⋂	⋂	PROPN
fuelectenerg-1427	592	44	ifb	ifb	PROPN
fuelectenerg-1427	592	45	,	,	PUNCT
fuelectenerg-1427	592	46	a	a	PRON
fuelectenerg-1427	592	47	)	)	PUNCT
fuelectenerg-1427	592	48	.	.	PUNCT
fuelectenerg-1427	593	1	(	(	PUNCT
fuelectenerg-1427	593	2	27	27	NUM
fuelectenerg-1427	593	3	)	)	PUNCT
fuelectenerg-1427	593	4	the	the	DET
fuelectenerg-1427	593	5	galois	galois	PROPN
fuelectenerg-1427	593	6	-	-	PUNCT
fuelectenerg-1427	593	7	based	base	VERB
fuelectenerg-1427	593	8	shannon	shannon	NOUN
fuelectenerg-1427	593	9	and	and	CCONJ
fuelectenerg-1427	593	10	davio	davio	NOUN
fuelectenerg-1427	593	11	ternary	ternary	ADJ
fuelectenerg-1427	593	12	expansions	expansion	NOUN
fuelectenerg-1427	593	13	(	(	PUNCT
fuelectenerg-1427	593	14	i.e.	i.e.	X
fuelectenerg-1427	593	15	,	,	PUNCT
fuelectenerg-1427	593	16	flattened	flatten	VERB
fuelectenerg-1427	593	17	forms	form	NOUN
fuelectenerg-1427	593	18	)	)	PUNCT
fuelectenerg-1427	593	19	can	can	AUX
fuelectenerg-1427	593	20	be	be	AUX
fuelectenerg-1427	593	21	represented	represent	VERB
fuelectenerg-1427	593	22	in	in	ADP
fuelectenerg-1427	593	23	ternary	ternary	ADJ
fuelectenerg-1427	593	24	dts	dts	NOUN
fuelectenerg-1427	593	25	(	(	PUNCT
fuelectenerg-1427	593	26	tdts	tdts	ADJ
fuelectenerg-1427	593	27	)	)	PUNCT
fuelectenerg-1427	593	28	and	and	CCONJ
fuelectenerg-1427	593	29	the	the	DET
fuelectenerg-1427	593	30	corresponding	corresponding	ADJ
fuelectenerg-1427	593	31	varieties	variety	NOUN
fuelectenerg-1427	593	32	of	of	ADP
fuelectenerg-1427	593	33	ternary	ternary	ADJ
fuelectenerg-1427	593	34	dds	dds	PROPN
fuelectenerg-1427	593	35	(	(	PUNCT
fuelectenerg-1427	593	36	tdds	tdds	PROPN
fuelectenerg-1427	593	37	)	)	PUNCT
fuelectenerg-1427	593	38	according	accord	VERB
fuelectenerg-1427	593	39	to	to	ADP
fuelectenerg-1427	593	40	the	the	DET
fuelectenerg-1427	593	41	corresponding	corresponding	ADJ
fuelectenerg-1427	593	42	reduction	reduction	NOUN
fuelectenerg-1427	593	43	rules	rule	NOUN
fuelectenerg-1427	593	44	that	that	PRON
fuelectenerg-1427	593	45	are	be	AUX
fuelectenerg-1427	593	46	used	use	VERB
fuelectenerg-1427	593	47	[	[	PUNCT
fuelectenerg-1427	593	48	1	1	NUM
fuelectenerg-1427	593	49	,	,	PUNCT
fuelectenerg-1427	593	50	17	17	NUM
fuelectenerg-1427	593	51	]	]	PUNCT
fuelectenerg-1427	593	52	.	.	PUNCT
fuelectenerg-1427	594	1	for	for	ADP
fuelectenerg-1427	594	2	one	one	NUM
fuelectenerg-1427	594	3	107	107	NUM
fuelectenerg-1427	594	4	an	an	DET
fuelectenerg-1427	594	5	extended	extended	ADJ
fuelectenerg-1427	594	6	green	green	ADJ
fuelectenerg-1427	594	7	sasao	sasao	PROPN
fuelectenerg-1427	594	8	hierarchy	hierarchy	NOUN
fuelectenerg-1427	594	9	of	of	ADP
fuelectenerg-1427	594	10	canonical	canonical	ADJ
fuelectenerg-1427	594	11	ternary	ternary	ADJ
fuelectenerg-1427	594	12	galois	galois	NOUN
fuelectenerg-1427	594	13	forms	form	NOUN
fuelectenerg-1427	594	14	...	...	PUNCT
fuelectenerg-1427	594	15	f	f	X
fuelectenerg-1427	594	16	=	=	SYM
fuelectenerg-1427	594	17	�	�	PROPN
fuelectenerg-1427	594	18	0x	0x	PROPN
fuelectenerg-1427	594	19	1x	1x	NUM
fuelectenerg-1427	594	20	2x	2x	NUM
fuelectenerg-1427	594	21	�	�	PROPN
fuelectenerg-1427	594	22			PROPN
fuelectenerg-1427	594	23			NOUN
fuelectenerg-1427	594	24	1	1	NUM
fuelectenerg-1427	594	25	0	0	NUM
fuelectenerg-1427	594	26	0	0	NUM
fuelectenerg-1427	594	27	0	0	NUM
fuelectenerg-1427	594	28	1	1	NUM
fuelectenerg-1427	594	29	0	0	NUM
fuelectenerg-1427	594	30	0	0	NUM
fuelectenerg-1427	594	31	0	0	NUM
fuelectenerg-1427	594	32	1	1	NUM
fuelectenerg-1427	594	33			PROPN
fuelectenerg-1427	594	34			PROPN
fuelectenerg-1427	594	35			NOUN
fuelectenerg-1427	594	36			NUM
fuelectenerg-1427	594	37	f0	f0	PROPN
fuelectenerg-1427	594	38	f1	f1	PROPN
fuelectenerg-1427	594	39	f2	f2	PROPN
fuelectenerg-1427	594	40			PROPN
fuelectenerg-1427	594	41			PROPN
fuelectenerg-1427	594	42	,	,	PUNCT
fuelectenerg-1427	594	43	(	(	PUNCT
fuelectenerg-1427	594	44	19	19	NUM
fuelectenerg-1427	594	45	)	)	PUNCT
fuelectenerg-1427	594	46	f	f	NOUN
fuelectenerg-1427	594	47	=	=	SYM
fuelectenerg-1427	594	48	�	�	PROPN
fuelectenerg-1427	594	49	1	1	NUM
fuelectenerg-1427	594	50	x	x	SYM
fuelectenerg-1427	594	51	x2	x2	PROPN
fuelectenerg-1427	594	52	�	�	PROPN
fuelectenerg-1427	594	53			PROPN
fuelectenerg-1427	594	54			VERB
fuelectenerg-1427	594	55	1	1	NUM
fuelectenerg-1427	594	56	0	0	NUM
fuelectenerg-1427	594	57	0	0	NUM
fuelectenerg-1427	594	58	0	0	NUM
fuelectenerg-1427	594	59	2	2	NUM
fuelectenerg-1427	594	60	1	1	NUM
fuelectenerg-1427	594	61	2	2	NUM
fuelectenerg-1427	594	62	2	2	NUM
fuelectenerg-1427	594	63	2	2	NUM
fuelectenerg-1427	594	64			PROPN
fuelectenerg-1427	594	65			PROPN
fuelectenerg-1427	594	66			NOUN
fuelectenerg-1427	594	67			NUM
fuelectenerg-1427	594	68	f0	f0	PROPN
fuelectenerg-1427	594	69	f1	f1	PROPN
fuelectenerg-1427	594	70	f2	f2	PROPN
fuelectenerg-1427	594	71			PROPN
fuelectenerg-1427	594	72			PROPN
fuelectenerg-1427	594	73	,	,	PUNCT
fuelectenerg-1427	594	74	(	(	PUNCT
fuelectenerg-1427	594	75	20	20	NUM
fuelectenerg-1427	594	76	)	)	PUNCT
fuelectenerg-1427	594	77	f	f	NOUN
fuelectenerg-1427	594	78	=	=	SYM
fuelectenerg-1427	594	79	�	�	PROPN
fuelectenerg-1427	594	80	1	1	NUM
fuelectenerg-1427	594	81	x′	x′	PROPN
fuelectenerg-1427	594	82	(	(	PUNCT
fuelectenerg-1427	594	83	x′)2	x′)2	PROPN
fuelectenerg-1427	594	84	�	�	PROPN
fuelectenerg-1427	594	85			PROPN
fuelectenerg-1427	594	86			NOUN
fuelectenerg-1427	594	87	0	0	NUM
fuelectenerg-1427	594	88	0	0	NUM
fuelectenerg-1427	594	89	1	1	NUM
fuelectenerg-1427	594	90	2	2	NUM
fuelectenerg-1427	594	91	1	1	NUM
fuelectenerg-1427	594	92	0	0	NUM
fuelectenerg-1427	594	93	2	2	NUM
fuelectenerg-1427	594	94	2	2	NUM
fuelectenerg-1427	594	95	2	2	NUM
fuelectenerg-1427	594	96			PROPN
fuelectenerg-1427	594	97			PROPN
fuelectenerg-1427	594	98			NOUN
fuelectenerg-1427	594	99			NUM
fuelectenerg-1427	594	100	f0	f0	PROPN
fuelectenerg-1427	594	101	f1	f1	PROPN
fuelectenerg-1427	594	102	f2	f2	PROPN
fuelectenerg-1427	594	103			PROPN
fuelectenerg-1427	594	104			PROPN
fuelectenerg-1427	594	105	,	,	PUNCT
fuelectenerg-1427	594	106	(	(	PUNCT
fuelectenerg-1427	594	107	21	21	NUM
fuelectenerg-1427	594	108	)	)	PUNCT
fuelectenerg-1427	594	109	f	f	NOUN
fuelectenerg-1427	594	110	=	=	SYM
fuelectenerg-1427	594	111	�	�	PROPN
fuelectenerg-1427	594	112	1	1	NUM
fuelectenerg-1427	594	113	x′′	x′′	PROPN
fuelectenerg-1427	594	114	(	(	PUNCT
fuelectenerg-1427	594	115	x′′)2	x′′)2	PROPN
fuelectenerg-1427	594	116	�	�	PROPN
fuelectenerg-1427	594	117			PROPN
fuelectenerg-1427	594	118			NOUN
fuelectenerg-1427	594	119	0	0	NUM
fuelectenerg-1427	594	120	1	1	NUM
fuelectenerg-1427	594	121	0	0	NUM
fuelectenerg-1427	594	122	1	1	NUM
fuelectenerg-1427	594	123	0	0	NUM
fuelectenerg-1427	594	124	2	2	NUM
fuelectenerg-1427	594	125	2	2	NUM
fuelectenerg-1427	594	126	2	2	NUM
fuelectenerg-1427	594	127	2	2	NUM
fuelectenerg-1427	594	128			PROPN
fuelectenerg-1427	594	129			PROPN
fuelectenerg-1427	594	130			NOUN
fuelectenerg-1427	594	131			NUM
fuelectenerg-1427	594	132	f0	f0	PROPN
fuelectenerg-1427	594	133	f1	f1	PROPN
fuelectenerg-1427	594	134	f2	f2	PROPN
fuelectenerg-1427	594	135			PROPN
fuelectenerg-1427	594	136			PROPN
fuelectenerg-1427	594	137	.	.	PUNCT
fuelectenerg-1427	595	1	(	(	PUNCT
fuelectenerg-1427	595	2	22	22	NUM
fuelectenerg-1427	595	3	)	)	PUNCT
fuelectenerg-1427	595	4	the	the	DET
fuelectenerg-1427	595	5	recursive	recursive	ADJ
fuelectenerg-1427	595	6	generation	generation	NOUN
fuelectenerg-1427	595	7	using	use	VERB
fuelectenerg-1427	595	8	the	the	DET
fuelectenerg-1427	595	9	kronecker	kronecker	NOUN
fuelectenerg-1427	595	10	product	product	NOUN
fuelectenerg-1427	595	11	for	for	ADP
fuelectenerg-1427	595	12	arbitrary	arbitrary	ADJ
fuelectenerg-1427	595	13	number	number	NOUN
fuelectenerg-1427	595	14	of	of	ADP
fuelectenerg-1427	595	15	variables	variable	NOUN
fuelectenerg-1427	595	16	can	can	AUX
fuelectenerg-1427	595	17	be	be	AUX
fuelectenerg-1427	595	18	expressed	express	VERB
fuelectenerg-1427	595	19	formally	formally	ADV
fuelectenerg-1427	595	20	as	as	ADP
fuelectenerg-1427	595	21	in	in	ADP
fuelectenerg-1427	595	22	the	the	DET
fuelectenerg-1427	595	23	following	follow	VERB
fuelectenerg-1427	595	24	forms	form	NOUN
fuelectenerg-1427	595	25	for	for	ADP
fuelectenerg-1427	595	26	ternary	ternary	ADJ
fuelectenerg-1427	595	27	shannon	shannon	NOUN
fuelectenerg-1427	595	28	(	(	PUNCT
fuelectenerg-1427	595	29	s	s	NOUN
fuelectenerg-1427	595	30	)	)	PUNCT
fuelectenerg-1427	595	31	and	and	CCONJ
fuelectenerg-1427	595	32	davio	davio	NOUN
fuelectenerg-1427	595	33	(	(	PUNCT
fuelectenerg-1427	595	34	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	595	35	)	)	PUNCT
fuelectenerg-1427	595	36	expansions	expansion	NOUN
fuelectenerg-1427	595	37	,	,	PUNCT
fuelectenerg-1427	595	38	respectively	respectively	ADV
fuelectenerg-1427	595	39	:	:	PUNCT
fuelectenerg-1427	596	1	f	f	X
fuelectenerg-1427	596	2	=	=	SYM
fuelectenerg-1427	596	3	n	n	PRON
fuelectenerg-1427	596	4	�	�	PROPN
fuelectenerg-1427	596	5	i=1	i=1	PROPN
fuelectenerg-1427	596	6	�	�	PROPN
fuelectenerg-1427	596	7	0xi	0xi	PROPN
fuelectenerg-1427	596	8	1xi	1xi	PROPN
fuelectenerg-1427	596	9	2xi	2xi	ADJ
fuelectenerg-1427	596	10	�	�	PROPN
fuelectenerg-1427	596	11	n	n	CCONJ
fuelectenerg-1427	596	12	�	�	PROPN
fuelectenerg-1427	596	13	i=1	i=1	PROPN
fuelectenerg-1427	597	1	[	[	X
fuelectenerg-1427	597	2	s][	s][	PROPN
fuelectenerg-1427	597	3	�	�	PROPN
fuelectenerg-1427	597	4	f	f	X
fuelectenerg-1427	597	5	]	]	X
fuelectenerg-1427	597	6	,	,	PUNCT
fuelectenerg-1427	597	7	(	(	PUNCT
fuelectenerg-1427	597	8	23	23	NUM
fuelectenerg-1427	597	9	)	)	PUNCT
fuelectenerg-1427	597	10	f	f	NOUN
fuelectenerg-1427	598	1	=	=	SYM
fuelectenerg-1427	598	2	n	n	PRON
fuelectenerg-1427	598	3	�	�	PROPN
fuelectenerg-1427	598	4	i=1	i=1	PROPN
fuelectenerg-1427	598	5	�	�	PROPN
fuelectenerg-1427	598	6	1	1	NUM
fuelectenerg-1427	598	7	xi	xi	ADP
fuelectenerg-1427	598	8	x2	x2	INTJ
fuelectenerg-1427	598	9	i	i	PRON
fuelectenerg-1427	598	10	�	�	PROPN
fuelectenerg-1427	598	11	n	n	CCONJ
fuelectenerg-1427	598	12	�	�	PROPN
fuelectenerg-1427	598	13	i=1	i=1	X
fuelectenerg-1427	599	1	[	[	X
fuelectenerg-1427	599	2	d0][	d0][	NOUN
fuelectenerg-1427	599	3	�	�	X
fuelectenerg-1427	599	4	f	f	X
fuelectenerg-1427	599	5	]	]	X
fuelectenerg-1427	599	6	,	,	PUNCT
fuelectenerg-1427	599	7	(	(	PUNCT
fuelectenerg-1427	599	8	24	24	NUM
fuelectenerg-1427	599	9	)	)	PUNCT
fuelectenerg-1427	599	10	f	f	NOUN
fuelectenerg-1427	600	1	=	=	SYM
fuelectenerg-1427	600	2	n	n	PRON
fuelectenerg-1427	600	3	�	�	PROPN
fuelectenerg-1427	600	4	i=1	i=1	PROPN
fuelectenerg-1427	600	5	�	�	PROPN
fuelectenerg-1427	600	6	1	1	NUM
fuelectenerg-1427	600	7	x′i	x′i	PROPN
fuelectenerg-1427	600	8	(	(	PUNCT
fuelectenerg-1427	600	9	x′i	x′i	NOUN
fuelectenerg-1427	600	10	)	)	PUNCT
fuelectenerg-1427	600	11	2	2	NUM
fuelectenerg-1427	600	12	�	�	PROPN
fuelectenerg-1427	600	13	n	n	PRON
fuelectenerg-1427	600	14	�	�	PROPN
fuelectenerg-1427	600	15	i=1	i=1	PART
fuelectenerg-1427	601	1	[	[	X
fuelectenerg-1427	601	2	d1][	d1][	X
fuelectenerg-1427	601	3	�	�	NOUN
fuelectenerg-1427	601	4	f	f	X
fuelectenerg-1427	601	5	]	]	X
fuelectenerg-1427	601	6	,	,	PUNCT
fuelectenerg-1427	601	7	(	(	PUNCT
fuelectenerg-1427	601	8	25	25	NUM
fuelectenerg-1427	601	9	)	)	PUNCT
fuelectenerg-1427	601	10	f	f	NOUN
fuelectenerg-1427	602	1	=	=	SYM
fuelectenerg-1427	602	2	n	n	PRON
fuelectenerg-1427	602	3	�	�	PROPN
fuelectenerg-1427	602	4	i=1	i=1	PROPN
fuelectenerg-1427	602	5	�	�	PROPN
fuelectenerg-1427	602	6	1	1	NUM
fuelectenerg-1427	602	7	x′′i	x′′i	PROPN
fuelectenerg-1427	602	8	(	(	PUNCT
fuelectenerg-1427	602	9	x′′i	x′′i	PROPN
fuelectenerg-1427	602	10	)	)	PUNCT
fuelectenerg-1427	602	11	2	2	NUM
fuelectenerg-1427	602	12	�	�	PROPN
fuelectenerg-1427	602	13	n	n	CCONJ
fuelectenerg-1427	602	14	�	�	PROPN
fuelectenerg-1427	602	15	i=1	i=1	PROPN
fuelectenerg-1427	603	1	[	[	AUX
fuelectenerg-1427	603	2	d2][	d2][	PROPN
fuelectenerg-1427	603	3	�	�	PROPN
fuelectenerg-1427	603	4	f	f	PROPN
fuelectenerg-1427	603	5	]	]	PUNCT
fuelectenerg-1427	603	6	.	.	PUNCT
fuelectenerg-1427	604	1	(	(	PUNCT
fuelectenerg-1427	604	2	26	26	NUM
fuelectenerg-1427	604	3	)	)	PUNCT
fuelectenerg-1427	604	4	analogously	analogously	ADV
fuelectenerg-1427	604	5	to	to	ADP
fuelectenerg-1427	604	6	the	the	DET
fuelectenerg-1427	604	7	binary	binary	ADJ
fuelectenerg-1427	604	8	case	case	NOUN
fuelectenerg-1427	604	9	,	,	PUNCT
fuelectenerg-1427	604	10	we	we	PRON
fuelectenerg-1427	604	11	can	can	AUX
fuelectenerg-1427	604	12	have	have	VERB
fuelectenerg-1427	604	13	expansions	expansion	NOUN
fuelectenerg-1427	604	14	that	that	PRON
fuelectenerg-1427	604	15	are	be	AUX
fuelectenerg-1427	604	16	mixed	mix	VERB
fuelectenerg-1427	604	17	of	of	ADP
fuelectenerg-1427	604	18	shannon	shannon	PROPN
fuelectenerg-1427	604	19	(	(	PUNCT
fuelectenerg-1427	604	20	s	s	PROPN
fuelectenerg-1427	604	21	)	)	PUNCT
fuelectenerg-1427	604	22	for	for	ADP
fuelectenerg-1427	604	23	certain	certain	ADJ
fuelectenerg-1427	604	24	variables	variable	NOUN
fuelectenerg-1427	604	25	and	and	CCONJ
fuelectenerg-1427	604	26	davio	davio	NOUN
fuelectenerg-1427	604	27	(	(	PUNCT
fuelectenerg-1427	604	28	d0,d1,d2	d0,d1,d2	NOUN
fuelectenerg-1427	604	29	)	)	PUNCT
fuelectenerg-1427	604	30	for	for	ADP
fuelectenerg-1427	604	31	the	the	DET
fuelectenerg-1427	604	32	other	other	ADJ
fuelectenerg-1427	604	33	variables	variable	NOUN
fuelectenerg-1427	604	34	.	.	PUNCT
fuelectenerg-1427	605	1	this	this	PRON
fuelectenerg-1427	605	2	will	will	AUX
fuelectenerg-1427	605	3	lead	lead	VERB
fuelectenerg-1427	605	4	,	,	PUNCT
fuelectenerg-1427	605	5	analogously	analogously	ADV
fuelectenerg-1427	605	6	to	to	ADP
fuelectenerg-1427	605	7	the	the	DET
fuelectenerg-1427	605	8	binary	binary	ADJ
fuelectenerg-1427	605	9	case	case	NOUN
fuelectenerg-1427	605	10	,	,	PUNCT
fuelectenerg-1427	605	11	to	to	ADP
fuelectenerg-1427	605	12	the	the	DET
fuelectenerg-1427	605	13	kronecker	kronecker	NOUN
fuelectenerg-1427	605	14	ternary	ternary	ADJ
fuelectenerg-1427	605	15	decision	decision	NOUN
fuelectenerg-1427	605	16	trees	tree	NOUN
fuelectenerg-1427	605	17	(	(	PUNCT
fuelectenerg-1427	605	18	tdts	tdts	ADJ
fuelectenerg-1427	605	19	)	)	PUNCT
fuelectenerg-1427	605	20	.	.	PUNCT
fuelectenerg-1427	606	1	moreover	moreover	ADV
fuelectenerg-1427	606	2	,	,	PUNCT
fuelectenerg-1427	606	3	mixed	mixed	ADJ
fuelectenerg-1427	606	4	expansions	expansion	NOUN
fuelectenerg-1427	606	5	can	can	AUX
fuelectenerg-1427	606	6	be	be	AUX
fuelectenerg-1427	606	7	extended	extend	VERB
fuelectenerg-1427	606	8	to	to	PART
fuelectenerg-1427	606	9	include	include	VERB
fuelectenerg-1427	606	10	the	the	DET
fuelectenerg-1427	606	11	case	case	NOUN
fuelectenerg-1427	606	12	of	of	ADP
fuelectenerg-1427	606	13	pseudo	pseudo	NOUN
fuelectenerg-1427	606	14	kronecker	kronecker	NOUN
fuelectenerg-1427	606	15	tdts	tdts	NOUN
fuelectenerg-1427	607	1	[	[	X
fuelectenerg-1427	607	2	17	17	NUM
fuelectenerg-1427	607	3	]	]	SYM
fuelectenerg-1427	607	4	.	.	PUNCT
fuelectenerg-1427	608	1	2	2	NUM
fuelectenerg-1427	608	2	new	new	ADJ
fuelectenerg-1427	608	3	multiple	multiple	ADV
fuelectenerg-1427	608	4	-	-	PUNCT
fuelectenerg-1427	608	5	valued	value	VERB
fuelectenerg-1427	608	6	s	s	PROPN
fuelectenerg-1427	608	7	/	/	SYM
fuelectenerg-1427	608	8	d	d	NOUN
fuelectenerg-1427	608	9	trees	tree	NOUN
fuelectenerg-1427	608	10	and	and	CCONJ
fuelectenerg-1427	608	11	their	their	PRON
fuelectenerg-1427	608	12	canonical	canonical	ADJ
fuelectenerg-1427	608	13	galois	galois	PROPN
fuelectenerg-1427	608	14	sop	sop	NOUN
fuelectenerg-1427	608	15	forms	form	NOUN
fuelectenerg-1427	608	16	economical	economical	ADJ
fuelectenerg-1427	608	17	and	and	CCONJ
fuelectenerg-1427	608	18	highly	highly	ADV
fuelectenerg-1427	608	19	testable	testable	ADJ
fuelectenerg-1427	608	20	implementations	implementation	NOUN
fuelectenerg-1427	608	21	of	of	ADP
fuelectenerg-1427	608	22	boolean	boolean	ADJ
fuelectenerg-1427	608	23	functions	function	NOUN
fuelectenerg-1427	608	24	,	,	PUNCT
fuelectenerg-1427	608	25	based	base	VERB
fuelectenerg-1427	608	26	on	on	ADP
fuelectenerg-1427	608	27	reedmuller	reedmuller	NOUN
fuelectenerg-1427	608	28	(	(	PUNCT
fuelectenerg-1427	608	29	and	and	CCONJ
fuelectenerg-1427	608	30	-	-	PUNCT
fuelectenerg-1427	608	31	exor	exor	VERB
fuelectenerg-1427	608	32	)	)	PUNCT
fuelectenerg-1427	608	33	logic	logic	NOUN
fuelectenerg-1427	608	34	,	,	PUNCT
fuelectenerg-1427	608	35	play	play	VERB
fuelectenerg-1427	608	36	an	an	DET
fuelectenerg-1427	608	37	important	important	ADJ
fuelectenerg-1427	608	38	role	role	NOUN
fuelectenerg-1427	608	39	in	in	ADP
fuelectenerg-1427	608	40	logic	logic	ADJ
fuelectenerg-1427	608	41	synthesis	synthesis	NOUN
fuelectenerg-1427	608	42	and	and	CCONJ
fuelectenerg-1427	608	43	circuit	circuit	NOUN
fuelectenerg-1427	608	44	design	design	NOUN
fuelectenerg-1427	608	45	.	.	PUNCT
fuelectenerg-1427	609	1	the	the	DET
fuelectenerg-1427	609	2	and	and	CCONJ
fuelectenerg-1427	609	3	-	-	PUNCT
fuelectenerg-1427	609	4	exor	exor	PROPN
fuelectenerg-1427	609	5	circuits	circuit	NOUN
fuelectenerg-1427	609	6	include	include	VERB
fuelectenerg-1427	609	7	canonical	canonical	ADJ
fuelectenerg-1427	609	8	forms	form	NOUN
fuelectenerg-1427	609	9	which	which	PRON
fuelectenerg-1427	609	10	are	be	AUX
fuelectenerg-1427	609	11	expansions	expansion	NOUN
fuelectenerg-1427	609	12	that	that	PRON
fuelectenerg-1427	609	13	are	be	AUX
fuelectenerg-1427	609	14	unique	unique	ADJ
fuelectenerg-1427	609	15	representations	representation	NOUN
fuelectenerg-1427	609	16	of	of	ADP
fuelectenerg-1427	609	17	a	a	DET
fuelectenerg-1427	609	18	boolean	boolean	ADJ
fuelectenerg-1427	609	19	function	function	NOUN
fuelectenerg-1427	609	20	.	.	PUNCT
fuelectenerg-1427	610	1	several	several	ADJ
fuelectenerg-1427	610	2	large	large	ADJ
fuelectenerg-1427	610	3	families	family	NOUN
fuelectenerg-1427	610	4	of	of	ADP
fuelectenerg-1427	610	5	canonical	canonical	ADJ
fuelectenerg-1427	610	6	forms	form	NOUN
fuelectenerg-1427	610	7	:	:	PUNCT
fuelectenerg-1427	610	8	fixed	fix	VERB
fuelectenerg-1427	610	9	polarity	polarity	NOUN
fuelectenerg-1427	610	10	reed	reed	NOUN
fuelectenerg-1427	610	11	-	-	PUNCT
fuelectenerg-1427	610	12	muller	muller	NOUN
fuelectenerg-1427	610	13	(	(	PUNCT
fuelectenerg-1427	610	14	fprm	fprm	PROPN
fuelectenerg-1427	610	15	)	)	PUNCT
fuelectenerg-1427	610	16	forms	form	NOUN
fuelectenerg-1427	610	17	,	,	PUNCT
fuelectenerg-1427	610	18	generalized	generalized	ADJ
fuelectenerg-1427	610	19	reed	reed	NOUN
fuelectenerg-1427	610	20	-	-	PUNCT
fuelectenerg-1427	610	21	muller	muller	NOUN
fuelectenerg-1427	610	22	(	(	PUNCT
fuelectenerg-1427	610	23	grm	grm	NOUN
fuelectenerg-1427	610	24	)	)	PUNCT
fuelectenerg-1427	610	25	forms	form	NOUN
fuelectenerg-1427	610	26	,	,	PUNCT
fuelectenerg-1427	610	27	kronecker	kronecker	NOUN
fuelectenerg-1427	610	28	(	(	PUNCT
fuelectenerg-1427	610	29	kro	kro	PROPN
fuelectenerg-1427	610	30	)	)	PUNCT
fuelectenerg-1427	610	31	forms	form	NOUN
fuelectenerg-1427	610	32	and	and	CCONJ
fuelectenerg-1427	610	33	pseudo	pseudo	NOUN
fuelectenerg-1427	610	34	-	-	NOUN
fuelectenerg-1427	610	35	kronecker	kronecker	NOUN
fuelectenerg-1427	610	36	(	(	PUNCT
fuelectenerg-1427	610	37	psdkro	psdkro	NOUN
fuelectenerg-1427	610	38	)	)	PUNCT
fuelectenerg-1427	610	39	forms	form	NOUN
fuelectenerg-1427	610	40	,	,	PUNCT
fuelectenerg-1427	610	41	referred	refer	VERB
fuelectenerg-1427	610	42	to	to	ADP
fuelectenerg-1427	610	43	106	106	NUM
fuelectenerg-1427	610	44	56	56	NUM
fuelectenerg-1427	610	45	a.	a.	NOUN
fuelectenerg-1427	610	46	n.	n.	PROPN
fuelectenerg-1427	610	47	al	al	PROPN
fuelectenerg-1427	610	48	-	-	PUNCT
fuelectenerg-1427	610	49	rabadi	rabadi	VERB
fuelectenerg-1427	610	50	an	an	DET
fuelectenerg-1427	610	51	extended	extended	ADJ
fuelectenerg-1427	610	52	green	green	ADJ
fuelectenerg-1427	610	53	sasao	sasao	PROPN
fuelectenerg-1427	610	54	hierarchy	hierarchy	NOUN
fuelectenerg-1427	610	55	of	of	ADP
fuelectenerg-1427	610	56	canonical	canonical	ADJ
fuelectenerg-1427	610	57	ternary	ternary	ADJ
fuelectenerg-1427	610	58	galois	galois	NOUN
fuelectenerg-1427	610	59	forms	form	NOUN
fuelectenerg-1427	610	60	and	and	CCONJ
fuelectenerg-1427	610	61	universal	universal	ADJ
fuelectenerg-1427	610	62	logic	logic	NOUN
fuelectenerg-1427	610	63	modules	module	NOUN
fuelectenerg-1427	610	64	57	57	NUM
fuelectenerg-1427	610	65	an	an	DET
fuelectenerg-1427	610	66	extended	extended	ADJ
fuelectenerg-1427	610	67	green	green	ADJ
fuelectenerg-1427	610	68	sasao	sasao	PROPN
fuelectenerg-1427	610	69	hierarchy	hierarchy	NOUN
fuelectenerg-1427	610	70	of	of	ADP
fuelectenerg-1427	610	71	canonical	canonical	ADJ
fuelectenerg-1427	610	72	ternary	ternary	ADJ
fuelectenerg-1427	610	73	galois	galois	NOUN
fuelectenerg-1427	610	74	forms	form	NOUN
fuelectenerg-1427	610	75	...	...	PUNCT
fuelectenerg-1427	610	76	s	s	VERB
fuelectenerg-1427	610	77	a	a	PRON
fuelectenerg-1427	610	78	’	'	PUNCT
fuelectenerg-1427	610	79	a	a	PRON
fuelectenerg-1427	610	80	(	(	PUNCT
fuelectenerg-1427	610	81	)	)	PUNCT
fuelectenerg-1427	610	82	a	a	PRON
fuelectenerg-1427	610	83	pd	pd	PROPN
fuelectenerg-1427	610	84	1	1	NUM
fuelectenerg-1427	610	85	a	a	PRON
fuelectenerg-1427	610	86	(	(	PUNCT
fuelectenerg-1427	610	87	)	)	PUNCT
fuelectenerg-1427	610	88	b	b	NOUN
fuelectenerg-1427	610	89	nd	nd	ADP
fuelectenerg-1427	610	90	1	1	NUM
fuelectenerg-1427	610	91	a	a	PRON
fuelectenerg-1427	610	92	’	'	PUNCT
fuelectenerg-1427	610	93	d	d	ADP
fuelectenerg-1427	610	94	1	1	NUM
fuelectenerg-1427	610	95	a	a	PRON
fuelectenerg-1427	610	96	(	(	PUNCT
fuelectenerg-1427	610	97	)	)	PUNCT
fuelectenerg-1427	610	98	d	d	NOUN
fuelectenerg-1427	610	99	(	(	PUNCT
fuelectenerg-1427	610	100	)	)	PUNCT
fuelectenerg-1427	610	101	c	c	NOUN
fuelectenerg-1427	610	102	figure	figure	VERB
fuelectenerg-1427	610	103	3	3	NUM
fuelectenerg-1427	610	104	:	:	PUNCT
fuelectenerg-1427	610	105	two	two	NUM
fuelectenerg-1427	610	106	-	-	PUNCT
fuelectenerg-1427	610	107	valued	value	VERB
fuelectenerg-1427	610	108	nodes	node	NOUN
fuelectenerg-1427	610	109	:	:	PUNCT
fuelectenerg-1427	610	110	(	(	PUNCT
fuelectenerg-1427	610	111	a	a	X
fuelectenerg-1427	610	112	)	)	PUNCT
fuelectenerg-1427	610	113	shannon	shannon	NOUN
fuelectenerg-1427	610	114	,	,	PUNCT
fuelectenerg-1427	610	115	(	(	PUNCT
fuelectenerg-1427	610	116	b	b	NOUN
fuelectenerg-1427	610	117	)	)	PUNCT
fuelectenerg-1427	610	118	positive	positive	ADJ
fuelectenerg-1427	610	119	davio	davio	NOUN
fuelectenerg-1427	610	120	,	,	PUNCT
fuelectenerg-1427	610	121	(	(	PUNCT
fuelectenerg-1427	610	122	c	c	NOUN
fuelectenerg-1427	610	123	)	)	PUNCT
fuelectenerg-1427	610	124	negative	negative	ADJ
fuelectenerg-1427	610	125	davio	davio	NOUN
fuelectenerg-1427	610	126	,	,	PUNCT
fuelectenerg-1427	610	127	and	and	CCONJ
fuelectenerg-1427	610	128	(	(	PUNCT
fuelectenerg-1427	610	129	d	d	X
fuelectenerg-1427	610	130	)	)	PUNCT
fuelectenerg-1427	610	131	generalized	generalized	ADJ
fuelectenerg-1427	610	132	davio	davio	NOUN
fuelectenerg-1427	610	133	where	where	SCONJ
fuelectenerg-1427	610	134	a	a	DET
fuelectenerg-1427	610	135	∈	∈	NOUN
fuelectenerg-1427	610	136	{	{	PUNCT
fuelectenerg-1427	610	137	a	a	PRON
fuelectenerg-1427	610	138	,	,	PUNCT
fuelectenerg-1427	610	139	a′	a′	PROPN
fuelectenerg-1427	610	140	}	}	PUNCT
fuelectenerg-1427	610	141	.	.	PUNCT
fuelectenerg-1427	611	1	variable	variable	ADJ
fuelectenerg-1427	611	2	,	,	PUNCT
fuelectenerg-1427	611	3	that	that	PRON
fuelectenerg-1427	611	4	is	be	AUX
fuelectenerg-1427	611	5	one	one	NUM
fuelectenerg-1427	611	6	tree	tree	NOUN
fuelectenerg-1427	611	7	level	level	NOUN
fuelectenerg-1427	611	8	,	,	PUNCT
fuelectenerg-1427	611	9	figure	figure	NOUN
fuelectenerg-1427	611	10	4	4	NUM
fuelectenerg-1427	611	11	represents	represent	VERB
fuelectenerg-1427	611	12	the	the	DET
fuelectenerg-1427	611	13	expansion	expansion	NOUN
fuelectenerg-1427	611	14	nodes	node	NOUN
fuelectenerg-1427	611	15	for	for	ADP
fuelectenerg-1427	611	16	ternary	ternary	ADJ
fuelectenerg-1427	611	17	shannon	shannon	NOUN
fuelectenerg-1427	611	18	,	,	PUNCT
fuelectenerg-1427	611	19	davio	davio	NOUN
fuelectenerg-1427	611	20	and	and	CCONJ
fuelectenerg-1427	611	21	generalized	generalized	ADJ
fuelectenerg-1427	611	22	davio	davio	NOUN
fuelectenerg-1427	611	23	(	(	PUNCT
fuelectenerg-1427	611	24	d	d	NOUN
fuelectenerg-1427	611	25	)	)	PUNCT
fuelectenerg-1427	611	26	,	,	PUNCT
fuelectenerg-1427	611	27	respectively	respectively	ADV
fuelectenerg-1427	611	28	.	.	PUNCT
fuelectenerg-1427	612	1	s	s	PART
fuelectenerg-1427	612	2	0	0	NUM
fuelectenerg-1427	612	3	x	x	SYM
fuelectenerg-1427	612	4	1	1	NUM
fuelectenerg-1427	612	5	x	x	SYM
fuelectenerg-1427	612	6	2	2	NUM
fuelectenerg-1427	612	7	x	x	SYM
fuelectenerg-1427	612	8	(	(	PUNCT
fuelectenerg-1427	612	9	a	a	PRON
fuelectenerg-1427	612	10	)	)	PUNCT
fuelectenerg-1427	612	11	d0	d0	NOUN
fuelectenerg-1427	612	12	1	1	NUM
fuelectenerg-1427	612	13	x	x	SYM
fuelectenerg-1427	612	14	2	2	NUM
fuelectenerg-1427	612	15	(	(	PUNCT
fuelectenerg-1427	612	16	b	b	NOUN
fuelectenerg-1427	612	17	)	)	PUNCT
fuelectenerg-1427	612	18	d2	d2	PROPN
fuelectenerg-1427	612	19	1	1	NUM
fuelectenerg-1427	612	20	(	(	PUNCT
fuelectenerg-1427	612	21	d	d	NOUN
fuelectenerg-1427	612	22	)	)	PUNCT
fuelectenerg-1427	613	1	d	d	NOUN
fuelectenerg-1427	613	2	1	1	NUM
fuelectenerg-1427	613	3	(	(	PUNCT
fuelectenerg-1427	613	4	e	e	NOUN
fuelectenerg-1427	613	5	)	)	PUNCT
fuelectenerg-1427	613	6	d1	d1	NOUN
fuelectenerg-1427	613	7	1	1	NUM
fuelectenerg-1427	613	8	(	(	PUNCT
fuelectenerg-1427	613	9	’	'	PUNCT
fuelectenerg-1427	613	10	)	)	PUNCT
fuelectenerg-1427	613	11	x	x	SYM
fuelectenerg-1427	613	12	2	2	NUM
fuelectenerg-1427	613	13	(	(	PUNCT
fuelectenerg-1427	613	14	’’	’'	PUNCT
fuelectenerg-1427	613	15	)	)	PUNCT
fuelectenerg-1427	613	16	x	x	SYM
fuelectenerg-1427	613	17	2	2	NUM
fuelectenerg-1427	613	18	(	(	PUNCT
fuelectenerg-1427	613	19	)	)	PUNCT
fuelectenerg-1427	613	20	x	x	SYM
fuelectenerg-1427	613	21	2	2	NUM
fuelectenerg-1427	613	22	(	(	PUNCT
fuelectenerg-1427	613	23	c	c	NOUN
fuelectenerg-1427	613	24	)	)	PUNCT
fuelectenerg-1427	613	25	x	x	SYM
fuelectenerg-1427	613	26	xx	xx	X
fuelectenerg-1427	613	27	’	'	PUNCT
fuelectenerg-1427	613	28	x	x	NOUN
fuelectenerg-1427	613	29	’’	’'	PUNCT
fuelectenerg-1427	613	30	figure	figure	VERB
fuelectenerg-1427	613	31	4	4	NUM
fuelectenerg-1427	613	32	:	:	PUNCT
fuelectenerg-1427	613	33	ternary	ternary	ADJ
fuelectenerg-1427	613	34	nodes	node	NOUN
fuelectenerg-1427	613	35	for	for	ADP
fuelectenerg-1427	613	36	ternary	ternary	ADJ
fuelectenerg-1427	613	37	decision	decision	NOUN
fuelectenerg-1427	613	38	trees	tree	NOUN
fuelectenerg-1427	613	39	:	:	PUNCT
fuelectenerg-1427	613	40	(	(	PUNCT
fuelectenerg-1427	613	41	a	a	X
fuelectenerg-1427	613	42	)	)	PUNCT
fuelectenerg-1427	613	43	shannon	shannon	NOUN
fuelectenerg-1427	613	44	,	,	PUNCT
fuelectenerg-1427	613	45	(	(	PUNCT
fuelectenerg-1427	613	46	b	b	X
fuelectenerg-1427	613	47	)	)	PUNCT
fuelectenerg-1427	613	48	davio0	davio0	PROPN
fuelectenerg-1427	613	49	,	,	PUNCT
fuelectenerg-1427	613	50	(	(	PUNCT
fuelectenerg-1427	613	51	c	c	X
fuelectenerg-1427	613	52	)	)	PUNCT
fuelectenerg-1427	613	53	davio1	davio1	NOUN
fuelectenerg-1427	613	54	,	,	PUNCT
fuelectenerg-1427	613	55	(	(	PUNCT
fuelectenerg-1427	613	56	d	d	NOUN
fuelectenerg-1427	613	57	)	)	PUNCT
fuelectenerg-1427	613	58	davio2	davio2	PROPN
fuelectenerg-1427	613	59	,	,	PUNCT
fuelectenerg-1427	613	60	and	and	CCONJ
fuelectenerg-1427	613	61	(	(	PUNCT
fuelectenerg-1427	613	62	e	e	NOUN
fuelectenerg-1427	613	63	)	)	PUNCT
fuelectenerg-1427	613	64	generalized	generalized	ADJ
fuelectenerg-1427	613	65	davio	davio	NOUN
fuelectenerg-1427	613	66	(	(	PUNCT
fuelectenerg-1427	613	67	d	d	NOUN
fuelectenerg-1427	613	68	)	)	PUNCT
fuelectenerg-1427	613	69	where	where	SCONJ
fuelectenerg-1427	613	70	x	x	SYM
fuelectenerg-1427	613	71	∈	∈	PROPN
fuelectenerg-1427	613	72	{	{	PUNCT
fuelectenerg-1427	613	73	x	x	NOUN
fuelectenerg-1427	613	74	,	,	PUNCT
fuelectenerg-1427	613	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	613	76	}	}	PUNCT
fuelectenerg-1427	613	77	.	.	PUNCT
fuelectenerg-1427	614	1	in	in	ADP
fuelectenerg-1427	614	2	correspondence	correspondence	NOUN
fuelectenerg-1427	614	3	to	to	ADP
fuelectenerg-1427	614	4	the	the	DET
fuelectenerg-1427	614	5	binary	binary	PROPN
fuelectenerg-1427	614	6	s	s	PROPN
fuelectenerg-1427	614	7	/	/	SYM
fuelectenerg-1427	614	8	d	d	NOUN
fuelectenerg-1427	614	9	trees	tree	NOUN
fuelectenerg-1427	614	10	,	,	PUNCT
fuelectenerg-1427	614	11	one	one	PRON
fuelectenerg-1427	614	12	can	can	AUX
fuelectenerg-1427	614	13	produce	produce	VERB
fuelectenerg-1427	614	14	ternary	ternary	ADJ
fuelectenerg-1427	614	15	s	s	NOUN
fuelectenerg-1427	614	16	/	/	SYM
fuelectenerg-1427	614	17	d	d	NOUN
fuelectenerg-1427	614	18	trees	tree	NOUN
fuelectenerg-1427	614	19	.	.	PUNCT
fuelectenerg-1427	615	1	to	to	PART
fuelectenerg-1427	615	2	define	define	VERB
fuelectenerg-1427	615	3	the	the	DET
fuelectenerg-1427	615	4	ternary	ternary	ADJ
fuelectenerg-1427	615	5	s	s	NOUN
fuelectenerg-1427	615	6	/	/	SYM
fuelectenerg-1427	615	7	d	d	NOUN
fuelectenerg-1427	615	8	trees	tree	NOUN
fuelectenerg-1427	615	9	,	,	PUNCT
fuelectenerg-1427	615	10	we	we	PRON
fuelectenerg-1427	615	11	define	define	VERB
fuelectenerg-1427	615	12	the	the	DET
fuelectenerg-1427	615	13	generalized	generalized	ADJ
fuelectenerg-1427	615	14	davio	davio	NOUN
fuelectenerg-1427	615	15	node	node	NOUN
fuelectenerg-1427	615	16	over	over	ADP
fuelectenerg-1427	615	17	ternary	ternary	ADJ
fuelectenerg-1427	615	18	galois	galois	PROPN
fuelectenerg-1427	615	19	radix	radix	NOUN
fuelectenerg-1427	615	20	as	as	SCONJ
fuelectenerg-1427	615	21	shown	show	VERB
fuelectenerg-1427	615	22	in	in	ADP
fuelectenerg-1427	615	23	figure	figure	NOUN
fuelectenerg-1427	615	24	4(e	4(e	NUM
fuelectenerg-1427	615	25	)	)	PUNCT
fuelectenerg-1427	615	26	.	.	PUNCT
fuelectenerg-1427	616	1	our	our	PRON
fuelectenerg-1427	616	2	notation	notation	NOUN
fuelectenerg-1427	616	3	here	here	ADV
fuelectenerg-1427	616	4	is	be	AUX
fuelectenerg-1427	616	5	that	that	PRON
fuelectenerg-1427	616	6	(	(	PUNCT
fuelectenerg-1427	616	7	x	x	X
fuelectenerg-1427	616	8	)	)	PUNCT
fuelectenerg-1427	616	9	corresponds	correspond	VERB
fuelectenerg-1427	616	10	to	to	ADP
fuelectenerg-1427	616	11	the	the	DET
fuelectenerg-1427	616	12	three	three	NUM
fuelectenerg-1427	616	13	possible	possible	ADJ
fuelectenerg-1427	616	14	shifts	shift	NOUN
fuelectenerg-1427	616	15	of	of	ADP
fuelectenerg-1427	616	16	the	the	DET
fuelectenerg-1427	616	17	variable	variable	NOUN
fuelectenerg-1427	616	18	x	x	NOUN
fuelectenerg-1427	616	19	as	as	SCONJ
fuelectenerg-1427	616	20	follows	follow	VERB
fuelectenerg-1427	616	21	:	:	PUNCT
fuelectenerg-1427	616	22	x	x	SYM
fuelectenerg-1427	616	23	∈	∈	NOUN
fuelectenerg-1427	616	24	{	{	PUNCT
fuelectenerg-1427	616	25	x	x	NOUN
fuelectenerg-1427	616	26	,	,	PUNCT
fuelectenerg-1427	616	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	616	28	}	}	PUNCT
fuelectenerg-1427	616	29	,	,	PUNCT
fuelectenerg-1427	616	30	over	over	ADP
fuelectenerg-1427	616	31	gf(3	gf(3	PROPN
fuelectenerg-1427	616	32	)	)	PUNCT
fuelectenerg-1427	616	33	.	.	PUNCT
fuelectenerg-1427	617	1	(	(	PUNCT
fuelectenerg-1427	617	2	28	28	NUM
fuelectenerg-1427	617	3	)	)	PUNCT
fuelectenerg-1427	617	4	definition	definition	NOUN
fuelectenerg-1427	617	5	1	1	NUM
fuelectenerg-1427	617	6	.	.	PUNCT
fuelectenerg-1427	618	1	the	the	DET
fuelectenerg-1427	618	2	ternary	ternary	ADJ
fuelectenerg-1427	618	3	tree	tree	NOUN
fuelectenerg-1427	618	4	with	with	ADP
fuelectenerg-1427	618	5	ternary	ternary	ADJ
fuelectenerg-1427	618	6	shannon	shannon	NOUN
fuelectenerg-1427	618	7	and	and	CCONJ
fuelectenerg-1427	618	8	ternary	ternary	ADJ
fuelectenerg-1427	618	9	generalized	generalized	ADJ
fuelectenerg-1427	618	10	davio	davio	NOUN
fuelectenerg-1427	618	11	nodes	node	NOUN
fuelectenerg-1427	618	12	,	,	PUNCT
fuelectenerg-1427	618	13	that	that	PRON
fuelectenerg-1427	618	14	generates	generate	VERB
fuelectenerg-1427	618	15	other	other	ADJ
fuelectenerg-1427	618	16	ternary	ternary	ADJ
fuelectenerg-1427	618	17	trees	tree	NOUN
fuelectenerg-1427	618	18	,	,	PUNCT
fuelectenerg-1427	618	19	is	be	AUX
fuelectenerg-1427	618	20	called	call	VERB
fuelectenerg-1427	618	21	ternary	ternary	ADJ
fuelectenerg-1427	618	22	shannon	shannon	NOUN
fuelectenerg-1427	618	23	-	-	PUNCT
fuelectenerg-1427	618	24	davio	davio	NOUN
fuelectenerg-1427	618	25	(	(	PUNCT
fuelectenerg-1427	618	26	s	s	NOUN
fuelectenerg-1427	618	27	/	/	SYM
fuelectenerg-1427	618	28	d	d	NOUN
fuelectenerg-1427	618	29	)	)	PUNCT
fuelectenerg-1427	618	30	tree	tree	NOUN
fuelectenerg-1427	618	31	.	.	PUNCT
fuelectenerg-1427	619	1	utilizing	utilize	VERB
fuelectenerg-1427	619	2	the	the	DET
fuelectenerg-1427	619	3	definition	definition	NOUN
fuelectenerg-1427	619	4	of	of	ADP
fuelectenerg-1427	619	5	ternary	ternary	ADJ
fuelectenerg-1427	619	6	shannon	shannon	NOUN
fuelectenerg-1427	619	7	in	in	ADP
fuelectenerg-1427	619	8	figure	figure	NOUN
fuelectenerg-1427	619	9	4(a	4(a	NUM
fuelectenerg-1427	619	10	)	)	PUNCT
fuelectenerg-1427	619	11	and	and	CCONJ
fuelectenerg-1427	619	12	ternary	ternary	ADJ
fuelectenerg-1427	619	13	generalized	generalized	ADJ
fuelectenerg-1427	619	14	davio	davio	NOUN
fuelectenerg-1427	619	15	in	in	ADP
fuelectenerg-1427	619	16	figure	figure	NOUN
fuelectenerg-1427	619	17	4(e	4(e	NUM
fuelectenerg-1427	619	18	)	)	PUNCT
fuelectenerg-1427	619	19	,	,	PUNCT
fuelectenerg-1427	619	20	we	we	PRON
fuelectenerg-1427	619	21	obtain	obtain	VERB
fuelectenerg-1427	619	22	the	the	DET
fuelectenerg-1427	619	23	ternary	ternary	ADJ
fuelectenerg-1427	619	24	shannon	shannon	NOUN
fuelectenerg-1427	619	25	-	-	PUNCT
fuelectenerg-1427	619	26	davio	davio	NOUN
fuelectenerg-1427	619	27	trees	tree	NOUN
fuelectenerg-1427	619	28	(	(	PUNCT
fuelectenerg-1427	619	29	ternary	ternary	NOUN
fuelectenerg-1427	619	30	s	s	PROPN
fuelectenerg-1427	619	31	/	/	SYM
fuelectenerg-1427	619	32	d	d	NOUN
fuelectenerg-1427	619	33	trees	tree	NOUN
fuelectenerg-1427	619	34	)	)	PUNCT
fuelectenerg-1427	619	35	for	for	ADP
fuelectenerg-1427	619	36	two	two	NUM
fuelectenerg-1427	619	37	variables	variable	NOUN
fuelectenerg-1427	619	38	as	as	SCONJ
fuelectenerg-1427	619	39	shown	show	VERB
fuelectenerg-1427	619	40	in	in	ADP
fuelectenerg-1427	619	41	figure	figure	NOUN
fuelectenerg-1427	619	42	5	5	NUM
fuelectenerg-1427	619	43	.	.	PUNCT
fuelectenerg-1427	619	44	from	from	ADP
fuelectenerg-1427	619	45	the	the	DET
fuelectenerg-1427	619	46	ternary	ternary	ADJ
fuelectenerg-1427	619	47	s	s	PROPN
fuelectenerg-1427	619	48	/	/	SYM
fuelectenerg-1427	619	49	d	d	ADJ
fuelectenerg-1427	619	50	dts	dts	NOUN
fuelectenerg-1427	619	51	shown	show	VERB
fuelectenerg-1427	619	52	in	in	ADP
fuelectenerg-1427	619	53	figure	figure	NOUN
fuelectenerg-1427	619	54	5	5	NUM
fuelectenerg-1427	619	55	,	,	PUNCT
fuelectenerg-1427	619	56	if	if	SCONJ
fuelectenerg-1427	619	57	we	we	PRON
fuelectenerg-1427	619	58	take	take	VERB
fuelectenerg-1427	619	59	any	any	DET
fuelectenerg-1427	619	60	s	s	PROPN
fuelectenerg-1427	619	61	/	/	SYM
fuelectenerg-1427	619	62	d	d	NOUN
fuelectenerg-1427	619	63	tree	tree	NOUN
fuelectenerg-1427	619	64	and	and	CCONJ
fuelectenerg-1427	619	65	multiply	multiply	VERB
fuelectenerg-1427	619	66	the	the	DET
fuelectenerg-1427	619	67	second	second	ADJ
fuelectenerg-1427	619	68	-	-	PUNCT
fuelectenerg-1427	619	69	level	level	NOUN
fuelectenerg-1427	619	70	cofactors	cofactor	NOUN
fuelectenerg-1427	619	71	(	(	PUNCT
fuelectenerg-1427	619	72	which	which	PRON
fuelectenerg-1427	619	73	are	be	AUX
fuelectenerg-1427	619	74	in	in	ADP
fuelectenerg-1427	619	75	the	the	DET
fuelectenerg-1427	619	76	tdt	tdt	PROPN
fuelectenerg-1427	619	77	leaves	leave	NOUN
fuelectenerg-1427	619	78	)	)	PUNCT
fuelectenerg-1427	619	79	each	each	PRON
fuelectenerg-1427	619	80	by	by	ADP
fuelectenerg-1427	619	81	the	the	DET
fuelectenerg-1427	619	82	corresponding	corresponding	ADJ
fuelectenerg-1427	619	83	path	path	NOUN
fuelectenerg-1427	619	84	in	in	ADP
fuelectenerg-1427	619	85	that	that	DET
fuelectenerg-1427	619	86	tdt	tdt	PROPN
fuelectenerg-1427	619	87	,	,	PUNCT
fuelectenerg-1427	619	88	and	and	CCONJ
fuelectenerg-1427	619	89	sum	sum	VERB
fuelectenerg-1427	619	90	all	all	DET
fuelectenerg-1427	619	91	the	the	DET
fuelectenerg-1427	619	92	resulting	result	VERB
fuelectenerg-1427	619	93	cubes	cube	NOUN
fuelectenerg-1427	619	94	(	(	PUNCT
fuelectenerg-1427	619	95	terms	term	NOUN
fuelectenerg-1427	619	96	)	)	PUNCT
fuelectenerg-1427	619	97	over	over	ADP
fuelectenerg-1427	619	98	gf(3	gf(3	PROPN
fuelectenerg-1427	619	99	)	)	PUNCT
fuelectenerg-1427	619	100	,	,	PUNCT
fuelectenerg-1427	619	101	we	we	PRON
fuelectenerg-1427	619	102	obtain	obtain	VERB
fuelectenerg-1427	619	103	the	the	DET
fuelectenerg-1427	619	104	flattened	flatten	VERB
fuelectenerg-1427	619	105	form	form	NOUN
fuelectenerg-1427	619	106	of	of	ADP
fuelectenerg-1427	619	107	the	the	DET
fuelectenerg-1427	619	108	function	function	NOUN
fuelectenerg-1427	619	109	f	f	PROPN
fuelectenerg-1427	619	110	,	,	PUNCT
fuelectenerg-1427	619	111	as	as	ADP
fuelectenerg-1427	619	112	a	a	DET
fuelectenerg-1427	619	113	certain	certain	ADJ
fuelectenerg-1427	619	114	gfsop	gfsop	NOUN
fuelectenerg-1427	619	115	expression	expression	NOUN
fuelectenerg-1427	619	116	.	.	PUNCT
fuelectenerg-1427	620	1	for	for	ADP
fuelectenerg-1427	620	2	each	each	DET
fuelectenerg-1427	620	3	tdt	tdt	PROPN
fuelectenerg-1427	620	4	in	in	ADP
fuelectenerg-1427	620	5	figure	figure	NOUN
fuelectenerg-1427	620	6	5	5	NUM
fuelectenerg-1427	620	7	,	,	PUNCT
fuelectenerg-1427	620	8	there	there	PRON
fuelectenerg-1427	620	9	are	be	VERB
fuelectenerg-1427	620	10	as	as	ADV
fuelectenerg-1427	620	11	many	many	ADJ
fuelectenerg-1427	620	12	forms	form	NOUN
fuelectenerg-1427	620	13	obtained	obtain	VERB
fuelectenerg-1427	620	14	for	for	ADP
fuelectenerg-1427	620	15	the	the	DET
fuelectenerg-1427	620	16	function	function	NOUN
fuelectenerg-1427	620	17	f	f	PROPN
fuelectenerg-1427	620	18	as	as	ADP
fuelectenerg-1427	620	19	the	the	DET
fuelectenerg-1427	620	20	number	number	NOUN
fuelectenerg-1427	620	21	of	of	ADP
fuelectenerg-1427	620	22	possible	possible	ADJ
fuelectenerg-1427	620	23	permutations	permutation	NOUN
fuelectenerg-1427	620	24	of	of	ADP
fuelectenerg-1427	620	25	the	the	DET
fuelectenerg-1427	620	26	polarities	polarity	NOUN
fuelectenerg-1427	620	27	of	of	ADP
fuelectenerg-1427	620	28	the	the	DET
fuelectenerg-1427	620	29	variables	variable	NOUN
fuelectenerg-1427	620	30	in	in	ADP
fuelectenerg-1427	620	31	the	the	DET
fuelectenerg-1427	620	32	second	second	ADJ
fuelectenerg-1427	620	33	-	-	PUNCT
fuelectenerg-1427	620	34	level	level	NOUN
fuelectenerg-1427	620	35	branches	branch	NOUN
fuelectenerg-1427	620	36	of	of	ADP
fuelectenerg-1427	620	37	each	each	DET
fuelectenerg-1427	620	38	tdt	tdt	PROPN
fuelectenerg-1427	620	39	.	.	PUNCT
fuelectenerg-1427	621	1	definition	definition	NOUN
fuelectenerg-1427	621	2	2	2	NUM
fuelectenerg-1427	621	3	.	.	PUNCT
fuelectenerg-1427	622	1	the	the	DET
fuelectenerg-1427	622	2	family	family	NOUN
fuelectenerg-1427	622	3	of	of	ADP
fuelectenerg-1427	622	4	all	all	DET
fuelectenerg-1427	622	5	possible	possible	ADJ
fuelectenerg-1427	622	6	forms	form	NOUN
fuelectenerg-1427	622	7	obtained	obtain	VERB
fuelectenerg-1427	622	8	per	per	ADP
fuelectenerg-1427	622	9	ternary	ternary	NOUN
fuelectenerg-1427	622	10	s	s	PROPN
fuelectenerg-1427	622	11	/	/	SYM
fuelectenerg-1427	622	12	d	d	NOUN
fuelectenerg-1427	622	13	tree	tree	NOUN
fuelectenerg-1427	622	14	is	be	AUX
fuelectenerg-1427	622	15	called	call	VERB
fuelectenerg-1427	622	16	ternary	ternary	ADJ
fuelectenerg-1427	622	17	inclusive	inclusive	ADJ
fuelectenerg-1427	622	18	forms	form	NOUN
fuelectenerg-1427	622	19	(	(	PUNCT
fuelectenerg-1427	622	20	tifs	tifs	PROPN
fuelectenerg-1427	622	21	)	)	PUNCT
fuelectenerg-1427	622	22	.	.	PUNCT
fuelectenerg-1427	623	1	the	the	DET
fuelectenerg-1427	623	2	numbers	number	NOUN
fuelectenerg-1427	623	3	of	of	ADP
fuelectenerg-1427	623	4	these	these	DET
fuelectenerg-1427	623	5	tifs	tif	NOUN
fuelectenerg-1427	623	6	per	per	ADP
fuelectenerg-1427	623	7	tdt	tdt	PROPN
fuelectenerg-1427	623	8	for	for	ADP
fuelectenerg-1427	623	9	two	two	NUM
fuelectenerg-1427	623	10	variables	variable	NOUN
fuelectenerg-1427	623	11	are	be	AUX
fuelectenerg-1427	623	12	shown	show	VERB
fuelectenerg-1427	623	13	on	on	ADP
fuelectenerg-1427	623	14	top	top	NOUN
fuelectenerg-1427	623	15	of	of	ADP
fuelectenerg-1427	623	16	each	each	DET
fuelectenerg-1427	623	17	s	s	PROPN
fuelectenerg-1427	623	18	/	/	SYM
fuelectenerg-1427	623	19	d	d	PROPN
fuelectenerg-1427	623	20	tdt	tdt	PROPN
fuelectenerg-1427	623	21	in	in	ADP
fuelectenerg-1427	623	22	figure	figure	NOUN
fuelectenerg-1427	623	23	5	5	NUM
fuelectenerg-1427	623	24	.	.	PUNCT
fuelectenerg-1427	623	25	by	by	ADP
fuelectenerg-1427	623	26	observing	observe	VERB
fuelectenerg-1427	623	27	figure	figure	NOUN
fuelectenerg-1427	623	28	5	5	NUM
fuelectenerg-1427	623	29	,	,	PUNCT
fuelectenerg-1427	623	30	we	we	PRON
fuelectenerg-1427	623	31	can	can	AUX
fuelectenerg-1427	623	32	generate	generate	VERB
fuelectenerg-1427	623	33	the	the	DET
fuelectenerg-1427	623	34	corresponding	corresponding	ADJ
fuelectenerg-1427	623	35	flattened	flatten	VERB
fuelectenerg-1427	623	36	forms	form	NOUN
fuelectenerg-1427	623	37	by	by	ADP
fuelectenerg-1427	623	38	two	two	NUM
fuelectenerg-1427	623	39	methods	method	NOUN
fuelectenerg-1427	623	40	.	.	PUNCT
fuelectenerg-1427	624	1	a	a	DET
fuelectenerg-1427	624	2	classical	classical	ADJ
fuelectenerg-1427	624	3	method	method	NOUN
fuelectenerg-1427	624	4	,	,	PUNCT
fuelectenerg-1427	624	5	per	per	ADP
fuelectenerg-1427	624	6	analogy	analogy	NOUN
fuelectenerg-1427	624	7	with	with	ADP
fuelectenerg-1427	624	8	well	well	ADV
fuelectenerg-1427	624	9	-	-	PUNCT
fuelectenerg-1427	624	10	known	know	VERB
fuelectenerg-1427	624	11	binary	binary	ADJ
fuelectenerg-1427	624	12	forms	form	NOUN
fuelectenerg-1427	624	13	,	,	PUNCT
fuelectenerg-1427	624	14	would	would	AUX
fuelectenerg-1427	624	15	be	be	AUX
fuelectenerg-1427	624	16	to	to	PART
fuelectenerg-1427	624	17	create	create	VERB
fuelectenerg-1427	624	18	every	every	DET
fuelectenerg-1427	624	19	transform	transform	NOUN
fuelectenerg-1427	624	20	matrix	matrix	NOUN
fuelectenerg-1427	624	21	for	for	ADP
fuelectenerg-1427	624	22	every	every	DET
fuelectenerg-1427	624	23	tif	tif	PROPN
fuelectenerg-1427	624	24	s	s	PROPN
fuelectenerg-1427	624	25	/	/	SYM
fuelectenerg-1427	624	26	d	d	NOUN
fuelectenerg-1427	624	27	tree	tree	NOUN
fuelectenerg-1427	624	28	and	and	CCONJ
fuelectenerg-1427	624	29	then	then	ADV
fuelectenerg-1427	624	30	expand	expand	VERB
fuelectenerg-1427	624	31	using	use	VERB
fuelectenerg-1427	624	32	that	that	DET
fuelectenerg-1427	624	33	transform	transform	NOUN
fuelectenerg-1427	624	34	matrix	matrix	NOUN
fuelectenerg-1427	624	35	.	.	PUNCT
fuelectenerg-1427	625	1	a	a	DET
fuelectenerg-1427	625	2	better	well	ADJ
fuelectenerg-1427	625	3	method	method	NOUN
fuelectenerg-1427	625	4	is	be	AUX
fuelectenerg-1427	625	5	to	to	PART
fuelectenerg-1427	625	6	create	create	VERB
fuelectenerg-1427	625	7	one	one	NUM
fuelectenerg-1427	625	8	flattened	flatten	VERB
fuelectenerg-1427	625	9	108	108	NUM
fuelectenerg-1427	625	10	an	an	DET
fuelectenerg-1427	625	11	extended	extend	VERB
fuelectenerg-1427	625	12	green	green	ADJ
fuelectenerg-1427	625	13	sasao	sasao	PROPN
fuelectenerg-1427	625	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	625	15	of	of	ADP
fuelectenerg-1427	625	16	canonical	canonical	ADJ
fuelectenerg-1427	625	17	ternary	ternary	ADJ
fuelectenerg-1427	625	18	galois	galois	NOUN
fuelectenerg-1427	625	19	forms	form	NOUN
fuelectenerg-1427	625	20	...	...	PUNCT
fuelectenerg-1427	625	21	s	s	VERB
fuelectenerg-1427	625	22	a	a	PRON
fuelectenerg-1427	625	23	’	'	PUNCT
fuelectenerg-1427	625	24	a	a	PRON
fuelectenerg-1427	625	25	(	(	PUNCT
fuelectenerg-1427	625	26	)	)	PUNCT
fuelectenerg-1427	625	27	a	a	PRON
fuelectenerg-1427	625	28	pd	pd	PROPN
fuelectenerg-1427	625	29	1	1	NUM
fuelectenerg-1427	625	30	a	a	PRON
fuelectenerg-1427	625	31	(	(	PUNCT
fuelectenerg-1427	625	32	)	)	PUNCT
fuelectenerg-1427	625	33	b	b	NOUN
fuelectenerg-1427	625	34	nd	nd	ADP
fuelectenerg-1427	625	35	1	1	NUM
fuelectenerg-1427	625	36	a	a	PRON
fuelectenerg-1427	625	37	’	'	PUNCT
fuelectenerg-1427	625	38	d	d	ADP
fuelectenerg-1427	625	39	1	1	NUM
fuelectenerg-1427	625	40	a	a	PRON
fuelectenerg-1427	625	41	(	(	PUNCT
fuelectenerg-1427	625	42	)	)	PUNCT
fuelectenerg-1427	625	43	d	d	NOUN
fuelectenerg-1427	625	44	(	(	PUNCT
fuelectenerg-1427	625	45	)	)	PUNCT
fuelectenerg-1427	625	46	c	c	NOUN
fuelectenerg-1427	625	47	figure	figure	VERB
fuelectenerg-1427	625	48	3	3	NUM
fuelectenerg-1427	625	49	:	:	PUNCT
fuelectenerg-1427	625	50	two	two	NUM
fuelectenerg-1427	625	51	-	-	PUNCT
fuelectenerg-1427	625	52	valued	value	VERB
fuelectenerg-1427	625	53	nodes	node	NOUN
fuelectenerg-1427	625	54	:	:	PUNCT
fuelectenerg-1427	625	55	(	(	PUNCT
fuelectenerg-1427	625	56	a	a	X
fuelectenerg-1427	625	57	)	)	PUNCT
fuelectenerg-1427	625	58	shannon	shannon	NOUN
fuelectenerg-1427	625	59	,	,	PUNCT
fuelectenerg-1427	625	60	(	(	PUNCT
fuelectenerg-1427	625	61	b	b	NOUN
fuelectenerg-1427	625	62	)	)	PUNCT
fuelectenerg-1427	625	63	positive	positive	ADJ
fuelectenerg-1427	625	64	davio	davio	NOUN
fuelectenerg-1427	625	65	,	,	PUNCT
fuelectenerg-1427	625	66	(	(	PUNCT
fuelectenerg-1427	625	67	c	c	NOUN
fuelectenerg-1427	625	68	)	)	PUNCT
fuelectenerg-1427	625	69	negative	negative	ADJ
fuelectenerg-1427	625	70	davio	davio	NOUN
fuelectenerg-1427	625	71	,	,	PUNCT
fuelectenerg-1427	625	72	and	and	CCONJ
fuelectenerg-1427	625	73	(	(	PUNCT
fuelectenerg-1427	625	74	d	d	X
fuelectenerg-1427	625	75	)	)	PUNCT
fuelectenerg-1427	625	76	generalized	generalized	ADJ
fuelectenerg-1427	625	77	davio	davio	NOUN
fuelectenerg-1427	625	78	where	where	SCONJ
fuelectenerg-1427	625	79	a	a	DET
fuelectenerg-1427	625	80	∈	∈	NOUN
fuelectenerg-1427	625	81	{	{	PUNCT
fuelectenerg-1427	625	82	a	a	PRON
fuelectenerg-1427	625	83	,	,	PUNCT
fuelectenerg-1427	625	84	a′	a′	PROPN
fuelectenerg-1427	625	85	}	}	PUNCT
fuelectenerg-1427	625	86	.	.	PUNCT
fuelectenerg-1427	626	1	variable	variable	ADJ
fuelectenerg-1427	626	2	,	,	PUNCT
fuelectenerg-1427	626	3	that	that	PRON
fuelectenerg-1427	626	4	is	be	AUX
fuelectenerg-1427	626	5	one	one	NUM
fuelectenerg-1427	626	6	tree	tree	NOUN
fuelectenerg-1427	626	7	level	level	NOUN
fuelectenerg-1427	626	8	,	,	PUNCT
fuelectenerg-1427	626	9	figure	figure	NOUN
fuelectenerg-1427	626	10	4	4	NUM
fuelectenerg-1427	626	11	represents	represent	VERB
fuelectenerg-1427	626	12	the	the	DET
fuelectenerg-1427	626	13	expansion	expansion	NOUN
fuelectenerg-1427	626	14	nodes	node	NOUN
fuelectenerg-1427	626	15	for	for	ADP
fuelectenerg-1427	626	16	ternary	ternary	ADJ
fuelectenerg-1427	626	17	shannon	shannon	NOUN
fuelectenerg-1427	626	18	,	,	PUNCT
fuelectenerg-1427	626	19	davio	davio	NOUN
fuelectenerg-1427	626	20	and	and	CCONJ
fuelectenerg-1427	626	21	generalized	generalized	ADJ
fuelectenerg-1427	626	22	davio	davio	NOUN
fuelectenerg-1427	626	23	(	(	PUNCT
fuelectenerg-1427	626	24	d	d	NOUN
fuelectenerg-1427	626	25	)	)	PUNCT
fuelectenerg-1427	626	26	,	,	PUNCT
fuelectenerg-1427	626	27	respectively	respectively	ADV
fuelectenerg-1427	626	28	.	.	PUNCT
fuelectenerg-1427	627	1	s	s	PART
fuelectenerg-1427	627	2	0	0	NUM
fuelectenerg-1427	627	3	x	x	SYM
fuelectenerg-1427	627	4	1	1	NUM
fuelectenerg-1427	627	5	x	x	SYM
fuelectenerg-1427	627	6	2	2	NUM
fuelectenerg-1427	627	7	x	x	SYM
fuelectenerg-1427	627	8	(	(	PUNCT
fuelectenerg-1427	627	9	a	a	PRON
fuelectenerg-1427	627	10	)	)	PUNCT
fuelectenerg-1427	627	11	d0	d0	NOUN
fuelectenerg-1427	627	12	1	1	NUM
fuelectenerg-1427	627	13	x	x	SYM
fuelectenerg-1427	627	14	2	2	NUM
fuelectenerg-1427	627	15	(	(	PUNCT
fuelectenerg-1427	627	16	b	b	NOUN
fuelectenerg-1427	627	17	)	)	PUNCT
fuelectenerg-1427	627	18	d2	d2	PROPN
fuelectenerg-1427	627	19	1	1	NUM
fuelectenerg-1427	627	20	(	(	PUNCT
fuelectenerg-1427	627	21	d	d	NOUN
fuelectenerg-1427	627	22	)	)	PUNCT
fuelectenerg-1427	628	1	d	d	NOUN
fuelectenerg-1427	628	2	1	1	NUM
fuelectenerg-1427	628	3	(	(	PUNCT
fuelectenerg-1427	628	4	e	e	NOUN
fuelectenerg-1427	628	5	)	)	PUNCT
fuelectenerg-1427	628	6	d1	d1	NOUN
fuelectenerg-1427	628	7	1	1	NUM
fuelectenerg-1427	628	8	(	(	PUNCT
fuelectenerg-1427	628	9	’	'	PUNCT
fuelectenerg-1427	628	10	)	)	PUNCT
fuelectenerg-1427	628	11	x	x	SYM
fuelectenerg-1427	628	12	2	2	NUM
fuelectenerg-1427	628	13	(	(	PUNCT
fuelectenerg-1427	628	14	’’	’'	PUNCT
fuelectenerg-1427	628	15	)	)	PUNCT
fuelectenerg-1427	628	16	x	x	SYM
fuelectenerg-1427	628	17	2	2	NUM
fuelectenerg-1427	628	18	(	(	PUNCT
fuelectenerg-1427	628	19	)	)	PUNCT
fuelectenerg-1427	628	20	x	x	SYM
fuelectenerg-1427	628	21	2	2	NUM
fuelectenerg-1427	628	22	(	(	PUNCT
fuelectenerg-1427	628	23	c	c	NOUN
fuelectenerg-1427	628	24	)	)	PUNCT
fuelectenerg-1427	628	25	x	x	SYM
fuelectenerg-1427	628	26	xx	xx	X
fuelectenerg-1427	628	27	’	'	PUNCT
fuelectenerg-1427	628	28	x	x	NOUN
fuelectenerg-1427	628	29	’’	’'	PUNCT
fuelectenerg-1427	628	30	figure	figure	VERB
fuelectenerg-1427	628	31	4	4	NUM
fuelectenerg-1427	628	32	:	:	PUNCT
fuelectenerg-1427	628	33	ternary	ternary	ADJ
fuelectenerg-1427	628	34	nodes	node	NOUN
fuelectenerg-1427	628	35	for	for	ADP
fuelectenerg-1427	628	36	ternary	ternary	ADJ
fuelectenerg-1427	628	37	decision	decision	NOUN
fuelectenerg-1427	628	38	trees	tree	NOUN
fuelectenerg-1427	628	39	:	:	PUNCT
fuelectenerg-1427	628	40	(	(	PUNCT
fuelectenerg-1427	628	41	a	a	X
fuelectenerg-1427	628	42	)	)	PUNCT
fuelectenerg-1427	628	43	shannon	shannon	NOUN
fuelectenerg-1427	628	44	,	,	PUNCT
fuelectenerg-1427	628	45	(	(	PUNCT
fuelectenerg-1427	628	46	b	b	X
fuelectenerg-1427	628	47	)	)	PUNCT
fuelectenerg-1427	628	48	davio0	davio0	PROPN
fuelectenerg-1427	628	49	,	,	PUNCT
fuelectenerg-1427	628	50	(	(	PUNCT
fuelectenerg-1427	628	51	c	c	X
fuelectenerg-1427	628	52	)	)	PUNCT
fuelectenerg-1427	628	53	davio1	davio1	NOUN
fuelectenerg-1427	628	54	,	,	PUNCT
fuelectenerg-1427	628	55	(	(	PUNCT
fuelectenerg-1427	628	56	d	d	NOUN
fuelectenerg-1427	628	57	)	)	PUNCT
fuelectenerg-1427	628	58	davio2	davio2	PROPN
fuelectenerg-1427	628	59	,	,	PUNCT
fuelectenerg-1427	628	60	and	and	CCONJ
fuelectenerg-1427	628	61	(	(	PUNCT
fuelectenerg-1427	628	62	e	e	NOUN
fuelectenerg-1427	628	63	)	)	PUNCT
fuelectenerg-1427	628	64	generalized	generalized	ADJ
fuelectenerg-1427	628	65	davio	davio	NOUN
fuelectenerg-1427	628	66	(	(	PUNCT
fuelectenerg-1427	628	67	d	d	NOUN
fuelectenerg-1427	628	68	)	)	PUNCT
fuelectenerg-1427	628	69	where	where	SCONJ
fuelectenerg-1427	628	70	x	x	SYM
fuelectenerg-1427	628	71	∈	∈	PROPN
fuelectenerg-1427	628	72	{	{	PUNCT
fuelectenerg-1427	628	73	x	x	NOUN
fuelectenerg-1427	628	74	,	,	PUNCT
fuelectenerg-1427	628	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	628	76	}	}	PUNCT
fuelectenerg-1427	628	77	.	.	PUNCT
fuelectenerg-1427	629	1	in	in	ADP
fuelectenerg-1427	629	2	correspondence	correspondence	NOUN
fuelectenerg-1427	629	3	to	to	ADP
fuelectenerg-1427	629	4	the	the	DET
fuelectenerg-1427	629	5	binary	binary	PROPN
fuelectenerg-1427	629	6	s	s	PROPN
fuelectenerg-1427	629	7	/	/	SYM
fuelectenerg-1427	629	8	d	d	NOUN
fuelectenerg-1427	629	9	trees	tree	NOUN
fuelectenerg-1427	629	10	,	,	PUNCT
fuelectenerg-1427	629	11	one	one	PRON
fuelectenerg-1427	629	12	can	can	AUX
fuelectenerg-1427	629	13	produce	produce	VERB
fuelectenerg-1427	629	14	ternary	ternary	ADJ
fuelectenerg-1427	629	15	s	s	NOUN
fuelectenerg-1427	629	16	/	/	SYM
fuelectenerg-1427	629	17	d	d	NOUN
fuelectenerg-1427	629	18	trees	tree	NOUN
fuelectenerg-1427	629	19	.	.	PUNCT
fuelectenerg-1427	630	1	to	to	PART
fuelectenerg-1427	630	2	define	define	VERB
fuelectenerg-1427	630	3	the	the	DET
fuelectenerg-1427	630	4	ternary	ternary	ADJ
fuelectenerg-1427	630	5	s	s	NOUN
fuelectenerg-1427	630	6	/	/	SYM
fuelectenerg-1427	630	7	d	d	NOUN
fuelectenerg-1427	630	8	trees	tree	NOUN
fuelectenerg-1427	630	9	,	,	PUNCT
fuelectenerg-1427	630	10	we	we	PRON
fuelectenerg-1427	630	11	define	define	VERB
fuelectenerg-1427	630	12	the	the	DET
fuelectenerg-1427	630	13	generalized	generalized	ADJ
fuelectenerg-1427	630	14	davio	davio	NOUN
fuelectenerg-1427	630	15	node	node	NOUN
fuelectenerg-1427	630	16	over	over	ADP
fuelectenerg-1427	630	17	ternary	ternary	ADJ
fuelectenerg-1427	630	18	galois	galois	PROPN
fuelectenerg-1427	630	19	radix	radix	NOUN
fuelectenerg-1427	630	20	as	as	SCONJ
fuelectenerg-1427	630	21	shown	show	VERB
fuelectenerg-1427	630	22	in	in	ADP
fuelectenerg-1427	630	23	figure	figure	NOUN
fuelectenerg-1427	630	24	4(e	4(e	NUM
fuelectenerg-1427	630	25	)	)	PUNCT
fuelectenerg-1427	630	26	.	.	PUNCT
fuelectenerg-1427	631	1	our	our	PRON
fuelectenerg-1427	631	2	notation	notation	NOUN
fuelectenerg-1427	631	3	here	here	ADV
fuelectenerg-1427	631	4	is	be	AUX
fuelectenerg-1427	631	5	that	that	PRON
fuelectenerg-1427	631	6	(	(	PUNCT
fuelectenerg-1427	631	7	x	x	X
fuelectenerg-1427	631	8	)	)	PUNCT
fuelectenerg-1427	631	9	corresponds	correspond	VERB
fuelectenerg-1427	631	10	to	to	ADP
fuelectenerg-1427	631	11	the	the	DET
fuelectenerg-1427	631	12	three	three	NUM
fuelectenerg-1427	631	13	possible	possible	ADJ
fuelectenerg-1427	631	14	shifts	shift	NOUN
fuelectenerg-1427	631	15	of	of	ADP
fuelectenerg-1427	631	16	the	the	DET
fuelectenerg-1427	631	17	variable	variable	NOUN
fuelectenerg-1427	631	18	x	x	NOUN
fuelectenerg-1427	631	19	as	as	SCONJ
fuelectenerg-1427	631	20	follows	follow	VERB
fuelectenerg-1427	631	21	:	:	PUNCT
fuelectenerg-1427	631	22	x	x	SYM
fuelectenerg-1427	631	23	∈	∈	NOUN
fuelectenerg-1427	631	24	{	{	PUNCT
fuelectenerg-1427	631	25	x	x	NOUN
fuelectenerg-1427	631	26	,	,	PUNCT
fuelectenerg-1427	631	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	631	28	}	}	PUNCT
fuelectenerg-1427	631	29	,	,	PUNCT
fuelectenerg-1427	631	30	over	over	ADP
fuelectenerg-1427	631	31	gf(3	gf(3	PROPN
fuelectenerg-1427	631	32	)	)	PUNCT
fuelectenerg-1427	631	33	.	.	PUNCT
fuelectenerg-1427	632	1	(	(	PUNCT
fuelectenerg-1427	632	2	28	28	NUM
fuelectenerg-1427	632	3	)	)	PUNCT
fuelectenerg-1427	632	4	definition	definition	NOUN
fuelectenerg-1427	632	5	1	1	NUM
fuelectenerg-1427	632	6	.	.	PUNCT
fuelectenerg-1427	633	1	the	the	DET
fuelectenerg-1427	633	2	ternary	ternary	ADJ
fuelectenerg-1427	633	3	tree	tree	NOUN
fuelectenerg-1427	633	4	with	with	ADP
fuelectenerg-1427	633	5	ternary	ternary	ADJ
fuelectenerg-1427	633	6	shannon	shannon	NOUN
fuelectenerg-1427	633	7	and	and	CCONJ
fuelectenerg-1427	633	8	ternary	ternary	ADJ
fuelectenerg-1427	633	9	generalized	generalized	ADJ
fuelectenerg-1427	633	10	davio	davio	NOUN
fuelectenerg-1427	633	11	nodes	node	NOUN
fuelectenerg-1427	633	12	,	,	PUNCT
fuelectenerg-1427	633	13	that	that	PRON
fuelectenerg-1427	633	14	generates	generate	VERB
fuelectenerg-1427	633	15	other	other	ADJ
fuelectenerg-1427	633	16	ternary	ternary	ADJ
fuelectenerg-1427	633	17	trees	tree	NOUN
fuelectenerg-1427	633	18	,	,	PUNCT
fuelectenerg-1427	633	19	is	be	AUX
fuelectenerg-1427	633	20	called	call	VERB
fuelectenerg-1427	633	21	ternary	ternary	ADJ
fuelectenerg-1427	633	22	shannon	shannon	NOUN
fuelectenerg-1427	633	23	-	-	PUNCT
fuelectenerg-1427	633	24	davio	davio	NOUN
fuelectenerg-1427	633	25	(	(	PUNCT
fuelectenerg-1427	633	26	s	s	NOUN
fuelectenerg-1427	633	27	/	/	SYM
fuelectenerg-1427	633	28	d	d	NOUN
fuelectenerg-1427	633	29	)	)	PUNCT
fuelectenerg-1427	633	30	tree	tree	NOUN
fuelectenerg-1427	633	31	.	.	PUNCT
fuelectenerg-1427	634	1	utilizing	utilize	VERB
fuelectenerg-1427	634	2	the	the	DET
fuelectenerg-1427	634	3	definition	definition	NOUN
fuelectenerg-1427	634	4	of	of	ADP
fuelectenerg-1427	634	5	ternary	ternary	ADJ
fuelectenerg-1427	634	6	shannon	shannon	NOUN
fuelectenerg-1427	634	7	in	in	ADP
fuelectenerg-1427	634	8	figure	figure	NOUN
fuelectenerg-1427	634	9	4(a	4(a	NUM
fuelectenerg-1427	634	10	)	)	PUNCT
fuelectenerg-1427	634	11	and	and	CCONJ
fuelectenerg-1427	634	12	ternary	ternary	ADJ
fuelectenerg-1427	634	13	generalized	generalized	ADJ
fuelectenerg-1427	634	14	davio	davio	NOUN
fuelectenerg-1427	634	15	in	in	ADP
fuelectenerg-1427	634	16	figure	figure	NOUN
fuelectenerg-1427	634	17	4(e	4(e	NUM
fuelectenerg-1427	634	18	)	)	PUNCT
fuelectenerg-1427	634	19	,	,	PUNCT
fuelectenerg-1427	634	20	we	we	PRON
fuelectenerg-1427	634	21	obtain	obtain	VERB
fuelectenerg-1427	634	22	the	the	DET
fuelectenerg-1427	634	23	ternary	ternary	ADJ
fuelectenerg-1427	634	24	shannon	shannon	NOUN
fuelectenerg-1427	634	25	-	-	PUNCT
fuelectenerg-1427	634	26	davio	davio	NOUN
fuelectenerg-1427	634	27	trees	tree	NOUN
fuelectenerg-1427	634	28	(	(	PUNCT
fuelectenerg-1427	634	29	ternary	ternary	NOUN
fuelectenerg-1427	634	30	s	s	PROPN
fuelectenerg-1427	634	31	/	/	SYM
fuelectenerg-1427	634	32	d	d	NOUN
fuelectenerg-1427	634	33	trees	tree	NOUN
fuelectenerg-1427	634	34	)	)	PUNCT
fuelectenerg-1427	634	35	for	for	ADP
fuelectenerg-1427	634	36	two	two	NUM
fuelectenerg-1427	634	37	variables	variable	NOUN
fuelectenerg-1427	634	38	as	as	SCONJ
fuelectenerg-1427	634	39	shown	show	VERB
fuelectenerg-1427	634	40	in	in	ADP
fuelectenerg-1427	634	41	figure	figure	NOUN
fuelectenerg-1427	634	42	5	5	NUM
fuelectenerg-1427	634	43	.	.	PUNCT
fuelectenerg-1427	634	44	from	from	ADP
fuelectenerg-1427	634	45	the	the	DET
fuelectenerg-1427	634	46	ternary	ternary	ADJ
fuelectenerg-1427	634	47	s	s	PROPN
fuelectenerg-1427	634	48	/	/	SYM
fuelectenerg-1427	634	49	d	d	ADJ
fuelectenerg-1427	634	50	dts	dts	NOUN
fuelectenerg-1427	634	51	shown	show	VERB
fuelectenerg-1427	634	52	in	in	ADP
fuelectenerg-1427	634	53	figure	figure	NOUN
fuelectenerg-1427	634	54	5	5	NUM
fuelectenerg-1427	634	55	,	,	PUNCT
fuelectenerg-1427	634	56	if	if	SCONJ
fuelectenerg-1427	634	57	we	we	PRON
fuelectenerg-1427	634	58	take	take	VERB
fuelectenerg-1427	634	59	any	any	DET
fuelectenerg-1427	634	60	s	s	PROPN
fuelectenerg-1427	634	61	/	/	SYM
fuelectenerg-1427	634	62	d	d	NOUN
fuelectenerg-1427	634	63	tree	tree	NOUN
fuelectenerg-1427	634	64	and	and	CCONJ
fuelectenerg-1427	634	65	multiply	multiply	VERB
fuelectenerg-1427	634	66	the	the	DET
fuelectenerg-1427	634	67	second	second	ADJ
fuelectenerg-1427	634	68	-	-	PUNCT
fuelectenerg-1427	634	69	level	level	NOUN
fuelectenerg-1427	634	70	cofactors	cofactor	NOUN
fuelectenerg-1427	634	71	(	(	PUNCT
fuelectenerg-1427	634	72	which	which	PRON
fuelectenerg-1427	634	73	are	be	AUX
fuelectenerg-1427	634	74	in	in	ADP
fuelectenerg-1427	634	75	the	the	DET
fuelectenerg-1427	634	76	tdt	tdt	PROPN
fuelectenerg-1427	634	77	leaves	leave	NOUN
fuelectenerg-1427	634	78	)	)	PUNCT
fuelectenerg-1427	634	79	each	each	PRON
fuelectenerg-1427	634	80	by	by	ADP
fuelectenerg-1427	634	81	the	the	DET
fuelectenerg-1427	634	82	corresponding	corresponding	ADJ
fuelectenerg-1427	634	83	path	path	NOUN
fuelectenerg-1427	634	84	in	in	ADP
fuelectenerg-1427	634	85	that	that	DET
fuelectenerg-1427	634	86	tdt	tdt	PROPN
fuelectenerg-1427	634	87	,	,	PUNCT
fuelectenerg-1427	634	88	and	and	CCONJ
fuelectenerg-1427	634	89	sum	sum	VERB
fuelectenerg-1427	634	90	all	all	DET
fuelectenerg-1427	634	91	the	the	DET
fuelectenerg-1427	634	92	resulting	result	VERB
fuelectenerg-1427	634	93	cubes	cube	NOUN
fuelectenerg-1427	634	94	(	(	PUNCT
fuelectenerg-1427	634	95	terms	term	NOUN
fuelectenerg-1427	634	96	)	)	PUNCT
fuelectenerg-1427	634	97	over	over	ADP
fuelectenerg-1427	634	98	gf(3	gf(3	PROPN
fuelectenerg-1427	634	99	)	)	PUNCT
fuelectenerg-1427	634	100	,	,	PUNCT
fuelectenerg-1427	634	101	we	we	PRON
fuelectenerg-1427	634	102	obtain	obtain	VERB
fuelectenerg-1427	634	103	the	the	DET
fuelectenerg-1427	634	104	flattened	flatten	VERB
fuelectenerg-1427	634	105	form	form	NOUN
fuelectenerg-1427	634	106	of	of	ADP
fuelectenerg-1427	634	107	the	the	DET
fuelectenerg-1427	634	108	function	function	NOUN
fuelectenerg-1427	634	109	f	f	PROPN
fuelectenerg-1427	634	110	,	,	PUNCT
fuelectenerg-1427	634	111	as	as	ADP
fuelectenerg-1427	634	112	a	a	DET
fuelectenerg-1427	634	113	certain	certain	ADJ
fuelectenerg-1427	634	114	gfsop	gfsop	NOUN
fuelectenerg-1427	634	115	expression	expression	NOUN
fuelectenerg-1427	634	116	.	.	PUNCT
fuelectenerg-1427	635	1	for	for	ADP
fuelectenerg-1427	635	2	each	each	DET
fuelectenerg-1427	635	3	tdt	tdt	PROPN
fuelectenerg-1427	635	4	in	in	ADP
fuelectenerg-1427	635	5	figure	figure	NOUN
fuelectenerg-1427	635	6	5	5	NUM
fuelectenerg-1427	635	7	,	,	PUNCT
fuelectenerg-1427	635	8	there	there	PRON
fuelectenerg-1427	635	9	are	be	VERB
fuelectenerg-1427	635	10	as	as	ADV
fuelectenerg-1427	635	11	many	many	ADJ
fuelectenerg-1427	635	12	forms	form	NOUN
fuelectenerg-1427	635	13	obtained	obtain	VERB
fuelectenerg-1427	635	14	for	for	ADP
fuelectenerg-1427	635	15	the	the	DET
fuelectenerg-1427	635	16	function	function	NOUN
fuelectenerg-1427	635	17	f	f	PROPN
fuelectenerg-1427	635	18	as	as	ADP
fuelectenerg-1427	635	19	the	the	DET
fuelectenerg-1427	635	20	number	number	NOUN
fuelectenerg-1427	635	21	of	of	ADP
fuelectenerg-1427	635	22	possible	possible	ADJ
fuelectenerg-1427	635	23	permutations	permutation	NOUN
fuelectenerg-1427	635	24	of	of	ADP
fuelectenerg-1427	635	25	the	the	DET
fuelectenerg-1427	635	26	polarities	polarity	NOUN
fuelectenerg-1427	635	27	of	of	ADP
fuelectenerg-1427	635	28	the	the	DET
fuelectenerg-1427	635	29	variables	variable	NOUN
fuelectenerg-1427	635	30	in	in	ADP
fuelectenerg-1427	635	31	the	the	DET
fuelectenerg-1427	635	32	second	second	ADJ
fuelectenerg-1427	635	33	-	-	PUNCT
fuelectenerg-1427	635	34	level	level	NOUN
fuelectenerg-1427	635	35	branches	branch	NOUN
fuelectenerg-1427	635	36	of	of	ADP
fuelectenerg-1427	635	37	each	each	DET
fuelectenerg-1427	635	38	tdt	tdt	PROPN
fuelectenerg-1427	635	39	.	.	PUNCT
fuelectenerg-1427	636	1	definition	definition	NOUN
fuelectenerg-1427	636	2	2	2	NUM
fuelectenerg-1427	636	3	.	.	PUNCT
fuelectenerg-1427	637	1	the	the	DET
fuelectenerg-1427	637	2	family	family	NOUN
fuelectenerg-1427	637	3	of	of	ADP
fuelectenerg-1427	637	4	all	all	DET
fuelectenerg-1427	637	5	possible	possible	ADJ
fuelectenerg-1427	637	6	forms	form	NOUN
fuelectenerg-1427	637	7	obtained	obtain	VERB
fuelectenerg-1427	637	8	per	per	ADP
fuelectenerg-1427	637	9	ternary	ternary	NOUN
fuelectenerg-1427	637	10	s	s	PROPN
fuelectenerg-1427	637	11	/	/	SYM
fuelectenerg-1427	637	12	d	d	NOUN
fuelectenerg-1427	637	13	tree	tree	NOUN
fuelectenerg-1427	637	14	is	be	AUX
fuelectenerg-1427	637	15	called	call	VERB
fuelectenerg-1427	637	16	ternary	ternary	ADJ
fuelectenerg-1427	637	17	inclusive	inclusive	ADJ
fuelectenerg-1427	637	18	forms	form	NOUN
fuelectenerg-1427	637	19	(	(	PUNCT
fuelectenerg-1427	637	20	tifs	tifs	PROPN
fuelectenerg-1427	637	21	)	)	PUNCT
fuelectenerg-1427	637	22	.	.	PUNCT
fuelectenerg-1427	638	1	the	the	DET
fuelectenerg-1427	638	2	numbers	number	NOUN
fuelectenerg-1427	638	3	of	of	ADP
fuelectenerg-1427	638	4	these	these	DET
fuelectenerg-1427	638	5	tifs	tif	NOUN
fuelectenerg-1427	638	6	per	per	ADP
fuelectenerg-1427	638	7	tdt	tdt	PROPN
fuelectenerg-1427	638	8	for	for	ADP
fuelectenerg-1427	638	9	two	two	NUM
fuelectenerg-1427	638	10	variables	variable	NOUN
fuelectenerg-1427	638	11	are	be	AUX
fuelectenerg-1427	638	12	shown	show	VERB
fuelectenerg-1427	638	13	on	on	ADP
fuelectenerg-1427	638	14	top	top	NOUN
fuelectenerg-1427	638	15	of	of	ADP
fuelectenerg-1427	638	16	each	each	DET
fuelectenerg-1427	638	17	s	s	PROPN
fuelectenerg-1427	638	18	/	/	SYM
fuelectenerg-1427	638	19	d	d	PROPN
fuelectenerg-1427	638	20	tdt	tdt	PROPN
fuelectenerg-1427	638	21	in	in	ADP
fuelectenerg-1427	638	22	figure	figure	NOUN
fuelectenerg-1427	638	23	5	5	NUM
fuelectenerg-1427	638	24	.	.	PUNCT
fuelectenerg-1427	638	25	by	by	ADP
fuelectenerg-1427	638	26	observing	observe	VERB
fuelectenerg-1427	638	27	figure	figure	NOUN
fuelectenerg-1427	638	28	5	5	NUM
fuelectenerg-1427	638	29	,	,	PUNCT
fuelectenerg-1427	638	30	we	we	PRON
fuelectenerg-1427	638	31	can	can	AUX
fuelectenerg-1427	638	32	generate	generate	VERB
fuelectenerg-1427	638	33	the	the	DET
fuelectenerg-1427	638	34	corresponding	corresponding	ADJ
fuelectenerg-1427	638	35	flattened	flatten	VERB
fuelectenerg-1427	638	36	forms	form	NOUN
fuelectenerg-1427	638	37	by	by	ADP
fuelectenerg-1427	638	38	two	two	NUM
fuelectenerg-1427	638	39	methods	method	NOUN
fuelectenerg-1427	638	40	.	.	PUNCT
fuelectenerg-1427	639	1	a	a	DET
fuelectenerg-1427	639	2	classical	classical	ADJ
fuelectenerg-1427	639	3	method	method	NOUN
fuelectenerg-1427	639	4	,	,	PUNCT
fuelectenerg-1427	639	5	per	per	ADP
fuelectenerg-1427	639	6	analogy	analogy	NOUN
fuelectenerg-1427	639	7	with	with	ADP
fuelectenerg-1427	639	8	well	well	ADV
fuelectenerg-1427	639	9	-	-	PUNCT
fuelectenerg-1427	639	10	known	know	VERB
fuelectenerg-1427	639	11	binary	binary	ADJ
fuelectenerg-1427	639	12	forms	form	NOUN
fuelectenerg-1427	639	13	,	,	PUNCT
fuelectenerg-1427	639	14	would	would	AUX
fuelectenerg-1427	639	15	be	be	AUX
fuelectenerg-1427	639	16	to	to	PART
fuelectenerg-1427	639	17	create	create	VERB
fuelectenerg-1427	639	18	every	every	DET
fuelectenerg-1427	639	19	transform	transform	NOUN
fuelectenerg-1427	639	20	matrix	matrix	NOUN
fuelectenerg-1427	639	21	for	for	ADP
fuelectenerg-1427	639	22	every	every	DET
fuelectenerg-1427	639	23	tif	tif	PROPN
fuelectenerg-1427	639	24	s	s	PROPN
fuelectenerg-1427	639	25	/	/	SYM
fuelectenerg-1427	639	26	d	d	NOUN
fuelectenerg-1427	639	27	tree	tree	NOUN
fuelectenerg-1427	639	28	and	and	CCONJ
fuelectenerg-1427	639	29	then	then	ADV
fuelectenerg-1427	639	30	expand	expand	VERB
fuelectenerg-1427	639	31	using	use	VERB
fuelectenerg-1427	639	32	that	that	DET
fuelectenerg-1427	639	33	transform	transform	NOUN
fuelectenerg-1427	639	34	matrix	matrix	NOUN
fuelectenerg-1427	639	35	.	.	PUNCT
fuelectenerg-1427	640	1	a	a	DET
fuelectenerg-1427	640	2	better	well	ADJ
fuelectenerg-1427	640	3	method	method	NOUN
fuelectenerg-1427	640	4	is	be	AUX
fuelectenerg-1427	640	5	to	to	PART
fuelectenerg-1427	640	6	create	create	VERB
fuelectenerg-1427	640	7	one	one	NUM
fuelectenerg-1427	640	8	flattened	flatten	VERB
fuelectenerg-1427	640	9	108	108	NUM
fuelectenerg-1427	640	10	an	an	DET
fuelectenerg-1427	640	11	extended	extend	VERB
fuelectenerg-1427	640	12	green	green	ADJ
fuelectenerg-1427	640	13	sasao	sasao	PROPN
fuelectenerg-1427	640	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	640	15	of	of	ADP
fuelectenerg-1427	640	16	canonical	canonical	ADJ
fuelectenerg-1427	640	17	ternary	ternary	ADJ
fuelectenerg-1427	640	18	galois	galois	NOUN
fuelectenerg-1427	640	19	forms	form	NOUN
fuelectenerg-1427	640	20	...	...	PUNCT
fuelectenerg-1427	640	21	s	s	VERB
fuelectenerg-1427	640	22	a	a	PRON
fuelectenerg-1427	640	23	’	'	PUNCT
fuelectenerg-1427	640	24	a	a	PRON
fuelectenerg-1427	640	25	(	(	PUNCT
fuelectenerg-1427	640	26	)	)	PUNCT
fuelectenerg-1427	640	27	a	a	PRON
fuelectenerg-1427	640	28	pd	pd	PROPN
fuelectenerg-1427	640	29	1	1	NUM
fuelectenerg-1427	640	30	a	a	PRON
fuelectenerg-1427	640	31	(	(	PUNCT
fuelectenerg-1427	640	32	)	)	PUNCT
fuelectenerg-1427	640	33	b	b	NOUN
fuelectenerg-1427	640	34	nd	nd	ADP
fuelectenerg-1427	640	35	1	1	NUM
fuelectenerg-1427	640	36	a	a	PRON
fuelectenerg-1427	640	37	’	'	PUNCT
fuelectenerg-1427	640	38	d	d	ADP
fuelectenerg-1427	640	39	1	1	NUM
fuelectenerg-1427	640	40	a	a	PRON
fuelectenerg-1427	640	41	(	(	PUNCT
fuelectenerg-1427	640	42	)	)	PUNCT
fuelectenerg-1427	640	43	d	d	NOUN
fuelectenerg-1427	640	44	(	(	PUNCT
fuelectenerg-1427	640	45	)	)	PUNCT
fuelectenerg-1427	640	46	c	c	NOUN
fuelectenerg-1427	640	47	figure	figure	VERB
fuelectenerg-1427	640	48	3	3	NUM
fuelectenerg-1427	640	49	:	:	PUNCT
fuelectenerg-1427	640	50	two	two	NUM
fuelectenerg-1427	640	51	-	-	PUNCT
fuelectenerg-1427	640	52	valued	value	VERB
fuelectenerg-1427	640	53	nodes	node	NOUN
fuelectenerg-1427	640	54	:	:	PUNCT
fuelectenerg-1427	640	55	(	(	PUNCT
fuelectenerg-1427	640	56	a	a	X
fuelectenerg-1427	640	57	)	)	PUNCT
fuelectenerg-1427	640	58	shannon	shannon	NOUN
fuelectenerg-1427	640	59	,	,	PUNCT
fuelectenerg-1427	640	60	(	(	PUNCT
fuelectenerg-1427	640	61	b	b	NOUN
fuelectenerg-1427	640	62	)	)	PUNCT
fuelectenerg-1427	640	63	positive	positive	ADJ
fuelectenerg-1427	640	64	davio	davio	NOUN
fuelectenerg-1427	640	65	,	,	PUNCT
fuelectenerg-1427	640	66	(	(	PUNCT
fuelectenerg-1427	640	67	c	c	NOUN
fuelectenerg-1427	640	68	)	)	PUNCT
fuelectenerg-1427	640	69	negative	negative	ADJ
fuelectenerg-1427	640	70	davio	davio	NOUN
fuelectenerg-1427	640	71	,	,	PUNCT
fuelectenerg-1427	640	72	and	and	CCONJ
fuelectenerg-1427	640	73	(	(	PUNCT
fuelectenerg-1427	640	74	d	d	X
fuelectenerg-1427	640	75	)	)	PUNCT
fuelectenerg-1427	640	76	generalized	generalized	ADJ
fuelectenerg-1427	640	77	davio	davio	NOUN
fuelectenerg-1427	640	78	where	where	SCONJ
fuelectenerg-1427	640	79	a	a	DET
fuelectenerg-1427	640	80	∈	∈	NOUN
fuelectenerg-1427	640	81	{	{	PUNCT
fuelectenerg-1427	640	82	a	a	PRON
fuelectenerg-1427	640	83	,	,	PUNCT
fuelectenerg-1427	640	84	a′	a′	PROPN
fuelectenerg-1427	640	85	}	}	PUNCT
fuelectenerg-1427	640	86	.	.	PUNCT
fuelectenerg-1427	641	1	variable	variable	ADJ
fuelectenerg-1427	641	2	,	,	PUNCT
fuelectenerg-1427	641	3	that	that	PRON
fuelectenerg-1427	641	4	is	be	AUX
fuelectenerg-1427	641	5	one	one	NUM
fuelectenerg-1427	641	6	tree	tree	NOUN
fuelectenerg-1427	641	7	level	level	NOUN
fuelectenerg-1427	641	8	,	,	PUNCT
fuelectenerg-1427	641	9	figure	figure	NOUN
fuelectenerg-1427	641	10	4	4	NUM
fuelectenerg-1427	641	11	represents	represent	VERB
fuelectenerg-1427	641	12	the	the	DET
fuelectenerg-1427	641	13	expansion	expansion	NOUN
fuelectenerg-1427	641	14	nodes	node	NOUN
fuelectenerg-1427	641	15	for	for	ADP
fuelectenerg-1427	641	16	ternary	ternary	ADJ
fuelectenerg-1427	641	17	shannon	shannon	NOUN
fuelectenerg-1427	641	18	,	,	PUNCT
fuelectenerg-1427	641	19	davio	davio	NOUN
fuelectenerg-1427	641	20	and	and	CCONJ
fuelectenerg-1427	641	21	generalized	generalized	ADJ
fuelectenerg-1427	641	22	davio	davio	NOUN
fuelectenerg-1427	641	23	(	(	PUNCT
fuelectenerg-1427	641	24	d	d	NOUN
fuelectenerg-1427	641	25	)	)	PUNCT
fuelectenerg-1427	641	26	,	,	PUNCT
fuelectenerg-1427	641	27	respectively	respectively	ADV
fuelectenerg-1427	641	28	.	.	PUNCT
fuelectenerg-1427	642	1	s	s	PART
fuelectenerg-1427	642	2	0	0	NUM
fuelectenerg-1427	642	3	x	x	SYM
fuelectenerg-1427	642	4	1	1	NUM
fuelectenerg-1427	642	5	x	x	SYM
fuelectenerg-1427	642	6	2	2	NUM
fuelectenerg-1427	642	7	x	x	SYM
fuelectenerg-1427	642	8	(	(	PUNCT
fuelectenerg-1427	642	9	a	a	PRON
fuelectenerg-1427	642	10	)	)	PUNCT
fuelectenerg-1427	642	11	d0	d0	NOUN
fuelectenerg-1427	642	12	1	1	NUM
fuelectenerg-1427	642	13	x	x	SYM
fuelectenerg-1427	642	14	2	2	NUM
fuelectenerg-1427	642	15	(	(	PUNCT
fuelectenerg-1427	642	16	b	b	NOUN
fuelectenerg-1427	642	17	)	)	PUNCT
fuelectenerg-1427	642	18	d2	d2	PROPN
fuelectenerg-1427	642	19	1	1	NUM
fuelectenerg-1427	642	20	(	(	PUNCT
fuelectenerg-1427	642	21	d	d	NOUN
fuelectenerg-1427	642	22	)	)	PUNCT
fuelectenerg-1427	643	1	d	d	NOUN
fuelectenerg-1427	643	2	1	1	NUM
fuelectenerg-1427	643	3	(	(	PUNCT
fuelectenerg-1427	643	4	e	e	NOUN
fuelectenerg-1427	643	5	)	)	PUNCT
fuelectenerg-1427	643	6	d1	d1	NOUN
fuelectenerg-1427	643	7	1	1	NUM
fuelectenerg-1427	643	8	(	(	PUNCT
fuelectenerg-1427	643	9	’	'	PUNCT
fuelectenerg-1427	643	10	)	)	PUNCT
fuelectenerg-1427	643	11	x	x	SYM
fuelectenerg-1427	643	12	2	2	NUM
fuelectenerg-1427	643	13	(	(	PUNCT
fuelectenerg-1427	643	14	’’	’'	PUNCT
fuelectenerg-1427	643	15	)	)	PUNCT
fuelectenerg-1427	643	16	x	x	SYM
fuelectenerg-1427	643	17	2	2	NUM
fuelectenerg-1427	643	18	(	(	PUNCT
fuelectenerg-1427	643	19	)	)	PUNCT
fuelectenerg-1427	643	20	x	x	SYM
fuelectenerg-1427	643	21	2	2	NUM
fuelectenerg-1427	643	22	(	(	PUNCT
fuelectenerg-1427	643	23	c	c	NOUN
fuelectenerg-1427	643	24	)	)	PUNCT
fuelectenerg-1427	643	25	x	x	SYM
fuelectenerg-1427	643	26	xx	xx	X
fuelectenerg-1427	643	27	’	'	PUNCT
fuelectenerg-1427	643	28	x	x	NOUN
fuelectenerg-1427	643	29	’’	’'	PUNCT
fuelectenerg-1427	643	30	figure	figure	VERB
fuelectenerg-1427	643	31	4	4	NUM
fuelectenerg-1427	643	32	:	:	PUNCT
fuelectenerg-1427	643	33	ternary	ternary	ADJ
fuelectenerg-1427	643	34	nodes	node	NOUN
fuelectenerg-1427	643	35	for	for	ADP
fuelectenerg-1427	643	36	ternary	ternary	ADJ
fuelectenerg-1427	643	37	decision	decision	NOUN
fuelectenerg-1427	643	38	trees	tree	NOUN
fuelectenerg-1427	643	39	:	:	PUNCT
fuelectenerg-1427	643	40	(	(	PUNCT
fuelectenerg-1427	643	41	a	a	X
fuelectenerg-1427	643	42	)	)	PUNCT
fuelectenerg-1427	643	43	shannon	shannon	NOUN
fuelectenerg-1427	643	44	,	,	PUNCT
fuelectenerg-1427	643	45	(	(	PUNCT
fuelectenerg-1427	643	46	b	b	X
fuelectenerg-1427	643	47	)	)	PUNCT
fuelectenerg-1427	643	48	davio0	davio0	PROPN
fuelectenerg-1427	643	49	,	,	PUNCT
fuelectenerg-1427	643	50	(	(	PUNCT
fuelectenerg-1427	643	51	c	c	X
fuelectenerg-1427	643	52	)	)	PUNCT
fuelectenerg-1427	643	53	davio1	davio1	NOUN
fuelectenerg-1427	643	54	,	,	PUNCT
fuelectenerg-1427	643	55	(	(	PUNCT
fuelectenerg-1427	643	56	d	d	NOUN
fuelectenerg-1427	643	57	)	)	PUNCT
fuelectenerg-1427	643	58	davio2	davio2	PROPN
fuelectenerg-1427	643	59	,	,	PUNCT
fuelectenerg-1427	643	60	and	and	CCONJ
fuelectenerg-1427	643	61	(	(	PUNCT
fuelectenerg-1427	643	62	e	e	NOUN
fuelectenerg-1427	643	63	)	)	PUNCT
fuelectenerg-1427	643	64	generalized	generalized	ADJ
fuelectenerg-1427	643	65	davio	davio	NOUN
fuelectenerg-1427	643	66	(	(	PUNCT
fuelectenerg-1427	643	67	d	d	NOUN
fuelectenerg-1427	643	68	)	)	PUNCT
fuelectenerg-1427	643	69	where	where	SCONJ
fuelectenerg-1427	643	70	x	x	SYM
fuelectenerg-1427	643	71	∈	∈	PROPN
fuelectenerg-1427	643	72	{	{	PUNCT
fuelectenerg-1427	643	73	x	x	NOUN
fuelectenerg-1427	643	74	,	,	PUNCT
fuelectenerg-1427	643	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	643	76	}	}	PUNCT
fuelectenerg-1427	643	77	.	.	PUNCT
fuelectenerg-1427	644	1	in	in	ADP
fuelectenerg-1427	644	2	correspondence	correspondence	NOUN
fuelectenerg-1427	644	3	to	to	ADP
fuelectenerg-1427	644	4	the	the	DET
fuelectenerg-1427	644	5	binary	binary	PROPN
fuelectenerg-1427	644	6	s	s	PROPN
fuelectenerg-1427	644	7	/	/	SYM
fuelectenerg-1427	644	8	d	d	NOUN
fuelectenerg-1427	644	9	trees	tree	NOUN
fuelectenerg-1427	644	10	,	,	PUNCT
fuelectenerg-1427	644	11	one	one	PRON
fuelectenerg-1427	644	12	can	can	AUX
fuelectenerg-1427	644	13	produce	produce	VERB
fuelectenerg-1427	644	14	ternary	ternary	ADJ
fuelectenerg-1427	644	15	s	s	NOUN
fuelectenerg-1427	644	16	/	/	SYM
fuelectenerg-1427	644	17	d	d	NOUN
fuelectenerg-1427	644	18	trees	tree	NOUN
fuelectenerg-1427	644	19	.	.	PUNCT
fuelectenerg-1427	645	1	to	to	PART
fuelectenerg-1427	645	2	define	define	VERB
fuelectenerg-1427	645	3	the	the	DET
fuelectenerg-1427	645	4	ternary	ternary	ADJ
fuelectenerg-1427	645	5	s	s	NOUN
fuelectenerg-1427	645	6	/	/	SYM
fuelectenerg-1427	645	7	d	d	NOUN
fuelectenerg-1427	645	8	trees	tree	NOUN
fuelectenerg-1427	645	9	,	,	PUNCT
fuelectenerg-1427	645	10	we	we	PRON
fuelectenerg-1427	645	11	define	define	VERB
fuelectenerg-1427	645	12	the	the	DET
fuelectenerg-1427	645	13	generalized	generalized	ADJ
fuelectenerg-1427	645	14	davio	davio	NOUN
fuelectenerg-1427	645	15	node	node	NOUN
fuelectenerg-1427	645	16	over	over	ADP
fuelectenerg-1427	645	17	ternary	ternary	ADJ
fuelectenerg-1427	645	18	galois	galois	PROPN
fuelectenerg-1427	645	19	radix	radix	NOUN
fuelectenerg-1427	645	20	as	as	SCONJ
fuelectenerg-1427	645	21	shown	show	VERB
fuelectenerg-1427	645	22	in	in	ADP
fuelectenerg-1427	645	23	figure	figure	NOUN
fuelectenerg-1427	645	24	4(e	4(e	NUM
fuelectenerg-1427	645	25	)	)	PUNCT
fuelectenerg-1427	645	26	.	.	PUNCT
fuelectenerg-1427	646	1	our	our	PRON
fuelectenerg-1427	646	2	notation	notation	NOUN
fuelectenerg-1427	646	3	here	here	ADV
fuelectenerg-1427	646	4	is	be	AUX
fuelectenerg-1427	646	5	that	that	PRON
fuelectenerg-1427	646	6	(	(	PUNCT
fuelectenerg-1427	646	7	x	x	X
fuelectenerg-1427	646	8	)	)	PUNCT
fuelectenerg-1427	646	9	corresponds	correspond	VERB
fuelectenerg-1427	646	10	to	to	ADP
fuelectenerg-1427	646	11	the	the	DET
fuelectenerg-1427	646	12	three	three	NUM
fuelectenerg-1427	646	13	possible	possible	ADJ
fuelectenerg-1427	646	14	shifts	shift	NOUN
fuelectenerg-1427	646	15	of	of	ADP
fuelectenerg-1427	646	16	the	the	DET
fuelectenerg-1427	646	17	variable	variable	NOUN
fuelectenerg-1427	646	18	x	x	NOUN
fuelectenerg-1427	646	19	as	as	SCONJ
fuelectenerg-1427	646	20	follows	follow	VERB
fuelectenerg-1427	646	21	:	:	PUNCT
fuelectenerg-1427	646	22	x	x	SYM
fuelectenerg-1427	646	23	∈	∈	NOUN
fuelectenerg-1427	646	24	{	{	PUNCT
fuelectenerg-1427	646	25	x	x	NOUN
fuelectenerg-1427	646	26	,	,	PUNCT
fuelectenerg-1427	646	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	646	28	}	}	PUNCT
fuelectenerg-1427	646	29	,	,	PUNCT
fuelectenerg-1427	646	30	over	over	ADP
fuelectenerg-1427	646	31	gf(3	gf(3	PROPN
fuelectenerg-1427	646	32	)	)	PUNCT
fuelectenerg-1427	646	33	.	.	PUNCT
fuelectenerg-1427	647	1	(	(	PUNCT
fuelectenerg-1427	647	2	28	28	NUM
fuelectenerg-1427	647	3	)	)	PUNCT
fuelectenerg-1427	647	4	definition	definition	NOUN
fuelectenerg-1427	647	5	1	1	NUM
fuelectenerg-1427	647	6	.	.	PUNCT
fuelectenerg-1427	648	1	the	the	DET
fuelectenerg-1427	648	2	ternary	ternary	ADJ
fuelectenerg-1427	648	3	tree	tree	NOUN
fuelectenerg-1427	648	4	with	with	ADP
fuelectenerg-1427	648	5	ternary	ternary	ADJ
fuelectenerg-1427	648	6	shannon	shannon	NOUN
fuelectenerg-1427	648	7	and	and	CCONJ
fuelectenerg-1427	648	8	ternary	ternary	ADJ
fuelectenerg-1427	648	9	generalized	generalized	ADJ
fuelectenerg-1427	648	10	davio	davio	NOUN
fuelectenerg-1427	648	11	nodes	node	NOUN
fuelectenerg-1427	648	12	,	,	PUNCT
fuelectenerg-1427	648	13	that	that	PRON
fuelectenerg-1427	648	14	generates	generate	VERB
fuelectenerg-1427	648	15	other	other	ADJ
fuelectenerg-1427	648	16	ternary	ternary	ADJ
fuelectenerg-1427	648	17	trees	tree	NOUN
fuelectenerg-1427	648	18	,	,	PUNCT
fuelectenerg-1427	648	19	is	be	AUX
fuelectenerg-1427	648	20	called	call	VERB
fuelectenerg-1427	648	21	ternary	ternary	ADJ
fuelectenerg-1427	648	22	shannon	shannon	NOUN
fuelectenerg-1427	648	23	-	-	PUNCT
fuelectenerg-1427	648	24	davio	davio	NOUN
fuelectenerg-1427	648	25	(	(	PUNCT
fuelectenerg-1427	648	26	s	s	NOUN
fuelectenerg-1427	648	27	/	/	SYM
fuelectenerg-1427	648	28	d	d	NOUN
fuelectenerg-1427	648	29	)	)	PUNCT
fuelectenerg-1427	648	30	tree	tree	NOUN
fuelectenerg-1427	648	31	.	.	PUNCT
fuelectenerg-1427	649	1	utilizing	utilize	VERB
fuelectenerg-1427	649	2	the	the	DET
fuelectenerg-1427	649	3	definition	definition	NOUN
fuelectenerg-1427	649	4	of	of	ADP
fuelectenerg-1427	649	5	ternary	ternary	ADJ
fuelectenerg-1427	649	6	shannon	shannon	NOUN
fuelectenerg-1427	649	7	in	in	ADP
fuelectenerg-1427	649	8	figure	figure	NOUN
fuelectenerg-1427	649	9	4(a	4(a	NUM
fuelectenerg-1427	649	10	)	)	PUNCT
fuelectenerg-1427	649	11	and	and	CCONJ
fuelectenerg-1427	649	12	ternary	ternary	ADJ
fuelectenerg-1427	649	13	generalized	generalized	ADJ
fuelectenerg-1427	649	14	davio	davio	NOUN
fuelectenerg-1427	649	15	in	in	ADP
fuelectenerg-1427	649	16	figure	figure	NOUN
fuelectenerg-1427	649	17	4(e	4(e	NUM
fuelectenerg-1427	649	18	)	)	PUNCT
fuelectenerg-1427	649	19	,	,	PUNCT
fuelectenerg-1427	649	20	we	we	PRON
fuelectenerg-1427	649	21	obtain	obtain	VERB
fuelectenerg-1427	649	22	the	the	DET
fuelectenerg-1427	649	23	ternary	ternary	ADJ
fuelectenerg-1427	649	24	shannon	shannon	NOUN
fuelectenerg-1427	649	25	-	-	PUNCT
fuelectenerg-1427	649	26	davio	davio	NOUN
fuelectenerg-1427	649	27	trees	tree	NOUN
fuelectenerg-1427	649	28	(	(	PUNCT
fuelectenerg-1427	649	29	ternary	ternary	NOUN
fuelectenerg-1427	649	30	s	s	PROPN
fuelectenerg-1427	649	31	/	/	SYM
fuelectenerg-1427	649	32	d	d	NOUN
fuelectenerg-1427	649	33	trees	tree	NOUN
fuelectenerg-1427	649	34	)	)	PUNCT
fuelectenerg-1427	649	35	for	for	ADP
fuelectenerg-1427	649	36	two	two	NUM
fuelectenerg-1427	649	37	variables	variable	NOUN
fuelectenerg-1427	649	38	as	as	SCONJ
fuelectenerg-1427	649	39	shown	show	VERB
fuelectenerg-1427	649	40	in	in	ADP
fuelectenerg-1427	649	41	figure	figure	NOUN
fuelectenerg-1427	649	42	5	5	NUM
fuelectenerg-1427	649	43	.	.	PUNCT
fuelectenerg-1427	649	44	from	from	ADP
fuelectenerg-1427	649	45	the	the	DET
fuelectenerg-1427	649	46	ternary	ternary	ADJ
fuelectenerg-1427	649	47	s	s	PROPN
fuelectenerg-1427	649	48	/	/	SYM
fuelectenerg-1427	649	49	d	d	ADJ
fuelectenerg-1427	649	50	dts	dts	NOUN
fuelectenerg-1427	649	51	shown	show	VERB
fuelectenerg-1427	649	52	in	in	ADP
fuelectenerg-1427	649	53	figure	figure	NOUN
fuelectenerg-1427	649	54	5	5	NUM
fuelectenerg-1427	649	55	,	,	PUNCT
fuelectenerg-1427	649	56	if	if	SCONJ
fuelectenerg-1427	649	57	we	we	PRON
fuelectenerg-1427	649	58	take	take	VERB
fuelectenerg-1427	649	59	any	any	DET
fuelectenerg-1427	649	60	s	s	PROPN
fuelectenerg-1427	649	61	/	/	SYM
fuelectenerg-1427	649	62	d	d	NOUN
fuelectenerg-1427	649	63	tree	tree	NOUN
fuelectenerg-1427	649	64	and	and	CCONJ
fuelectenerg-1427	649	65	multiply	multiply	VERB
fuelectenerg-1427	649	66	the	the	DET
fuelectenerg-1427	649	67	second	second	ADJ
fuelectenerg-1427	649	68	-	-	PUNCT
fuelectenerg-1427	649	69	level	level	NOUN
fuelectenerg-1427	649	70	cofactors	cofactor	NOUN
fuelectenerg-1427	649	71	(	(	PUNCT
fuelectenerg-1427	649	72	which	which	PRON
fuelectenerg-1427	649	73	are	be	AUX
fuelectenerg-1427	649	74	in	in	ADP
fuelectenerg-1427	649	75	the	the	DET
fuelectenerg-1427	649	76	tdt	tdt	PROPN
fuelectenerg-1427	649	77	leaves	leave	NOUN
fuelectenerg-1427	649	78	)	)	PUNCT
fuelectenerg-1427	649	79	each	each	PRON
fuelectenerg-1427	649	80	by	by	ADP
fuelectenerg-1427	649	81	the	the	DET
fuelectenerg-1427	649	82	corresponding	corresponding	ADJ
fuelectenerg-1427	649	83	path	path	NOUN
fuelectenerg-1427	649	84	in	in	ADP
fuelectenerg-1427	649	85	that	that	DET
fuelectenerg-1427	649	86	tdt	tdt	PROPN
fuelectenerg-1427	649	87	,	,	PUNCT
fuelectenerg-1427	649	88	and	and	CCONJ
fuelectenerg-1427	649	89	sum	sum	VERB
fuelectenerg-1427	649	90	all	all	DET
fuelectenerg-1427	649	91	the	the	DET
fuelectenerg-1427	649	92	resulting	result	VERB
fuelectenerg-1427	649	93	cubes	cube	NOUN
fuelectenerg-1427	649	94	(	(	PUNCT
fuelectenerg-1427	649	95	terms	term	NOUN
fuelectenerg-1427	649	96	)	)	PUNCT
fuelectenerg-1427	649	97	over	over	ADP
fuelectenerg-1427	649	98	gf(3	gf(3	PROPN
fuelectenerg-1427	649	99	)	)	PUNCT
fuelectenerg-1427	649	100	,	,	PUNCT
fuelectenerg-1427	649	101	we	we	PRON
fuelectenerg-1427	649	102	obtain	obtain	VERB
fuelectenerg-1427	649	103	the	the	DET
fuelectenerg-1427	649	104	flattened	flatten	VERB
fuelectenerg-1427	649	105	form	form	NOUN
fuelectenerg-1427	649	106	of	of	ADP
fuelectenerg-1427	649	107	the	the	DET
fuelectenerg-1427	649	108	function	function	NOUN
fuelectenerg-1427	649	109	f	f	PROPN
fuelectenerg-1427	649	110	,	,	PUNCT
fuelectenerg-1427	649	111	as	as	ADP
fuelectenerg-1427	649	112	a	a	DET
fuelectenerg-1427	649	113	certain	certain	ADJ
fuelectenerg-1427	649	114	gfsop	gfsop	NOUN
fuelectenerg-1427	649	115	expression	expression	NOUN
fuelectenerg-1427	649	116	.	.	PUNCT
fuelectenerg-1427	650	1	for	for	ADP
fuelectenerg-1427	650	2	each	each	DET
fuelectenerg-1427	650	3	tdt	tdt	PROPN
fuelectenerg-1427	650	4	in	in	ADP
fuelectenerg-1427	650	5	figure	figure	NOUN
fuelectenerg-1427	650	6	5	5	NUM
fuelectenerg-1427	650	7	,	,	PUNCT
fuelectenerg-1427	650	8	there	there	PRON
fuelectenerg-1427	650	9	are	be	VERB
fuelectenerg-1427	650	10	as	as	ADV
fuelectenerg-1427	650	11	many	many	ADJ
fuelectenerg-1427	650	12	forms	form	NOUN
fuelectenerg-1427	650	13	obtained	obtain	VERB
fuelectenerg-1427	650	14	for	for	ADP
fuelectenerg-1427	650	15	the	the	DET
fuelectenerg-1427	650	16	function	function	NOUN
fuelectenerg-1427	650	17	f	f	PROPN
fuelectenerg-1427	650	18	as	as	ADP
fuelectenerg-1427	650	19	the	the	DET
fuelectenerg-1427	650	20	number	number	NOUN
fuelectenerg-1427	650	21	of	of	ADP
fuelectenerg-1427	650	22	possible	possible	ADJ
fuelectenerg-1427	650	23	permutations	permutation	NOUN
fuelectenerg-1427	650	24	of	of	ADP
fuelectenerg-1427	650	25	the	the	DET
fuelectenerg-1427	650	26	polarities	polarity	NOUN
fuelectenerg-1427	650	27	of	of	ADP
fuelectenerg-1427	650	28	the	the	DET
fuelectenerg-1427	650	29	variables	variable	NOUN
fuelectenerg-1427	650	30	in	in	ADP
fuelectenerg-1427	650	31	the	the	DET
fuelectenerg-1427	650	32	second	second	ADJ
fuelectenerg-1427	650	33	-	-	PUNCT
fuelectenerg-1427	650	34	level	level	NOUN
fuelectenerg-1427	650	35	branches	branch	NOUN
fuelectenerg-1427	650	36	of	of	ADP
fuelectenerg-1427	650	37	each	each	DET
fuelectenerg-1427	650	38	tdt	tdt	PROPN
fuelectenerg-1427	650	39	.	.	PUNCT
fuelectenerg-1427	651	1	definition	definition	NOUN
fuelectenerg-1427	651	2	2	2	NUM
fuelectenerg-1427	651	3	.	.	PUNCT
fuelectenerg-1427	652	1	the	the	DET
fuelectenerg-1427	652	2	family	family	NOUN
fuelectenerg-1427	652	3	of	of	ADP
fuelectenerg-1427	652	4	all	all	DET
fuelectenerg-1427	652	5	possible	possible	ADJ
fuelectenerg-1427	652	6	forms	form	NOUN
fuelectenerg-1427	652	7	obtained	obtain	VERB
fuelectenerg-1427	652	8	per	per	ADP
fuelectenerg-1427	652	9	ternary	ternary	NOUN
fuelectenerg-1427	652	10	s	s	PROPN
fuelectenerg-1427	652	11	/	/	SYM
fuelectenerg-1427	652	12	d	d	NOUN
fuelectenerg-1427	652	13	tree	tree	NOUN
fuelectenerg-1427	652	14	is	be	AUX
fuelectenerg-1427	652	15	called	call	VERB
fuelectenerg-1427	652	16	ternary	ternary	ADJ
fuelectenerg-1427	652	17	inclusive	inclusive	ADJ
fuelectenerg-1427	652	18	forms	form	NOUN
fuelectenerg-1427	652	19	(	(	PUNCT
fuelectenerg-1427	652	20	tifs	tifs	PROPN
fuelectenerg-1427	652	21	)	)	PUNCT
fuelectenerg-1427	652	22	.	.	PUNCT
fuelectenerg-1427	653	1	the	the	DET
fuelectenerg-1427	653	2	numbers	number	NOUN
fuelectenerg-1427	653	3	of	of	ADP
fuelectenerg-1427	653	4	these	these	DET
fuelectenerg-1427	653	5	tifs	tif	NOUN
fuelectenerg-1427	653	6	per	per	ADP
fuelectenerg-1427	653	7	tdt	tdt	PROPN
fuelectenerg-1427	653	8	for	for	ADP
fuelectenerg-1427	653	9	two	two	NUM
fuelectenerg-1427	653	10	variables	variable	NOUN
fuelectenerg-1427	653	11	are	be	AUX
fuelectenerg-1427	653	12	shown	show	VERB
fuelectenerg-1427	653	13	on	on	ADP
fuelectenerg-1427	653	14	top	top	NOUN
fuelectenerg-1427	653	15	of	of	ADP
fuelectenerg-1427	653	16	each	each	DET
fuelectenerg-1427	653	17	s	s	PROPN
fuelectenerg-1427	653	18	/	/	SYM
fuelectenerg-1427	653	19	d	d	PROPN
fuelectenerg-1427	653	20	tdt	tdt	PROPN
fuelectenerg-1427	653	21	in	in	ADP
fuelectenerg-1427	653	22	figure	figure	NOUN
fuelectenerg-1427	653	23	5	5	NUM
fuelectenerg-1427	653	24	.	.	PUNCT
fuelectenerg-1427	653	25	by	by	ADP
fuelectenerg-1427	653	26	observing	observe	VERB
fuelectenerg-1427	653	27	figure	figure	NOUN
fuelectenerg-1427	653	28	5	5	NUM
fuelectenerg-1427	653	29	,	,	PUNCT
fuelectenerg-1427	653	30	we	we	PRON
fuelectenerg-1427	653	31	can	can	AUX
fuelectenerg-1427	653	32	generate	generate	VERB
fuelectenerg-1427	653	33	the	the	DET
fuelectenerg-1427	653	34	corresponding	corresponding	ADJ
fuelectenerg-1427	653	35	flattened	flatten	VERB
fuelectenerg-1427	653	36	forms	form	NOUN
fuelectenerg-1427	653	37	by	by	ADP
fuelectenerg-1427	653	38	two	two	NUM
fuelectenerg-1427	653	39	methods	method	NOUN
fuelectenerg-1427	653	40	.	.	PUNCT
fuelectenerg-1427	654	1	a	a	DET
fuelectenerg-1427	654	2	classical	classical	ADJ
fuelectenerg-1427	654	3	method	method	NOUN
fuelectenerg-1427	654	4	,	,	PUNCT
fuelectenerg-1427	654	5	per	per	ADP
fuelectenerg-1427	654	6	analogy	analogy	NOUN
fuelectenerg-1427	654	7	with	with	ADP
fuelectenerg-1427	654	8	well	well	ADV
fuelectenerg-1427	654	9	-	-	PUNCT
fuelectenerg-1427	654	10	known	know	VERB
fuelectenerg-1427	654	11	binary	binary	ADJ
fuelectenerg-1427	654	12	forms	form	NOUN
fuelectenerg-1427	654	13	,	,	PUNCT
fuelectenerg-1427	654	14	would	would	AUX
fuelectenerg-1427	654	15	be	be	AUX
fuelectenerg-1427	654	16	to	to	PART
fuelectenerg-1427	654	17	create	create	VERB
fuelectenerg-1427	654	18	every	every	DET
fuelectenerg-1427	654	19	transform	transform	NOUN
fuelectenerg-1427	654	20	matrix	matrix	NOUN
fuelectenerg-1427	654	21	for	for	ADP
fuelectenerg-1427	654	22	every	every	DET
fuelectenerg-1427	654	23	tif	tif	PROPN
fuelectenerg-1427	654	24	s	s	PROPN
fuelectenerg-1427	654	25	/	/	SYM
fuelectenerg-1427	654	26	d	d	NOUN
fuelectenerg-1427	654	27	tree	tree	NOUN
fuelectenerg-1427	654	28	and	and	CCONJ
fuelectenerg-1427	654	29	then	then	ADV
fuelectenerg-1427	654	30	expand	expand	VERB
fuelectenerg-1427	654	31	using	use	VERB
fuelectenerg-1427	654	32	that	that	DET
fuelectenerg-1427	654	33	transform	transform	NOUN
fuelectenerg-1427	654	34	matrix	matrix	NOUN
fuelectenerg-1427	654	35	.	.	PUNCT
fuelectenerg-1427	655	1	a	a	DET
fuelectenerg-1427	655	2	better	well	ADJ
fuelectenerg-1427	655	3	method	method	NOUN
fuelectenerg-1427	655	4	is	be	AUX
fuelectenerg-1427	655	5	to	to	PART
fuelectenerg-1427	655	6	create	create	VERB
fuelectenerg-1427	655	7	one	one	NUM
fuelectenerg-1427	655	8	flattened	flatten	VERB
fuelectenerg-1427	655	9	108	108	NUM
fuelectenerg-1427	655	10	an	an	DET
fuelectenerg-1427	655	11	extended	extend	VERB
fuelectenerg-1427	655	12	green	green	ADJ
fuelectenerg-1427	655	13	sasao	sasao	PROPN
fuelectenerg-1427	655	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	655	15	of	of	ADP
fuelectenerg-1427	655	16	canonical	canonical	ADJ
fuelectenerg-1427	655	17	ternary	ternary	ADJ
fuelectenerg-1427	655	18	galois	galois	NOUN
fuelectenerg-1427	655	19	forms	form	NOUN
fuelectenerg-1427	655	20	...	...	PUNCT
fuelectenerg-1427	655	21	s	s	VERB
fuelectenerg-1427	655	22	a	a	PRON
fuelectenerg-1427	655	23	’	'	PUNCT
fuelectenerg-1427	655	24	a	a	PRON
fuelectenerg-1427	655	25	(	(	PUNCT
fuelectenerg-1427	655	26	)	)	PUNCT
fuelectenerg-1427	655	27	a	a	PRON
fuelectenerg-1427	655	28	pd	pd	PROPN
fuelectenerg-1427	655	29	1	1	NUM
fuelectenerg-1427	655	30	a	a	PRON
fuelectenerg-1427	655	31	(	(	PUNCT
fuelectenerg-1427	655	32	)	)	PUNCT
fuelectenerg-1427	655	33	b	b	NOUN
fuelectenerg-1427	655	34	nd	nd	ADP
fuelectenerg-1427	655	35	1	1	NUM
fuelectenerg-1427	655	36	a	a	PRON
fuelectenerg-1427	655	37	’	'	PUNCT
fuelectenerg-1427	655	38	d	d	ADP
fuelectenerg-1427	655	39	1	1	NUM
fuelectenerg-1427	655	40	a	a	PRON
fuelectenerg-1427	655	41	(	(	PUNCT
fuelectenerg-1427	655	42	)	)	PUNCT
fuelectenerg-1427	655	43	d	d	NOUN
fuelectenerg-1427	655	44	(	(	PUNCT
fuelectenerg-1427	655	45	)	)	PUNCT
fuelectenerg-1427	655	46	c	c	NOUN
fuelectenerg-1427	655	47	figure	figure	VERB
fuelectenerg-1427	655	48	3	3	NUM
fuelectenerg-1427	655	49	:	:	PUNCT
fuelectenerg-1427	655	50	two	two	NUM
fuelectenerg-1427	655	51	-	-	PUNCT
fuelectenerg-1427	655	52	valued	value	VERB
fuelectenerg-1427	655	53	nodes	node	NOUN
fuelectenerg-1427	655	54	:	:	PUNCT
fuelectenerg-1427	655	55	(	(	PUNCT
fuelectenerg-1427	655	56	a	a	X
fuelectenerg-1427	655	57	)	)	PUNCT
fuelectenerg-1427	655	58	shannon	shannon	NOUN
fuelectenerg-1427	655	59	,	,	PUNCT
fuelectenerg-1427	655	60	(	(	PUNCT
fuelectenerg-1427	655	61	b	b	NOUN
fuelectenerg-1427	655	62	)	)	PUNCT
fuelectenerg-1427	655	63	positive	positive	ADJ
fuelectenerg-1427	655	64	davio	davio	NOUN
fuelectenerg-1427	655	65	,	,	PUNCT
fuelectenerg-1427	655	66	(	(	PUNCT
fuelectenerg-1427	655	67	c	c	NOUN
fuelectenerg-1427	655	68	)	)	PUNCT
fuelectenerg-1427	655	69	negative	negative	ADJ
fuelectenerg-1427	655	70	davio	davio	NOUN
fuelectenerg-1427	655	71	,	,	PUNCT
fuelectenerg-1427	655	72	and	and	CCONJ
fuelectenerg-1427	655	73	(	(	PUNCT
fuelectenerg-1427	655	74	d	d	X
fuelectenerg-1427	655	75	)	)	PUNCT
fuelectenerg-1427	655	76	generalized	generalized	ADJ
fuelectenerg-1427	655	77	davio	davio	NOUN
fuelectenerg-1427	655	78	where	where	SCONJ
fuelectenerg-1427	655	79	a	a	DET
fuelectenerg-1427	655	80	∈	∈	NOUN
fuelectenerg-1427	655	81	{	{	PUNCT
fuelectenerg-1427	655	82	a	a	PRON
fuelectenerg-1427	655	83	,	,	PUNCT
fuelectenerg-1427	655	84	a′	a′	PROPN
fuelectenerg-1427	655	85	}	}	PUNCT
fuelectenerg-1427	655	86	.	.	PUNCT
fuelectenerg-1427	656	1	variable	variable	ADJ
fuelectenerg-1427	656	2	,	,	PUNCT
fuelectenerg-1427	656	3	that	that	PRON
fuelectenerg-1427	656	4	is	be	AUX
fuelectenerg-1427	656	5	one	one	NUM
fuelectenerg-1427	656	6	tree	tree	NOUN
fuelectenerg-1427	656	7	level	level	NOUN
fuelectenerg-1427	656	8	,	,	PUNCT
fuelectenerg-1427	656	9	figure	figure	NOUN
fuelectenerg-1427	656	10	4	4	NUM
fuelectenerg-1427	656	11	represents	represent	VERB
fuelectenerg-1427	656	12	the	the	DET
fuelectenerg-1427	656	13	expansion	expansion	NOUN
fuelectenerg-1427	656	14	nodes	node	NOUN
fuelectenerg-1427	656	15	for	for	ADP
fuelectenerg-1427	656	16	ternary	ternary	ADJ
fuelectenerg-1427	656	17	shannon	shannon	NOUN
fuelectenerg-1427	656	18	,	,	PUNCT
fuelectenerg-1427	656	19	davio	davio	NOUN
fuelectenerg-1427	656	20	and	and	CCONJ
fuelectenerg-1427	656	21	generalized	generalized	ADJ
fuelectenerg-1427	656	22	davio	davio	NOUN
fuelectenerg-1427	656	23	(	(	PUNCT
fuelectenerg-1427	656	24	d	d	NOUN
fuelectenerg-1427	656	25	)	)	PUNCT
fuelectenerg-1427	656	26	,	,	PUNCT
fuelectenerg-1427	656	27	respectively	respectively	ADV
fuelectenerg-1427	656	28	.	.	PUNCT
fuelectenerg-1427	657	1	s	s	PART
fuelectenerg-1427	657	2	0	0	NUM
fuelectenerg-1427	657	3	x	x	SYM
fuelectenerg-1427	657	4	1	1	NUM
fuelectenerg-1427	657	5	x	x	SYM
fuelectenerg-1427	657	6	2	2	NUM
fuelectenerg-1427	657	7	x	x	SYM
fuelectenerg-1427	657	8	(	(	PUNCT
fuelectenerg-1427	657	9	a	a	PRON
fuelectenerg-1427	657	10	)	)	PUNCT
fuelectenerg-1427	657	11	d0	d0	NOUN
fuelectenerg-1427	657	12	1	1	NUM
fuelectenerg-1427	657	13	x	x	SYM
fuelectenerg-1427	657	14	2	2	NUM
fuelectenerg-1427	657	15	(	(	PUNCT
fuelectenerg-1427	657	16	b	b	NOUN
fuelectenerg-1427	657	17	)	)	PUNCT
fuelectenerg-1427	657	18	d2	d2	PROPN
fuelectenerg-1427	657	19	1	1	NUM
fuelectenerg-1427	657	20	(	(	PUNCT
fuelectenerg-1427	657	21	d	d	NOUN
fuelectenerg-1427	657	22	)	)	PUNCT
fuelectenerg-1427	658	1	d	d	NOUN
fuelectenerg-1427	658	2	1	1	NUM
fuelectenerg-1427	658	3	(	(	PUNCT
fuelectenerg-1427	658	4	e	e	NOUN
fuelectenerg-1427	658	5	)	)	PUNCT
fuelectenerg-1427	658	6	d1	d1	NOUN
fuelectenerg-1427	658	7	1	1	NUM
fuelectenerg-1427	658	8	(	(	PUNCT
fuelectenerg-1427	658	9	’	'	PUNCT
fuelectenerg-1427	658	10	)	)	PUNCT
fuelectenerg-1427	658	11	x	x	SYM
fuelectenerg-1427	658	12	2	2	NUM
fuelectenerg-1427	658	13	(	(	PUNCT
fuelectenerg-1427	658	14	’’	’'	PUNCT
fuelectenerg-1427	658	15	)	)	PUNCT
fuelectenerg-1427	658	16	x	x	SYM
fuelectenerg-1427	658	17	2	2	NUM
fuelectenerg-1427	658	18	(	(	PUNCT
fuelectenerg-1427	658	19	)	)	PUNCT
fuelectenerg-1427	658	20	x	x	SYM
fuelectenerg-1427	658	21	2	2	NUM
fuelectenerg-1427	658	22	(	(	PUNCT
fuelectenerg-1427	658	23	c	c	NOUN
fuelectenerg-1427	658	24	)	)	PUNCT
fuelectenerg-1427	658	25	x	x	SYM
fuelectenerg-1427	658	26	xx	xx	X
fuelectenerg-1427	658	27	’	'	PUNCT
fuelectenerg-1427	658	28	x	x	NOUN
fuelectenerg-1427	658	29	’’	’'	PUNCT
fuelectenerg-1427	658	30	figure	figure	VERB
fuelectenerg-1427	658	31	4	4	NUM
fuelectenerg-1427	658	32	:	:	PUNCT
fuelectenerg-1427	658	33	ternary	ternary	ADJ
fuelectenerg-1427	658	34	nodes	node	NOUN
fuelectenerg-1427	658	35	for	for	ADP
fuelectenerg-1427	658	36	ternary	ternary	ADJ
fuelectenerg-1427	658	37	decision	decision	NOUN
fuelectenerg-1427	658	38	trees	tree	NOUN
fuelectenerg-1427	658	39	:	:	PUNCT
fuelectenerg-1427	658	40	(	(	PUNCT
fuelectenerg-1427	658	41	a	a	X
fuelectenerg-1427	658	42	)	)	PUNCT
fuelectenerg-1427	658	43	shannon	shannon	NOUN
fuelectenerg-1427	658	44	,	,	PUNCT
fuelectenerg-1427	658	45	(	(	PUNCT
fuelectenerg-1427	658	46	b	b	X
fuelectenerg-1427	658	47	)	)	PUNCT
fuelectenerg-1427	658	48	davio0	davio0	PROPN
fuelectenerg-1427	658	49	,	,	PUNCT
fuelectenerg-1427	658	50	(	(	PUNCT
fuelectenerg-1427	658	51	c	c	X
fuelectenerg-1427	658	52	)	)	PUNCT
fuelectenerg-1427	658	53	davio1	davio1	NOUN
fuelectenerg-1427	658	54	,	,	PUNCT
fuelectenerg-1427	658	55	(	(	PUNCT
fuelectenerg-1427	658	56	d	d	NOUN
fuelectenerg-1427	658	57	)	)	PUNCT
fuelectenerg-1427	658	58	davio2	davio2	PROPN
fuelectenerg-1427	658	59	,	,	PUNCT
fuelectenerg-1427	658	60	and	and	CCONJ
fuelectenerg-1427	658	61	(	(	PUNCT
fuelectenerg-1427	658	62	e	e	NOUN
fuelectenerg-1427	658	63	)	)	PUNCT
fuelectenerg-1427	658	64	generalized	generalized	ADJ
fuelectenerg-1427	658	65	davio	davio	NOUN
fuelectenerg-1427	658	66	(	(	PUNCT
fuelectenerg-1427	658	67	d	d	NOUN
fuelectenerg-1427	658	68	)	)	PUNCT
fuelectenerg-1427	658	69	where	where	SCONJ
fuelectenerg-1427	658	70	x	x	SYM
fuelectenerg-1427	658	71	∈	∈	PROPN
fuelectenerg-1427	658	72	{	{	PUNCT
fuelectenerg-1427	658	73	x	x	NOUN
fuelectenerg-1427	658	74	,	,	PUNCT
fuelectenerg-1427	658	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	658	76	}	}	PUNCT
fuelectenerg-1427	658	77	.	.	PUNCT
fuelectenerg-1427	659	1	in	in	ADP
fuelectenerg-1427	659	2	correspondence	correspondence	NOUN
fuelectenerg-1427	659	3	to	to	ADP
fuelectenerg-1427	659	4	the	the	DET
fuelectenerg-1427	659	5	binary	binary	PROPN
fuelectenerg-1427	659	6	s	s	PROPN
fuelectenerg-1427	659	7	/	/	SYM
fuelectenerg-1427	659	8	d	d	NOUN
fuelectenerg-1427	659	9	trees	tree	NOUN
fuelectenerg-1427	659	10	,	,	PUNCT
fuelectenerg-1427	659	11	one	one	PRON
fuelectenerg-1427	659	12	can	can	AUX
fuelectenerg-1427	659	13	produce	produce	VERB
fuelectenerg-1427	659	14	ternary	ternary	ADJ
fuelectenerg-1427	659	15	s	s	NOUN
fuelectenerg-1427	659	16	/	/	SYM
fuelectenerg-1427	659	17	d	d	NOUN
fuelectenerg-1427	659	18	trees	tree	NOUN
fuelectenerg-1427	659	19	.	.	PUNCT
fuelectenerg-1427	660	1	to	to	PART
fuelectenerg-1427	660	2	define	define	VERB
fuelectenerg-1427	660	3	the	the	DET
fuelectenerg-1427	660	4	ternary	ternary	ADJ
fuelectenerg-1427	660	5	s	s	NOUN
fuelectenerg-1427	660	6	/	/	SYM
fuelectenerg-1427	660	7	d	d	NOUN
fuelectenerg-1427	660	8	trees	tree	NOUN
fuelectenerg-1427	660	9	,	,	PUNCT
fuelectenerg-1427	660	10	we	we	PRON
fuelectenerg-1427	660	11	define	define	VERB
fuelectenerg-1427	660	12	the	the	DET
fuelectenerg-1427	660	13	generalized	generalized	ADJ
fuelectenerg-1427	660	14	davio	davio	NOUN
fuelectenerg-1427	660	15	node	node	NOUN
fuelectenerg-1427	660	16	over	over	ADP
fuelectenerg-1427	660	17	ternary	ternary	ADJ
fuelectenerg-1427	660	18	galois	galois	PROPN
fuelectenerg-1427	660	19	radix	radix	NOUN
fuelectenerg-1427	660	20	as	as	SCONJ
fuelectenerg-1427	660	21	shown	show	VERB
fuelectenerg-1427	660	22	in	in	ADP
fuelectenerg-1427	660	23	figure	figure	NOUN
fuelectenerg-1427	660	24	4(e	4(e	NUM
fuelectenerg-1427	660	25	)	)	PUNCT
fuelectenerg-1427	660	26	.	.	PUNCT
fuelectenerg-1427	661	1	our	our	PRON
fuelectenerg-1427	661	2	notation	notation	NOUN
fuelectenerg-1427	661	3	here	here	ADV
fuelectenerg-1427	661	4	is	be	AUX
fuelectenerg-1427	661	5	that	that	PRON
fuelectenerg-1427	661	6	(	(	PUNCT
fuelectenerg-1427	661	7	x	x	X
fuelectenerg-1427	661	8	)	)	PUNCT
fuelectenerg-1427	661	9	corresponds	correspond	VERB
fuelectenerg-1427	661	10	to	to	ADP
fuelectenerg-1427	661	11	the	the	DET
fuelectenerg-1427	661	12	three	three	NUM
fuelectenerg-1427	661	13	possible	possible	ADJ
fuelectenerg-1427	661	14	shifts	shift	NOUN
fuelectenerg-1427	661	15	of	of	ADP
fuelectenerg-1427	661	16	the	the	DET
fuelectenerg-1427	661	17	variable	variable	NOUN
fuelectenerg-1427	661	18	x	x	NOUN
fuelectenerg-1427	661	19	as	as	SCONJ
fuelectenerg-1427	661	20	follows	follow	VERB
fuelectenerg-1427	661	21	:	:	PUNCT
fuelectenerg-1427	661	22	x	x	SYM
fuelectenerg-1427	661	23	∈	∈	NOUN
fuelectenerg-1427	661	24	{	{	PUNCT
fuelectenerg-1427	661	25	x	x	NOUN
fuelectenerg-1427	661	26	,	,	PUNCT
fuelectenerg-1427	661	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	661	28	}	}	PUNCT
fuelectenerg-1427	661	29	,	,	PUNCT
fuelectenerg-1427	661	30	over	over	ADP
fuelectenerg-1427	661	31	gf(3	gf(3	PROPN
fuelectenerg-1427	661	32	)	)	PUNCT
fuelectenerg-1427	661	33	.	.	PUNCT
fuelectenerg-1427	662	1	(	(	PUNCT
fuelectenerg-1427	662	2	28	28	NUM
fuelectenerg-1427	662	3	)	)	PUNCT
fuelectenerg-1427	662	4	definition	definition	NOUN
fuelectenerg-1427	662	5	1	1	NUM
fuelectenerg-1427	662	6	.	.	PUNCT
fuelectenerg-1427	663	1	the	the	DET
fuelectenerg-1427	663	2	ternary	ternary	ADJ
fuelectenerg-1427	663	3	tree	tree	NOUN
fuelectenerg-1427	663	4	with	with	ADP
fuelectenerg-1427	663	5	ternary	ternary	ADJ
fuelectenerg-1427	663	6	shannon	shannon	NOUN
fuelectenerg-1427	663	7	and	and	CCONJ
fuelectenerg-1427	663	8	ternary	ternary	ADJ
fuelectenerg-1427	663	9	generalized	generalized	ADJ
fuelectenerg-1427	663	10	davio	davio	NOUN
fuelectenerg-1427	663	11	nodes	node	NOUN
fuelectenerg-1427	663	12	,	,	PUNCT
fuelectenerg-1427	663	13	that	that	PRON
fuelectenerg-1427	663	14	generates	generate	VERB
fuelectenerg-1427	663	15	other	other	ADJ
fuelectenerg-1427	663	16	ternary	ternary	ADJ
fuelectenerg-1427	663	17	trees	tree	NOUN
fuelectenerg-1427	663	18	,	,	PUNCT
fuelectenerg-1427	663	19	is	be	AUX
fuelectenerg-1427	663	20	called	call	VERB
fuelectenerg-1427	663	21	ternary	ternary	ADJ
fuelectenerg-1427	663	22	shannon	shannon	NOUN
fuelectenerg-1427	663	23	-	-	PUNCT
fuelectenerg-1427	663	24	davio	davio	NOUN
fuelectenerg-1427	663	25	(	(	PUNCT
fuelectenerg-1427	663	26	s	s	NOUN
fuelectenerg-1427	663	27	/	/	SYM
fuelectenerg-1427	663	28	d	d	NOUN
fuelectenerg-1427	663	29	)	)	PUNCT
fuelectenerg-1427	663	30	tree	tree	NOUN
fuelectenerg-1427	663	31	.	.	PUNCT
fuelectenerg-1427	664	1	utilizing	utilize	VERB
fuelectenerg-1427	664	2	the	the	DET
fuelectenerg-1427	664	3	definition	definition	NOUN
fuelectenerg-1427	664	4	of	of	ADP
fuelectenerg-1427	664	5	ternary	ternary	ADJ
fuelectenerg-1427	664	6	shannon	shannon	NOUN
fuelectenerg-1427	664	7	in	in	ADP
fuelectenerg-1427	664	8	figure	figure	NOUN
fuelectenerg-1427	664	9	4(a	4(a	NUM
fuelectenerg-1427	664	10	)	)	PUNCT
fuelectenerg-1427	664	11	and	and	CCONJ
fuelectenerg-1427	664	12	ternary	ternary	ADJ
fuelectenerg-1427	664	13	generalized	generalized	ADJ
fuelectenerg-1427	664	14	davio	davio	NOUN
fuelectenerg-1427	664	15	in	in	ADP
fuelectenerg-1427	664	16	figure	figure	NOUN
fuelectenerg-1427	664	17	4(e	4(e	NUM
fuelectenerg-1427	664	18	)	)	PUNCT
fuelectenerg-1427	664	19	,	,	PUNCT
fuelectenerg-1427	664	20	we	we	PRON
fuelectenerg-1427	664	21	obtain	obtain	VERB
fuelectenerg-1427	664	22	the	the	DET
fuelectenerg-1427	664	23	ternary	ternary	ADJ
fuelectenerg-1427	664	24	shannon	shannon	NOUN
fuelectenerg-1427	664	25	-	-	PUNCT
fuelectenerg-1427	664	26	davio	davio	NOUN
fuelectenerg-1427	664	27	trees	tree	NOUN
fuelectenerg-1427	664	28	(	(	PUNCT
fuelectenerg-1427	664	29	ternary	ternary	NOUN
fuelectenerg-1427	664	30	s	s	PROPN
fuelectenerg-1427	664	31	/	/	SYM
fuelectenerg-1427	664	32	d	d	NOUN
fuelectenerg-1427	664	33	trees	tree	NOUN
fuelectenerg-1427	664	34	)	)	PUNCT
fuelectenerg-1427	664	35	for	for	ADP
fuelectenerg-1427	664	36	two	two	NUM
fuelectenerg-1427	664	37	variables	variable	NOUN
fuelectenerg-1427	664	38	as	as	SCONJ
fuelectenerg-1427	664	39	shown	show	VERB
fuelectenerg-1427	664	40	in	in	ADP
fuelectenerg-1427	664	41	figure	figure	NOUN
fuelectenerg-1427	664	42	5	5	NUM
fuelectenerg-1427	664	43	.	.	PUNCT
fuelectenerg-1427	664	44	from	from	ADP
fuelectenerg-1427	664	45	the	the	DET
fuelectenerg-1427	664	46	ternary	ternary	ADJ
fuelectenerg-1427	664	47	s	s	PROPN
fuelectenerg-1427	664	48	/	/	SYM
fuelectenerg-1427	664	49	d	d	ADJ
fuelectenerg-1427	664	50	dts	dts	NOUN
fuelectenerg-1427	664	51	shown	show	VERB
fuelectenerg-1427	664	52	in	in	ADP
fuelectenerg-1427	664	53	figure	figure	NOUN
fuelectenerg-1427	664	54	5	5	NUM
fuelectenerg-1427	664	55	,	,	PUNCT
fuelectenerg-1427	664	56	if	if	SCONJ
fuelectenerg-1427	664	57	we	we	PRON
fuelectenerg-1427	664	58	take	take	VERB
fuelectenerg-1427	664	59	any	any	DET
fuelectenerg-1427	664	60	s	s	PROPN
fuelectenerg-1427	664	61	/	/	SYM
fuelectenerg-1427	664	62	d	d	NOUN
fuelectenerg-1427	664	63	tree	tree	NOUN
fuelectenerg-1427	664	64	and	and	CCONJ
fuelectenerg-1427	664	65	multiply	multiply	VERB
fuelectenerg-1427	664	66	the	the	DET
fuelectenerg-1427	664	67	second	second	ADJ
fuelectenerg-1427	664	68	-	-	PUNCT
fuelectenerg-1427	664	69	level	level	NOUN
fuelectenerg-1427	664	70	cofactors	cofactor	NOUN
fuelectenerg-1427	664	71	(	(	PUNCT
fuelectenerg-1427	664	72	which	which	PRON
fuelectenerg-1427	664	73	are	be	AUX
fuelectenerg-1427	664	74	in	in	ADP
fuelectenerg-1427	664	75	the	the	DET
fuelectenerg-1427	664	76	tdt	tdt	PROPN
fuelectenerg-1427	664	77	leaves	leave	NOUN
fuelectenerg-1427	664	78	)	)	PUNCT
fuelectenerg-1427	664	79	each	each	PRON
fuelectenerg-1427	664	80	by	by	ADP
fuelectenerg-1427	664	81	the	the	DET
fuelectenerg-1427	664	82	corresponding	corresponding	ADJ
fuelectenerg-1427	664	83	path	path	NOUN
fuelectenerg-1427	664	84	in	in	ADP
fuelectenerg-1427	664	85	that	that	DET
fuelectenerg-1427	664	86	tdt	tdt	PROPN
fuelectenerg-1427	664	87	,	,	PUNCT
fuelectenerg-1427	664	88	and	and	CCONJ
fuelectenerg-1427	664	89	sum	sum	VERB
fuelectenerg-1427	664	90	all	all	DET
fuelectenerg-1427	664	91	the	the	DET
fuelectenerg-1427	664	92	resulting	result	VERB
fuelectenerg-1427	664	93	cubes	cube	NOUN
fuelectenerg-1427	664	94	(	(	PUNCT
fuelectenerg-1427	664	95	terms	term	NOUN
fuelectenerg-1427	664	96	)	)	PUNCT
fuelectenerg-1427	664	97	over	over	ADP
fuelectenerg-1427	664	98	gf(3	gf(3	PROPN
fuelectenerg-1427	664	99	)	)	PUNCT
fuelectenerg-1427	664	100	,	,	PUNCT
fuelectenerg-1427	664	101	we	we	PRON
fuelectenerg-1427	664	102	obtain	obtain	VERB
fuelectenerg-1427	664	103	the	the	DET
fuelectenerg-1427	664	104	flattened	flatten	VERB
fuelectenerg-1427	664	105	form	form	NOUN
fuelectenerg-1427	664	106	of	of	ADP
fuelectenerg-1427	664	107	the	the	DET
fuelectenerg-1427	664	108	function	function	NOUN
fuelectenerg-1427	664	109	f	f	PROPN
fuelectenerg-1427	664	110	,	,	PUNCT
fuelectenerg-1427	664	111	as	as	ADP
fuelectenerg-1427	664	112	a	a	DET
fuelectenerg-1427	664	113	certain	certain	ADJ
fuelectenerg-1427	664	114	gfsop	gfsop	NOUN
fuelectenerg-1427	664	115	expression	expression	NOUN
fuelectenerg-1427	664	116	.	.	PUNCT
fuelectenerg-1427	665	1	for	for	ADP
fuelectenerg-1427	665	2	each	each	DET
fuelectenerg-1427	665	3	tdt	tdt	PROPN
fuelectenerg-1427	665	4	in	in	ADP
fuelectenerg-1427	665	5	figure	figure	NOUN
fuelectenerg-1427	665	6	5	5	NUM
fuelectenerg-1427	665	7	,	,	PUNCT
fuelectenerg-1427	665	8	there	there	PRON
fuelectenerg-1427	665	9	are	be	VERB
fuelectenerg-1427	665	10	as	as	ADV
fuelectenerg-1427	665	11	many	many	ADJ
fuelectenerg-1427	665	12	forms	form	NOUN
fuelectenerg-1427	665	13	obtained	obtain	VERB
fuelectenerg-1427	665	14	for	for	ADP
fuelectenerg-1427	665	15	the	the	DET
fuelectenerg-1427	665	16	function	function	NOUN
fuelectenerg-1427	665	17	f	f	PROPN
fuelectenerg-1427	665	18	as	as	ADP
fuelectenerg-1427	665	19	the	the	DET
fuelectenerg-1427	665	20	number	number	NOUN
fuelectenerg-1427	665	21	of	of	ADP
fuelectenerg-1427	665	22	possible	possible	ADJ
fuelectenerg-1427	665	23	permutations	permutation	NOUN
fuelectenerg-1427	665	24	of	of	ADP
fuelectenerg-1427	665	25	the	the	DET
fuelectenerg-1427	665	26	polarities	polarity	NOUN
fuelectenerg-1427	665	27	of	of	ADP
fuelectenerg-1427	665	28	the	the	DET
fuelectenerg-1427	665	29	variables	variable	NOUN
fuelectenerg-1427	665	30	in	in	ADP
fuelectenerg-1427	665	31	the	the	DET
fuelectenerg-1427	665	32	second	second	ADJ
fuelectenerg-1427	665	33	-	-	PUNCT
fuelectenerg-1427	665	34	level	level	NOUN
fuelectenerg-1427	665	35	branches	branch	NOUN
fuelectenerg-1427	665	36	of	of	ADP
fuelectenerg-1427	665	37	each	each	DET
fuelectenerg-1427	665	38	tdt	tdt	PROPN
fuelectenerg-1427	665	39	.	.	PUNCT
fuelectenerg-1427	666	1	definition	definition	NOUN
fuelectenerg-1427	666	2	2	2	NUM
fuelectenerg-1427	666	3	.	.	PUNCT
fuelectenerg-1427	667	1	the	the	DET
fuelectenerg-1427	667	2	family	family	NOUN
fuelectenerg-1427	667	3	of	of	ADP
fuelectenerg-1427	667	4	all	all	DET
fuelectenerg-1427	667	5	possible	possible	ADJ
fuelectenerg-1427	667	6	forms	form	NOUN
fuelectenerg-1427	667	7	obtained	obtain	VERB
fuelectenerg-1427	667	8	per	per	ADP
fuelectenerg-1427	667	9	ternary	ternary	NOUN
fuelectenerg-1427	667	10	s	s	PROPN
fuelectenerg-1427	667	11	/	/	SYM
fuelectenerg-1427	667	12	d	d	NOUN
fuelectenerg-1427	667	13	tree	tree	NOUN
fuelectenerg-1427	667	14	is	be	AUX
fuelectenerg-1427	667	15	called	call	VERB
fuelectenerg-1427	667	16	ternary	ternary	ADJ
fuelectenerg-1427	667	17	inclusive	inclusive	ADJ
fuelectenerg-1427	667	18	forms	form	NOUN
fuelectenerg-1427	667	19	(	(	PUNCT
fuelectenerg-1427	667	20	tifs	tifs	PROPN
fuelectenerg-1427	667	21	)	)	PUNCT
fuelectenerg-1427	667	22	.	.	PUNCT
fuelectenerg-1427	668	1	the	the	DET
fuelectenerg-1427	668	2	numbers	number	NOUN
fuelectenerg-1427	668	3	of	of	ADP
fuelectenerg-1427	668	4	these	these	DET
fuelectenerg-1427	668	5	tifs	tif	NOUN
fuelectenerg-1427	668	6	per	per	ADP
fuelectenerg-1427	668	7	tdt	tdt	PROPN
fuelectenerg-1427	668	8	for	for	ADP
fuelectenerg-1427	668	9	two	two	NUM
fuelectenerg-1427	668	10	variables	variable	NOUN
fuelectenerg-1427	668	11	are	be	AUX
fuelectenerg-1427	668	12	shown	show	VERB
fuelectenerg-1427	668	13	on	on	ADP
fuelectenerg-1427	668	14	top	top	NOUN
fuelectenerg-1427	668	15	of	of	ADP
fuelectenerg-1427	668	16	each	each	DET
fuelectenerg-1427	668	17	s	s	PROPN
fuelectenerg-1427	668	18	/	/	SYM
fuelectenerg-1427	668	19	d	d	PROPN
fuelectenerg-1427	668	20	tdt	tdt	PROPN
fuelectenerg-1427	668	21	in	in	ADP
fuelectenerg-1427	668	22	figure	figure	NOUN
fuelectenerg-1427	668	23	5	5	NUM
fuelectenerg-1427	668	24	.	.	PUNCT
fuelectenerg-1427	668	25	by	by	ADP
fuelectenerg-1427	668	26	observing	observe	VERB
fuelectenerg-1427	668	27	figure	figure	NOUN
fuelectenerg-1427	668	28	5	5	NUM
fuelectenerg-1427	668	29	,	,	PUNCT
fuelectenerg-1427	668	30	we	we	PRON
fuelectenerg-1427	668	31	can	can	AUX
fuelectenerg-1427	668	32	generate	generate	VERB
fuelectenerg-1427	668	33	the	the	DET
fuelectenerg-1427	668	34	corresponding	corresponding	ADJ
fuelectenerg-1427	668	35	flattened	flatten	VERB
fuelectenerg-1427	668	36	forms	form	NOUN
fuelectenerg-1427	668	37	by	by	ADP
fuelectenerg-1427	668	38	two	two	NUM
fuelectenerg-1427	668	39	methods	method	NOUN
fuelectenerg-1427	668	40	.	.	PUNCT
fuelectenerg-1427	669	1	a	a	DET
fuelectenerg-1427	669	2	classical	classical	ADJ
fuelectenerg-1427	669	3	method	method	NOUN
fuelectenerg-1427	669	4	,	,	PUNCT
fuelectenerg-1427	669	5	per	per	ADP
fuelectenerg-1427	669	6	analogy	analogy	NOUN
fuelectenerg-1427	669	7	with	with	ADP
fuelectenerg-1427	669	8	well	well	ADV
fuelectenerg-1427	669	9	-	-	PUNCT
fuelectenerg-1427	669	10	known	know	VERB
fuelectenerg-1427	669	11	binary	binary	ADJ
fuelectenerg-1427	669	12	forms	form	NOUN
fuelectenerg-1427	669	13	,	,	PUNCT
fuelectenerg-1427	669	14	would	would	AUX
fuelectenerg-1427	669	15	be	be	AUX
fuelectenerg-1427	669	16	to	to	PART
fuelectenerg-1427	669	17	create	create	VERB
fuelectenerg-1427	669	18	every	every	DET
fuelectenerg-1427	669	19	transform	transform	NOUN
fuelectenerg-1427	669	20	matrix	matrix	NOUN
fuelectenerg-1427	669	21	for	for	ADP
fuelectenerg-1427	669	22	every	every	DET
fuelectenerg-1427	669	23	tif	tif	PROPN
fuelectenerg-1427	669	24	s	s	PROPN
fuelectenerg-1427	669	25	/	/	SYM
fuelectenerg-1427	669	26	d	d	NOUN
fuelectenerg-1427	669	27	tree	tree	NOUN
fuelectenerg-1427	669	28	and	and	CCONJ
fuelectenerg-1427	669	29	then	then	ADV
fuelectenerg-1427	669	30	expand	expand	VERB
fuelectenerg-1427	669	31	using	use	VERB
fuelectenerg-1427	669	32	that	that	DET
fuelectenerg-1427	669	33	transform	transform	NOUN
fuelectenerg-1427	669	34	matrix	matrix	NOUN
fuelectenerg-1427	669	35	.	.	PUNCT
fuelectenerg-1427	670	1	a	a	DET
fuelectenerg-1427	670	2	better	well	ADJ
fuelectenerg-1427	670	3	method	method	NOUN
fuelectenerg-1427	670	4	is	be	AUX
fuelectenerg-1427	670	5	to	to	PART
fuelectenerg-1427	670	6	create	create	VERB
fuelectenerg-1427	670	7	one	one	NUM
fuelectenerg-1427	670	8	flattened	flatten	VERB
fuelectenerg-1427	670	9	108	108	NUM
fuelectenerg-1427	670	10	an	an	DET
fuelectenerg-1427	670	11	extended	extend	VERB
fuelectenerg-1427	670	12	green	green	ADJ
fuelectenerg-1427	670	13	sasao	sasao	PROPN
fuelectenerg-1427	670	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	670	15	of	of	ADP
fuelectenerg-1427	670	16	canonical	canonical	ADJ
fuelectenerg-1427	670	17	ternary	ternary	ADJ
fuelectenerg-1427	670	18	galois	galois	NOUN
fuelectenerg-1427	670	19	forms	form	NOUN
fuelectenerg-1427	670	20	...	...	PUNCT
fuelectenerg-1427	670	21	s	s	VERB
fuelectenerg-1427	670	22	a	a	PRON
fuelectenerg-1427	670	23	’	'	PUNCT
fuelectenerg-1427	670	24	a	a	PRON
fuelectenerg-1427	670	25	(	(	PUNCT
fuelectenerg-1427	670	26	)	)	PUNCT
fuelectenerg-1427	670	27	a	a	PRON
fuelectenerg-1427	670	28	pd	pd	PROPN
fuelectenerg-1427	670	29	1	1	NUM
fuelectenerg-1427	670	30	a	a	PRON
fuelectenerg-1427	670	31	(	(	PUNCT
fuelectenerg-1427	670	32	)	)	PUNCT
fuelectenerg-1427	670	33	b	b	NOUN
fuelectenerg-1427	670	34	nd	nd	ADP
fuelectenerg-1427	670	35	1	1	NUM
fuelectenerg-1427	670	36	a	a	PRON
fuelectenerg-1427	670	37	’	'	PUNCT
fuelectenerg-1427	670	38	d	d	ADP
fuelectenerg-1427	670	39	1	1	NUM
fuelectenerg-1427	670	40	a	a	PRON
fuelectenerg-1427	670	41	(	(	PUNCT
fuelectenerg-1427	670	42	)	)	PUNCT
fuelectenerg-1427	670	43	d	d	NOUN
fuelectenerg-1427	670	44	(	(	PUNCT
fuelectenerg-1427	670	45	)	)	PUNCT
fuelectenerg-1427	670	46	c	c	NOUN
fuelectenerg-1427	670	47	figure	figure	VERB
fuelectenerg-1427	670	48	3	3	NUM
fuelectenerg-1427	670	49	:	:	PUNCT
fuelectenerg-1427	670	50	two	two	NUM
fuelectenerg-1427	670	51	-	-	PUNCT
fuelectenerg-1427	670	52	valued	value	VERB
fuelectenerg-1427	670	53	nodes	node	NOUN
fuelectenerg-1427	670	54	:	:	PUNCT
fuelectenerg-1427	670	55	(	(	PUNCT
fuelectenerg-1427	670	56	a	a	X
fuelectenerg-1427	670	57	)	)	PUNCT
fuelectenerg-1427	670	58	shannon	shannon	NOUN
fuelectenerg-1427	670	59	,	,	PUNCT
fuelectenerg-1427	670	60	(	(	PUNCT
fuelectenerg-1427	670	61	b	b	NOUN
fuelectenerg-1427	670	62	)	)	PUNCT
fuelectenerg-1427	670	63	positive	positive	ADJ
fuelectenerg-1427	670	64	davio	davio	NOUN
fuelectenerg-1427	670	65	,	,	PUNCT
fuelectenerg-1427	670	66	(	(	PUNCT
fuelectenerg-1427	670	67	c	c	NOUN
fuelectenerg-1427	670	68	)	)	PUNCT
fuelectenerg-1427	670	69	negative	negative	ADJ
fuelectenerg-1427	670	70	davio	davio	NOUN
fuelectenerg-1427	670	71	,	,	PUNCT
fuelectenerg-1427	670	72	and	and	CCONJ
fuelectenerg-1427	670	73	(	(	PUNCT
fuelectenerg-1427	670	74	d	d	X
fuelectenerg-1427	670	75	)	)	PUNCT
fuelectenerg-1427	670	76	generalized	generalized	ADJ
fuelectenerg-1427	670	77	davio	davio	NOUN
fuelectenerg-1427	670	78	where	where	SCONJ
fuelectenerg-1427	670	79	a	a	DET
fuelectenerg-1427	670	80	∈	∈	NOUN
fuelectenerg-1427	670	81	{	{	PUNCT
fuelectenerg-1427	670	82	a	a	PRON
fuelectenerg-1427	670	83	,	,	PUNCT
fuelectenerg-1427	670	84	a′	a′	PROPN
fuelectenerg-1427	670	85	}	}	PUNCT
fuelectenerg-1427	670	86	.	.	PUNCT
fuelectenerg-1427	671	1	variable	variable	ADJ
fuelectenerg-1427	671	2	,	,	PUNCT
fuelectenerg-1427	671	3	that	that	PRON
fuelectenerg-1427	671	4	is	be	AUX
fuelectenerg-1427	671	5	one	one	NUM
fuelectenerg-1427	671	6	tree	tree	NOUN
fuelectenerg-1427	671	7	level	level	NOUN
fuelectenerg-1427	671	8	,	,	PUNCT
fuelectenerg-1427	671	9	figure	figure	NOUN
fuelectenerg-1427	671	10	4	4	NUM
fuelectenerg-1427	671	11	represents	represent	VERB
fuelectenerg-1427	671	12	the	the	DET
fuelectenerg-1427	671	13	expansion	expansion	NOUN
fuelectenerg-1427	671	14	nodes	node	NOUN
fuelectenerg-1427	671	15	for	for	ADP
fuelectenerg-1427	671	16	ternary	ternary	ADJ
fuelectenerg-1427	671	17	shannon	shannon	NOUN
fuelectenerg-1427	671	18	,	,	PUNCT
fuelectenerg-1427	671	19	davio	davio	NOUN
fuelectenerg-1427	671	20	and	and	CCONJ
fuelectenerg-1427	671	21	generalized	generalized	ADJ
fuelectenerg-1427	671	22	davio	davio	NOUN
fuelectenerg-1427	671	23	(	(	PUNCT
fuelectenerg-1427	671	24	d	d	NOUN
fuelectenerg-1427	671	25	)	)	PUNCT
fuelectenerg-1427	671	26	,	,	PUNCT
fuelectenerg-1427	671	27	respectively	respectively	ADV
fuelectenerg-1427	671	28	.	.	PUNCT
fuelectenerg-1427	672	1	s	s	PART
fuelectenerg-1427	672	2	0	0	NUM
fuelectenerg-1427	672	3	x	x	SYM
fuelectenerg-1427	672	4	1	1	NUM
fuelectenerg-1427	672	5	x	x	SYM
fuelectenerg-1427	672	6	2	2	NUM
fuelectenerg-1427	672	7	x	x	SYM
fuelectenerg-1427	672	8	(	(	PUNCT
fuelectenerg-1427	672	9	a	a	PRON
fuelectenerg-1427	672	10	)	)	PUNCT
fuelectenerg-1427	672	11	d0	d0	NOUN
fuelectenerg-1427	672	12	1	1	NUM
fuelectenerg-1427	672	13	x	x	SYM
fuelectenerg-1427	672	14	2	2	NUM
fuelectenerg-1427	672	15	(	(	PUNCT
fuelectenerg-1427	672	16	b	b	NOUN
fuelectenerg-1427	672	17	)	)	PUNCT
fuelectenerg-1427	672	18	d2	d2	PROPN
fuelectenerg-1427	672	19	1	1	NUM
fuelectenerg-1427	672	20	(	(	PUNCT
fuelectenerg-1427	672	21	d	d	NOUN
fuelectenerg-1427	672	22	)	)	PUNCT
fuelectenerg-1427	673	1	d	d	NOUN
fuelectenerg-1427	673	2	1	1	NUM
fuelectenerg-1427	673	3	(	(	PUNCT
fuelectenerg-1427	673	4	e	e	NOUN
fuelectenerg-1427	673	5	)	)	PUNCT
fuelectenerg-1427	673	6	d1	d1	NOUN
fuelectenerg-1427	673	7	1	1	NUM
fuelectenerg-1427	673	8	(	(	PUNCT
fuelectenerg-1427	673	9	’	'	PUNCT
fuelectenerg-1427	673	10	)	)	PUNCT
fuelectenerg-1427	673	11	x	x	SYM
fuelectenerg-1427	673	12	2	2	NUM
fuelectenerg-1427	673	13	(	(	PUNCT
fuelectenerg-1427	673	14	’’	’'	PUNCT
fuelectenerg-1427	673	15	)	)	PUNCT
fuelectenerg-1427	673	16	x	x	SYM
fuelectenerg-1427	673	17	2	2	NUM
fuelectenerg-1427	673	18	(	(	PUNCT
fuelectenerg-1427	673	19	)	)	PUNCT
fuelectenerg-1427	673	20	x	x	SYM
fuelectenerg-1427	673	21	2	2	NUM
fuelectenerg-1427	673	22	(	(	PUNCT
fuelectenerg-1427	673	23	c	c	NOUN
fuelectenerg-1427	673	24	)	)	PUNCT
fuelectenerg-1427	673	25	x	x	SYM
fuelectenerg-1427	673	26	xx	xx	X
fuelectenerg-1427	673	27	’	'	PUNCT
fuelectenerg-1427	673	28	x	x	NOUN
fuelectenerg-1427	673	29	’’	’'	PUNCT
fuelectenerg-1427	673	30	figure	figure	VERB
fuelectenerg-1427	673	31	4	4	NUM
fuelectenerg-1427	673	32	:	:	PUNCT
fuelectenerg-1427	673	33	ternary	ternary	ADJ
fuelectenerg-1427	673	34	nodes	node	NOUN
fuelectenerg-1427	673	35	for	for	ADP
fuelectenerg-1427	673	36	ternary	ternary	ADJ
fuelectenerg-1427	673	37	decision	decision	NOUN
fuelectenerg-1427	673	38	trees	tree	NOUN
fuelectenerg-1427	673	39	:	:	PUNCT
fuelectenerg-1427	673	40	(	(	PUNCT
fuelectenerg-1427	673	41	a	a	X
fuelectenerg-1427	673	42	)	)	PUNCT
fuelectenerg-1427	673	43	shannon	shannon	NOUN
fuelectenerg-1427	673	44	,	,	PUNCT
fuelectenerg-1427	673	45	(	(	PUNCT
fuelectenerg-1427	673	46	b	b	X
fuelectenerg-1427	673	47	)	)	PUNCT
fuelectenerg-1427	673	48	davio0	davio0	PROPN
fuelectenerg-1427	673	49	,	,	PUNCT
fuelectenerg-1427	673	50	(	(	PUNCT
fuelectenerg-1427	673	51	c	c	X
fuelectenerg-1427	673	52	)	)	PUNCT
fuelectenerg-1427	673	53	davio1	davio1	NOUN
fuelectenerg-1427	673	54	,	,	PUNCT
fuelectenerg-1427	673	55	(	(	PUNCT
fuelectenerg-1427	673	56	d	d	NOUN
fuelectenerg-1427	673	57	)	)	PUNCT
fuelectenerg-1427	673	58	davio2	davio2	PROPN
fuelectenerg-1427	673	59	,	,	PUNCT
fuelectenerg-1427	673	60	and	and	CCONJ
fuelectenerg-1427	673	61	(	(	PUNCT
fuelectenerg-1427	673	62	e	e	NOUN
fuelectenerg-1427	673	63	)	)	PUNCT
fuelectenerg-1427	673	64	generalized	generalized	ADJ
fuelectenerg-1427	673	65	davio	davio	NOUN
fuelectenerg-1427	673	66	(	(	PUNCT
fuelectenerg-1427	673	67	d	d	NOUN
fuelectenerg-1427	673	68	)	)	PUNCT
fuelectenerg-1427	673	69	where	where	SCONJ
fuelectenerg-1427	673	70	x	x	SYM
fuelectenerg-1427	673	71	∈	∈	PROPN
fuelectenerg-1427	673	72	{	{	PUNCT
fuelectenerg-1427	673	73	x	x	NOUN
fuelectenerg-1427	673	74	,	,	PUNCT
fuelectenerg-1427	673	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	673	76	}	}	PUNCT
fuelectenerg-1427	673	77	.	.	PUNCT
fuelectenerg-1427	674	1	in	in	ADP
fuelectenerg-1427	674	2	correspondence	correspondence	NOUN
fuelectenerg-1427	674	3	to	to	ADP
fuelectenerg-1427	674	4	the	the	DET
fuelectenerg-1427	674	5	binary	binary	PROPN
fuelectenerg-1427	674	6	s	s	PROPN
fuelectenerg-1427	674	7	/	/	SYM
fuelectenerg-1427	674	8	d	d	NOUN
fuelectenerg-1427	674	9	trees	tree	NOUN
fuelectenerg-1427	674	10	,	,	PUNCT
fuelectenerg-1427	674	11	one	one	PRON
fuelectenerg-1427	674	12	can	can	AUX
fuelectenerg-1427	674	13	produce	produce	VERB
fuelectenerg-1427	674	14	ternary	ternary	ADJ
fuelectenerg-1427	674	15	s	s	NOUN
fuelectenerg-1427	674	16	/	/	SYM
fuelectenerg-1427	674	17	d	d	NOUN
fuelectenerg-1427	674	18	trees	tree	NOUN
fuelectenerg-1427	674	19	.	.	PUNCT
fuelectenerg-1427	675	1	to	to	PART
fuelectenerg-1427	675	2	define	define	VERB
fuelectenerg-1427	675	3	the	the	DET
fuelectenerg-1427	675	4	ternary	ternary	ADJ
fuelectenerg-1427	675	5	s	s	NOUN
fuelectenerg-1427	675	6	/	/	SYM
fuelectenerg-1427	675	7	d	d	NOUN
fuelectenerg-1427	675	8	trees	tree	NOUN
fuelectenerg-1427	675	9	,	,	PUNCT
fuelectenerg-1427	675	10	we	we	PRON
fuelectenerg-1427	675	11	define	define	VERB
fuelectenerg-1427	675	12	the	the	DET
fuelectenerg-1427	675	13	generalized	generalized	ADJ
fuelectenerg-1427	675	14	davio	davio	NOUN
fuelectenerg-1427	675	15	node	node	NOUN
fuelectenerg-1427	675	16	over	over	ADP
fuelectenerg-1427	675	17	ternary	ternary	ADJ
fuelectenerg-1427	675	18	galois	galois	PROPN
fuelectenerg-1427	675	19	radix	radix	NOUN
fuelectenerg-1427	675	20	as	as	SCONJ
fuelectenerg-1427	675	21	shown	show	VERB
fuelectenerg-1427	675	22	in	in	ADP
fuelectenerg-1427	675	23	figure	figure	NOUN
fuelectenerg-1427	675	24	4(e	4(e	NUM
fuelectenerg-1427	675	25	)	)	PUNCT
fuelectenerg-1427	675	26	.	.	PUNCT
fuelectenerg-1427	676	1	our	our	PRON
fuelectenerg-1427	676	2	notation	notation	NOUN
fuelectenerg-1427	676	3	here	here	ADV
fuelectenerg-1427	676	4	is	be	AUX
fuelectenerg-1427	676	5	that	that	PRON
fuelectenerg-1427	676	6	(	(	PUNCT
fuelectenerg-1427	676	7	x	x	X
fuelectenerg-1427	676	8	)	)	PUNCT
fuelectenerg-1427	676	9	corresponds	correspond	VERB
fuelectenerg-1427	676	10	to	to	ADP
fuelectenerg-1427	676	11	the	the	DET
fuelectenerg-1427	676	12	three	three	NUM
fuelectenerg-1427	676	13	possible	possible	ADJ
fuelectenerg-1427	676	14	shifts	shift	NOUN
fuelectenerg-1427	676	15	of	of	ADP
fuelectenerg-1427	676	16	the	the	DET
fuelectenerg-1427	676	17	variable	variable	NOUN
fuelectenerg-1427	676	18	x	x	NOUN
fuelectenerg-1427	676	19	as	as	SCONJ
fuelectenerg-1427	676	20	follows	follow	VERB
fuelectenerg-1427	676	21	:	:	PUNCT
fuelectenerg-1427	676	22	x	x	SYM
fuelectenerg-1427	676	23	∈	∈	NOUN
fuelectenerg-1427	676	24	{	{	PUNCT
fuelectenerg-1427	676	25	x	x	NOUN
fuelectenerg-1427	676	26	,	,	PUNCT
fuelectenerg-1427	676	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	676	28	}	}	PUNCT
fuelectenerg-1427	676	29	,	,	PUNCT
fuelectenerg-1427	676	30	over	over	ADP
fuelectenerg-1427	676	31	gf(3	gf(3	PROPN
fuelectenerg-1427	676	32	)	)	PUNCT
fuelectenerg-1427	676	33	.	.	PUNCT
fuelectenerg-1427	677	1	(	(	PUNCT
fuelectenerg-1427	677	2	28	28	NUM
fuelectenerg-1427	677	3	)	)	PUNCT
fuelectenerg-1427	677	4	definition	definition	NOUN
fuelectenerg-1427	677	5	1	1	NUM
fuelectenerg-1427	677	6	.	.	PUNCT
fuelectenerg-1427	678	1	the	the	DET
fuelectenerg-1427	678	2	ternary	ternary	ADJ
fuelectenerg-1427	678	3	tree	tree	NOUN
fuelectenerg-1427	678	4	with	with	ADP
fuelectenerg-1427	678	5	ternary	ternary	ADJ
fuelectenerg-1427	678	6	shannon	shannon	NOUN
fuelectenerg-1427	678	7	and	and	CCONJ
fuelectenerg-1427	678	8	ternary	ternary	ADJ
fuelectenerg-1427	678	9	generalized	generalized	ADJ
fuelectenerg-1427	678	10	davio	davio	NOUN
fuelectenerg-1427	678	11	nodes	node	NOUN
fuelectenerg-1427	678	12	,	,	PUNCT
fuelectenerg-1427	678	13	that	that	PRON
fuelectenerg-1427	678	14	generates	generate	VERB
fuelectenerg-1427	678	15	other	other	ADJ
fuelectenerg-1427	678	16	ternary	ternary	ADJ
fuelectenerg-1427	678	17	trees	tree	NOUN
fuelectenerg-1427	678	18	,	,	PUNCT
fuelectenerg-1427	678	19	is	be	AUX
fuelectenerg-1427	678	20	called	call	VERB
fuelectenerg-1427	678	21	ternary	ternary	ADJ
fuelectenerg-1427	678	22	shannon	shannon	NOUN
fuelectenerg-1427	678	23	-	-	PUNCT
fuelectenerg-1427	678	24	davio	davio	NOUN
fuelectenerg-1427	678	25	(	(	PUNCT
fuelectenerg-1427	678	26	s	s	NOUN
fuelectenerg-1427	678	27	/	/	SYM
fuelectenerg-1427	678	28	d	d	NOUN
fuelectenerg-1427	678	29	)	)	PUNCT
fuelectenerg-1427	678	30	tree	tree	NOUN
fuelectenerg-1427	678	31	.	.	PUNCT
fuelectenerg-1427	679	1	utilizing	utilize	VERB
fuelectenerg-1427	679	2	the	the	DET
fuelectenerg-1427	679	3	definition	definition	NOUN
fuelectenerg-1427	679	4	of	of	ADP
fuelectenerg-1427	679	5	ternary	ternary	ADJ
fuelectenerg-1427	679	6	shannon	shannon	NOUN
fuelectenerg-1427	679	7	in	in	ADP
fuelectenerg-1427	679	8	figure	figure	NOUN
fuelectenerg-1427	679	9	4(a	4(a	NUM
fuelectenerg-1427	679	10	)	)	PUNCT
fuelectenerg-1427	679	11	and	and	CCONJ
fuelectenerg-1427	679	12	ternary	ternary	ADJ
fuelectenerg-1427	679	13	generalized	generalized	ADJ
fuelectenerg-1427	679	14	davio	davio	NOUN
fuelectenerg-1427	679	15	in	in	ADP
fuelectenerg-1427	679	16	figure	figure	NOUN
fuelectenerg-1427	679	17	4(e	4(e	NUM
fuelectenerg-1427	679	18	)	)	PUNCT
fuelectenerg-1427	679	19	,	,	PUNCT
fuelectenerg-1427	679	20	we	we	PRON
fuelectenerg-1427	679	21	obtain	obtain	VERB
fuelectenerg-1427	679	22	the	the	DET
fuelectenerg-1427	679	23	ternary	ternary	ADJ
fuelectenerg-1427	679	24	shannon	shannon	NOUN
fuelectenerg-1427	679	25	-	-	PUNCT
fuelectenerg-1427	679	26	davio	davio	NOUN
fuelectenerg-1427	679	27	trees	tree	NOUN
fuelectenerg-1427	679	28	(	(	PUNCT
fuelectenerg-1427	679	29	ternary	ternary	NOUN
fuelectenerg-1427	679	30	s	s	PROPN
fuelectenerg-1427	679	31	/	/	SYM
fuelectenerg-1427	679	32	d	d	NOUN
fuelectenerg-1427	679	33	trees	tree	NOUN
fuelectenerg-1427	679	34	)	)	PUNCT
fuelectenerg-1427	679	35	for	for	ADP
fuelectenerg-1427	679	36	two	two	NUM
fuelectenerg-1427	679	37	variables	variable	NOUN
fuelectenerg-1427	679	38	as	as	SCONJ
fuelectenerg-1427	679	39	shown	show	VERB
fuelectenerg-1427	679	40	in	in	ADP
fuelectenerg-1427	679	41	figure	figure	NOUN
fuelectenerg-1427	679	42	5	5	NUM
fuelectenerg-1427	679	43	.	.	PUNCT
fuelectenerg-1427	679	44	from	from	ADP
fuelectenerg-1427	679	45	the	the	DET
fuelectenerg-1427	679	46	ternary	ternary	ADJ
fuelectenerg-1427	679	47	s	s	PROPN
fuelectenerg-1427	679	48	/	/	SYM
fuelectenerg-1427	679	49	d	d	ADJ
fuelectenerg-1427	679	50	dts	dts	NOUN
fuelectenerg-1427	679	51	shown	show	VERB
fuelectenerg-1427	679	52	in	in	ADP
fuelectenerg-1427	679	53	figure	figure	NOUN
fuelectenerg-1427	679	54	5	5	NUM
fuelectenerg-1427	679	55	,	,	PUNCT
fuelectenerg-1427	679	56	if	if	SCONJ
fuelectenerg-1427	679	57	we	we	PRON
fuelectenerg-1427	679	58	take	take	VERB
fuelectenerg-1427	679	59	any	any	DET
fuelectenerg-1427	679	60	s	s	PROPN
fuelectenerg-1427	679	61	/	/	SYM
fuelectenerg-1427	679	62	d	d	NOUN
fuelectenerg-1427	679	63	tree	tree	NOUN
fuelectenerg-1427	679	64	and	and	CCONJ
fuelectenerg-1427	679	65	multiply	multiply	VERB
fuelectenerg-1427	679	66	the	the	DET
fuelectenerg-1427	679	67	second	second	ADJ
fuelectenerg-1427	679	68	-	-	PUNCT
fuelectenerg-1427	679	69	level	level	NOUN
fuelectenerg-1427	679	70	cofactors	cofactor	NOUN
fuelectenerg-1427	679	71	(	(	PUNCT
fuelectenerg-1427	679	72	which	which	PRON
fuelectenerg-1427	679	73	are	be	AUX
fuelectenerg-1427	679	74	in	in	ADP
fuelectenerg-1427	679	75	the	the	DET
fuelectenerg-1427	679	76	tdt	tdt	PROPN
fuelectenerg-1427	679	77	leaves	leave	NOUN
fuelectenerg-1427	679	78	)	)	PUNCT
fuelectenerg-1427	679	79	each	each	PRON
fuelectenerg-1427	679	80	by	by	ADP
fuelectenerg-1427	679	81	the	the	DET
fuelectenerg-1427	679	82	corresponding	corresponding	ADJ
fuelectenerg-1427	679	83	path	path	NOUN
fuelectenerg-1427	679	84	in	in	ADP
fuelectenerg-1427	679	85	that	that	DET
fuelectenerg-1427	679	86	tdt	tdt	PROPN
fuelectenerg-1427	679	87	,	,	PUNCT
fuelectenerg-1427	679	88	and	and	CCONJ
fuelectenerg-1427	679	89	sum	sum	VERB
fuelectenerg-1427	679	90	all	all	DET
fuelectenerg-1427	679	91	the	the	DET
fuelectenerg-1427	679	92	resulting	result	VERB
fuelectenerg-1427	679	93	cubes	cube	NOUN
fuelectenerg-1427	679	94	(	(	PUNCT
fuelectenerg-1427	679	95	terms	term	NOUN
fuelectenerg-1427	679	96	)	)	PUNCT
fuelectenerg-1427	679	97	over	over	ADP
fuelectenerg-1427	679	98	gf(3	gf(3	PROPN
fuelectenerg-1427	679	99	)	)	PUNCT
fuelectenerg-1427	679	100	,	,	PUNCT
fuelectenerg-1427	679	101	we	we	PRON
fuelectenerg-1427	679	102	obtain	obtain	VERB
fuelectenerg-1427	679	103	the	the	DET
fuelectenerg-1427	679	104	flattened	flatten	VERB
fuelectenerg-1427	679	105	form	form	NOUN
fuelectenerg-1427	679	106	of	of	ADP
fuelectenerg-1427	679	107	the	the	DET
fuelectenerg-1427	679	108	function	function	NOUN
fuelectenerg-1427	679	109	f	f	PROPN
fuelectenerg-1427	679	110	,	,	PUNCT
fuelectenerg-1427	679	111	as	as	ADP
fuelectenerg-1427	679	112	a	a	DET
fuelectenerg-1427	679	113	certain	certain	ADJ
fuelectenerg-1427	679	114	gfsop	gfsop	NOUN
fuelectenerg-1427	679	115	expression	expression	NOUN
fuelectenerg-1427	679	116	.	.	PUNCT
fuelectenerg-1427	680	1	for	for	ADP
fuelectenerg-1427	680	2	each	each	DET
fuelectenerg-1427	680	3	tdt	tdt	PROPN
fuelectenerg-1427	680	4	in	in	ADP
fuelectenerg-1427	680	5	figure	figure	NOUN
fuelectenerg-1427	680	6	5	5	NUM
fuelectenerg-1427	680	7	,	,	PUNCT
fuelectenerg-1427	680	8	there	there	PRON
fuelectenerg-1427	680	9	are	be	VERB
fuelectenerg-1427	680	10	as	as	ADV
fuelectenerg-1427	680	11	many	many	ADJ
fuelectenerg-1427	680	12	forms	form	NOUN
fuelectenerg-1427	680	13	obtained	obtain	VERB
fuelectenerg-1427	680	14	for	for	ADP
fuelectenerg-1427	680	15	the	the	DET
fuelectenerg-1427	680	16	function	function	NOUN
fuelectenerg-1427	680	17	f	f	PROPN
fuelectenerg-1427	680	18	as	as	ADP
fuelectenerg-1427	680	19	the	the	DET
fuelectenerg-1427	680	20	number	number	NOUN
fuelectenerg-1427	680	21	of	of	ADP
fuelectenerg-1427	680	22	possible	possible	ADJ
fuelectenerg-1427	680	23	permutations	permutation	NOUN
fuelectenerg-1427	680	24	of	of	ADP
fuelectenerg-1427	680	25	the	the	DET
fuelectenerg-1427	680	26	polarities	polarity	NOUN
fuelectenerg-1427	680	27	of	of	ADP
fuelectenerg-1427	680	28	the	the	DET
fuelectenerg-1427	680	29	variables	variable	NOUN
fuelectenerg-1427	680	30	in	in	ADP
fuelectenerg-1427	680	31	the	the	DET
fuelectenerg-1427	680	32	second	second	ADJ
fuelectenerg-1427	680	33	-	-	PUNCT
fuelectenerg-1427	680	34	level	level	NOUN
fuelectenerg-1427	680	35	branches	branch	NOUN
fuelectenerg-1427	680	36	of	of	ADP
fuelectenerg-1427	680	37	each	each	DET
fuelectenerg-1427	680	38	tdt	tdt	PROPN
fuelectenerg-1427	680	39	.	.	PUNCT
fuelectenerg-1427	681	1	definition	definition	NOUN
fuelectenerg-1427	681	2	2	2	NUM
fuelectenerg-1427	681	3	.	.	PUNCT
fuelectenerg-1427	682	1	the	the	DET
fuelectenerg-1427	682	2	family	family	NOUN
fuelectenerg-1427	682	3	of	of	ADP
fuelectenerg-1427	682	4	all	all	DET
fuelectenerg-1427	682	5	possible	possible	ADJ
fuelectenerg-1427	682	6	forms	form	NOUN
fuelectenerg-1427	682	7	obtained	obtain	VERB
fuelectenerg-1427	682	8	per	per	ADP
fuelectenerg-1427	682	9	ternary	ternary	NOUN
fuelectenerg-1427	682	10	s	s	PROPN
fuelectenerg-1427	682	11	/	/	SYM
fuelectenerg-1427	682	12	d	d	NOUN
fuelectenerg-1427	682	13	tree	tree	NOUN
fuelectenerg-1427	682	14	is	be	AUX
fuelectenerg-1427	682	15	called	call	VERB
fuelectenerg-1427	682	16	ternary	ternary	ADJ
fuelectenerg-1427	682	17	inclusive	inclusive	ADJ
fuelectenerg-1427	682	18	forms	form	NOUN
fuelectenerg-1427	682	19	(	(	PUNCT
fuelectenerg-1427	682	20	tifs	tifs	PROPN
fuelectenerg-1427	682	21	)	)	PUNCT
fuelectenerg-1427	682	22	.	.	PUNCT
fuelectenerg-1427	683	1	the	the	DET
fuelectenerg-1427	683	2	numbers	number	NOUN
fuelectenerg-1427	683	3	of	of	ADP
fuelectenerg-1427	683	4	these	these	DET
fuelectenerg-1427	683	5	tifs	tif	NOUN
fuelectenerg-1427	683	6	per	per	ADP
fuelectenerg-1427	683	7	tdt	tdt	PROPN
fuelectenerg-1427	683	8	for	for	ADP
fuelectenerg-1427	683	9	two	two	NUM
fuelectenerg-1427	683	10	variables	variable	NOUN
fuelectenerg-1427	683	11	are	be	AUX
fuelectenerg-1427	683	12	shown	show	VERB
fuelectenerg-1427	683	13	on	on	ADP
fuelectenerg-1427	683	14	top	top	NOUN
fuelectenerg-1427	683	15	of	of	ADP
fuelectenerg-1427	683	16	each	each	DET
fuelectenerg-1427	683	17	s	s	PROPN
fuelectenerg-1427	683	18	/	/	SYM
fuelectenerg-1427	683	19	d	d	PROPN
fuelectenerg-1427	683	20	tdt	tdt	PROPN
fuelectenerg-1427	683	21	in	in	ADP
fuelectenerg-1427	683	22	figure	figure	NOUN
fuelectenerg-1427	683	23	5	5	NUM
fuelectenerg-1427	683	24	.	.	PUNCT
fuelectenerg-1427	683	25	by	by	ADP
fuelectenerg-1427	683	26	observing	observe	VERB
fuelectenerg-1427	683	27	figure	figure	NOUN
fuelectenerg-1427	683	28	5	5	NUM
fuelectenerg-1427	683	29	,	,	PUNCT
fuelectenerg-1427	683	30	we	we	PRON
fuelectenerg-1427	683	31	can	can	AUX
fuelectenerg-1427	683	32	generate	generate	VERB
fuelectenerg-1427	683	33	the	the	DET
fuelectenerg-1427	683	34	corresponding	corresponding	ADJ
fuelectenerg-1427	683	35	flattened	flatten	VERB
fuelectenerg-1427	683	36	forms	form	NOUN
fuelectenerg-1427	683	37	by	by	ADP
fuelectenerg-1427	683	38	two	two	NUM
fuelectenerg-1427	683	39	methods	method	NOUN
fuelectenerg-1427	683	40	.	.	PUNCT
fuelectenerg-1427	684	1	a	a	DET
fuelectenerg-1427	684	2	classical	classical	ADJ
fuelectenerg-1427	684	3	method	method	NOUN
fuelectenerg-1427	684	4	,	,	PUNCT
fuelectenerg-1427	684	5	per	per	ADP
fuelectenerg-1427	684	6	analogy	analogy	NOUN
fuelectenerg-1427	684	7	with	with	ADP
fuelectenerg-1427	684	8	well	well	ADV
fuelectenerg-1427	684	9	-	-	PUNCT
fuelectenerg-1427	684	10	known	know	VERB
fuelectenerg-1427	684	11	binary	binary	ADJ
fuelectenerg-1427	684	12	forms	form	NOUN
fuelectenerg-1427	684	13	,	,	PUNCT
fuelectenerg-1427	684	14	would	would	AUX
fuelectenerg-1427	684	15	be	be	AUX
fuelectenerg-1427	684	16	to	to	PART
fuelectenerg-1427	684	17	create	create	VERB
fuelectenerg-1427	684	18	every	every	DET
fuelectenerg-1427	684	19	transform	transform	NOUN
fuelectenerg-1427	684	20	matrix	matrix	NOUN
fuelectenerg-1427	684	21	for	for	ADP
fuelectenerg-1427	684	22	every	every	DET
fuelectenerg-1427	684	23	tif	tif	PROPN
fuelectenerg-1427	684	24	s	s	PROPN
fuelectenerg-1427	684	25	/	/	SYM
fuelectenerg-1427	684	26	d	d	NOUN
fuelectenerg-1427	684	27	tree	tree	NOUN
fuelectenerg-1427	684	28	and	and	CCONJ
fuelectenerg-1427	684	29	then	then	ADV
fuelectenerg-1427	684	30	expand	expand	VERB
fuelectenerg-1427	684	31	using	use	VERB
fuelectenerg-1427	684	32	that	that	DET
fuelectenerg-1427	684	33	transform	transform	NOUN
fuelectenerg-1427	684	34	matrix	matrix	NOUN
fuelectenerg-1427	684	35	.	.	PUNCT
fuelectenerg-1427	685	1	a	a	DET
fuelectenerg-1427	685	2	better	well	ADJ
fuelectenerg-1427	685	3	method	method	NOUN
fuelectenerg-1427	685	4	is	be	AUX
fuelectenerg-1427	685	5	to	to	PART
fuelectenerg-1427	685	6	create	create	VERB
fuelectenerg-1427	685	7	one	one	NUM
fuelectenerg-1427	685	8	flattened	flatten	VERB
fuelectenerg-1427	685	9	108	108	NUM
fuelectenerg-1427	685	10	an	an	DET
fuelectenerg-1427	685	11	extended	extend	VERB
fuelectenerg-1427	685	12	green	green	ADJ
fuelectenerg-1427	685	13	sasao	sasao	PROPN
fuelectenerg-1427	685	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	685	15	of	of	ADP
fuelectenerg-1427	685	16	canonical	canonical	ADJ
fuelectenerg-1427	685	17	ternary	ternary	ADJ
fuelectenerg-1427	685	18	galois	galois	NOUN
fuelectenerg-1427	685	19	forms	form	NOUN
fuelectenerg-1427	685	20	...	...	PUNCT
fuelectenerg-1427	685	21	s	s	VERB
fuelectenerg-1427	685	22	a	a	PRON
fuelectenerg-1427	685	23	’	'	PUNCT
fuelectenerg-1427	685	24	a	a	PRON
fuelectenerg-1427	685	25	(	(	PUNCT
fuelectenerg-1427	685	26	)	)	PUNCT
fuelectenerg-1427	685	27	a	a	PRON
fuelectenerg-1427	685	28	pd	pd	PROPN
fuelectenerg-1427	685	29	1	1	NUM
fuelectenerg-1427	685	30	a	a	PRON
fuelectenerg-1427	685	31	(	(	PUNCT
fuelectenerg-1427	685	32	)	)	PUNCT
fuelectenerg-1427	685	33	b	b	NOUN
fuelectenerg-1427	685	34	nd	nd	ADP
fuelectenerg-1427	685	35	1	1	NUM
fuelectenerg-1427	685	36	a	a	PRON
fuelectenerg-1427	685	37	’	'	PUNCT
fuelectenerg-1427	685	38	d	d	ADP
fuelectenerg-1427	685	39	1	1	NUM
fuelectenerg-1427	685	40	a	a	PRON
fuelectenerg-1427	685	41	(	(	PUNCT
fuelectenerg-1427	685	42	)	)	PUNCT
fuelectenerg-1427	685	43	d	d	NOUN
fuelectenerg-1427	685	44	(	(	PUNCT
fuelectenerg-1427	685	45	)	)	PUNCT
fuelectenerg-1427	685	46	c	c	NOUN
fuelectenerg-1427	685	47	figure	figure	VERB
fuelectenerg-1427	685	48	3	3	NUM
fuelectenerg-1427	685	49	:	:	PUNCT
fuelectenerg-1427	685	50	two	two	NUM
fuelectenerg-1427	685	51	-	-	PUNCT
fuelectenerg-1427	685	52	valued	value	VERB
fuelectenerg-1427	685	53	nodes	node	NOUN
fuelectenerg-1427	685	54	:	:	PUNCT
fuelectenerg-1427	685	55	(	(	PUNCT
fuelectenerg-1427	685	56	a	a	X
fuelectenerg-1427	685	57	)	)	PUNCT
fuelectenerg-1427	685	58	shannon	shannon	NOUN
fuelectenerg-1427	685	59	,	,	PUNCT
fuelectenerg-1427	685	60	(	(	PUNCT
fuelectenerg-1427	685	61	b	b	NOUN
fuelectenerg-1427	685	62	)	)	PUNCT
fuelectenerg-1427	685	63	positive	positive	ADJ
fuelectenerg-1427	685	64	davio	davio	NOUN
fuelectenerg-1427	685	65	,	,	PUNCT
fuelectenerg-1427	685	66	(	(	PUNCT
fuelectenerg-1427	685	67	c	c	NOUN
fuelectenerg-1427	685	68	)	)	PUNCT
fuelectenerg-1427	685	69	negative	negative	ADJ
fuelectenerg-1427	685	70	davio	davio	NOUN
fuelectenerg-1427	685	71	,	,	PUNCT
fuelectenerg-1427	685	72	and	and	CCONJ
fuelectenerg-1427	685	73	(	(	PUNCT
fuelectenerg-1427	685	74	d	d	X
fuelectenerg-1427	685	75	)	)	PUNCT
fuelectenerg-1427	685	76	generalized	generalized	ADJ
fuelectenerg-1427	685	77	davio	davio	NOUN
fuelectenerg-1427	685	78	where	where	SCONJ
fuelectenerg-1427	685	79	a	a	DET
fuelectenerg-1427	685	80	∈	∈	NOUN
fuelectenerg-1427	685	81	{	{	PUNCT
fuelectenerg-1427	685	82	a	a	PRON
fuelectenerg-1427	685	83	,	,	PUNCT
fuelectenerg-1427	685	84	a′	a′	PROPN
fuelectenerg-1427	685	85	}	}	PUNCT
fuelectenerg-1427	685	86	.	.	PUNCT
fuelectenerg-1427	686	1	variable	variable	ADJ
fuelectenerg-1427	686	2	,	,	PUNCT
fuelectenerg-1427	686	3	that	that	PRON
fuelectenerg-1427	686	4	is	be	AUX
fuelectenerg-1427	686	5	one	one	NUM
fuelectenerg-1427	686	6	tree	tree	NOUN
fuelectenerg-1427	686	7	level	level	NOUN
fuelectenerg-1427	686	8	,	,	PUNCT
fuelectenerg-1427	686	9	figure	figure	NOUN
fuelectenerg-1427	686	10	4	4	NUM
fuelectenerg-1427	686	11	represents	represent	VERB
fuelectenerg-1427	686	12	the	the	DET
fuelectenerg-1427	686	13	expansion	expansion	NOUN
fuelectenerg-1427	686	14	nodes	node	NOUN
fuelectenerg-1427	686	15	for	for	ADP
fuelectenerg-1427	686	16	ternary	ternary	ADJ
fuelectenerg-1427	686	17	shannon	shannon	NOUN
fuelectenerg-1427	686	18	,	,	PUNCT
fuelectenerg-1427	686	19	davio	davio	NOUN
fuelectenerg-1427	686	20	and	and	CCONJ
fuelectenerg-1427	686	21	generalized	generalized	ADJ
fuelectenerg-1427	686	22	davio	davio	NOUN
fuelectenerg-1427	686	23	(	(	PUNCT
fuelectenerg-1427	686	24	d	d	NOUN
fuelectenerg-1427	686	25	)	)	PUNCT
fuelectenerg-1427	686	26	,	,	PUNCT
fuelectenerg-1427	686	27	respectively	respectively	ADV
fuelectenerg-1427	686	28	.	.	PUNCT
fuelectenerg-1427	687	1	s	s	PART
fuelectenerg-1427	687	2	0	0	NUM
fuelectenerg-1427	687	3	x	x	SYM
fuelectenerg-1427	687	4	1	1	NUM
fuelectenerg-1427	687	5	x	x	SYM
fuelectenerg-1427	687	6	2	2	NUM
fuelectenerg-1427	687	7	x	x	SYM
fuelectenerg-1427	687	8	(	(	PUNCT
fuelectenerg-1427	687	9	a	a	PRON
fuelectenerg-1427	687	10	)	)	PUNCT
fuelectenerg-1427	687	11	d0	d0	NOUN
fuelectenerg-1427	687	12	1	1	NUM
fuelectenerg-1427	687	13	x	x	SYM
fuelectenerg-1427	687	14	2	2	NUM
fuelectenerg-1427	687	15	(	(	PUNCT
fuelectenerg-1427	687	16	b	b	NOUN
fuelectenerg-1427	687	17	)	)	PUNCT
fuelectenerg-1427	687	18	d2	d2	PROPN
fuelectenerg-1427	687	19	1	1	NUM
fuelectenerg-1427	687	20	(	(	PUNCT
fuelectenerg-1427	687	21	d	d	NOUN
fuelectenerg-1427	687	22	)	)	PUNCT
fuelectenerg-1427	688	1	d	d	NOUN
fuelectenerg-1427	688	2	1	1	NUM
fuelectenerg-1427	688	3	(	(	PUNCT
fuelectenerg-1427	688	4	e	e	NOUN
fuelectenerg-1427	688	5	)	)	PUNCT
fuelectenerg-1427	688	6	d1	d1	NOUN
fuelectenerg-1427	688	7	1	1	NUM
fuelectenerg-1427	688	8	(	(	PUNCT
fuelectenerg-1427	688	9	’	'	PUNCT
fuelectenerg-1427	688	10	)	)	PUNCT
fuelectenerg-1427	688	11	x	x	SYM
fuelectenerg-1427	688	12	2	2	NUM
fuelectenerg-1427	688	13	(	(	PUNCT
fuelectenerg-1427	688	14	’’	’'	PUNCT
fuelectenerg-1427	688	15	)	)	PUNCT
fuelectenerg-1427	688	16	x	x	SYM
fuelectenerg-1427	688	17	2	2	NUM
fuelectenerg-1427	688	18	(	(	PUNCT
fuelectenerg-1427	688	19	)	)	PUNCT
fuelectenerg-1427	688	20	x	x	SYM
fuelectenerg-1427	688	21	2	2	NUM
fuelectenerg-1427	688	22	(	(	PUNCT
fuelectenerg-1427	688	23	c	c	NOUN
fuelectenerg-1427	688	24	)	)	PUNCT
fuelectenerg-1427	688	25	x	x	SYM
fuelectenerg-1427	688	26	xx	xx	X
fuelectenerg-1427	688	27	’	'	PUNCT
fuelectenerg-1427	688	28	x	x	NOUN
fuelectenerg-1427	688	29	’’	’'	PUNCT
fuelectenerg-1427	688	30	figure	figure	VERB
fuelectenerg-1427	688	31	4	4	NUM
fuelectenerg-1427	688	32	:	:	PUNCT
fuelectenerg-1427	688	33	ternary	ternary	ADJ
fuelectenerg-1427	688	34	nodes	node	NOUN
fuelectenerg-1427	688	35	for	for	ADP
fuelectenerg-1427	688	36	ternary	ternary	ADJ
fuelectenerg-1427	688	37	decision	decision	NOUN
fuelectenerg-1427	688	38	trees	tree	NOUN
fuelectenerg-1427	688	39	:	:	PUNCT
fuelectenerg-1427	688	40	(	(	PUNCT
fuelectenerg-1427	688	41	a	a	X
fuelectenerg-1427	688	42	)	)	PUNCT
fuelectenerg-1427	688	43	shannon	shannon	NOUN
fuelectenerg-1427	688	44	,	,	PUNCT
fuelectenerg-1427	688	45	(	(	PUNCT
fuelectenerg-1427	688	46	b	b	X
fuelectenerg-1427	688	47	)	)	PUNCT
fuelectenerg-1427	688	48	davio0	davio0	PROPN
fuelectenerg-1427	688	49	,	,	PUNCT
fuelectenerg-1427	688	50	(	(	PUNCT
fuelectenerg-1427	688	51	c	c	X
fuelectenerg-1427	688	52	)	)	PUNCT
fuelectenerg-1427	688	53	davio1	davio1	NOUN
fuelectenerg-1427	688	54	,	,	PUNCT
fuelectenerg-1427	688	55	(	(	PUNCT
fuelectenerg-1427	688	56	d	d	NOUN
fuelectenerg-1427	688	57	)	)	PUNCT
fuelectenerg-1427	688	58	davio2	davio2	PROPN
fuelectenerg-1427	688	59	,	,	PUNCT
fuelectenerg-1427	688	60	and	and	CCONJ
fuelectenerg-1427	688	61	(	(	PUNCT
fuelectenerg-1427	688	62	e	e	NOUN
fuelectenerg-1427	688	63	)	)	PUNCT
fuelectenerg-1427	688	64	generalized	generalized	ADJ
fuelectenerg-1427	688	65	davio	davio	NOUN
fuelectenerg-1427	688	66	(	(	PUNCT
fuelectenerg-1427	688	67	d	d	NOUN
fuelectenerg-1427	688	68	)	)	PUNCT
fuelectenerg-1427	688	69	where	where	SCONJ
fuelectenerg-1427	688	70	x	x	SYM
fuelectenerg-1427	688	71	∈	∈	PROPN
fuelectenerg-1427	688	72	{	{	PUNCT
fuelectenerg-1427	688	73	x	x	NOUN
fuelectenerg-1427	688	74	,	,	PUNCT
fuelectenerg-1427	688	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	688	76	}	}	PUNCT
fuelectenerg-1427	688	77	.	.	PUNCT
fuelectenerg-1427	689	1	in	in	ADP
fuelectenerg-1427	689	2	correspondence	correspondence	NOUN
fuelectenerg-1427	689	3	to	to	ADP
fuelectenerg-1427	689	4	the	the	DET
fuelectenerg-1427	689	5	binary	binary	PROPN
fuelectenerg-1427	689	6	s	s	PROPN
fuelectenerg-1427	689	7	/	/	SYM
fuelectenerg-1427	689	8	d	d	NOUN
fuelectenerg-1427	689	9	trees	tree	NOUN
fuelectenerg-1427	689	10	,	,	PUNCT
fuelectenerg-1427	689	11	one	one	PRON
fuelectenerg-1427	689	12	can	can	AUX
fuelectenerg-1427	689	13	produce	produce	VERB
fuelectenerg-1427	689	14	ternary	ternary	ADJ
fuelectenerg-1427	689	15	s	s	NOUN
fuelectenerg-1427	689	16	/	/	SYM
fuelectenerg-1427	689	17	d	d	NOUN
fuelectenerg-1427	689	18	trees	tree	NOUN
fuelectenerg-1427	689	19	.	.	PUNCT
fuelectenerg-1427	690	1	to	to	PART
fuelectenerg-1427	690	2	define	define	VERB
fuelectenerg-1427	690	3	the	the	DET
fuelectenerg-1427	690	4	ternary	ternary	ADJ
fuelectenerg-1427	690	5	s	s	NOUN
fuelectenerg-1427	690	6	/	/	SYM
fuelectenerg-1427	690	7	d	d	NOUN
fuelectenerg-1427	690	8	trees	tree	NOUN
fuelectenerg-1427	690	9	,	,	PUNCT
fuelectenerg-1427	690	10	we	we	PRON
fuelectenerg-1427	690	11	define	define	VERB
fuelectenerg-1427	690	12	the	the	DET
fuelectenerg-1427	690	13	generalized	generalized	ADJ
fuelectenerg-1427	690	14	davio	davio	NOUN
fuelectenerg-1427	690	15	node	node	NOUN
fuelectenerg-1427	690	16	over	over	ADP
fuelectenerg-1427	690	17	ternary	ternary	ADJ
fuelectenerg-1427	690	18	galois	galois	PROPN
fuelectenerg-1427	690	19	radix	radix	NOUN
fuelectenerg-1427	690	20	as	as	SCONJ
fuelectenerg-1427	690	21	shown	show	VERB
fuelectenerg-1427	690	22	in	in	ADP
fuelectenerg-1427	690	23	figure	figure	NOUN
fuelectenerg-1427	690	24	4(e	4(e	NUM
fuelectenerg-1427	690	25	)	)	PUNCT
fuelectenerg-1427	690	26	.	.	PUNCT
fuelectenerg-1427	691	1	our	our	PRON
fuelectenerg-1427	691	2	notation	notation	NOUN
fuelectenerg-1427	691	3	here	here	ADV
fuelectenerg-1427	691	4	is	be	AUX
fuelectenerg-1427	691	5	that	that	PRON
fuelectenerg-1427	691	6	(	(	PUNCT
fuelectenerg-1427	691	7	x	x	X
fuelectenerg-1427	691	8	)	)	PUNCT
fuelectenerg-1427	691	9	corresponds	correspond	VERB
fuelectenerg-1427	691	10	to	to	ADP
fuelectenerg-1427	691	11	the	the	DET
fuelectenerg-1427	691	12	three	three	NUM
fuelectenerg-1427	691	13	possible	possible	ADJ
fuelectenerg-1427	691	14	shifts	shift	NOUN
fuelectenerg-1427	691	15	of	of	ADP
fuelectenerg-1427	691	16	the	the	DET
fuelectenerg-1427	691	17	variable	variable	NOUN
fuelectenerg-1427	691	18	x	x	NOUN
fuelectenerg-1427	691	19	as	as	SCONJ
fuelectenerg-1427	691	20	follows	follow	VERB
fuelectenerg-1427	691	21	:	:	PUNCT
fuelectenerg-1427	691	22	x	x	SYM
fuelectenerg-1427	691	23	∈	∈	NOUN
fuelectenerg-1427	691	24	{	{	PUNCT
fuelectenerg-1427	691	25	x	x	NOUN
fuelectenerg-1427	691	26	,	,	PUNCT
fuelectenerg-1427	691	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	691	28	}	}	PUNCT
fuelectenerg-1427	691	29	,	,	PUNCT
fuelectenerg-1427	691	30	over	over	ADP
fuelectenerg-1427	691	31	gf(3	gf(3	PROPN
fuelectenerg-1427	691	32	)	)	PUNCT
fuelectenerg-1427	691	33	.	.	PUNCT
fuelectenerg-1427	692	1	(	(	PUNCT
fuelectenerg-1427	692	2	28	28	NUM
fuelectenerg-1427	692	3	)	)	PUNCT
fuelectenerg-1427	692	4	definition	definition	NOUN
fuelectenerg-1427	692	5	1	1	NUM
fuelectenerg-1427	692	6	.	.	PUNCT
fuelectenerg-1427	693	1	the	the	DET
fuelectenerg-1427	693	2	ternary	ternary	ADJ
fuelectenerg-1427	693	3	tree	tree	NOUN
fuelectenerg-1427	693	4	with	with	ADP
fuelectenerg-1427	693	5	ternary	ternary	ADJ
fuelectenerg-1427	693	6	shannon	shannon	NOUN
fuelectenerg-1427	693	7	and	and	CCONJ
fuelectenerg-1427	693	8	ternary	ternary	ADJ
fuelectenerg-1427	693	9	generalized	generalized	ADJ
fuelectenerg-1427	693	10	davio	davio	NOUN
fuelectenerg-1427	693	11	nodes	node	NOUN
fuelectenerg-1427	693	12	,	,	PUNCT
fuelectenerg-1427	693	13	that	that	PRON
fuelectenerg-1427	693	14	generates	generate	VERB
fuelectenerg-1427	693	15	other	other	ADJ
fuelectenerg-1427	693	16	ternary	ternary	ADJ
fuelectenerg-1427	693	17	trees	tree	NOUN
fuelectenerg-1427	693	18	,	,	PUNCT
fuelectenerg-1427	693	19	is	be	AUX
fuelectenerg-1427	693	20	called	call	VERB
fuelectenerg-1427	693	21	ternary	ternary	ADJ
fuelectenerg-1427	693	22	shannon	shannon	NOUN
fuelectenerg-1427	693	23	-	-	PUNCT
fuelectenerg-1427	693	24	davio	davio	NOUN
fuelectenerg-1427	693	25	(	(	PUNCT
fuelectenerg-1427	693	26	s	s	NOUN
fuelectenerg-1427	693	27	/	/	SYM
fuelectenerg-1427	693	28	d	d	NOUN
fuelectenerg-1427	693	29	)	)	PUNCT
fuelectenerg-1427	693	30	tree	tree	NOUN
fuelectenerg-1427	693	31	.	.	PUNCT
fuelectenerg-1427	694	1	utilizing	utilize	VERB
fuelectenerg-1427	694	2	the	the	DET
fuelectenerg-1427	694	3	definition	definition	NOUN
fuelectenerg-1427	694	4	of	of	ADP
fuelectenerg-1427	694	5	ternary	ternary	ADJ
fuelectenerg-1427	694	6	shannon	shannon	NOUN
fuelectenerg-1427	694	7	in	in	ADP
fuelectenerg-1427	694	8	figure	figure	NOUN
fuelectenerg-1427	694	9	4(a	4(a	NUM
fuelectenerg-1427	694	10	)	)	PUNCT
fuelectenerg-1427	694	11	and	and	CCONJ
fuelectenerg-1427	694	12	ternary	ternary	ADJ
fuelectenerg-1427	694	13	generalized	generalized	ADJ
fuelectenerg-1427	694	14	davio	davio	NOUN
fuelectenerg-1427	694	15	in	in	ADP
fuelectenerg-1427	694	16	figure	figure	NOUN
fuelectenerg-1427	694	17	4(e	4(e	NUM
fuelectenerg-1427	694	18	)	)	PUNCT
fuelectenerg-1427	694	19	,	,	PUNCT
fuelectenerg-1427	694	20	we	we	PRON
fuelectenerg-1427	694	21	obtain	obtain	VERB
fuelectenerg-1427	694	22	the	the	DET
fuelectenerg-1427	694	23	ternary	ternary	ADJ
fuelectenerg-1427	694	24	shannon	shannon	NOUN
fuelectenerg-1427	694	25	-	-	PUNCT
fuelectenerg-1427	694	26	davio	davio	NOUN
fuelectenerg-1427	694	27	trees	tree	NOUN
fuelectenerg-1427	694	28	(	(	PUNCT
fuelectenerg-1427	694	29	ternary	ternary	NOUN
fuelectenerg-1427	694	30	s	s	PROPN
fuelectenerg-1427	694	31	/	/	SYM
fuelectenerg-1427	694	32	d	d	NOUN
fuelectenerg-1427	694	33	trees	tree	NOUN
fuelectenerg-1427	694	34	)	)	PUNCT
fuelectenerg-1427	694	35	for	for	ADP
fuelectenerg-1427	694	36	two	two	NUM
fuelectenerg-1427	694	37	variables	variable	NOUN
fuelectenerg-1427	694	38	as	as	SCONJ
fuelectenerg-1427	694	39	shown	show	VERB
fuelectenerg-1427	694	40	in	in	ADP
fuelectenerg-1427	694	41	figure	figure	NOUN
fuelectenerg-1427	694	42	5	5	NUM
fuelectenerg-1427	694	43	.	.	PUNCT
fuelectenerg-1427	694	44	from	from	ADP
fuelectenerg-1427	694	45	the	the	DET
fuelectenerg-1427	694	46	ternary	ternary	ADJ
fuelectenerg-1427	694	47	s	s	PROPN
fuelectenerg-1427	694	48	/	/	SYM
fuelectenerg-1427	694	49	d	d	ADJ
fuelectenerg-1427	694	50	dts	dts	NOUN
fuelectenerg-1427	694	51	shown	show	VERB
fuelectenerg-1427	694	52	in	in	ADP
fuelectenerg-1427	694	53	figure	figure	NOUN
fuelectenerg-1427	694	54	5	5	NUM
fuelectenerg-1427	694	55	,	,	PUNCT
fuelectenerg-1427	694	56	if	if	SCONJ
fuelectenerg-1427	694	57	we	we	PRON
fuelectenerg-1427	694	58	take	take	VERB
fuelectenerg-1427	694	59	any	any	DET
fuelectenerg-1427	694	60	s	s	PROPN
fuelectenerg-1427	694	61	/	/	SYM
fuelectenerg-1427	694	62	d	d	NOUN
fuelectenerg-1427	694	63	tree	tree	NOUN
fuelectenerg-1427	694	64	and	and	CCONJ
fuelectenerg-1427	694	65	multiply	multiply	VERB
fuelectenerg-1427	694	66	the	the	DET
fuelectenerg-1427	694	67	second	second	ADJ
fuelectenerg-1427	694	68	-	-	PUNCT
fuelectenerg-1427	694	69	level	level	NOUN
fuelectenerg-1427	694	70	cofactors	cofactor	NOUN
fuelectenerg-1427	694	71	(	(	PUNCT
fuelectenerg-1427	694	72	which	which	PRON
fuelectenerg-1427	694	73	are	be	AUX
fuelectenerg-1427	694	74	in	in	ADP
fuelectenerg-1427	694	75	the	the	DET
fuelectenerg-1427	694	76	tdt	tdt	PROPN
fuelectenerg-1427	694	77	leaves	leave	NOUN
fuelectenerg-1427	694	78	)	)	PUNCT
fuelectenerg-1427	694	79	each	each	PRON
fuelectenerg-1427	694	80	by	by	ADP
fuelectenerg-1427	694	81	the	the	DET
fuelectenerg-1427	694	82	corresponding	corresponding	ADJ
fuelectenerg-1427	694	83	path	path	NOUN
fuelectenerg-1427	694	84	in	in	ADP
fuelectenerg-1427	694	85	that	that	DET
fuelectenerg-1427	694	86	tdt	tdt	PROPN
fuelectenerg-1427	694	87	,	,	PUNCT
fuelectenerg-1427	694	88	and	and	CCONJ
fuelectenerg-1427	694	89	sum	sum	VERB
fuelectenerg-1427	694	90	all	all	DET
fuelectenerg-1427	694	91	the	the	DET
fuelectenerg-1427	694	92	resulting	result	VERB
fuelectenerg-1427	694	93	cubes	cube	NOUN
fuelectenerg-1427	694	94	(	(	PUNCT
fuelectenerg-1427	694	95	terms	term	NOUN
fuelectenerg-1427	694	96	)	)	PUNCT
fuelectenerg-1427	694	97	over	over	ADP
fuelectenerg-1427	694	98	gf(3	gf(3	PROPN
fuelectenerg-1427	694	99	)	)	PUNCT
fuelectenerg-1427	694	100	,	,	PUNCT
fuelectenerg-1427	694	101	we	we	PRON
fuelectenerg-1427	694	102	obtain	obtain	VERB
fuelectenerg-1427	694	103	the	the	DET
fuelectenerg-1427	694	104	flattened	flatten	VERB
fuelectenerg-1427	694	105	form	form	NOUN
fuelectenerg-1427	694	106	of	of	ADP
fuelectenerg-1427	694	107	the	the	DET
fuelectenerg-1427	694	108	function	function	NOUN
fuelectenerg-1427	694	109	f	f	PROPN
fuelectenerg-1427	694	110	,	,	PUNCT
fuelectenerg-1427	694	111	as	as	ADP
fuelectenerg-1427	694	112	a	a	DET
fuelectenerg-1427	694	113	certain	certain	ADJ
fuelectenerg-1427	694	114	gfsop	gfsop	NOUN
fuelectenerg-1427	694	115	expression	expression	NOUN
fuelectenerg-1427	694	116	.	.	PUNCT
fuelectenerg-1427	695	1	for	for	ADP
fuelectenerg-1427	695	2	each	each	DET
fuelectenerg-1427	695	3	tdt	tdt	PROPN
fuelectenerg-1427	695	4	in	in	ADP
fuelectenerg-1427	695	5	figure	figure	NOUN
fuelectenerg-1427	695	6	5	5	NUM
fuelectenerg-1427	695	7	,	,	PUNCT
fuelectenerg-1427	695	8	there	there	PRON
fuelectenerg-1427	695	9	are	be	VERB
fuelectenerg-1427	695	10	as	as	ADV
fuelectenerg-1427	695	11	many	many	ADJ
fuelectenerg-1427	695	12	forms	form	NOUN
fuelectenerg-1427	695	13	obtained	obtain	VERB
fuelectenerg-1427	695	14	for	for	ADP
fuelectenerg-1427	695	15	the	the	DET
fuelectenerg-1427	695	16	function	function	NOUN
fuelectenerg-1427	695	17	f	f	PROPN
fuelectenerg-1427	695	18	as	as	ADP
fuelectenerg-1427	695	19	the	the	DET
fuelectenerg-1427	695	20	number	number	NOUN
fuelectenerg-1427	695	21	of	of	ADP
fuelectenerg-1427	695	22	possible	possible	ADJ
fuelectenerg-1427	695	23	permutations	permutation	NOUN
fuelectenerg-1427	695	24	of	of	ADP
fuelectenerg-1427	695	25	the	the	DET
fuelectenerg-1427	695	26	polarities	polarity	NOUN
fuelectenerg-1427	695	27	of	of	ADP
fuelectenerg-1427	695	28	the	the	DET
fuelectenerg-1427	695	29	variables	variable	NOUN
fuelectenerg-1427	695	30	in	in	ADP
fuelectenerg-1427	695	31	the	the	DET
fuelectenerg-1427	695	32	second	second	ADJ
fuelectenerg-1427	695	33	-	-	PUNCT
fuelectenerg-1427	695	34	level	level	NOUN
fuelectenerg-1427	695	35	branches	branch	NOUN
fuelectenerg-1427	695	36	of	of	ADP
fuelectenerg-1427	695	37	each	each	DET
fuelectenerg-1427	695	38	tdt	tdt	PROPN
fuelectenerg-1427	695	39	.	.	PUNCT
fuelectenerg-1427	696	1	definition	definition	NOUN
fuelectenerg-1427	696	2	2	2	NUM
fuelectenerg-1427	696	3	.	.	PUNCT
fuelectenerg-1427	697	1	the	the	DET
fuelectenerg-1427	697	2	family	family	NOUN
fuelectenerg-1427	697	3	of	of	ADP
fuelectenerg-1427	697	4	all	all	DET
fuelectenerg-1427	697	5	possible	possible	ADJ
fuelectenerg-1427	697	6	forms	form	NOUN
fuelectenerg-1427	697	7	obtained	obtain	VERB
fuelectenerg-1427	697	8	per	per	ADP
fuelectenerg-1427	697	9	ternary	ternary	NOUN
fuelectenerg-1427	697	10	s	s	PROPN
fuelectenerg-1427	697	11	/	/	SYM
fuelectenerg-1427	697	12	d	d	NOUN
fuelectenerg-1427	697	13	tree	tree	NOUN
fuelectenerg-1427	697	14	is	be	AUX
fuelectenerg-1427	697	15	called	call	VERB
fuelectenerg-1427	697	16	ternary	ternary	ADJ
fuelectenerg-1427	697	17	inclusive	inclusive	ADJ
fuelectenerg-1427	697	18	forms	form	NOUN
fuelectenerg-1427	697	19	(	(	PUNCT
fuelectenerg-1427	697	20	tifs	tifs	PROPN
fuelectenerg-1427	697	21	)	)	PUNCT
fuelectenerg-1427	697	22	.	.	PUNCT
fuelectenerg-1427	698	1	the	the	DET
fuelectenerg-1427	698	2	numbers	number	NOUN
fuelectenerg-1427	698	3	of	of	ADP
fuelectenerg-1427	698	4	these	these	DET
fuelectenerg-1427	698	5	tifs	tif	NOUN
fuelectenerg-1427	698	6	per	per	ADP
fuelectenerg-1427	698	7	tdt	tdt	PROPN
fuelectenerg-1427	698	8	for	for	ADP
fuelectenerg-1427	698	9	two	two	NUM
fuelectenerg-1427	698	10	variables	variable	NOUN
fuelectenerg-1427	698	11	are	be	AUX
fuelectenerg-1427	698	12	shown	show	VERB
fuelectenerg-1427	698	13	on	on	ADP
fuelectenerg-1427	698	14	top	top	NOUN
fuelectenerg-1427	698	15	of	of	ADP
fuelectenerg-1427	698	16	each	each	DET
fuelectenerg-1427	698	17	s	s	PROPN
fuelectenerg-1427	698	18	/	/	SYM
fuelectenerg-1427	698	19	d	d	PROPN
fuelectenerg-1427	698	20	tdt	tdt	PROPN
fuelectenerg-1427	698	21	in	in	ADP
fuelectenerg-1427	698	22	figure	figure	NOUN
fuelectenerg-1427	698	23	5	5	NUM
fuelectenerg-1427	698	24	.	.	PUNCT
fuelectenerg-1427	698	25	by	by	ADP
fuelectenerg-1427	698	26	observing	observe	VERB
fuelectenerg-1427	698	27	figure	figure	NOUN
fuelectenerg-1427	698	28	5	5	NUM
fuelectenerg-1427	698	29	,	,	PUNCT
fuelectenerg-1427	698	30	we	we	PRON
fuelectenerg-1427	698	31	can	can	AUX
fuelectenerg-1427	698	32	generate	generate	VERB
fuelectenerg-1427	698	33	the	the	DET
fuelectenerg-1427	698	34	corresponding	corresponding	ADJ
fuelectenerg-1427	698	35	flattened	flatten	VERB
fuelectenerg-1427	698	36	forms	form	NOUN
fuelectenerg-1427	698	37	by	by	ADP
fuelectenerg-1427	698	38	two	two	NUM
fuelectenerg-1427	698	39	methods	method	NOUN
fuelectenerg-1427	698	40	.	.	PUNCT
fuelectenerg-1427	699	1	a	a	DET
fuelectenerg-1427	699	2	classical	classical	ADJ
fuelectenerg-1427	699	3	method	method	NOUN
fuelectenerg-1427	699	4	,	,	PUNCT
fuelectenerg-1427	699	5	per	per	ADP
fuelectenerg-1427	699	6	analogy	analogy	NOUN
fuelectenerg-1427	699	7	with	with	ADP
fuelectenerg-1427	699	8	well	well	ADV
fuelectenerg-1427	699	9	-	-	PUNCT
fuelectenerg-1427	699	10	known	know	VERB
fuelectenerg-1427	699	11	binary	binary	ADJ
fuelectenerg-1427	699	12	forms	form	NOUN
fuelectenerg-1427	699	13	,	,	PUNCT
fuelectenerg-1427	699	14	would	would	AUX
fuelectenerg-1427	699	15	be	be	AUX
fuelectenerg-1427	699	16	to	to	PART
fuelectenerg-1427	699	17	create	create	VERB
fuelectenerg-1427	699	18	every	every	DET
fuelectenerg-1427	699	19	transform	transform	NOUN
fuelectenerg-1427	699	20	matrix	matrix	NOUN
fuelectenerg-1427	699	21	for	for	ADP
fuelectenerg-1427	699	22	every	every	DET
fuelectenerg-1427	699	23	tif	tif	PROPN
fuelectenerg-1427	699	24	s	s	PROPN
fuelectenerg-1427	699	25	/	/	SYM
fuelectenerg-1427	699	26	d	d	NOUN
fuelectenerg-1427	699	27	tree	tree	NOUN
fuelectenerg-1427	699	28	and	and	CCONJ
fuelectenerg-1427	699	29	then	then	ADV
fuelectenerg-1427	699	30	expand	expand	VERB
fuelectenerg-1427	699	31	using	use	VERB
fuelectenerg-1427	699	32	that	that	DET
fuelectenerg-1427	699	33	transform	transform	NOUN
fuelectenerg-1427	699	34	matrix	matrix	NOUN
fuelectenerg-1427	699	35	.	.	PUNCT
fuelectenerg-1427	700	1	a	a	DET
fuelectenerg-1427	700	2	better	well	ADJ
fuelectenerg-1427	700	3	method	method	NOUN
fuelectenerg-1427	700	4	is	be	AUX
fuelectenerg-1427	700	5	to	to	PART
fuelectenerg-1427	700	6	create	create	VERB
fuelectenerg-1427	700	7	one	one	NUM
fuelectenerg-1427	700	8	flattened	flatten	VERB
fuelectenerg-1427	700	9	108	108	NUM
fuelectenerg-1427	700	10	an	an	DET
fuelectenerg-1427	700	11	extended	extend	VERB
fuelectenerg-1427	700	12	green	green	ADJ
fuelectenerg-1427	700	13	sasao	sasao	PROPN
fuelectenerg-1427	700	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	700	15	of	of	ADP
fuelectenerg-1427	700	16	canonical	canonical	ADJ
fuelectenerg-1427	700	17	ternary	ternary	ADJ
fuelectenerg-1427	700	18	galois	galois	NOUN
fuelectenerg-1427	700	19	forms	form	NOUN
fuelectenerg-1427	700	20	...	...	PUNCT
fuelectenerg-1427	700	21	s	s	VERB
fuelectenerg-1427	700	22	a	a	PRON
fuelectenerg-1427	700	23	’	'	PUNCT
fuelectenerg-1427	700	24	a	a	PRON
fuelectenerg-1427	700	25	(	(	PUNCT
fuelectenerg-1427	700	26	)	)	PUNCT
fuelectenerg-1427	700	27	a	a	PRON
fuelectenerg-1427	700	28	pd	pd	PROPN
fuelectenerg-1427	700	29	1	1	NUM
fuelectenerg-1427	700	30	a	a	PRON
fuelectenerg-1427	700	31	(	(	PUNCT
fuelectenerg-1427	700	32	)	)	PUNCT
fuelectenerg-1427	700	33	b	b	NOUN
fuelectenerg-1427	700	34	nd	nd	ADP
fuelectenerg-1427	700	35	1	1	NUM
fuelectenerg-1427	700	36	a	a	PRON
fuelectenerg-1427	700	37	’	'	PUNCT
fuelectenerg-1427	700	38	d	d	ADP
fuelectenerg-1427	700	39	1	1	NUM
fuelectenerg-1427	700	40	a	a	PRON
fuelectenerg-1427	700	41	(	(	PUNCT
fuelectenerg-1427	700	42	)	)	PUNCT
fuelectenerg-1427	700	43	d	d	NOUN
fuelectenerg-1427	700	44	(	(	PUNCT
fuelectenerg-1427	700	45	)	)	PUNCT
fuelectenerg-1427	700	46	c	c	NOUN
fuelectenerg-1427	700	47	figure	figure	VERB
fuelectenerg-1427	700	48	3	3	NUM
fuelectenerg-1427	700	49	:	:	PUNCT
fuelectenerg-1427	700	50	two	two	NUM
fuelectenerg-1427	700	51	-	-	PUNCT
fuelectenerg-1427	700	52	valued	value	VERB
fuelectenerg-1427	700	53	nodes	node	NOUN
fuelectenerg-1427	700	54	:	:	PUNCT
fuelectenerg-1427	700	55	(	(	PUNCT
fuelectenerg-1427	700	56	a	a	X
fuelectenerg-1427	700	57	)	)	PUNCT
fuelectenerg-1427	700	58	shannon	shannon	NOUN
fuelectenerg-1427	700	59	,	,	PUNCT
fuelectenerg-1427	700	60	(	(	PUNCT
fuelectenerg-1427	700	61	b	b	NOUN
fuelectenerg-1427	700	62	)	)	PUNCT
fuelectenerg-1427	700	63	positive	positive	ADJ
fuelectenerg-1427	700	64	davio	davio	NOUN
fuelectenerg-1427	700	65	,	,	PUNCT
fuelectenerg-1427	700	66	(	(	PUNCT
fuelectenerg-1427	700	67	c	c	NOUN
fuelectenerg-1427	700	68	)	)	PUNCT
fuelectenerg-1427	700	69	negative	negative	ADJ
fuelectenerg-1427	700	70	davio	davio	NOUN
fuelectenerg-1427	700	71	,	,	PUNCT
fuelectenerg-1427	700	72	and	and	CCONJ
fuelectenerg-1427	700	73	(	(	PUNCT
fuelectenerg-1427	700	74	d	d	X
fuelectenerg-1427	700	75	)	)	PUNCT
fuelectenerg-1427	700	76	generalized	generalized	ADJ
fuelectenerg-1427	700	77	davio	davio	NOUN
fuelectenerg-1427	700	78	where	where	SCONJ
fuelectenerg-1427	700	79	a	a	DET
fuelectenerg-1427	700	80	∈	∈	NOUN
fuelectenerg-1427	700	81	{	{	PUNCT
fuelectenerg-1427	700	82	a	a	PRON
fuelectenerg-1427	700	83	,	,	PUNCT
fuelectenerg-1427	700	84	a′	a′	PROPN
fuelectenerg-1427	700	85	}	}	PUNCT
fuelectenerg-1427	700	86	.	.	PUNCT
fuelectenerg-1427	701	1	variable	variable	ADJ
fuelectenerg-1427	701	2	,	,	PUNCT
fuelectenerg-1427	701	3	that	that	PRON
fuelectenerg-1427	701	4	is	be	AUX
fuelectenerg-1427	701	5	one	one	NUM
fuelectenerg-1427	701	6	tree	tree	NOUN
fuelectenerg-1427	701	7	level	level	NOUN
fuelectenerg-1427	701	8	,	,	PUNCT
fuelectenerg-1427	701	9	figure	figure	NOUN
fuelectenerg-1427	701	10	4	4	NUM
fuelectenerg-1427	701	11	represents	represent	VERB
fuelectenerg-1427	701	12	the	the	DET
fuelectenerg-1427	701	13	expansion	expansion	NOUN
fuelectenerg-1427	701	14	nodes	node	NOUN
fuelectenerg-1427	701	15	for	for	ADP
fuelectenerg-1427	701	16	ternary	ternary	ADJ
fuelectenerg-1427	701	17	shannon	shannon	NOUN
fuelectenerg-1427	701	18	,	,	PUNCT
fuelectenerg-1427	701	19	davio	davio	NOUN
fuelectenerg-1427	701	20	and	and	CCONJ
fuelectenerg-1427	701	21	generalized	generalized	ADJ
fuelectenerg-1427	701	22	davio	davio	NOUN
fuelectenerg-1427	701	23	(	(	PUNCT
fuelectenerg-1427	701	24	d	d	NOUN
fuelectenerg-1427	701	25	)	)	PUNCT
fuelectenerg-1427	701	26	,	,	PUNCT
fuelectenerg-1427	701	27	respectively	respectively	ADV
fuelectenerg-1427	701	28	.	.	PUNCT
fuelectenerg-1427	702	1	s	s	PART
fuelectenerg-1427	702	2	0	0	NUM
fuelectenerg-1427	702	3	x	x	SYM
fuelectenerg-1427	702	4	1	1	NUM
fuelectenerg-1427	702	5	x	x	SYM
fuelectenerg-1427	702	6	2	2	NUM
fuelectenerg-1427	702	7	x	x	SYM
fuelectenerg-1427	702	8	(	(	PUNCT
fuelectenerg-1427	702	9	a	a	PRON
fuelectenerg-1427	702	10	)	)	PUNCT
fuelectenerg-1427	702	11	d0	d0	NOUN
fuelectenerg-1427	702	12	1	1	NUM
fuelectenerg-1427	702	13	x	x	SYM
fuelectenerg-1427	702	14	2	2	NUM
fuelectenerg-1427	702	15	(	(	PUNCT
fuelectenerg-1427	702	16	b	b	NOUN
fuelectenerg-1427	702	17	)	)	PUNCT
fuelectenerg-1427	702	18	d2	d2	PROPN
fuelectenerg-1427	702	19	1	1	NUM
fuelectenerg-1427	702	20	(	(	PUNCT
fuelectenerg-1427	702	21	d	d	NOUN
fuelectenerg-1427	702	22	)	)	PUNCT
fuelectenerg-1427	703	1	d	d	NOUN
fuelectenerg-1427	703	2	1	1	NUM
fuelectenerg-1427	703	3	(	(	PUNCT
fuelectenerg-1427	703	4	e	e	NOUN
fuelectenerg-1427	703	5	)	)	PUNCT
fuelectenerg-1427	703	6	d1	d1	NOUN
fuelectenerg-1427	703	7	1	1	NUM
fuelectenerg-1427	703	8	(	(	PUNCT
fuelectenerg-1427	703	9	’	'	PUNCT
fuelectenerg-1427	703	10	)	)	PUNCT
fuelectenerg-1427	703	11	x	x	SYM
fuelectenerg-1427	703	12	2	2	NUM
fuelectenerg-1427	703	13	(	(	PUNCT
fuelectenerg-1427	703	14	’’	’'	PUNCT
fuelectenerg-1427	703	15	)	)	PUNCT
fuelectenerg-1427	703	16	x	x	SYM
fuelectenerg-1427	703	17	2	2	NUM
fuelectenerg-1427	703	18	(	(	PUNCT
fuelectenerg-1427	703	19	)	)	PUNCT
fuelectenerg-1427	703	20	x	x	SYM
fuelectenerg-1427	703	21	2	2	NUM
fuelectenerg-1427	703	22	(	(	PUNCT
fuelectenerg-1427	703	23	c	c	NOUN
fuelectenerg-1427	703	24	)	)	PUNCT
fuelectenerg-1427	703	25	x	x	SYM
fuelectenerg-1427	703	26	xx	xx	X
fuelectenerg-1427	703	27	’	'	PUNCT
fuelectenerg-1427	703	28	x	x	NOUN
fuelectenerg-1427	703	29	’’	’'	PUNCT
fuelectenerg-1427	703	30	figure	figure	VERB
fuelectenerg-1427	703	31	4	4	NUM
fuelectenerg-1427	703	32	:	:	PUNCT
fuelectenerg-1427	703	33	ternary	ternary	ADJ
fuelectenerg-1427	703	34	nodes	node	NOUN
fuelectenerg-1427	703	35	for	for	ADP
fuelectenerg-1427	703	36	ternary	ternary	ADJ
fuelectenerg-1427	703	37	decision	decision	NOUN
fuelectenerg-1427	703	38	trees	tree	NOUN
fuelectenerg-1427	703	39	:	:	PUNCT
fuelectenerg-1427	703	40	(	(	PUNCT
fuelectenerg-1427	703	41	a	a	X
fuelectenerg-1427	703	42	)	)	PUNCT
fuelectenerg-1427	703	43	shannon	shannon	NOUN
fuelectenerg-1427	703	44	,	,	PUNCT
fuelectenerg-1427	703	45	(	(	PUNCT
fuelectenerg-1427	703	46	b	b	X
fuelectenerg-1427	703	47	)	)	PUNCT
fuelectenerg-1427	703	48	davio0	davio0	PROPN
fuelectenerg-1427	703	49	,	,	PUNCT
fuelectenerg-1427	703	50	(	(	PUNCT
fuelectenerg-1427	703	51	c	c	X
fuelectenerg-1427	703	52	)	)	PUNCT
fuelectenerg-1427	703	53	davio1	davio1	NOUN
fuelectenerg-1427	703	54	,	,	PUNCT
fuelectenerg-1427	703	55	(	(	PUNCT
fuelectenerg-1427	703	56	d	d	NOUN
fuelectenerg-1427	703	57	)	)	PUNCT
fuelectenerg-1427	703	58	davio2	davio2	PROPN
fuelectenerg-1427	703	59	,	,	PUNCT
fuelectenerg-1427	703	60	and	and	CCONJ
fuelectenerg-1427	703	61	(	(	PUNCT
fuelectenerg-1427	703	62	e	e	NOUN
fuelectenerg-1427	703	63	)	)	PUNCT
fuelectenerg-1427	703	64	generalized	generalized	ADJ
fuelectenerg-1427	703	65	davio	davio	NOUN
fuelectenerg-1427	703	66	(	(	PUNCT
fuelectenerg-1427	703	67	d	d	NOUN
fuelectenerg-1427	703	68	)	)	PUNCT
fuelectenerg-1427	703	69	where	where	SCONJ
fuelectenerg-1427	703	70	x	x	SYM
fuelectenerg-1427	703	71	∈	∈	PROPN
fuelectenerg-1427	703	72	{	{	PUNCT
fuelectenerg-1427	703	73	x	x	NOUN
fuelectenerg-1427	703	74	,	,	PUNCT
fuelectenerg-1427	703	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	703	76	}	}	PUNCT
fuelectenerg-1427	703	77	.	.	PUNCT
fuelectenerg-1427	704	1	in	in	ADP
fuelectenerg-1427	704	2	correspondence	correspondence	NOUN
fuelectenerg-1427	704	3	to	to	ADP
fuelectenerg-1427	704	4	the	the	DET
fuelectenerg-1427	704	5	binary	binary	PROPN
fuelectenerg-1427	704	6	s	s	PROPN
fuelectenerg-1427	704	7	/	/	SYM
fuelectenerg-1427	704	8	d	d	NOUN
fuelectenerg-1427	704	9	trees	tree	NOUN
fuelectenerg-1427	704	10	,	,	PUNCT
fuelectenerg-1427	704	11	one	one	PRON
fuelectenerg-1427	704	12	can	can	AUX
fuelectenerg-1427	704	13	produce	produce	VERB
fuelectenerg-1427	704	14	ternary	ternary	ADJ
fuelectenerg-1427	704	15	s	s	NOUN
fuelectenerg-1427	704	16	/	/	SYM
fuelectenerg-1427	704	17	d	d	NOUN
fuelectenerg-1427	704	18	trees	tree	NOUN
fuelectenerg-1427	704	19	.	.	PUNCT
fuelectenerg-1427	705	1	to	to	PART
fuelectenerg-1427	705	2	define	define	VERB
fuelectenerg-1427	705	3	the	the	DET
fuelectenerg-1427	705	4	ternary	ternary	ADJ
fuelectenerg-1427	705	5	s	s	NOUN
fuelectenerg-1427	705	6	/	/	SYM
fuelectenerg-1427	705	7	d	d	NOUN
fuelectenerg-1427	705	8	trees	tree	NOUN
fuelectenerg-1427	705	9	,	,	PUNCT
fuelectenerg-1427	705	10	we	we	PRON
fuelectenerg-1427	705	11	define	define	VERB
fuelectenerg-1427	705	12	the	the	DET
fuelectenerg-1427	705	13	generalized	generalized	ADJ
fuelectenerg-1427	705	14	davio	davio	NOUN
fuelectenerg-1427	705	15	node	node	NOUN
fuelectenerg-1427	705	16	over	over	ADP
fuelectenerg-1427	705	17	ternary	ternary	ADJ
fuelectenerg-1427	705	18	galois	galois	PROPN
fuelectenerg-1427	705	19	radix	radix	NOUN
fuelectenerg-1427	705	20	as	as	SCONJ
fuelectenerg-1427	705	21	shown	show	VERB
fuelectenerg-1427	705	22	in	in	ADP
fuelectenerg-1427	705	23	figure	figure	NOUN
fuelectenerg-1427	705	24	4(e	4(e	NUM
fuelectenerg-1427	705	25	)	)	PUNCT
fuelectenerg-1427	705	26	.	.	PUNCT
fuelectenerg-1427	706	1	our	our	PRON
fuelectenerg-1427	706	2	notation	notation	NOUN
fuelectenerg-1427	706	3	here	here	ADV
fuelectenerg-1427	706	4	is	be	AUX
fuelectenerg-1427	706	5	that	that	PRON
fuelectenerg-1427	706	6	(	(	PUNCT
fuelectenerg-1427	706	7	x	x	X
fuelectenerg-1427	706	8	)	)	PUNCT
fuelectenerg-1427	706	9	corresponds	correspond	VERB
fuelectenerg-1427	706	10	to	to	ADP
fuelectenerg-1427	706	11	the	the	DET
fuelectenerg-1427	706	12	three	three	NUM
fuelectenerg-1427	706	13	possible	possible	ADJ
fuelectenerg-1427	706	14	shifts	shift	NOUN
fuelectenerg-1427	706	15	of	of	ADP
fuelectenerg-1427	706	16	the	the	DET
fuelectenerg-1427	706	17	variable	variable	NOUN
fuelectenerg-1427	706	18	x	x	NOUN
fuelectenerg-1427	706	19	as	as	SCONJ
fuelectenerg-1427	706	20	follows	follow	VERB
fuelectenerg-1427	706	21	:	:	PUNCT
fuelectenerg-1427	706	22	x	x	SYM
fuelectenerg-1427	706	23	∈	∈	NOUN
fuelectenerg-1427	706	24	{	{	PUNCT
fuelectenerg-1427	706	25	x	x	NOUN
fuelectenerg-1427	706	26	,	,	PUNCT
fuelectenerg-1427	706	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	706	28	}	}	PUNCT
fuelectenerg-1427	706	29	,	,	PUNCT
fuelectenerg-1427	706	30	over	over	ADP
fuelectenerg-1427	706	31	gf(3	gf(3	PROPN
fuelectenerg-1427	706	32	)	)	PUNCT
fuelectenerg-1427	706	33	.	.	PUNCT
fuelectenerg-1427	707	1	(	(	PUNCT
fuelectenerg-1427	707	2	28	28	NUM
fuelectenerg-1427	707	3	)	)	PUNCT
fuelectenerg-1427	707	4	definition	definition	NOUN
fuelectenerg-1427	707	5	1	1	NUM
fuelectenerg-1427	707	6	.	.	PUNCT
fuelectenerg-1427	708	1	the	the	DET
fuelectenerg-1427	708	2	ternary	ternary	ADJ
fuelectenerg-1427	708	3	tree	tree	NOUN
fuelectenerg-1427	708	4	with	with	ADP
fuelectenerg-1427	708	5	ternary	ternary	ADJ
fuelectenerg-1427	708	6	shannon	shannon	NOUN
fuelectenerg-1427	708	7	and	and	CCONJ
fuelectenerg-1427	708	8	ternary	ternary	ADJ
fuelectenerg-1427	708	9	generalized	generalized	ADJ
fuelectenerg-1427	708	10	davio	davio	NOUN
fuelectenerg-1427	708	11	nodes	node	NOUN
fuelectenerg-1427	708	12	,	,	PUNCT
fuelectenerg-1427	708	13	that	that	PRON
fuelectenerg-1427	708	14	generates	generate	VERB
fuelectenerg-1427	708	15	other	other	ADJ
fuelectenerg-1427	708	16	ternary	ternary	ADJ
fuelectenerg-1427	708	17	trees	tree	NOUN
fuelectenerg-1427	708	18	,	,	PUNCT
fuelectenerg-1427	708	19	is	be	AUX
fuelectenerg-1427	708	20	called	call	VERB
fuelectenerg-1427	708	21	ternary	ternary	ADJ
fuelectenerg-1427	708	22	shannon	shannon	NOUN
fuelectenerg-1427	708	23	-	-	PUNCT
fuelectenerg-1427	708	24	davio	davio	NOUN
fuelectenerg-1427	708	25	(	(	PUNCT
fuelectenerg-1427	708	26	s	s	NOUN
fuelectenerg-1427	708	27	/	/	SYM
fuelectenerg-1427	708	28	d	d	NOUN
fuelectenerg-1427	708	29	)	)	PUNCT
fuelectenerg-1427	708	30	tree	tree	NOUN
fuelectenerg-1427	708	31	.	.	PUNCT
fuelectenerg-1427	709	1	utilizing	utilize	VERB
fuelectenerg-1427	709	2	the	the	DET
fuelectenerg-1427	709	3	definition	definition	NOUN
fuelectenerg-1427	709	4	of	of	ADP
fuelectenerg-1427	709	5	ternary	ternary	ADJ
fuelectenerg-1427	709	6	shannon	shannon	NOUN
fuelectenerg-1427	709	7	in	in	ADP
fuelectenerg-1427	709	8	figure	figure	NOUN
fuelectenerg-1427	709	9	4(a	4(a	NUM
fuelectenerg-1427	709	10	)	)	PUNCT
fuelectenerg-1427	709	11	and	and	CCONJ
fuelectenerg-1427	709	12	ternary	ternary	ADJ
fuelectenerg-1427	709	13	generalized	generalized	ADJ
fuelectenerg-1427	709	14	davio	davio	NOUN
fuelectenerg-1427	709	15	in	in	ADP
fuelectenerg-1427	709	16	figure	figure	NOUN
fuelectenerg-1427	709	17	4(e	4(e	NUM
fuelectenerg-1427	709	18	)	)	PUNCT
fuelectenerg-1427	709	19	,	,	PUNCT
fuelectenerg-1427	709	20	we	we	PRON
fuelectenerg-1427	709	21	obtain	obtain	VERB
fuelectenerg-1427	709	22	the	the	DET
fuelectenerg-1427	709	23	ternary	ternary	ADJ
fuelectenerg-1427	709	24	shannon	shannon	NOUN
fuelectenerg-1427	709	25	-	-	PUNCT
fuelectenerg-1427	709	26	davio	davio	NOUN
fuelectenerg-1427	709	27	trees	tree	NOUN
fuelectenerg-1427	709	28	(	(	PUNCT
fuelectenerg-1427	709	29	ternary	ternary	NOUN
fuelectenerg-1427	709	30	s	s	PROPN
fuelectenerg-1427	709	31	/	/	SYM
fuelectenerg-1427	709	32	d	d	NOUN
fuelectenerg-1427	709	33	trees	tree	NOUN
fuelectenerg-1427	709	34	)	)	PUNCT
fuelectenerg-1427	709	35	for	for	ADP
fuelectenerg-1427	709	36	two	two	NUM
fuelectenerg-1427	709	37	variables	variable	NOUN
fuelectenerg-1427	709	38	as	as	SCONJ
fuelectenerg-1427	709	39	shown	show	VERB
fuelectenerg-1427	709	40	in	in	ADP
fuelectenerg-1427	709	41	figure	figure	NOUN
fuelectenerg-1427	709	42	5	5	NUM
fuelectenerg-1427	709	43	.	.	PUNCT
fuelectenerg-1427	709	44	from	from	ADP
fuelectenerg-1427	709	45	the	the	DET
fuelectenerg-1427	709	46	ternary	ternary	ADJ
fuelectenerg-1427	709	47	s	s	PROPN
fuelectenerg-1427	709	48	/	/	SYM
fuelectenerg-1427	709	49	d	d	ADJ
fuelectenerg-1427	709	50	dts	dts	NOUN
fuelectenerg-1427	709	51	shown	show	VERB
fuelectenerg-1427	709	52	in	in	ADP
fuelectenerg-1427	709	53	figure	figure	NOUN
fuelectenerg-1427	709	54	5	5	NUM
fuelectenerg-1427	709	55	,	,	PUNCT
fuelectenerg-1427	709	56	if	if	SCONJ
fuelectenerg-1427	709	57	we	we	PRON
fuelectenerg-1427	709	58	take	take	VERB
fuelectenerg-1427	709	59	any	any	DET
fuelectenerg-1427	709	60	s	s	PROPN
fuelectenerg-1427	709	61	/	/	SYM
fuelectenerg-1427	709	62	d	d	NOUN
fuelectenerg-1427	709	63	tree	tree	NOUN
fuelectenerg-1427	709	64	and	and	CCONJ
fuelectenerg-1427	709	65	multiply	multiply	VERB
fuelectenerg-1427	709	66	the	the	DET
fuelectenerg-1427	709	67	second	second	ADJ
fuelectenerg-1427	709	68	-	-	PUNCT
fuelectenerg-1427	709	69	level	level	NOUN
fuelectenerg-1427	709	70	cofactors	cofactor	NOUN
fuelectenerg-1427	709	71	(	(	PUNCT
fuelectenerg-1427	709	72	which	which	PRON
fuelectenerg-1427	709	73	are	be	AUX
fuelectenerg-1427	709	74	in	in	ADP
fuelectenerg-1427	709	75	the	the	DET
fuelectenerg-1427	709	76	tdt	tdt	PROPN
fuelectenerg-1427	709	77	leaves	leave	NOUN
fuelectenerg-1427	709	78	)	)	PUNCT
fuelectenerg-1427	709	79	each	each	PRON
fuelectenerg-1427	709	80	by	by	ADP
fuelectenerg-1427	709	81	the	the	DET
fuelectenerg-1427	709	82	corresponding	corresponding	ADJ
fuelectenerg-1427	709	83	path	path	NOUN
fuelectenerg-1427	709	84	in	in	ADP
fuelectenerg-1427	709	85	that	that	DET
fuelectenerg-1427	709	86	tdt	tdt	PROPN
fuelectenerg-1427	709	87	,	,	PUNCT
fuelectenerg-1427	709	88	and	and	CCONJ
fuelectenerg-1427	709	89	sum	sum	VERB
fuelectenerg-1427	709	90	all	all	DET
fuelectenerg-1427	709	91	the	the	DET
fuelectenerg-1427	709	92	resulting	result	VERB
fuelectenerg-1427	709	93	cubes	cube	NOUN
fuelectenerg-1427	709	94	(	(	PUNCT
fuelectenerg-1427	709	95	terms	term	NOUN
fuelectenerg-1427	709	96	)	)	PUNCT
fuelectenerg-1427	709	97	over	over	ADP
fuelectenerg-1427	709	98	gf(3	gf(3	PROPN
fuelectenerg-1427	709	99	)	)	PUNCT
fuelectenerg-1427	709	100	,	,	PUNCT
fuelectenerg-1427	709	101	we	we	PRON
fuelectenerg-1427	709	102	obtain	obtain	VERB
fuelectenerg-1427	709	103	the	the	DET
fuelectenerg-1427	709	104	flattened	flatten	VERB
fuelectenerg-1427	709	105	form	form	NOUN
fuelectenerg-1427	709	106	of	of	ADP
fuelectenerg-1427	709	107	the	the	DET
fuelectenerg-1427	709	108	function	function	NOUN
fuelectenerg-1427	709	109	f	f	PROPN
fuelectenerg-1427	709	110	,	,	PUNCT
fuelectenerg-1427	709	111	as	as	ADP
fuelectenerg-1427	709	112	a	a	DET
fuelectenerg-1427	709	113	certain	certain	ADJ
fuelectenerg-1427	709	114	gfsop	gfsop	NOUN
fuelectenerg-1427	709	115	expression	expression	NOUN
fuelectenerg-1427	709	116	.	.	PUNCT
fuelectenerg-1427	710	1	for	for	ADP
fuelectenerg-1427	710	2	each	each	DET
fuelectenerg-1427	710	3	tdt	tdt	PROPN
fuelectenerg-1427	710	4	in	in	ADP
fuelectenerg-1427	710	5	figure	figure	NOUN
fuelectenerg-1427	710	6	5	5	NUM
fuelectenerg-1427	710	7	,	,	PUNCT
fuelectenerg-1427	710	8	there	there	PRON
fuelectenerg-1427	710	9	are	be	VERB
fuelectenerg-1427	710	10	as	as	ADV
fuelectenerg-1427	710	11	many	many	ADJ
fuelectenerg-1427	710	12	forms	form	NOUN
fuelectenerg-1427	710	13	obtained	obtain	VERB
fuelectenerg-1427	710	14	for	for	ADP
fuelectenerg-1427	710	15	the	the	DET
fuelectenerg-1427	710	16	function	function	NOUN
fuelectenerg-1427	710	17	f	f	PROPN
fuelectenerg-1427	710	18	as	as	ADP
fuelectenerg-1427	710	19	the	the	DET
fuelectenerg-1427	710	20	number	number	NOUN
fuelectenerg-1427	710	21	of	of	ADP
fuelectenerg-1427	710	22	possible	possible	ADJ
fuelectenerg-1427	710	23	permutations	permutation	NOUN
fuelectenerg-1427	710	24	of	of	ADP
fuelectenerg-1427	710	25	the	the	DET
fuelectenerg-1427	710	26	polarities	polarity	NOUN
fuelectenerg-1427	710	27	of	of	ADP
fuelectenerg-1427	710	28	the	the	DET
fuelectenerg-1427	710	29	variables	variable	NOUN
fuelectenerg-1427	710	30	in	in	ADP
fuelectenerg-1427	710	31	the	the	DET
fuelectenerg-1427	710	32	second	second	ADJ
fuelectenerg-1427	710	33	-	-	PUNCT
fuelectenerg-1427	710	34	level	level	NOUN
fuelectenerg-1427	710	35	branches	branch	NOUN
fuelectenerg-1427	710	36	of	of	ADP
fuelectenerg-1427	710	37	each	each	DET
fuelectenerg-1427	710	38	tdt	tdt	PROPN
fuelectenerg-1427	710	39	.	.	PUNCT
fuelectenerg-1427	711	1	definition	definition	NOUN
fuelectenerg-1427	711	2	2	2	NUM
fuelectenerg-1427	711	3	.	.	PUNCT
fuelectenerg-1427	712	1	the	the	DET
fuelectenerg-1427	712	2	family	family	NOUN
fuelectenerg-1427	712	3	of	of	ADP
fuelectenerg-1427	712	4	all	all	DET
fuelectenerg-1427	712	5	possible	possible	ADJ
fuelectenerg-1427	712	6	forms	form	NOUN
fuelectenerg-1427	712	7	obtained	obtain	VERB
fuelectenerg-1427	712	8	per	per	ADP
fuelectenerg-1427	712	9	ternary	ternary	NOUN
fuelectenerg-1427	712	10	s	s	PROPN
fuelectenerg-1427	712	11	/	/	SYM
fuelectenerg-1427	712	12	d	d	NOUN
fuelectenerg-1427	712	13	tree	tree	NOUN
fuelectenerg-1427	712	14	is	be	AUX
fuelectenerg-1427	712	15	called	call	VERB
fuelectenerg-1427	712	16	ternary	ternary	ADJ
fuelectenerg-1427	712	17	inclusive	inclusive	ADJ
fuelectenerg-1427	712	18	forms	form	NOUN
fuelectenerg-1427	712	19	(	(	PUNCT
fuelectenerg-1427	712	20	tifs	tifs	PROPN
fuelectenerg-1427	712	21	)	)	PUNCT
fuelectenerg-1427	712	22	.	.	PUNCT
fuelectenerg-1427	713	1	the	the	DET
fuelectenerg-1427	713	2	numbers	number	NOUN
fuelectenerg-1427	713	3	of	of	ADP
fuelectenerg-1427	713	4	these	these	DET
fuelectenerg-1427	713	5	tifs	tif	NOUN
fuelectenerg-1427	713	6	per	per	ADP
fuelectenerg-1427	713	7	tdt	tdt	PROPN
fuelectenerg-1427	713	8	for	for	ADP
fuelectenerg-1427	713	9	two	two	NUM
fuelectenerg-1427	713	10	variables	variable	NOUN
fuelectenerg-1427	713	11	are	be	AUX
fuelectenerg-1427	713	12	shown	show	VERB
fuelectenerg-1427	713	13	on	on	ADP
fuelectenerg-1427	713	14	top	top	NOUN
fuelectenerg-1427	713	15	of	of	ADP
fuelectenerg-1427	713	16	each	each	DET
fuelectenerg-1427	713	17	s	s	PROPN
fuelectenerg-1427	713	18	/	/	SYM
fuelectenerg-1427	713	19	d	d	PROPN
fuelectenerg-1427	713	20	tdt	tdt	PROPN
fuelectenerg-1427	713	21	in	in	ADP
fuelectenerg-1427	713	22	figure	figure	NOUN
fuelectenerg-1427	713	23	5	5	NUM
fuelectenerg-1427	713	24	.	.	PUNCT
fuelectenerg-1427	713	25	by	by	ADP
fuelectenerg-1427	713	26	observing	observe	VERB
fuelectenerg-1427	713	27	figure	figure	NOUN
fuelectenerg-1427	713	28	5	5	NUM
fuelectenerg-1427	713	29	,	,	PUNCT
fuelectenerg-1427	713	30	we	we	PRON
fuelectenerg-1427	713	31	can	can	AUX
fuelectenerg-1427	713	32	generate	generate	VERB
fuelectenerg-1427	713	33	the	the	DET
fuelectenerg-1427	713	34	corresponding	corresponding	ADJ
fuelectenerg-1427	713	35	flattened	flatten	VERB
fuelectenerg-1427	713	36	forms	form	NOUN
fuelectenerg-1427	713	37	by	by	ADP
fuelectenerg-1427	713	38	two	two	NUM
fuelectenerg-1427	713	39	methods	method	NOUN
fuelectenerg-1427	713	40	.	.	PUNCT
fuelectenerg-1427	714	1	a	a	DET
fuelectenerg-1427	714	2	classical	classical	ADJ
fuelectenerg-1427	714	3	method	method	NOUN
fuelectenerg-1427	714	4	,	,	PUNCT
fuelectenerg-1427	714	5	per	per	ADP
fuelectenerg-1427	714	6	analogy	analogy	NOUN
fuelectenerg-1427	714	7	with	with	ADP
fuelectenerg-1427	714	8	well	well	ADV
fuelectenerg-1427	714	9	-	-	PUNCT
fuelectenerg-1427	714	10	known	know	VERB
fuelectenerg-1427	714	11	binary	binary	ADJ
fuelectenerg-1427	714	12	forms	form	NOUN
fuelectenerg-1427	714	13	,	,	PUNCT
fuelectenerg-1427	714	14	would	would	AUX
fuelectenerg-1427	714	15	be	be	AUX
fuelectenerg-1427	714	16	to	to	PART
fuelectenerg-1427	714	17	create	create	VERB
fuelectenerg-1427	714	18	every	every	DET
fuelectenerg-1427	714	19	transform	transform	NOUN
fuelectenerg-1427	714	20	matrix	matrix	NOUN
fuelectenerg-1427	714	21	for	for	ADP
fuelectenerg-1427	714	22	every	every	DET
fuelectenerg-1427	714	23	tif	tif	PROPN
fuelectenerg-1427	714	24	s	s	PROPN
fuelectenerg-1427	714	25	/	/	SYM
fuelectenerg-1427	714	26	d	d	NOUN
fuelectenerg-1427	714	27	tree	tree	NOUN
fuelectenerg-1427	714	28	and	and	CCONJ
fuelectenerg-1427	714	29	then	then	ADV
fuelectenerg-1427	714	30	expand	expand	VERB
fuelectenerg-1427	714	31	using	use	VERB
fuelectenerg-1427	714	32	that	that	DET
fuelectenerg-1427	714	33	transform	transform	NOUN
fuelectenerg-1427	714	34	matrix	matrix	NOUN
fuelectenerg-1427	714	35	.	.	PUNCT
fuelectenerg-1427	715	1	a	a	DET
fuelectenerg-1427	715	2	better	well	ADJ
fuelectenerg-1427	715	3	method	method	NOUN
fuelectenerg-1427	715	4	is	be	AUX
fuelectenerg-1427	715	5	to	to	PART
fuelectenerg-1427	715	6	create	create	VERB
fuelectenerg-1427	715	7	one	one	NUM
fuelectenerg-1427	715	8	flattened	flatten	VERB
fuelectenerg-1427	715	9	108	108	NUM
fuelectenerg-1427	715	10	an	an	DET
fuelectenerg-1427	715	11	extended	extend	VERB
fuelectenerg-1427	715	12	green	green	ADJ
fuelectenerg-1427	715	13	sasao	sasao	PROPN
fuelectenerg-1427	715	14	hierarchy	hierarchy	NOUN
fuelectenerg-1427	715	15	of	of	ADP
fuelectenerg-1427	715	16	canonical	canonical	ADJ
fuelectenerg-1427	715	17	ternary	ternary	ADJ
fuelectenerg-1427	715	18	galois	galois	NOUN
fuelectenerg-1427	715	19	forms	form	NOUN
fuelectenerg-1427	715	20	...	...	PUNCT
fuelectenerg-1427	715	21	form	form	NOUN
fuelectenerg-1427	715	22	which	which	PRON
fuelectenerg-1427	715	23	is	be	AUX
fuelectenerg-1427	715	24	an	an	DET
fuelectenerg-1427	715	25	expansion	expansion	NOUN
fuelectenerg-1427	715	26	over	over	ADP
fuelectenerg-1427	715	27	certain	certain	ADJ
fuelectenerg-1427	715	28	transform	transform	NOUN
fuelectenerg-1427	715	29	matrix	matrix	NOUN
fuelectenerg-1427	715	30	(	(	PUNCT
fuelectenerg-1427	715	31	i.e.	i.e.	X
fuelectenerg-1427	715	32	,	,	PUNCT
fuelectenerg-1427	715	33	certain	certain	ADJ
fuelectenerg-1427	715	34	tif	tif	PROPN
fuelectenerg-1427	715	35	)	)	PUNCT
fuelectenerg-1427	715	36	and	and	CCONJ
fuelectenerg-1427	715	37	then	then	ADV
fuelectenerg-1427	715	38	transform	transform	VERB
fuelectenerg-1427	715	39	systematically	systematically	ADV
fuelectenerg-1427	715	40	from	from	ADP
fuelectenerg-1427	715	41	one	one	NUM
fuelectenerg-1427	715	42	form	form	NOUN
fuelectenerg-1427	715	43	to	to	ADP
fuelectenerg-1427	715	44	another	another	DET
fuelectenerg-1427	715	45	form	form	NOUN
fuelectenerg-1427	715	46	without	without	ADP
fuelectenerg-1427	715	47	the	the	DET
fuelectenerg-1427	715	48	need	need	NOUN
fuelectenerg-1427	715	49	to	to	PART
fuelectenerg-1427	715	50	create	create	VERB
fuelectenerg-1427	715	51	all	all	PRON
fuelectenerg-1427	715	52	transform	transform	VERB
fuelectenerg-1427	715	53	matrices	matrix	NOUN
fuelectenerg-1427	715	54	from	from	ADP
fuelectenerg-1427	715	55	the	the	DET
fuelectenerg-1427	715	56	corresponding	correspond	VERB
fuelectenerg-1427	715	57	s	s	PROPN
fuelectenerg-1427	715	58	/	/	SYM
fuelectenerg-1427	715	59	d	d	NOUN
fuelectenerg-1427	715	60	trees	tree	NOUN
fuelectenerg-1427	715	61	.	.	PUNCT
fuelectenerg-1427	716	1	this	this	DET
fuelectenerg-1427	716	2	general	general	ADJ
fuelectenerg-1427	716	3	approach	approach	NOUN
fuelectenerg-1427	716	4	can	can	AUX
fuelectenerg-1427	716	5	lead	lead	VERB
fuelectenerg-1427	716	6	to	to	ADP
fuelectenerg-1427	716	7	several	several	ADJ
fuelectenerg-1427	716	8	algorithms	algorithm	NOUN
fuelectenerg-1427	716	9	of	of	ADP
fuelectenerg-1427	716	10	various	various	ADJ
fuelectenerg-1427	716	11	complexities	complexity	NOUN
fuelectenerg-1427	716	12	that	that	PRON
fuelectenerg-1427	716	13	generalize	generalize	VERB
fuelectenerg-1427	716	14	the	the	DET
fuelectenerg-1427	716	15	existing	exist	VERB
fuelectenerg-1427	716	16	binary	binary	ADJ
fuelectenerg-1427	716	17	algorithms	algorithm	NOUN
fuelectenerg-1427	716	18	to	to	PART
fuelectenerg-1427	716	19	obtain	obtain	VERB
fuelectenerg-1427	716	20	the	the	DET
fuelectenerg-1427	716	21	corresponding	corresponding	ADJ
fuelectenerg-1427	716	22	forms	form	NOUN
fuelectenerg-1427	716	23	such	such	ADJ
fuelectenerg-1427	716	24	as	as	ADP
fuelectenerg-1427	716	25	fprm	fprm	PROPN
fuelectenerg-1427	716	26	,	,	PUNCT
fuelectenerg-1427	716	27	grm	grm	NOUN
fuelectenerg-1427	716	28	and	and	CCONJ
fuelectenerg-1427	716	29	if	if	SCONJ
fuelectenerg-1427	716	30	forms	form	NOUN
fuelectenerg-1427	716	31	.	.	PUNCT
fuelectenerg-1427	716	32	example	example	NOUN
fuelectenerg-1427	717	1	3	3	NUM
fuelectenerg-1427	717	2	.	.	PUNCT
fuelectenerg-1427	717	3	using	use	VERB
fuelectenerg-1427	717	4	the	the	DET
fuelectenerg-1427	717	5	result	result	NOUN
fuelectenerg-1427	717	6	of	of	ADP
fuelectenerg-1427	717	7	example	example	NOUN
fuelectenerg-1427	717	8	2	2	NUM
fuelectenerg-1427	717	9	for	for	ADP
fuelectenerg-1427	717	10	the	the	DET
fuelectenerg-1427	717	11	expansion	expansion	NOUN
fuelectenerg-1427	717	12	of	of	ADP
fuelectenerg-1427	717	13	f	f	PROPN
fuelectenerg-1427	717	14	(	(	PUNCT
fuelectenerg-1427	717	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	717	16	)	)	PUNCT
fuelectenerg-1427	717	17	in	in	ADP
fuelectenerg-1427	717	18	terms	term	NOUN
fuelectenerg-1427	717	19	of	of	ADP
fuelectenerg-1427	717	20	the	the	DET
fuelectenerg-1427	717	21	ternary	ternary	ADJ
fuelectenerg-1427	717	22	shannon	shannon	NOUN
fuelectenerg-1427	717	23	expansion	expansion	NOUN
fuelectenerg-1427	717	24	(	(	PUNCT
fuelectenerg-1427	717	25	that	that	PRON
fuelectenerg-1427	717	26	resembles	resemble	VERB
fuelectenerg-1427	717	27	the	the	DET
fuelectenerg-1427	717	28	s	s	NOUN
fuelectenerg-1427	717	29	/	/	SYM
fuelectenerg-1427	717	30	d	d	NOUN
fuelectenerg-1427	717	31	tree	tree	NOUN
fuelectenerg-1427	717	32	for	for	ADP
fuelectenerg-1427	717	33	shannon	shannon	PROPN
fuelectenerg-1427	717	34	nodes	node	NOUN
fuelectenerg-1427	717	35	in	in	ADP
fuelectenerg-1427	717	36	both	both	DET
fuelectenerg-1427	717	37	levels	level	NOUN
fuelectenerg-1427	717	38	):	):	PUNCT
fuelectenerg-1427	717	39	f	f	X
fuelectenerg-1427	717	40	=	=	PUNCT
fuelectenerg-1427	717	41	0x1	0x1	NOUN
fuelectenerg-1427	717	42	1x2	1x2	NUM
fuelectenerg-1427	718	1	+2	+2	PRON
fuelectenerg-1427	718	2	·	·	PUNCT
fuelectenerg-1427	718	3	0x1	0x1	NOUN
fuelectenerg-1427	718	4	2x2	2x2	NUM
fuelectenerg-1427	718	5	+2	+2	PRON
fuelectenerg-1427	718	6	·	·	PUNCT
fuelectenerg-1427	718	7	1x1	1x1	NUM
fuelectenerg-1427	718	8	0x2	0x2	VERB
fuelectenerg-1427	718	9	+2	+2	PROPN
fuelectenerg-1427	718	10	·	·	PUNCT
fuelectenerg-1427	718	11	1x1	1x1	NUM
fuelectenerg-1427	718	12	1x2	1x2	NUM
fuelectenerg-1427	718	13	+2	+2	PRON
fuelectenerg-1427	718	14	·	·	PUNCT
fuelectenerg-1427	719	1	1x1	1x1	NUM
fuelectenerg-1427	719	2	2x2	2x2	NUM
fuelectenerg-1427	719	3	+	+	SYM
fuelectenerg-1427	719	4	2x1	2x1	NUM
fuelectenerg-1427	719	5	0x2	0x2	NOUN
fuelectenerg-1427	719	6	+2	+2	PROPN
fuelectenerg-1427	719	7	·	·	PUNCT
fuelectenerg-1427	719	8	2x1	2x1	NUM
fuelectenerg-1427	719	9	2x2	2x2	NUM
fuelectenerg-1427	719	10	,	,	PUNCT
fuelectenerg-1427	719	11	(	(	PUNCT
fuelectenerg-1427	719	12	29	29	NUM
fuelectenerg-1427	719	13	)	)	PUNCT
fuelectenerg-1427	719	14	we	we	PRON
fuelectenerg-1427	719	15	can	can	AUX
fuelectenerg-1427	719	16	substitute	substitute	VERB
fuelectenerg-1427	719	17	any	any	PRON
fuelectenerg-1427	719	18	of	of	ADP
fuelectenerg-1427	719	19	equations	equation	NOUN
fuelectenerg-1427	719	20	(	(	PUNCT
fuelectenerg-1427	719	21	7	7	NUM
fuelectenerg-1427	719	22	)	)	PUNCT
fuelectenerg-1427	719	23	(	(	PUNCT
fuelectenerg-1427	719	24	15	15	NUM
fuelectenerg-1427	719	25	)	)	PUNCT
fuelectenerg-1427	719	26	,	,	PUNCT
fuelectenerg-1427	719	27	or	or	CCONJ
fuelectenerg-1427	719	28	a	a	DET
fuelectenerg-1427	719	29	mix	mix	NOUN
fuelectenerg-1427	719	30	of	of	ADP
fuelectenerg-1427	719	31	these	these	DET
fuelectenerg-1427	719	32	equations	equation	NOUN
fuelectenerg-1427	719	33	,	,	PUNCT
fuelectenerg-1427	719	34	to	to	PART
fuelectenerg-1427	719	35	transform	transform	VERB
fuelectenerg-1427	719	36	one	one	NUM
fuelectenerg-1427	719	37	flattened	flatten	VERB
fuelectenerg-1427	719	38	form	form	NOUN
fuelectenerg-1427	719	39	to	to	ADP
fuelectenerg-1427	719	40	another	another	PRON
fuelectenerg-1427	719	41	.	.	PUNCT
fuelectenerg-1427	720	1	for	for	ADP
fuelectenerg-1427	720	2	example	example	NOUN
fuelectenerg-1427	720	3	,	,	PUNCT
fuelectenerg-1427	720	4	if	if	SCONJ
fuelectenerg-1427	720	5	we	we	PRON
fuelectenerg-1427	720	6	substitute	substitute	VERB
fuelectenerg-1427	720	7	equations	equation	NOUN
fuelectenerg-1427	720	8	(	(	PUNCT
fuelectenerg-1427	720	9	7	7	NUM
fuelectenerg-1427	720	10	)	)	PUNCT
fuelectenerg-1427	720	11	and	and	CCONJ
fuelectenerg-1427	720	12	(	(	PUNCT
fuelectenerg-1427	720	13	11	11	NUM
fuelectenerg-1427	720	14	)	)	PUNCT
fuelectenerg-1427	720	15	,	,	PUNCT
fuelectenerg-1427	720	16	we	we	PRON
fuelectenerg-1427	720	17	obtain	obtain	VERB
fuelectenerg-1427	720	18	:	:	PUNCT
fuelectenerg-1427	720	19	f	f	PROPN
fuelectenerg-1427	720	20	=(	=(	NOUN
fuelectenerg-1427	720	21	2(x1	2(x1	NUM
fuelectenerg-1427	720	22	)	)	PUNCT
fuelectenerg-1427	720	23	2	2	NUM
fuelectenerg-1427	720	24	+1)(2(x′2	+1)(2(x′2	NOUN
fuelectenerg-1427	720	25	)	)	PUNCT
fuelectenerg-1427	720	26	2	2	NUM
fuelectenerg-1427	720	27	+	+	SYM
fuelectenerg-1427	720	28	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	720	29	)	)	PUNCT
fuelectenerg-1427	720	30	2	2	NUM
fuelectenerg-1427	720	31	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	720	32	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	720	33	)	)	PUNCT
fuelectenerg-1427	720	34	2	2	NUM
fuelectenerg-1427	720	35	+	+	CCONJ
fuelectenerg-1427	720	36	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	720	37	)	)	PUNCT
fuelectenerg-1427	720	38	2	2	NUM
fuelectenerg-1427	720	39	+1	+1	PROPN
fuelectenerg-1427	720	40	)	)	PUNCT
fuelectenerg-1427	720	41	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	720	42	)	)	PUNCT
fuelectenerg-1427	720	43	2	2	NUM
fuelectenerg-1427	721	1	+	+	CCONJ
fuelectenerg-1427	721	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	721	3	′	′	NOUN
fuelectenerg-1427	721	4	2	2	NUM
fuelectenerg-1427	721	5	)	)	PUNCT
fuelectenerg-1427	721	6	2	2	NUM
fuelectenerg-1427	721	7	+	+	CCONJ
fuelectenerg-1427	721	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	721	9	)	)	PUNCT
fuelectenerg-1427	721	10	2	2	NUM
fuelectenerg-1427	721	11	+	+	NUM
fuelectenerg-1427	721	12	x′1	x′1	X
fuelectenerg-1427	721	13	)	)	PUNCT
fuelectenerg-1427	721	14	·	·	PUNCT
fuelectenerg-1427	722	1	2x2	2x2	NUM
fuelectenerg-1427	722	2	+	+	NUM
fuelectenerg-1427	722	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	722	4	)	)	PUNCT
fuelectenerg-1427	722	5	2	2	NUM
fuelectenerg-1427	722	6	+1	+1	NOUN
fuelectenerg-1427	722	7	)	)	PUNCT
fuelectenerg-1427	722	8	+2	+2	PROPN
fuelectenerg-1427	722	9	·	·	PUNCT
fuelectenerg-1427	723	1	2x1	2x1	NUM
fuelectenerg-1427	723	2	2x2	2x2	NUM
fuelectenerg-1427	723	3	,	,	PUNCT
fuelectenerg-1427	723	4	(	(	PUNCT
fuelectenerg-1427	723	5	30	30	NUM
fuelectenerg-1427	723	6	)	)	PUNCT
fuelectenerg-1427	723	7	by	by	ADP
fuelectenerg-1427	723	8	utilizing	utilize	VERB
fuelectenerg-1427	723	9	gf	gf	NOUN
fuelectenerg-1427	723	10	addition	addition	NOUN
fuelectenerg-1427	723	11	and	and	CCONJ
fuelectenerg-1427	723	12	multiplication	multiplication	NOUN
fuelectenerg-1427	723	13	operators	operator	NOUN
fuelectenerg-1427	723	14	from	from	ADP
fuelectenerg-1427	723	15	figure	figure	NOUN
fuelectenerg-1427	723	16	1	1	NUM
fuelectenerg-1427	723	17	,	,	PUNCT
fuelectenerg-1427	723	18	equation	equation	NOUN
fuelectenerg-1427	723	19	(	(	PUNCT
fuelectenerg-1427	723	20	30	30	NUM
fuelectenerg-1427	723	21	)	)	PUNCT
fuelectenerg-1427	723	22	can	can	AUX
fuelectenerg-1427	723	23	be	be	AUX
fuelectenerg-1427	723	24	transformed	transform	VERB
fuelectenerg-1427	723	25	to	to	ADP
fuelectenerg-1427	723	26	:	:	PUNCT
fuelectenerg-1427	723	27	f	f	PROPN
fuelectenerg-1427	723	28	=(	=(	PROPN
fuelectenerg-1427	723	29	x1	x1	PROPN
fuelectenerg-1427	723	30	)	)	PUNCT
fuelectenerg-1427	723	31	2(x′2	2(x′2	NOUN
fuelectenerg-1427	723	32	)	)	PUNCT
fuelectenerg-1427	723	33	2	2	NUM
fuelectenerg-1427	723	34	+2(x1	+2(x1	NOUN
fuelectenerg-1427	723	35	)	)	PUNCT
fuelectenerg-1427	723	36	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	723	37	)	)	PUNCT
fuelectenerg-1427	723	38	2	2	NUM
fuelectenerg-1427	724	1	+	+	CCONJ
fuelectenerg-1427	724	2	x′2	x′2	X
fuelectenerg-1427	725	1	+	+	ADJ
fuelectenerg-1427	725	2	(	(	PUNCT
fuelectenerg-1427	725	3	x1	x1	ADJ
fuelectenerg-1427	725	4	)	)	PUNCT
fuelectenerg-1427	725	5	2	2	NUM
fuelectenerg-1427	725	6	(	(	PUNCT
fuelectenerg-1427	725	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	725	8	(	(	PUNCT
fuelectenerg-1427	725	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	725	10	)	)	PUNCT
fuelectenerg-1427	725	11	2(x2	2(x2	NUM
fuelectenerg-1427	725	12	)	)	PUNCT
fuelectenerg-1427	725	13	2	2	NUM
fuelectenerg-1427	726	1	+	+	NOUN
fuelectenerg-1427	726	2	(	(	PUNCT
fuelectenerg-1427	726	3	x′1	x′1	NOUN
fuelectenerg-1427	726	4	)	)	PUNCT
fuelectenerg-1427	726	5	2	2	NUM
fuelectenerg-1427	727	1	+	+	NOUN
fuelectenerg-1427	727	2	(	(	PUNCT
fuelectenerg-1427	727	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	727	4	)	)	PUNCT
fuelectenerg-1427	727	5	2	2	NUM
fuelectenerg-1427	727	6	+2x′1	+2x′1	ADP
fuelectenerg-1427	727	7	+2(x′1	+2(x′1	PROPN
fuelectenerg-1427	727	8	)	)	PUNCT
fuelectenerg-1427	727	9	2(x′2	2(x′2	NOUN
fuelectenerg-1427	727	10	)	)	PUNCT
fuelectenerg-1427	727	11	2	2	NUM
fuelectenerg-1427	728	1	+	+	ADJ
fuelectenerg-1427	728	2	(	(	PUNCT
fuelectenerg-1427	728	3	x′1	x′1	NOUN
fuelectenerg-1427	728	4	)	)	PUNCT
fuelectenerg-1427	728	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	728	6	(	(	PUNCT
fuelectenerg-1427	728	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	728	8	′	′	NUM
fuelectenerg-1427	728	9	2	2	NUM
fuelectenerg-1427	728	10	)	)	PUNCT
fuelectenerg-1427	728	11	2	2	NUM
fuelectenerg-1427	728	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	728	13	+	+	PROPN
fuelectenerg-1427	728	14	(	(	PUNCT
fuelectenerg-1427	728	15	x′1	x′1	NOUN
fuelectenerg-1427	728	16	)	)	PUNCT
fuelectenerg-1427	728	17	2	2	NUM
fuelectenerg-1427	728	18	·	·	SYM
fuelectenerg-1427	728	19	2x2	2x2	NUM
fuelectenerg-1427	728	20	+2(x′1	+2(x′1	NOUN
fuelectenerg-1427	728	21	)	)	PUNCT
fuelectenerg-1427	728	22	2x2	2x2	NUM
fuelectenerg-1427	729	1	+2	+2	PROPN
fuelectenerg-1427	729	2	(	(	PUNCT
fuelectenerg-1427	729	3	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	729	4	)	)	PUNCT
fuelectenerg-1427	729	5	2	2	NUM
fuelectenerg-1427	729	6	+	+	SYM
fuelectenerg-1427	729	7	2x1	2x1	NUM
fuelectenerg-1427	729	8	+2	+2	NOUN
fuelectenerg-1427	729	9	(	(	PUNCT
fuelectenerg-1427	729	10	2x1	2x1	NUM
fuelectenerg-1427	729	11	)	)	PUNCT
fuelectenerg-1427	729	12	(	(	PUNCT
fuelectenerg-1427	729	13	2x2	2x2	NUM
fuelectenerg-1427	729	14	)	)	PUNCT
fuelectenerg-1427	729	15	.	.	PUNCT
fuelectenerg-1427	730	1	(	(	PUNCT
fuelectenerg-1427	730	2	31	31	NUM
fuelectenerg-1427	730	3	)	)	PUNCT
fuelectenerg-1427	730	4	let	let	VERB
fuelectenerg-1427	730	5	us	we	PRON
fuelectenerg-1427	730	6	define	define	VERB
fuelectenerg-1427	730	7	,	,	PUNCT
fuelectenerg-1427	730	8	as	as	ADP
fuelectenerg-1427	730	9	one	one	NUM
fuelectenerg-1427	730	10	of	of	ADP
fuelectenerg-1427	730	11	possible	possible	ADJ
fuelectenerg-1427	730	12	definitions	definition	NOUN
fuelectenerg-1427	730	13	,	,	PUNCT
fuelectenerg-1427	730	14	the	the	DET
fuelectenerg-1427	730	15	cost	cost	NOUN
fuelectenerg-1427	730	16	of	of	ADP
fuelectenerg-1427	730	17	the	the	DET
fuelectenerg-1427	730	18	flattened	flatten	VERB
fuelectenerg-1427	730	19	form	form	NOUN
fuelectenerg-1427	730	20	(	(	PUNCT
fuelectenerg-1427	730	21	expression	expression	NOUN
fuelectenerg-1427	730	22	)	)	PUNCT
fuelectenerg-1427	730	23	to	to	PART
fuelectenerg-1427	730	24	be	be	AUX
fuelectenerg-1427	730	25	:	:	PUNCT
fuelectenerg-1427	730	26	cost	cost	NOUN
fuelectenerg-1427	730	27	=	=	SYM
fuelectenerg-1427	730	28	#	#	NOUN
fuelectenerg-1427	730	29	cubes	cube	NOUN
fuelectenerg-1427	730	30	(	(	PUNCT
fuelectenerg-1427	730	31	32	32	NUM
fuelectenerg-1427	730	32	)	)	PUNCT
fuelectenerg-1427	730	33	then	then	ADV
fuelectenerg-1427	730	34	,	,	PUNCT
fuelectenerg-1427	730	35	we	we	PRON
fuelectenerg-1427	730	36	observe	observe	VERB
fuelectenerg-1427	730	37	that	that	SCONJ
fuelectenerg-1427	730	38	equation	equation	NOUN
fuelectenerg-1427	730	39	(	(	PUNCT
fuelectenerg-1427	730	40	29	29	NUM
fuelectenerg-1427	730	41	)	)	PUNCT
fuelectenerg-1427	730	42	has	have	VERB
fuelectenerg-1427	730	43	the	the	DET
fuelectenerg-1427	730	44	cost	cost	NOUN
fuelectenerg-1427	730	45	of	of	ADP
fuelectenerg-1427	730	46	seven	seven	NUM
fuelectenerg-1427	730	47	,	,	PUNCT
fuelectenerg-1427	730	48	while	while	SCONJ
fuelectenerg-1427	730	49	equation	equation	NOUN
fuelectenerg-1427	730	50	(	(	PUNCT
fuelectenerg-1427	730	51	31	31	NUM
fuelectenerg-1427	730	52	)	)	PUNCT
fuelectenerg-1427	730	53	has	have	VERB
fuelectenerg-1427	730	54	the	the	DET
fuelectenerg-1427	730	55	cost	cost	NOUN
fuelectenerg-1427	730	56	of	of	ADP
fuelectenerg-1427	730	57	19	19	NUM
fuelectenerg-1427	730	58	.	.	PUNCT
fuelectenerg-1427	731	1	thus	thus	ADV
fuelectenerg-1427	731	2	,	,	PUNCT
fuelectenerg-1427	731	3	the	the	DET
fuelectenerg-1427	731	4	inverse	inverse	NOUN
fuelectenerg-1427	731	5	transformations	transformation	NOUN
fuelectenerg-1427	731	6	applied	apply	VERB
fuelectenerg-1427	731	7	to	to	ADP
fuelectenerg-1427	731	8	equation	equation	NOUN
fuelectenerg-1427	731	9	(	(	PUNCT
fuelectenerg-1427	731	10	31	31	NUM
fuelectenerg-1427	731	11	)	)	PUNCT
fuelectenerg-1427	731	12	would	would	AUX
fuelectenerg-1427	731	13	lead	lead	VERB
fuelectenerg-1427	731	14	to	to	ADP
fuelectenerg-1427	731	15	equation	equation	NOUN
fuelectenerg-1427	731	16	(	(	PUNCT
fuelectenerg-1427	731	17	29	29	NUM
fuelectenerg-1427	731	18	)	)	PUNCT
fuelectenerg-1427	731	19	and	and	CCONJ
fuelectenerg-1427	731	20	a	a	DET
fuelectenerg-1427	731	21	reduction	reduction	NOUN
fuelectenerg-1427	731	22	of	of	ADP
fuelectenerg-1427	731	23	cost	cost	NOUN
fuelectenerg-1427	731	24	from	from	ADP
fuelectenerg-1427	731	25	19	19	NUM
fuelectenerg-1427	731	26	to	to	PART
fuelectenerg-1427	731	27	seven	seven	NUM
fuelectenerg-1427	731	28	.	.	PUNCT
fuelectenerg-1427	732	1	using	use	VERB
fuelectenerg-1427	732	2	the	the	DET
fuelectenerg-1427	732	3	same	same	ADJ
fuelectenerg-1427	732	4	approach	approach	NOUN
fuelectenerg-1427	732	5	,	,	PUNCT
fuelectenerg-1427	732	6	we	we	PRON
fuelectenerg-1427	732	7	can	can	AUX
fuelectenerg-1427	732	8	generate	generate	VERB
fuelectenerg-1427	732	9	a	a	DET
fuelectenerg-1427	732	10	subset	subset	NOUN
fuelectenerg-1427	732	11	of	of	ADP
fuelectenerg-1427	732	12	possible	possible	ADJ
fuelectenerg-1427	732	13	gfsop	gfsop	NOUN
fuelectenerg-1427	732	14	expressions	expression	NOUN
fuelectenerg-1427	732	15	(	(	PUNCT
fuelectenerg-1427	732	16	flattened	flatten	VERB
fuelectenerg-1427	732	17	forms	form	NOUN
fuelectenerg-1427	732	18	)	)	PUNCT
fuelectenerg-1427	732	19	.	.	PUNCT
fuelectenerg-1427	733	1	note	note	VERB
fuelectenerg-1427	733	2	that	that	SCONJ
fuelectenerg-1427	733	3	all	all	PRON
fuelectenerg-1427	733	4	of	of	ADP
fuelectenerg-1427	733	5	these	these	DET
fuelectenerg-1427	733	6	gfsop	gfsop	NOUN
fuelectenerg-1427	733	7	expressions	expression	NOUN
fuelectenerg-1427	733	8	are	be	AUX
fuelectenerg-1427	733	9	equivalent	equivalent	ADJ
fuelectenerg-1427	733	10	since	since	SCONJ
fuelectenerg-1427	733	11	they	they	PRON
fuelectenerg-1427	733	12	produce	produce	VERB
fuelectenerg-1427	733	13	the	the	DET
fuelectenerg-1427	733	14	same	same	ADJ
fuelectenerg-1427	733	15	function	function	NOUN
fuelectenerg-1427	733	16	in	in	ADP
fuelectenerg-1427	733	17	different	different	ADJ
fuelectenerg-1427	733	18	forms	form	NOUN
fuelectenerg-1427	733	19	.	.	PUNCT
fuelectenerg-1427	734	1	yet	yet	ADV
fuelectenerg-1427	734	2	,	,	PUNCT
fuelectenerg-1427	734	3	as	as	SCONJ
fuelectenerg-1427	734	4	can	can	AUX
fuelectenerg-1427	734	5	be	be	AUX
fuelectenerg-1427	734	6	observed	observe	VERB
fuelectenerg-1427	734	7	from	from	ADP
fuelectenerg-1427	734	8	equation	equation	NOUN
fuelectenerg-1427	734	9	(	(	PUNCT
fuelectenerg-1427	734	10	31	31	NUM
fuelectenerg-1427	734	11	)	)	PUNCT
fuelectenerg-1427	734	12	,	,	PUNCT
fuelectenerg-1427	734	13	by	by	ADP
fuelectenerg-1427	734	14	further	further	ADJ
fuelectenerg-1427	734	15	transformations	transformation	NOUN
fuelectenerg-1427	734	16	of	of	ADP
fuelectenerg-1427	734	17	equation	equation	NOUN
fuelectenerg-1427	734	18	(	(	PUNCT
fuelectenerg-1427	734	19	29	29	NUM
fuelectenerg-1427	734	20	)	)	PUNCT
fuelectenerg-1427	734	21	from	from	ADP
fuelectenerg-1427	734	22	one	one	NUM
fuelectenerg-1427	734	23	form	form	NOUN
fuelectenerg-1427	734	24	to	to	ADP
fuelectenerg-1427	734	25	another	another	PRON
fuelectenerg-1427	734	26	,	,	PUNCT
fuelectenerg-1427	734	27	some	some	DET
fuelectenerg-1427	734	28	transformations	transformation	NOUN
fuelectenerg-1427	734	29	produce	produce	VERB
fuelectenerg-1427	734	30	flattened	flatten	VERB
fuelectenerg-1427	734	31	forms	form	NOUN
fuelectenerg-1427	734	32	with	with	ADP
fuelectenerg-1427	734	33	a	a	DET
fuelectenerg-1427	734	34	smaller	small	ADJ
fuelectenerg-1427	734	35	number	number	NOUN
fuelectenerg-1427	734	36	of	of	ADP
fuelectenerg-1427	734	37	cubes	cube	NOUN
fuelectenerg-1427	734	38	than	than	ADP
fuelectenerg-1427	734	39	the	the	DET
fuelectenerg-1427	734	40	others	other	NOUN
fuelectenerg-1427	734	41	.	.	PUNCT
fuelectenerg-1427	735	1	from	from	ADP
fuelectenerg-1427	735	2	this	this	DET
fuelectenerg-1427	735	3	observation	observation	NOUN
fuelectenerg-1427	735	4	rises	rise	VERB
fuelectenerg-1427	735	5	the	the	DET
fuelectenerg-1427	735	6	idea	idea	NOUN
fuelectenerg-1427	735	7	of	of	ADP
fuelectenerg-1427	735	8	a	a	DET
fuelectenerg-1427	735	9	possible	possible	ADJ
fuelectenerg-1427	735	10	application	application	NOUN
fuelectenerg-1427	735	11	of	of	ADP
fuelectenerg-1427	735	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	735	13	computing	computing	NOUN
fuelectenerg-1427	735	14	using	use	VERB
fuelectenerg-1427	735	15	the	the	DET
fuelectenerg-1427	735	16	s	s	PROPN
fuelectenerg-1427	735	17	/	/	SYM
fuelectenerg-1427	735	18	d	d	NOUN
fuelectenerg-1427	735	19	trees	tree	NOUN
fuelectenerg-1427	735	20	and	and	CCONJ
fuelectenerg-1427	735	21	related	related	ADJ
fuelectenerg-1427	735	22	transformations	transformation	NOUN
fuelectenerg-1427	735	23	to	to	PART
fuelectenerg-1427	735	24	produce	produce	VERB
fuelectenerg-1427	735	25	the	the	DET
fuelectenerg-1427	735	26	corresponding	corresponding	ADJ
fuelectenerg-1427	735	27	minimum	minimum	ADJ
fuelectenerg-1427	735	28	gfsops	gfsop	NOUN
fuelectenerg-1427	735	29	.	.	PUNCT
fuelectenerg-1427	736	1	analogous	analogous	ADJ
fuelectenerg-1427	736	2	to	to	ADP
fuelectenerg-1427	736	3	the	the	DET
fuelectenerg-1427	736	4	binary	binary	ADJ
fuelectenerg-1427	736	5	case	case	NOUN
fuelectenerg-1427	736	6	in	in	ADP
fuelectenerg-1427	736	7	equation	equation	NOUN
fuelectenerg-1427	736	8	(	(	PUNCT
fuelectenerg-1427	736	9	27	27	NUM
fuelectenerg-1427	736	10	)	)	PUNCT
fuelectenerg-1427	736	11	,	,	PUNCT
fuelectenerg-1427	736	12	the	the	DET
fuelectenerg-1427	736	13	ternary	ternary	ADJ
fuelectenerg-1427	736	14	gifs	gif	NOUN
fuelectenerg-1427	736	15	can	can	AUX
fuelectenerg-1427	736	16	be	be	AUX
fuelectenerg-1427	736	17	defined	define	VERB
fuelectenerg-1427	736	18	as	as	ADP
fuelectenerg-1427	736	19	the	the	DET
fuelectenerg-1427	736	20	union	union	NOUN
fuelectenerg-1427	736	21	of	of	ADP
fuelectenerg-1427	736	22	ternary	ternary	PROPN
fuelectenerg-1427	736	23	ifs	ifs	PROPN
fuelectenerg-1427	736	24	.	.	PUNCT
fuelectenerg-1427	737	1	definition	definition	NOUN
fuelectenerg-1427	737	2	3	3	NUM
fuelectenerg-1427	737	3	.	.	PUNCT
fuelectenerg-1427	738	1	the	the	DET
fuelectenerg-1427	738	2	family	family	NOUN
fuelectenerg-1427	738	3	of	of	ADP
fuelectenerg-1427	738	4	forms	form	NOUN
fuelectenerg-1427	738	5	,	,	PUNCT
fuelectenerg-1427	738	6	which	which	PRON
fuelectenerg-1427	738	7	is	be	AUX
fuelectenerg-1427	738	8	created	create	VERB
fuelectenerg-1427	738	9	as	as	ADP
fuelectenerg-1427	738	10	a	a	DET
fuelectenerg-1427	738	11	union	union	NOUN
fuelectenerg-1427	738	12	of	of	ADP
fuelectenerg-1427	738	13	sets	set	NOUN
fuelectenerg-1427	738	14	of	of	ADP
fuelectenerg-1427	738	15	tifs	tif	NOUN
fuelectenerg-1427	738	16	for	for	ADP
fuelectenerg-1427	738	17	all	all	DET
fuelectenerg-1427	738	18	variable	variable	ADJ
fuelectenerg-1427	738	19	orders	order	NOUN
fuelectenerg-1427	738	20	,	,	PUNCT
fuelectenerg-1427	738	21	is	be	AUX
fuelectenerg-1427	738	22	called	call	VERB
fuelectenerg-1427	738	23	ternary	ternary	ADJ
fuelectenerg-1427	738	24	generalized	generalized	ADJ
fuelectenerg-1427	738	25	inclusive	inclusive	ADJ
fuelectenerg-1427	738	26	forms	form	NOUN
fuelectenerg-1427	738	27	(	(	PUNCT
fuelectenerg-1427	738	28	tgifs	tgif	NOUN
fuelectenerg-1427	738	29	)	)	PUNCT
fuelectenerg-1427	738	30	.	.	PUNCT
fuelectenerg-1427	739	1	109	109	NUM
fuelectenerg-1427	739	2	an	an	DET
fuelectenerg-1427	739	3	extended	extend	VERB
fuelectenerg-1427	739	4	green	green	ADJ
fuelectenerg-1427	739	5	sasao	sasao	PROPN
fuelectenerg-1427	739	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	739	7	of	of	ADP
fuelectenerg-1427	739	8	canonical	canonical	ADJ
fuelectenerg-1427	739	9	ternary	ternary	ADJ
fuelectenerg-1427	739	10	galois	galois	NOUN
fuelectenerg-1427	739	11	forms	form	NOUN
fuelectenerg-1427	739	12	...	...	PUNCT
fuelectenerg-1427	739	13	form	form	NOUN
fuelectenerg-1427	739	14	which	which	PRON
fuelectenerg-1427	739	15	is	be	AUX
fuelectenerg-1427	739	16	an	an	DET
fuelectenerg-1427	739	17	expansion	expansion	NOUN
fuelectenerg-1427	739	18	over	over	ADP
fuelectenerg-1427	739	19	certain	certain	ADJ
fuelectenerg-1427	739	20	transform	transform	NOUN
fuelectenerg-1427	739	21	matrix	matrix	NOUN
fuelectenerg-1427	739	22	(	(	PUNCT
fuelectenerg-1427	739	23	i.e.	i.e.	X
fuelectenerg-1427	739	24	,	,	PUNCT
fuelectenerg-1427	739	25	certain	certain	ADJ
fuelectenerg-1427	739	26	tif	tif	PROPN
fuelectenerg-1427	739	27	)	)	PUNCT
fuelectenerg-1427	739	28	and	and	CCONJ
fuelectenerg-1427	739	29	then	then	ADV
fuelectenerg-1427	739	30	transform	transform	VERB
fuelectenerg-1427	739	31	systematically	systematically	ADV
fuelectenerg-1427	739	32	from	from	ADP
fuelectenerg-1427	739	33	one	one	NUM
fuelectenerg-1427	739	34	form	form	NOUN
fuelectenerg-1427	739	35	to	to	ADP
fuelectenerg-1427	739	36	another	another	DET
fuelectenerg-1427	739	37	form	form	NOUN
fuelectenerg-1427	739	38	without	without	ADP
fuelectenerg-1427	739	39	the	the	DET
fuelectenerg-1427	739	40	need	need	NOUN
fuelectenerg-1427	739	41	to	to	PART
fuelectenerg-1427	739	42	create	create	VERB
fuelectenerg-1427	739	43	all	all	PRON
fuelectenerg-1427	739	44	transform	transform	VERB
fuelectenerg-1427	739	45	matrices	matrix	NOUN
fuelectenerg-1427	739	46	from	from	ADP
fuelectenerg-1427	739	47	the	the	DET
fuelectenerg-1427	739	48	corresponding	correspond	VERB
fuelectenerg-1427	739	49	s	s	PROPN
fuelectenerg-1427	739	50	/	/	SYM
fuelectenerg-1427	739	51	d	d	NOUN
fuelectenerg-1427	739	52	trees	tree	NOUN
fuelectenerg-1427	739	53	.	.	PUNCT
fuelectenerg-1427	740	1	this	this	DET
fuelectenerg-1427	740	2	general	general	ADJ
fuelectenerg-1427	740	3	approach	approach	NOUN
fuelectenerg-1427	740	4	can	can	AUX
fuelectenerg-1427	740	5	lead	lead	VERB
fuelectenerg-1427	740	6	to	to	ADP
fuelectenerg-1427	740	7	several	several	ADJ
fuelectenerg-1427	740	8	algorithms	algorithm	NOUN
fuelectenerg-1427	740	9	of	of	ADP
fuelectenerg-1427	740	10	various	various	ADJ
fuelectenerg-1427	740	11	complexities	complexity	NOUN
fuelectenerg-1427	740	12	that	that	PRON
fuelectenerg-1427	740	13	generalize	generalize	VERB
fuelectenerg-1427	740	14	the	the	DET
fuelectenerg-1427	740	15	existing	exist	VERB
fuelectenerg-1427	740	16	binary	binary	ADJ
fuelectenerg-1427	740	17	algorithms	algorithm	NOUN
fuelectenerg-1427	740	18	to	to	PART
fuelectenerg-1427	740	19	obtain	obtain	VERB
fuelectenerg-1427	740	20	the	the	DET
fuelectenerg-1427	740	21	corresponding	corresponding	ADJ
fuelectenerg-1427	740	22	forms	form	NOUN
fuelectenerg-1427	740	23	such	such	ADJ
fuelectenerg-1427	740	24	as	as	ADP
fuelectenerg-1427	740	25	fprm	fprm	PROPN
fuelectenerg-1427	740	26	,	,	PUNCT
fuelectenerg-1427	740	27	grm	grm	NOUN
fuelectenerg-1427	740	28	and	and	CCONJ
fuelectenerg-1427	740	29	if	if	SCONJ
fuelectenerg-1427	740	30	forms	form	NOUN
fuelectenerg-1427	740	31	.	.	PUNCT
fuelectenerg-1427	740	32	example	example	NOUN
fuelectenerg-1427	741	1	3	3	NUM
fuelectenerg-1427	741	2	.	.	PUNCT
fuelectenerg-1427	741	3	using	use	VERB
fuelectenerg-1427	741	4	the	the	DET
fuelectenerg-1427	741	5	result	result	NOUN
fuelectenerg-1427	741	6	of	of	ADP
fuelectenerg-1427	741	7	example	example	NOUN
fuelectenerg-1427	741	8	2	2	NUM
fuelectenerg-1427	741	9	for	for	ADP
fuelectenerg-1427	741	10	the	the	DET
fuelectenerg-1427	741	11	expansion	expansion	NOUN
fuelectenerg-1427	741	12	of	of	ADP
fuelectenerg-1427	741	13	f	f	PROPN
fuelectenerg-1427	741	14	(	(	PUNCT
fuelectenerg-1427	741	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	741	16	)	)	PUNCT
fuelectenerg-1427	741	17	in	in	ADP
fuelectenerg-1427	741	18	terms	term	NOUN
fuelectenerg-1427	741	19	of	of	ADP
fuelectenerg-1427	741	20	the	the	DET
fuelectenerg-1427	741	21	ternary	ternary	ADJ
fuelectenerg-1427	741	22	shannon	shannon	NOUN
fuelectenerg-1427	741	23	expansion	expansion	NOUN
fuelectenerg-1427	741	24	(	(	PUNCT
fuelectenerg-1427	741	25	that	that	PRON
fuelectenerg-1427	741	26	resembles	resemble	VERB
fuelectenerg-1427	741	27	the	the	DET
fuelectenerg-1427	741	28	s	s	NOUN
fuelectenerg-1427	741	29	/	/	SYM
fuelectenerg-1427	741	30	d	d	NOUN
fuelectenerg-1427	741	31	tree	tree	NOUN
fuelectenerg-1427	741	32	for	for	ADP
fuelectenerg-1427	741	33	shannon	shannon	PROPN
fuelectenerg-1427	741	34	nodes	node	NOUN
fuelectenerg-1427	741	35	in	in	ADP
fuelectenerg-1427	741	36	both	both	DET
fuelectenerg-1427	741	37	levels	level	NOUN
fuelectenerg-1427	741	38	):	):	PUNCT
fuelectenerg-1427	741	39	f	f	X
fuelectenerg-1427	741	40	=	=	PUNCT
fuelectenerg-1427	741	41	0x1	0x1	NOUN
fuelectenerg-1427	741	42	1x2	1x2	NUM
fuelectenerg-1427	742	1	+2	+2	PRON
fuelectenerg-1427	742	2	·	·	PUNCT
fuelectenerg-1427	742	3	0x1	0x1	NOUN
fuelectenerg-1427	742	4	2x2	2x2	NUM
fuelectenerg-1427	742	5	+2	+2	PRON
fuelectenerg-1427	742	6	·	·	PUNCT
fuelectenerg-1427	742	7	1x1	1x1	NUM
fuelectenerg-1427	742	8	0x2	0x2	VERB
fuelectenerg-1427	742	9	+2	+2	PROPN
fuelectenerg-1427	742	10	·	·	PUNCT
fuelectenerg-1427	742	11	1x1	1x1	NUM
fuelectenerg-1427	742	12	1x2	1x2	NUM
fuelectenerg-1427	742	13	+2	+2	PRON
fuelectenerg-1427	742	14	·	·	PUNCT
fuelectenerg-1427	743	1	1x1	1x1	NUM
fuelectenerg-1427	743	2	2x2	2x2	NUM
fuelectenerg-1427	743	3	+	+	SYM
fuelectenerg-1427	743	4	2x1	2x1	NUM
fuelectenerg-1427	743	5	0x2	0x2	NOUN
fuelectenerg-1427	743	6	+2	+2	PROPN
fuelectenerg-1427	743	7	·	·	PUNCT
fuelectenerg-1427	743	8	2x1	2x1	NUM
fuelectenerg-1427	743	9	2x2	2x2	NUM
fuelectenerg-1427	743	10	,	,	PUNCT
fuelectenerg-1427	743	11	(	(	PUNCT
fuelectenerg-1427	743	12	29	29	NUM
fuelectenerg-1427	743	13	)	)	PUNCT
fuelectenerg-1427	743	14	we	we	PRON
fuelectenerg-1427	743	15	can	can	AUX
fuelectenerg-1427	743	16	substitute	substitute	VERB
fuelectenerg-1427	743	17	any	any	PRON
fuelectenerg-1427	743	18	of	of	ADP
fuelectenerg-1427	743	19	equations	equation	NOUN
fuelectenerg-1427	743	20	(	(	PUNCT
fuelectenerg-1427	743	21	7	7	NUM
fuelectenerg-1427	743	22	)	)	PUNCT
fuelectenerg-1427	743	23	(	(	PUNCT
fuelectenerg-1427	743	24	15	15	NUM
fuelectenerg-1427	743	25	)	)	PUNCT
fuelectenerg-1427	743	26	,	,	PUNCT
fuelectenerg-1427	743	27	or	or	CCONJ
fuelectenerg-1427	743	28	a	a	DET
fuelectenerg-1427	743	29	mix	mix	NOUN
fuelectenerg-1427	743	30	of	of	ADP
fuelectenerg-1427	743	31	these	these	DET
fuelectenerg-1427	743	32	equations	equation	NOUN
fuelectenerg-1427	743	33	,	,	PUNCT
fuelectenerg-1427	743	34	to	to	PART
fuelectenerg-1427	743	35	transform	transform	VERB
fuelectenerg-1427	743	36	one	one	NUM
fuelectenerg-1427	743	37	flattened	flatten	VERB
fuelectenerg-1427	743	38	form	form	NOUN
fuelectenerg-1427	743	39	to	to	ADP
fuelectenerg-1427	743	40	another	another	PRON
fuelectenerg-1427	743	41	.	.	PUNCT
fuelectenerg-1427	744	1	for	for	ADP
fuelectenerg-1427	744	2	example	example	NOUN
fuelectenerg-1427	744	3	,	,	PUNCT
fuelectenerg-1427	744	4	if	if	SCONJ
fuelectenerg-1427	744	5	we	we	PRON
fuelectenerg-1427	744	6	substitute	substitute	VERB
fuelectenerg-1427	744	7	equations	equation	NOUN
fuelectenerg-1427	744	8	(	(	PUNCT
fuelectenerg-1427	744	9	7	7	NUM
fuelectenerg-1427	744	10	)	)	PUNCT
fuelectenerg-1427	744	11	and	and	CCONJ
fuelectenerg-1427	744	12	(	(	PUNCT
fuelectenerg-1427	744	13	11	11	NUM
fuelectenerg-1427	744	14	)	)	PUNCT
fuelectenerg-1427	744	15	,	,	PUNCT
fuelectenerg-1427	744	16	we	we	PRON
fuelectenerg-1427	744	17	obtain	obtain	VERB
fuelectenerg-1427	744	18	:	:	PUNCT
fuelectenerg-1427	744	19	f	f	PROPN
fuelectenerg-1427	744	20	=(	=(	NOUN
fuelectenerg-1427	744	21	2(x1	2(x1	NUM
fuelectenerg-1427	744	22	)	)	PUNCT
fuelectenerg-1427	744	23	2	2	NUM
fuelectenerg-1427	744	24	+1)(2(x′2	+1)(2(x′2	NOUN
fuelectenerg-1427	744	25	)	)	PUNCT
fuelectenerg-1427	744	26	2	2	NUM
fuelectenerg-1427	744	27	+	+	SYM
fuelectenerg-1427	744	28	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	744	29	)	)	PUNCT
fuelectenerg-1427	744	30	2	2	NUM
fuelectenerg-1427	744	31	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	744	32	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	744	33	)	)	PUNCT
fuelectenerg-1427	744	34	2	2	NUM
fuelectenerg-1427	744	35	+	+	CCONJ
fuelectenerg-1427	744	36	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	744	37	)	)	PUNCT
fuelectenerg-1427	744	38	2	2	NUM
fuelectenerg-1427	744	39	+1	+1	PROPN
fuelectenerg-1427	744	40	)	)	PUNCT
fuelectenerg-1427	744	41	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	744	42	)	)	PUNCT
fuelectenerg-1427	744	43	2	2	NUM
fuelectenerg-1427	745	1	+	+	CCONJ
fuelectenerg-1427	745	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	745	3	′	′	NOUN
fuelectenerg-1427	745	4	2	2	NUM
fuelectenerg-1427	745	5	)	)	PUNCT
fuelectenerg-1427	745	6	2	2	NUM
fuelectenerg-1427	745	7	+	+	CCONJ
fuelectenerg-1427	745	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	745	9	)	)	PUNCT
fuelectenerg-1427	745	10	2	2	NUM
fuelectenerg-1427	745	11	+	+	NUM
fuelectenerg-1427	745	12	x′1	x′1	X
fuelectenerg-1427	745	13	)	)	PUNCT
fuelectenerg-1427	745	14	·	·	PUNCT
fuelectenerg-1427	746	1	2x2	2x2	NUM
fuelectenerg-1427	746	2	+	+	NUM
fuelectenerg-1427	746	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	746	4	)	)	PUNCT
fuelectenerg-1427	746	5	2	2	NUM
fuelectenerg-1427	746	6	+1	+1	NOUN
fuelectenerg-1427	746	7	)	)	PUNCT
fuelectenerg-1427	746	8	+2	+2	PROPN
fuelectenerg-1427	746	9	·	·	PUNCT
fuelectenerg-1427	747	1	2x1	2x1	NUM
fuelectenerg-1427	747	2	2x2	2x2	NUM
fuelectenerg-1427	747	3	,	,	PUNCT
fuelectenerg-1427	747	4	(	(	PUNCT
fuelectenerg-1427	747	5	30	30	NUM
fuelectenerg-1427	747	6	)	)	PUNCT
fuelectenerg-1427	747	7	by	by	ADP
fuelectenerg-1427	747	8	utilizing	utilize	VERB
fuelectenerg-1427	747	9	gf	gf	NOUN
fuelectenerg-1427	747	10	addition	addition	NOUN
fuelectenerg-1427	747	11	and	and	CCONJ
fuelectenerg-1427	747	12	multiplication	multiplication	NOUN
fuelectenerg-1427	747	13	operators	operator	NOUN
fuelectenerg-1427	747	14	from	from	ADP
fuelectenerg-1427	747	15	figure	figure	NOUN
fuelectenerg-1427	747	16	1	1	NUM
fuelectenerg-1427	747	17	,	,	PUNCT
fuelectenerg-1427	747	18	equation	equation	NOUN
fuelectenerg-1427	747	19	(	(	PUNCT
fuelectenerg-1427	747	20	30	30	NUM
fuelectenerg-1427	747	21	)	)	PUNCT
fuelectenerg-1427	747	22	can	can	AUX
fuelectenerg-1427	747	23	be	be	AUX
fuelectenerg-1427	747	24	transformed	transform	VERB
fuelectenerg-1427	747	25	to	to	ADP
fuelectenerg-1427	747	26	:	:	PUNCT
fuelectenerg-1427	747	27	f	f	PROPN
fuelectenerg-1427	747	28	=(	=(	PROPN
fuelectenerg-1427	747	29	x1	x1	PROPN
fuelectenerg-1427	747	30	)	)	PUNCT
fuelectenerg-1427	747	31	2(x′2	2(x′2	NOUN
fuelectenerg-1427	747	32	)	)	PUNCT
fuelectenerg-1427	747	33	2	2	NUM
fuelectenerg-1427	747	34	+2(x1	+2(x1	NOUN
fuelectenerg-1427	747	35	)	)	PUNCT
fuelectenerg-1427	747	36	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	747	37	)	)	PUNCT
fuelectenerg-1427	747	38	2	2	NUM
fuelectenerg-1427	748	1	+	+	CCONJ
fuelectenerg-1427	748	2	x′2	x′2	X
fuelectenerg-1427	749	1	+	+	ADJ
fuelectenerg-1427	749	2	(	(	PUNCT
fuelectenerg-1427	749	3	x1	x1	ADJ
fuelectenerg-1427	749	4	)	)	PUNCT
fuelectenerg-1427	749	5	2	2	NUM
fuelectenerg-1427	749	6	(	(	PUNCT
fuelectenerg-1427	749	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	749	8	(	(	PUNCT
fuelectenerg-1427	749	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	749	10	)	)	PUNCT
fuelectenerg-1427	749	11	2(x2	2(x2	NUM
fuelectenerg-1427	749	12	)	)	PUNCT
fuelectenerg-1427	749	13	2	2	NUM
fuelectenerg-1427	750	1	+	+	NOUN
fuelectenerg-1427	750	2	(	(	PUNCT
fuelectenerg-1427	750	3	x′1	x′1	NOUN
fuelectenerg-1427	750	4	)	)	PUNCT
fuelectenerg-1427	750	5	2	2	NUM
fuelectenerg-1427	751	1	+	+	NOUN
fuelectenerg-1427	751	2	(	(	PUNCT
fuelectenerg-1427	751	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	751	4	)	)	PUNCT
fuelectenerg-1427	751	5	2	2	NUM
fuelectenerg-1427	751	6	+2x′1	+2x′1	ADP
fuelectenerg-1427	751	7	+2(x′1	+2(x′1	PROPN
fuelectenerg-1427	751	8	)	)	PUNCT
fuelectenerg-1427	751	9	2(x′2	2(x′2	NOUN
fuelectenerg-1427	751	10	)	)	PUNCT
fuelectenerg-1427	751	11	2	2	NUM
fuelectenerg-1427	752	1	+	+	ADJ
fuelectenerg-1427	752	2	(	(	PUNCT
fuelectenerg-1427	752	3	x′1	x′1	NOUN
fuelectenerg-1427	752	4	)	)	PUNCT
fuelectenerg-1427	752	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	752	6	(	(	PUNCT
fuelectenerg-1427	752	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	752	8	′	′	NUM
fuelectenerg-1427	752	9	2	2	NUM
fuelectenerg-1427	752	10	)	)	PUNCT
fuelectenerg-1427	752	11	2	2	NUM
fuelectenerg-1427	752	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	752	13	+	+	PROPN
fuelectenerg-1427	752	14	(	(	PUNCT
fuelectenerg-1427	752	15	x′1	x′1	NOUN
fuelectenerg-1427	752	16	)	)	PUNCT
fuelectenerg-1427	752	17	2	2	NUM
fuelectenerg-1427	752	18	·	·	SYM
fuelectenerg-1427	752	19	2x2	2x2	NUM
fuelectenerg-1427	752	20	+2(x′1	+2(x′1	NOUN
fuelectenerg-1427	752	21	)	)	PUNCT
fuelectenerg-1427	752	22	2x2	2x2	NUM
fuelectenerg-1427	753	1	+2	+2	PROPN
fuelectenerg-1427	753	2	(	(	PUNCT
fuelectenerg-1427	753	3	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	753	4	)	)	PUNCT
fuelectenerg-1427	753	5	2	2	NUM
fuelectenerg-1427	753	6	+	+	SYM
fuelectenerg-1427	753	7	2x1	2x1	NUM
fuelectenerg-1427	753	8	+2	+2	NOUN
fuelectenerg-1427	753	9	(	(	PUNCT
fuelectenerg-1427	753	10	2x1	2x1	NUM
fuelectenerg-1427	753	11	)	)	PUNCT
fuelectenerg-1427	753	12	(	(	PUNCT
fuelectenerg-1427	753	13	2x2	2x2	NUM
fuelectenerg-1427	753	14	)	)	PUNCT
fuelectenerg-1427	753	15	.	.	PUNCT
fuelectenerg-1427	754	1	(	(	PUNCT
fuelectenerg-1427	754	2	31	31	NUM
fuelectenerg-1427	754	3	)	)	PUNCT
fuelectenerg-1427	754	4	let	let	VERB
fuelectenerg-1427	754	5	us	we	PRON
fuelectenerg-1427	754	6	define	define	VERB
fuelectenerg-1427	754	7	,	,	PUNCT
fuelectenerg-1427	754	8	as	as	ADP
fuelectenerg-1427	754	9	one	one	NUM
fuelectenerg-1427	754	10	of	of	ADP
fuelectenerg-1427	754	11	possible	possible	ADJ
fuelectenerg-1427	754	12	definitions	definition	NOUN
fuelectenerg-1427	754	13	,	,	PUNCT
fuelectenerg-1427	754	14	the	the	DET
fuelectenerg-1427	754	15	cost	cost	NOUN
fuelectenerg-1427	754	16	of	of	ADP
fuelectenerg-1427	754	17	the	the	DET
fuelectenerg-1427	754	18	flattened	flatten	VERB
fuelectenerg-1427	754	19	form	form	NOUN
fuelectenerg-1427	754	20	(	(	PUNCT
fuelectenerg-1427	754	21	expression	expression	NOUN
fuelectenerg-1427	754	22	)	)	PUNCT
fuelectenerg-1427	754	23	to	to	PART
fuelectenerg-1427	754	24	be	be	AUX
fuelectenerg-1427	754	25	:	:	PUNCT
fuelectenerg-1427	754	26	cost	cost	NOUN
fuelectenerg-1427	754	27	=	=	SYM
fuelectenerg-1427	754	28	#	#	NOUN
fuelectenerg-1427	754	29	cubes	cube	NOUN
fuelectenerg-1427	754	30	(	(	PUNCT
fuelectenerg-1427	754	31	32	32	NUM
fuelectenerg-1427	754	32	)	)	PUNCT
fuelectenerg-1427	754	33	then	then	ADV
fuelectenerg-1427	754	34	,	,	PUNCT
fuelectenerg-1427	754	35	we	we	PRON
fuelectenerg-1427	754	36	observe	observe	VERB
fuelectenerg-1427	754	37	that	that	SCONJ
fuelectenerg-1427	754	38	equation	equation	NOUN
fuelectenerg-1427	754	39	(	(	PUNCT
fuelectenerg-1427	754	40	29	29	NUM
fuelectenerg-1427	754	41	)	)	PUNCT
fuelectenerg-1427	754	42	has	have	VERB
fuelectenerg-1427	754	43	the	the	DET
fuelectenerg-1427	754	44	cost	cost	NOUN
fuelectenerg-1427	754	45	of	of	ADP
fuelectenerg-1427	754	46	seven	seven	NUM
fuelectenerg-1427	754	47	,	,	PUNCT
fuelectenerg-1427	754	48	while	while	SCONJ
fuelectenerg-1427	754	49	equation	equation	NOUN
fuelectenerg-1427	754	50	(	(	PUNCT
fuelectenerg-1427	754	51	31	31	NUM
fuelectenerg-1427	754	52	)	)	PUNCT
fuelectenerg-1427	754	53	has	have	VERB
fuelectenerg-1427	754	54	the	the	DET
fuelectenerg-1427	754	55	cost	cost	NOUN
fuelectenerg-1427	754	56	of	of	ADP
fuelectenerg-1427	754	57	19	19	NUM
fuelectenerg-1427	754	58	.	.	PUNCT
fuelectenerg-1427	755	1	thus	thus	ADV
fuelectenerg-1427	755	2	,	,	PUNCT
fuelectenerg-1427	755	3	the	the	DET
fuelectenerg-1427	755	4	inverse	inverse	NOUN
fuelectenerg-1427	755	5	transformations	transformation	NOUN
fuelectenerg-1427	755	6	applied	apply	VERB
fuelectenerg-1427	755	7	to	to	ADP
fuelectenerg-1427	755	8	equation	equation	NOUN
fuelectenerg-1427	755	9	(	(	PUNCT
fuelectenerg-1427	755	10	31	31	NUM
fuelectenerg-1427	755	11	)	)	PUNCT
fuelectenerg-1427	755	12	would	would	AUX
fuelectenerg-1427	755	13	lead	lead	VERB
fuelectenerg-1427	755	14	to	to	ADP
fuelectenerg-1427	755	15	equation	equation	NOUN
fuelectenerg-1427	755	16	(	(	PUNCT
fuelectenerg-1427	755	17	29	29	NUM
fuelectenerg-1427	755	18	)	)	PUNCT
fuelectenerg-1427	755	19	and	and	CCONJ
fuelectenerg-1427	755	20	a	a	DET
fuelectenerg-1427	755	21	reduction	reduction	NOUN
fuelectenerg-1427	755	22	of	of	ADP
fuelectenerg-1427	755	23	cost	cost	NOUN
fuelectenerg-1427	755	24	from	from	ADP
fuelectenerg-1427	755	25	19	19	NUM
fuelectenerg-1427	755	26	to	to	PART
fuelectenerg-1427	755	27	seven	seven	NUM
fuelectenerg-1427	755	28	.	.	PUNCT
fuelectenerg-1427	756	1	using	use	VERB
fuelectenerg-1427	756	2	the	the	DET
fuelectenerg-1427	756	3	same	same	ADJ
fuelectenerg-1427	756	4	approach	approach	NOUN
fuelectenerg-1427	756	5	,	,	PUNCT
fuelectenerg-1427	756	6	we	we	PRON
fuelectenerg-1427	756	7	can	can	AUX
fuelectenerg-1427	756	8	generate	generate	VERB
fuelectenerg-1427	756	9	a	a	DET
fuelectenerg-1427	756	10	subset	subset	NOUN
fuelectenerg-1427	756	11	of	of	ADP
fuelectenerg-1427	756	12	possible	possible	ADJ
fuelectenerg-1427	756	13	gfsop	gfsop	NOUN
fuelectenerg-1427	756	14	expressions	expression	NOUN
fuelectenerg-1427	756	15	(	(	PUNCT
fuelectenerg-1427	756	16	flattened	flatten	VERB
fuelectenerg-1427	756	17	forms	form	NOUN
fuelectenerg-1427	756	18	)	)	PUNCT
fuelectenerg-1427	756	19	.	.	PUNCT
fuelectenerg-1427	757	1	note	note	VERB
fuelectenerg-1427	757	2	that	that	SCONJ
fuelectenerg-1427	757	3	all	all	PRON
fuelectenerg-1427	757	4	of	of	ADP
fuelectenerg-1427	757	5	these	these	DET
fuelectenerg-1427	757	6	gfsop	gfsop	NOUN
fuelectenerg-1427	757	7	expressions	expression	NOUN
fuelectenerg-1427	757	8	are	be	AUX
fuelectenerg-1427	757	9	equivalent	equivalent	ADJ
fuelectenerg-1427	757	10	since	since	SCONJ
fuelectenerg-1427	757	11	they	they	PRON
fuelectenerg-1427	757	12	produce	produce	VERB
fuelectenerg-1427	757	13	the	the	DET
fuelectenerg-1427	757	14	same	same	ADJ
fuelectenerg-1427	757	15	function	function	NOUN
fuelectenerg-1427	757	16	in	in	ADP
fuelectenerg-1427	757	17	different	different	ADJ
fuelectenerg-1427	757	18	forms	form	NOUN
fuelectenerg-1427	757	19	.	.	PUNCT
fuelectenerg-1427	758	1	yet	yet	ADV
fuelectenerg-1427	758	2	,	,	PUNCT
fuelectenerg-1427	758	3	as	as	SCONJ
fuelectenerg-1427	758	4	can	can	AUX
fuelectenerg-1427	758	5	be	be	AUX
fuelectenerg-1427	758	6	observed	observe	VERB
fuelectenerg-1427	758	7	from	from	ADP
fuelectenerg-1427	758	8	equation	equation	NOUN
fuelectenerg-1427	758	9	(	(	PUNCT
fuelectenerg-1427	758	10	31	31	NUM
fuelectenerg-1427	758	11	)	)	PUNCT
fuelectenerg-1427	758	12	,	,	PUNCT
fuelectenerg-1427	758	13	by	by	ADP
fuelectenerg-1427	758	14	further	further	ADJ
fuelectenerg-1427	758	15	transformations	transformation	NOUN
fuelectenerg-1427	758	16	of	of	ADP
fuelectenerg-1427	758	17	equation	equation	NOUN
fuelectenerg-1427	758	18	(	(	PUNCT
fuelectenerg-1427	758	19	29	29	NUM
fuelectenerg-1427	758	20	)	)	PUNCT
fuelectenerg-1427	758	21	from	from	ADP
fuelectenerg-1427	758	22	one	one	NUM
fuelectenerg-1427	758	23	form	form	NOUN
fuelectenerg-1427	758	24	to	to	ADP
fuelectenerg-1427	758	25	another	another	PRON
fuelectenerg-1427	758	26	,	,	PUNCT
fuelectenerg-1427	758	27	some	some	DET
fuelectenerg-1427	758	28	transformations	transformation	NOUN
fuelectenerg-1427	758	29	produce	produce	VERB
fuelectenerg-1427	758	30	flattened	flatten	VERB
fuelectenerg-1427	758	31	forms	form	NOUN
fuelectenerg-1427	758	32	with	with	ADP
fuelectenerg-1427	758	33	a	a	DET
fuelectenerg-1427	758	34	smaller	small	ADJ
fuelectenerg-1427	758	35	number	number	NOUN
fuelectenerg-1427	758	36	of	of	ADP
fuelectenerg-1427	758	37	cubes	cube	NOUN
fuelectenerg-1427	758	38	than	than	ADP
fuelectenerg-1427	758	39	the	the	DET
fuelectenerg-1427	758	40	others	other	NOUN
fuelectenerg-1427	758	41	.	.	PUNCT
fuelectenerg-1427	759	1	from	from	ADP
fuelectenerg-1427	759	2	this	this	DET
fuelectenerg-1427	759	3	observation	observation	NOUN
fuelectenerg-1427	759	4	rises	rise	VERB
fuelectenerg-1427	759	5	the	the	DET
fuelectenerg-1427	759	6	idea	idea	NOUN
fuelectenerg-1427	759	7	of	of	ADP
fuelectenerg-1427	759	8	a	a	DET
fuelectenerg-1427	759	9	possible	possible	ADJ
fuelectenerg-1427	759	10	application	application	NOUN
fuelectenerg-1427	759	11	of	of	ADP
fuelectenerg-1427	759	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	759	13	computing	computing	NOUN
fuelectenerg-1427	759	14	using	use	VERB
fuelectenerg-1427	759	15	the	the	DET
fuelectenerg-1427	759	16	s	s	PROPN
fuelectenerg-1427	759	17	/	/	SYM
fuelectenerg-1427	759	18	d	d	NOUN
fuelectenerg-1427	759	19	trees	tree	NOUN
fuelectenerg-1427	759	20	and	and	CCONJ
fuelectenerg-1427	759	21	related	related	ADJ
fuelectenerg-1427	759	22	transformations	transformation	NOUN
fuelectenerg-1427	759	23	to	to	PART
fuelectenerg-1427	759	24	produce	produce	VERB
fuelectenerg-1427	759	25	the	the	DET
fuelectenerg-1427	759	26	corresponding	corresponding	ADJ
fuelectenerg-1427	759	27	minimum	minimum	ADJ
fuelectenerg-1427	759	28	gfsops	gfsop	NOUN
fuelectenerg-1427	759	29	.	.	PUNCT
fuelectenerg-1427	760	1	analogous	analogous	ADJ
fuelectenerg-1427	760	2	to	to	ADP
fuelectenerg-1427	760	3	the	the	DET
fuelectenerg-1427	760	4	binary	binary	ADJ
fuelectenerg-1427	760	5	case	case	NOUN
fuelectenerg-1427	760	6	in	in	ADP
fuelectenerg-1427	760	7	equation	equation	NOUN
fuelectenerg-1427	760	8	(	(	PUNCT
fuelectenerg-1427	760	9	27	27	NUM
fuelectenerg-1427	760	10	)	)	PUNCT
fuelectenerg-1427	760	11	,	,	PUNCT
fuelectenerg-1427	760	12	the	the	DET
fuelectenerg-1427	760	13	ternary	ternary	ADJ
fuelectenerg-1427	760	14	gifs	gif	NOUN
fuelectenerg-1427	760	15	can	can	AUX
fuelectenerg-1427	760	16	be	be	AUX
fuelectenerg-1427	760	17	defined	define	VERB
fuelectenerg-1427	760	18	as	as	ADP
fuelectenerg-1427	760	19	the	the	DET
fuelectenerg-1427	760	20	union	union	NOUN
fuelectenerg-1427	760	21	of	of	ADP
fuelectenerg-1427	760	22	ternary	ternary	PROPN
fuelectenerg-1427	760	23	ifs	ifs	PROPN
fuelectenerg-1427	760	24	.	.	PUNCT
fuelectenerg-1427	761	1	definition	definition	NOUN
fuelectenerg-1427	761	2	3	3	NUM
fuelectenerg-1427	761	3	.	.	PUNCT
fuelectenerg-1427	762	1	the	the	DET
fuelectenerg-1427	762	2	family	family	NOUN
fuelectenerg-1427	762	3	of	of	ADP
fuelectenerg-1427	762	4	forms	form	NOUN
fuelectenerg-1427	762	5	,	,	PUNCT
fuelectenerg-1427	762	6	which	which	PRON
fuelectenerg-1427	762	7	is	be	AUX
fuelectenerg-1427	762	8	created	create	VERB
fuelectenerg-1427	762	9	as	as	ADP
fuelectenerg-1427	762	10	a	a	DET
fuelectenerg-1427	762	11	union	union	NOUN
fuelectenerg-1427	762	12	of	of	ADP
fuelectenerg-1427	762	13	sets	set	NOUN
fuelectenerg-1427	762	14	of	of	ADP
fuelectenerg-1427	762	15	tifs	tif	NOUN
fuelectenerg-1427	762	16	for	for	ADP
fuelectenerg-1427	762	17	all	all	DET
fuelectenerg-1427	762	18	variable	variable	ADJ
fuelectenerg-1427	762	19	orders	order	NOUN
fuelectenerg-1427	762	20	,	,	PUNCT
fuelectenerg-1427	762	21	is	be	AUX
fuelectenerg-1427	762	22	called	call	VERB
fuelectenerg-1427	762	23	ternary	ternary	ADJ
fuelectenerg-1427	762	24	generalized	generalized	ADJ
fuelectenerg-1427	762	25	inclusive	inclusive	ADJ
fuelectenerg-1427	762	26	forms	form	NOUN
fuelectenerg-1427	762	27	(	(	PUNCT
fuelectenerg-1427	762	28	tgifs	tgif	NOUN
fuelectenerg-1427	762	29	)	)	PUNCT
fuelectenerg-1427	762	30	.	.	PUNCT
fuelectenerg-1427	763	1	109	109	NUM
fuelectenerg-1427	763	2	an	an	DET
fuelectenerg-1427	763	3	extended	extend	VERB
fuelectenerg-1427	763	4	green	green	ADJ
fuelectenerg-1427	763	5	sasao	sasao	PROPN
fuelectenerg-1427	763	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	763	7	of	of	ADP
fuelectenerg-1427	763	8	canonical	canonical	ADJ
fuelectenerg-1427	763	9	ternary	ternary	ADJ
fuelectenerg-1427	763	10	galois	galois	NOUN
fuelectenerg-1427	763	11	forms	form	NOUN
fuelectenerg-1427	763	12	...	...	PUNCT
fuelectenerg-1427	763	13	form	form	NOUN
fuelectenerg-1427	763	14	which	which	PRON
fuelectenerg-1427	763	15	is	be	AUX
fuelectenerg-1427	763	16	an	an	DET
fuelectenerg-1427	763	17	expansion	expansion	NOUN
fuelectenerg-1427	763	18	over	over	ADP
fuelectenerg-1427	763	19	certain	certain	ADJ
fuelectenerg-1427	763	20	transform	transform	NOUN
fuelectenerg-1427	763	21	matrix	matrix	NOUN
fuelectenerg-1427	763	22	(	(	PUNCT
fuelectenerg-1427	763	23	i.e.	i.e.	X
fuelectenerg-1427	763	24	,	,	PUNCT
fuelectenerg-1427	763	25	certain	certain	ADJ
fuelectenerg-1427	763	26	tif	tif	PROPN
fuelectenerg-1427	763	27	)	)	PUNCT
fuelectenerg-1427	763	28	and	and	CCONJ
fuelectenerg-1427	763	29	then	then	ADV
fuelectenerg-1427	763	30	transform	transform	VERB
fuelectenerg-1427	763	31	systematically	systematically	ADV
fuelectenerg-1427	763	32	from	from	ADP
fuelectenerg-1427	763	33	one	one	NUM
fuelectenerg-1427	763	34	form	form	NOUN
fuelectenerg-1427	763	35	to	to	ADP
fuelectenerg-1427	763	36	another	another	DET
fuelectenerg-1427	763	37	form	form	NOUN
fuelectenerg-1427	763	38	without	without	ADP
fuelectenerg-1427	763	39	the	the	DET
fuelectenerg-1427	763	40	need	need	NOUN
fuelectenerg-1427	763	41	to	to	PART
fuelectenerg-1427	763	42	create	create	VERB
fuelectenerg-1427	763	43	all	all	PRON
fuelectenerg-1427	763	44	transform	transform	VERB
fuelectenerg-1427	763	45	matrices	matrix	NOUN
fuelectenerg-1427	763	46	from	from	ADP
fuelectenerg-1427	763	47	the	the	DET
fuelectenerg-1427	763	48	corresponding	correspond	VERB
fuelectenerg-1427	763	49	s	s	PROPN
fuelectenerg-1427	763	50	/	/	SYM
fuelectenerg-1427	763	51	d	d	NOUN
fuelectenerg-1427	763	52	trees	tree	NOUN
fuelectenerg-1427	763	53	.	.	PUNCT
fuelectenerg-1427	764	1	this	this	DET
fuelectenerg-1427	764	2	general	general	ADJ
fuelectenerg-1427	764	3	approach	approach	NOUN
fuelectenerg-1427	764	4	can	can	AUX
fuelectenerg-1427	764	5	lead	lead	VERB
fuelectenerg-1427	764	6	to	to	ADP
fuelectenerg-1427	764	7	several	several	ADJ
fuelectenerg-1427	764	8	algorithms	algorithm	NOUN
fuelectenerg-1427	764	9	of	of	ADP
fuelectenerg-1427	764	10	various	various	ADJ
fuelectenerg-1427	764	11	complexities	complexity	NOUN
fuelectenerg-1427	764	12	that	that	PRON
fuelectenerg-1427	764	13	generalize	generalize	VERB
fuelectenerg-1427	764	14	the	the	DET
fuelectenerg-1427	764	15	existing	exist	VERB
fuelectenerg-1427	764	16	binary	binary	ADJ
fuelectenerg-1427	764	17	algorithms	algorithm	NOUN
fuelectenerg-1427	764	18	to	to	PART
fuelectenerg-1427	764	19	obtain	obtain	VERB
fuelectenerg-1427	764	20	the	the	DET
fuelectenerg-1427	764	21	corresponding	corresponding	ADJ
fuelectenerg-1427	764	22	forms	form	NOUN
fuelectenerg-1427	764	23	such	such	ADJ
fuelectenerg-1427	764	24	as	as	ADP
fuelectenerg-1427	764	25	fprm	fprm	PROPN
fuelectenerg-1427	764	26	,	,	PUNCT
fuelectenerg-1427	764	27	grm	grm	NOUN
fuelectenerg-1427	764	28	and	and	CCONJ
fuelectenerg-1427	764	29	if	if	SCONJ
fuelectenerg-1427	764	30	forms	form	NOUN
fuelectenerg-1427	764	31	.	.	PUNCT
fuelectenerg-1427	764	32	example	example	NOUN
fuelectenerg-1427	765	1	3	3	NUM
fuelectenerg-1427	765	2	.	.	PUNCT
fuelectenerg-1427	765	3	using	use	VERB
fuelectenerg-1427	765	4	the	the	DET
fuelectenerg-1427	765	5	result	result	NOUN
fuelectenerg-1427	765	6	of	of	ADP
fuelectenerg-1427	765	7	example	example	NOUN
fuelectenerg-1427	765	8	2	2	NUM
fuelectenerg-1427	765	9	for	for	ADP
fuelectenerg-1427	765	10	the	the	DET
fuelectenerg-1427	765	11	expansion	expansion	NOUN
fuelectenerg-1427	765	12	of	of	ADP
fuelectenerg-1427	765	13	f	f	PROPN
fuelectenerg-1427	765	14	(	(	PUNCT
fuelectenerg-1427	765	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	765	16	)	)	PUNCT
fuelectenerg-1427	765	17	in	in	ADP
fuelectenerg-1427	765	18	terms	term	NOUN
fuelectenerg-1427	765	19	of	of	ADP
fuelectenerg-1427	765	20	the	the	DET
fuelectenerg-1427	765	21	ternary	ternary	ADJ
fuelectenerg-1427	765	22	shannon	shannon	NOUN
fuelectenerg-1427	765	23	expansion	expansion	NOUN
fuelectenerg-1427	765	24	(	(	PUNCT
fuelectenerg-1427	765	25	that	that	PRON
fuelectenerg-1427	765	26	resembles	resemble	VERB
fuelectenerg-1427	765	27	the	the	DET
fuelectenerg-1427	765	28	s	s	NOUN
fuelectenerg-1427	765	29	/	/	SYM
fuelectenerg-1427	765	30	d	d	NOUN
fuelectenerg-1427	765	31	tree	tree	NOUN
fuelectenerg-1427	765	32	for	for	ADP
fuelectenerg-1427	765	33	shannon	shannon	PROPN
fuelectenerg-1427	765	34	nodes	node	NOUN
fuelectenerg-1427	765	35	in	in	ADP
fuelectenerg-1427	765	36	both	both	DET
fuelectenerg-1427	765	37	levels	level	NOUN
fuelectenerg-1427	765	38	):	):	PUNCT
fuelectenerg-1427	765	39	f	f	X
fuelectenerg-1427	765	40	=	=	PUNCT
fuelectenerg-1427	765	41	0x1	0x1	NOUN
fuelectenerg-1427	765	42	1x2	1x2	NUM
fuelectenerg-1427	766	1	+2	+2	PRON
fuelectenerg-1427	766	2	·	·	PUNCT
fuelectenerg-1427	766	3	0x1	0x1	NOUN
fuelectenerg-1427	766	4	2x2	2x2	NUM
fuelectenerg-1427	766	5	+2	+2	PRON
fuelectenerg-1427	766	6	·	·	PUNCT
fuelectenerg-1427	766	7	1x1	1x1	NUM
fuelectenerg-1427	766	8	0x2	0x2	VERB
fuelectenerg-1427	766	9	+2	+2	PROPN
fuelectenerg-1427	766	10	·	·	PUNCT
fuelectenerg-1427	766	11	1x1	1x1	NUM
fuelectenerg-1427	766	12	1x2	1x2	NUM
fuelectenerg-1427	766	13	+2	+2	PRON
fuelectenerg-1427	766	14	·	·	PUNCT
fuelectenerg-1427	767	1	1x1	1x1	NUM
fuelectenerg-1427	767	2	2x2	2x2	NUM
fuelectenerg-1427	767	3	+	+	SYM
fuelectenerg-1427	767	4	2x1	2x1	NUM
fuelectenerg-1427	767	5	0x2	0x2	NOUN
fuelectenerg-1427	767	6	+2	+2	PROPN
fuelectenerg-1427	767	7	·	·	PUNCT
fuelectenerg-1427	767	8	2x1	2x1	NUM
fuelectenerg-1427	767	9	2x2	2x2	NUM
fuelectenerg-1427	767	10	,	,	PUNCT
fuelectenerg-1427	767	11	(	(	PUNCT
fuelectenerg-1427	767	12	29	29	NUM
fuelectenerg-1427	767	13	)	)	PUNCT
fuelectenerg-1427	767	14	we	we	PRON
fuelectenerg-1427	767	15	can	can	AUX
fuelectenerg-1427	767	16	substitute	substitute	VERB
fuelectenerg-1427	767	17	any	any	PRON
fuelectenerg-1427	767	18	of	of	ADP
fuelectenerg-1427	767	19	equations	equation	NOUN
fuelectenerg-1427	767	20	(	(	PUNCT
fuelectenerg-1427	767	21	7	7	NUM
fuelectenerg-1427	767	22	)	)	PUNCT
fuelectenerg-1427	767	23	(	(	PUNCT
fuelectenerg-1427	767	24	15	15	NUM
fuelectenerg-1427	767	25	)	)	PUNCT
fuelectenerg-1427	767	26	,	,	PUNCT
fuelectenerg-1427	767	27	or	or	CCONJ
fuelectenerg-1427	767	28	a	a	DET
fuelectenerg-1427	767	29	mix	mix	NOUN
fuelectenerg-1427	767	30	of	of	ADP
fuelectenerg-1427	767	31	these	these	DET
fuelectenerg-1427	767	32	equations	equation	NOUN
fuelectenerg-1427	767	33	,	,	PUNCT
fuelectenerg-1427	767	34	to	to	PART
fuelectenerg-1427	767	35	transform	transform	VERB
fuelectenerg-1427	767	36	one	one	NUM
fuelectenerg-1427	767	37	flattened	flatten	VERB
fuelectenerg-1427	767	38	form	form	NOUN
fuelectenerg-1427	767	39	to	to	ADP
fuelectenerg-1427	767	40	another	another	PRON
fuelectenerg-1427	767	41	.	.	PUNCT
fuelectenerg-1427	768	1	for	for	ADP
fuelectenerg-1427	768	2	example	example	NOUN
fuelectenerg-1427	768	3	,	,	PUNCT
fuelectenerg-1427	768	4	if	if	SCONJ
fuelectenerg-1427	768	5	we	we	PRON
fuelectenerg-1427	768	6	substitute	substitute	VERB
fuelectenerg-1427	768	7	equations	equation	NOUN
fuelectenerg-1427	768	8	(	(	PUNCT
fuelectenerg-1427	768	9	7	7	NUM
fuelectenerg-1427	768	10	)	)	PUNCT
fuelectenerg-1427	768	11	and	and	CCONJ
fuelectenerg-1427	768	12	(	(	PUNCT
fuelectenerg-1427	768	13	11	11	NUM
fuelectenerg-1427	768	14	)	)	PUNCT
fuelectenerg-1427	768	15	,	,	PUNCT
fuelectenerg-1427	768	16	we	we	PRON
fuelectenerg-1427	768	17	obtain	obtain	VERB
fuelectenerg-1427	768	18	:	:	PUNCT
fuelectenerg-1427	768	19	f	f	PROPN
fuelectenerg-1427	768	20	=(	=(	NOUN
fuelectenerg-1427	768	21	2(x1	2(x1	NUM
fuelectenerg-1427	768	22	)	)	PUNCT
fuelectenerg-1427	768	23	2	2	NUM
fuelectenerg-1427	768	24	+1)(2(x′2	+1)(2(x′2	NOUN
fuelectenerg-1427	768	25	)	)	PUNCT
fuelectenerg-1427	768	26	2	2	NUM
fuelectenerg-1427	768	27	+	+	SYM
fuelectenerg-1427	768	28	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	768	29	)	)	PUNCT
fuelectenerg-1427	768	30	2	2	NUM
fuelectenerg-1427	768	31	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	768	32	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	768	33	)	)	PUNCT
fuelectenerg-1427	768	34	2	2	NUM
fuelectenerg-1427	768	35	+	+	CCONJ
fuelectenerg-1427	768	36	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	768	37	)	)	PUNCT
fuelectenerg-1427	768	38	2	2	NUM
fuelectenerg-1427	768	39	+1	+1	PROPN
fuelectenerg-1427	768	40	)	)	PUNCT
fuelectenerg-1427	768	41	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	768	42	)	)	PUNCT
fuelectenerg-1427	768	43	2	2	NUM
fuelectenerg-1427	769	1	+	+	CCONJ
fuelectenerg-1427	769	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	769	3	′	′	NOUN
fuelectenerg-1427	769	4	2	2	NUM
fuelectenerg-1427	769	5	)	)	PUNCT
fuelectenerg-1427	769	6	2	2	NUM
fuelectenerg-1427	769	7	+	+	CCONJ
fuelectenerg-1427	769	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	769	9	)	)	PUNCT
fuelectenerg-1427	769	10	2	2	NUM
fuelectenerg-1427	769	11	+	+	NUM
fuelectenerg-1427	769	12	x′1	x′1	X
fuelectenerg-1427	769	13	)	)	PUNCT
fuelectenerg-1427	769	14	·	·	PUNCT
fuelectenerg-1427	770	1	2x2	2x2	NUM
fuelectenerg-1427	770	2	+	+	NUM
fuelectenerg-1427	770	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	770	4	)	)	PUNCT
fuelectenerg-1427	770	5	2	2	NUM
fuelectenerg-1427	770	6	+1	+1	NOUN
fuelectenerg-1427	770	7	)	)	PUNCT
fuelectenerg-1427	770	8	+2	+2	PROPN
fuelectenerg-1427	770	9	·	·	PUNCT
fuelectenerg-1427	771	1	2x1	2x1	NUM
fuelectenerg-1427	771	2	2x2	2x2	NUM
fuelectenerg-1427	771	3	,	,	PUNCT
fuelectenerg-1427	771	4	(	(	PUNCT
fuelectenerg-1427	771	5	30	30	NUM
fuelectenerg-1427	771	6	)	)	PUNCT
fuelectenerg-1427	771	7	by	by	ADP
fuelectenerg-1427	771	8	utilizing	utilize	VERB
fuelectenerg-1427	771	9	gf	gf	NOUN
fuelectenerg-1427	771	10	addition	addition	NOUN
fuelectenerg-1427	771	11	and	and	CCONJ
fuelectenerg-1427	771	12	multiplication	multiplication	NOUN
fuelectenerg-1427	771	13	operators	operator	NOUN
fuelectenerg-1427	771	14	from	from	ADP
fuelectenerg-1427	771	15	figure	figure	NOUN
fuelectenerg-1427	771	16	1	1	NUM
fuelectenerg-1427	771	17	,	,	PUNCT
fuelectenerg-1427	771	18	equation	equation	NOUN
fuelectenerg-1427	771	19	(	(	PUNCT
fuelectenerg-1427	771	20	30	30	NUM
fuelectenerg-1427	771	21	)	)	PUNCT
fuelectenerg-1427	771	22	can	can	AUX
fuelectenerg-1427	771	23	be	be	AUX
fuelectenerg-1427	771	24	transformed	transform	VERB
fuelectenerg-1427	771	25	to	to	ADP
fuelectenerg-1427	771	26	:	:	PUNCT
fuelectenerg-1427	771	27	f	f	PROPN
fuelectenerg-1427	771	28	=(	=(	PROPN
fuelectenerg-1427	771	29	x1	x1	PROPN
fuelectenerg-1427	771	30	)	)	PUNCT
fuelectenerg-1427	771	31	2(x′2	2(x′2	NOUN
fuelectenerg-1427	771	32	)	)	PUNCT
fuelectenerg-1427	771	33	2	2	NUM
fuelectenerg-1427	771	34	+2(x1	+2(x1	NOUN
fuelectenerg-1427	771	35	)	)	PUNCT
fuelectenerg-1427	771	36	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	771	37	)	)	PUNCT
fuelectenerg-1427	771	38	2	2	NUM
fuelectenerg-1427	772	1	+	+	CCONJ
fuelectenerg-1427	772	2	x′2	x′2	X
fuelectenerg-1427	773	1	+	+	ADJ
fuelectenerg-1427	773	2	(	(	PUNCT
fuelectenerg-1427	773	3	x1	x1	ADJ
fuelectenerg-1427	773	4	)	)	PUNCT
fuelectenerg-1427	773	5	2	2	NUM
fuelectenerg-1427	773	6	(	(	PUNCT
fuelectenerg-1427	773	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	773	8	(	(	PUNCT
fuelectenerg-1427	773	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	773	10	)	)	PUNCT
fuelectenerg-1427	773	11	2(x2	2(x2	NUM
fuelectenerg-1427	773	12	)	)	PUNCT
fuelectenerg-1427	773	13	2	2	NUM
fuelectenerg-1427	774	1	+	+	NOUN
fuelectenerg-1427	774	2	(	(	PUNCT
fuelectenerg-1427	774	3	x′1	x′1	NOUN
fuelectenerg-1427	774	4	)	)	PUNCT
fuelectenerg-1427	774	5	2	2	NUM
fuelectenerg-1427	775	1	+	+	NOUN
fuelectenerg-1427	775	2	(	(	PUNCT
fuelectenerg-1427	775	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	775	4	)	)	PUNCT
fuelectenerg-1427	775	5	2	2	NUM
fuelectenerg-1427	775	6	+2x′1	+2x′1	ADP
fuelectenerg-1427	775	7	+2(x′1	+2(x′1	PROPN
fuelectenerg-1427	775	8	)	)	PUNCT
fuelectenerg-1427	775	9	2(x′2	2(x′2	NOUN
fuelectenerg-1427	775	10	)	)	PUNCT
fuelectenerg-1427	775	11	2	2	NUM
fuelectenerg-1427	776	1	+	+	ADJ
fuelectenerg-1427	776	2	(	(	PUNCT
fuelectenerg-1427	776	3	x′1	x′1	NOUN
fuelectenerg-1427	776	4	)	)	PUNCT
fuelectenerg-1427	776	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	776	6	(	(	PUNCT
fuelectenerg-1427	776	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	776	8	′	′	NUM
fuelectenerg-1427	776	9	2	2	NUM
fuelectenerg-1427	776	10	)	)	PUNCT
fuelectenerg-1427	776	11	2	2	NUM
fuelectenerg-1427	776	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	776	13	+	+	PROPN
fuelectenerg-1427	776	14	(	(	PUNCT
fuelectenerg-1427	776	15	x′1	x′1	NOUN
fuelectenerg-1427	776	16	)	)	PUNCT
fuelectenerg-1427	776	17	2	2	NUM
fuelectenerg-1427	776	18	·	·	SYM
fuelectenerg-1427	776	19	2x2	2x2	NUM
fuelectenerg-1427	776	20	+2(x′1	+2(x′1	NOUN
fuelectenerg-1427	776	21	)	)	PUNCT
fuelectenerg-1427	776	22	2x2	2x2	NUM
fuelectenerg-1427	777	1	+2	+2	PROPN
fuelectenerg-1427	777	2	(	(	PUNCT
fuelectenerg-1427	777	3	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	777	4	)	)	PUNCT
fuelectenerg-1427	777	5	2	2	NUM
fuelectenerg-1427	777	6	+	+	SYM
fuelectenerg-1427	777	7	2x1	2x1	NUM
fuelectenerg-1427	777	8	+2	+2	NOUN
fuelectenerg-1427	777	9	(	(	PUNCT
fuelectenerg-1427	777	10	2x1	2x1	NUM
fuelectenerg-1427	777	11	)	)	PUNCT
fuelectenerg-1427	777	12	(	(	PUNCT
fuelectenerg-1427	777	13	2x2	2x2	NUM
fuelectenerg-1427	777	14	)	)	PUNCT
fuelectenerg-1427	777	15	.	.	PUNCT
fuelectenerg-1427	778	1	(	(	PUNCT
fuelectenerg-1427	778	2	31	31	NUM
fuelectenerg-1427	778	3	)	)	PUNCT
fuelectenerg-1427	778	4	let	let	VERB
fuelectenerg-1427	778	5	us	we	PRON
fuelectenerg-1427	778	6	define	define	VERB
fuelectenerg-1427	778	7	,	,	PUNCT
fuelectenerg-1427	778	8	as	as	ADP
fuelectenerg-1427	778	9	one	one	NUM
fuelectenerg-1427	778	10	of	of	ADP
fuelectenerg-1427	778	11	possible	possible	ADJ
fuelectenerg-1427	778	12	definitions	definition	NOUN
fuelectenerg-1427	778	13	,	,	PUNCT
fuelectenerg-1427	778	14	the	the	DET
fuelectenerg-1427	778	15	cost	cost	NOUN
fuelectenerg-1427	778	16	of	of	ADP
fuelectenerg-1427	778	17	the	the	DET
fuelectenerg-1427	778	18	flattened	flatten	VERB
fuelectenerg-1427	778	19	form	form	NOUN
fuelectenerg-1427	778	20	(	(	PUNCT
fuelectenerg-1427	778	21	expression	expression	NOUN
fuelectenerg-1427	778	22	)	)	PUNCT
fuelectenerg-1427	778	23	to	to	PART
fuelectenerg-1427	778	24	be	be	AUX
fuelectenerg-1427	778	25	:	:	PUNCT
fuelectenerg-1427	778	26	cost	cost	NOUN
fuelectenerg-1427	778	27	=	=	SYM
fuelectenerg-1427	778	28	#	#	NOUN
fuelectenerg-1427	778	29	cubes	cube	NOUN
fuelectenerg-1427	778	30	(	(	PUNCT
fuelectenerg-1427	778	31	32	32	NUM
fuelectenerg-1427	778	32	)	)	PUNCT
fuelectenerg-1427	778	33	then	then	ADV
fuelectenerg-1427	778	34	,	,	PUNCT
fuelectenerg-1427	778	35	we	we	PRON
fuelectenerg-1427	778	36	observe	observe	VERB
fuelectenerg-1427	778	37	that	that	SCONJ
fuelectenerg-1427	778	38	equation	equation	NOUN
fuelectenerg-1427	778	39	(	(	PUNCT
fuelectenerg-1427	778	40	29	29	NUM
fuelectenerg-1427	778	41	)	)	PUNCT
fuelectenerg-1427	778	42	has	have	VERB
fuelectenerg-1427	778	43	the	the	DET
fuelectenerg-1427	778	44	cost	cost	NOUN
fuelectenerg-1427	778	45	of	of	ADP
fuelectenerg-1427	778	46	seven	seven	NUM
fuelectenerg-1427	778	47	,	,	PUNCT
fuelectenerg-1427	778	48	while	while	SCONJ
fuelectenerg-1427	778	49	equation	equation	NOUN
fuelectenerg-1427	778	50	(	(	PUNCT
fuelectenerg-1427	778	51	31	31	NUM
fuelectenerg-1427	778	52	)	)	PUNCT
fuelectenerg-1427	778	53	has	have	VERB
fuelectenerg-1427	778	54	the	the	DET
fuelectenerg-1427	778	55	cost	cost	NOUN
fuelectenerg-1427	778	56	of	of	ADP
fuelectenerg-1427	778	57	19	19	NUM
fuelectenerg-1427	778	58	.	.	PUNCT
fuelectenerg-1427	779	1	thus	thus	ADV
fuelectenerg-1427	779	2	,	,	PUNCT
fuelectenerg-1427	779	3	the	the	DET
fuelectenerg-1427	779	4	inverse	inverse	NOUN
fuelectenerg-1427	779	5	transformations	transformation	NOUN
fuelectenerg-1427	779	6	applied	apply	VERB
fuelectenerg-1427	779	7	to	to	ADP
fuelectenerg-1427	779	8	equation	equation	NOUN
fuelectenerg-1427	779	9	(	(	PUNCT
fuelectenerg-1427	779	10	31	31	NUM
fuelectenerg-1427	779	11	)	)	PUNCT
fuelectenerg-1427	779	12	would	would	AUX
fuelectenerg-1427	779	13	lead	lead	VERB
fuelectenerg-1427	779	14	to	to	ADP
fuelectenerg-1427	779	15	equation	equation	NOUN
fuelectenerg-1427	779	16	(	(	PUNCT
fuelectenerg-1427	779	17	29	29	NUM
fuelectenerg-1427	779	18	)	)	PUNCT
fuelectenerg-1427	779	19	and	and	CCONJ
fuelectenerg-1427	779	20	a	a	DET
fuelectenerg-1427	779	21	reduction	reduction	NOUN
fuelectenerg-1427	779	22	of	of	ADP
fuelectenerg-1427	779	23	cost	cost	NOUN
fuelectenerg-1427	779	24	from	from	ADP
fuelectenerg-1427	779	25	19	19	NUM
fuelectenerg-1427	779	26	to	to	PART
fuelectenerg-1427	779	27	seven	seven	NUM
fuelectenerg-1427	779	28	.	.	PUNCT
fuelectenerg-1427	780	1	using	use	VERB
fuelectenerg-1427	780	2	the	the	DET
fuelectenerg-1427	780	3	same	same	ADJ
fuelectenerg-1427	780	4	approach	approach	NOUN
fuelectenerg-1427	780	5	,	,	PUNCT
fuelectenerg-1427	780	6	we	we	PRON
fuelectenerg-1427	780	7	can	can	AUX
fuelectenerg-1427	780	8	generate	generate	VERB
fuelectenerg-1427	780	9	a	a	DET
fuelectenerg-1427	780	10	subset	subset	NOUN
fuelectenerg-1427	780	11	of	of	ADP
fuelectenerg-1427	780	12	possible	possible	ADJ
fuelectenerg-1427	780	13	gfsop	gfsop	NOUN
fuelectenerg-1427	780	14	expressions	expression	NOUN
fuelectenerg-1427	780	15	(	(	PUNCT
fuelectenerg-1427	780	16	flattened	flatten	VERB
fuelectenerg-1427	780	17	forms	form	NOUN
fuelectenerg-1427	780	18	)	)	PUNCT
fuelectenerg-1427	780	19	.	.	PUNCT
fuelectenerg-1427	781	1	note	note	VERB
fuelectenerg-1427	781	2	that	that	SCONJ
fuelectenerg-1427	781	3	all	all	PRON
fuelectenerg-1427	781	4	of	of	ADP
fuelectenerg-1427	781	5	these	these	DET
fuelectenerg-1427	781	6	gfsop	gfsop	NOUN
fuelectenerg-1427	781	7	expressions	expression	NOUN
fuelectenerg-1427	781	8	are	be	AUX
fuelectenerg-1427	781	9	equivalent	equivalent	ADJ
fuelectenerg-1427	781	10	since	since	SCONJ
fuelectenerg-1427	781	11	they	they	PRON
fuelectenerg-1427	781	12	produce	produce	VERB
fuelectenerg-1427	781	13	the	the	DET
fuelectenerg-1427	781	14	same	same	ADJ
fuelectenerg-1427	781	15	function	function	NOUN
fuelectenerg-1427	781	16	in	in	ADP
fuelectenerg-1427	781	17	different	different	ADJ
fuelectenerg-1427	781	18	forms	form	NOUN
fuelectenerg-1427	781	19	.	.	PUNCT
fuelectenerg-1427	782	1	yet	yet	ADV
fuelectenerg-1427	782	2	,	,	PUNCT
fuelectenerg-1427	782	3	as	as	SCONJ
fuelectenerg-1427	782	4	can	can	AUX
fuelectenerg-1427	782	5	be	be	AUX
fuelectenerg-1427	782	6	observed	observe	VERB
fuelectenerg-1427	782	7	from	from	ADP
fuelectenerg-1427	782	8	equation	equation	NOUN
fuelectenerg-1427	782	9	(	(	PUNCT
fuelectenerg-1427	782	10	31	31	NUM
fuelectenerg-1427	782	11	)	)	PUNCT
fuelectenerg-1427	782	12	,	,	PUNCT
fuelectenerg-1427	782	13	by	by	ADP
fuelectenerg-1427	782	14	further	further	ADJ
fuelectenerg-1427	782	15	transformations	transformation	NOUN
fuelectenerg-1427	782	16	of	of	ADP
fuelectenerg-1427	782	17	equation	equation	NOUN
fuelectenerg-1427	782	18	(	(	PUNCT
fuelectenerg-1427	782	19	29	29	NUM
fuelectenerg-1427	782	20	)	)	PUNCT
fuelectenerg-1427	782	21	from	from	ADP
fuelectenerg-1427	782	22	one	one	NUM
fuelectenerg-1427	782	23	form	form	NOUN
fuelectenerg-1427	782	24	to	to	ADP
fuelectenerg-1427	782	25	another	another	PRON
fuelectenerg-1427	782	26	,	,	PUNCT
fuelectenerg-1427	782	27	some	some	DET
fuelectenerg-1427	782	28	transformations	transformation	NOUN
fuelectenerg-1427	782	29	produce	produce	VERB
fuelectenerg-1427	782	30	flattened	flatten	VERB
fuelectenerg-1427	782	31	forms	form	NOUN
fuelectenerg-1427	782	32	with	with	ADP
fuelectenerg-1427	782	33	a	a	DET
fuelectenerg-1427	782	34	smaller	small	ADJ
fuelectenerg-1427	782	35	number	number	NOUN
fuelectenerg-1427	782	36	of	of	ADP
fuelectenerg-1427	782	37	cubes	cube	NOUN
fuelectenerg-1427	782	38	than	than	ADP
fuelectenerg-1427	782	39	the	the	DET
fuelectenerg-1427	782	40	others	other	NOUN
fuelectenerg-1427	782	41	.	.	PUNCT
fuelectenerg-1427	783	1	from	from	ADP
fuelectenerg-1427	783	2	this	this	DET
fuelectenerg-1427	783	3	observation	observation	NOUN
fuelectenerg-1427	783	4	rises	rise	VERB
fuelectenerg-1427	783	5	the	the	DET
fuelectenerg-1427	783	6	idea	idea	NOUN
fuelectenerg-1427	783	7	of	of	ADP
fuelectenerg-1427	783	8	a	a	DET
fuelectenerg-1427	783	9	possible	possible	ADJ
fuelectenerg-1427	783	10	application	application	NOUN
fuelectenerg-1427	783	11	of	of	ADP
fuelectenerg-1427	783	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	783	13	computing	computing	NOUN
fuelectenerg-1427	783	14	using	use	VERB
fuelectenerg-1427	783	15	the	the	DET
fuelectenerg-1427	783	16	s	s	PROPN
fuelectenerg-1427	783	17	/	/	SYM
fuelectenerg-1427	783	18	d	d	NOUN
fuelectenerg-1427	783	19	trees	tree	NOUN
fuelectenerg-1427	783	20	and	and	CCONJ
fuelectenerg-1427	783	21	related	related	ADJ
fuelectenerg-1427	783	22	transformations	transformation	NOUN
fuelectenerg-1427	783	23	to	to	PART
fuelectenerg-1427	783	24	produce	produce	VERB
fuelectenerg-1427	783	25	the	the	DET
fuelectenerg-1427	783	26	corresponding	corresponding	ADJ
fuelectenerg-1427	783	27	minimum	minimum	ADJ
fuelectenerg-1427	783	28	gfsops	gfsop	NOUN
fuelectenerg-1427	783	29	.	.	PUNCT
fuelectenerg-1427	784	1	analogous	analogous	ADJ
fuelectenerg-1427	784	2	to	to	ADP
fuelectenerg-1427	784	3	the	the	DET
fuelectenerg-1427	784	4	binary	binary	ADJ
fuelectenerg-1427	784	5	case	case	NOUN
fuelectenerg-1427	784	6	in	in	ADP
fuelectenerg-1427	784	7	equation	equation	NOUN
fuelectenerg-1427	784	8	(	(	PUNCT
fuelectenerg-1427	784	9	27	27	NUM
fuelectenerg-1427	784	10	)	)	PUNCT
fuelectenerg-1427	784	11	,	,	PUNCT
fuelectenerg-1427	784	12	the	the	DET
fuelectenerg-1427	784	13	ternary	ternary	ADJ
fuelectenerg-1427	784	14	gifs	gif	NOUN
fuelectenerg-1427	784	15	can	can	AUX
fuelectenerg-1427	784	16	be	be	AUX
fuelectenerg-1427	784	17	defined	define	VERB
fuelectenerg-1427	784	18	as	as	ADP
fuelectenerg-1427	784	19	the	the	DET
fuelectenerg-1427	784	20	union	union	NOUN
fuelectenerg-1427	784	21	of	of	ADP
fuelectenerg-1427	784	22	ternary	ternary	PROPN
fuelectenerg-1427	784	23	ifs	ifs	PROPN
fuelectenerg-1427	784	24	.	.	PUNCT
fuelectenerg-1427	785	1	definition	definition	NOUN
fuelectenerg-1427	785	2	3	3	NUM
fuelectenerg-1427	785	3	.	.	PUNCT
fuelectenerg-1427	786	1	the	the	DET
fuelectenerg-1427	786	2	family	family	NOUN
fuelectenerg-1427	786	3	of	of	ADP
fuelectenerg-1427	786	4	forms	form	NOUN
fuelectenerg-1427	786	5	,	,	PUNCT
fuelectenerg-1427	786	6	which	which	PRON
fuelectenerg-1427	786	7	is	be	AUX
fuelectenerg-1427	786	8	created	create	VERB
fuelectenerg-1427	786	9	as	as	ADP
fuelectenerg-1427	786	10	a	a	DET
fuelectenerg-1427	786	11	union	union	NOUN
fuelectenerg-1427	786	12	of	of	ADP
fuelectenerg-1427	786	13	sets	set	NOUN
fuelectenerg-1427	786	14	of	of	ADP
fuelectenerg-1427	786	15	tifs	tif	NOUN
fuelectenerg-1427	786	16	for	for	ADP
fuelectenerg-1427	786	17	all	all	DET
fuelectenerg-1427	786	18	variable	variable	ADJ
fuelectenerg-1427	786	19	orders	order	NOUN
fuelectenerg-1427	786	20	,	,	PUNCT
fuelectenerg-1427	786	21	is	be	AUX
fuelectenerg-1427	786	22	called	call	VERB
fuelectenerg-1427	786	23	ternary	ternary	ADJ
fuelectenerg-1427	786	24	generalized	generalized	ADJ
fuelectenerg-1427	786	25	inclusive	inclusive	ADJ
fuelectenerg-1427	786	26	forms	form	NOUN
fuelectenerg-1427	786	27	(	(	PUNCT
fuelectenerg-1427	786	28	tgifs	tgif	NOUN
fuelectenerg-1427	786	29	)	)	PUNCT
fuelectenerg-1427	786	30	.	.	PUNCT
fuelectenerg-1427	787	1	109	109	NUM
fuelectenerg-1427	787	2	an	an	DET
fuelectenerg-1427	787	3	extended	extend	VERB
fuelectenerg-1427	787	4	green	green	ADJ
fuelectenerg-1427	787	5	sasao	sasao	PROPN
fuelectenerg-1427	787	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	787	7	of	of	ADP
fuelectenerg-1427	787	8	canonical	canonical	ADJ
fuelectenerg-1427	787	9	ternary	ternary	ADJ
fuelectenerg-1427	787	10	galois	galois	NOUN
fuelectenerg-1427	787	11	forms	form	NOUN
fuelectenerg-1427	787	12	...	...	PUNCT
fuelectenerg-1427	787	13	form	form	NOUN
fuelectenerg-1427	787	14	which	which	PRON
fuelectenerg-1427	787	15	is	be	AUX
fuelectenerg-1427	787	16	an	an	DET
fuelectenerg-1427	787	17	expansion	expansion	NOUN
fuelectenerg-1427	787	18	over	over	ADP
fuelectenerg-1427	787	19	certain	certain	ADJ
fuelectenerg-1427	787	20	transform	transform	NOUN
fuelectenerg-1427	787	21	matrix	matrix	NOUN
fuelectenerg-1427	787	22	(	(	PUNCT
fuelectenerg-1427	787	23	i.e.	i.e.	X
fuelectenerg-1427	787	24	,	,	PUNCT
fuelectenerg-1427	787	25	certain	certain	ADJ
fuelectenerg-1427	787	26	tif	tif	PROPN
fuelectenerg-1427	787	27	)	)	PUNCT
fuelectenerg-1427	787	28	and	and	CCONJ
fuelectenerg-1427	787	29	then	then	ADV
fuelectenerg-1427	787	30	transform	transform	VERB
fuelectenerg-1427	787	31	systematically	systematically	ADV
fuelectenerg-1427	787	32	from	from	ADP
fuelectenerg-1427	787	33	one	one	NUM
fuelectenerg-1427	787	34	form	form	NOUN
fuelectenerg-1427	787	35	to	to	ADP
fuelectenerg-1427	787	36	another	another	DET
fuelectenerg-1427	787	37	form	form	NOUN
fuelectenerg-1427	787	38	without	without	ADP
fuelectenerg-1427	787	39	the	the	DET
fuelectenerg-1427	787	40	need	need	NOUN
fuelectenerg-1427	787	41	to	to	PART
fuelectenerg-1427	787	42	create	create	VERB
fuelectenerg-1427	787	43	all	all	PRON
fuelectenerg-1427	787	44	transform	transform	VERB
fuelectenerg-1427	787	45	matrices	matrix	NOUN
fuelectenerg-1427	787	46	from	from	ADP
fuelectenerg-1427	787	47	the	the	DET
fuelectenerg-1427	787	48	corresponding	correspond	VERB
fuelectenerg-1427	787	49	s	s	PROPN
fuelectenerg-1427	787	50	/	/	SYM
fuelectenerg-1427	787	51	d	d	NOUN
fuelectenerg-1427	787	52	trees	tree	NOUN
fuelectenerg-1427	787	53	.	.	PUNCT
fuelectenerg-1427	788	1	this	this	DET
fuelectenerg-1427	788	2	general	general	ADJ
fuelectenerg-1427	788	3	approach	approach	NOUN
fuelectenerg-1427	788	4	can	can	AUX
fuelectenerg-1427	788	5	lead	lead	VERB
fuelectenerg-1427	788	6	to	to	ADP
fuelectenerg-1427	788	7	several	several	ADJ
fuelectenerg-1427	788	8	algorithms	algorithm	NOUN
fuelectenerg-1427	788	9	of	of	ADP
fuelectenerg-1427	788	10	various	various	ADJ
fuelectenerg-1427	788	11	complexities	complexity	NOUN
fuelectenerg-1427	788	12	that	that	PRON
fuelectenerg-1427	788	13	generalize	generalize	VERB
fuelectenerg-1427	788	14	the	the	DET
fuelectenerg-1427	788	15	existing	exist	VERB
fuelectenerg-1427	788	16	binary	binary	ADJ
fuelectenerg-1427	788	17	algorithms	algorithm	NOUN
fuelectenerg-1427	788	18	to	to	PART
fuelectenerg-1427	788	19	obtain	obtain	VERB
fuelectenerg-1427	788	20	the	the	DET
fuelectenerg-1427	788	21	corresponding	corresponding	ADJ
fuelectenerg-1427	788	22	forms	form	NOUN
fuelectenerg-1427	788	23	such	such	ADJ
fuelectenerg-1427	788	24	as	as	ADP
fuelectenerg-1427	788	25	fprm	fprm	PROPN
fuelectenerg-1427	788	26	,	,	PUNCT
fuelectenerg-1427	788	27	grm	grm	NOUN
fuelectenerg-1427	788	28	and	and	CCONJ
fuelectenerg-1427	788	29	if	if	SCONJ
fuelectenerg-1427	788	30	forms	form	NOUN
fuelectenerg-1427	788	31	.	.	PUNCT
fuelectenerg-1427	788	32	example	example	NOUN
fuelectenerg-1427	789	1	3	3	NUM
fuelectenerg-1427	789	2	.	.	PUNCT
fuelectenerg-1427	789	3	using	use	VERB
fuelectenerg-1427	789	4	the	the	DET
fuelectenerg-1427	789	5	result	result	NOUN
fuelectenerg-1427	789	6	of	of	ADP
fuelectenerg-1427	789	7	example	example	NOUN
fuelectenerg-1427	789	8	2	2	NUM
fuelectenerg-1427	789	9	for	for	ADP
fuelectenerg-1427	789	10	the	the	DET
fuelectenerg-1427	789	11	expansion	expansion	NOUN
fuelectenerg-1427	789	12	of	of	ADP
fuelectenerg-1427	789	13	f	f	PROPN
fuelectenerg-1427	789	14	(	(	PUNCT
fuelectenerg-1427	789	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	789	16	)	)	PUNCT
fuelectenerg-1427	789	17	in	in	ADP
fuelectenerg-1427	789	18	terms	term	NOUN
fuelectenerg-1427	789	19	of	of	ADP
fuelectenerg-1427	789	20	the	the	DET
fuelectenerg-1427	789	21	ternary	ternary	ADJ
fuelectenerg-1427	789	22	shannon	shannon	NOUN
fuelectenerg-1427	789	23	expansion	expansion	NOUN
fuelectenerg-1427	789	24	(	(	PUNCT
fuelectenerg-1427	789	25	that	that	PRON
fuelectenerg-1427	789	26	resembles	resemble	VERB
fuelectenerg-1427	789	27	the	the	DET
fuelectenerg-1427	789	28	s	s	NOUN
fuelectenerg-1427	789	29	/	/	SYM
fuelectenerg-1427	789	30	d	d	NOUN
fuelectenerg-1427	789	31	tree	tree	NOUN
fuelectenerg-1427	789	32	for	for	ADP
fuelectenerg-1427	789	33	shannon	shannon	PROPN
fuelectenerg-1427	789	34	nodes	node	NOUN
fuelectenerg-1427	789	35	in	in	ADP
fuelectenerg-1427	789	36	both	both	DET
fuelectenerg-1427	789	37	levels	level	NOUN
fuelectenerg-1427	789	38	):	):	PUNCT
fuelectenerg-1427	789	39	f	f	X
fuelectenerg-1427	789	40	=	=	PUNCT
fuelectenerg-1427	789	41	0x1	0x1	NOUN
fuelectenerg-1427	789	42	1x2	1x2	NUM
fuelectenerg-1427	790	1	+2	+2	PRON
fuelectenerg-1427	790	2	·	·	PUNCT
fuelectenerg-1427	790	3	0x1	0x1	NOUN
fuelectenerg-1427	790	4	2x2	2x2	NUM
fuelectenerg-1427	790	5	+2	+2	PRON
fuelectenerg-1427	790	6	·	·	PUNCT
fuelectenerg-1427	790	7	1x1	1x1	NUM
fuelectenerg-1427	790	8	0x2	0x2	VERB
fuelectenerg-1427	790	9	+2	+2	PROPN
fuelectenerg-1427	790	10	·	·	PUNCT
fuelectenerg-1427	790	11	1x1	1x1	NUM
fuelectenerg-1427	790	12	1x2	1x2	NUM
fuelectenerg-1427	790	13	+2	+2	PRON
fuelectenerg-1427	790	14	·	·	PUNCT
fuelectenerg-1427	791	1	1x1	1x1	NUM
fuelectenerg-1427	791	2	2x2	2x2	NUM
fuelectenerg-1427	791	3	+	+	SYM
fuelectenerg-1427	791	4	2x1	2x1	NUM
fuelectenerg-1427	791	5	0x2	0x2	NOUN
fuelectenerg-1427	791	6	+2	+2	PROPN
fuelectenerg-1427	791	7	·	·	PUNCT
fuelectenerg-1427	791	8	2x1	2x1	NUM
fuelectenerg-1427	791	9	2x2	2x2	NUM
fuelectenerg-1427	791	10	,	,	PUNCT
fuelectenerg-1427	791	11	(	(	PUNCT
fuelectenerg-1427	791	12	29	29	NUM
fuelectenerg-1427	791	13	)	)	PUNCT
fuelectenerg-1427	791	14	we	we	PRON
fuelectenerg-1427	791	15	can	can	AUX
fuelectenerg-1427	791	16	substitute	substitute	VERB
fuelectenerg-1427	791	17	any	any	PRON
fuelectenerg-1427	791	18	of	of	ADP
fuelectenerg-1427	791	19	equations	equation	NOUN
fuelectenerg-1427	791	20	(	(	PUNCT
fuelectenerg-1427	791	21	7	7	NUM
fuelectenerg-1427	791	22	)	)	PUNCT
fuelectenerg-1427	791	23	(	(	PUNCT
fuelectenerg-1427	791	24	15	15	NUM
fuelectenerg-1427	791	25	)	)	PUNCT
fuelectenerg-1427	791	26	,	,	PUNCT
fuelectenerg-1427	791	27	or	or	CCONJ
fuelectenerg-1427	791	28	a	a	DET
fuelectenerg-1427	791	29	mix	mix	NOUN
fuelectenerg-1427	791	30	of	of	ADP
fuelectenerg-1427	791	31	these	these	DET
fuelectenerg-1427	791	32	equations	equation	NOUN
fuelectenerg-1427	791	33	,	,	PUNCT
fuelectenerg-1427	791	34	to	to	PART
fuelectenerg-1427	791	35	transform	transform	VERB
fuelectenerg-1427	791	36	one	one	NUM
fuelectenerg-1427	791	37	flattened	flatten	VERB
fuelectenerg-1427	791	38	form	form	NOUN
fuelectenerg-1427	791	39	to	to	ADP
fuelectenerg-1427	791	40	another	another	PRON
fuelectenerg-1427	791	41	.	.	PUNCT
fuelectenerg-1427	792	1	for	for	ADP
fuelectenerg-1427	792	2	example	example	NOUN
fuelectenerg-1427	792	3	,	,	PUNCT
fuelectenerg-1427	792	4	if	if	SCONJ
fuelectenerg-1427	792	5	we	we	PRON
fuelectenerg-1427	792	6	substitute	substitute	VERB
fuelectenerg-1427	792	7	equations	equation	NOUN
fuelectenerg-1427	792	8	(	(	PUNCT
fuelectenerg-1427	792	9	7	7	NUM
fuelectenerg-1427	792	10	)	)	PUNCT
fuelectenerg-1427	792	11	and	and	CCONJ
fuelectenerg-1427	792	12	(	(	PUNCT
fuelectenerg-1427	792	13	11	11	NUM
fuelectenerg-1427	792	14	)	)	PUNCT
fuelectenerg-1427	792	15	,	,	PUNCT
fuelectenerg-1427	792	16	we	we	PRON
fuelectenerg-1427	792	17	obtain	obtain	VERB
fuelectenerg-1427	792	18	:	:	PUNCT
fuelectenerg-1427	792	19	f	f	PROPN
fuelectenerg-1427	792	20	=(	=(	NOUN
fuelectenerg-1427	792	21	2(x1	2(x1	NUM
fuelectenerg-1427	792	22	)	)	PUNCT
fuelectenerg-1427	792	23	2	2	NUM
fuelectenerg-1427	792	24	+1)(2(x′2	+1)(2(x′2	NOUN
fuelectenerg-1427	792	25	)	)	PUNCT
fuelectenerg-1427	792	26	2	2	NUM
fuelectenerg-1427	792	27	+	+	SYM
fuelectenerg-1427	792	28	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	792	29	)	)	PUNCT
fuelectenerg-1427	792	30	2	2	NUM
fuelectenerg-1427	792	31	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	792	32	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	792	33	)	)	PUNCT
fuelectenerg-1427	792	34	2	2	NUM
fuelectenerg-1427	792	35	+	+	CCONJ
fuelectenerg-1427	792	36	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	792	37	)	)	PUNCT
fuelectenerg-1427	792	38	2	2	NUM
fuelectenerg-1427	792	39	+1	+1	PROPN
fuelectenerg-1427	792	40	)	)	PUNCT
fuelectenerg-1427	792	41	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	792	42	)	)	PUNCT
fuelectenerg-1427	792	43	2	2	NUM
fuelectenerg-1427	793	1	+	+	CCONJ
fuelectenerg-1427	793	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	793	3	′	′	NOUN
fuelectenerg-1427	793	4	2	2	NUM
fuelectenerg-1427	793	5	)	)	PUNCT
fuelectenerg-1427	793	6	2	2	NUM
fuelectenerg-1427	793	7	+	+	CCONJ
fuelectenerg-1427	793	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	793	9	)	)	PUNCT
fuelectenerg-1427	793	10	2	2	NUM
fuelectenerg-1427	793	11	+	+	NUM
fuelectenerg-1427	793	12	x′1	x′1	X
fuelectenerg-1427	793	13	)	)	PUNCT
fuelectenerg-1427	793	14	·	·	PUNCT
fuelectenerg-1427	794	1	2x2	2x2	NUM
fuelectenerg-1427	794	2	+	+	NUM
fuelectenerg-1427	794	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	794	4	)	)	PUNCT
fuelectenerg-1427	794	5	2	2	NUM
fuelectenerg-1427	794	6	+1	+1	NOUN
fuelectenerg-1427	794	7	)	)	PUNCT
fuelectenerg-1427	794	8	+2	+2	PROPN
fuelectenerg-1427	794	9	·	·	PUNCT
fuelectenerg-1427	795	1	2x1	2x1	NUM
fuelectenerg-1427	795	2	2x2	2x2	NUM
fuelectenerg-1427	795	3	,	,	PUNCT
fuelectenerg-1427	795	4	(	(	PUNCT
fuelectenerg-1427	795	5	30	30	NUM
fuelectenerg-1427	795	6	)	)	PUNCT
fuelectenerg-1427	795	7	by	by	ADP
fuelectenerg-1427	795	8	utilizing	utilize	VERB
fuelectenerg-1427	795	9	gf	gf	NOUN
fuelectenerg-1427	795	10	addition	addition	NOUN
fuelectenerg-1427	795	11	and	and	CCONJ
fuelectenerg-1427	795	12	multiplication	multiplication	NOUN
fuelectenerg-1427	795	13	operators	operator	NOUN
fuelectenerg-1427	795	14	from	from	ADP
fuelectenerg-1427	795	15	figure	figure	NOUN
fuelectenerg-1427	795	16	1	1	NUM
fuelectenerg-1427	795	17	,	,	PUNCT
fuelectenerg-1427	795	18	equation	equation	NOUN
fuelectenerg-1427	795	19	(	(	PUNCT
fuelectenerg-1427	795	20	30	30	NUM
fuelectenerg-1427	795	21	)	)	PUNCT
fuelectenerg-1427	795	22	can	can	AUX
fuelectenerg-1427	795	23	be	be	AUX
fuelectenerg-1427	795	24	transformed	transform	VERB
fuelectenerg-1427	795	25	to	to	ADP
fuelectenerg-1427	795	26	:	:	PUNCT
fuelectenerg-1427	795	27	f	f	PROPN
fuelectenerg-1427	795	28	=(	=(	PROPN
fuelectenerg-1427	795	29	x1	x1	PROPN
fuelectenerg-1427	795	30	)	)	PUNCT
fuelectenerg-1427	795	31	2(x′2	2(x′2	NOUN
fuelectenerg-1427	795	32	)	)	PUNCT
fuelectenerg-1427	795	33	2	2	NUM
fuelectenerg-1427	795	34	+2(x1	+2(x1	NOUN
fuelectenerg-1427	795	35	)	)	PUNCT
fuelectenerg-1427	795	36	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	795	37	)	)	PUNCT
fuelectenerg-1427	795	38	2	2	NUM
fuelectenerg-1427	796	1	+	+	CCONJ
fuelectenerg-1427	796	2	x′2	x′2	X
fuelectenerg-1427	797	1	+	+	ADJ
fuelectenerg-1427	797	2	(	(	PUNCT
fuelectenerg-1427	797	3	x1	x1	ADJ
fuelectenerg-1427	797	4	)	)	PUNCT
fuelectenerg-1427	797	5	2	2	NUM
fuelectenerg-1427	797	6	(	(	PUNCT
fuelectenerg-1427	797	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	797	8	(	(	PUNCT
fuelectenerg-1427	797	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	797	10	)	)	PUNCT
fuelectenerg-1427	797	11	2(x2	2(x2	NUM
fuelectenerg-1427	797	12	)	)	PUNCT
fuelectenerg-1427	797	13	2	2	NUM
fuelectenerg-1427	798	1	+	+	NOUN
fuelectenerg-1427	798	2	(	(	PUNCT
fuelectenerg-1427	798	3	x′1	x′1	NOUN
fuelectenerg-1427	798	4	)	)	PUNCT
fuelectenerg-1427	798	5	2	2	NUM
fuelectenerg-1427	799	1	+	+	NOUN
fuelectenerg-1427	799	2	(	(	PUNCT
fuelectenerg-1427	799	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	799	4	)	)	PUNCT
fuelectenerg-1427	799	5	2	2	NUM
fuelectenerg-1427	799	6	+2x′1	+2x′1	ADP
fuelectenerg-1427	799	7	+2(x′1	+2(x′1	PROPN
fuelectenerg-1427	799	8	)	)	PUNCT
fuelectenerg-1427	799	9	2(x′2	2(x′2	NOUN
fuelectenerg-1427	799	10	)	)	PUNCT
fuelectenerg-1427	799	11	2	2	NUM
fuelectenerg-1427	800	1	+	+	ADJ
fuelectenerg-1427	800	2	(	(	PUNCT
fuelectenerg-1427	800	3	x′1	x′1	NOUN
fuelectenerg-1427	800	4	)	)	PUNCT
fuelectenerg-1427	800	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	800	6	(	(	PUNCT
fuelectenerg-1427	800	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	800	8	′	′	NUM
fuelectenerg-1427	800	9	2	2	NUM
fuelectenerg-1427	800	10	)	)	PUNCT
fuelectenerg-1427	800	11	2	2	NUM
fuelectenerg-1427	800	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	800	13	+	+	PROPN
fuelectenerg-1427	800	14	(	(	PUNCT
fuelectenerg-1427	800	15	x′1	x′1	NOUN
fuelectenerg-1427	800	16	)	)	PUNCT
fuelectenerg-1427	800	17	2	2	NUM
fuelectenerg-1427	800	18	·	·	SYM
fuelectenerg-1427	800	19	2x2	2x2	NUM
fuelectenerg-1427	800	20	+2(x′1	+2(x′1	NOUN
fuelectenerg-1427	800	21	)	)	PUNCT
fuelectenerg-1427	800	22	2x2	2x2	NUM
fuelectenerg-1427	801	1	+2	+2	PROPN
fuelectenerg-1427	801	2	(	(	PUNCT
fuelectenerg-1427	801	3	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	801	4	)	)	PUNCT
fuelectenerg-1427	801	5	2	2	NUM
fuelectenerg-1427	801	6	+	+	SYM
fuelectenerg-1427	801	7	2x1	2x1	NUM
fuelectenerg-1427	801	8	+2	+2	NOUN
fuelectenerg-1427	801	9	(	(	PUNCT
fuelectenerg-1427	801	10	2x1	2x1	NUM
fuelectenerg-1427	801	11	)	)	PUNCT
fuelectenerg-1427	801	12	(	(	PUNCT
fuelectenerg-1427	801	13	2x2	2x2	NUM
fuelectenerg-1427	801	14	)	)	PUNCT
fuelectenerg-1427	801	15	.	.	PUNCT
fuelectenerg-1427	802	1	(	(	PUNCT
fuelectenerg-1427	802	2	31	31	NUM
fuelectenerg-1427	802	3	)	)	PUNCT
fuelectenerg-1427	802	4	let	let	VERB
fuelectenerg-1427	802	5	us	we	PRON
fuelectenerg-1427	802	6	define	define	VERB
fuelectenerg-1427	802	7	,	,	PUNCT
fuelectenerg-1427	802	8	as	as	ADP
fuelectenerg-1427	802	9	one	one	NUM
fuelectenerg-1427	802	10	of	of	ADP
fuelectenerg-1427	802	11	possible	possible	ADJ
fuelectenerg-1427	802	12	definitions	definition	NOUN
fuelectenerg-1427	802	13	,	,	PUNCT
fuelectenerg-1427	802	14	the	the	DET
fuelectenerg-1427	802	15	cost	cost	NOUN
fuelectenerg-1427	802	16	of	of	ADP
fuelectenerg-1427	802	17	the	the	DET
fuelectenerg-1427	802	18	flattened	flatten	VERB
fuelectenerg-1427	802	19	form	form	NOUN
fuelectenerg-1427	802	20	(	(	PUNCT
fuelectenerg-1427	802	21	expression	expression	NOUN
fuelectenerg-1427	802	22	)	)	PUNCT
fuelectenerg-1427	802	23	to	to	PART
fuelectenerg-1427	802	24	be	be	AUX
fuelectenerg-1427	802	25	:	:	PUNCT
fuelectenerg-1427	802	26	cost	cost	NOUN
fuelectenerg-1427	802	27	=	=	SYM
fuelectenerg-1427	802	28	#	#	NOUN
fuelectenerg-1427	802	29	cubes	cube	NOUN
fuelectenerg-1427	802	30	(	(	PUNCT
fuelectenerg-1427	802	31	32	32	NUM
fuelectenerg-1427	802	32	)	)	PUNCT
fuelectenerg-1427	802	33	then	then	ADV
fuelectenerg-1427	802	34	,	,	PUNCT
fuelectenerg-1427	802	35	we	we	PRON
fuelectenerg-1427	802	36	observe	observe	VERB
fuelectenerg-1427	802	37	that	that	SCONJ
fuelectenerg-1427	802	38	equation	equation	NOUN
fuelectenerg-1427	802	39	(	(	PUNCT
fuelectenerg-1427	802	40	29	29	NUM
fuelectenerg-1427	802	41	)	)	PUNCT
fuelectenerg-1427	802	42	has	have	VERB
fuelectenerg-1427	802	43	the	the	DET
fuelectenerg-1427	802	44	cost	cost	NOUN
fuelectenerg-1427	802	45	of	of	ADP
fuelectenerg-1427	802	46	seven	seven	NUM
fuelectenerg-1427	802	47	,	,	PUNCT
fuelectenerg-1427	802	48	while	while	SCONJ
fuelectenerg-1427	802	49	equation	equation	NOUN
fuelectenerg-1427	802	50	(	(	PUNCT
fuelectenerg-1427	802	51	31	31	NUM
fuelectenerg-1427	802	52	)	)	PUNCT
fuelectenerg-1427	802	53	has	have	VERB
fuelectenerg-1427	802	54	the	the	DET
fuelectenerg-1427	802	55	cost	cost	NOUN
fuelectenerg-1427	802	56	of	of	ADP
fuelectenerg-1427	802	57	19	19	NUM
fuelectenerg-1427	802	58	.	.	PUNCT
fuelectenerg-1427	803	1	thus	thus	ADV
fuelectenerg-1427	803	2	,	,	PUNCT
fuelectenerg-1427	803	3	the	the	DET
fuelectenerg-1427	803	4	inverse	inverse	NOUN
fuelectenerg-1427	803	5	transformations	transformation	NOUN
fuelectenerg-1427	803	6	applied	apply	VERB
fuelectenerg-1427	803	7	to	to	ADP
fuelectenerg-1427	803	8	equation	equation	NOUN
fuelectenerg-1427	803	9	(	(	PUNCT
fuelectenerg-1427	803	10	31	31	NUM
fuelectenerg-1427	803	11	)	)	PUNCT
fuelectenerg-1427	803	12	would	would	AUX
fuelectenerg-1427	803	13	lead	lead	VERB
fuelectenerg-1427	803	14	to	to	ADP
fuelectenerg-1427	803	15	equation	equation	NOUN
fuelectenerg-1427	803	16	(	(	PUNCT
fuelectenerg-1427	803	17	29	29	NUM
fuelectenerg-1427	803	18	)	)	PUNCT
fuelectenerg-1427	803	19	and	and	CCONJ
fuelectenerg-1427	803	20	a	a	DET
fuelectenerg-1427	803	21	reduction	reduction	NOUN
fuelectenerg-1427	803	22	of	of	ADP
fuelectenerg-1427	803	23	cost	cost	NOUN
fuelectenerg-1427	803	24	from	from	ADP
fuelectenerg-1427	803	25	19	19	NUM
fuelectenerg-1427	803	26	to	to	PART
fuelectenerg-1427	803	27	seven	seven	NUM
fuelectenerg-1427	803	28	.	.	PUNCT
fuelectenerg-1427	804	1	using	use	VERB
fuelectenerg-1427	804	2	the	the	DET
fuelectenerg-1427	804	3	same	same	ADJ
fuelectenerg-1427	804	4	approach	approach	NOUN
fuelectenerg-1427	804	5	,	,	PUNCT
fuelectenerg-1427	804	6	we	we	PRON
fuelectenerg-1427	804	7	can	can	AUX
fuelectenerg-1427	804	8	generate	generate	VERB
fuelectenerg-1427	804	9	a	a	DET
fuelectenerg-1427	804	10	subset	subset	NOUN
fuelectenerg-1427	804	11	of	of	ADP
fuelectenerg-1427	804	12	possible	possible	ADJ
fuelectenerg-1427	804	13	gfsop	gfsop	NOUN
fuelectenerg-1427	804	14	expressions	expression	NOUN
fuelectenerg-1427	804	15	(	(	PUNCT
fuelectenerg-1427	804	16	flattened	flatten	VERB
fuelectenerg-1427	804	17	forms	form	NOUN
fuelectenerg-1427	804	18	)	)	PUNCT
fuelectenerg-1427	804	19	.	.	PUNCT
fuelectenerg-1427	805	1	note	note	VERB
fuelectenerg-1427	805	2	that	that	SCONJ
fuelectenerg-1427	805	3	all	all	PRON
fuelectenerg-1427	805	4	of	of	ADP
fuelectenerg-1427	805	5	these	these	DET
fuelectenerg-1427	805	6	gfsop	gfsop	NOUN
fuelectenerg-1427	805	7	expressions	expression	NOUN
fuelectenerg-1427	805	8	are	be	AUX
fuelectenerg-1427	805	9	equivalent	equivalent	ADJ
fuelectenerg-1427	805	10	since	since	SCONJ
fuelectenerg-1427	805	11	they	they	PRON
fuelectenerg-1427	805	12	produce	produce	VERB
fuelectenerg-1427	805	13	the	the	DET
fuelectenerg-1427	805	14	same	same	ADJ
fuelectenerg-1427	805	15	function	function	NOUN
fuelectenerg-1427	805	16	in	in	ADP
fuelectenerg-1427	805	17	different	different	ADJ
fuelectenerg-1427	805	18	forms	form	NOUN
fuelectenerg-1427	805	19	.	.	PUNCT
fuelectenerg-1427	806	1	yet	yet	ADV
fuelectenerg-1427	806	2	,	,	PUNCT
fuelectenerg-1427	806	3	as	as	SCONJ
fuelectenerg-1427	806	4	can	can	AUX
fuelectenerg-1427	806	5	be	be	AUX
fuelectenerg-1427	806	6	observed	observe	VERB
fuelectenerg-1427	806	7	from	from	ADP
fuelectenerg-1427	806	8	equation	equation	NOUN
fuelectenerg-1427	806	9	(	(	PUNCT
fuelectenerg-1427	806	10	31	31	NUM
fuelectenerg-1427	806	11	)	)	PUNCT
fuelectenerg-1427	806	12	,	,	PUNCT
fuelectenerg-1427	806	13	by	by	ADP
fuelectenerg-1427	806	14	further	further	ADJ
fuelectenerg-1427	806	15	transformations	transformation	NOUN
fuelectenerg-1427	806	16	of	of	ADP
fuelectenerg-1427	806	17	equation	equation	NOUN
fuelectenerg-1427	806	18	(	(	PUNCT
fuelectenerg-1427	806	19	29	29	NUM
fuelectenerg-1427	806	20	)	)	PUNCT
fuelectenerg-1427	806	21	from	from	ADP
fuelectenerg-1427	806	22	one	one	NUM
fuelectenerg-1427	806	23	form	form	NOUN
fuelectenerg-1427	806	24	to	to	ADP
fuelectenerg-1427	806	25	another	another	PRON
fuelectenerg-1427	806	26	,	,	PUNCT
fuelectenerg-1427	806	27	some	some	DET
fuelectenerg-1427	806	28	transformations	transformation	NOUN
fuelectenerg-1427	806	29	produce	produce	VERB
fuelectenerg-1427	806	30	flattened	flatten	VERB
fuelectenerg-1427	806	31	forms	form	NOUN
fuelectenerg-1427	806	32	with	with	ADP
fuelectenerg-1427	806	33	a	a	DET
fuelectenerg-1427	806	34	smaller	small	ADJ
fuelectenerg-1427	806	35	number	number	NOUN
fuelectenerg-1427	806	36	of	of	ADP
fuelectenerg-1427	806	37	cubes	cube	NOUN
fuelectenerg-1427	806	38	than	than	ADP
fuelectenerg-1427	806	39	the	the	DET
fuelectenerg-1427	806	40	others	other	NOUN
fuelectenerg-1427	806	41	.	.	PUNCT
fuelectenerg-1427	807	1	from	from	ADP
fuelectenerg-1427	807	2	this	this	DET
fuelectenerg-1427	807	3	observation	observation	NOUN
fuelectenerg-1427	807	4	rises	rise	VERB
fuelectenerg-1427	807	5	the	the	DET
fuelectenerg-1427	807	6	idea	idea	NOUN
fuelectenerg-1427	807	7	of	of	ADP
fuelectenerg-1427	807	8	a	a	DET
fuelectenerg-1427	807	9	possible	possible	ADJ
fuelectenerg-1427	807	10	application	application	NOUN
fuelectenerg-1427	807	11	of	of	ADP
fuelectenerg-1427	807	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	807	13	computing	computing	NOUN
fuelectenerg-1427	807	14	using	use	VERB
fuelectenerg-1427	807	15	the	the	DET
fuelectenerg-1427	807	16	s	s	PROPN
fuelectenerg-1427	807	17	/	/	SYM
fuelectenerg-1427	807	18	d	d	NOUN
fuelectenerg-1427	807	19	trees	tree	NOUN
fuelectenerg-1427	807	20	and	and	CCONJ
fuelectenerg-1427	807	21	related	related	ADJ
fuelectenerg-1427	807	22	transformations	transformation	NOUN
fuelectenerg-1427	807	23	to	to	PART
fuelectenerg-1427	807	24	produce	produce	VERB
fuelectenerg-1427	807	25	the	the	DET
fuelectenerg-1427	807	26	corresponding	corresponding	ADJ
fuelectenerg-1427	807	27	minimum	minimum	ADJ
fuelectenerg-1427	807	28	gfsops	gfsop	NOUN
fuelectenerg-1427	807	29	.	.	PUNCT
fuelectenerg-1427	808	1	analogous	analogous	ADJ
fuelectenerg-1427	808	2	to	to	ADP
fuelectenerg-1427	808	3	the	the	DET
fuelectenerg-1427	808	4	binary	binary	ADJ
fuelectenerg-1427	808	5	case	case	NOUN
fuelectenerg-1427	808	6	in	in	ADP
fuelectenerg-1427	808	7	equation	equation	NOUN
fuelectenerg-1427	808	8	(	(	PUNCT
fuelectenerg-1427	808	9	27	27	NUM
fuelectenerg-1427	808	10	)	)	PUNCT
fuelectenerg-1427	808	11	,	,	PUNCT
fuelectenerg-1427	808	12	the	the	DET
fuelectenerg-1427	808	13	ternary	ternary	ADJ
fuelectenerg-1427	808	14	gifs	gif	NOUN
fuelectenerg-1427	808	15	can	can	AUX
fuelectenerg-1427	808	16	be	be	AUX
fuelectenerg-1427	808	17	defined	define	VERB
fuelectenerg-1427	808	18	as	as	ADP
fuelectenerg-1427	808	19	the	the	DET
fuelectenerg-1427	808	20	union	union	NOUN
fuelectenerg-1427	808	21	of	of	ADP
fuelectenerg-1427	808	22	ternary	ternary	PROPN
fuelectenerg-1427	808	23	ifs	ifs	PROPN
fuelectenerg-1427	808	24	.	.	PUNCT
fuelectenerg-1427	809	1	definition	definition	NOUN
fuelectenerg-1427	809	2	3	3	NUM
fuelectenerg-1427	809	3	.	.	PUNCT
fuelectenerg-1427	810	1	the	the	DET
fuelectenerg-1427	810	2	family	family	NOUN
fuelectenerg-1427	810	3	of	of	ADP
fuelectenerg-1427	810	4	forms	form	NOUN
fuelectenerg-1427	810	5	,	,	PUNCT
fuelectenerg-1427	810	6	which	which	PRON
fuelectenerg-1427	810	7	is	be	AUX
fuelectenerg-1427	810	8	created	create	VERB
fuelectenerg-1427	810	9	as	as	ADP
fuelectenerg-1427	810	10	a	a	DET
fuelectenerg-1427	810	11	union	union	NOUN
fuelectenerg-1427	810	12	of	of	ADP
fuelectenerg-1427	810	13	sets	set	NOUN
fuelectenerg-1427	810	14	of	of	ADP
fuelectenerg-1427	810	15	tifs	tif	NOUN
fuelectenerg-1427	810	16	for	for	ADP
fuelectenerg-1427	810	17	all	all	DET
fuelectenerg-1427	810	18	variable	variable	ADJ
fuelectenerg-1427	810	19	orders	order	NOUN
fuelectenerg-1427	810	20	,	,	PUNCT
fuelectenerg-1427	810	21	is	be	AUX
fuelectenerg-1427	810	22	called	call	VERB
fuelectenerg-1427	810	23	ternary	ternary	ADJ
fuelectenerg-1427	810	24	generalized	generalized	ADJ
fuelectenerg-1427	810	25	inclusive	inclusive	ADJ
fuelectenerg-1427	810	26	forms	form	NOUN
fuelectenerg-1427	810	27	(	(	PUNCT
fuelectenerg-1427	810	28	tgifs	tgif	NOUN
fuelectenerg-1427	810	29	)	)	PUNCT
fuelectenerg-1427	810	30	.	.	PUNCT
fuelectenerg-1427	811	1	109	109	NUM
fuelectenerg-1427	811	2	an	an	DET
fuelectenerg-1427	811	3	extended	extend	VERB
fuelectenerg-1427	811	4	green	green	ADJ
fuelectenerg-1427	811	5	sasao	sasao	PROPN
fuelectenerg-1427	811	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	811	7	of	of	ADP
fuelectenerg-1427	811	8	canonical	canonical	ADJ
fuelectenerg-1427	811	9	ternary	ternary	ADJ
fuelectenerg-1427	811	10	galois	galois	NOUN
fuelectenerg-1427	811	11	forms	form	NOUN
fuelectenerg-1427	811	12	...	...	PUNCT
fuelectenerg-1427	811	13	s	s	VERB
fuelectenerg-1427	811	14	a	a	PRON
fuelectenerg-1427	811	15	’	'	PUNCT
fuelectenerg-1427	811	16	a	a	PRON
fuelectenerg-1427	811	17	(	(	PUNCT
fuelectenerg-1427	811	18	)	)	PUNCT
fuelectenerg-1427	811	19	a	a	PRON
fuelectenerg-1427	811	20	pd	pd	PROPN
fuelectenerg-1427	811	21	1	1	NUM
fuelectenerg-1427	811	22	a	a	PRON
fuelectenerg-1427	811	23	(	(	PUNCT
fuelectenerg-1427	811	24	)	)	PUNCT
fuelectenerg-1427	811	25	b	b	NOUN
fuelectenerg-1427	811	26	nd	nd	ADP
fuelectenerg-1427	811	27	1	1	NUM
fuelectenerg-1427	811	28	a	a	PRON
fuelectenerg-1427	811	29	’	'	PUNCT
fuelectenerg-1427	811	30	d	d	ADP
fuelectenerg-1427	811	31	1	1	NUM
fuelectenerg-1427	811	32	a	a	PRON
fuelectenerg-1427	811	33	(	(	PUNCT
fuelectenerg-1427	811	34	)	)	PUNCT
fuelectenerg-1427	811	35	d	d	NOUN
fuelectenerg-1427	811	36	(	(	PUNCT
fuelectenerg-1427	811	37	)	)	PUNCT
fuelectenerg-1427	811	38	c	c	NOUN
fuelectenerg-1427	811	39	figure	figure	VERB
fuelectenerg-1427	811	40	3	3	NUM
fuelectenerg-1427	811	41	:	:	PUNCT
fuelectenerg-1427	811	42	two	two	NUM
fuelectenerg-1427	811	43	-	-	PUNCT
fuelectenerg-1427	811	44	valued	value	VERB
fuelectenerg-1427	811	45	nodes	node	NOUN
fuelectenerg-1427	811	46	:	:	PUNCT
fuelectenerg-1427	811	47	(	(	PUNCT
fuelectenerg-1427	811	48	a	a	X
fuelectenerg-1427	811	49	)	)	PUNCT
fuelectenerg-1427	811	50	shannon	shannon	NOUN
fuelectenerg-1427	811	51	,	,	PUNCT
fuelectenerg-1427	811	52	(	(	PUNCT
fuelectenerg-1427	811	53	b	b	NOUN
fuelectenerg-1427	811	54	)	)	PUNCT
fuelectenerg-1427	811	55	positive	positive	ADJ
fuelectenerg-1427	811	56	davio	davio	NOUN
fuelectenerg-1427	811	57	,	,	PUNCT
fuelectenerg-1427	811	58	(	(	PUNCT
fuelectenerg-1427	811	59	c	c	NOUN
fuelectenerg-1427	811	60	)	)	PUNCT
fuelectenerg-1427	811	61	negative	negative	ADJ
fuelectenerg-1427	811	62	davio	davio	NOUN
fuelectenerg-1427	811	63	,	,	PUNCT
fuelectenerg-1427	811	64	and	and	CCONJ
fuelectenerg-1427	811	65	(	(	PUNCT
fuelectenerg-1427	811	66	d	d	X
fuelectenerg-1427	811	67	)	)	PUNCT
fuelectenerg-1427	811	68	generalized	generalized	ADJ
fuelectenerg-1427	811	69	davio	davio	NOUN
fuelectenerg-1427	811	70	where	where	SCONJ
fuelectenerg-1427	811	71	a	a	DET
fuelectenerg-1427	811	72	∈	∈	NOUN
fuelectenerg-1427	811	73	{	{	PUNCT
fuelectenerg-1427	811	74	a	a	PRON
fuelectenerg-1427	811	75	,	,	PUNCT
fuelectenerg-1427	811	76	a′	a′	PROPN
fuelectenerg-1427	811	77	}	}	PUNCT
fuelectenerg-1427	811	78	.	.	PUNCT
fuelectenerg-1427	812	1	variable	variable	ADJ
fuelectenerg-1427	812	2	,	,	PUNCT
fuelectenerg-1427	812	3	that	that	PRON
fuelectenerg-1427	812	4	is	be	AUX
fuelectenerg-1427	812	5	one	one	NUM
fuelectenerg-1427	812	6	tree	tree	NOUN
fuelectenerg-1427	812	7	level	level	NOUN
fuelectenerg-1427	812	8	,	,	PUNCT
fuelectenerg-1427	812	9	figure	figure	NOUN
fuelectenerg-1427	812	10	4	4	NUM
fuelectenerg-1427	812	11	represents	represent	VERB
fuelectenerg-1427	812	12	the	the	DET
fuelectenerg-1427	812	13	expansion	expansion	NOUN
fuelectenerg-1427	812	14	nodes	node	NOUN
fuelectenerg-1427	812	15	for	for	ADP
fuelectenerg-1427	812	16	ternary	ternary	ADJ
fuelectenerg-1427	812	17	shannon	shannon	NOUN
fuelectenerg-1427	812	18	,	,	PUNCT
fuelectenerg-1427	812	19	davio	davio	NOUN
fuelectenerg-1427	812	20	and	and	CCONJ
fuelectenerg-1427	812	21	generalized	generalized	ADJ
fuelectenerg-1427	812	22	davio	davio	NOUN
fuelectenerg-1427	812	23	(	(	PUNCT
fuelectenerg-1427	812	24	d	d	NOUN
fuelectenerg-1427	812	25	)	)	PUNCT
fuelectenerg-1427	812	26	,	,	PUNCT
fuelectenerg-1427	812	27	respectively	respectively	ADV
fuelectenerg-1427	812	28	.	.	PUNCT
fuelectenerg-1427	813	1	s	s	PART
fuelectenerg-1427	813	2	0	0	NUM
fuelectenerg-1427	813	3	x	x	SYM
fuelectenerg-1427	813	4	1	1	NUM
fuelectenerg-1427	813	5	x	x	SYM
fuelectenerg-1427	813	6	2	2	NUM
fuelectenerg-1427	813	7	x	x	SYM
fuelectenerg-1427	813	8	(	(	PUNCT
fuelectenerg-1427	813	9	a	a	PRON
fuelectenerg-1427	813	10	)	)	PUNCT
fuelectenerg-1427	813	11	d0	d0	NOUN
fuelectenerg-1427	813	12	1	1	NUM
fuelectenerg-1427	813	13	x	x	SYM
fuelectenerg-1427	813	14	2	2	NUM
fuelectenerg-1427	813	15	(	(	PUNCT
fuelectenerg-1427	813	16	b	b	NOUN
fuelectenerg-1427	813	17	)	)	PUNCT
fuelectenerg-1427	813	18	d2	d2	PROPN
fuelectenerg-1427	813	19	1	1	NUM
fuelectenerg-1427	813	20	(	(	PUNCT
fuelectenerg-1427	813	21	d	d	NOUN
fuelectenerg-1427	813	22	)	)	PUNCT
fuelectenerg-1427	814	1	d	d	NOUN
fuelectenerg-1427	814	2	1	1	NUM
fuelectenerg-1427	814	3	(	(	PUNCT
fuelectenerg-1427	814	4	e	e	NOUN
fuelectenerg-1427	814	5	)	)	PUNCT
fuelectenerg-1427	814	6	d1	d1	NOUN
fuelectenerg-1427	814	7	1	1	NUM
fuelectenerg-1427	814	8	(	(	PUNCT
fuelectenerg-1427	814	9	’	'	PUNCT
fuelectenerg-1427	814	10	)	)	PUNCT
fuelectenerg-1427	814	11	x	x	SYM
fuelectenerg-1427	814	12	2	2	NUM
fuelectenerg-1427	814	13	(	(	PUNCT
fuelectenerg-1427	814	14	’’	’'	PUNCT
fuelectenerg-1427	814	15	)	)	PUNCT
fuelectenerg-1427	814	16	x	x	SYM
fuelectenerg-1427	814	17	2	2	NUM
fuelectenerg-1427	814	18	(	(	PUNCT
fuelectenerg-1427	814	19	)	)	PUNCT
fuelectenerg-1427	814	20	x	x	SYM
fuelectenerg-1427	814	21	2	2	NUM
fuelectenerg-1427	814	22	(	(	PUNCT
fuelectenerg-1427	814	23	c	c	NOUN
fuelectenerg-1427	814	24	)	)	PUNCT
fuelectenerg-1427	814	25	x	x	SYM
fuelectenerg-1427	814	26	xx	xx	X
fuelectenerg-1427	814	27	’	'	PUNCT
fuelectenerg-1427	814	28	x	x	NOUN
fuelectenerg-1427	814	29	’’	’'	PUNCT
fuelectenerg-1427	814	30	figure	figure	VERB
fuelectenerg-1427	814	31	4	4	NUM
fuelectenerg-1427	814	32	:	:	PUNCT
fuelectenerg-1427	814	33	ternary	ternary	ADJ
fuelectenerg-1427	814	34	nodes	node	NOUN
fuelectenerg-1427	814	35	for	for	ADP
fuelectenerg-1427	814	36	ternary	ternary	ADJ
fuelectenerg-1427	814	37	decision	decision	NOUN
fuelectenerg-1427	814	38	trees	tree	NOUN
fuelectenerg-1427	814	39	:	:	PUNCT
fuelectenerg-1427	814	40	(	(	PUNCT
fuelectenerg-1427	814	41	a	a	X
fuelectenerg-1427	814	42	)	)	PUNCT
fuelectenerg-1427	814	43	shannon	shannon	NOUN
fuelectenerg-1427	814	44	,	,	PUNCT
fuelectenerg-1427	814	45	(	(	PUNCT
fuelectenerg-1427	814	46	b	b	X
fuelectenerg-1427	814	47	)	)	PUNCT
fuelectenerg-1427	814	48	davio0	davio0	PROPN
fuelectenerg-1427	814	49	,	,	PUNCT
fuelectenerg-1427	814	50	(	(	PUNCT
fuelectenerg-1427	814	51	c	c	X
fuelectenerg-1427	814	52	)	)	PUNCT
fuelectenerg-1427	814	53	davio1	davio1	NOUN
fuelectenerg-1427	814	54	,	,	PUNCT
fuelectenerg-1427	814	55	(	(	PUNCT
fuelectenerg-1427	814	56	d	d	NOUN
fuelectenerg-1427	814	57	)	)	PUNCT
fuelectenerg-1427	814	58	davio2	davio2	PROPN
fuelectenerg-1427	814	59	,	,	PUNCT
fuelectenerg-1427	814	60	and	and	CCONJ
fuelectenerg-1427	814	61	(	(	PUNCT
fuelectenerg-1427	814	62	e	e	NOUN
fuelectenerg-1427	814	63	)	)	PUNCT
fuelectenerg-1427	814	64	generalized	generalized	ADJ
fuelectenerg-1427	814	65	davio	davio	NOUN
fuelectenerg-1427	814	66	(	(	PUNCT
fuelectenerg-1427	814	67	d	d	NOUN
fuelectenerg-1427	814	68	)	)	PUNCT
fuelectenerg-1427	814	69	where	where	SCONJ
fuelectenerg-1427	814	70	x	x	SYM
fuelectenerg-1427	814	71	∈	∈	PROPN
fuelectenerg-1427	814	72	{	{	PUNCT
fuelectenerg-1427	814	73	x	x	NOUN
fuelectenerg-1427	814	74	,	,	PUNCT
fuelectenerg-1427	814	75	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	814	76	}	}	PUNCT
fuelectenerg-1427	814	77	.	.	PUNCT
fuelectenerg-1427	815	1	in	in	ADP
fuelectenerg-1427	815	2	correspondence	correspondence	NOUN
fuelectenerg-1427	815	3	to	to	ADP
fuelectenerg-1427	815	4	the	the	DET
fuelectenerg-1427	815	5	binary	binary	PROPN
fuelectenerg-1427	815	6	s	s	PROPN
fuelectenerg-1427	815	7	/	/	SYM
fuelectenerg-1427	815	8	d	d	NOUN
fuelectenerg-1427	815	9	trees	tree	NOUN
fuelectenerg-1427	815	10	,	,	PUNCT
fuelectenerg-1427	815	11	one	one	PRON
fuelectenerg-1427	815	12	can	can	AUX
fuelectenerg-1427	815	13	produce	produce	VERB
fuelectenerg-1427	815	14	ternary	ternary	ADJ
fuelectenerg-1427	815	15	s	s	NOUN
fuelectenerg-1427	815	16	/	/	SYM
fuelectenerg-1427	815	17	d	d	NOUN
fuelectenerg-1427	815	18	trees	tree	NOUN
fuelectenerg-1427	815	19	.	.	PUNCT
fuelectenerg-1427	816	1	to	to	PART
fuelectenerg-1427	816	2	define	define	VERB
fuelectenerg-1427	816	3	the	the	DET
fuelectenerg-1427	816	4	ternary	ternary	ADJ
fuelectenerg-1427	816	5	s	s	NOUN
fuelectenerg-1427	816	6	/	/	SYM
fuelectenerg-1427	816	7	d	d	NOUN
fuelectenerg-1427	816	8	trees	tree	NOUN
fuelectenerg-1427	816	9	,	,	PUNCT
fuelectenerg-1427	816	10	we	we	PRON
fuelectenerg-1427	816	11	define	define	VERB
fuelectenerg-1427	816	12	the	the	DET
fuelectenerg-1427	816	13	generalized	generalized	ADJ
fuelectenerg-1427	816	14	davio	davio	NOUN
fuelectenerg-1427	816	15	node	node	NOUN
fuelectenerg-1427	816	16	over	over	ADP
fuelectenerg-1427	816	17	ternary	ternary	ADJ
fuelectenerg-1427	816	18	galois	galois	PROPN
fuelectenerg-1427	816	19	radix	radix	NOUN
fuelectenerg-1427	816	20	as	as	SCONJ
fuelectenerg-1427	816	21	shown	show	VERB
fuelectenerg-1427	816	22	in	in	ADP
fuelectenerg-1427	816	23	figure	figure	NOUN
fuelectenerg-1427	816	24	4(e	4(e	NUM
fuelectenerg-1427	816	25	)	)	PUNCT
fuelectenerg-1427	816	26	.	.	PUNCT
fuelectenerg-1427	817	1	our	our	PRON
fuelectenerg-1427	817	2	notation	notation	NOUN
fuelectenerg-1427	817	3	here	here	ADV
fuelectenerg-1427	817	4	is	be	AUX
fuelectenerg-1427	817	5	that	that	PRON
fuelectenerg-1427	817	6	(	(	PUNCT
fuelectenerg-1427	817	7	x	x	X
fuelectenerg-1427	817	8	)	)	PUNCT
fuelectenerg-1427	817	9	corresponds	correspond	VERB
fuelectenerg-1427	817	10	to	to	ADP
fuelectenerg-1427	817	11	the	the	DET
fuelectenerg-1427	817	12	three	three	NUM
fuelectenerg-1427	817	13	possible	possible	ADJ
fuelectenerg-1427	817	14	shifts	shift	NOUN
fuelectenerg-1427	817	15	of	of	ADP
fuelectenerg-1427	817	16	the	the	DET
fuelectenerg-1427	817	17	variable	variable	NOUN
fuelectenerg-1427	817	18	x	x	NOUN
fuelectenerg-1427	817	19	as	as	SCONJ
fuelectenerg-1427	817	20	follows	follow	VERB
fuelectenerg-1427	817	21	:	:	PUNCT
fuelectenerg-1427	817	22	x	x	SYM
fuelectenerg-1427	817	23	∈	∈	NOUN
fuelectenerg-1427	817	24	{	{	PUNCT
fuelectenerg-1427	817	25	x	x	NOUN
fuelectenerg-1427	817	26	,	,	PUNCT
fuelectenerg-1427	817	27	x′,x′′	x′,x′′	PROPN
fuelectenerg-1427	817	28	}	}	PUNCT
fuelectenerg-1427	817	29	,	,	PUNCT
fuelectenerg-1427	817	30	over	over	ADP
fuelectenerg-1427	817	31	gf(3	gf(3	PROPN
fuelectenerg-1427	817	32	)	)	PUNCT
fuelectenerg-1427	817	33	.	.	PUNCT
fuelectenerg-1427	818	1	(	(	PUNCT
fuelectenerg-1427	818	2	28	28	NUM
fuelectenerg-1427	818	3	)	)	PUNCT
fuelectenerg-1427	818	4	definition	definition	NOUN
fuelectenerg-1427	818	5	1	1	NUM
fuelectenerg-1427	818	6	.	.	PUNCT
fuelectenerg-1427	819	1	the	the	DET
fuelectenerg-1427	819	2	ternary	ternary	ADJ
fuelectenerg-1427	819	3	tree	tree	NOUN
fuelectenerg-1427	819	4	with	with	ADP
fuelectenerg-1427	819	5	ternary	ternary	ADJ
fuelectenerg-1427	819	6	shannon	shannon	NOUN
fuelectenerg-1427	819	7	and	and	CCONJ
fuelectenerg-1427	819	8	ternary	ternary	ADJ
fuelectenerg-1427	819	9	generalized	generalized	ADJ
fuelectenerg-1427	819	10	davio	davio	NOUN
fuelectenerg-1427	819	11	nodes	node	NOUN
fuelectenerg-1427	819	12	,	,	PUNCT
fuelectenerg-1427	819	13	that	that	PRON
fuelectenerg-1427	819	14	generates	generate	VERB
fuelectenerg-1427	819	15	other	other	ADJ
fuelectenerg-1427	819	16	ternary	ternary	ADJ
fuelectenerg-1427	819	17	trees	tree	NOUN
fuelectenerg-1427	819	18	,	,	PUNCT
fuelectenerg-1427	819	19	is	be	AUX
fuelectenerg-1427	819	20	called	call	VERB
fuelectenerg-1427	819	21	ternary	ternary	ADJ
fuelectenerg-1427	819	22	shannon	shannon	NOUN
fuelectenerg-1427	819	23	-	-	PUNCT
fuelectenerg-1427	819	24	davio	davio	NOUN
fuelectenerg-1427	819	25	(	(	PUNCT
fuelectenerg-1427	819	26	s	s	NOUN
fuelectenerg-1427	819	27	/	/	SYM
fuelectenerg-1427	819	28	d	d	NOUN
fuelectenerg-1427	819	29	)	)	PUNCT
fuelectenerg-1427	819	30	tree	tree	NOUN
fuelectenerg-1427	819	31	.	.	PUNCT
fuelectenerg-1427	820	1	utilizing	utilize	VERB
fuelectenerg-1427	820	2	the	the	DET
fuelectenerg-1427	820	3	definition	definition	NOUN
fuelectenerg-1427	820	4	of	of	ADP
fuelectenerg-1427	820	5	ternary	ternary	ADJ
fuelectenerg-1427	820	6	shannon	shannon	NOUN
fuelectenerg-1427	820	7	in	in	ADP
fuelectenerg-1427	820	8	figure	figure	NOUN
fuelectenerg-1427	820	9	4(a	4(a	NUM
fuelectenerg-1427	820	10	)	)	PUNCT
fuelectenerg-1427	820	11	and	and	CCONJ
fuelectenerg-1427	820	12	ternary	ternary	ADJ
fuelectenerg-1427	820	13	generalized	generalized	ADJ
fuelectenerg-1427	820	14	davio	davio	NOUN
fuelectenerg-1427	820	15	in	in	ADP
fuelectenerg-1427	820	16	figure	figure	NOUN
fuelectenerg-1427	820	17	4(e	4(e	NUM
fuelectenerg-1427	820	18	)	)	PUNCT
fuelectenerg-1427	820	19	,	,	PUNCT
fuelectenerg-1427	820	20	we	we	PRON
fuelectenerg-1427	820	21	obtain	obtain	VERB
fuelectenerg-1427	820	22	the	the	DET
fuelectenerg-1427	820	23	ternary	ternary	ADJ
fuelectenerg-1427	820	24	shannon	shannon	NOUN
fuelectenerg-1427	820	25	-	-	PUNCT
fuelectenerg-1427	820	26	davio	davio	NOUN
fuelectenerg-1427	820	27	trees	tree	NOUN
fuelectenerg-1427	820	28	(	(	PUNCT
fuelectenerg-1427	820	29	ternary	ternary	NOUN
fuelectenerg-1427	820	30	s	s	PROPN
fuelectenerg-1427	820	31	/	/	SYM
fuelectenerg-1427	820	32	d	d	NOUN
fuelectenerg-1427	820	33	trees	tree	NOUN
fuelectenerg-1427	820	34	)	)	PUNCT
fuelectenerg-1427	820	35	for	for	ADP
fuelectenerg-1427	820	36	two	two	NUM
fuelectenerg-1427	820	37	variables	variable	NOUN
fuelectenerg-1427	820	38	as	as	SCONJ
fuelectenerg-1427	820	39	shown	show	VERB
fuelectenerg-1427	820	40	in	in	ADP
fuelectenerg-1427	820	41	figure	figure	NOUN
fuelectenerg-1427	820	42	5	5	NUM
fuelectenerg-1427	820	43	.	.	PUNCT
fuelectenerg-1427	820	44	from	from	ADP
fuelectenerg-1427	820	45	the	the	DET
fuelectenerg-1427	820	46	ternary	ternary	ADJ
fuelectenerg-1427	820	47	s	s	PROPN
fuelectenerg-1427	820	48	/	/	SYM
fuelectenerg-1427	820	49	d	d	ADJ
fuelectenerg-1427	820	50	dts	dts	NOUN
fuelectenerg-1427	820	51	shown	show	VERB
fuelectenerg-1427	820	52	in	in	ADP
fuelectenerg-1427	820	53	figure	figure	NOUN
fuelectenerg-1427	820	54	5	5	NUM
fuelectenerg-1427	820	55	,	,	PUNCT
fuelectenerg-1427	820	56	if	if	SCONJ
fuelectenerg-1427	820	57	we	we	PRON
fuelectenerg-1427	820	58	take	take	VERB
fuelectenerg-1427	820	59	any	any	DET
fuelectenerg-1427	820	60	s	s	PROPN
fuelectenerg-1427	820	61	/	/	SYM
fuelectenerg-1427	820	62	d	d	NOUN
fuelectenerg-1427	820	63	tree	tree	NOUN
fuelectenerg-1427	820	64	and	and	CCONJ
fuelectenerg-1427	820	65	multiply	multiply	VERB
fuelectenerg-1427	820	66	the	the	DET
fuelectenerg-1427	820	67	second	second	ADJ
fuelectenerg-1427	820	68	-	-	PUNCT
fuelectenerg-1427	820	69	level	level	NOUN
fuelectenerg-1427	820	70	cofactors	cofactor	NOUN
fuelectenerg-1427	820	71	(	(	PUNCT
fuelectenerg-1427	820	72	which	which	PRON
fuelectenerg-1427	820	73	are	be	AUX
fuelectenerg-1427	820	74	in	in	ADP
fuelectenerg-1427	820	75	the	the	DET
fuelectenerg-1427	820	76	tdt	tdt	PROPN
fuelectenerg-1427	820	77	leaves	leave	NOUN
fuelectenerg-1427	820	78	)	)	PUNCT
fuelectenerg-1427	820	79	each	each	PRON
fuelectenerg-1427	820	80	by	by	ADP
fuelectenerg-1427	820	81	the	the	DET
fuelectenerg-1427	820	82	corresponding	corresponding	ADJ
fuelectenerg-1427	820	83	path	path	NOUN
fuelectenerg-1427	820	84	in	in	ADP
fuelectenerg-1427	820	85	that	that	DET
fuelectenerg-1427	820	86	tdt	tdt	PROPN
fuelectenerg-1427	820	87	,	,	PUNCT
fuelectenerg-1427	820	88	and	and	CCONJ
fuelectenerg-1427	820	89	sum	sum	VERB
fuelectenerg-1427	820	90	all	all	DET
fuelectenerg-1427	820	91	the	the	DET
fuelectenerg-1427	820	92	resulting	result	VERB
fuelectenerg-1427	820	93	cubes	cube	NOUN
fuelectenerg-1427	820	94	(	(	PUNCT
fuelectenerg-1427	820	95	terms	term	NOUN
fuelectenerg-1427	820	96	)	)	PUNCT
fuelectenerg-1427	820	97	over	over	ADP
fuelectenerg-1427	820	98	gf(3	gf(3	PROPN
fuelectenerg-1427	820	99	)	)	PUNCT
fuelectenerg-1427	820	100	,	,	PUNCT
fuelectenerg-1427	820	101	we	we	PRON
fuelectenerg-1427	820	102	obtain	obtain	VERB
fuelectenerg-1427	820	103	the	the	DET
fuelectenerg-1427	820	104	flattened	flatten	VERB
fuelectenerg-1427	820	105	form	form	NOUN
fuelectenerg-1427	820	106	of	of	ADP
fuelectenerg-1427	820	107	the	the	DET
fuelectenerg-1427	820	108	function	function	NOUN
fuelectenerg-1427	820	109	f	f	PROPN
fuelectenerg-1427	820	110	,	,	PUNCT
fuelectenerg-1427	820	111	as	as	ADP
fuelectenerg-1427	820	112	a	a	DET
fuelectenerg-1427	820	113	certain	certain	ADJ
fuelectenerg-1427	820	114	gfsop	gfsop	NOUN
fuelectenerg-1427	820	115	expression	expression	NOUN
fuelectenerg-1427	820	116	.	.	PUNCT
fuelectenerg-1427	821	1	for	for	ADP
fuelectenerg-1427	821	2	each	each	DET
fuelectenerg-1427	821	3	tdt	tdt	PROPN
fuelectenerg-1427	821	4	in	in	ADP
fuelectenerg-1427	821	5	figure	figure	NOUN
fuelectenerg-1427	821	6	5	5	NUM
fuelectenerg-1427	821	7	,	,	PUNCT
fuelectenerg-1427	821	8	there	there	PRON
fuelectenerg-1427	821	9	are	be	VERB
fuelectenerg-1427	821	10	as	as	ADV
fuelectenerg-1427	821	11	many	many	ADJ
fuelectenerg-1427	821	12	forms	form	NOUN
fuelectenerg-1427	821	13	obtained	obtain	VERB
fuelectenerg-1427	821	14	for	for	ADP
fuelectenerg-1427	821	15	the	the	DET
fuelectenerg-1427	821	16	function	function	NOUN
fuelectenerg-1427	821	17	f	f	PROPN
fuelectenerg-1427	821	18	as	as	ADP
fuelectenerg-1427	821	19	the	the	DET
fuelectenerg-1427	821	20	number	number	NOUN
fuelectenerg-1427	821	21	of	of	ADP
fuelectenerg-1427	821	22	possible	possible	ADJ
fuelectenerg-1427	821	23	permutations	permutation	NOUN
fuelectenerg-1427	821	24	of	of	ADP
fuelectenerg-1427	821	25	the	the	DET
fuelectenerg-1427	821	26	polarities	polarity	NOUN
fuelectenerg-1427	821	27	of	of	ADP
fuelectenerg-1427	821	28	the	the	DET
fuelectenerg-1427	821	29	variables	variable	NOUN
fuelectenerg-1427	821	30	in	in	ADP
fuelectenerg-1427	821	31	the	the	DET
fuelectenerg-1427	821	32	second	second	ADJ
fuelectenerg-1427	821	33	-	-	PUNCT
fuelectenerg-1427	821	34	level	level	NOUN
fuelectenerg-1427	821	35	branches	branch	NOUN
fuelectenerg-1427	821	36	of	of	ADP
fuelectenerg-1427	821	37	each	each	DET
fuelectenerg-1427	821	38	tdt	tdt	PROPN
fuelectenerg-1427	821	39	.	.	PUNCT
fuelectenerg-1427	822	1	definition	definition	NOUN
fuelectenerg-1427	822	2	2	2	NUM
fuelectenerg-1427	822	3	.	.	PUNCT
fuelectenerg-1427	823	1	the	the	DET
fuelectenerg-1427	823	2	family	family	NOUN
fuelectenerg-1427	823	3	of	of	ADP
fuelectenerg-1427	823	4	all	all	DET
fuelectenerg-1427	823	5	possible	possible	ADJ
fuelectenerg-1427	823	6	forms	form	NOUN
fuelectenerg-1427	823	7	obtained	obtain	VERB
fuelectenerg-1427	823	8	per	per	ADP
fuelectenerg-1427	823	9	ternary	ternary	NOUN
fuelectenerg-1427	823	10	s	s	PROPN
fuelectenerg-1427	823	11	/	/	SYM
fuelectenerg-1427	823	12	d	d	NOUN
fuelectenerg-1427	823	13	tree	tree	NOUN
fuelectenerg-1427	823	14	is	be	AUX
fuelectenerg-1427	823	15	called	call	VERB
fuelectenerg-1427	823	16	ternary	ternary	ADJ
fuelectenerg-1427	823	17	inclusive	inclusive	ADJ
fuelectenerg-1427	823	18	forms	form	NOUN
fuelectenerg-1427	823	19	(	(	PUNCT
fuelectenerg-1427	823	20	tifs	tifs	PROPN
fuelectenerg-1427	823	21	)	)	PUNCT
fuelectenerg-1427	823	22	.	.	PUNCT
fuelectenerg-1427	824	1	the	the	DET
fuelectenerg-1427	824	2	numbers	number	NOUN
fuelectenerg-1427	824	3	of	of	ADP
fuelectenerg-1427	824	4	these	these	DET
fuelectenerg-1427	824	5	tifs	tif	NOUN
fuelectenerg-1427	824	6	per	per	ADP
fuelectenerg-1427	824	7	tdt	tdt	PROPN
fuelectenerg-1427	824	8	for	for	ADP
fuelectenerg-1427	824	9	two	two	NUM
fuelectenerg-1427	824	10	variables	variable	NOUN
fuelectenerg-1427	824	11	are	be	AUX
fuelectenerg-1427	824	12	shown	show	VERB
fuelectenerg-1427	824	13	on	on	ADP
fuelectenerg-1427	824	14	top	top	NOUN
fuelectenerg-1427	824	15	of	of	ADP
fuelectenerg-1427	824	16	each	each	DET
fuelectenerg-1427	824	17	s	s	PROPN
fuelectenerg-1427	824	18	/	/	SYM
fuelectenerg-1427	824	19	d	d	PROPN
fuelectenerg-1427	824	20	tdt	tdt	PROPN
fuelectenerg-1427	824	21	in	in	ADP
fuelectenerg-1427	824	22	figure	figure	NOUN
fuelectenerg-1427	824	23	5	5	NUM
fuelectenerg-1427	824	24	.	.	PUNCT
fuelectenerg-1427	824	25	by	by	ADP
fuelectenerg-1427	824	26	observing	observe	VERB
fuelectenerg-1427	824	27	figure	figure	NOUN
fuelectenerg-1427	824	28	5	5	NUM
fuelectenerg-1427	824	29	,	,	PUNCT
fuelectenerg-1427	824	30	we	we	PRON
fuelectenerg-1427	824	31	can	can	AUX
fuelectenerg-1427	824	32	generate	generate	VERB
fuelectenerg-1427	824	33	the	the	DET
fuelectenerg-1427	824	34	corresponding	corresponding	ADJ
fuelectenerg-1427	824	35	flattened	flatten	VERB
fuelectenerg-1427	824	36	forms	form	NOUN
fuelectenerg-1427	824	37	by	by	ADP
fuelectenerg-1427	824	38	two	two	NUM
fuelectenerg-1427	824	39	methods	method	NOUN
fuelectenerg-1427	824	40	.	.	PUNCT
fuelectenerg-1427	825	1	a	a	DET
fuelectenerg-1427	825	2	classical	classical	ADJ
fuelectenerg-1427	825	3	method	method	NOUN
fuelectenerg-1427	825	4	,	,	PUNCT
fuelectenerg-1427	825	5	per	per	ADP
fuelectenerg-1427	825	6	analogy	analogy	NOUN
fuelectenerg-1427	825	7	with	with	ADP
fuelectenerg-1427	825	8	well	well	ADV
fuelectenerg-1427	825	9	-	-	PUNCT
fuelectenerg-1427	825	10	known	know	VERB
fuelectenerg-1427	825	11	binary	binary	ADJ
fuelectenerg-1427	825	12	forms	form	NOUN
fuelectenerg-1427	825	13	,	,	PUNCT
fuelectenerg-1427	825	14	would	would	AUX
fuelectenerg-1427	825	15	be	be	AUX
fuelectenerg-1427	825	16	to	to	PART
fuelectenerg-1427	825	17	create	create	VERB
fuelectenerg-1427	825	18	every	every	DET
fuelectenerg-1427	825	19	transform	transform	NOUN
fuelectenerg-1427	825	20	matrix	matrix	NOUN
fuelectenerg-1427	825	21	for	for	ADP
fuelectenerg-1427	825	22	every	every	DET
fuelectenerg-1427	825	23	tif	tif	PROPN
fuelectenerg-1427	825	24	s	s	PROPN
fuelectenerg-1427	825	25	/	/	SYM
fuelectenerg-1427	825	26	d	d	NOUN
fuelectenerg-1427	825	27	tree	tree	NOUN
fuelectenerg-1427	825	28	and	and	CCONJ
fuelectenerg-1427	825	29	then	then	ADV
fuelectenerg-1427	825	30	expand	expand	VERB
fuelectenerg-1427	825	31	using	use	VERB
fuelectenerg-1427	825	32	that	that	DET
fuelectenerg-1427	825	33	transform	transform	NOUN
fuelectenerg-1427	825	34	matrix	matrix	NOUN
fuelectenerg-1427	825	35	.	.	PUNCT
fuelectenerg-1427	826	1	a	a	DET
fuelectenerg-1427	826	2	better	well	ADJ
fuelectenerg-1427	826	3	method	method	NOUN
fuelectenerg-1427	826	4	is	be	AUX
fuelectenerg-1427	826	5	to	to	PART
fuelectenerg-1427	826	6	create	create	VERB
fuelectenerg-1427	826	7	one	one	NUM
fuelectenerg-1427	826	8	flattened	flatten	VERB
fuelectenerg-1427	826	9	108	108	NUM
fuelectenerg-1427	826	10	56	56	NUM
fuelectenerg-1427	826	11	a.	a.	NOUN
fuelectenerg-1427	826	12	n.	n.	PROPN
fuelectenerg-1427	826	13	al	al	PROPN
fuelectenerg-1427	826	14	-	-	PUNCT
fuelectenerg-1427	826	15	rabadi	rabadi	VERB
fuelectenerg-1427	826	16	an	an	DET
fuelectenerg-1427	826	17	extended	extended	ADJ
fuelectenerg-1427	826	18	green	green	ADJ
fuelectenerg-1427	826	19	sasao	sasao	PROPN
fuelectenerg-1427	826	20	hierarchy	hierarchy	NOUN
fuelectenerg-1427	826	21	of	of	ADP
fuelectenerg-1427	826	22	canonical	canonical	ADJ
fuelectenerg-1427	826	23	ternary	ternary	ADJ
fuelectenerg-1427	826	24	galois	galois	NOUN
fuelectenerg-1427	826	25	forms	form	NOUN
fuelectenerg-1427	826	26	and	and	CCONJ
fuelectenerg-1427	826	27	universal	universal	ADJ
fuelectenerg-1427	826	28	logic	logic	NOUN
fuelectenerg-1427	826	29	modules	module	NOUN
fuelectenerg-1427	826	30	57	57	NUM
fuelectenerg-1427	826	31	an	an	DET
fuelectenerg-1427	826	32	extended	extended	ADJ
fuelectenerg-1427	826	33	green	green	ADJ
fuelectenerg-1427	826	34	sasao	sasao	PROPN
fuelectenerg-1427	826	35	hierarchy	hierarchy	NOUN
fuelectenerg-1427	826	36	of	of	ADP
fuelectenerg-1427	826	37	canonical	canonical	ADJ
fuelectenerg-1427	826	38	ternary	ternary	ADJ
fuelectenerg-1427	826	39	galois	galois	NOUN
fuelectenerg-1427	826	40	forms	form	NOUN
fuelectenerg-1427	826	41	...	...	PUNCT
fuelectenerg-1427	826	42	form	form	NOUN
fuelectenerg-1427	826	43	which	which	PRON
fuelectenerg-1427	826	44	is	be	AUX
fuelectenerg-1427	826	45	an	an	DET
fuelectenerg-1427	826	46	expansion	expansion	NOUN
fuelectenerg-1427	826	47	over	over	ADP
fuelectenerg-1427	826	48	certain	certain	ADJ
fuelectenerg-1427	826	49	transform	transform	NOUN
fuelectenerg-1427	826	50	matrix	matrix	NOUN
fuelectenerg-1427	826	51	(	(	PUNCT
fuelectenerg-1427	826	52	i.e.	i.e.	X
fuelectenerg-1427	826	53	,	,	PUNCT
fuelectenerg-1427	826	54	certain	certain	ADJ
fuelectenerg-1427	826	55	tif	tif	PROPN
fuelectenerg-1427	826	56	)	)	PUNCT
fuelectenerg-1427	826	57	and	and	CCONJ
fuelectenerg-1427	826	58	then	then	ADV
fuelectenerg-1427	826	59	transform	transform	VERB
fuelectenerg-1427	826	60	systematically	systematically	ADV
fuelectenerg-1427	826	61	from	from	ADP
fuelectenerg-1427	826	62	one	one	NUM
fuelectenerg-1427	826	63	form	form	NOUN
fuelectenerg-1427	826	64	to	to	ADP
fuelectenerg-1427	826	65	another	another	DET
fuelectenerg-1427	826	66	form	form	NOUN
fuelectenerg-1427	826	67	without	without	ADP
fuelectenerg-1427	826	68	the	the	DET
fuelectenerg-1427	826	69	need	need	NOUN
fuelectenerg-1427	826	70	to	to	PART
fuelectenerg-1427	826	71	create	create	VERB
fuelectenerg-1427	826	72	all	all	PRON
fuelectenerg-1427	826	73	transform	transform	VERB
fuelectenerg-1427	826	74	matrices	matrix	NOUN
fuelectenerg-1427	826	75	from	from	ADP
fuelectenerg-1427	826	76	the	the	DET
fuelectenerg-1427	826	77	corresponding	correspond	VERB
fuelectenerg-1427	826	78	s	s	PROPN
fuelectenerg-1427	826	79	/	/	SYM
fuelectenerg-1427	826	80	d	d	NOUN
fuelectenerg-1427	826	81	trees	tree	NOUN
fuelectenerg-1427	826	82	.	.	PUNCT
fuelectenerg-1427	827	1	this	this	DET
fuelectenerg-1427	827	2	general	general	ADJ
fuelectenerg-1427	827	3	approach	approach	NOUN
fuelectenerg-1427	827	4	can	can	AUX
fuelectenerg-1427	827	5	lead	lead	VERB
fuelectenerg-1427	827	6	to	to	ADP
fuelectenerg-1427	827	7	several	several	ADJ
fuelectenerg-1427	827	8	algorithms	algorithm	NOUN
fuelectenerg-1427	827	9	of	of	ADP
fuelectenerg-1427	827	10	various	various	ADJ
fuelectenerg-1427	827	11	complexities	complexity	NOUN
fuelectenerg-1427	827	12	that	that	PRON
fuelectenerg-1427	827	13	generalize	generalize	VERB
fuelectenerg-1427	827	14	the	the	DET
fuelectenerg-1427	827	15	existing	exist	VERB
fuelectenerg-1427	827	16	binary	binary	ADJ
fuelectenerg-1427	827	17	algorithms	algorithm	NOUN
fuelectenerg-1427	827	18	to	to	PART
fuelectenerg-1427	827	19	obtain	obtain	VERB
fuelectenerg-1427	827	20	the	the	DET
fuelectenerg-1427	827	21	corresponding	corresponding	ADJ
fuelectenerg-1427	827	22	forms	form	NOUN
fuelectenerg-1427	827	23	such	such	ADJ
fuelectenerg-1427	827	24	as	as	ADP
fuelectenerg-1427	827	25	fprm	fprm	PROPN
fuelectenerg-1427	827	26	,	,	PUNCT
fuelectenerg-1427	827	27	grm	grm	NOUN
fuelectenerg-1427	827	28	and	and	CCONJ
fuelectenerg-1427	827	29	if	if	SCONJ
fuelectenerg-1427	827	30	forms	form	NOUN
fuelectenerg-1427	827	31	.	.	PUNCT
fuelectenerg-1427	827	32	example	example	NOUN
fuelectenerg-1427	828	1	3	3	NUM
fuelectenerg-1427	828	2	.	.	PUNCT
fuelectenerg-1427	828	3	using	use	VERB
fuelectenerg-1427	828	4	the	the	DET
fuelectenerg-1427	828	5	result	result	NOUN
fuelectenerg-1427	828	6	of	of	ADP
fuelectenerg-1427	828	7	example	example	NOUN
fuelectenerg-1427	828	8	2	2	NUM
fuelectenerg-1427	828	9	for	for	ADP
fuelectenerg-1427	828	10	the	the	DET
fuelectenerg-1427	828	11	expansion	expansion	NOUN
fuelectenerg-1427	828	12	of	of	ADP
fuelectenerg-1427	828	13	f	f	PROPN
fuelectenerg-1427	828	14	(	(	PUNCT
fuelectenerg-1427	828	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	828	16	)	)	PUNCT
fuelectenerg-1427	828	17	in	in	ADP
fuelectenerg-1427	828	18	terms	term	NOUN
fuelectenerg-1427	828	19	of	of	ADP
fuelectenerg-1427	828	20	the	the	DET
fuelectenerg-1427	828	21	ternary	ternary	ADJ
fuelectenerg-1427	828	22	shannon	shannon	NOUN
fuelectenerg-1427	828	23	expansion	expansion	NOUN
fuelectenerg-1427	828	24	(	(	PUNCT
fuelectenerg-1427	828	25	that	that	PRON
fuelectenerg-1427	828	26	resembles	resemble	VERB
fuelectenerg-1427	828	27	the	the	DET
fuelectenerg-1427	828	28	s	s	NOUN
fuelectenerg-1427	828	29	/	/	SYM
fuelectenerg-1427	828	30	d	d	NOUN
fuelectenerg-1427	828	31	tree	tree	NOUN
fuelectenerg-1427	828	32	for	for	ADP
fuelectenerg-1427	828	33	shannon	shannon	PROPN
fuelectenerg-1427	828	34	nodes	node	NOUN
fuelectenerg-1427	828	35	in	in	ADP
fuelectenerg-1427	828	36	both	both	DET
fuelectenerg-1427	828	37	levels	level	NOUN
fuelectenerg-1427	828	38	):	):	PUNCT
fuelectenerg-1427	828	39	f	f	X
fuelectenerg-1427	828	40	=	=	PUNCT
fuelectenerg-1427	828	41	0x1	0x1	NOUN
fuelectenerg-1427	828	42	1x2	1x2	NUM
fuelectenerg-1427	829	1	+	+	CCONJ
fuelectenerg-1427	829	2	2	2	NUM
fuelectenerg-1427	829	3	·	·	PUNCT
fuelectenerg-1427	829	4	0x1	0x1	NOUN
fuelectenerg-1427	829	5	2x2	2x2	NUM
fuelectenerg-1427	830	1	+	+	CCONJ
fuelectenerg-1427	830	2	2	2	NUM
fuelectenerg-1427	830	3	·	·	SYM
fuelectenerg-1427	830	4	1x1	1x1	NUM
fuelectenerg-1427	830	5	0x2	0x2	NOUN
fuelectenerg-1427	830	6	+2	+2	PROPN
fuelectenerg-1427	830	7	·	·	PUNCT
fuelectenerg-1427	830	8	1x1	1x1	NUM
fuelectenerg-1427	830	9	1x2	1x2	NUM
fuelectenerg-1427	830	10	+2	+2	PRON
fuelectenerg-1427	830	11	·	·	PUNCT
fuelectenerg-1427	831	1	1x1	1x1	NUM
fuelectenerg-1427	831	2	2x2	2x2	NUM
fuelectenerg-1427	831	3	+	+	SYM
fuelectenerg-1427	831	4	2x1	2x1	NUM
fuelectenerg-1427	831	5	0x2	0x2	NOUN
fuelectenerg-1427	831	6	+2	+2	PROPN
fuelectenerg-1427	831	7	·	·	PUNCT
fuelectenerg-1427	831	8	2x1	2x1	NUM
fuelectenerg-1427	831	9	2x2	2x2	NUM
fuelectenerg-1427	831	10	,	,	PUNCT
fuelectenerg-1427	831	11	(	(	PUNCT
fuelectenerg-1427	831	12	29	29	NUM
fuelectenerg-1427	831	13	)	)	PUNCT
fuelectenerg-1427	831	14	we	we	PRON
fuelectenerg-1427	831	15	can	can	AUX
fuelectenerg-1427	831	16	substitute	substitute	VERB
fuelectenerg-1427	831	17	any	any	PRON
fuelectenerg-1427	831	18	of	of	ADP
fuelectenerg-1427	831	19	equations	equation	NOUN
fuelectenerg-1427	831	20	(	(	PUNCT
fuelectenerg-1427	831	21	7	7	NUM
fuelectenerg-1427	831	22	)	)	PUNCT
fuelectenerg-1427	831	23	(	(	PUNCT
fuelectenerg-1427	831	24	15	15	NUM
fuelectenerg-1427	831	25	)	)	PUNCT
fuelectenerg-1427	831	26	,	,	PUNCT
fuelectenerg-1427	831	27	or	or	CCONJ
fuelectenerg-1427	831	28	a	a	DET
fuelectenerg-1427	831	29	mix	mix	NOUN
fuelectenerg-1427	831	30	of	of	ADP
fuelectenerg-1427	831	31	these	these	DET
fuelectenerg-1427	831	32	equations	equation	NOUN
fuelectenerg-1427	831	33	,	,	PUNCT
fuelectenerg-1427	831	34	to	to	PART
fuelectenerg-1427	831	35	transform	transform	VERB
fuelectenerg-1427	831	36	one	one	NUM
fuelectenerg-1427	831	37	flattened	flatten	VERB
fuelectenerg-1427	831	38	form	form	NOUN
fuelectenerg-1427	831	39	to	to	ADP
fuelectenerg-1427	831	40	another	another	PRON
fuelectenerg-1427	831	41	.	.	PUNCT
fuelectenerg-1427	832	1	for	for	ADP
fuelectenerg-1427	832	2	example	example	NOUN
fuelectenerg-1427	832	3	,	,	PUNCT
fuelectenerg-1427	832	4	if	if	SCONJ
fuelectenerg-1427	832	5	we	we	PRON
fuelectenerg-1427	832	6	substitute	substitute	VERB
fuelectenerg-1427	832	7	equations	equation	NOUN
fuelectenerg-1427	832	8	(	(	PUNCT
fuelectenerg-1427	832	9	7	7	NUM
fuelectenerg-1427	832	10	)	)	PUNCT
fuelectenerg-1427	832	11	and	and	CCONJ
fuelectenerg-1427	832	12	(	(	PUNCT
fuelectenerg-1427	832	13	11	11	NUM
fuelectenerg-1427	832	14	)	)	PUNCT
fuelectenerg-1427	832	15	,	,	PUNCT
fuelectenerg-1427	832	16	we	we	PRON
fuelectenerg-1427	832	17	obtain	obtain	VERB
fuelectenerg-1427	832	18	:	:	PUNCT
fuelectenerg-1427	832	19	f	f	PROPN
fuelectenerg-1427	832	20	=(	=(	NOUN
fuelectenerg-1427	832	21	2(x1	2(x1	NUM
fuelectenerg-1427	832	22	)	)	PUNCT
fuelectenerg-1427	832	23	2	2	NUM
fuelectenerg-1427	832	24	+	+	SYM
fuelectenerg-1427	833	1	1)(2(x′2	1)(2(x′2	NUM
fuelectenerg-1427	833	2	)	)	PUNCT
fuelectenerg-1427	833	3	2	2	NUM
fuelectenerg-1427	833	4	+	+	SYM
fuelectenerg-1427	833	5	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	833	6	)	)	PUNCT
fuelectenerg-1427	833	7	2	2	NUM
fuelectenerg-1427	833	8	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	833	9	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	833	10	)	)	PUNCT
fuelectenerg-1427	833	11	2	2	NUM
fuelectenerg-1427	833	12	+	+	CCONJ
fuelectenerg-1427	833	13	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	833	14	)	)	PUNCT
fuelectenerg-1427	833	15	2	2	NUM
fuelectenerg-1427	833	16	+1	+1	NOUN
fuelectenerg-1427	833	17	)	)	PUNCT
fuelectenerg-1427	833	18	+	+	CCONJ
fuelectenerg-1427	833	19	2(2(x′1	2(2(x′1	NUM
fuelectenerg-1427	833	20	)	)	PUNCT
fuelectenerg-1427	833	21	2	2	NUM
fuelectenerg-1427	834	1	+	+	CCONJ
fuelectenerg-1427	834	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	834	3	′	′	NOUN
fuelectenerg-1427	834	4	2	2	NUM
fuelectenerg-1427	834	5	)	)	PUNCT
fuelectenerg-1427	834	6	2	2	NUM
fuelectenerg-1427	834	7	+	+	CCONJ
fuelectenerg-1427	834	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	834	9	)	)	PUNCT
fuelectenerg-1427	834	10	2	2	NUM
fuelectenerg-1427	834	11	+	+	NUM
fuelectenerg-1427	834	12	x′1	x′1	X
fuelectenerg-1427	834	13	)	)	PUNCT
fuelectenerg-1427	834	14	·	·	PUNCT
fuelectenerg-1427	835	1	2x2	2x2	NUM
fuelectenerg-1427	835	2	+	+	NUM
fuelectenerg-1427	835	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	835	4	)	)	PUNCT
fuelectenerg-1427	835	5	2	2	NUM
fuelectenerg-1427	835	6	+1	+1	NOUN
fuelectenerg-1427	835	7	)	)	PUNCT
fuelectenerg-1427	835	8	+	+	CCONJ
fuelectenerg-1427	835	9	2	2	NUM
fuelectenerg-1427	835	10	·	·	SYM
fuelectenerg-1427	835	11	2x1	2x1	NUM
fuelectenerg-1427	835	12	2x2	2x2	NUM
fuelectenerg-1427	835	13	,	,	PUNCT
fuelectenerg-1427	835	14	(	(	PUNCT
fuelectenerg-1427	835	15	30	30	NUM
fuelectenerg-1427	835	16	)	)	PUNCT
fuelectenerg-1427	835	17	by	by	ADP
fuelectenerg-1427	835	18	utilizing	utilize	VERB
fuelectenerg-1427	835	19	gf	gf	NOUN
fuelectenerg-1427	835	20	addition	addition	NOUN
fuelectenerg-1427	835	21	and	and	CCONJ
fuelectenerg-1427	835	22	multiplication	multiplication	NOUN
fuelectenerg-1427	835	23	operators	operator	NOUN
fuelectenerg-1427	835	24	from	from	ADP
fuelectenerg-1427	835	25	figure	figure	NOUN
fuelectenerg-1427	835	26	1	1	NUM
fuelectenerg-1427	835	27	,	,	PUNCT
fuelectenerg-1427	835	28	equation	equation	NOUN
fuelectenerg-1427	835	29	(	(	PUNCT
fuelectenerg-1427	835	30	30	30	NUM
fuelectenerg-1427	835	31	)	)	PUNCT
fuelectenerg-1427	835	32	can	can	AUX
fuelectenerg-1427	835	33	be	be	AUX
fuelectenerg-1427	835	34	transformed	transform	VERB
fuelectenerg-1427	835	35	to	to	ADP
fuelectenerg-1427	835	36	:	:	PUNCT
fuelectenerg-1427	835	37	f	f	PROPN
fuelectenerg-1427	835	38	=(	=(	PROPN
fuelectenerg-1427	835	39	x1	x1	PROPN
fuelectenerg-1427	835	40	)	)	PUNCT
fuelectenerg-1427	835	41	2(x′2	2(x′2	NOUN
fuelectenerg-1427	835	42	)	)	PUNCT
fuelectenerg-1427	835	43	2	2	NUM
fuelectenerg-1427	836	1	+	+	CCONJ
fuelectenerg-1427	836	2	2(x1	2(x1	NUM
fuelectenerg-1427	836	3	)	)	PUNCT
fuelectenerg-1427	836	4	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	836	5	)	)	PUNCT
fuelectenerg-1427	836	6	2	2	NUM
fuelectenerg-1427	837	1	+	+	CCONJ
fuelectenerg-1427	837	2	x′2	x′2	X
fuelectenerg-1427	838	1	+	+	ADJ
fuelectenerg-1427	838	2	(	(	PUNCT
fuelectenerg-1427	838	3	x1	x1	ADJ
fuelectenerg-1427	838	4	)	)	PUNCT
fuelectenerg-1427	838	5	2	2	NUM
fuelectenerg-1427	838	6	(	(	PUNCT
fuelectenerg-1427	838	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	838	8	(	(	PUNCT
fuelectenerg-1427	838	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	838	10	)	)	PUNCT
fuelectenerg-1427	838	11	2(x2	2(x2	NUM
fuelectenerg-1427	838	12	)	)	PUNCT
fuelectenerg-1427	838	13	2	2	NUM
fuelectenerg-1427	839	1	+	+	NOUN
fuelectenerg-1427	839	2	(	(	PUNCT
fuelectenerg-1427	839	3	x′1	x′1	NOUN
fuelectenerg-1427	839	4	)	)	PUNCT
fuelectenerg-1427	839	5	2	2	NUM
fuelectenerg-1427	840	1	+	+	NOUN
fuelectenerg-1427	840	2	(	(	PUNCT
fuelectenerg-1427	840	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	840	4	)	)	PUNCT
fuelectenerg-1427	840	5	2	2	NUM
fuelectenerg-1427	841	1	+	+	CCONJ
fuelectenerg-1427	841	2	2x′1	2x′1	NUM
fuelectenerg-1427	841	3	+2(x′1	+2(x′1	ADJ
fuelectenerg-1427	841	4	)	)	PUNCT
fuelectenerg-1427	841	5	2(x′2	2(x′2	NOUN
fuelectenerg-1427	841	6	)	)	PUNCT
fuelectenerg-1427	841	7	2	2	NUM
fuelectenerg-1427	842	1	+	+	ADJ
fuelectenerg-1427	842	2	(	(	PUNCT
fuelectenerg-1427	842	3	x′1	x′1	NOUN
fuelectenerg-1427	842	4	)	)	PUNCT
fuelectenerg-1427	842	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	842	6	(	(	PUNCT
fuelectenerg-1427	842	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	842	8	′	′	NUM
fuelectenerg-1427	842	9	2	2	NUM
fuelectenerg-1427	842	10	)	)	PUNCT
fuelectenerg-1427	842	11	2	2	NUM
fuelectenerg-1427	842	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	842	13	+	+	PROPN
fuelectenerg-1427	842	14	(	(	PUNCT
fuelectenerg-1427	842	15	x′1	x′1	NOUN
fuelectenerg-1427	842	16	)	)	PUNCT
fuelectenerg-1427	842	17	2	2	NUM
fuelectenerg-1427	842	18	·	·	PUNCT
fuelectenerg-1427	842	19	2x2	2x2	NUM
fuelectenerg-1427	842	20	+	+	CCONJ
fuelectenerg-1427	842	21	2(x′1	2(x′1	NUM
fuelectenerg-1427	842	22	)	)	PUNCT
fuelectenerg-1427	842	23	2x2	2x2	NUM
fuelectenerg-1427	843	1	+	+	CCONJ
fuelectenerg-1427	843	2	2	2	NUM
fuelectenerg-1427	843	3	(	(	PUNCT
fuelectenerg-1427	843	4	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	843	5	)	)	PUNCT
fuelectenerg-1427	843	6	2	2	NUM
fuelectenerg-1427	844	1	+	+	SYM
fuelectenerg-1427	844	2	2x1	2x1	NUM
fuelectenerg-1427	844	3	+2	+2	NOUN
fuelectenerg-1427	844	4	(	(	PUNCT
fuelectenerg-1427	844	5	2x1	2x1	NUM
fuelectenerg-1427	844	6	)	)	PUNCT
fuelectenerg-1427	844	7	(	(	PUNCT
fuelectenerg-1427	844	8	2x2	2x2	NUM
fuelectenerg-1427	844	9	)	)	PUNCT
fuelectenerg-1427	844	10	.	.	PUNCT
fuelectenerg-1427	845	1	(	(	PUNCT
fuelectenerg-1427	845	2	31	31	NUM
fuelectenerg-1427	845	3	)	)	PUNCT
fuelectenerg-1427	845	4	let	let	VERB
fuelectenerg-1427	845	5	us	we	PRON
fuelectenerg-1427	845	6	define	define	VERB
fuelectenerg-1427	845	7	,	,	PUNCT
fuelectenerg-1427	845	8	as	as	ADP
fuelectenerg-1427	845	9	one	one	NUM
fuelectenerg-1427	845	10	of	of	ADP
fuelectenerg-1427	845	11	possible	possible	ADJ
fuelectenerg-1427	845	12	definitions	definition	NOUN
fuelectenerg-1427	845	13	,	,	PUNCT
fuelectenerg-1427	845	14	the	the	DET
fuelectenerg-1427	845	15	cost	cost	NOUN
fuelectenerg-1427	845	16	of	of	ADP
fuelectenerg-1427	845	17	the	the	DET
fuelectenerg-1427	845	18	flattened	flatten	VERB
fuelectenerg-1427	845	19	form	form	NOUN
fuelectenerg-1427	845	20	(	(	PUNCT
fuelectenerg-1427	845	21	expression	expression	NOUN
fuelectenerg-1427	845	22	)	)	PUNCT
fuelectenerg-1427	845	23	to	to	PART
fuelectenerg-1427	845	24	be	be	AUX
fuelectenerg-1427	845	25	:	:	PUNCT
fuelectenerg-1427	845	26	cost	cost	NOUN
fuelectenerg-1427	845	27	=	=	SYM
fuelectenerg-1427	845	28	#	#	NOUN
fuelectenerg-1427	845	29	cubes	cube	NOUN
fuelectenerg-1427	845	30	(	(	PUNCT
fuelectenerg-1427	845	31	32	32	NUM
fuelectenerg-1427	845	32	)	)	PUNCT
fuelectenerg-1427	845	33	then	then	ADV
fuelectenerg-1427	845	34	,	,	PUNCT
fuelectenerg-1427	845	35	we	we	PRON
fuelectenerg-1427	845	36	observe	observe	VERB
fuelectenerg-1427	845	37	that	that	SCONJ
fuelectenerg-1427	845	38	equation	equation	NOUN
fuelectenerg-1427	845	39	(	(	PUNCT
fuelectenerg-1427	845	40	29	29	NUM
fuelectenerg-1427	845	41	)	)	PUNCT
fuelectenerg-1427	845	42	has	have	VERB
fuelectenerg-1427	845	43	the	the	DET
fuelectenerg-1427	845	44	cost	cost	NOUN
fuelectenerg-1427	845	45	of	of	ADP
fuelectenerg-1427	845	46	seven	seven	NUM
fuelectenerg-1427	845	47	,	,	PUNCT
fuelectenerg-1427	845	48	while	while	SCONJ
fuelectenerg-1427	845	49	equation	equation	NOUN
fuelectenerg-1427	845	50	(	(	PUNCT
fuelectenerg-1427	845	51	31	31	NUM
fuelectenerg-1427	845	52	)	)	PUNCT
fuelectenerg-1427	845	53	has	have	VERB
fuelectenerg-1427	845	54	the	the	DET
fuelectenerg-1427	845	55	cost	cost	NOUN
fuelectenerg-1427	845	56	of	of	ADP
fuelectenerg-1427	845	57	19	19	NUM
fuelectenerg-1427	845	58	.	.	PUNCT
fuelectenerg-1427	846	1	thus	thus	ADV
fuelectenerg-1427	846	2	,	,	PUNCT
fuelectenerg-1427	846	3	the	the	DET
fuelectenerg-1427	846	4	inverse	inverse	NOUN
fuelectenerg-1427	846	5	transformations	transformation	NOUN
fuelectenerg-1427	846	6	applied	apply	VERB
fuelectenerg-1427	846	7	to	to	ADP
fuelectenerg-1427	846	8	equation	equation	NOUN
fuelectenerg-1427	846	9	(	(	PUNCT
fuelectenerg-1427	846	10	31	31	NUM
fuelectenerg-1427	846	11	)	)	PUNCT
fuelectenerg-1427	846	12	would	would	AUX
fuelectenerg-1427	846	13	lead	lead	VERB
fuelectenerg-1427	846	14	to	to	ADP
fuelectenerg-1427	846	15	equation	equation	NOUN
fuelectenerg-1427	846	16	(	(	PUNCT
fuelectenerg-1427	846	17	29	29	NUM
fuelectenerg-1427	846	18	)	)	PUNCT
fuelectenerg-1427	846	19	and	and	CCONJ
fuelectenerg-1427	846	20	a	a	DET
fuelectenerg-1427	846	21	reduction	reduction	NOUN
fuelectenerg-1427	846	22	of	of	ADP
fuelectenerg-1427	846	23	cost	cost	NOUN
fuelectenerg-1427	846	24	from	from	ADP
fuelectenerg-1427	846	25	19	19	NUM
fuelectenerg-1427	846	26	to	to	PART
fuelectenerg-1427	846	27	seven	seven	NUM
fuelectenerg-1427	846	28	.	.	PUNCT
fuelectenerg-1427	847	1	using	use	VERB
fuelectenerg-1427	847	2	the	the	DET
fuelectenerg-1427	847	3	same	same	ADJ
fuelectenerg-1427	847	4	approach	approach	NOUN
fuelectenerg-1427	847	5	,	,	PUNCT
fuelectenerg-1427	847	6	we	we	PRON
fuelectenerg-1427	847	7	can	can	AUX
fuelectenerg-1427	847	8	generate	generate	VERB
fuelectenerg-1427	847	9	a	a	DET
fuelectenerg-1427	847	10	subset	subset	NOUN
fuelectenerg-1427	847	11	of	of	ADP
fuelectenerg-1427	847	12	possible	possible	ADJ
fuelectenerg-1427	847	13	gfsop	gfsop	NOUN
fuelectenerg-1427	847	14	expressions	expression	NOUN
fuelectenerg-1427	847	15	(	(	PUNCT
fuelectenerg-1427	847	16	flattened	flatten	VERB
fuelectenerg-1427	847	17	forms	form	NOUN
fuelectenerg-1427	847	18	)	)	PUNCT
fuelectenerg-1427	847	19	.	.	PUNCT
fuelectenerg-1427	848	1	note	note	VERB
fuelectenerg-1427	848	2	that	that	SCONJ
fuelectenerg-1427	848	3	all	all	PRON
fuelectenerg-1427	848	4	of	of	ADP
fuelectenerg-1427	848	5	these	these	DET
fuelectenerg-1427	848	6	gfsop	gfsop	NOUN
fuelectenerg-1427	848	7	expressions	expression	NOUN
fuelectenerg-1427	848	8	are	be	AUX
fuelectenerg-1427	848	9	equivalent	equivalent	ADJ
fuelectenerg-1427	848	10	since	since	SCONJ
fuelectenerg-1427	848	11	they	they	PRON
fuelectenerg-1427	848	12	produce	produce	VERB
fuelectenerg-1427	848	13	the	the	DET
fuelectenerg-1427	848	14	same	same	ADJ
fuelectenerg-1427	848	15	function	function	NOUN
fuelectenerg-1427	848	16	in	in	ADP
fuelectenerg-1427	848	17	different	different	ADJ
fuelectenerg-1427	848	18	forms	form	NOUN
fuelectenerg-1427	848	19	.	.	PUNCT
fuelectenerg-1427	849	1	yet	yet	ADV
fuelectenerg-1427	849	2	,	,	PUNCT
fuelectenerg-1427	849	3	as	as	SCONJ
fuelectenerg-1427	849	4	can	can	AUX
fuelectenerg-1427	849	5	be	be	AUX
fuelectenerg-1427	849	6	observed	observe	VERB
fuelectenerg-1427	849	7	from	from	ADP
fuelectenerg-1427	849	8	equation	equation	NOUN
fuelectenerg-1427	849	9	(	(	PUNCT
fuelectenerg-1427	849	10	31	31	NUM
fuelectenerg-1427	849	11	)	)	PUNCT
fuelectenerg-1427	849	12	,	,	PUNCT
fuelectenerg-1427	849	13	by	by	ADP
fuelectenerg-1427	849	14	further	further	ADJ
fuelectenerg-1427	849	15	transformations	transformation	NOUN
fuelectenerg-1427	849	16	of	of	ADP
fuelectenerg-1427	849	17	equation	equation	NOUN
fuelectenerg-1427	849	18	(	(	PUNCT
fuelectenerg-1427	849	19	29	29	NUM
fuelectenerg-1427	849	20	)	)	PUNCT
fuelectenerg-1427	849	21	from	from	ADP
fuelectenerg-1427	849	22	one	one	NUM
fuelectenerg-1427	849	23	form	form	NOUN
fuelectenerg-1427	849	24	to	to	ADP
fuelectenerg-1427	849	25	another	another	PRON
fuelectenerg-1427	849	26	,	,	PUNCT
fuelectenerg-1427	849	27	some	some	DET
fuelectenerg-1427	849	28	transformations	transformation	NOUN
fuelectenerg-1427	849	29	produce	produce	VERB
fuelectenerg-1427	849	30	flattened	flatten	VERB
fuelectenerg-1427	849	31	forms	form	NOUN
fuelectenerg-1427	849	32	with	with	ADP
fuelectenerg-1427	849	33	a	a	DET
fuelectenerg-1427	849	34	smaller	small	ADJ
fuelectenerg-1427	849	35	number	number	NOUN
fuelectenerg-1427	849	36	of	of	ADP
fuelectenerg-1427	849	37	cubes	cube	NOUN
fuelectenerg-1427	849	38	than	than	ADP
fuelectenerg-1427	849	39	the	the	DET
fuelectenerg-1427	849	40	others	other	NOUN
fuelectenerg-1427	849	41	.	.	PUNCT
fuelectenerg-1427	850	1	from	from	ADP
fuelectenerg-1427	850	2	this	this	DET
fuelectenerg-1427	850	3	observation	observation	NOUN
fuelectenerg-1427	850	4	rises	rise	VERB
fuelectenerg-1427	850	5	the	the	DET
fuelectenerg-1427	850	6	idea	idea	NOUN
fuelectenerg-1427	850	7	of	of	ADP
fuelectenerg-1427	850	8	a	a	DET
fuelectenerg-1427	850	9	possible	possible	ADJ
fuelectenerg-1427	850	10	application	application	NOUN
fuelectenerg-1427	850	11	of	of	ADP
fuelectenerg-1427	850	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	850	13	computing	computing	NOUN
fuelectenerg-1427	850	14	using	use	VERB
fuelectenerg-1427	850	15	the	the	DET
fuelectenerg-1427	850	16	s	s	PROPN
fuelectenerg-1427	850	17	/	/	SYM
fuelectenerg-1427	850	18	d	d	NOUN
fuelectenerg-1427	850	19	trees	tree	NOUN
fuelectenerg-1427	850	20	and	and	CCONJ
fuelectenerg-1427	850	21	related	related	ADJ
fuelectenerg-1427	850	22	transformations	transformation	NOUN
fuelectenerg-1427	850	23	to	to	PART
fuelectenerg-1427	850	24	produce	produce	VERB
fuelectenerg-1427	850	25	the	the	DET
fuelectenerg-1427	850	26	corresponding	corresponding	ADJ
fuelectenerg-1427	850	27	minimum	minimum	ADJ
fuelectenerg-1427	850	28	gfsops	gfsop	NOUN
fuelectenerg-1427	850	29	.	.	PUNCT
fuelectenerg-1427	851	1	analogous	analogous	ADJ
fuelectenerg-1427	851	2	to	to	ADP
fuelectenerg-1427	851	3	the	the	DET
fuelectenerg-1427	851	4	binary	binary	ADJ
fuelectenerg-1427	851	5	case	case	NOUN
fuelectenerg-1427	851	6	in	in	ADP
fuelectenerg-1427	851	7	equation	equation	NOUN
fuelectenerg-1427	851	8	(	(	PUNCT
fuelectenerg-1427	851	9	27	27	NUM
fuelectenerg-1427	851	10	)	)	PUNCT
fuelectenerg-1427	851	11	,	,	PUNCT
fuelectenerg-1427	851	12	the	the	DET
fuelectenerg-1427	851	13	ternary	ternary	ADJ
fuelectenerg-1427	851	14	gifs	gif	NOUN
fuelectenerg-1427	851	15	can	can	AUX
fuelectenerg-1427	851	16	be	be	AUX
fuelectenerg-1427	851	17	defined	define	VERB
fuelectenerg-1427	851	18	as	as	ADP
fuelectenerg-1427	851	19	the	the	DET
fuelectenerg-1427	851	20	union	union	NOUN
fuelectenerg-1427	851	21	of	of	ADP
fuelectenerg-1427	851	22	ternary	ternary	PROPN
fuelectenerg-1427	851	23	ifs	ifs	PROPN
fuelectenerg-1427	851	24	.	.	PUNCT
fuelectenerg-1427	852	1	definition	definition	NOUN
fuelectenerg-1427	852	2	3	3	NUM
fuelectenerg-1427	852	3	.	.	PUNCT
fuelectenerg-1427	853	1	the	the	DET
fuelectenerg-1427	853	2	family	family	NOUN
fuelectenerg-1427	853	3	of	of	ADP
fuelectenerg-1427	853	4	forms	form	NOUN
fuelectenerg-1427	853	5	,	,	PUNCT
fuelectenerg-1427	853	6	which	which	PRON
fuelectenerg-1427	853	7	is	be	AUX
fuelectenerg-1427	853	8	created	create	VERB
fuelectenerg-1427	853	9	as	as	ADP
fuelectenerg-1427	853	10	a	a	DET
fuelectenerg-1427	853	11	union	union	NOUN
fuelectenerg-1427	853	12	of	of	ADP
fuelectenerg-1427	853	13	sets	set	NOUN
fuelectenerg-1427	853	14	of	of	ADP
fuelectenerg-1427	853	15	tifs	tif	NOUN
fuelectenerg-1427	853	16	for	for	ADP
fuelectenerg-1427	853	17	all	all	DET
fuelectenerg-1427	853	18	variable	variable	ADJ
fuelectenerg-1427	853	19	orders	order	NOUN
fuelectenerg-1427	853	20	,	,	PUNCT
fuelectenerg-1427	853	21	is	be	AUX
fuelectenerg-1427	853	22	called	call	VERB
fuelectenerg-1427	853	23	ternary	ternary	ADJ
fuelectenerg-1427	853	24	generalized	generalized	ADJ
fuelectenerg-1427	853	25	inclusive	inclusive	ADJ
fuelectenerg-1427	853	26	forms	form	NOUN
fuelectenerg-1427	853	27	(	(	PUNCT
fuelectenerg-1427	853	28	tgifs	tgif	NOUN
fuelectenerg-1427	853	29	)	)	PUNCT
fuelectenerg-1427	853	30	.	.	PUNCT
fuelectenerg-1427	854	1	109	109	NUM
fuelectenerg-1427	854	2	an	an	DET
fuelectenerg-1427	854	3	extended	extend	VERB
fuelectenerg-1427	854	4	green	green	ADJ
fuelectenerg-1427	854	5	sasao	sasao	PROPN
fuelectenerg-1427	854	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	854	7	of	of	ADP
fuelectenerg-1427	854	8	canonical	canonical	ADJ
fuelectenerg-1427	854	9	ternary	ternary	ADJ
fuelectenerg-1427	854	10	galois	galois	NOUN
fuelectenerg-1427	854	11	forms	form	NOUN
fuelectenerg-1427	854	12	...	...	PUNCT
fuelectenerg-1427	854	13	form	form	NOUN
fuelectenerg-1427	854	14	which	which	PRON
fuelectenerg-1427	854	15	is	be	AUX
fuelectenerg-1427	854	16	an	an	DET
fuelectenerg-1427	854	17	expansion	expansion	NOUN
fuelectenerg-1427	854	18	over	over	ADP
fuelectenerg-1427	854	19	certain	certain	ADJ
fuelectenerg-1427	854	20	transform	transform	NOUN
fuelectenerg-1427	854	21	matrix	matrix	NOUN
fuelectenerg-1427	854	22	(	(	PUNCT
fuelectenerg-1427	854	23	i.e.	i.e.	X
fuelectenerg-1427	854	24	,	,	PUNCT
fuelectenerg-1427	854	25	certain	certain	ADJ
fuelectenerg-1427	854	26	tif	tif	PROPN
fuelectenerg-1427	854	27	)	)	PUNCT
fuelectenerg-1427	854	28	and	and	CCONJ
fuelectenerg-1427	854	29	then	then	ADV
fuelectenerg-1427	854	30	transform	transform	VERB
fuelectenerg-1427	854	31	systematically	systematically	ADV
fuelectenerg-1427	854	32	from	from	ADP
fuelectenerg-1427	854	33	one	one	NUM
fuelectenerg-1427	854	34	form	form	NOUN
fuelectenerg-1427	854	35	to	to	ADP
fuelectenerg-1427	854	36	another	another	DET
fuelectenerg-1427	854	37	form	form	NOUN
fuelectenerg-1427	854	38	without	without	ADP
fuelectenerg-1427	854	39	the	the	DET
fuelectenerg-1427	854	40	need	need	NOUN
fuelectenerg-1427	854	41	to	to	PART
fuelectenerg-1427	854	42	create	create	VERB
fuelectenerg-1427	854	43	all	all	PRON
fuelectenerg-1427	854	44	transform	transform	VERB
fuelectenerg-1427	854	45	matrices	matrix	NOUN
fuelectenerg-1427	854	46	from	from	ADP
fuelectenerg-1427	854	47	the	the	DET
fuelectenerg-1427	854	48	corresponding	correspond	VERB
fuelectenerg-1427	854	49	s	s	PROPN
fuelectenerg-1427	854	50	/	/	SYM
fuelectenerg-1427	854	51	d	d	NOUN
fuelectenerg-1427	854	52	trees	tree	NOUN
fuelectenerg-1427	854	53	.	.	PUNCT
fuelectenerg-1427	855	1	this	this	DET
fuelectenerg-1427	855	2	general	general	ADJ
fuelectenerg-1427	855	3	approach	approach	NOUN
fuelectenerg-1427	855	4	can	can	AUX
fuelectenerg-1427	855	5	lead	lead	VERB
fuelectenerg-1427	855	6	to	to	ADP
fuelectenerg-1427	855	7	several	several	ADJ
fuelectenerg-1427	855	8	algorithms	algorithm	NOUN
fuelectenerg-1427	855	9	of	of	ADP
fuelectenerg-1427	855	10	various	various	ADJ
fuelectenerg-1427	855	11	complexities	complexity	NOUN
fuelectenerg-1427	855	12	that	that	PRON
fuelectenerg-1427	855	13	generalize	generalize	VERB
fuelectenerg-1427	855	14	the	the	DET
fuelectenerg-1427	855	15	existing	exist	VERB
fuelectenerg-1427	855	16	binary	binary	ADJ
fuelectenerg-1427	855	17	algorithms	algorithm	NOUN
fuelectenerg-1427	855	18	to	to	PART
fuelectenerg-1427	855	19	obtain	obtain	VERB
fuelectenerg-1427	855	20	the	the	DET
fuelectenerg-1427	855	21	corresponding	corresponding	ADJ
fuelectenerg-1427	855	22	forms	form	NOUN
fuelectenerg-1427	855	23	such	such	ADJ
fuelectenerg-1427	855	24	as	as	ADP
fuelectenerg-1427	855	25	fprm	fprm	PROPN
fuelectenerg-1427	855	26	,	,	PUNCT
fuelectenerg-1427	855	27	grm	grm	NOUN
fuelectenerg-1427	855	28	and	and	CCONJ
fuelectenerg-1427	855	29	if	if	SCONJ
fuelectenerg-1427	855	30	forms	form	NOUN
fuelectenerg-1427	855	31	.	.	PUNCT
fuelectenerg-1427	855	32	example	example	NOUN
fuelectenerg-1427	856	1	3	3	NUM
fuelectenerg-1427	856	2	.	.	PUNCT
fuelectenerg-1427	856	3	using	use	VERB
fuelectenerg-1427	856	4	the	the	DET
fuelectenerg-1427	856	5	result	result	NOUN
fuelectenerg-1427	856	6	of	of	ADP
fuelectenerg-1427	856	7	example	example	NOUN
fuelectenerg-1427	856	8	2	2	NUM
fuelectenerg-1427	856	9	for	for	ADP
fuelectenerg-1427	856	10	the	the	DET
fuelectenerg-1427	856	11	expansion	expansion	NOUN
fuelectenerg-1427	856	12	of	of	ADP
fuelectenerg-1427	856	13	f	f	PROPN
fuelectenerg-1427	856	14	(	(	PUNCT
fuelectenerg-1427	856	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	856	16	)	)	PUNCT
fuelectenerg-1427	856	17	in	in	ADP
fuelectenerg-1427	856	18	terms	term	NOUN
fuelectenerg-1427	856	19	of	of	ADP
fuelectenerg-1427	856	20	the	the	DET
fuelectenerg-1427	856	21	ternary	ternary	ADJ
fuelectenerg-1427	856	22	shannon	shannon	NOUN
fuelectenerg-1427	856	23	expansion	expansion	NOUN
fuelectenerg-1427	856	24	(	(	PUNCT
fuelectenerg-1427	856	25	that	that	PRON
fuelectenerg-1427	856	26	resembles	resemble	VERB
fuelectenerg-1427	856	27	the	the	DET
fuelectenerg-1427	856	28	s	s	NOUN
fuelectenerg-1427	856	29	/	/	SYM
fuelectenerg-1427	856	30	d	d	NOUN
fuelectenerg-1427	856	31	tree	tree	NOUN
fuelectenerg-1427	856	32	for	for	ADP
fuelectenerg-1427	856	33	shannon	shannon	PROPN
fuelectenerg-1427	856	34	nodes	node	NOUN
fuelectenerg-1427	856	35	in	in	ADP
fuelectenerg-1427	856	36	both	both	DET
fuelectenerg-1427	856	37	levels	level	NOUN
fuelectenerg-1427	856	38	):	):	PUNCT
fuelectenerg-1427	856	39	f	f	X
fuelectenerg-1427	856	40	=	=	PUNCT
fuelectenerg-1427	856	41	0x1	0x1	NOUN
fuelectenerg-1427	856	42	1x2	1x2	NUM
fuelectenerg-1427	857	1	+	+	CCONJ
fuelectenerg-1427	857	2	2	2	NUM
fuelectenerg-1427	857	3	·	·	PUNCT
fuelectenerg-1427	857	4	0x1	0x1	NOUN
fuelectenerg-1427	857	5	2x2	2x2	NUM
fuelectenerg-1427	858	1	+	+	CCONJ
fuelectenerg-1427	858	2	2	2	NUM
fuelectenerg-1427	858	3	·	·	SYM
fuelectenerg-1427	858	4	1x1	1x1	NUM
fuelectenerg-1427	858	5	0x2	0x2	NOUN
fuelectenerg-1427	858	6	+2	+2	PROPN
fuelectenerg-1427	858	7	·	·	PUNCT
fuelectenerg-1427	858	8	1x1	1x1	NUM
fuelectenerg-1427	858	9	1x2	1x2	NUM
fuelectenerg-1427	858	10	+2	+2	PRON
fuelectenerg-1427	858	11	·	·	PUNCT
fuelectenerg-1427	859	1	1x1	1x1	NUM
fuelectenerg-1427	859	2	2x2	2x2	NUM
fuelectenerg-1427	859	3	+	+	SYM
fuelectenerg-1427	859	4	2x1	2x1	NUM
fuelectenerg-1427	859	5	0x2	0x2	NOUN
fuelectenerg-1427	859	6	+2	+2	PROPN
fuelectenerg-1427	859	7	·	·	PUNCT
fuelectenerg-1427	859	8	2x1	2x1	NUM
fuelectenerg-1427	859	9	2x2	2x2	NUM
fuelectenerg-1427	859	10	,	,	PUNCT
fuelectenerg-1427	859	11	(	(	PUNCT
fuelectenerg-1427	859	12	29	29	NUM
fuelectenerg-1427	859	13	)	)	PUNCT
fuelectenerg-1427	859	14	we	we	PRON
fuelectenerg-1427	859	15	can	can	AUX
fuelectenerg-1427	859	16	substitute	substitute	VERB
fuelectenerg-1427	859	17	any	any	PRON
fuelectenerg-1427	859	18	of	of	ADP
fuelectenerg-1427	859	19	equations	equation	NOUN
fuelectenerg-1427	859	20	(	(	PUNCT
fuelectenerg-1427	859	21	7	7	NUM
fuelectenerg-1427	859	22	)	)	PUNCT
fuelectenerg-1427	859	23	(	(	PUNCT
fuelectenerg-1427	859	24	15	15	NUM
fuelectenerg-1427	859	25	)	)	PUNCT
fuelectenerg-1427	859	26	,	,	PUNCT
fuelectenerg-1427	859	27	or	or	CCONJ
fuelectenerg-1427	859	28	a	a	DET
fuelectenerg-1427	859	29	mix	mix	NOUN
fuelectenerg-1427	859	30	of	of	ADP
fuelectenerg-1427	859	31	these	these	DET
fuelectenerg-1427	859	32	equations	equation	NOUN
fuelectenerg-1427	859	33	,	,	PUNCT
fuelectenerg-1427	859	34	to	to	PART
fuelectenerg-1427	859	35	transform	transform	VERB
fuelectenerg-1427	859	36	one	one	NUM
fuelectenerg-1427	859	37	flattened	flatten	VERB
fuelectenerg-1427	859	38	form	form	NOUN
fuelectenerg-1427	859	39	to	to	ADP
fuelectenerg-1427	859	40	another	another	PRON
fuelectenerg-1427	859	41	.	.	PUNCT
fuelectenerg-1427	860	1	for	for	ADP
fuelectenerg-1427	860	2	example	example	NOUN
fuelectenerg-1427	860	3	,	,	PUNCT
fuelectenerg-1427	860	4	if	if	SCONJ
fuelectenerg-1427	860	5	we	we	PRON
fuelectenerg-1427	860	6	substitute	substitute	VERB
fuelectenerg-1427	860	7	equations	equation	NOUN
fuelectenerg-1427	860	8	(	(	PUNCT
fuelectenerg-1427	860	9	7	7	NUM
fuelectenerg-1427	860	10	)	)	PUNCT
fuelectenerg-1427	860	11	and	and	CCONJ
fuelectenerg-1427	860	12	(	(	PUNCT
fuelectenerg-1427	860	13	11	11	NUM
fuelectenerg-1427	860	14	)	)	PUNCT
fuelectenerg-1427	860	15	,	,	PUNCT
fuelectenerg-1427	860	16	we	we	PRON
fuelectenerg-1427	860	17	obtain	obtain	VERB
fuelectenerg-1427	860	18	:	:	PUNCT
fuelectenerg-1427	860	19	f	f	PROPN
fuelectenerg-1427	860	20	=(	=(	NOUN
fuelectenerg-1427	860	21	2(x1	2(x1	NUM
fuelectenerg-1427	860	22	)	)	PUNCT
fuelectenerg-1427	860	23	2	2	NUM
fuelectenerg-1427	860	24	+	+	SYM
fuelectenerg-1427	861	1	1)(2(x′2	1)(2(x′2	NUM
fuelectenerg-1427	861	2	)	)	PUNCT
fuelectenerg-1427	861	3	2	2	NUM
fuelectenerg-1427	861	4	+	+	SYM
fuelectenerg-1427	861	5	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	861	6	)	)	PUNCT
fuelectenerg-1427	861	7	2	2	NUM
fuelectenerg-1427	861	8	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	861	9	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	861	10	)	)	PUNCT
fuelectenerg-1427	861	11	2	2	NUM
fuelectenerg-1427	861	12	+	+	CCONJ
fuelectenerg-1427	861	13	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	861	14	)	)	PUNCT
fuelectenerg-1427	861	15	2	2	NUM
fuelectenerg-1427	861	16	+1	+1	NOUN
fuelectenerg-1427	861	17	)	)	PUNCT
fuelectenerg-1427	861	18	+	+	CCONJ
fuelectenerg-1427	861	19	2(2(x′1	2(2(x′1	NUM
fuelectenerg-1427	861	20	)	)	PUNCT
fuelectenerg-1427	861	21	2	2	NUM
fuelectenerg-1427	862	1	+	+	CCONJ
fuelectenerg-1427	862	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	862	3	′	′	NOUN
fuelectenerg-1427	862	4	2	2	NUM
fuelectenerg-1427	862	5	)	)	PUNCT
fuelectenerg-1427	862	6	2	2	NUM
fuelectenerg-1427	862	7	+	+	CCONJ
fuelectenerg-1427	862	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	862	9	)	)	PUNCT
fuelectenerg-1427	862	10	2	2	NUM
fuelectenerg-1427	862	11	+	+	NUM
fuelectenerg-1427	862	12	x′1	x′1	X
fuelectenerg-1427	862	13	)	)	PUNCT
fuelectenerg-1427	862	14	·	·	PUNCT
fuelectenerg-1427	863	1	2x2	2x2	NUM
fuelectenerg-1427	863	2	+	+	NUM
fuelectenerg-1427	863	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	863	4	)	)	PUNCT
fuelectenerg-1427	863	5	2	2	NUM
fuelectenerg-1427	863	6	+1	+1	NOUN
fuelectenerg-1427	863	7	)	)	PUNCT
fuelectenerg-1427	863	8	+	+	CCONJ
fuelectenerg-1427	863	9	2	2	NUM
fuelectenerg-1427	863	10	·	·	SYM
fuelectenerg-1427	863	11	2x1	2x1	NUM
fuelectenerg-1427	863	12	2x2	2x2	NUM
fuelectenerg-1427	863	13	,	,	PUNCT
fuelectenerg-1427	863	14	(	(	PUNCT
fuelectenerg-1427	863	15	30	30	NUM
fuelectenerg-1427	863	16	)	)	PUNCT
fuelectenerg-1427	863	17	by	by	ADP
fuelectenerg-1427	863	18	utilizing	utilize	VERB
fuelectenerg-1427	863	19	gf	gf	NOUN
fuelectenerg-1427	863	20	addition	addition	NOUN
fuelectenerg-1427	863	21	and	and	CCONJ
fuelectenerg-1427	863	22	multiplication	multiplication	NOUN
fuelectenerg-1427	863	23	operators	operator	NOUN
fuelectenerg-1427	863	24	from	from	ADP
fuelectenerg-1427	863	25	figure	figure	NOUN
fuelectenerg-1427	863	26	1	1	NUM
fuelectenerg-1427	863	27	,	,	PUNCT
fuelectenerg-1427	863	28	equation	equation	NOUN
fuelectenerg-1427	863	29	(	(	PUNCT
fuelectenerg-1427	863	30	30	30	NUM
fuelectenerg-1427	863	31	)	)	PUNCT
fuelectenerg-1427	863	32	can	can	AUX
fuelectenerg-1427	863	33	be	be	AUX
fuelectenerg-1427	863	34	transformed	transform	VERB
fuelectenerg-1427	863	35	to	to	ADP
fuelectenerg-1427	863	36	:	:	PUNCT
fuelectenerg-1427	863	37	f	f	PROPN
fuelectenerg-1427	863	38	=(	=(	PROPN
fuelectenerg-1427	863	39	x1	x1	PROPN
fuelectenerg-1427	863	40	)	)	PUNCT
fuelectenerg-1427	863	41	2(x′2	2(x′2	NOUN
fuelectenerg-1427	863	42	)	)	PUNCT
fuelectenerg-1427	863	43	2	2	NUM
fuelectenerg-1427	864	1	+	+	CCONJ
fuelectenerg-1427	864	2	2(x1	2(x1	NUM
fuelectenerg-1427	864	3	)	)	PUNCT
fuelectenerg-1427	864	4	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	864	5	)	)	PUNCT
fuelectenerg-1427	864	6	2	2	NUM
fuelectenerg-1427	865	1	+	+	CCONJ
fuelectenerg-1427	865	2	x′2	x′2	X
fuelectenerg-1427	866	1	+	+	ADJ
fuelectenerg-1427	866	2	(	(	PUNCT
fuelectenerg-1427	866	3	x1	x1	ADJ
fuelectenerg-1427	866	4	)	)	PUNCT
fuelectenerg-1427	866	5	2	2	NUM
fuelectenerg-1427	866	6	(	(	PUNCT
fuelectenerg-1427	866	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	866	8	(	(	PUNCT
fuelectenerg-1427	866	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	866	10	)	)	PUNCT
fuelectenerg-1427	866	11	2(x2	2(x2	NUM
fuelectenerg-1427	866	12	)	)	PUNCT
fuelectenerg-1427	866	13	2	2	NUM
fuelectenerg-1427	867	1	+	+	NOUN
fuelectenerg-1427	867	2	(	(	PUNCT
fuelectenerg-1427	867	3	x′1	x′1	NOUN
fuelectenerg-1427	867	4	)	)	PUNCT
fuelectenerg-1427	867	5	2	2	NUM
fuelectenerg-1427	868	1	+	+	NOUN
fuelectenerg-1427	868	2	(	(	PUNCT
fuelectenerg-1427	868	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	868	4	)	)	PUNCT
fuelectenerg-1427	868	5	2	2	NUM
fuelectenerg-1427	869	1	+	+	CCONJ
fuelectenerg-1427	869	2	2x′1	2x′1	NUM
fuelectenerg-1427	869	3	+2(x′1	+2(x′1	ADJ
fuelectenerg-1427	869	4	)	)	PUNCT
fuelectenerg-1427	869	5	2(x′2	2(x′2	NOUN
fuelectenerg-1427	869	6	)	)	PUNCT
fuelectenerg-1427	869	7	2	2	NUM
fuelectenerg-1427	870	1	+	+	ADJ
fuelectenerg-1427	870	2	(	(	PUNCT
fuelectenerg-1427	870	3	x′1	x′1	NOUN
fuelectenerg-1427	870	4	)	)	PUNCT
fuelectenerg-1427	870	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	870	6	(	(	PUNCT
fuelectenerg-1427	870	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	870	8	′	′	NUM
fuelectenerg-1427	870	9	2	2	NUM
fuelectenerg-1427	870	10	)	)	PUNCT
fuelectenerg-1427	870	11	2	2	NUM
fuelectenerg-1427	870	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	870	13	+	+	PROPN
fuelectenerg-1427	870	14	(	(	PUNCT
fuelectenerg-1427	870	15	x′1	x′1	NOUN
fuelectenerg-1427	870	16	)	)	PUNCT
fuelectenerg-1427	870	17	2	2	NUM
fuelectenerg-1427	870	18	·	·	PUNCT
fuelectenerg-1427	870	19	2x2	2x2	NUM
fuelectenerg-1427	870	20	+	+	CCONJ
fuelectenerg-1427	870	21	2(x′1	2(x′1	NUM
fuelectenerg-1427	870	22	)	)	PUNCT
fuelectenerg-1427	870	23	2x2	2x2	NUM
fuelectenerg-1427	871	1	+	+	CCONJ
fuelectenerg-1427	871	2	2	2	NUM
fuelectenerg-1427	871	3	(	(	PUNCT
fuelectenerg-1427	871	4	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	871	5	)	)	PUNCT
fuelectenerg-1427	871	6	2	2	NUM
fuelectenerg-1427	872	1	+	+	SYM
fuelectenerg-1427	872	2	2x1	2x1	NUM
fuelectenerg-1427	872	3	+2	+2	NOUN
fuelectenerg-1427	872	4	(	(	PUNCT
fuelectenerg-1427	872	5	2x1	2x1	NUM
fuelectenerg-1427	872	6	)	)	PUNCT
fuelectenerg-1427	872	7	(	(	PUNCT
fuelectenerg-1427	872	8	2x2	2x2	NUM
fuelectenerg-1427	872	9	)	)	PUNCT
fuelectenerg-1427	872	10	.	.	PUNCT
fuelectenerg-1427	873	1	(	(	PUNCT
fuelectenerg-1427	873	2	31	31	NUM
fuelectenerg-1427	873	3	)	)	PUNCT
fuelectenerg-1427	873	4	let	let	VERB
fuelectenerg-1427	873	5	us	we	PRON
fuelectenerg-1427	873	6	define	define	VERB
fuelectenerg-1427	873	7	,	,	PUNCT
fuelectenerg-1427	873	8	as	as	ADP
fuelectenerg-1427	873	9	one	one	NUM
fuelectenerg-1427	873	10	of	of	ADP
fuelectenerg-1427	873	11	possible	possible	ADJ
fuelectenerg-1427	873	12	definitions	definition	NOUN
fuelectenerg-1427	873	13	,	,	PUNCT
fuelectenerg-1427	873	14	the	the	DET
fuelectenerg-1427	873	15	cost	cost	NOUN
fuelectenerg-1427	873	16	of	of	ADP
fuelectenerg-1427	873	17	the	the	DET
fuelectenerg-1427	873	18	flattened	flatten	VERB
fuelectenerg-1427	873	19	form	form	NOUN
fuelectenerg-1427	873	20	(	(	PUNCT
fuelectenerg-1427	873	21	expression	expression	NOUN
fuelectenerg-1427	873	22	)	)	PUNCT
fuelectenerg-1427	873	23	to	to	PART
fuelectenerg-1427	873	24	be	be	AUX
fuelectenerg-1427	873	25	:	:	PUNCT
fuelectenerg-1427	873	26	cost	cost	NOUN
fuelectenerg-1427	873	27	=	=	SYM
fuelectenerg-1427	873	28	#	#	NOUN
fuelectenerg-1427	873	29	cubes	cube	NOUN
fuelectenerg-1427	873	30	(	(	PUNCT
fuelectenerg-1427	873	31	32	32	NUM
fuelectenerg-1427	873	32	)	)	PUNCT
fuelectenerg-1427	873	33	then	then	ADV
fuelectenerg-1427	873	34	,	,	PUNCT
fuelectenerg-1427	873	35	we	we	PRON
fuelectenerg-1427	873	36	observe	observe	VERB
fuelectenerg-1427	873	37	that	that	SCONJ
fuelectenerg-1427	873	38	equation	equation	NOUN
fuelectenerg-1427	873	39	(	(	PUNCT
fuelectenerg-1427	873	40	29	29	NUM
fuelectenerg-1427	873	41	)	)	PUNCT
fuelectenerg-1427	873	42	has	have	VERB
fuelectenerg-1427	873	43	the	the	DET
fuelectenerg-1427	873	44	cost	cost	NOUN
fuelectenerg-1427	873	45	of	of	ADP
fuelectenerg-1427	873	46	seven	seven	NUM
fuelectenerg-1427	873	47	,	,	PUNCT
fuelectenerg-1427	873	48	while	while	SCONJ
fuelectenerg-1427	873	49	equation	equation	NOUN
fuelectenerg-1427	873	50	(	(	PUNCT
fuelectenerg-1427	873	51	31	31	NUM
fuelectenerg-1427	873	52	)	)	PUNCT
fuelectenerg-1427	873	53	has	have	VERB
fuelectenerg-1427	873	54	the	the	DET
fuelectenerg-1427	873	55	cost	cost	NOUN
fuelectenerg-1427	873	56	of	of	ADP
fuelectenerg-1427	873	57	19	19	NUM
fuelectenerg-1427	873	58	.	.	PUNCT
fuelectenerg-1427	874	1	thus	thus	ADV
fuelectenerg-1427	874	2	,	,	PUNCT
fuelectenerg-1427	874	3	the	the	DET
fuelectenerg-1427	874	4	inverse	inverse	NOUN
fuelectenerg-1427	874	5	transformations	transformation	NOUN
fuelectenerg-1427	874	6	applied	apply	VERB
fuelectenerg-1427	874	7	to	to	ADP
fuelectenerg-1427	874	8	equation	equation	NOUN
fuelectenerg-1427	874	9	(	(	PUNCT
fuelectenerg-1427	874	10	31	31	NUM
fuelectenerg-1427	874	11	)	)	PUNCT
fuelectenerg-1427	874	12	would	would	AUX
fuelectenerg-1427	874	13	lead	lead	VERB
fuelectenerg-1427	874	14	to	to	ADP
fuelectenerg-1427	874	15	equation	equation	NOUN
fuelectenerg-1427	874	16	(	(	PUNCT
fuelectenerg-1427	874	17	29	29	NUM
fuelectenerg-1427	874	18	)	)	PUNCT
fuelectenerg-1427	874	19	and	and	CCONJ
fuelectenerg-1427	874	20	a	a	DET
fuelectenerg-1427	874	21	reduction	reduction	NOUN
fuelectenerg-1427	874	22	of	of	ADP
fuelectenerg-1427	874	23	cost	cost	NOUN
fuelectenerg-1427	874	24	from	from	ADP
fuelectenerg-1427	874	25	19	19	NUM
fuelectenerg-1427	874	26	to	to	PART
fuelectenerg-1427	874	27	seven	seven	NUM
fuelectenerg-1427	874	28	.	.	PUNCT
fuelectenerg-1427	875	1	using	use	VERB
fuelectenerg-1427	875	2	the	the	DET
fuelectenerg-1427	875	3	same	same	ADJ
fuelectenerg-1427	875	4	approach	approach	NOUN
fuelectenerg-1427	875	5	,	,	PUNCT
fuelectenerg-1427	875	6	we	we	PRON
fuelectenerg-1427	875	7	can	can	AUX
fuelectenerg-1427	875	8	generate	generate	VERB
fuelectenerg-1427	875	9	a	a	DET
fuelectenerg-1427	875	10	subset	subset	NOUN
fuelectenerg-1427	875	11	of	of	ADP
fuelectenerg-1427	875	12	possible	possible	ADJ
fuelectenerg-1427	875	13	gfsop	gfsop	NOUN
fuelectenerg-1427	875	14	expressions	expression	NOUN
fuelectenerg-1427	875	15	(	(	PUNCT
fuelectenerg-1427	875	16	flattened	flatten	VERB
fuelectenerg-1427	875	17	forms	form	NOUN
fuelectenerg-1427	875	18	)	)	PUNCT
fuelectenerg-1427	875	19	.	.	PUNCT
fuelectenerg-1427	876	1	note	note	VERB
fuelectenerg-1427	876	2	that	that	SCONJ
fuelectenerg-1427	876	3	all	all	PRON
fuelectenerg-1427	876	4	of	of	ADP
fuelectenerg-1427	876	5	these	these	DET
fuelectenerg-1427	876	6	gfsop	gfsop	NOUN
fuelectenerg-1427	876	7	expressions	expression	NOUN
fuelectenerg-1427	876	8	are	be	AUX
fuelectenerg-1427	876	9	equivalent	equivalent	ADJ
fuelectenerg-1427	876	10	since	since	SCONJ
fuelectenerg-1427	876	11	they	they	PRON
fuelectenerg-1427	876	12	produce	produce	VERB
fuelectenerg-1427	876	13	the	the	DET
fuelectenerg-1427	876	14	same	same	ADJ
fuelectenerg-1427	876	15	function	function	NOUN
fuelectenerg-1427	876	16	in	in	ADP
fuelectenerg-1427	876	17	different	different	ADJ
fuelectenerg-1427	876	18	forms	form	NOUN
fuelectenerg-1427	876	19	.	.	PUNCT
fuelectenerg-1427	877	1	yet	yet	ADV
fuelectenerg-1427	877	2	,	,	PUNCT
fuelectenerg-1427	877	3	as	as	SCONJ
fuelectenerg-1427	877	4	can	can	AUX
fuelectenerg-1427	877	5	be	be	AUX
fuelectenerg-1427	877	6	observed	observe	VERB
fuelectenerg-1427	877	7	from	from	ADP
fuelectenerg-1427	877	8	equation	equation	NOUN
fuelectenerg-1427	877	9	(	(	PUNCT
fuelectenerg-1427	877	10	31	31	NUM
fuelectenerg-1427	877	11	)	)	PUNCT
fuelectenerg-1427	877	12	,	,	PUNCT
fuelectenerg-1427	877	13	by	by	ADP
fuelectenerg-1427	877	14	further	further	ADJ
fuelectenerg-1427	877	15	transformations	transformation	NOUN
fuelectenerg-1427	877	16	of	of	ADP
fuelectenerg-1427	877	17	equation	equation	NOUN
fuelectenerg-1427	877	18	(	(	PUNCT
fuelectenerg-1427	877	19	29	29	NUM
fuelectenerg-1427	877	20	)	)	PUNCT
fuelectenerg-1427	877	21	from	from	ADP
fuelectenerg-1427	877	22	one	one	NUM
fuelectenerg-1427	877	23	form	form	NOUN
fuelectenerg-1427	877	24	to	to	ADP
fuelectenerg-1427	877	25	another	another	PRON
fuelectenerg-1427	877	26	,	,	PUNCT
fuelectenerg-1427	877	27	some	some	DET
fuelectenerg-1427	877	28	transformations	transformation	NOUN
fuelectenerg-1427	877	29	produce	produce	VERB
fuelectenerg-1427	877	30	flattened	flatten	VERB
fuelectenerg-1427	877	31	forms	form	NOUN
fuelectenerg-1427	877	32	with	with	ADP
fuelectenerg-1427	877	33	a	a	DET
fuelectenerg-1427	877	34	smaller	small	ADJ
fuelectenerg-1427	877	35	number	number	NOUN
fuelectenerg-1427	877	36	of	of	ADP
fuelectenerg-1427	877	37	cubes	cube	NOUN
fuelectenerg-1427	877	38	than	than	ADP
fuelectenerg-1427	877	39	the	the	DET
fuelectenerg-1427	877	40	others	other	NOUN
fuelectenerg-1427	877	41	.	.	PUNCT
fuelectenerg-1427	878	1	from	from	ADP
fuelectenerg-1427	878	2	this	this	DET
fuelectenerg-1427	878	3	observation	observation	NOUN
fuelectenerg-1427	878	4	rises	rise	VERB
fuelectenerg-1427	878	5	the	the	DET
fuelectenerg-1427	878	6	idea	idea	NOUN
fuelectenerg-1427	878	7	of	of	ADP
fuelectenerg-1427	878	8	a	a	DET
fuelectenerg-1427	878	9	possible	possible	ADJ
fuelectenerg-1427	878	10	application	application	NOUN
fuelectenerg-1427	878	11	of	of	ADP
fuelectenerg-1427	878	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	878	13	computing	computing	NOUN
fuelectenerg-1427	878	14	using	use	VERB
fuelectenerg-1427	878	15	the	the	DET
fuelectenerg-1427	878	16	s	s	PROPN
fuelectenerg-1427	878	17	/	/	SYM
fuelectenerg-1427	878	18	d	d	NOUN
fuelectenerg-1427	878	19	trees	tree	NOUN
fuelectenerg-1427	878	20	and	and	CCONJ
fuelectenerg-1427	878	21	related	related	ADJ
fuelectenerg-1427	878	22	transformations	transformation	NOUN
fuelectenerg-1427	878	23	to	to	PART
fuelectenerg-1427	878	24	produce	produce	VERB
fuelectenerg-1427	878	25	the	the	DET
fuelectenerg-1427	878	26	corresponding	corresponding	ADJ
fuelectenerg-1427	878	27	minimum	minimum	ADJ
fuelectenerg-1427	878	28	gfsops	gfsop	NOUN
fuelectenerg-1427	878	29	.	.	PUNCT
fuelectenerg-1427	879	1	analogous	analogous	ADJ
fuelectenerg-1427	879	2	to	to	ADP
fuelectenerg-1427	879	3	the	the	DET
fuelectenerg-1427	879	4	binary	binary	ADJ
fuelectenerg-1427	879	5	case	case	NOUN
fuelectenerg-1427	879	6	in	in	ADP
fuelectenerg-1427	879	7	equation	equation	NOUN
fuelectenerg-1427	879	8	(	(	PUNCT
fuelectenerg-1427	879	9	27	27	NUM
fuelectenerg-1427	879	10	)	)	PUNCT
fuelectenerg-1427	879	11	,	,	PUNCT
fuelectenerg-1427	879	12	the	the	DET
fuelectenerg-1427	879	13	ternary	ternary	ADJ
fuelectenerg-1427	879	14	gifs	gif	NOUN
fuelectenerg-1427	879	15	can	can	AUX
fuelectenerg-1427	879	16	be	be	AUX
fuelectenerg-1427	879	17	defined	define	VERB
fuelectenerg-1427	879	18	as	as	ADP
fuelectenerg-1427	879	19	the	the	DET
fuelectenerg-1427	879	20	union	union	NOUN
fuelectenerg-1427	879	21	of	of	ADP
fuelectenerg-1427	879	22	ternary	ternary	PROPN
fuelectenerg-1427	879	23	ifs	ifs	PROPN
fuelectenerg-1427	879	24	.	.	PUNCT
fuelectenerg-1427	880	1	definition	definition	NOUN
fuelectenerg-1427	880	2	3	3	NUM
fuelectenerg-1427	880	3	.	.	PUNCT
fuelectenerg-1427	881	1	the	the	DET
fuelectenerg-1427	881	2	family	family	NOUN
fuelectenerg-1427	881	3	of	of	ADP
fuelectenerg-1427	881	4	forms	form	NOUN
fuelectenerg-1427	881	5	,	,	PUNCT
fuelectenerg-1427	881	6	which	which	PRON
fuelectenerg-1427	881	7	is	be	AUX
fuelectenerg-1427	881	8	created	create	VERB
fuelectenerg-1427	881	9	as	as	ADP
fuelectenerg-1427	881	10	a	a	DET
fuelectenerg-1427	881	11	union	union	NOUN
fuelectenerg-1427	881	12	of	of	ADP
fuelectenerg-1427	881	13	sets	set	NOUN
fuelectenerg-1427	881	14	of	of	ADP
fuelectenerg-1427	881	15	tifs	tif	NOUN
fuelectenerg-1427	881	16	for	for	ADP
fuelectenerg-1427	881	17	all	all	DET
fuelectenerg-1427	881	18	variable	variable	ADJ
fuelectenerg-1427	881	19	orders	order	NOUN
fuelectenerg-1427	881	20	,	,	PUNCT
fuelectenerg-1427	881	21	is	be	AUX
fuelectenerg-1427	881	22	called	call	VERB
fuelectenerg-1427	881	23	ternary	ternary	ADJ
fuelectenerg-1427	881	24	generalized	generalized	ADJ
fuelectenerg-1427	881	25	inclusive	inclusive	ADJ
fuelectenerg-1427	881	26	forms	form	NOUN
fuelectenerg-1427	881	27	(	(	PUNCT
fuelectenerg-1427	881	28	tgifs	tgif	NOUN
fuelectenerg-1427	881	29	)	)	PUNCT
fuelectenerg-1427	881	30	.	.	PUNCT
fuelectenerg-1427	882	1	109	109	NUM
fuelectenerg-1427	882	2	an	an	DET
fuelectenerg-1427	882	3	extended	extend	VERB
fuelectenerg-1427	882	4	green	green	ADJ
fuelectenerg-1427	882	5	sasao	sasao	PROPN
fuelectenerg-1427	882	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	882	7	of	of	ADP
fuelectenerg-1427	882	8	canonical	canonical	ADJ
fuelectenerg-1427	882	9	ternary	ternary	ADJ
fuelectenerg-1427	882	10	galois	galois	NOUN
fuelectenerg-1427	882	11	forms	form	NOUN
fuelectenerg-1427	882	12	...	...	PUNCT
fuelectenerg-1427	882	13	form	form	NOUN
fuelectenerg-1427	882	14	which	which	PRON
fuelectenerg-1427	882	15	is	be	AUX
fuelectenerg-1427	882	16	an	an	DET
fuelectenerg-1427	882	17	expansion	expansion	NOUN
fuelectenerg-1427	882	18	over	over	ADP
fuelectenerg-1427	882	19	certain	certain	ADJ
fuelectenerg-1427	882	20	transform	transform	NOUN
fuelectenerg-1427	882	21	matrix	matrix	NOUN
fuelectenerg-1427	882	22	(	(	PUNCT
fuelectenerg-1427	882	23	i.e.	i.e.	X
fuelectenerg-1427	882	24	,	,	PUNCT
fuelectenerg-1427	882	25	certain	certain	ADJ
fuelectenerg-1427	882	26	tif	tif	PROPN
fuelectenerg-1427	882	27	)	)	PUNCT
fuelectenerg-1427	882	28	and	and	CCONJ
fuelectenerg-1427	882	29	then	then	ADV
fuelectenerg-1427	882	30	transform	transform	VERB
fuelectenerg-1427	882	31	systematically	systematically	ADV
fuelectenerg-1427	882	32	from	from	ADP
fuelectenerg-1427	882	33	one	one	NUM
fuelectenerg-1427	882	34	form	form	NOUN
fuelectenerg-1427	882	35	to	to	ADP
fuelectenerg-1427	882	36	another	another	DET
fuelectenerg-1427	882	37	form	form	NOUN
fuelectenerg-1427	882	38	without	without	ADP
fuelectenerg-1427	882	39	the	the	DET
fuelectenerg-1427	882	40	need	need	NOUN
fuelectenerg-1427	882	41	to	to	PART
fuelectenerg-1427	882	42	create	create	VERB
fuelectenerg-1427	882	43	all	all	PRON
fuelectenerg-1427	882	44	transform	transform	VERB
fuelectenerg-1427	882	45	matrices	matrix	NOUN
fuelectenerg-1427	882	46	from	from	ADP
fuelectenerg-1427	882	47	the	the	DET
fuelectenerg-1427	882	48	corresponding	correspond	VERB
fuelectenerg-1427	882	49	s	s	PROPN
fuelectenerg-1427	882	50	/	/	SYM
fuelectenerg-1427	882	51	d	d	NOUN
fuelectenerg-1427	882	52	trees	tree	NOUN
fuelectenerg-1427	882	53	.	.	PUNCT
fuelectenerg-1427	883	1	this	this	DET
fuelectenerg-1427	883	2	general	general	ADJ
fuelectenerg-1427	883	3	approach	approach	NOUN
fuelectenerg-1427	883	4	can	can	AUX
fuelectenerg-1427	883	5	lead	lead	VERB
fuelectenerg-1427	883	6	to	to	ADP
fuelectenerg-1427	883	7	several	several	ADJ
fuelectenerg-1427	883	8	algorithms	algorithm	NOUN
fuelectenerg-1427	883	9	of	of	ADP
fuelectenerg-1427	883	10	various	various	ADJ
fuelectenerg-1427	883	11	complexities	complexity	NOUN
fuelectenerg-1427	883	12	that	that	PRON
fuelectenerg-1427	883	13	generalize	generalize	VERB
fuelectenerg-1427	883	14	the	the	DET
fuelectenerg-1427	883	15	existing	exist	VERB
fuelectenerg-1427	883	16	binary	binary	ADJ
fuelectenerg-1427	883	17	algorithms	algorithm	NOUN
fuelectenerg-1427	883	18	to	to	PART
fuelectenerg-1427	883	19	obtain	obtain	VERB
fuelectenerg-1427	883	20	the	the	DET
fuelectenerg-1427	883	21	corresponding	corresponding	ADJ
fuelectenerg-1427	883	22	forms	form	NOUN
fuelectenerg-1427	883	23	such	such	ADJ
fuelectenerg-1427	883	24	as	as	ADP
fuelectenerg-1427	883	25	fprm	fprm	PROPN
fuelectenerg-1427	883	26	,	,	PUNCT
fuelectenerg-1427	883	27	grm	grm	NOUN
fuelectenerg-1427	883	28	and	and	CCONJ
fuelectenerg-1427	883	29	if	if	SCONJ
fuelectenerg-1427	883	30	forms	form	NOUN
fuelectenerg-1427	883	31	.	.	PUNCT
fuelectenerg-1427	883	32	example	example	NOUN
fuelectenerg-1427	884	1	3	3	NUM
fuelectenerg-1427	884	2	.	.	PUNCT
fuelectenerg-1427	884	3	using	use	VERB
fuelectenerg-1427	884	4	the	the	DET
fuelectenerg-1427	884	5	result	result	NOUN
fuelectenerg-1427	884	6	of	of	ADP
fuelectenerg-1427	884	7	example	example	NOUN
fuelectenerg-1427	884	8	2	2	NUM
fuelectenerg-1427	884	9	for	for	ADP
fuelectenerg-1427	884	10	the	the	DET
fuelectenerg-1427	884	11	expansion	expansion	NOUN
fuelectenerg-1427	884	12	of	of	ADP
fuelectenerg-1427	884	13	f	f	PROPN
fuelectenerg-1427	884	14	(	(	PUNCT
fuelectenerg-1427	884	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	884	16	)	)	PUNCT
fuelectenerg-1427	884	17	in	in	ADP
fuelectenerg-1427	884	18	terms	term	NOUN
fuelectenerg-1427	884	19	of	of	ADP
fuelectenerg-1427	884	20	the	the	DET
fuelectenerg-1427	884	21	ternary	ternary	ADJ
fuelectenerg-1427	884	22	shannon	shannon	NOUN
fuelectenerg-1427	884	23	expansion	expansion	NOUN
fuelectenerg-1427	884	24	(	(	PUNCT
fuelectenerg-1427	884	25	that	that	PRON
fuelectenerg-1427	884	26	resembles	resemble	VERB
fuelectenerg-1427	884	27	the	the	DET
fuelectenerg-1427	884	28	s	s	NOUN
fuelectenerg-1427	884	29	/	/	SYM
fuelectenerg-1427	884	30	d	d	NOUN
fuelectenerg-1427	884	31	tree	tree	NOUN
fuelectenerg-1427	884	32	for	for	ADP
fuelectenerg-1427	884	33	shannon	shannon	PROPN
fuelectenerg-1427	884	34	nodes	node	NOUN
fuelectenerg-1427	884	35	in	in	ADP
fuelectenerg-1427	884	36	both	both	DET
fuelectenerg-1427	884	37	levels	level	NOUN
fuelectenerg-1427	884	38	):	):	PUNCT
fuelectenerg-1427	884	39	f	f	X
fuelectenerg-1427	884	40	=	=	PUNCT
fuelectenerg-1427	884	41	0x1	0x1	NOUN
fuelectenerg-1427	884	42	1x2	1x2	NUM
fuelectenerg-1427	885	1	+	+	CCONJ
fuelectenerg-1427	885	2	2	2	NUM
fuelectenerg-1427	885	3	·	·	PUNCT
fuelectenerg-1427	885	4	0x1	0x1	NOUN
fuelectenerg-1427	885	5	2x2	2x2	NUM
fuelectenerg-1427	886	1	+	+	CCONJ
fuelectenerg-1427	886	2	2	2	NUM
fuelectenerg-1427	886	3	·	·	SYM
fuelectenerg-1427	886	4	1x1	1x1	NUM
fuelectenerg-1427	886	5	0x2	0x2	NOUN
fuelectenerg-1427	886	6	+2	+2	PROPN
fuelectenerg-1427	886	7	·	·	PUNCT
fuelectenerg-1427	886	8	1x1	1x1	NUM
fuelectenerg-1427	886	9	1x2	1x2	NUM
fuelectenerg-1427	886	10	+2	+2	PRON
fuelectenerg-1427	886	11	·	·	PUNCT
fuelectenerg-1427	887	1	1x1	1x1	NUM
fuelectenerg-1427	887	2	2x2	2x2	NUM
fuelectenerg-1427	887	3	+	+	SYM
fuelectenerg-1427	887	4	2x1	2x1	NUM
fuelectenerg-1427	887	5	0x2	0x2	NOUN
fuelectenerg-1427	887	6	+2	+2	PROPN
fuelectenerg-1427	887	7	·	·	PUNCT
fuelectenerg-1427	887	8	2x1	2x1	NUM
fuelectenerg-1427	887	9	2x2	2x2	NUM
fuelectenerg-1427	887	10	,	,	PUNCT
fuelectenerg-1427	887	11	(	(	PUNCT
fuelectenerg-1427	887	12	29	29	NUM
fuelectenerg-1427	887	13	)	)	PUNCT
fuelectenerg-1427	887	14	we	we	PRON
fuelectenerg-1427	887	15	can	can	AUX
fuelectenerg-1427	887	16	substitute	substitute	VERB
fuelectenerg-1427	887	17	any	any	PRON
fuelectenerg-1427	887	18	of	of	ADP
fuelectenerg-1427	887	19	equations	equation	NOUN
fuelectenerg-1427	887	20	(	(	PUNCT
fuelectenerg-1427	887	21	7	7	NUM
fuelectenerg-1427	887	22	)	)	PUNCT
fuelectenerg-1427	887	23	(	(	PUNCT
fuelectenerg-1427	887	24	15	15	NUM
fuelectenerg-1427	887	25	)	)	PUNCT
fuelectenerg-1427	887	26	,	,	PUNCT
fuelectenerg-1427	887	27	or	or	CCONJ
fuelectenerg-1427	887	28	a	a	DET
fuelectenerg-1427	887	29	mix	mix	NOUN
fuelectenerg-1427	887	30	of	of	ADP
fuelectenerg-1427	887	31	these	these	DET
fuelectenerg-1427	887	32	equations	equation	NOUN
fuelectenerg-1427	887	33	,	,	PUNCT
fuelectenerg-1427	887	34	to	to	PART
fuelectenerg-1427	887	35	transform	transform	VERB
fuelectenerg-1427	887	36	one	one	NUM
fuelectenerg-1427	887	37	flattened	flatten	VERB
fuelectenerg-1427	887	38	form	form	NOUN
fuelectenerg-1427	887	39	to	to	ADP
fuelectenerg-1427	887	40	another	another	PRON
fuelectenerg-1427	887	41	.	.	PUNCT
fuelectenerg-1427	888	1	for	for	ADP
fuelectenerg-1427	888	2	example	example	NOUN
fuelectenerg-1427	888	3	,	,	PUNCT
fuelectenerg-1427	888	4	if	if	SCONJ
fuelectenerg-1427	888	5	we	we	PRON
fuelectenerg-1427	888	6	substitute	substitute	VERB
fuelectenerg-1427	888	7	equations	equation	NOUN
fuelectenerg-1427	888	8	(	(	PUNCT
fuelectenerg-1427	888	9	7	7	NUM
fuelectenerg-1427	888	10	)	)	PUNCT
fuelectenerg-1427	888	11	and	and	CCONJ
fuelectenerg-1427	888	12	(	(	PUNCT
fuelectenerg-1427	888	13	11	11	NUM
fuelectenerg-1427	888	14	)	)	PUNCT
fuelectenerg-1427	888	15	,	,	PUNCT
fuelectenerg-1427	888	16	we	we	PRON
fuelectenerg-1427	888	17	obtain	obtain	VERB
fuelectenerg-1427	888	18	:	:	PUNCT
fuelectenerg-1427	888	19	f	f	PROPN
fuelectenerg-1427	888	20	=(	=(	NOUN
fuelectenerg-1427	888	21	2(x1	2(x1	NUM
fuelectenerg-1427	888	22	)	)	PUNCT
fuelectenerg-1427	888	23	2	2	NUM
fuelectenerg-1427	888	24	+	+	SYM
fuelectenerg-1427	889	1	1)(2(x′2	1)(2(x′2	NUM
fuelectenerg-1427	889	2	)	)	PUNCT
fuelectenerg-1427	889	3	2	2	NUM
fuelectenerg-1427	889	4	+	+	SYM
fuelectenerg-1427	889	5	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	889	6	)	)	PUNCT
fuelectenerg-1427	889	7	2	2	NUM
fuelectenerg-1427	889	8	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	889	9	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	889	10	)	)	PUNCT
fuelectenerg-1427	889	11	2	2	NUM
fuelectenerg-1427	889	12	+	+	CCONJ
fuelectenerg-1427	889	13	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	889	14	)	)	PUNCT
fuelectenerg-1427	889	15	2	2	NUM
fuelectenerg-1427	889	16	+1	+1	NOUN
fuelectenerg-1427	889	17	)	)	PUNCT
fuelectenerg-1427	889	18	+	+	CCONJ
fuelectenerg-1427	889	19	2(2(x′1	2(2(x′1	NUM
fuelectenerg-1427	889	20	)	)	PUNCT
fuelectenerg-1427	889	21	2	2	NUM
fuelectenerg-1427	890	1	+	+	CCONJ
fuelectenerg-1427	890	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	890	3	′	′	NOUN
fuelectenerg-1427	890	4	2	2	NUM
fuelectenerg-1427	890	5	)	)	PUNCT
fuelectenerg-1427	890	6	2	2	NUM
fuelectenerg-1427	890	7	+	+	CCONJ
fuelectenerg-1427	890	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	890	9	)	)	PUNCT
fuelectenerg-1427	890	10	2	2	NUM
fuelectenerg-1427	890	11	+	+	NUM
fuelectenerg-1427	890	12	x′1	x′1	X
fuelectenerg-1427	890	13	)	)	PUNCT
fuelectenerg-1427	890	14	·	·	PUNCT
fuelectenerg-1427	891	1	2x2	2x2	NUM
fuelectenerg-1427	891	2	+	+	NUM
fuelectenerg-1427	891	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	891	4	)	)	PUNCT
fuelectenerg-1427	891	5	2	2	NUM
fuelectenerg-1427	891	6	+1	+1	NOUN
fuelectenerg-1427	891	7	)	)	PUNCT
fuelectenerg-1427	891	8	+	+	CCONJ
fuelectenerg-1427	891	9	2	2	NUM
fuelectenerg-1427	891	10	·	·	SYM
fuelectenerg-1427	891	11	2x1	2x1	NUM
fuelectenerg-1427	891	12	2x2	2x2	NUM
fuelectenerg-1427	891	13	,	,	PUNCT
fuelectenerg-1427	891	14	(	(	PUNCT
fuelectenerg-1427	891	15	30	30	NUM
fuelectenerg-1427	891	16	)	)	PUNCT
fuelectenerg-1427	891	17	by	by	ADP
fuelectenerg-1427	891	18	utilizing	utilize	VERB
fuelectenerg-1427	891	19	gf	gf	NOUN
fuelectenerg-1427	891	20	addition	addition	NOUN
fuelectenerg-1427	891	21	and	and	CCONJ
fuelectenerg-1427	891	22	multiplication	multiplication	NOUN
fuelectenerg-1427	891	23	operators	operator	NOUN
fuelectenerg-1427	891	24	from	from	ADP
fuelectenerg-1427	891	25	figure	figure	NOUN
fuelectenerg-1427	891	26	1	1	NUM
fuelectenerg-1427	891	27	,	,	PUNCT
fuelectenerg-1427	891	28	equation	equation	NOUN
fuelectenerg-1427	891	29	(	(	PUNCT
fuelectenerg-1427	891	30	30	30	NUM
fuelectenerg-1427	891	31	)	)	PUNCT
fuelectenerg-1427	891	32	can	can	AUX
fuelectenerg-1427	891	33	be	be	AUX
fuelectenerg-1427	891	34	transformed	transform	VERB
fuelectenerg-1427	891	35	to	to	ADP
fuelectenerg-1427	891	36	:	:	PUNCT
fuelectenerg-1427	891	37	f	f	PROPN
fuelectenerg-1427	891	38	=(	=(	PROPN
fuelectenerg-1427	891	39	x1	x1	PROPN
fuelectenerg-1427	891	40	)	)	PUNCT
fuelectenerg-1427	891	41	2(x′2	2(x′2	NOUN
fuelectenerg-1427	891	42	)	)	PUNCT
fuelectenerg-1427	891	43	2	2	NUM
fuelectenerg-1427	892	1	+	+	CCONJ
fuelectenerg-1427	892	2	2(x1	2(x1	NUM
fuelectenerg-1427	892	3	)	)	PUNCT
fuelectenerg-1427	892	4	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	892	5	)	)	PUNCT
fuelectenerg-1427	892	6	2	2	NUM
fuelectenerg-1427	893	1	+	+	CCONJ
fuelectenerg-1427	893	2	x′2	x′2	X
fuelectenerg-1427	894	1	+	+	ADJ
fuelectenerg-1427	894	2	(	(	PUNCT
fuelectenerg-1427	894	3	x1	x1	ADJ
fuelectenerg-1427	894	4	)	)	PUNCT
fuelectenerg-1427	894	5	2	2	NUM
fuelectenerg-1427	894	6	(	(	PUNCT
fuelectenerg-1427	894	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	894	8	(	(	PUNCT
fuelectenerg-1427	894	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	894	10	)	)	PUNCT
fuelectenerg-1427	894	11	2(x2	2(x2	NUM
fuelectenerg-1427	894	12	)	)	PUNCT
fuelectenerg-1427	894	13	2	2	NUM
fuelectenerg-1427	895	1	+	+	NOUN
fuelectenerg-1427	895	2	(	(	PUNCT
fuelectenerg-1427	895	3	x′1	x′1	NOUN
fuelectenerg-1427	895	4	)	)	PUNCT
fuelectenerg-1427	895	5	2	2	NUM
fuelectenerg-1427	896	1	+	+	NOUN
fuelectenerg-1427	896	2	(	(	PUNCT
fuelectenerg-1427	896	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	896	4	)	)	PUNCT
fuelectenerg-1427	896	5	2	2	NUM
fuelectenerg-1427	897	1	+	+	CCONJ
fuelectenerg-1427	897	2	2x′1	2x′1	NUM
fuelectenerg-1427	897	3	+2(x′1	+2(x′1	ADJ
fuelectenerg-1427	897	4	)	)	PUNCT
fuelectenerg-1427	897	5	2(x′2	2(x′2	NOUN
fuelectenerg-1427	897	6	)	)	PUNCT
fuelectenerg-1427	897	7	2	2	NUM
fuelectenerg-1427	898	1	+	+	ADJ
fuelectenerg-1427	898	2	(	(	PUNCT
fuelectenerg-1427	898	3	x′1	x′1	NOUN
fuelectenerg-1427	898	4	)	)	PUNCT
fuelectenerg-1427	898	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	898	6	(	(	PUNCT
fuelectenerg-1427	898	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	898	8	′	′	NUM
fuelectenerg-1427	898	9	2	2	NUM
fuelectenerg-1427	898	10	)	)	PUNCT
fuelectenerg-1427	898	11	2	2	NUM
fuelectenerg-1427	898	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	898	13	+	+	PROPN
fuelectenerg-1427	898	14	(	(	PUNCT
fuelectenerg-1427	898	15	x′1	x′1	NOUN
fuelectenerg-1427	898	16	)	)	PUNCT
fuelectenerg-1427	898	17	2	2	NUM
fuelectenerg-1427	898	18	·	·	PUNCT
fuelectenerg-1427	898	19	2x2	2x2	NUM
fuelectenerg-1427	898	20	+	+	CCONJ
fuelectenerg-1427	898	21	2(x′1	2(x′1	NUM
fuelectenerg-1427	898	22	)	)	PUNCT
fuelectenerg-1427	898	23	2x2	2x2	NUM
fuelectenerg-1427	899	1	+	+	CCONJ
fuelectenerg-1427	899	2	2	2	NUM
fuelectenerg-1427	899	3	(	(	PUNCT
fuelectenerg-1427	899	4	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	899	5	)	)	PUNCT
fuelectenerg-1427	899	6	2	2	NUM
fuelectenerg-1427	900	1	+	+	SYM
fuelectenerg-1427	900	2	2x1	2x1	NUM
fuelectenerg-1427	900	3	+2	+2	NOUN
fuelectenerg-1427	900	4	(	(	PUNCT
fuelectenerg-1427	900	5	2x1	2x1	NUM
fuelectenerg-1427	900	6	)	)	PUNCT
fuelectenerg-1427	900	7	(	(	PUNCT
fuelectenerg-1427	900	8	2x2	2x2	NUM
fuelectenerg-1427	900	9	)	)	PUNCT
fuelectenerg-1427	900	10	.	.	PUNCT
fuelectenerg-1427	901	1	(	(	PUNCT
fuelectenerg-1427	901	2	31	31	NUM
fuelectenerg-1427	901	3	)	)	PUNCT
fuelectenerg-1427	901	4	let	let	VERB
fuelectenerg-1427	901	5	us	we	PRON
fuelectenerg-1427	901	6	define	define	VERB
fuelectenerg-1427	901	7	,	,	PUNCT
fuelectenerg-1427	901	8	as	as	ADP
fuelectenerg-1427	901	9	one	one	NUM
fuelectenerg-1427	901	10	of	of	ADP
fuelectenerg-1427	901	11	possible	possible	ADJ
fuelectenerg-1427	901	12	definitions	definition	NOUN
fuelectenerg-1427	901	13	,	,	PUNCT
fuelectenerg-1427	901	14	the	the	DET
fuelectenerg-1427	901	15	cost	cost	NOUN
fuelectenerg-1427	901	16	of	of	ADP
fuelectenerg-1427	901	17	the	the	DET
fuelectenerg-1427	901	18	flattened	flatten	VERB
fuelectenerg-1427	901	19	form	form	NOUN
fuelectenerg-1427	901	20	(	(	PUNCT
fuelectenerg-1427	901	21	expression	expression	NOUN
fuelectenerg-1427	901	22	)	)	PUNCT
fuelectenerg-1427	901	23	to	to	PART
fuelectenerg-1427	901	24	be	be	AUX
fuelectenerg-1427	901	25	:	:	PUNCT
fuelectenerg-1427	901	26	cost	cost	NOUN
fuelectenerg-1427	901	27	=	=	SYM
fuelectenerg-1427	901	28	#	#	NOUN
fuelectenerg-1427	901	29	cubes	cube	NOUN
fuelectenerg-1427	901	30	(	(	PUNCT
fuelectenerg-1427	901	31	32	32	NUM
fuelectenerg-1427	901	32	)	)	PUNCT
fuelectenerg-1427	901	33	then	then	ADV
fuelectenerg-1427	901	34	,	,	PUNCT
fuelectenerg-1427	901	35	we	we	PRON
fuelectenerg-1427	901	36	observe	observe	VERB
fuelectenerg-1427	901	37	that	that	SCONJ
fuelectenerg-1427	901	38	equation	equation	NOUN
fuelectenerg-1427	901	39	(	(	PUNCT
fuelectenerg-1427	901	40	29	29	NUM
fuelectenerg-1427	901	41	)	)	PUNCT
fuelectenerg-1427	901	42	has	have	VERB
fuelectenerg-1427	901	43	the	the	DET
fuelectenerg-1427	901	44	cost	cost	NOUN
fuelectenerg-1427	901	45	of	of	ADP
fuelectenerg-1427	901	46	seven	seven	NUM
fuelectenerg-1427	901	47	,	,	PUNCT
fuelectenerg-1427	901	48	while	while	SCONJ
fuelectenerg-1427	901	49	equation	equation	NOUN
fuelectenerg-1427	901	50	(	(	PUNCT
fuelectenerg-1427	901	51	31	31	NUM
fuelectenerg-1427	901	52	)	)	PUNCT
fuelectenerg-1427	901	53	has	have	VERB
fuelectenerg-1427	901	54	the	the	DET
fuelectenerg-1427	901	55	cost	cost	NOUN
fuelectenerg-1427	901	56	of	of	ADP
fuelectenerg-1427	901	57	19	19	NUM
fuelectenerg-1427	901	58	.	.	PUNCT
fuelectenerg-1427	902	1	thus	thus	ADV
fuelectenerg-1427	902	2	,	,	PUNCT
fuelectenerg-1427	902	3	the	the	DET
fuelectenerg-1427	902	4	inverse	inverse	NOUN
fuelectenerg-1427	902	5	transformations	transformation	NOUN
fuelectenerg-1427	902	6	applied	apply	VERB
fuelectenerg-1427	902	7	to	to	ADP
fuelectenerg-1427	902	8	equation	equation	NOUN
fuelectenerg-1427	902	9	(	(	PUNCT
fuelectenerg-1427	902	10	31	31	NUM
fuelectenerg-1427	902	11	)	)	PUNCT
fuelectenerg-1427	902	12	would	would	AUX
fuelectenerg-1427	902	13	lead	lead	VERB
fuelectenerg-1427	902	14	to	to	ADP
fuelectenerg-1427	902	15	equation	equation	NOUN
fuelectenerg-1427	902	16	(	(	PUNCT
fuelectenerg-1427	902	17	29	29	NUM
fuelectenerg-1427	902	18	)	)	PUNCT
fuelectenerg-1427	902	19	and	and	CCONJ
fuelectenerg-1427	902	20	a	a	DET
fuelectenerg-1427	902	21	reduction	reduction	NOUN
fuelectenerg-1427	902	22	of	of	ADP
fuelectenerg-1427	902	23	cost	cost	NOUN
fuelectenerg-1427	902	24	from	from	ADP
fuelectenerg-1427	902	25	19	19	NUM
fuelectenerg-1427	902	26	to	to	PART
fuelectenerg-1427	902	27	seven	seven	NUM
fuelectenerg-1427	902	28	.	.	PUNCT
fuelectenerg-1427	903	1	using	use	VERB
fuelectenerg-1427	903	2	the	the	DET
fuelectenerg-1427	903	3	same	same	ADJ
fuelectenerg-1427	903	4	approach	approach	NOUN
fuelectenerg-1427	903	5	,	,	PUNCT
fuelectenerg-1427	903	6	we	we	PRON
fuelectenerg-1427	903	7	can	can	AUX
fuelectenerg-1427	903	8	generate	generate	VERB
fuelectenerg-1427	903	9	a	a	DET
fuelectenerg-1427	903	10	subset	subset	NOUN
fuelectenerg-1427	903	11	of	of	ADP
fuelectenerg-1427	903	12	possible	possible	ADJ
fuelectenerg-1427	903	13	gfsop	gfsop	NOUN
fuelectenerg-1427	903	14	expressions	expression	NOUN
fuelectenerg-1427	903	15	(	(	PUNCT
fuelectenerg-1427	903	16	flattened	flatten	VERB
fuelectenerg-1427	903	17	forms	form	NOUN
fuelectenerg-1427	903	18	)	)	PUNCT
fuelectenerg-1427	903	19	.	.	PUNCT
fuelectenerg-1427	904	1	note	note	VERB
fuelectenerg-1427	904	2	that	that	SCONJ
fuelectenerg-1427	904	3	all	all	PRON
fuelectenerg-1427	904	4	of	of	ADP
fuelectenerg-1427	904	5	these	these	DET
fuelectenerg-1427	904	6	gfsop	gfsop	NOUN
fuelectenerg-1427	904	7	expressions	expression	NOUN
fuelectenerg-1427	904	8	are	be	AUX
fuelectenerg-1427	904	9	equivalent	equivalent	ADJ
fuelectenerg-1427	904	10	since	since	SCONJ
fuelectenerg-1427	904	11	they	they	PRON
fuelectenerg-1427	904	12	produce	produce	VERB
fuelectenerg-1427	904	13	the	the	DET
fuelectenerg-1427	904	14	same	same	ADJ
fuelectenerg-1427	904	15	function	function	NOUN
fuelectenerg-1427	904	16	in	in	ADP
fuelectenerg-1427	904	17	different	different	ADJ
fuelectenerg-1427	904	18	forms	form	NOUN
fuelectenerg-1427	904	19	.	.	PUNCT
fuelectenerg-1427	905	1	yet	yet	ADV
fuelectenerg-1427	905	2	,	,	PUNCT
fuelectenerg-1427	905	3	as	as	SCONJ
fuelectenerg-1427	905	4	can	can	AUX
fuelectenerg-1427	905	5	be	be	AUX
fuelectenerg-1427	905	6	observed	observe	VERB
fuelectenerg-1427	905	7	from	from	ADP
fuelectenerg-1427	905	8	equation	equation	NOUN
fuelectenerg-1427	905	9	(	(	PUNCT
fuelectenerg-1427	905	10	31	31	NUM
fuelectenerg-1427	905	11	)	)	PUNCT
fuelectenerg-1427	905	12	,	,	PUNCT
fuelectenerg-1427	905	13	by	by	ADP
fuelectenerg-1427	905	14	further	further	ADJ
fuelectenerg-1427	905	15	transformations	transformation	NOUN
fuelectenerg-1427	905	16	of	of	ADP
fuelectenerg-1427	905	17	equation	equation	NOUN
fuelectenerg-1427	905	18	(	(	PUNCT
fuelectenerg-1427	905	19	29	29	NUM
fuelectenerg-1427	905	20	)	)	PUNCT
fuelectenerg-1427	905	21	from	from	ADP
fuelectenerg-1427	905	22	one	one	NUM
fuelectenerg-1427	905	23	form	form	NOUN
fuelectenerg-1427	905	24	to	to	ADP
fuelectenerg-1427	905	25	another	another	PRON
fuelectenerg-1427	905	26	,	,	PUNCT
fuelectenerg-1427	905	27	some	some	DET
fuelectenerg-1427	905	28	transformations	transformation	NOUN
fuelectenerg-1427	905	29	produce	produce	VERB
fuelectenerg-1427	905	30	flattened	flatten	VERB
fuelectenerg-1427	905	31	forms	form	NOUN
fuelectenerg-1427	905	32	with	with	ADP
fuelectenerg-1427	905	33	a	a	DET
fuelectenerg-1427	905	34	smaller	small	ADJ
fuelectenerg-1427	905	35	number	number	NOUN
fuelectenerg-1427	905	36	of	of	ADP
fuelectenerg-1427	905	37	cubes	cube	NOUN
fuelectenerg-1427	905	38	than	than	ADP
fuelectenerg-1427	905	39	the	the	DET
fuelectenerg-1427	905	40	others	other	NOUN
fuelectenerg-1427	905	41	.	.	PUNCT
fuelectenerg-1427	906	1	from	from	ADP
fuelectenerg-1427	906	2	this	this	DET
fuelectenerg-1427	906	3	observation	observation	NOUN
fuelectenerg-1427	906	4	rises	rise	VERB
fuelectenerg-1427	906	5	the	the	DET
fuelectenerg-1427	906	6	idea	idea	NOUN
fuelectenerg-1427	906	7	of	of	ADP
fuelectenerg-1427	906	8	a	a	DET
fuelectenerg-1427	906	9	possible	possible	ADJ
fuelectenerg-1427	906	10	application	application	NOUN
fuelectenerg-1427	906	11	of	of	ADP
fuelectenerg-1427	906	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	906	13	computing	computing	NOUN
fuelectenerg-1427	906	14	using	use	VERB
fuelectenerg-1427	906	15	the	the	DET
fuelectenerg-1427	906	16	s	s	PROPN
fuelectenerg-1427	906	17	/	/	SYM
fuelectenerg-1427	906	18	d	d	NOUN
fuelectenerg-1427	906	19	trees	tree	NOUN
fuelectenerg-1427	906	20	and	and	CCONJ
fuelectenerg-1427	906	21	related	related	ADJ
fuelectenerg-1427	906	22	transformations	transformation	NOUN
fuelectenerg-1427	906	23	to	to	PART
fuelectenerg-1427	906	24	produce	produce	VERB
fuelectenerg-1427	906	25	the	the	DET
fuelectenerg-1427	906	26	corresponding	corresponding	ADJ
fuelectenerg-1427	906	27	minimum	minimum	ADJ
fuelectenerg-1427	906	28	gfsops	gfsop	NOUN
fuelectenerg-1427	906	29	.	.	PUNCT
fuelectenerg-1427	907	1	analogous	analogous	ADJ
fuelectenerg-1427	907	2	to	to	ADP
fuelectenerg-1427	907	3	the	the	DET
fuelectenerg-1427	907	4	binary	binary	ADJ
fuelectenerg-1427	907	5	case	case	NOUN
fuelectenerg-1427	907	6	in	in	ADP
fuelectenerg-1427	907	7	equation	equation	NOUN
fuelectenerg-1427	907	8	(	(	PUNCT
fuelectenerg-1427	907	9	27	27	NUM
fuelectenerg-1427	907	10	)	)	PUNCT
fuelectenerg-1427	907	11	,	,	PUNCT
fuelectenerg-1427	907	12	the	the	DET
fuelectenerg-1427	907	13	ternary	ternary	ADJ
fuelectenerg-1427	907	14	gifs	gif	NOUN
fuelectenerg-1427	907	15	can	can	AUX
fuelectenerg-1427	907	16	be	be	AUX
fuelectenerg-1427	907	17	defined	define	VERB
fuelectenerg-1427	907	18	as	as	ADP
fuelectenerg-1427	907	19	the	the	DET
fuelectenerg-1427	907	20	union	union	NOUN
fuelectenerg-1427	907	21	of	of	ADP
fuelectenerg-1427	907	22	ternary	ternary	PROPN
fuelectenerg-1427	907	23	ifs	ifs	PROPN
fuelectenerg-1427	907	24	.	.	PUNCT
fuelectenerg-1427	908	1	definition	definition	NOUN
fuelectenerg-1427	908	2	3	3	NUM
fuelectenerg-1427	908	3	.	.	PUNCT
fuelectenerg-1427	909	1	the	the	DET
fuelectenerg-1427	909	2	family	family	NOUN
fuelectenerg-1427	909	3	of	of	ADP
fuelectenerg-1427	909	4	forms	form	NOUN
fuelectenerg-1427	909	5	,	,	PUNCT
fuelectenerg-1427	909	6	which	which	PRON
fuelectenerg-1427	909	7	is	be	AUX
fuelectenerg-1427	909	8	created	create	VERB
fuelectenerg-1427	909	9	as	as	ADP
fuelectenerg-1427	909	10	a	a	DET
fuelectenerg-1427	909	11	union	union	NOUN
fuelectenerg-1427	909	12	of	of	ADP
fuelectenerg-1427	909	13	sets	set	NOUN
fuelectenerg-1427	909	14	of	of	ADP
fuelectenerg-1427	909	15	tifs	tif	NOUN
fuelectenerg-1427	909	16	for	for	ADP
fuelectenerg-1427	909	17	all	all	DET
fuelectenerg-1427	909	18	variable	variable	ADJ
fuelectenerg-1427	909	19	orders	order	NOUN
fuelectenerg-1427	909	20	,	,	PUNCT
fuelectenerg-1427	909	21	is	be	AUX
fuelectenerg-1427	909	22	called	call	VERB
fuelectenerg-1427	909	23	ternary	ternary	ADJ
fuelectenerg-1427	909	24	generalized	generalized	ADJ
fuelectenerg-1427	909	25	inclusive	inclusive	ADJ
fuelectenerg-1427	909	26	forms	form	NOUN
fuelectenerg-1427	909	27	(	(	PUNCT
fuelectenerg-1427	909	28	tgifs	tgif	NOUN
fuelectenerg-1427	909	29	)	)	PUNCT
fuelectenerg-1427	909	30	.	.	PUNCT
fuelectenerg-1427	910	1	109	109	NUM
fuelectenerg-1427	910	2	an	an	DET
fuelectenerg-1427	910	3	extended	extend	VERB
fuelectenerg-1427	910	4	green	green	ADJ
fuelectenerg-1427	910	5	sasao	sasao	PROPN
fuelectenerg-1427	910	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	910	7	of	of	ADP
fuelectenerg-1427	910	8	canonical	canonical	ADJ
fuelectenerg-1427	910	9	ternary	ternary	ADJ
fuelectenerg-1427	910	10	galois	galois	NOUN
fuelectenerg-1427	910	11	forms	form	NOUN
fuelectenerg-1427	910	12	...	...	PUNCT
fuelectenerg-1427	910	13	form	form	NOUN
fuelectenerg-1427	910	14	which	which	PRON
fuelectenerg-1427	910	15	is	be	AUX
fuelectenerg-1427	910	16	an	an	DET
fuelectenerg-1427	910	17	expansion	expansion	NOUN
fuelectenerg-1427	910	18	over	over	ADP
fuelectenerg-1427	910	19	certain	certain	ADJ
fuelectenerg-1427	910	20	transform	transform	NOUN
fuelectenerg-1427	910	21	matrix	matrix	NOUN
fuelectenerg-1427	910	22	(	(	PUNCT
fuelectenerg-1427	910	23	i.e.	i.e.	X
fuelectenerg-1427	910	24	,	,	PUNCT
fuelectenerg-1427	910	25	certain	certain	ADJ
fuelectenerg-1427	910	26	tif	tif	PROPN
fuelectenerg-1427	910	27	)	)	PUNCT
fuelectenerg-1427	910	28	and	and	CCONJ
fuelectenerg-1427	910	29	then	then	ADV
fuelectenerg-1427	910	30	transform	transform	VERB
fuelectenerg-1427	910	31	systematically	systematically	ADV
fuelectenerg-1427	910	32	from	from	ADP
fuelectenerg-1427	910	33	one	one	NUM
fuelectenerg-1427	910	34	form	form	NOUN
fuelectenerg-1427	910	35	to	to	ADP
fuelectenerg-1427	910	36	another	another	DET
fuelectenerg-1427	910	37	form	form	NOUN
fuelectenerg-1427	910	38	without	without	ADP
fuelectenerg-1427	910	39	the	the	DET
fuelectenerg-1427	910	40	need	need	NOUN
fuelectenerg-1427	910	41	to	to	PART
fuelectenerg-1427	910	42	create	create	VERB
fuelectenerg-1427	910	43	all	all	PRON
fuelectenerg-1427	910	44	transform	transform	VERB
fuelectenerg-1427	910	45	matrices	matrix	NOUN
fuelectenerg-1427	910	46	from	from	ADP
fuelectenerg-1427	910	47	the	the	DET
fuelectenerg-1427	910	48	corresponding	correspond	VERB
fuelectenerg-1427	910	49	s	s	PROPN
fuelectenerg-1427	910	50	/	/	SYM
fuelectenerg-1427	910	51	d	d	NOUN
fuelectenerg-1427	910	52	trees	tree	NOUN
fuelectenerg-1427	910	53	.	.	PUNCT
fuelectenerg-1427	911	1	this	this	DET
fuelectenerg-1427	911	2	general	general	ADJ
fuelectenerg-1427	911	3	approach	approach	NOUN
fuelectenerg-1427	911	4	can	can	AUX
fuelectenerg-1427	911	5	lead	lead	VERB
fuelectenerg-1427	911	6	to	to	ADP
fuelectenerg-1427	911	7	several	several	ADJ
fuelectenerg-1427	911	8	algorithms	algorithm	NOUN
fuelectenerg-1427	911	9	of	of	ADP
fuelectenerg-1427	911	10	various	various	ADJ
fuelectenerg-1427	911	11	complexities	complexity	NOUN
fuelectenerg-1427	911	12	that	that	PRON
fuelectenerg-1427	911	13	generalize	generalize	VERB
fuelectenerg-1427	911	14	the	the	DET
fuelectenerg-1427	911	15	existing	exist	VERB
fuelectenerg-1427	911	16	binary	binary	ADJ
fuelectenerg-1427	911	17	algorithms	algorithm	NOUN
fuelectenerg-1427	911	18	to	to	PART
fuelectenerg-1427	911	19	obtain	obtain	VERB
fuelectenerg-1427	911	20	the	the	DET
fuelectenerg-1427	911	21	corresponding	corresponding	ADJ
fuelectenerg-1427	911	22	forms	form	NOUN
fuelectenerg-1427	911	23	such	such	ADJ
fuelectenerg-1427	911	24	as	as	ADP
fuelectenerg-1427	911	25	fprm	fprm	PROPN
fuelectenerg-1427	911	26	,	,	PUNCT
fuelectenerg-1427	911	27	grm	grm	NOUN
fuelectenerg-1427	911	28	and	and	CCONJ
fuelectenerg-1427	911	29	if	if	SCONJ
fuelectenerg-1427	911	30	forms	form	NOUN
fuelectenerg-1427	911	31	.	.	PUNCT
fuelectenerg-1427	911	32	example	example	NOUN
fuelectenerg-1427	912	1	3	3	NUM
fuelectenerg-1427	912	2	.	.	PUNCT
fuelectenerg-1427	912	3	using	use	VERB
fuelectenerg-1427	912	4	the	the	DET
fuelectenerg-1427	912	5	result	result	NOUN
fuelectenerg-1427	912	6	of	of	ADP
fuelectenerg-1427	912	7	example	example	NOUN
fuelectenerg-1427	912	8	2	2	NUM
fuelectenerg-1427	912	9	for	for	ADP
fuelectenerg-1427	912	10	the	the	DET
fuelectenerg-1427	912	11	expansion	expansion	NOUN
fuelectenerg-1427	912	12	of	of	ADP
fuelectenerg-1427	912	13	f	f	PROPN
fuelectenerg-1427	912	14	(	(	PUNCT
fuelectenerg-1427	912	15	x1,x2	x1,x2	PROPN
fuelectenerg-1427	912	16	)	)	PUNCT
fuelectenerg-1427	912	17	in	in	ADP
fuelectenerg-1427	912	18	terms	term	NOUN
fuelectenerg-1427	912	19	of	of	ADP
fuelectenerg-1427	912	20	the	the	DET
fuelectenerg-1427	912	21	ternary	ternary	ADJ
fuelectenerg-1427	912	22	shannon	shannon	NOUN
fuelectenerg-1427	912	23	expansion	expansion	NOUN
fuelectenerg-1427	912	24	(	(	PUNCT
fuelectenerg-1427	912	25	that	that	PRON
fuelectenerg-1427	912	26	resembles	resemble	VERB
fuelectenerg-1427	912	27	the	the	DET
fuelectenerg-1427	912	28	s	s	NOUN
fuelectenerg-1427	912	29	/	/	SYM
fuelectenerg-1427	912	30	d	d	NOUN
fuelectenerg-1427	912	31	tree	tree	NOUN
fuelectenerg-1427	912	32	for	for	ADP
fuelectenerg-1427	912	33	shannon	shannon	PROPN
fuelectenerg-1427	912	34	nodes	node	NOUN
fuelectenerg-1427	912	35	in	in	ADP
fuelectenerg-1427	912	36	both	both	DET
fuelectenerg-1427	912	37	levels	level	NOUN
fuelectenerg-1427	912	38	):	):	PUNCT
fuelectenerg-1427	912	39	f	f	X
fuelectenerg-1427	912	40	=	=	PUNCT
fuelectenerg-1427	912	41	0x1	0x1	NOUN
fuelectenerg-1427	912	42	1x2	1x2	NUM
fuelectenerg-1427	913	1	+	+	CCONJ
fuelectenerg-1427	913	2	2	2	NUM
fuelectenerg-1427	913	3	·	·	PUNCT
fuelectenerg-1427	913	4	0x1	0x1	NOUN
fuelectenerg-1427	913	5	2x2	2x2	NUM
fuelectenerg-1427	914	1	+	+	CCONJ
fuelectenerg-1427	914	2	2	2	NUM
fuelectenerg-1427	914	3	·	·	SYM
fuelectenerg-1427	914	4	1x1	1x1	NUM
fuelectenerg-1427	914	5	0x2	0x2	NOUN
fuelectenerg-1427	914	6	+2	+2	PROPN
fuelectenerg-1427	914	7	·	·	PUNCT
fuelectenerg-1427	914	8	1x1	1x1	NUM
fuelectenerg-1427	914	9	1x2	1x2	NUM
fuelectenerg-1427	914	10	+2	+2	PRON
fuelectenerg-1427	914	11	·	·	PUNCT
fuelectenerg-1427	915	1	1x1	1x1	NUM
fuelectenerg-1427	915	2	2x2	2x2	NUM
fuelectenerg-1427	915	3	+	+	SYM
fuelectenerg-1427	915	4	2x1	2x1	NUM
fuelectenerg-1427	915	5	0x2	0x2	NOUN
fuelectenerg-1427	915	6	+2	+2	PROPN
fuelectenerg-1427	915	7	·	·	PUNCT
fuelectenerg-1427	915	8	2x1	2x1	NUM
fuelectenerg-1427	915	9	2x2	2x2	NUM
fuelectenerg-1427	915	10	,	,	PUNCT
fuelectenerg-1427	915	11	(	(	PUNCT
fuelectenerg-1427	915	12	29	29	NUM
fuelectenerg-1427	915	13	)	)	PUNCT
fuelectenerg-1427	915	14	we	we	PRON
fuelectenerg-1427	915	15	can	can	AUX
fuelectenerg-1427	915	16	substitute	substitute	VERB
fuelectenerg-1427	915	17	any	any	PRON
fuelectenerg-1427	915	18	of	of	ADP
fuelectenerg-1427	915	19	equations	equation	NOUN
fuelectenerg-1427	915	20	(	(	PUNCT
fuelectenerg-1427	915	21	7	7	NUM
fuelectenerg-1427	915	22	)	)	PUNCT
fuelectenerg-1427	915	23	(	(	PUNCT
fuelectenerg-1427	915	24	15	15	NUM
fuelectenerg-1427	915	25	)	)	PUNCT
fuelectenerg-1427	915	26	,	,	PUNCT
fuelectenerg-1427	915	27	or	or	CCONJ
fuelectenerg-1427	915	28	a	a	DET
fuelectenerg-1427	915	29	mix	mix	NOUN
fuelectenerg-1427	915	30	of	of	ADP
fuelectenerg-1427	915	31	these	these	DET
fuelectenerg-1427	915	32	equations	equation	NOUN
fuelectenerg-1427	915	33	,	,	PUNCT
fuelectenerg-1427	915	34	to	to	PART
fuelectenerg-1427	915	35	transform	transform	VERB
fuelectenerg-1427	915	36	one	one	NUM
fuelectenerg-1427	915	37	flattened	flatten	VERB
fuelectenerg-1427	915	38	form	form	NOUN
fuelectenerg-1427	915	39	to	to	ADP
fuelectenerg-1427	915	40	another	another	PRON
fuelectenerg-1427	915	41	.	.	PUNCT
fuelectenerg-1427	916	1	for	for	ADP
fuelectenerg-1427	916	2	example	example	NOUN
fuelectenerg-1427	916	3	,	,	PUNCT
fuelectenerg-1427	916	4	if	if	SCONJ
fuelectenerg-1427	916	5	we	we	PRON
fuelectenerg-1427	916	6	substitute	substitute	VERB
fuelectenerg-1427	916	7	equations	equation	NOUN
fuelectenerg-1427	916	8	(	(	PUNCT
fuelectenerg-1427	916	9	7	7	NUM
fuelectenerg-1427	916	10	)	)	PUNCT
fuelectenerg-1427	916	11	and	and	CCONJ
fuelectenerg-1427	916	12	(	(	PUNCT
fuelectenerg-1427	916	13	11	11	NUM
fuelectenerg-1427	916	14	)	)	PUNCT
fuelectenerg-1427	916	15	,	,	PUNCT
fuelectenerg-1427	916	16	we	we	PRON
fuelectenerg-1427	916	17	obtain	obtain	VERB
fuelectenerg-1427	916	18	:	:	PUNCT
fuelectenerg-1427	916	19	f	f	PROPN
fuelectenerg-1427	916	20	=(	=(	NOUN
fuelectenerg-1427	916	21	2(x1	2(x1	NUM
fuelectenerg-1427	916	22	)	)	PUNCT
fuelectenerg-1427	916	23	2	2	NUM
fuelectenerg-1427	916	24	+	+	SYM
fuelectenerg-1427	917	1	1)(2(x′2	1)(2(x′2	NUM
fuelectenerg-1427	917	2	)	)	PUNCT
fuelectenerg-1427	917	3	2	2	NUM
fuelectenerg-1427	917	4	+	+	SYM
fuelectenerg-1427	917	5	x′2)+2(2(x1	x′2)+2(2(x1	NUM
fuelectenerg-1427	917	6	)	)	PUNCT
fuelectenerg-1427	917	7	2	2	NUM
fuelectenerg-1427	917	8	+1)2x2	+1)2x2	SYM
fuelectenerg-1427	917	9	+2(2(x′1	+2(2(x′1	PROPN
fuelectenerg-1427	917	10	)	)	PUNCT
fuelectenerg-1427	917	11	2	2	NUM
fuelectenerg-1427	917	12	+	+	CCONJ
fuelectenerg-1427	917	13	x′1)(2(x2	x′1)(2(x2	NOUN
fuelectenerg-1427	917	14	)	)	PUNCT
fuelectenerg-1427	917	15	2	2	NUM
fuelectenerg-1427	917	16	+1	+1	NOUN
fuelectenerg-1427	917	17	)	)	PUNCT
fuelectenerg-1427	917	18	+	+	CCONJ
fuelectenerg-1427	917	19	2(2(x′1	2(2(x′1	NUM
fuelectenerg-1427	917	20	)	)	PUNCT
fuelectenerg-1427	917	21	2	2	NUM
fuelectenerg-1427	918	1	+	+	CCONJ
fuelectenerg-1427	918	2	x′1)(2(x	x′1)(2(x	PROPN
fuelectenerg-1427	918	3	′	′	NOUN
fuelectenerg-1427	918	4	2	2	NUM
fuelectenerg-1427	918	5	)	)	PUNCT
fuelectenerg-1427	918	6	2	2	NUM
fuelectenerg-1427	918	7	+	+	CCONJ
fuelectenerg-1427	918	8	x′2)+2(2(x′1	x′2)+2(2(x′1	NOUN
fuelectenerg-1427	918	9	)	)	PUNCT
fuelectenerg-1427	918	10	2	2	NUM
fuelectenerg-1427	918	11	+	+	NUM
fuelectenerg-1427	918	12	x′1	x′1	X
fuelectenerg-1427	918	13	)	)	PUNCT
fuelectenerg-1427	918	14	·	·	PUNCT
fuelectenerg-1427	919	1	2x2	2x2	NUM
fuelectenerg-1427	919	2	+	+	NUM
fuelectenerg-1427	919	3	2x1(2(x2	2x1(2(x2	NUM
fuelectenerg-1427	919	4	)	)	PUNCT
fuelectenerg-1427	919	5	2	2	NUM
fuelectenerg-1427	919	6	+1	+1	NOUN
fuelectenerg-1427	919	7	)	)	PUNCT
fuelectenerg-1427	919	8	+	+	CCONJ
fuelectenerg-1427	919	9	2	2	NUM
fuelectenerg-1427	919	10	·	·	SYM
fuelectenerg-1427	919	11	2x1	2x1	NUM
fuelectenerg-1427	919	12	2x2	2x2	NUM
fuelectenerg-1427	919	13	,	,	PUNCT
fuelectenerg-1427	919	14	(	(	PUNCT
fuelectenerg-1427	919	15	30	30	NUM
fuelectenerg-1427	919	16	)	)	PUNCT
fuelectenerg-1427	919	17	by	by	ADP
fuelectenerg-1427	919	18	utilizing	utilize	VERB
fuelectenerg-1427	919	19	gf	gf	NOUN
fuelectenerg-1427	919	20	addition	addition	NOUN
fuelectenerg-1427	919	21	and	and	CCONJ
fuelectenerg-1427	919	22	multiplication	multiplication	NOUN
fuelectenerg-1427	919	23	operators	operator	NOUN
fuelectenerg-1427	919	24	from	from	ADP
fuelectenerg-1427	919	25	figure	figure	NOUN
fuelectenerg-1427	919	26	1	1	NUM
fuelectenerg-1427	919	27	,	,	PUNCT
fuelectenerg-1427	919	28	equation	equation	NOUN
fuelectenerg-1427	919	29	(	(	PUNCT
fuelectenerg-1427	919	30	30	30	NUM
fuelectenerg-1427	919	31	)	)	PUNCT
fuelectenerg-1427	919	32	can	can	AUX
fuelectenerg-1427	919	33	be	be	AUX
fuelectenerg-1427	919	34	transformed	transform	VERB
fuelectenerg-1427	919	35	to	to	ADP
fuelectenerg-1427	919	36	:	:	PUNCT
fuelectenerg-1427	919	37	f	f	PROPN
fuelectenerg-1427	919	38	=(	=(	PROPN
fuelectenerg-1427	919	39	x1	x1	PROPN
fuelectenerg-1427	919	40	)	)	PUNCT
fuelectenerg-1427	919	41	2(x′2	2(x′2	NOUN
fuelectenerg-1427	919	42	)	)	PUNCT
fuelectenerg-1427	919	43	2	2	NUM
fuelectenerg-1427	920	1	+	+	CCONJ
fuelectenerg-1427	920	2	2(x1	2(x1	NUM
fuelectenerg-1427	920	3	)	)	PUNCT
fuelectenerg-1427	920	4	2(x′2)+2(x′2	2(x′2)+2(x′2	NUM
fuelectenerg-1427	920	5	)	)	PUNCT
fuelectenerg-1427	920	6	2	2	NUM
fuelectenerg-1427	921	1	+	+	CCONJ
fuelectenerg-1427	921	2	x′2	x′2	X
fuelectenerg-1427	922	1	+	+	ADJ
fuelectenerg-1427	922	2	(	(	PUNCT
fuelectenerg-1427	922	3	x1	x1	ADJ
fuelectenerg-1427	922	4	)	)	PUNCT
fuelectenerg-1427	922	5	2	2	NUM
fuelectenerg-1427	922	6	(	(	PUNCT
fuelectenerg-1427	922	7	2x2)+2	2x2)+2	NUM
fuelectenerg-1427	922	8	(	(	PUNCT
fuelectenerg-1427	922	9	2x2)+2(x′1	2x2)+2(x′1	NOUN
fuelectenerg-1427	922	10	)	)	PUNCT
fuelectenerg-1427	922	11	2(x2	2(x2	NUM
fuelectenerg-1427	922	12	)	)	PUNCT
fuelectenerg-1427	922	13	2	2	NUM
fuelectenerg-1427	923	1	+	+	NOUN
fuelectenerg-1427	923	2	(	(	PUNCT
fuelectenerg-1427	923	3	x′1	x′1	NOUN
fuelectenerg-1427	923	4	)	)	PUNCT
fuelectenerg-1427	923	5	2	2	NUM
fuelectenerg-1427	924	1	+	+	NOUN
fuelectenerg-1427	924	2	(	(	PUNCT
fuelectenerg-1427	924	3	x′1)(x2	x′1)(x2	NOUN
fuelectenerg-1427	924	4	)	)	PUNCT
fuelectenerg-1427	924	5	2	2	NUM
fuelectenerg-1427	925	1	+	+	CCONJ
fuelectenerg-1427	925	2	2x′1	2x′1	NUM
fuelectenerg-1427	925	3	+2(x′1	+2(x′1	ADJ
fuelectenerg-1427	925	4	)	)	PUNCT
fuelectenerg-1427	925	5	2(x′2	2(x′2	NOUN
fuelectenerg-1427	925	6	)	)	PUNCT
fuelectenerg-1427	925	7	2	2	NUM
fuelectenerg-1427	926	1	+	+	ADJ
fuelectenerg-1427	926	2	(	(	PUNCT
fuelectenerg-1427	926	3	x′1	x′1	NOUN
fuelectenerg-1427	926	4	)	)	PUNCT
fuelectenerg-1427	926	5	2(x′2)+	2(x′2)+	NUM
fuelectenerg-1427	926	6	(	(	PUNCT
fuelectenerg-1427	926	7	x′1)(x	x′1)(x	PROPN
fuelectenerg-1427	926	8	′	′	NUM
fuelectenerg-1427	926	9	2	2	NUM
fuelectenerg-1427	926	10	)	)	PUNCT
fuelectenerg-1427	926	11	2	2	NUM
fuelectenerg-1427	926	12	+2x′1x′2	+2x′1x′2	PROPN
fuelectenerg-1427	926	13	+	+	PROPN
fuelectenerg-1427	926	14	(	(	PUNCT
fuelectenerg-1427	926	15	x′1	x′1	NOUN
fuelectenerg-1427	926	16	)	)	PUNCT
fuelectenerg-1427	926	17	2	2	NUM
fuelectenerg-1427	926	18	·	·	PUNCT
fuelectenerg-1427	926	19	2x2	2x2	NUM
fuelectenerg-1427	926	20	+	+	CCONJ
fuelectenerg-1427	926	21	2(x′1	2(x′1	NUM
fuelectenerg-1427	926	22	)	)	PUNCT
fuelectenerg-1427	926	23	2x2	2x2	NUM
fuelectenerg-1427	927	1	+	+	CCONJ
fuelectenerg-1427	927	2	2	2	NUM
fuelectenerg-1427	927	3	(	(	PUNCT
fuelectenerg-1427	927	4	2x1)(x2	2x1)(x2	NUM
fuelectenerg-1427	927	5	)	)	PUNCT
fuelectenerg-1427	927	6	2	2	NUM
fuelectenerg-1427	928	1	+	+	SYM
fuelectenerg-1427	928	2	2x1	2x1	NUM
fuelectenerg-1427	928	3	+2	+2	NOUN
fuelectenerg-1427	928	4	(	(	PUNCT
fuelectenerg-1427	928	5	2x1	2x1	NUM
fuelectenerg-1427	928	6	)	)	PUNCT
fuelectenerg-1427	928	7	(	(	PUNCT
fuelectenerg-1427	928	8	2x2	2x2	NUM
fuelectenerg-1427	928	9	)	)	PUNCT
fuelectenerg-1427	928	10	.	.	PUNCT
fuelectenerg-1427	929	1	(	(	PUNCT
fuelectenerg-1427	929	2	31	31	NUM
fuelectenerg-1427	929	3	)	)	PUNCT
fuelectenerg-1427	929	4	let	let	VERB
fuelectenerg-1427	929	5	us	we	PRON
fuelectenerg-1427	929	6	define	define	VERB
fuelectenerg-1427	929	7	,	,	PUNCT
fuelectenerg-1427	929	8	as	as	ADP
fuelectenerg-1427	929	9	one	one	NUM
fuelectenerg-1427	929	10	of	of	ADP
fuelectenerg-1427	929	11	possible	possible	ADJ
fuelectenerg-1427	929	12	definitions	definition	NOUN
fuelectenerg-1427	929	13	,	,	PUNCT
fuelectenerg-1427	929	14	the	the	DET
fuelectenerg-1427	929	15	cost	cost	NOUN
fuelectenerg-1427	929	16	of	of	ADP
fuelectenerg-1427	929	17	the	the	DET
fuelectenerg-1427	929	18	flattened	flatten	VERB
fuelectenerg-1427	929	19	form	form	NOUN
fuelectenerg-1427	929	20	(	(	PUNCT
fuelectenerg-1427	929	21	expression	expression	NOUN
fuelectenerg-1427	929	22	)	)	PUNCT
fuelectenerg-1427	929	23	to	to	PART
fuelectenerg-1427	929	24	be	be	AUX
fuelectenerg-1427	929	25	:	:	PUNCT
fuelectenerg-1427	929	26	cost	cost	NOUN
fuelectenerg-1427	929	27	=	=	SYM
fuelectenerg-1427	929	28	#	#	NOUN
fuelectenerg-1427	929	29	cubes	cube	NOUN
fuelectenerg-1427	929	30	(	(	PUNCT
fuelectenerg-1427	929	31	32	32	NUM
fuelectenerg-1427	929	32	)	)	PUNCT
fuelectenerg-1427	929	33	then	then	ADV
fuelectenerg-1427	929	34	,	,	PUNCT
fuelectenerg-1427	929	35	we	we	PRON
fuelectenerg-1427	929	36	observe	observe	VERB
fuelectenerg-1427	929	37	that	that	SCONJ
fuelectenerg-1427	929	38	equation	equation	NOUN
fuelectenerg-1427	929	39	(	(	PUNCT
fuelectenerg-1427	929	40	29	29	NUM
fuelectenerg-1427	929	41	)	)	PUNCT
fuelectenerg-1427	929	42	has	have	VERB
fuelectenerg-1427	929	43	the	the	DET
fuelectenerg-1427	929	44	cost	cost	NOUN
fuelectenerg-1427	929	45	of	of	ADP
fuelectenerg-1427	929	46	seven	seven	NUM
fuelectenerg-1427	929	47	,	,	PUNCT
fuelectenerg-1427	929	48	while	while	SCONJ
fuelectenerg-1427	929	49	equation	equation	NOUN
fuelectenerg-1427	929	50	(	(	PUNCT
fuelectenerg-1427	929	51	31	31	NUM
fuelectenerg-1427	929	52	)	)	PUNCT
fuelectenerg-1427	929	53	has	have	VERB
fuelectenerg-1427	929	54	the	the	DET
fuelectenerg-1427	929	55	cost	cost	NOUN
fuelectenerg-1427	929	56	of	of	ADP
fuelectenerg-1427	929	57	19	19	NUM
fuelectenerg-1427	929	58	.	.	PUNCT
fuelectenerg-1427	930	1	thus	thus	ADV
fuelectenerg-1427	930	2	,	,	PUNCT
fuelectenerg-1427	930	3	the	the	DET
fuelectenerg-1427	930	4	inverse	inverse	NOUN
fuelectenerg-1427	930	5	transformations	transformation	NOUN
fuelectenerg-1427	930	6	applied	apply	VERB
fuelectenerg-1427	930	7	to	to	ADP
fuelectenerg-1427	930	8	equation	equation	NOUN
fuelectenerg-1427	930	9	(	(	PUNCT
fuelectenerg-1427	930	10	31	31	NUM
fuelectenerg-1427	930	11	)	)	PUNCT
fuelectenerg-1427	930	12	would	would	AUX
fuelectenerg-1427	930	13	lead	lead	VERB
fuelectenerg-1427	930	14	to	to	ADP
fuelectenerg-1427	930	15	equation	equation	NOUN
fuelectenerg-1427	930	16	(	(	PUNCT
fuelectenerg-1427	930	17	29	29	NUM
fuelectenerg-1427	930	18	)	)	PUNCT
fuelectenerg-1427	930	19	and	and	CCONJ
fuelectenerg-1427	930	20	a	a	DET
fuelectenerg-1427	930	21	reduction	reduction	NOUN
fuelectenerg-1427	930	22	of	of	ADP
fuelectenerg-1427	930	23	cost	cost	NOUN
fuelectenerg-1427	930	24	from	from	ADP
fuelectenerg-1427	930	25	19	19	NUM
fuelectenerg-1427	930	26	to	to	PART
fuelectenerg-1427	930	27	seven	seven	NUM
fuelectenerg-1427	930	28	.	.	PUNCT
fuelectenerg-1427	931	1	using	use	VERB
fuelectenerg-1427	931	2	the	the	DET
fuelectenerg-1427	931	3	same	same	ADJ
fuelectenerg-1427	931	4	approach	approach	NOUN
fuelectenerg-1427	931	5	,	,	PUNCT
fuelectenerg-1427	931	6	we	we	PRON
fuelectenerg-1427	931	7	can	can	AUX
fuelectenerg-1427	931	8	generate	generate	VERB
fuelectenerg-1427	931	9	a	a	DET
fuelectenerg-1427	931	10	subset	subset	NOUN
fuelectenerg-1427	931	11	of	of	ADP
fuelectenerg-1427	931	12	possible	possible	ADJ
fuelectenerg-1427	931	13	gfsop	gfsop	NOUN
fuelectenerg-1427	931	14	expressions	expression	NOUN
fuelectenerg-1427	931	15	(	(	PUNCT
fuelectenerg-1427	931	16	flattened	flatten	VERB
fuelectenerg-1427	931	17	forms	form	NOUN
fuelectenerg-1427	931	18	)	)	PUNCT
fuelectenerg-1427	931	19	.	.	PUNCT
fuelectenerg-1427	932	1	note	note	VERB
fuelectenerg-1427	932	2	that	that	SCONJ
fuelectenerg-1427	932	3	all	all	PRON
fuelectenerg-1427	932	4	of	of	ADP
fuelectenerg-1427	932	5	these	these	DET
fuelectenerg-1427	932	6	gfsop	gfsop	NOUN
fuelectenerg-1427	932	7	expressions	expression	NOUN
fuelectenerg-1427	932	8	are	be	AUX
fuelectenerg-1427	932	9	equivalent	equivalent	ADJ
fuelectenerg-1427	932	10	since	since	SCONJ
fuelectenerg-1427	932	11	they	they	PRON
fuelectenerg-1427	932	12	produce	produce	VERB
fuelectenerg-1427	932	13	the	the	DET
fuelectenerg-1427	932	14	same	same	ADJ
fuelectenerg-1427	932	15	function	function	NOUN
fuelectenerg-1427	932	16	in	in	ADP
fuelectenerg-1427	932	17	different	different	ADJ
fuelectenerg-1427	932	18	forms	form	NOUN
fuelectenerg-1427	932	19	.	.	PUNCT
fuelectenerg-1427	933	1	yet	yet	ADV
fuelectenerg-1427	933	2	,	,	PUNCT
fuelectenerg-1427	933	3	as	as	SCONJ
fuelectenerg-1427	933	4	can	can	AUX
fuelectenerg-1427	933	5	be	be	AUX
fuelectenerg-1427	933	6	observed	observe	VERB
fuelectenerg-1427	933	7	from	from	ADP
fuelectenerg-1427	933	8	equation	equation	NOUN
fuelectenerg-1427	933	9	(	(	PUNCT
fuelectenerg-1427	933	10	31	31	NUM
fuelectenerg-1427	933	11	)	)	PUNCT
fuelectenerg-1427	933	12	,	,	PUNCT
fuelectenerg-1427	933	13	by	by	ADP
fuelectenerg-1427	933	14	further	further	ADJ
fuelectenerg-1427	933	15	transformations	transformation	NOUN
fuelectenerg-1427	933	16	of	of	ADP
fuelectenerg-1427	933	17	equation	equation	NOUN
fuelectenerg-1427	933	18	(	(	PUNCT
fuelectenerg-1427	933	19	29	29	NUM
fuelectenerg-1427	933	20	)	)	PUNCT
fuelectenerg-1427	933	21	from	from	ADP
fuelectenerg-1427	933	22	one	one	NUM
fuelectenerg-1427	933	23	form	form	NOUN
fuelectenerg-1427	933	24	to	to	ADP
fuelectenerg-1427	933	25	another	another	PRON
fuelectenerg-1427	933	26	,	,	PUNCT
fuelectenerg-1427	933	27	some	some	DET
fuelectenerg-1427	933	28	transformations	transformation	NOUN
fuelectenerg-1427	933	29	produce	produce	VERB
fuelectenerg-1427	933	30	flattened	flatten	VERB
fuelectenerg-1427	933	31	forms	form	NOUN
fuelectenerg-1427	933	32	with	with	ADP
fuelectenerg-1427	933	33	a	a	DET
fuelectenerg-1427	933	34	smaller	small	ADJ
fuelectenerg-1427	933	35	number	number	NOUN
fuelectenerg-1427	933	36	of	of	ADP
fuelectenerg-1427	933	37	cubes	cube	NOUN
fuelectenerg-1427	933	38	than	than	ADP
fuelectenerg-1427	933	39	the	the	DET
fuelectenerg-1427	933	40	others	other	NOUN
fuelectenerg-1427	933	41	.	.	PUNCT
fuelectenerg-1427	934	1	from	from	ADP
fuelectenerg-1427	934	2	this	this	DET
fuelectenerg-1427	934	3	observation	observation	NOUN
fuelectenerg-1427	934	4	rises	rise	VERB
fuelectenerg-1427	934	5	the	the	DET
fuelectenerg-1427	934	6	idea	idea	NOUN
fuelectenerg-1427	934	7	of	of	ADP
fuelectenerg-1427	934	8	a	a	DET
fuelectenerg-1427	934	9	possible	possible	ADJ
fuelectenerg-1427	934	10	application	application	NOUN
fuelectenerg-1427	934	11	of	of	ADP
fuelectenerg-1427	934	12	evolutionary	evolutionary	ADJ
fuelectenerg-1427	934	13	computing	computing	NOUN
fuelectenerg-1427	934	14	using	use	VERB
fuelectenerg-1427	934	15	the	the	DET
fuelectenerg-1427	934	16	s	s	PROPN
fuelectenerg-1427	934	17	/	/	SYM
fuelectenerg-1427	934	18	d	d	NOUN
fuelectenerg-1427	934	19	trees	tree	NOUN
fuelectenerg-1427	934	20	and	and	CCONJ
fuelectenerg-1427	934	21	related	related	ADJ
fuelectenerg-1427	934	22	transformations	transformation	NOUN
fuelectenerg-1427	934	23	to	to	PART
fuelectenerg-1427	934	24	produce	produce	VERB
fuelectenerg-1427	934	25	the	the	DET
fuelectenerg-1427	934	26	corresponding	corresponding	ADJ
fuelectenerg-1427	934	27	minimum	minimum	ADJ
fuelectenerg-1427	934	28	gfsops	gfsop	NOUN
fuelectenerg-1427	934	29	.	.	PUNCT
fuelectenerg-1427	935	1	analogous	analogous	ADJ
fuelectenerg-1427	935	2	to	to	ADP
fuelectenerg-1427	935	3	the	the	DET
fuelectenerg-1427	935	4	binary	binary	ADJ
fuelectenerg-1427	935	5	case	case	NOUN
fuelectenerg-1427	935	6	in	in	ADP
fuelectenerg-1427	935	7	equation	equation	NOUN
fuelectenerg-1427	935	8	(	(	PUNCT
fuelectenerg-1427	935	9	27	27	NUM
fuelectenerg-1427	935	10	)	)	PUNCT
fuelectenerg-1427	935	11	,	,	PUNCT
fuelectenerg-1427	935	12	the	the	DET
fuelectenerg-1427	935	13	ternary	ternary	ADJ
fuelectenerg-1427	935	14	gifs	gif	NOUN
fuelectenerg-1427	935	15	can	can	AUX
fuelectenerg-1427	935	16	be	be	AUX
fuelectenerg-1427	935	17	defined	define	VERB
fuelectenerg-1427	935	18	as	as	ADP
fuelectenerg-1427	935	19	the	the	DET
fuelectenerg-1427	935	20	union	union	NOUN
fuelectenerg-1427	935	21	of	of	ADP
fuelectenerg-1427	935	22	ternary	ternary	PROPN
fuelectenerg-1427	935	23	ifs	ifs	PROPN
fuelectenerg-1427	935	24	.	.	PUNCT
fuelectenerg-1427	936	1	definition	definition	NOUN
fuelectenerg-1427	936	2	3	3	NUM
fuelectenerg-1427	936	3	.	.	PUNCT
fuelectenerg-1427	937	1	the	the	DET
fuelectenerg-1427	937	2	family	family	NOUN
fuelectenerg-1427	937	3	of	of	ADP
fuelectenerg-1427	937	4	forms	form	NOUN
fuelectenerg-1427	937	5	,	,	PUNCT
fuelectenerg-1427	937	6	which	which	PRON
fuelectenerg-1427	937	7	is	be	AUX
fuelectenerg-1427	937	8	created	create	VERB
fuelectenerg-1427	937	9	as	as	ADP
fuelectenerg-1427	937	10	a	a	DET
fuelectenerg-1427	937	11	union	union	NOUN
fuelectenerg-1427	937	12	of	of	ADP
fuelectenerg-1427	937	13	sets	set	NOUN
fuelectenerg-1427	937	14	of	of	ADP
fuelectenerg-1427	937	15	tifs	tif	NOUN
fuelectenerg-1427	937	16	for	for	ADP
fuelectenerg-1427	937	17	all	all	DET
fuelectenerg-1427	937	18	variable	variable	ADJ
fuelectenerg-1427	937	19	orders	order	NOUN
fuelectenerg-1427	937	20	,	,	PUNCT
fuelectenerg-1427	937	21	is	be	AUX
fuelectenerg-1427	937	22	called	call	VERB
fuelectenerg-1427	937	23	ternary	ternary	ADJ
fuelectenerg-1427	937	24	generalized	generalized	ADJ
fuelectenerg-1427	937	25	inclusive	inclusive	ADJ
fuelectenerg-1427	937	26	forms	form	NOUN
fuelectenerg-1427	937	27	(	(	PUNCT
fuelectenerg-1427	937	28	tgifs	tgif	NOUN
fuelectenerg-1427	937	29	)	)	PUNCT
fuelectenerg-1427	937	30	.	.	PUNCT
fuelectenerg-1427	938	1	109	109	NUM
fuelectenerg-1427	938	2	58	58	NUM
fuelectenerg-1427	938	3	a.	a.	NOUN
fuelectenerg-1427	938	4	n.	n.	PROPN
fuelectenerg-1427	938	5	al	al	PROPN
fuelectenerg-1427	938	6	-	-	PUNCT
fuelectenerg-1427	938	7	rabadi	rabadi	VERB
fuelectenerg-1427	938	8	an	an	DET
fuelectenerg-1427	938	9	extended	extended	ADJ
fuelectenerg-1427	938	10	green	green	ADJ
fuelectenerg-1427	938	11	sasao	sasao	PROPN
fuelectenerg-1427	938	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	938	13	of	of	ADP
fuelectenerg-1427	938	14	canonical	canonical	ADJ
fuelectenerg-1427	938	15	ternary	ternary	ADJ
fuelectenerg-1427	938	16	galois	galois	NOUN
fuelectenerg-1427	938	17	forms	form	NOUN
fuelectenerg-1427	938	18	and	and	CCONJ
fuelectenerg-1427	938	19	universal	universal	ADJ
fuelectenerg-1427	938	20	logic	logic	NOUN
fuelectenerg-1427	938	21	modules	module	VERB
fuelectenerg-1427	938	22	59	59	NUM
fuelectenerg-1427	938	23	an	an	DET
fuelectenerg-1427	938	24	extended	extended	ADJ
fuelectenerg-1427	938	25	green	green	ADJ
fuelectenerg-1427	938	26	sasao	sasao	PROPN
fuelectenerg-1427	938	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	938	28	of	of	ADP
fuelectenerg-1427	938	29	canonical	canonical	ADJ
fuelectenerg-1427	938	30	ternary	ternary	ADJ
fuelectenerg-1427	938	31	galois	galois	NOUN
fuelectenerg-1427	938	32	forms	form	NOUN
fuelectenerg-1427	938	33	...	...	PUNCT
fuelectenerg-1427	939	1	s	s	PART
fuelectenerg-1427	939	2	s	s	X
fuelectenerg-1427	939	3	s	s	X
fuelectenerg-1427	939	4	s	s	NOUN
fuelectenerg-1427	939	5	0	0	NUM
fuelectenerg-1427	939	6	b	b	SYM
fuelectenerg-1427	939	7	1	1	NUM
fuelectenerg-1427	939	8	b	b	SYM
fuelectenerg-1427	939	9	2	2	NUM
fuelectenerg-1427	939	10	b	b	NOUN
fuelectenerg-1427	939	11	s	s	X
fuelectenerg-1427	939	12	s	s	NOUN
fuelectenerg-1427	939	13	d	d	X
fuelectenerg-1427	939	14	d	d	X
fuelectenerg-1427	939	15	s	s	X
fuelectenerg-1427	939	16	s	s	X
fuelectenerg-1427	939	17	s	s	X
fuelectenerg-1427	939	18	d	d	NOUN
fuelectenerg-1427	939	19	1	1	NUM
fuelectenerg-1427	939	20	(	(	PUNCT
fuelectenerg-1427	939	21	a	a	PRON
fuelectenerg-1427	939	22	,	,	PUNCT
fuelectenerg-1427	939	23	)	)	PUNCT
fuelectenerg-1427	939	24	2	2	NUM
fuelectenerg-1427	939	25	a	a	PRON
fuelectenerg-1427	939	26	,	,	PUNCT
fuelectenerg-1427	939	27	s	s	NOUN
fuelectenerg-1427	939	28	d	d	X
fuelectenerg-1427	939	29	d	d	PROPN
fuelectenerg-1427	939	30	d	d	PROPN
fuelectenerg-1427	939	31	1	1	NUM
fuelectenerg-1427	939	32	(	(	PUNCT
fuelectenerg-1427	939	33	a	a	PRON
fuelectenerg-1427	939	34	,	,	PUNCT
fuelectenerg-1427	939	35	)	)	PUNCT
fuelectenerg-1427	939	36	2	2	NUM
fuelectenerg-1427	939	37	a	a	PRON
fuelectenerg-1427	939	38	,	,	PUNCT
fuelectenerg-1427	939	39	s	s	X
fuelectenerg-1427	939	40	s	s	NOUN
fuelectenerg-1427	939	41	s	s	NOUN
fuelectenerg-1427	939	42	0	0	NUM
fuelectenerg-1427	939	43	b	b	NOUN
fuelectenerg-1427	939	44	0	0	NUM
fuelectenerg-1427	939	45	b	b	SYM
fuelectenerg-1427	939	46	1	1	NUM
fuelectenerg-1427	939	47	b	b	SYM
fuelectenerg-1427	939	48	1	1	NUM
fuelectenerg-1427	939	49	b	b	SYM
fuelectenerg-1427	939	50	2	2	NUM
fuelectenerg-1427	939	51	b	b	SYM
fuelectenerg-1427	939	52	2	2	NUM
fuelectenerg-1427	939	53	b	b	NOUN
fuelectenerg-1427	939	54	d	d	SYM
fuelectenerg-1427	939	55	1	1	NUM
fuelectenerg-1427	939	56	1	1	NUM
fuelectenerg-1427	939	57	1	1	NUM
fuelectenerg-1427	939	58	1	1	NUM
fuelectenerg-1427	939	59	1	1	NUM
fuelectenerg-1427	939	60	1	1	NUM
fuelectenerg-1427	939	61	1	1	NUM
fuelectenerg-1427	939	62	1	1	NUM
fuelectenerg-1427	939	63	1	1	NUM
fuelectenerg-1427	939	64	1	1	NUM
fuelectenerg-1427	939	65	11	11	NUM
fuelectenerg-1427	939	66	1	1	NUM
fuelectenerg-1427	939	67	1	1	NUM
fuelectenerg-1427	939	68	1	1	NUM
fuelectenerg-1427	939	69	1	1	NUM
fuelectenerg-1427	939	70	1	1	NUM
fuelectenerg-1427	939	71	1	1	NUM
fuelectenerg-1427	939	72	1	1	NUM
fuelectenerg-1427	939	73	1	1	NUM
fuelectenerg-1427	939	74	1	1	NUM
fuelectenerg-1427	939	75	1	1	NUM
fuelectenerg-1427	939	76	1(b	1(b	NUM
fuelectenerg-1427	939	77	,	,	PUNCT
fuelectenerg-1427	939	78	)	)	PUNCT
fuelectenerg-1427	939	79	2	2	NUM
fuelectenerg-1427	939	80	(	(	PUNCT
fuelectenerg-1427	939	81	b	b	NOUN
fuelectenerg-1427	939	82	,	,	PUNCT
fuelectenerg-1427	939	83	)	)	PUNCT
fuelectenerg-1427	939	84	2	2	NUM
fuelectenerg-1427	939	85	(	(	PUNCT
fuelectenerg-1427	939	86	b	b	NOUN
fuelectenerg-1427	939	87	,	,	PUNCT
fuelectenerg-1427	939	88	)	)	PUNCT
fuelectenerg-1427	939	89	2	2	NUM
fuelectenerg-1427	939	90	(	(	PUNCT
fuelectenerg-1427	939	91	b	b	NOUN
fuelectenerg-1427	939	92	,	,	PUNCT
fuelectenerg-1427	939	93	)	)	PUNCT
fuelectenerg-1427	939	94	2	2	NUM
fuelectenerg-1427	939	95	(	(	PUNCT
fuelectenerg-1427	939	96	b	b	NOUN
fuelectenerg-1427	939	97	,	,	PUNCT
fuelectenerg-1427	939	98	)	)	PUNCT
fuelectenerg-1427	939	99	2	2	NUM
fuelectenerg-1427	939	100	(	(	PUNCT
fuelectenerg-1427	939	101	b	b	NOUN
fuelectenerg-1427	939	102	,	,	PUNCT
fuelectenerg-1427	939	103	)	)	PUNCT
fuelectenerg-1427	939	104	2	2	NUM
fuelectenerg-1427	939	105	(	(	PUNCT
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fuelectenerg-1427	942	19	a	a	DET
fuelectenerg-1427	942	20	1	1	NUM
fuelectenerg-1427	942	21	a	a	DET
fuelectenerg-1427	942	22	1	1	NUM
fuelectenerg-1427	942	23	a	a	DET
fuelectenerg-1427	942	24	1	1	NUM
fuelectenerg-1427	942	25	b	b	SYM
fuelectenerg-1427	942	26	1	1	NUM
fuelectenerg-1427	942	27	b	b	SYM
fuelectenerg-1427	942	28	1	1	NUM
fuelectenerg-1427	942	29	a	a	DET
fuelectenerg-1427	942	30	1	1	NUM
fuelectenerg-1427	942	31	a	a	DET
fuelectenerg-1427	942	32	1	1	NUM
fuelectenerg-1427	942	33	a	a	DET
fuelectenerg-1427	942	34	1	1	NUM
fuelectenerg-1427	942	35	a	a	DET
fuelectenerg-1427	942	36	1	1	NUM
fuelectenerg-1427	942	37	a	a	DET
fuelectenerg-1427	942	38	1	1	NUM
fuelectenerg-1427	942	39	a	a	DET
fuelectenerg-1427	942	40	2	2	NUM
fuelectenerg-1427	942	41	a	a	DET
fuelectenerg-1427	942	42	2	2	NUM
fuelectenerg-1427	942	43	a	a	DET
fuelectenerg-1427	942	44	2	2	NUM
fuelectenerg-1427	942	45	b	b	SYM
fuelectenerg-1427	942	46	2	2	NUM
fuelectenerg-1427	942	47	b	b	SYM
fuelectenerg-1427	942	48	2	2	NUM
fuelectenerg-1427	942	49	a	a	DET
fuelectenerg-1427	942	50	2	2	NUM
fuelectenerg-1427	942	51	a	a	DET
fuelectenerg-1427	942	52	2	2	NUM
fuelectenerg-1427	942	53	a	a	DET
fuelectenerg-1427	942	54	2	2	NUM
fuelectenerg-1427	942	55	a	a	DET
fuelectenerg-1427	942	56	2	2	NUM
fuelectenerg-1427	942	57	a	a	DET
fuelectenerg-1427	942	58	2	2	NUM
fuelectenerg-1427	942	59	a	a	DET
fuelectenerg-1427	942	60	(	(	PUNCT
fuelectenerg-1427	942	61	a	a	PRON
fuelectenerg-1427	942	62	)	)	PUNCT
fuelectenerg-1427	942	63	figure	figure	NOUN
fuelectenerg-1427	942	64	5	5	NUM
fuelectenerg-1427	942	65	:	:	PUNCT
fuelectenerg-1427	942	66	ternary	ternary	ADJ
fuelectenerg-1427	942	67	if	if	SCONJ
fuelectenerg-1427	942	68	(	(	PUNCT
fuelectenerg-1427	942	69	tif	tif	PROPN
fuelectenerg-1427	942	70	)	)	PUNCT
fuelectenerg-1427	942	71	s	s	PROPN
fuelectenerg-1427	942	72	/	/	SYM
fuelectenerg-1427	942	73	d	d	NOUN
fuelectenerg-1427	942	74	trees	tree	NOUN
fuelectenerg-1427	942	75	and	and	CCONJ
fuelectenerg-1427	942	76	their	their	PRON
fuelectenerg-1427	942	77	numbers	number	NOUN
fuelectenerg-1427	942	78	:	:	PUNCT
fuelectenerg-1427	942	79	(	(	PUNCT
fuelectenerg-1427	942	80	a	a	X
fuelectenerg-1427	942	81	)	)	PUNCT
fuelectenerg-1427	942	82	2	2	NUM
fuelectenerg-1427	942	83	-	-	PUNCT
fuelectenerg-1427	942	84	variable	variable	ADJ
fuelectenerg-1427	942	85	order	order	NOUN
fuelectenerg-1427	942	86	{	{	PUNCT
fuelectenerg-1427	942	87	a	a	DET
fuelectenerg-1427	942	88	,	,	PUNCT
fuelectenerg-1427	942	89	b	b	NOUN
fuelectenerg-1427	942	90	}	}	PUNCT
fuelectenerg-1427	942	91	and	and	CCONJ
fuelectenerg-1427	942	92	(	(	PUNCT
fuelectenerg-1427	942	93	b	b	X
fuelectenerg-1427	942	94	)	)	PUNCT
fuelectenerg-1427	942	95	2variable	2variable	NUM
fuelectenerg-1427	942	96	order	order	NOUN
fuelectenerg-1427	942	97	{	{	PUNCT
fuelectenerg-1427	942	98	b	b	NOUN
fuelectenerg-1427	942	99	,	,	PUNCT
fuelectenerg-1427	942	100	a	a	PRON
fuelectenerg-1427	942	101	}	}	PUNCT
fuelectenerg-1427	942	102	.	.	PUNCT
fuelectenerg-1427	943	1	variables	variable	NOUN
fuelectenerg-1427	943	2	{	{	PUNCT
fuelectenerg-1427	943	3	a	a	DET
fuelectenerg-1427	943	4	,	,	PUNCT
fuelectenerg-1427	943	5	b	b	NOUN
fuelectenerg-1427	943	6	}	}	PUNCT
fuelectenerg-1427	943	7	are	be	AUX
fuelectenerg-1427	943	8	defined	define	VERB
fuelectenerg-1427	943	9	as	as	ADP
fuelectenerg-1427	943	10	in	in	ADP
fuelectenerg-1427	943	11	eq	eq	ADP
fuelectenerg-1427	943	12	.	.	PUNCT
fuelectenerg-1427	944	1	(	(	PUNCT
fuelectenerg-1427	944	2	28	28	NUM
fuelectenerg-1427	944	3	)	)	PUNCT
fuelectenerg-1427	944	4	for	for	ADP
fuelectenerg-1427	944	5	generalized	generalized	ADJ
fuelectenerg-1427	944	6	davio	davio	NOUN
fuelectenerg-1427	944	7	(	(	PUNCT
fuelectenerg-1427	944	8	d	d	NOUN
fuelectenerg-1427	944	9	)	)	PUNCT
fuelectenerg-1427	944	10	where	where	SCONJ
fuelectenerg-1427	944	11	in	in	ADP
fuelectenerg-1427	944	12	this	this	DET
fuelectenerg-1427	944	13	figure	figure	NOUN
fuelectenerg-1427	944	14	(	(	PUNCT
fuelectenerg-1427	944	15	a,≡	a,≡	NOUN
fuelectenerg-1427	944	16	a	a	X
fuelectenerg-1427	944	17	)	)	PUNCT
fuelectenerg-1427	944	18	and	and	CCONJ
fuelectenerg-1427	944	19	(	(	PUNCT
fuelectenerg-1427	944	20	b,≡	b,≡	X
fuelectenerg-1427	944	21	b	b	X
fuelectenerg-1427	944	22	)	)	PUNCT
fuelectenerg-1427	944	23	.	.	PUNCT
fuelectenerg-1427	945	1	theorem	theorem	NOUN
fuelectenerg-1427	945	2	2	2	NUM
fuelectenerg-1427	945	3	.	.	PUNCT
fuelectenerg-1427	946	1	the	the	DET
fuelectenerg-1427	946	2	total	total	ADJ
fuelectenerg-1427	946	3	number	number	NOUN
fuelectenerg-1427	946	4	of	of	ADP
fuelectenerg-1427	946	5	the	the	DET
fuelectenerg-1427	946	6	ternary	ternary	ADJ
fuelectenerg-1427	946	7	ifs	ifs	PROPN
fuelectenerg-1427	946	8	,	,	PUNCT
fuelectenerg-1427	946	9	for	for	ADP
fuelectenerg-1427	946	10	two	two	NUM
fuelectenerg-1427	946	11	variables	variable	NOUN
fuelectenerg-1427	946	12	and	and	CCONJ
fuelectenerg-1427	946	13	for	for	ADP
fuelectenerg-1427	946	14	orders	order	NOUN
fuelectenerg-1427	946	15	{	{	PUNCT
fuelectenerg-1427	946	16	a	a	DET
fuelectenerg-1427	946	17	,	,	PUNCT
fuelectenerg-1427	946	18	b	b	NOUN
fuelectenerg-1427	946	19	}	}	PUNCT
fuelectenerg-1427	946	20	and	and	CCONJ
fuelectenerg-1427	946	21	{	{	PUNCT
fuelectenerg-1427	946	22	b	b	NOUN
fuelectenerg-1427	946	23	,	,	PUNCT
fuelectenerg-1427	946	24	a	a	PRON
fuelectenerg-1427	946	25	}	}	PUNCT
fuelectenerg-1427	946	26	,	,	PUNCT
fuelectenerg-1427	946	27	and	and	CCONJ
fuelectenerg-1427	946	28	the	the	DET
fuelectenerg-1427	946	29	total	total	ADJ
fuelectenerg-1427	946	30	number	number	NOUN
fuelectenerg-1427	946	31	of	of	ADP
fuelectenerg-1427	946	32	ternary	ternary	ADJ
fuelectenerg-1427	946	33	generalized	generalize	VERB
fuelectenerg-1427	946	34	ifs	ifs	PROPN
fuelectenerg-1427	946	35	,	,	PUNCT
fuelectenerg-1427	946	36	for	for	ADP
fuelectenerg-1427	946	37	two	two	NUM
fuelectenerg-1427	946	38	variables	variable	NOUN
fuelectenerg-1427	946	39	,	,	PUNCT
fuelectenerg-1427	946	40	are	be	AUX
fuelectenerg-1427	946	41	respectively	respectively	ADV
fuelectenerg-1427	946	42	:	:	PUNCT
fuelectenerg-1427	946	43	#	#	SYM
fuelectenerg-1427	946	44	tifa	tifa	NOUN
fuelectenerg-1427	946	45	,	,	PUNCT
fuelectenerg-1427	946	46	b	b	NOUN
fuelectenerg-1427	946	47	=	=	SYM
fuelectenerg-1427	946	48	1	1	NUM
fuelectenerg-1427	946	49	·	·	PUNCT
fuelectenerg-1427	946	50	(	(	PUNCT
fuelectenerg-1427	946	51	3)0	3)0	NUM
fuelectenerg-1427	946	52	+	+	CCONJ
fuelectenerg-1427	946	53	3	3	NUM
fuelectenerg-1427	946	54	·	·	PUNCT
fuelectenerg-1427	946	55	(	(	PUNCT
fuelectenerg-1427	946	56	3)2	3)2	NUM
fuelectenerg-1427	946	57	+	+	SYM
fuelectenerg-1427	946	58	3	3	NUM
fuelectenerg-1427	946	59	·	·	PUNCT
fuelectenerg-1427	946	60	(	(	PUNCT
fuelectenerg-1427	946	61	3)4	3)4	NUM
fuelectenerg-1427	946	62	+	+	NOUN
fuelectenerg-1427	946	63	2	2	NUM
fuelectenerg-1427	946	64	·	·	PUNCT
fuelectenerg-1427	946	65	(	(	PUNCT
fuelectenerg-1427	946	66	3)6	3)6	NUM
fuelectenerg-1427	946	67	+	+	SYM
fuelectenerg-1427	946	68	3	3	NUM
fuelectenerg-1427	946	69	·	·	PUNCT
fuelectenerg-1427	946	70	(	(	PUNCT
fuelectenerg-1427	946	71	3)8	3)8	NUM
fuelectenerg-1427	946	72	+	+	SYM
fuelectenerg-1427	946	73	3	3	NUM
fuelectenerg-1427	946	74	·	·	PUNCT
fuelectenerg-1427	946	75	(	(	PUNCT
fuelectenerg-1427	946	76	3)10	3)10	NUM
fuelectenerg-1427	946	77	+	+	ADJ
fuelectenerg-1427	946	78	1	1	NUM
fuelectenerg-1427	946	79	·	·	PUNCT
fuelectenerg-1427	946	80	(	(	PUNCT
fuelectenerg-1427	946	81	3)12	3)12	NUM
fuelectenerg-1427	946	82	=	=	SYM
fuelectenerg-1427	946	83	730,000	730,000	NUM
fuelectenerg-1427	946	84	,	,	PUNCT
fuelectenerg-1427	946	85	(	(	PUNCT
fuelectenerg-1427	946	86	33	33	NUM
fuelectenerg-1427	946	87	)	)	PUNCT
fuelectenerg-1427	946	88	#	#	SYM
fuelectenerg-1427	946	89	tifb	tifb	NOUN
fuelectenerg-1427	946	90	,	,	PUNCT
fuelectenerg-1427	946	91	a	a	DET
fuelectenerg-1427	946	92	=	=	SYM
fuelectenerg-1427	946	93	1	1	NUM
fuelectenerg-1427	946	94	·	·	PUNCT
fuelectenerg-1427	946	95	(	(	PUNCT
fuelectenerg-1427	946	96	3)0	3)0	NUM
fuelectenerg-1427	946	97	+	+	CCONJ
fuelectenerg-1427	946	98	3	3	NUM
fuelectenerg-1427	946	99	·	·	PUNCT
fuelectenerg-1427	946	100	(	(	PUNCT
fuelectenerg-1427	946	101	3)2	3)2	NUM
fuelectenerg-1427	946	102	+	+	SYM
fuelectenerg-1427	946	103	3	3	NUM
fuelectenerg-1427	946	104	·	·	PUNCT
fuelectenerg-1427	946	105	(	(	PUNCT
fuelectenerg-1427	946	106	3)4	3)4	NUM
fuelectenerg-1427	946	107	+	+	NOUN
fuelectenerg-1427	946	108	2	2	NUM
fuelectenerg-1427	946	109	·	·	PUNCT
fuelectenerg-1427	946	110	(	(	PUNCT
fuelectenerg-1427	946	111	3)6	3)6	NUM
fuelectenerg-1427	946	112	+	+	SYM
fuelectenerg-1427	946	113	3	3	NUM
fuelectenerg-1427	946	114	·	·	PUNCT
fuelectenerg-1427	946	115	(	(	PUNCT
fuelectenerg-1427	946	116	3)8	3)8	NUM
fuelectenerg-1427	946	117	+	+	SYM
fuelectenerg-1427	946	118	3	3	NUM
fuelectenerg-1427	946	119	·	·	PUNCT
fuelectenerg-1427	946	120	(	(	PUNCT
fuelectenerg-1427	946	121	3)10	3)10	NUM
fuelectenerg-1427	946	122	+	+	ADJ
fuelectenerg-1427	946	123	1	1	NUM
fuelectenerg-1427	946	124	·	·	PUNCT
fuelectenerg-1427	946	125	(	(	PUNCT
fuelectenerg-1427	946	126	3)12	3)12	NUM
fuelectenerg-1427	946	127	=	=	SYM
fuelectenerg-1427	946	128	730,000	730,000	NUM
fuelectenerg-1427	946	129	,	,	PUNCT
fuelectenerg-1427	946	130	(	(	PUNCT
fuelectenerg-1427	946	131	34	34	NUM
fuelectenerg-1427	946	132	)	)	PUNCT
fuelectenerg-1427	946	133	#	#	NOUN
fuelectenerg-1427	946	134	tgif	tgif	NOUN
fuelectenerg-1427	946	135	=	=	PUNCT
fuelectenerg-1427	946	136	#	#	NUM
fuelectenerg-1427	946	137	tifa	tifa	NOUN
fuelectenerg-1427	946	138	,	,	PUNCT
fuelectenerg-1427	946	139	b	b	NOUN
fuelectenerg-1427	946	140	+	+	CCONJ
fuelectenerg-1427	946	141	#	#	SYM
fuelectenerg-1427	946	142	tifb	tifb	NOUN
fuelectenerg-1427	946	143	,	,	PUNCT
fuelectenerg-1427	946	144	a−#(tifa	a−#(tifa	PROPN
fuelectenerg-1427	946	145	,	,	PUNCT
fuelectenerg-1427	946	146	b	b	NOUN
fuelectenerg-1427	946	147	∩tifb	∩tifb	NOUN
fuelectenerg-1427	946	148	,	,	PUNCT
fuelectenerg-1427	946	149	a	a	PRON
fuelectenerg-1427	946	150	)	)	PUNCT
fuelectenerg-1427	946	151	=	=	SYM
fuelectenerg-1427	946	152	2	2	NUM
fuelectenerg-1427	946	153	·	·	SYM
fuelectenerg-1427	946	154	#	#	NOUN
fuelectenerg-1427	946	155	tif−#(tifa	tif−#(tifa	NUM
fuelectenerg-1427	946	156	,	,	PUNCT
fuelectenerg-1427	946	157	b	b	NOUN
fuelectenerg-1427	946	158	∩tifb	∩tifb	NOUN
fuelectenerg-1427	946	159	,	,	PUNCT
fuelectenerg-1427	946	160	a	a	PRON
fuelectenerg-1427	946	161	)	)	PUNCT
fuelectenerg-1427	946	162	=	=	SYM
fuelectenerg-1427	946	163	2	2	NUM
fuelectenerg-1427	946	164	·	·	PUNCT
fuelectenerg-1427	946	165	(	(	PUNCT
fuelectenerg-1427	946	166	730,000)−	730,000)−	NUM
fuelectenerg-1427	946	167	(	(	PUNCT
fuelectenerg-1427	946	168	1	1	NUM
fuelectenerg-1427	946	169	·	·	PUNCT
fuelectenerg-1427	946	170	(	(	PUNCT
fuelectenerg-1427	946	171	3)0	3)0	NUM
fuelectenerg-1427	946	172	+	+	PROPN
fuelectenerg-1427	946	173	2	2	NUM
fuelectenerg-1427	946	174	·	·	PUNCT
fuelectenerg-1427	946	175	(	(	PUNCT
fuelectenerg-1427	946	176	3)6	3)6	NUM
fuelectenerg-1427	946	177	+	+	SYM
fuelectenerg-1427	946	178	1	1	NUM
fuelectenerg-1427	946	179	·	·	PUNCT
fuelectenerg-1427	946	180	(	(	PUNCT
fuelectenerg-1427	946	181	3)12	3)12	NUM
fuelectenerg-1427	946	182	)	)	PUNCT
fuelectenerg-1427	946	183	=	=	SYM
fuelectenerg-1427	947	1	927,100	927,100	NUM
fuelectenerg-1427	947	2	.	.	PUNCT
fuelectenerg-1427	948	1	(	(	PUNCT
fuelectenerg-1427	948	2	35	35	NUM
fuelectenerg-1427	948	3	)	)	PUNCT
fuelectenerg-1427	948	4	proof	proof	NOUN
fuelectenerg-1427	948	5	.	.	PUNCT
fuelectenerg-1427	949	1	by	by	ADP
fuelectenerg-1427	949	2	observing	observe	VERB
fuelectenerg-1427	949	3	figure	figure	NOUN
fuelectenerg-1427	949	4	5	5	NUM
fuelectenerg-1427	949	5	,	,	PUNCT
fuelectenerg-1427	949	6	we	we	PRON
fuelectenerg-1427	949	7	note	note	VERB
fuelectenerg-1427	949	8	that	that	SCONJ
fuelectenerg-1427	949	9	the	the	DET
fuelectenerg-1427	949	10	total	total	ADJ
fuelectenerg-1427	949	11	number	number	NOUN
fuelectenerg-1427	949	12	of	of	ADP
fuelectenerg-1427	949	13	tifs	tifs	PROPN
fuelectenerg-1427	949	14	for	for	ADP
fuelectenerg-1427	949	15	orders	order	NOUN
fuelectenerg-1427	949	16	{	{	PUNCT
fuelectenerg-1427	949	17	a	a	DET
fuelectenerg-1427	949	18	,	,	PUNCT
fuelectenerg-1427	949	19	b	b	NOUN
fuelectenerg-1427	949	20	}	}	PUNCT
fuelectenerg-1427	949	21	and	and	CCONJ
fuelectenerg-1427	949	22	{	{	PUNCT
fuelectenerg-1427	949	23	b	b	NOUN
fuelectenerg-1427	949	24	,	,	PUNCT
fuelectenerg-1427	949	25	a	a	PRON
fuelectenerg-1427	949	26	}	}	PUNCT
fuelectenerg-1427	949	27	is	be	AUX
fuelectenerg-1427	949	28	the	the	DET
fuelectenerg-1427	949	29	sum	sum	NOUN
fuelectenerg-1427	949	30	of	of	ADP
fuelectenerg-1427	949	31	the	the	DET
fuelectenerg-1427	949	32	numbers	number	NOUN
fuelectenerg-1427	949	33	on	on	ADP
fuelectenerg-1427	949	34	top	top	NOUN
fuelectenerg-1427	949	35	of	of	ADP
fuelectenerg-1427	949	36	s	s	PROPN
fuelectenerg-1427	949	37	/	/	SYM
fuelectenerg-1427	949	38	d	d	NOUN
fuelectenerg-1427	949	39	trees	tree	NOUN
fuelectenerg-1427	949	40	that	that	PRON
fuelectenerg-1427	949	41	leads	lead	VERB
fuelectenerg-1427	949	42	to	to	ADP
fuelectenerg-1427	949	43	equations	equation	NOUN
fuelectenerg-1427	949	44	(	(	PUNCT
fuelectenerg-1427	949	45	33	33	NUM
fuelectenerg-1427	949	46	)	)	PUNCT
fuelectenerg-1427	949	47	(	(	PUNCT
fuelectenerg-1427	949	48	35	35	NUM
fuelectenerg-1427	949	49	)	)	PUNCT
fuelectenerg-1427	949	50	,	,	PUNCT
fuelectenerg-1427	949	51	respectively	respectively	ADV
fuelectenerg-1427	949	52	.	.	PUNCT
fuelectenerg-1427	950	1	2.2	2.2	NUM
fuelectenerg-1427	950	2	properties	property	NOUN
fuelectenerg-1427	950	3	of	of	ADP
fuelectenerg-1427	950	4	tifs	tifs	PROPN
fuelectenerg-1427	950	5	and	and	CCONJ
fuelectenerg-1427	950	6	tgifs	tgif	VERB
fuelectenerg-1427	950	7	the	the	DET
fuelectenerg-1427	950	8	following	follow	VERB
fuelectenerg-1427	950	9	present	present	ADJ
fuelectenerg-1427	950	10	basic	basic	ADJ
fuelectenerg-1427	950	11	properties	property	NOUN
fuelectenerg-1427	950	12	of	of	ADP
fuelectenerg-1427	950	13	the	the	DET
fuelectenerg-1427	950	14	presented	present	VERB
fuelectenerg-1427	950	15	tifs	tifs	PROPN
fuelectenerg-1427	950	16	and	and	CCONJ
fuelectenerg-1427	950	17	tgifs	tgif	NOUN
fuelectenerg-1427	950	18	.	.	PUNCT
fuelectenerg-1427	950	19	theorem	theorem	NOUN
fuelectenerg-1427	950	20	3	3	NUM
fuelectenerg-1427	950	21	.	.	PUNCT
fuelectenerg-1427	951	1	each	each	DET
fuelectenerg-1427	951	2	ternary	ternary	ADJ
fuelectenerg-1427	951	3	inclusive	inclusive	ADJ
fuelectenerg-1427	951	4	form	form	NOUN
fuelectenerg-1427	951	5	(	(	PUNCT
fuelectenerg-1427	951	6	tif	tif	PROPN
fuelectenerg-1427	951	7	)	)	PUNCT
fuelectenerg-1427	951	8	is	be	AUX
fuelectenerg-1427	951	9	canonical	canonical	ADJ
fuelectenerg-1427	951	10	.	.	PUNCT
fuelectenerg-1427	952	1	110	110	NUM
fuelectenerg-1427	952	2	an	an	DET
fuelectenerg-1427	952	3	extended	extend	VERB
fuelectenerg-1427	952	4	green	green	ADJ
fuelectenerg-1427	952	5	sasao	sasao	PROPN
fuelectenerg-1427	952	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	952	7	of	of	ADP
fuelectenerg-1427	952	8	canonical	canonical	ADJ
fuelectenerg-1427	952	9	ternary	ternary	ADJ
fuelectenerg-1427	952	10	galois	galois	NOUN
fuelectenerg-1427	952	11	forms	form	NOUN
fuelectenerg-1427	952	12	...	...	PUNCT
fuelectenerg-1427	953	1	s	s	PART
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fuelectenerg-1427	953	3	s	s	X
fuelectenerg-1427	953	4	s	s	NOUN
fuelectenerg-1427	953	5	0	0	NUM
fuelectenerg-1427	953	6	b	b	SYM
fuelectenerg-1427	953	7	1	1	NUM
fuelectenerg-1427	953	8	b	b	SYM
fuelectenerg-1427	953	9	2	2	NUM
fuelectenerg-1427	953	10	b	b	NOUN
fuelectenerg-1427	953	11	s	s	X
fuelectenerg-1427	953	12	s	s	NOUN
fuelectenerg-1427	953	13	d	d	X
fuelectenerg-1427	953	14	d	d	X
fuelectenerg-1427	953	15	s	s	X
fuelectenerg-1427	953	16	s	s	X
fuelectenerg-1427	953	17	s	s	X
fuelectenerg-1427	953	18	d	d	NOUN
fuelectenerg-1427	953	19	1	1	NUM
fuelectenerg-1427	953	20	(	(	PUNCT
fuelectenerg-1427	953	21	a	a	PRON
fuelectenerg-1427	953	22	,	,	PUNCT
fuelectenerg-1427	953	23	)	)	PUNCT
fuelectenerg-1427	953	24	2	2	NUM
fuelectenerg-1427	953	25	a	a	PRON
fuelectenerg-1427	953	26	,	,	PUNCT
fuelectenerg-1427	953	27	s	s	NOUN
fuelectenerg-1427	953	28	d	d	X
fuelectenerg-1427	953	29	d	d	PROPN
fuelectenerg-1427	953	30	d	d	PROPN
fuelectenerg-1427	953	31	1	1	NUM
fuelectenerg-1427	953	32	(	(	PUNCT
fuelectenerg-1427	953	33	a	a	PRON
fuelectenerg-1427	953	34	,	,	PUNCT
fuelectenerg-1427	953	35	)	)	PUNCT
fuelectenerg-1427	953	36	2	2	NUM
fuelectenerg-1427	953	37	a	a	PRON
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fuelectenerg-1427	953	42	0	0	NUM
fuelectenerg-1427	953	43	b	b	NOUN
fuelectenerg-1427	953	44	0	0	NUM
fuelectenerg-1427	953	45	b	b	SYM
fuelectenerg-1427	953	46	1	1	NUM
fuelectenerg-1427	953	47	b	b	SYM
fuelectenerg-1427	953	48	1	1	NUM
fuelectenerg-1427	953	49	b	b	SYM
fuelectenerg-1427	953	50	2	2	NUM
fuelectenerg-1427	953	51	b	b	SYM
fuelectenerg-1427	953	52	2	2	NUM
fuelectenerg-1427	953	53	b	b	NOUN
fuelectenerg-1427	953	54	d	d	SYM
fuelectenerg-1427	953	55	1	1	NUM
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fuelectenerg-1427	953	57	1	1	NUM
fuelectenerg-1427	953	58	1	1	NUM
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fuelectenerg-1427	953	63	1	1	NUM
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fuelectenerg-1427	953	65	11	11	NUM
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fuelectenerg-1427	953	67	1	1	NUM
fuelectenerg-1427	953	68	1	1	NUM
fuelectenerg-1427	953	69	1	1	NUM
fuelectenerg-1427	953	70	1	1	NUM
fuelectenerg-1427	953	71	1	1	NUM
fuelectenerg-1427	953	72	1	1	NUM
fuelectenerg-1427	953	73	1	1	NUM
fuelectenerg-1427	953	74	1	1	NUM
fuelectenerg-1427	953	75	1	1	NUM
fuelectenerg-1427	953	76	1(b	1(b	NUM
fuelectenerg-1427	953	77	,	,	PUNCT
fuelectenerg-1427	953	78	)	)	PUNCT
fuelectenerg-1427	953	79	2	2	NUM
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fuelectenerg-1427	953	81	b	b	NOUN
fuelectenerg-1427	953	82	,	,	PUNCT
fuelectenerg-1427	953	83	)	)	PUNCT
fuelectenerg-1427	953	84	2	2	NUM
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fuelectenerg-1427	953	88	)	)	PUNCT
fuelectenerg-1427	953	89	2	2	NUM
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fuelectenerg-1427	953	91	b	b	NOUN
fuelectenerg-1427	953	92	,	,	PUNCT
fuelectenerg-1427	953	93	)	)	PUNCT
fuelectenerg-1427	953	94	2	2	NUM
fuelectenerg-1427	953	95	(	(	PUNCT
fuelectenerg-1427	953	96	b	b	NOUN
fuelectenerg-1427	953	97	,	,	PUNCT
fuelectenerg-1427	953	98	)	)	PUNCT
fuelectenerg-1427	953	99	2	2	NUM
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fuelectenerg-1427	953	101	b	b	NOUN
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fuelectenerg-1427	953	104	2	2	NUM
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fuelectenerg-1427	953	109	2	2	NUM
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fuelectenerg-1427	953	118	)	)	PUNCT
fuelectenerg-1427	953	119	2	2	NUM
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fuelectenerg-1427	953	121	b	b	NOUN
fuelectenerg-1427	953	122	,	,	PUNCT
fuelectenerg-1427	953	123	)	)	PUNCT
fuelectenerg-1427	953	124	2	2	NUM
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fuelectenerg-1427	953	126	b	b	NOUN
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fuelectenerg-1427	953	129	2	2	NUM
fuelectenerg-1427	953	130	(	(	PUNCT
fuelectenerg-1427	953	131	b	b	NOUN
fuelectenerg-1427	953	132	,	,	PUNCT
fuelectenerg-1427	953	133	)	)	PUNCT
fuelectenerg-1427	953	134	2	2	NUM
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fuelectenerg-1427	953	136	b	b	NOUN
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fuelectenerg-1427	953	138	)	)	PUNCT
fuelectenerg-1427	953	139	2	2	NUM
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fuelectenerg-1427	953	141	b	b	NOUN
fuelectenerg-1427	953	142	,	,	PUNCT
fuelectenerg-1427	953	143	)	)	PUNCT
fuelectenerg-1427	953	144	2	2	NUM
fuelectenerg-1427	953	145	(	(	PUNCT
fuelectenerg-1427	953	146	b	b	NOUN
fuelectenerg-1427	953	147	,	,	PUNCT
fuelectenerg-1427	953	148	)	)	PUNCT
fuelectenerg-1427	953	149	2	2	NUM
fuelectenerg-1427	953	150	(	(	PUNCT
fuelectenerg-1427	953	151	b	b	NOUN
fuelectenerg-1427	953	152	,	,	PUNCT
fuelectenerg-1427	953	153	)	)	PUNCT
fuelectenerg-1427	953	154	2	2	NUM
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fuelectenerg-1427	953	156	b	b	NOUN
fuelectenerg-1427	953	157	,	,	PUNCT
fuelectenerg-1427	953	158	)	)	PUNCT
fuelectenerg-1427	953	159	2	2	NUM
fuelectenerg-1427	953	160	(	(	PUNCT
fuelectenerg-1427	953	161	b	b	NOUN
fuelectenerg-1427	953	162	,	,	PUNCT
fuelectenerg-1427	953	163	)	)	PUNCT
fuelectenerg-1427	953	164	2	2	NUM
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fuelectenerg-1427	953	166	b	b	NOUN
fuelectenerg-1427	953	167	,	,	PUNCT
fuelectenerg-1427	953	168	)	)	PUNCT
fuelectenerg-1427	953	169	2	2	NUM
fuelectenerg-1427	953	170	(	(	PUNCT
fuelectenerg-1427	953	171	b	b	NOUN
fuelectenerg-1427	953	172	,	,	PUNCT
fuelectenerg-1427	953	173	)	)	PUNCT
fuelectenerg-1427	953	174	2	2	NUM
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fuelectenerg-1427	953	179	2	2	NUM
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fuelectenerg-1427	953	184	2	2	NUM
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fuelectenerg-1427	953	189	2	2	NUM
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fuelectenerg-1427	953	194	2	2	NUM
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fuelectenerg-1427	953	197	b	b	PROPN
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fuelectenerg-1427	953	199	b	b	PROPN
fuelectenerg-1427	953	200	,	,	PUNCT
fuelectenerg-1427	953	201	b	b	PROPN
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fuelectenerg-1427	953	203	b	b	PROPN
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fuelectenerg-1427	953	205	b	b	PROPN
fuelectenerg-1427	953	206	,	,	PUNCT
fuelectenerg-1427	953	207	b	b	PROPN
fuelectenerg-1427	953	208	,	,	PUNCT
fuelectenerg-1427	953	209	b	b	PROPN
fuelectenerg-1427	953	210	,	,	PUNCT
fuelectenerg-1427	953	211	b	b	PROPN
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fuelectenerg-1427	953	218	,	,	PUNCT
fuelectenerg-1427	953	219	b	b	PROPN
fuelectenerg-1427	953	220	,	,	PUNCT
fuelectenerg-1427	953	221	b	b	PROPN
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fuelectenerg-1427	953	223	b	b	PROPN
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fuelectenerg-1427	953	225	b	b	PROPN
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fuelectenerg-1427	953	231	b	b	PROPN
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fuelectenerg-1427	953	233	b	b	PROPN
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fuelectenerg-1427	953	235	b	b	PROPN
fuelectenerg-1427	953	236	,	,	PUNCT
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fuelectenerg-1427	953	241	s	s	NOUN
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fuelectenerg-1427	953	243	d	d	X
fuelectenerg-1427	953	244	d	d	X
fuelectenerg-1427	953	245	s	s	X
fuelectenerg-1427	953	246	s	s	X
fuelectenerg-1427	953	247	d	d	X
fuelectenerg-1427	953	248	d	d	SYM
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fuelectenerg-1427	953	251	a	a	PRON
fuelectenerg-1427	953	252	,	,	PUNCT
fuelectenerg-1427	953	253	)	)	PUNCT
fuelectenerg-1427	953	254	2	2	NUM
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fuelectenerg-1427	953	257	sd	sd	ADP
fuelectenerg-1427	953	258	d	d	PROPN
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fuelectenerg-1427	953	260	1	1	NUM
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fuelectenerg-1427	954	3	b	b	NOUN
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fuelectenerg-1427	954	5	b	b	NOUN
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fuelectenerg-1427	954	7	b	b	NOUN
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fuelectenerg-1427	954	9	b	b	NOUN
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fuelectenerg-1427	954	13	b	b	NOUN
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fuelectenerg-1427	954	17	b	b	NOUN
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fuelectenerg-1427	954	21	b	b	NOUN
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fuelectenerg-1427	954	23	b	b	NOUN
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fuelectenerg-1427	954	25	b	b	NOUN
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fuelectenerg-1427	954	27	b	b	NOUN
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fuelectenerg-1427	954	30	b	b	PROPN
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fuelectenerg-1427	954	34	b	b	SYM
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fuelectenerg-1427	954	36	b	b	SYM
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fuelectenerg-1427	954	38	b	b	SYM
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fuelectenerg-1427	954	40	b	b	SYM
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fuelectenerg-1427	954	42	b	b	SYM
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fuelectenerg-1427	954	44	b	b	SYM
fuelectenerg-1427	954	45	1	1	NUM
fuelectenerg-1427	954	46	b	b	SYM
fuelectenerg-1427	954	47	1	1	NUM
fuelectenerg-1427	954	48	b	b	SYM
fuelectenerg-1427	954	49	1	1	NUM
fuelectenerg-1427	954	50	b	b	SYM
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fuelectenerg-1427	954	52	b	b	SYM
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fuelectenerg-1427	954	70	1	1	NUM
fuelectenerg-1427	954	71	b	b	SYM
fuelectenerg-1427	954	72	2	2	NUM
fuelectenerg-1427	954	73	b	b	SYM
fuelectenerg-1427	954	74	2	2	NUM
fuelectenerg-1427	954	75	b	b	SYM
fuelectenerg-1427	954	76	2	2	NUM
fuelectenerg-1427	954	77	b	b	SYM
fuelectenerg-1427	954	78	2	2	NUM
fuelectenerg-1427	954	79	b	b	SYM
fuelectenerg-1427	954	80	2	2	NUM
fuelectenerg-1427	954	81	b	b	SYM
fuelectenerg-1427	954	82	2	2	NUM
fuelectenerg-1427	954	83	b	b	SYM
fuelectenerg-1427	954	84	2	2	NUM
fuelectenerg-1427	954	85	b	b	SYM
fuelectenerg-1427	954	86	2	2	NUM
fuelectenerg-1427	954	87	b	b	SYM
fuelectenerg-1427	954	88	2	2	NUM
fuelectenerg-1427	954	89	b	b	SYM
fuelectenerg-1427	954	90	2	2	NUM
fuelectenerg-1427	954	91	b	b	SYM
fuelectenerg-1427	954	92	2	2	NUM
fuelectenerg-1427	954	93	b	b	SYM
fuelectenerg-1427	954	94	2	2	NUM
fuelectenerg-1427	954	95	b	b	SYM
fuelectenerg-1427	954	96	2	2	NUM
fuelectenerg-1427	954	97	b	b	SYM
fuelectenerg-1427	954	98	2	2	NUM
fuelectenerg-1427	954	99	b	b	SYM
fuelectenerg-1427	954	100	2	2	NUM
fuelectenerg-1427	954	101	b	b	SYM
fuelectenerg-1427	954	102	2	2	NUM
fuelectenerg-1427	954	103	b2	b2	NOUN
fuelectenerg-1427	954	104	b	b	NOUN
fuelectenerg-1427	954	105	2	2	NUM
fuelectenerg-1427	954	106	b	b	SYM
fuelectenerg-1427	954	107	2	2	NUM
fuelectenerg-1427	954	108	b	b	NOUN
fuelectenerg-1427	954	109	d	d	PROPN
fuelectenerg-1427	954	110	1	1	NUM
fuelectenerg-1427	954	111	b	b	PROPN
fuelectenerg-1427	954	112	,	,	PUNCT
fuelectenerg-1427	954	113	s	s	PART
fuelectenerg-1427	954	114	sd	sd	NOUN
fuelectenerg-1427	954	115	d	d	PROPN
fuelectenerg-1427	954	116	s	s	X
fuelectenerg-1427	954	117	s	s	X
fuelectenerg-1427	954	118	s	s	X
fuelectenerg-1427	954	119	sd	sd	NOUN
fuelectenerg-1427	954	120	d	d	NOUN
fuelectenerg-1427	954	121	1	1	NUM
fuelectenerg-1427	954	122	(	(	PUNCT
fuelectenerg-1427	954	123	a	a	PRON
fuelectenerg-1427	954	124	,	,	PUNCT
fuelectenerg-1427	954	125	)	)	PUNCT
fuelectenerg-1427	954	126	2	2	NUM
fuelectenerg-1427	954	127	a	a	PRON
fuelectenerg-1427	954	128	,	,	PUNCT
fuelectenerg-1427	954	129	d	d	PROPN
fuelectenerg-1427	954	130	d	d	PROPN
fuelectenerg-1427	954	131	d	d	PROPN
fuelectenerg-1427	954	132	d	d	PROPN
fuelectenerg-1427	954	133	1	1	NUM
fuelectenerg-1427	954	134	(	(	PUNCT
fuelectenerg-1427	954	135	a	a	PRON
fuelectenerg-1427	954	136	,	,	PUNCT
fuelectenerg-1427	954	137	)	)	PUNCT
fuelectenerg-1427	954	138	2	2	NUM
fuelectenerg-1427	954	139	a	a	PRON
fuelectenerg-1427	954	140	,	,	PUNCT
fuelectenerg-1427	954	141	s	s	X
fuelectenerg-1427	954	142	s	s	NOUN
fuelectenerg-1427	954	143	s	s	X
fuelectenerg-1427	954	144	d	d	X
fuelectenerg-1427	954	145	s	s	X
fuelectenerg-1427	954	146	d	d	X
fuelectenerg-1427	954	147	dd	dd	NOUN
fuelectenerg-1427	954	148	d	d	PROPN
fuelectenerg-1427	954	149	d	d	PROPN
fuelectenerg-1427	954	150	1	1	NUM
fuelectenerg-1427	954	151	(	(	PUNCT
fuelectenerg-1427	954	152	a	a	PRON
fuelectenerg-1427	954	153	,	,	PUNCT
fuelectenerg-1427	954	154	)	)	PUNCT
fuelectenerg-1427	954	155	2	2	NUM
fuelectenerg-1427	954	156	a	a	PRON
fuelectenerg-1427	954	157	,	,	PUNCT
fuelectenerg-1427	954	158	s	s	NOUN
fuelectenerg-1427	954	159	d0	d0	NOUN
fuelectenerg-1427	954	160	d1	d1	PROPN
fuelectenerg-1427	954	161	d	d	X
fuelectenerg-1427	954	162	1	1	NUM
fuelectenerg-1427	954	163	(	(	PUNCT
fuelectenerg-1427	954	164	a	a	PRON
fuelectenerg-1427	954	165	,	,	PUNCT
fuelectenerg-1427	954	166	)	)	PUNCT
fuelectenerg-1427	954	167	2	2	NUM
fuelectenerg-1427	954	168	a	a	PRON
fuelectenerg-1427	954	169	,	,	PUNCT
fuelectenerg-1427	954	170	n=1	n=1	PROPN
fuelectenerg-1427	954	171	n=81	n=81	PRON
fuelectenerg-1427	954	172	n=729	n=729	PROPN
fuelectenerg-1427	954	173	n=59049	n=59049	PROPN
fuelectenerg-1427	954	174	n=9	n=9	PROPN
fuelectenerg-1427	954	175	n=81	n=81	VERB
fuelectenerg-1427	954	176	n=6561	n=6561	PROPN
fuelectenerg-1427	954	177	n=59049	n=59049	PROPN
fuelectenerg-1427	954	178	n=9	n=9	PROPN
fuelectenerg-1427	954	179	n=81	n=81	ADP
fuelectenerg-1427	954	180	n=6561	n=6561	PROPN
fuelectenerg-1427	954	181	n=59049	n=59049	PROPN
fuelectenerg-1427	954	182	n=9	n=9	PROPN
fuelectenerg-1427	954	183	n=729	n=729	X
fuelectenerg-1427	954	184	n=6561	n=6561	PROPN
fuelectenerg-1427	955	1	n=531441	n=531441	ADV
fuelectenerg-1427	955	2	0	0	PUNCT
fuelectenerg-1427	956	1	a	a	DET
fuelectenerg-1427	956	2	0	0	NUM
fuelectenerg-1427	956	3	a	a	DET
fuelectenerg-1427	956	4	0	0	NUM
fuelectenerg-1427	956	5	b	b	NOUN
fuelectenerg-1427	956	6	0	0	NUM
fuelectenerg-1427	956	7	b	b	NOUN
fuelectenerg-1427	956	8	0	0	NUM
fuelectenerg-1427	956	9	a	a	DET
fuelectenerg-1427	956	10	0	0	NUM
fuelectenerg-1427	956	11	a	a	DET
fuelectenerg-1427	956	12	0	0	NUM
fuelectenerg-1427	956	13	a	a	DET
fuelectenerg-1427	956	14	0	0	NUM
fuelectenerg-1427	956	15	a	a	DET
fuelectenerg-1427	956	16	0	0	NUM
fuelectenerg-1427	956	17	a	a	DET
fuelectenerg-1427	956	18	0	0	NUM
fuelectenerg-1427	956	19	a	a	DET
fuelectenerg-1427	956	20	1	1	NUM
fuelectenerg-1427	956	21	a	a	DET
fuelectenerg-1427	956	22	1	1	NUM
fuelectenerg-1427	956	23	a	a	DET
fuelectenerg-1427	956	24	1	1	NUM
fuelectenerg-1427	956	25	b	b	SYM
fuelectenerg-1427	956	26	1	1	NUM
fuelectenerg-1427	956	27	b	b	SYM
fuelectenerg-1427	956	28	1	1	NUM
fuelectenerg-1427	956	29	a	a	DET
fuelectenerg-1427	956	30	1	1	NUM
fuelectenerg-1427	956	31	a	a	DET
fuelectenerg-1427	956	32	1	1	NUM
fuelectenerg-1427	956	33	a	a	DET
fuelectenerg-1427	956	34	1	1	NUM
fuelectenerg-1427	956	35	a	a	DET
fuelectenerg-1427	956	36	1	1	NUM
fuelectenerg-1427	956	37	a	a	DET
fuelectenerg-1427	956	38	1	1	NUM
fuelectenerg-1427	956	39	a	a	DET
fuelectenerg-1427	956	40	2	2	NUM
fuelectenerg-1427	956	41	a	a	DET
fuelectenerg-1427	956	42	2	2	NUM
fuelectenerg-1427	956	43	a	a	DET
fuelectenerg-1427	956	44	2	2	NUM
fuelectenerg-1427	956	45	b	b	SYM
fuelectenerg-1427	956	46	2	2	NUM
fuelectenerg-1427	956	47	b	b	SYM
fuelectenerg-1427	956	48	2	2	NUM
fuelectenerg-1427	956	49	a	a	DET
fuelectenerg-1427	956	50	2	2	NUM
fuelectenerg-1427	956	51	a	a	DET
fuelectenerg-1427	956	52	2	2	NUM
fuelectenerg-1427	956	53	a	a	DET
fuelectenerg-1427	956	54	2	2	NUM
fuelectenerg-1427	956	55	a	a	DET
fuelectenerg-1427	956	56	2	2	NUM
fuelectenerg-1427	956	57	a	a	DET
fuelectenerg-1427	956	58	2	2	NUM
fuelectenerg-1427	956	59	a	a	DET
fuelectenerg-1427	956	60	(	(	PUNCT
fuelectenerg-1427	956	61	a	a	PRON
fuelectenerg-1427	956	62	)	)	PUNCT
fuelectenerg-1427	956	63	figure	figure	NOUN
fuelectenerg-1427	956	64	5	5	NUM
fuelectenerg-1427	956	65	:	:	PUNCT
fuelectenerg-1427	956	66	ternary	ternary	ADJ
fuelectenerg-1427	956	67	if	if	SCONJ
fuelectenerg-1427	956	68	(	(	PUNCT
fuelectenerg-1427	956	69	tif	tif	PROPN
fuelectenerg-1427	956	70	)	)	PUNCT
fuelectenerg-1427	956	71	s	s	PROPN
fuelectenerg-1427	956	72	/	/	SYM
fuelectenerg-1427	956	73	d	d	NOUN
fuelectenerg-1427	956	74	trees	tree	NOUN
fuelectenerg-1427	956	75	and	and	CCONJ
fuelectenerg-1427	956	76	their	their	PRON
fuelectenerg-1427	956	77	numbers	number	NOUN
fuelectenerg-1427	956	78	:	:	PUNCT
fuelectenerg-1427	956	79	(	(	PUNCT
fuelectenerg-1427	956	80	a	a	X
fuelectenerg-1427	956	81	)	)	PUNCT
fuelectenerg-1427	956	82	2	2	NUM
fuelectenerg-1427	956	83	-	-	PUNCT
fuelectenerg-1427	956	84	variable	variable	ADJ
fuelectenerg-1427	956	85	order	order	NOUN
fuelectenerg-1427	956	86	{	{	PUNCT
fuelectenerg-1427	956	87	a	a	DET
fuelectenerg-1427	956	88	,	,	PUNCT
fuelectenerg-1427	956	89	b	b	NOUN
fuelectenerg-1427	956	90	}	}	PUNCT
fuelectenerg-1427	956	91	and	and	CCONJ
fuelectenerg-1427	956	92	(	(	PUNCT
fuelectenerg-1427	956	93	b	b	X
fuelectenerg-1427	956	94	)	)	PUNCT
fuelectenerg-1427	956	95	2variable	2variable	NUM
fuelectenerg-1427	956	96	order	order	NOUN
fuelectenerg-1427	956	97	{	{	PUNCT
fuelectenerg-1427	956	98	b	b	NOUN
fuelectenerg-1427	956	99	,	,	PUNCT
fuelectenerg-1427	956	100	a	a	PRON
fuelectenerg-1427	956	101	}	}	PUNCT
fuelectenerg-1427	956	102	.	.	PUNCT
fuelectenerg-1427	957	1	variables	variable	NOUN
fuelectenerg-1427	957	2	{	{	PUNCT
fuelectenerg-1427	957	3	a	a	DET
fuelectenerg-1427	957	4	,	,	PUNCT
fuelectenerg-1427	957	5	b	b	NOUN
fuelectenerg-1427	957	6	}	}	PUNCT
fuelectenerg-1427	957	7	are	be	AUX
fuelectenerg-1427	957	8	defined	define	VERB
fuelectenerg-1427	957	9	as	as	ADP
fuelectenerg-1427	957	10	in	in	ADP
fuelectenerg-1427	957	11	eq	eq	ADP
fuelectenerg-1427	957	12	.	.	PUNCT
fuelectenerg-1427	958	1	(	(	PUNCT
fuelectenerg-1427	958	2	28	28	NUM
fuelectenerg-1427	958	3	)	)	PUNCT
fuelectenerg-1427	958	4	for	for	ADP
fuelectenerg-1427	958	5	generalized	generalized	ADJ
fuelectenerg-1427	958	6	davio	davio	NOUN
fuelectenerg-1427	958	7	(	(	PUNCT
fuelectenerg-1427	958	8	d	d	NOUN
fuelectenerg-1427	958	9	)	)	PUNCT
fuelectenerg-1427	958	10	where	where	SCONJ
fuelectenerg-1427	958	11	in	in	ADP
fuelectenerg-1427	958	12	this	this	DET
fuelectenerg-1427	958	13	figure	figure	NOUN
fuelectenerg-1427	958	14	(	(	PUNCT
fuelectenerg-1427	958	15	a,≡	a,≡	NOUN
fuelectenerg-1427	958	16	a	a	X
fuelectenerg-1427	958	17	)	)	PUNCT
fuelectenerg-1427	958	18	and	and	CCONJ
fuelectenerg-1427	958	19	(	(	PUNCT
fuelectenerg-1427	958	20	b,≡	b,≡	X
fuelectenerg-1427	958	21	b	b	X
fuelectenerg-1427	958	22	)	)	PUNCT
fuelectenerg-1427	958	23	.	.	PUNCT
fuelectenerg-1427	959	1	theorem	theorem	NOUN
fuelectenerg-1427	959	2	2	2	NUM
fuelectenerg-1427	959	3	.	.	PUNCT
fuelectenerg-1427	960	1	the	the	DET
fuelectenerg-1427	960	2	total	total	ADJ
fuelectenerg-1427	960	3	number	number	NOUN
fuelectenerg-1427	960	4	of	of	ADP
fuelectenerg-1427	960	5	the	the	DET
fuelectenerg-1427	960	6	ternary	ternary	ADJ
fuelectenerg-1427	960	7	ifs	ifs	PROPN
fuelectenerg-1427	960	8	,	,	PUNCT
fuelectenerg-1427	960	9	for	for	ADP
fuelectenerg-1427	960	10	two	two	NUM
fuelectenerg-1427	960	11	variables	variable	NOUN
fuelectenerg-1427	960	12	and	and	CCONJ
fuelectenerg-1427	960	13	for	for	ADP
fuelectenerg-1427	960	14	orders	order	NOUN
fuelectenerg-1427	960	15	{	{	PUNCT
fuelectenerg-1427	960	16	a	a	DET
fuelectenerg-1427	960	17	,	,	PUNCT
fuelectenerg-1427	960	18	b	b	NOUN
fuelectenerg-1427	960	19	}	}	PUNCT
fuelectenerg-1427	960	20	and	and	CCONJ
fuelectenerg-1427	960	21	{	{	PUNCT
fuelectenerg-1427	960	22	b	b	NOUN
fuelectenerg-1427	960	23	,	,	PUNCT
fuelectenerg-1427	960	24	a	a	PRON
fuelectenerg-1427	960	25	}	}	PUNCT
fuelectenerg-1427	960	26	,	,	PUNCT
fuelectenerg-1427	960	27	and	and	CCONJ
fuelectenerg-1427	960	28	the	the	DET
fuelectenerg-1427	960	29	total	total	ADJ
fuelectenerg-1427	960	30	number	number	NOUN
fuelectenerg-1427	960	31	of	of	ADP
fuelectenerg-1427	960	32	ternary	ternary	ADJ
fuelectenerg-1427	960	33	generalized	generalize	VERB
fuelectenerg-1427	960	34	ifs	ifs	PROPN
fuelectenerg-1427	960	35	,	,	PUNCT
fuelectenerg-1427	960	36	for	for	ADP
fuelectenerg-1427	960	37	two	two	NUM
fuelectenerg-1427	960	38	variables	variable	NOUN
fuelectenerg-1427	960	39	,	,	PUNCT
fuelectenerg-1427	960	40	are	be	AUX
fuelectenerg-1427	960	41	respectively	respectively	ADV
fuelectenerg-1427	960	42	:	:	PUNCT
fuelectenerg-1427	960	43	#	#	SYM
fuelectenerg-1427	960	44	tifa	tifa	NOUN
fuelectenerg-1427	960	45	,	,	PUNCT
fuelectenerg-1427	960	46	b	b	NOUN
fuelectenerg-1427	960	47	=	=	SYM
fuelectenerg-1427	960	48	1	1	NUM
fuelectenerg-1427	960	49	·	·	PUNCT
fuelectenerg-1427	960	50	(	(	PUNCT
fuelectenerg-1427	960	51	3)0	3)0	NUM
fuelectenerg-1427	960	52	+	+	CCONJ
fuelectenerg-1427	960	53	3	3	NUM
fuelectenerg-1427	960	54	·	·	PUNCT
fuelectenerg-1427	960	55	(	(	PUNCT
fuelectenerg-1427	960	56	3)2	3)2	NUM
fuelectenerg-1427	960	57	+	+	SYM
fuelectenerg-1427	960	58	3	3	NUM
fuelectenerg-1427	960	59	·	·	PUNCT
fuelectenerg-1427	960	60	(	(	PUNCT
fuelectenerg-1427	960	61	3)4	3)4	NUM
fuelectenerg-1427	960	62	+	+	NOUN
fuelectenerg-1427	960	63	2	2	NUM
fuelectenerg-1427	960	64	·	·	PUNCT
fuelectenerg-1427	960	65	(	(	PUNCT
fuelectenerg-1427	960	66	3)6	3)6	NUM
fuelectenerg-1427	960	67	+	+	SYM
fuelectenerg-1427	960	68	3	3	NUM
fuelectenerg-1427	960	69	·	·	PUNCT
fuelectenerg-1427	960	70	(	(	PUNCT
fuelectenerg-1427	960	71	3)8	3)8	NUM
fuelectenerg-1427	960	72	+	+	SYM
fuelectenerg-1427	960	73	3	3	NUM
fuelectenerg-1427	960	74	·	·	PUNCT
fuelectenerg-1427	960	75	(	(	PUNCT
fuelectenerg-1427	960	76	3)10	3)10	NUM
fuelectenerg-1427	960	77	+	+	ADJ
fuelectenerg-1427	960	78	1	1	NUM
fuelectenerg-1427	960	79	·	·	PUNCT
fuelectenerg-1427	960	80	(	(	PUNCT
fuelectenerg-1427	960	81	3)12	3)12	NUM
fuelectenerg-1427	960	82	=	=	SYM
fuelectenerg-1427	960	83	730,000	730,000	NUM
fuelectenerg-1427	960	84	,	,	PUNCT
fuelectenerg-1427	960	85	(	(	PUNCT
fuelectenerg-1427	960	86	33	33	NUM
fuelectenerg-1427	960	87	)	)	PUNCT
fuelectenerg-1427	960	88	#	#	SYM
fuelectenerg-1427	960	89	tifb	tifb	NOUN
fuelectenerg-1427	960	90	,	,	PUNCT
fuelectenerg-1427	960	91	a	a	DET
fuelectenerg-1427	960	92	=	=	SYM
fuelectenerg-1427	960	93	1	1	NUM
fuelectenerg-1427	960	94	·	·	PUNCT
fuelectenerg-1427	960	95	(	(	PUNCT
fuelectenerg-1427	960	96	3)0	3)0	NUM
fuelectenerg-1427	960	97	+	+	CCONJ
fuelectenerg-1427	960	98	3	3	NUM
fuelectenerg-1427	960	99	·	·	PUNCT
fuelectenerg-1427	960	100	(	(	PUNCT
fuelectenerg-1427	960	101	3)2	3)2	NUM
fuelectenerg-1427	960	102	+	+	SYM
fuelectenerg-1427	960	103	3	3	NUM
fuelectenerg-1427	960	104	·	·	PUNCT
fuelectenerg-1427	960	105	(	(	PUNCT
fuelectenerg-1427	960	106	3)4	3)4	NUM
fuelectenerg-1427	960	107	+	+	NOUN
fuelectenerg-1427	960	108	2	2	NUM
fuelectenerg-1427	960	109	·	·	PUNCT
fuelectenerg-1427	960	110	(	(	PUNCT
fuelectenerg-1427	960	111	3)6	3)6	NUM
fuelectenerg-1427	960	112	+	+	SYM
fuelectenerg-1427	960	113	3	3	NUM
fuelectenerg-1427	960	114	·	·	PUNCT
fuelectenerg-1427	960	115	(	(	PUNCT
fuelectenerg-1427	960	116	3)8	3)8	NUM
fuelectenerg-1427	960	117	+	+	SYM
fuelectenerg-1427	960	118	3	3	NUM
fuelectenerg-1427	960	119	·	·	PUNCT
fuelectenerg-1427	960	120	(	(	PUNCT
fuelectenerg-1427	960	121	3)10	3)10	NUM
fuelectenerg-1427	960	122	+	+	ADJ
fuelectenerg-1427	960	123	1	1	NUM
fuelectenerg-1427	960	124	·	·	PUNCT
fuelectenerg-1427	960	125	(	(	PUNCT
fuelectenerg-1427	960	126	3)12	3)12	NUM
fuelectenerg-1427	960	127	=	=	SYM
fuelectenerg-1427	960	128	730,000	730,000	NUM
fuelectenerg-1427	960	129	,	,	PUNCT
fuelectenerg-1427	960	130	(	(	PUNCT
fuelectenerg-1427	960	131	34	34	NUM
fuelectenerg-1427	960	132	)	)	PUNCT
fuelectenerg-1427	960	133	#	#	NOUN
fuelectenerg-1427	960	134	tgif	tgif	NOUN
fuelectenerg-1427	960	135	=	=	PUNCT
fuelectenerg-1427	960	136	#	#	NUM
fuelectenerg-1427	960	137	tifa	tifa	NOUN
fuelectenerg-1427	960	138	,	,	PUNCT
fuelectenerg-1427	960	139	b	b	NOUN
fuelectenerg-1427	960	140	+	+	CCONJ
fuelectenerg-1427	960	141	#	#	SYM
fuelectenerg-1427	960	142	tifb	tifb	NOUN
fuelectenerg-1427	960	143	,	,	PUNCT
fuelectenerg-1427	960	144	a−#(tifa	a−#(tifa	PROPN
fuelectenerg-1427	960	145	,	,	PUNCT
fuelectenerg-1427	960	146	b	b	NOUN
fuelectenerg-1427	960	147	∩tifb	∩tifb	NOUN
fuelectenerg-1427	960	148	,	,	PUNCT
fuelectenerg-1427	960	149	a	a	PRON
fuelectenerg-1427	960	150	)	)	PUNCT
fuelectenerg-1427	960	151	=	=	SYM
fuelectenerg-1427	960	152	2	2	NUM
fuelectenerg-1427	960	153	·	·	SYM
fuelectenerg-1427	960	154	#	#	NOUN
fuelectenerg-1427	960	155	tif−#(tifa	tif−#(tifa	NUM
fuelectenerg-1427	960	156	,	,	PUNCT
fuelectenerg-1427	960	157	b	b	NOUN
fuelectenerg-1427	960	158	∩tifb	∩tifb	NOUN
fuelectenerg-1427	960	159	,	,	PUNCT
fuelectenerg-1427	960	160	a	a	PRON
fuelectenerg-1427	960	161	)	)	PUNCT
fuelectenerg-1427	960	162	=	=	SYM
fuelectenerg-1427	960	163	2	2	NUM
fuelectenerg-1427	960	164	·	·	PUNCT
fuelectenerg-1427	960	165	(	(	PUNCT
fuelectenerg-1427	960	166	730,000)−	730,000)−	NUM
fuelectenerg-1427	960	167	(	(	PUNCT
fuelectenerg-1427	960	168	1	1	NUM
fuelectenerg-1427	960	169	·	·	PUNCT
fuelectenerg-1427	960	170	(	(	PUNCT
fuelectenerg-1427	960	171	3)0	3)0	NUM
fuelectenerg-1427	960	172	+	+	PROPN
fuelectenerg-1427	960	173	2	2	NUM
fuelectenerg-1427	960	174	·	·	PUNCT
fuelectenerg-1427	960	175	(	(	PUNCT
fuelectenerg-1427	960	176	3)6	3)6	NUM
fuelectenerg-1427	960	177	+	+	SYM
fuelectenerg-1427	960	178	1	1	NUM
fuelectenerg-1427	960	179	·	·	PUNCT
fuelectenerg-1427	960	180	(	(	PUNCT
fuelectenerg-1427	960	181	3)12	3)12	NUM
fuelectenerg-1427	960	182	)	)	PUNCT
fuelectenerg-1427	960	183	=	=	SYM
fuelectenerg-1427	961	1	927,100	927,100	NUM
fuelectenerg-1427	961	2	.	.	PUNCT
fuelectenerg-1427	962	1	(	(	PUNCT
fuelectenerg-1427	962	2	35	35	NUM
fuelectenerg-1427	962	3	)	)	PUNCT
fuelectenerg-1427	962	4	proof	proof	NOUN
fuelectenerg-1427	962	5	.	.	PUNCT
fuelectenerg-1427	963	1	by	by	ADP
fuelectenerg-1427	963	2	observing	observe	VERB
fuelectenerg-1427	963	3	figure	figure	NOUN
fuelectenerg-1427	963	4	5	5	NUM
fuelectenerg-1427	963	5	,	,	PUNCT
fuelectenerg-1427	963	6	we	we	PRON
fuelectenerg-1427	963	7	note	note	VERB
fuelectenerg-1427	963	8	that	that	SCONJ
fuelectenerg-1427	963	9	the	the	DET
fuelectenerg-1427	963	10	total	total	ADJ
fuelectenerg-1427	963	11	number	number	NOUN
fuelectenerg-1427	963	12	of	of	ADP
fuelectenerg-1427	963	13	tifs	tifs	PROPN
fuelectenerg-1427	963	14	for	for	ADP
fuelectenerg-1427	963	15	orders	order	NOUN
fuelectenerg-1427	963	16	{	{	PUNCT
fuelectenerg-1427	963	17	a	a	DET
fuelectenerg-1427	963	18	,	,	PUNCT
fuelectenerg-1427	963	19	b	b	NOUN
fuelectenerg-1427	963	20	}	}	PUNCT
fuelectenerg-1427	963	21	and	and	CCONJ
fuelectenerg-1427	963	22	{	{	PUNCT
fuelectenerg-1427	963	23	b	b	NOUN
fuelectenerg-1427	963	24	,	,	PUNCT
fuelectenerg-1427	963	25	a	a	PRON
fuelectenerg-1427	963	26	}	}	PUNCT
fuelectenerg-1427	963	27	is	be	AUX
fuelectenerg-1427	963	28	the	the	DET
fuelectenerg-1427	963	29	sum	sum	NOUN
fuelectenerg-1427	963	30	of	of	ADP
fuelectenerg-1427	963	31	the	the	DET
fuelectenerg-1427	963	32	numbers	number	NOUN
fuelectenerg-1427	963	33	on	on	ADP
fuelectenerg-1427	963	34	top	top	NOUN
fuelectenerg-1427	963	35	of	of	ADP
fuelectenerg-1427	963	36	s	s	PROPN
fuelectenerg-1427	963	37	/	/	SYM
fuelectenerg-1427	963	38	d	d	NOUN
fuelectenerg-1427	963	39	trees	tree	NOUN
fuelectenerg-1427	963	40	that	that	PRON
fuelectenerg-1427	963	41	leads	lead	VERB
fuelectenerg-1427	963	42	to	to	ADP
fuelectenerg-1427	963	43	equations	equation	NOUN
fuelectenerg-1427	963	44	(	(	PUNCT
fuelectenerg-1427	963	45	33	33	NUM
fuelectenerg-1427	963	46	)	)	PUNCT
fuelectenerg-1427	963	47	(	(	PUNCT
fuelectenerg-1427	963	48	35	35	NUM
fuelectenerg-1427	963	49	)	)	PUNCT
fuelectenerg-1427	963	50	,	,	PUNCT
fuelectenerg-1427	963	51	respectively	respectively	ADV
fuelectenerg-1427	963	52	.	.	PUNCT
fuelectenerg-1427	964	1	2.2	2.2	NUM
fuelectenerg-1427	964	2	properties	property	NOUN
fuelectenerg-1427	964	3	of	of	ADP
fuelectenerg-1427	964	4	tifs	tifs	PROPN
fuelectenerg-1427	964	5	and	and	CCONJ
fuelectenerg-1427	964	6	tgifs	tgif	VERB
fuelectenerg-1427	964	7	the	the	DET
fuelectenerg-1427	964	8	following	follow	VERB
fuelectenerg-1427	964	9	present	present	ADJ
fuelectenerg-1427	964	10	basic	basic	ADJ
fuelectenerg-1427	964	11	properties	property	NOUN
fuelectenerg-1427	964	12	of	of	ADP
fuelectenerg-1427	964	13	the	the	DET
fuelectenerg-1427	964	14	presented	present	VERB
fuelectenerg-1427	964	15	tifs	tifs	PROPN
fuelectenerg-1427	964	16	and	and	CCONJ
fuelectenerg-1427	964	17	tgifs	tgif	NOUN
fuelectenerg-1427	964	18	.	.	PUNCT
fuelectenerg-1427	964	19	theorem	theorem	NOUN
fuelectenerg-1427	964	20	3	3	NUM
fuelectenerg-1427	964	21	.	.	PUNCT
fuelectenerg-1427	965	1	each	each	DET
fuelectenerg-1427	965	2	ternary	ternary	ADJ
fuelectenerg-1427	965	3	inclusive	inclusive	ADJ
fuelectenerg-1427	965	4	form	form	NOUN
fuelectenerg-1427	965	5	(	(	PUNCT
fuelectenerg-1427	965	6	tif	tif	PROPN
fuelectenerg-1427	965	7	)	)	PUNCT
fuelectenerg-1427	965	8	is	be	AUX
fuelectenerg-1427	965	9	canonical	canonical	ADJ
fuelectenerg-1427	965	10	.	.	PUNCT
fuelectenerg-1427	966	1	110	110	NUM
fuelectenerg-1427	966	2	an	an	DET
fuelectenerg-1427	966	3	extended	extend	VERB
fuelectenerg-1427	966	4	green	green	ADJ
fuelectenerg-1427	966	5	sasao	sasao	PROPN
fuelectenerg-1427	966	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	966	7	of	of	ADP
fuelectenerg-1427	966	8	canonical	canonical	ADJ
fuelectenerg-1427	966	9	ternary	ternary	ADJ
fuelectenerg-1427	966	10	galois	galois	NOUN
fuelectenerg-1427	966	11	forms	form	NOUN
fuelectenerg-1427	966	12	...	...	PUNCT
fuelectenerg-1427	967	1	s	s	PART
fuelectenerg-1427	967	2	s	s	X
fuelectenerg-1427	967	3	s	s	X
fuelectenerg-1427	967	4	s	s	NOUN
fuelectenerg-1427	967	5	0	0	NUM
fuelectenerg-1427	967	6	b	b	SYM
fuelectenerg-1427	967	7	1	1	NUM
fuelectenerg-1427	967	8	b	b	SYM
fuelectenerg-1427	967	9	2	2	NUM
fuelectenerg-1427	967	10	b	b	NOUN
fuelectenerg-1427	967	11	s	s	X
fuelectenerg-1427	967	12	s	s	NOUN
fuelectenerg-1427	967	13	d	d	X
fuelectenerg-1427	967	14	d	d	X
fuelectenerg-1427	967	15	s	s	X
fuelectenerg-1427	967	16	s	s	X
fuelectenerg-1427	967	17	s	s	X
fuelectenerg-1427	967	18	d	d	NOUN
fuelectenerg-1427	967	19	1	1	NUM
fuelectenerg-1427	967	20	(	(	PUNCT
fuelectenerg-1427	967	21	a	a	PRON
fuelectenerg-1427	967	22	,	,	PUNCT
fuelectenerg-1427	967	23	)	)	PUNCT
fuelectenerg-1427	967	24	2	2	NUM
fuelectenerg-1427	967	25	a	a	PRON
fuelectenerg-1427	967	26	,	,	PUNCT
fuelectenerg-1427	967	27	s	s	NOUN
fuelectenerg-1427	967	28	d	d	X
fuelectenerg-1427	967	29	d	d	PROPN
fuelectenerg-1427	967	30	d	d	PROPN
fuelectenerg-1427	967	31	1	1	NUM
fuelectenerg-1427	967	32	(	(	PUNCT
fuelectenerg-1427	967	33	a	a	PRON
fuelectenerg-1427	967	34	,	,	PUNCT
fuelectenerg-1427	967	35	)	)	PUNCT
fuelectenerg-1427	967	36	2	2	NUM
fuelectenerg-1427	967	37	a	a	PRON
fuelectenerg-1427	967	38	,	,	PUNCT
fuelectenerg-1427	967	39	s	s	X
fuelectenerg-1427	967	40	s	s	NOUN
fuelectenerg-1427	967	41	s	s	NOUN
fuelectenerg-1427	967	42	0	0	NUM
fuelectenerg-1427	967	43	b	b	NOUN
fuelectenerg-1427	967	44	0	0	NUM
fuelectenerg-1427	967	45	b	b	SYM
fuelectenerg-1427	967	46	1	1	NUM
fuelectenerg-1427	967	47	b	b	SYM
fuelectenerg-1427	967	48	1	1	NUM
fuelectenerg-1427	967	49	b	b	SYM
fuelectenerg-1427	967	50	2	2	NUM
fuelectenerg-1427	967	51	b	b	SYM
fuelectenerg-1427	967	52	2	2	NUM
fuelectenerg-1427	967	53	b	b	NOUN
fuelectenerg-1427	967	54	d	d	SYM
fuelectenerg-1427	967	55	1	1	NUM
fuelectenerg-1427	967	56	1	1	NUM
fuelectenerg-1427	967	57	1	1	NUM
fuelectenerg-1427	967	58	1	1	NUM
fuelectenerg-1427	967	59	1	1	NUM
fuelectenerg-1427	967	60	1	1	NUM
fuelectenerg-1427	967	61	1	1	NUM
fuelectenerg-1427	967	62	1	1	NUM
fuelectenerg-1427	967	63	1	1	NUM
fuelectenerg-1427	967	64	1	1	NUM
fuelectenerg-1427	967	65	11	11	NUM
fuelectenerg-1427	967	66	1	1	NUM
fuelectenerg-1427	967	67	1	1	NUM
fuelectenerg-1427	967	68	1	1	NUM
fuelectenerg-1427	967	69	1	1	NUM
fuelectenerg-1427	967	70	1	1	NUM
fuelectenerg-1427	967	71	1	1	NUM
fuelectenerg-1427	967	72	1	1	NUM
fuelectenerg-1427	967	73	1	1	NUM
fuelectenerg-1427	967	74	1	1	NUM
fuelectenerg-1427	967	75	1	1	NUM
fuelectenerg-1427	967	76	1(b	1(b	NUM
fuelectenerg-1427	967	77	,	,	PUNCT
fuelectenerg-1427	967	78	)	)	PUNCT
fuelectenerg-1427	967	79	2	2	NUM
fuelectenerg-1427	967	80	(	(	PUNCT
fuelectenerg-1427	967	81	b	b	NOUN
fuelectenerg-1427	967	82	,	,	PUNCT
fuelectenerg-1427	967	83	)	)	PUNCT
fuelectenerg-1427	967	84	2	2	NUM
fuelectenerg-1427	967	85	(	(	PUNCT
fuelectenerg-1427	967	86	b	b	NOUN
fuelectenerg-1427	967	87	,	,	PUNCT
fuelectenerg-1427	967	88	)	)	PUNCT
fuelectenerg-1427	967	89	2	2	NUM
fuelectenerg-1427	967	90	(	(	PUNCT
fuelectenerg-1427	967	91	b	b	NOUN
fuelectenerg-1427	967	92	,	,	PUNCT
fuelectenerg-1427	967	93	)	)	PUNCT
fuelectenerg-1427	967	94	2	2	NUM
fuelectenerg-1427	967	95	(	(	PUNCT
fuelectenerg-1427	967	96	b	b	NOUN
fuelectenerg-1427	967	97	,	,	PUNCT
fuelectenerg-1427	967	98	)	)	PUNCT
fuelectenerg-1427	967	99	2	2	NUM
fuelectenerg-1427	967	100	(	(	PUNCT
fuelectenerg-1427	967	101	b	b	NOUN
fuelectenerg-1427	967	102	,	,	PUNCT
fuelectenerg-1427	967	103	)	)	PUNCT
fuelectenerg-1427	967	104	2	2	NUM
fuelectenerg-1427	967	105	(	(	PUNCT
fuelectenerg-1427	967	106	b	b	NOUN
fuelectenerg-1427	967	107	,	,	PUNCT
fuelectenerg-1427	967	108	)	)	PUNCT
fuelectenerg-1427	967	109	2	2	NUM
fuelectenerg-1427	967	110	(	(	PUNCT
fuelectenerg-1427	967	111	b	b	NOUN
fuelectenerg-1427	967	112	,	,	PUNCT
fuelectenerg-1427	967	113	)	)	PUNCT
fuelectenerg-1427	967	114	2	2	NUM
fuelectenerg-1427	967	115	(	(	PUNCT
fuelectenerg-1427	967	116	b	b	NOUN
fuelectenerg-1427	967	117	,	,	PUNCT
fuelectenerg-1427	967	118	)	)	PUNCT
fuelectenerg-1427	967	119	2	2	NUM
fuelectenerg-1427	967	120	(	(	PUNCT
fuelectenerg-1427	967	121	b	b	NOUN
fuelectenerg-1427	967	122	,	,	PUNCT
fuelectenerg-1427	967	123	)	)	PUNCT
fuelectenerg-1427	967	124	2	2	NUM
fuelectenerg-1427	967	125	(	(	PUNCT
fuelectenerg-1427	967	126	b	b	NOUN
fuelectenerg-1427	967	127	,	,	PUNCT
fuelectenerg-1427	967	128	)	)	PUNCT
fuelectenerg-1427	967	129	2	2	NUM
fuelectenerg-1427	967	130	(	(	PUNCT
fuelectenerg-1427	967	131	b	b	NOUN
fuelectenerg-1427	967	132	,	,	PUNCT
fuelectenerg-1427	967	133	)	)	PUNCT
fuelectenerg-1427	967	134	2	2	NUM
fuelectenerg-1427	967	135	(	(	PUNCT
fuelectenerg-1427	967	136	b	b	NOUN
fuelectenerg-1427	967	137	,	,	PUNCT
fuelectenerg-1427	967	138	)	)	PUNCT
fuelectenerg-1427	967	139	2	2	NUM
fuelectenerg-1427	967	140	(	(	PUNCT
fuelectenerg-1427	967	141	b	b	NOUN
fuelectenerg-1427	967	142	,	,	PUNCT
fuelectenerg-1427	967	143	)	)	PUNCT
fuelectenerg-1427	967	144	2	2	NUM
fuelectenerg-1427	967	145	(	(	PUNCT
fuelectenerg-1427	967	146	b	b	NOUN
fuelectenerg-1427	967	147	,	,	PUNCT
fuelectenerg-1427	967	148	)	)	PUNCT
fuelectenerg-1427	967	149	2	2	NUM
fuelectenerg-1427	967	150	(	(	PUNCT
fuelectenerg-1427	967	151	b	b	NOUN
fuelectenerg-1427	967	152	,	,	PUNCT
fuelectenerg-1427	967	153	)	)	PUNCT
fuelectenerg-1427	967	154	2	2	NUM
fuelectenerg-1427	967	155	(	(	PUNCT
fuelectenerg-1427	967	156	b	b	NOUN
fuelectenerg-1427	967	157	,	,	PUNCT
fuelectenerg-1427	967	158	)	)	PUNCT
fuelectenerg-1427	967	159	2	2	NUM
fuelectenerg-1427	967	160	(	(	PUNCT
fuelectenerg-1427	967	161	b	b	NOUN
fuelectenerg-1427	967	162	,	,	PUNCT
fuelectenerg-1427	967	163	)	)	PUNCT
fuelectenerg-1427	967	164	2	2	NUM
fuelectenerg-1427	967	165	(	(	PUNCT
fuelectenerg-1427	967	166	b	b	NOUN
fuelectenerg-1427	967	167	,	,	PUNCT
fuelectenerg-1427	967	168	)	)	PUNCT
fuelectenerg-1427	967	169	2	2	NUM
fuelectenerg-1427	967	170	(	(	PUNCT
fuelectenerg-1427	967	171	b	b	NOUN
fuelectenerg-1427	967	172	,	,	PUNCT
fuelectenerg-1427	967	173	)	)	PUNCT
fuelectenerg-1427	967	174	2	2	NUM
fuelectenerg-1427	967	175	(	(	PUNCT
fuelectenerg-1427	967	176	b	b	NOUN
fuelectenerg-1427	967	177	,	,	PUNCT
fuelectenerg-1427	967	178	)	)	PUNCT
fuelectenerg-1427	967	179	2	2	NUM
fuelectenerg-1427	967	180	(	(	PUNCT
fuelectenerg-1427	967	181	b	b	NOUN
fuelectenerg-1427	967	182	,	,	PUNCT
fuelectenerg-1427	967	183	)	)	PUNCT
fuelectenerg-1427	967	184	2	2	NUM
fuelectenerg-1427	967	185	(	(	PUNCT
fuelectenerg-1427	967	186	b	b	NOUN
fuelectenerg-1427	967	187	,	,	PUNCT
fuelectenerg-1427	967	188	)	)	PUNCT
fuelectenerg-1427	967	189	2	2	NUM
fuelectenerg-1427	967	190	(	(	PUNCT
fuelectenerg-1427	967	191	b	b	NOUN
fuelectenerg-1427	967	192	,	,	PUNCT
fuelectenerg-1427	967	193	)	)	PUNCT
fuelectenerg-1427	967	194	2	2	NUM
fuelectenerg-1427	967	195	b	b	PROPN
fuelectenerg-1427	967	196	,	,	PUNCT
fuelectenerg-1427	967	197	b	b	PROPN
fuelectenerg-1427	967	198	,	,	PUNCT
fuelectenerg-1427	967	199	b	b	PROPN
fuelectenerg-1427	967	200	,	,	PUNCT
fuelectenerg-1427	967	201	b	b	PROPN
fuelectenerg-1427	967	202	,	,	PUNCT
fuelectenerg-1427	967	203	b	b	PROPN
fuelectenerg-1427	967	204	,	,	PUNCT
fuelectenerg-1427	967	205	b	b	PROPN
fuelectenerg-1427	967	206	,	,	PUNCT
fuelectenerg-1427	967	207	b	b	PROPN
fuelectenerg-1427	967	208	,	,	PUNCT
fuelectenerg-1427	967	209	b	b	PROPN
fuelectenerg-1427	967	210	,	,	PUNCT
fuelectenerg-1427	967	211	b	b	PROPN
fuelectenerg-1427	967	212	,	,	PUNCT
fuelectenerg-1427	967	213	b	b	PROPN
fuelectenerg-1427	967	214	,	,	PUNCT
fuelectenerg-1427	967	215	b	b	PROPN
fuelectenerg-1427	967	216	,	,	PUNCT
fuelectenerg-1427	967	217	b	b	PROPN
fuelectenerg-1427	967	218	,	,	PUNCT
fuelectenerg-1427	967	219	b	b	PROPN
fuelectenerg-1427	967	220	,	,	PUNCT
fuelectenerg-1427	967	221	b	b	PROPN
fuelectenerg-1427	967	222	,	,	PUNCT
fuelectenerg-1427	967	223	b	b	PROPN
fuelectenerg-1427	967	224	,	,	PUNCT
fuelectenerg-1427	967	225	b	b	PROPN
fuelectenerg-1427	967	226	,	,	PUNCT
fuelectenerg-1427	967	227	b	b	PROPN
fuelectenerg-1427	967	228	,	,	PUNCT
fuelectenerg-1427	967	229	b	b	PROPN
fuelectenerg-1427	967	230	,	,	PUNCT
fuelectenerg-1427	967	231	b	b	PROPN
fuelectenerg-1427	967	232	,	,	PUNCT
fuelectenerg-1427	967	233	b	b	PROPN
fuelectenerg-1427	967	234	,	,	PUNCT
fuelectenerg-1427	967	235	b	b	PROPN
fuelectenerg-1427	967	236	,	,	PUNCT
fuelectenerg-1427	967	237	b	b	PROPN
fuelectenerg-1427	967	238	,	,	PUNCT
fuelectenerg-1427	967	239	b	b	NOUN
fuelectenerg-1427	967	240	,	,	PUNCT
fuelectenerg-1427	967	241	s	s	NOUN
fuelectenerg-1427	967	242	s	s	X
fuelectenerg-1427	967	243	d	d	X
fuelectenerg-1427	967	244	d	d	X
fuelectenerg-1427	967	245	s	s	X
fuelectenerg-1427	967	246	s	s	X
fuelectenerg-1427	967	247	d	d	X
fuelectenerg-1427	967	248	d	d	SYM
fuelectenerg-1427	967	249	1	1	NUM
fuelectenerg-1427	967	250	(	(	PUNCT
fuelectenerg-1427	967	251	a	a	PRON
fuelectenerg-1427	967	252	,	,	PUNCT
fuelectenerg-1427	967	253	)	)	PUNCT
fuelectenerg-1427	967	254	2	2	NUM
fuelectenerg-1427	967	255	a	a	NOUN
fuelectenerg-1427	967	256	,	,	PUNCT
fuelectenerg-1427	967	257	sd	sd	ADP
fuelectenerg-1427	967	258	d	d	PROPN
fuelectenerg-1427	967	259	d	d	PROPN
fuelectenerg-1427	967	260	1	1	NUM
fuelectenerg-1427	967	261	(	(	PUNCT
fuelectenerg-1427	967	262	a	a	PRON
fuelectenerg-1427	967	263	,	,	PUNCT
fuelectenerg-1427	967	264	)	)	PUNCT
fuelectenerg-1427	967	265	2	2	NUM
fuelectenerg-1427	967	266	a	a	PRON
fuelectenerg-1427	967	267	,	,	PUNCT
fuelectenerg-1427	967	268	s	s	X
fuelectenerg-1427	967	269	s	s	NOUN
fuelectenerg-1427	967	270	s	s	NOUN
fuelectenerg-1427	967	271	0	0	NUM
fuelectenerg-1427	967	272	b	b	NOUN
fuelectenerg-1427	967	273	0	0	NUM
fuelectenerg-1427	968	1	b	b	NOUN
fuelectenerg-1427	968	2	0	0	NUM
fuelectenerg-1427	968	3	b	b	NOUN
fuelectenerg-1427	968	4	0	0	NUM
fuelectenerg-1427	968	5	b	b	NOUN
fuelectenerg-1427	968	6	0	0	NUM
fuelectenerg-1427	968	7	b	b	NOUN
fuelectenerg-1427	968	8	0	0	NUM
fuelectenerg-1427	968	9	b	b	NOUN
fuelectenerg-1427	968	10	0	0	NUM
fuelectenerg-1427	968	11	b	b	NOUN
fuelectenerg-1427	968	12	0	0	NUM
fuelectenerg-1427	968	13	b	b	NOUN
fuelectenerg-1427	968	14	0	0	NUM
fuelectenerg-1427	968	15	b	b	NOUN
fuelectenerg-1427	968	16	0	0	NUM
fuelectenerg-1427	968	17	b	b	NOUN
fuelectenerg-1427	968	18	0	0	NUM
fuelectenerg-1427	968	19	b	b	NOUN
fuelectenerg-1427	968	20	0	0	NUM
fuelectenerg-1427	968	21	b	b	NOUN
fuelectenerg-1427	968	22	0	0	NUM
fuelectenerg-1427	968	23	b	b	NOUN
fuelectenerg-1427	968	24	0	0	NUM
fuelectenerg-1427	968	25	b	b	NOUN
fuelectenerg-1427	968	26	0	0	NUM
fuelectenerg-1427	968	27	b	b	NOUN
fuelectenerg-1427	968	28	0	0	NUM
fuelectenerg-1427	968	29	b0	b0	NOUN
fuelectenerg-1427	968	30	b	b	PROPN
fuelectenerg-1427	968	31	0	0	NUM
fuelectenerg-1427	968	32	b	b	PROPN
fuelectenerg-1427	968	33	0	0	NUM
fuelectenerg-1427	968	34	b	b	SYM
fuelectenerg-1427	968	35	1	1	NUM
fuelectenerg-1427	968	36	b	b	SYM
fuelectenerg-1427	968	37	1	1	NUM
fuelectenerg-1427	968	38	b	b	SYM
fuelectenerg-1427	968	39	1	1	NUM
fuelectenerg-1427	968	40	b	b	SYM
fuelectenerg-1427	968	41	1	1	NUM
fuelectenerg-1427	968	42	b	b	SYM
fuelectenerg-1427	968	43	1	1	NUM
fuelectenerg-1427	968	44	b	b	SYM
fuelectenerg-1427	968	45	1	1	NUM
fuelectenerg-1427	968	46	b	b	SYM
fuelectenerg-1427	968	47	1	1	NUM
fuelectenerg-1427	968	48	b	b	SYM
fuelectenerg-1427	968	49	1	1	NUM
fuelectenerg-1427	968	50	b	b	SYM
fuelectenerg-1427	968	51	1	1	NUM
fuelectenerg-1427	968	52	b	b	SYM
fuelectenerg-1427	968	53	1	1	NUM
fuelectenerg-1427	968	54	b	b	SYM
fuelectenerg-1427	968	55	1	1	NUM
fuelectenerg-1427	968	56	b	b	SYM
fuelectenerg-1427	968	57	1	1	NUM
fuelectenerg-1427	968	58	b	b	SYM
fuelectenerg-1427	968	59	1	1	NUM
fuelectenerg-1427	968	60	b	b	SYM
fuelectenerg-1427	968	61	1	1	NUM
fuelectenerg-1427	968	62	b	b	SYM
fuelectenerg-1427	968	63	1	1	NUM
fuelectenerg-1427	968	64	b	b	SYM
fuelectenerg-1427	968	65	1	1	NUM
fuelectenerg-1427	968	66	b1	b1	NOUN
fuelectenerg-1427	968	67	b	b	NOUN
fuelectenerg-1427	968	68	1	1	NUM
fuelectenerg-1427	968	69	b	b	SYM
fuelectenerg-1427	968	70	1	1	NUM
fuelectenerg-1427	968	71	b	b	SYM
fuelectenerg-1427	968	72	2	2	NUM
fuelectenerg-1427	968	73	b	b	SYM
fuelectenerg-1427	968	74	2	2	NUM
fuelectenerg-1427	968	75	b	b	SYM
fuelectenerg-1427	968	76	2	2	NUM
fuelectenerg-1427	968	77	b	b	SYM
fuelectenerg-1427	968	78	2	2	NUM
fuelectenerg-1427	968	79	b	b	SYM
fuelectenerg-1427	968	80	2	2	NUM
fuelectenerg-1427	968	81	b	b	SYM
fuelectenerg-1427	968	82	2	2	NUM
fuelectenerg-1427	968	83	b	b	SYM
fuelectenerg-1427	968	84	2	2	NUM
fuelectenerg-1427	968	85	b	b	SYM
fuelectenerg-1427	968	86	2	2	NUM
fuelectenerg-1427	968	87	b	b	SYM
fuelectenerg-1427	968	88	2	2	NUM
fuelectenerg-1427	968	89	b	b	SYM
fuelectenerg-1427	968	90	2	2	NUM
fuelectenerg-1427	968	91	b	b	SYM
fuelectenerg-1427	968	92	2	2	NUM
fuelectenerg-1427	968	93	b	b	SYM
fuelectenerg-1427	968	94	2	2	NUM
fuelectenerg-1427	968	95	b	b	SYM
fuelectenerg-1427	968	96	2	2	NUM
fuelectenerg-1427	968	97	b	b	SYM
fuelectenerg-1427	968	98	2	2	NUM
fuelectenerg-1427	968	99	b	b	SYM
fuelectenerg-1427	968	100	2	2	NUM
fuelectenerg-1427	968	101	b	b	SYM
fuelectenerg-1427	968	102	2	2	NUM
fuelectenerg-1427	968	103	b2	b2	NOUN
fuelectenerg-1427	968	104	b	b	NOUN
fuelectenerg-1427	968	105	2	2	NUM
fuelectenerg-1427	968	106	b	b	SYM
fuelectenerg-1427	968	107	2	2	NUM
fuelectenerg-1427	968	108	b	b	NOUN
fuelectenerg-1427	968	109	d	d	PROPN
fuelectenerg-1427	968	110	1	1	NUM
fuelectenerg-1427	968	111	b	b	PROPN
fuelectenerg-1427	968	112	,	,	PUNCT
fuelectenerg-1427	968	113	s	s	PART
fuelectenerg-1427	968	114	sd	sd	NOUN
fuelectenerg-1427	968	115	d	d	PROPN
fuelectenerg-1427	968	116	s	s	X
fuelectenerg-1427	968	117	s	s	X
fuelectenerg-1427	968	118	s	s	X
fuelectenerg-1427	968	119	sd	sd	NOUN
fuelectenerg-1427	968	120	d	d	NOUN
fuelectenerg-1427	968	121	1	1	NUM
fuelectenerg-1427	968	122	(	(	PUNCT
fuelectenerg-1427	968	123	a	a	PRON
fuelectenerg-1427	968	124	,	,	PUNCT
fuelectenerg-1427	968	125	)	)	PUNCT
fuelectenerg-1427	968	126	2	2	NUM
fuelectenerg-1427	968	127	a	a	PRON
fuelectenerg-1427	968	128	,	,	PUNCT
fuelectenerg-1427	968	129	d	d	PROPN
fuelectenerg-1427	968	130	d	d	PROPN
fuelectenerg-1427	968	131	d	d	PROPN
fuelectenerg-1427	968	132	d	d	PROPN
fuelectenerg-1427	968	133	1	1	NUM
fuelectenerg-1427	968	134	(	(	PUNCT
fuelectenerg-1427	968	135	a	a	PRON
fuelectenerg-1427	968	136	,	,	PUNCT
fuelectenerg-1427	968	137	)	)	PUNCT
fuelectenerg-1427	968	138	2	2	NUM
fuelectenerg-1427	968	139	a	a	PRON
fuelectenerg-1427	968	140	,	,	PUNCT
fuelectenerg-1427	968	141	s	s	X
fuelectenerg-1427	968	142	s	s	NOUN
fuelectenerg-1427	968	143	s	s	X
fuelectenerg-1427	968	144	d	d	X
fuelectenerg-1427	968	145	s	s	X
fuelectenerg-1427	968	146	d	d	X
fuelectenerg-1427	968	147	dd	dd	NOUN
fuelectenerg-1427	968	148	d	d	PROPN
fuelectenerg-1427	968	149	d	d	PROPN
fuelectenerg-1427	968	150	1	1	NUM
fuelectenerg-1427	968	151	(	(	PUNCT
fuelectenerg-1427	968	152	a	a	PRON
fuelectenerg-1427	968	153	,	,	PUNCT
fuelectenerg-1427	968	154	)	)	PUNCT
fuelectenerg-1427	968	155	2	2	NUM
fuelectenerg-1427	968	156	a	a	PRON
fuelectenerg-1427	968	157	,	,	PUNCT
fuelectenerg-1427	968	158	s	s	NOUN
fuelectenerg-1427	968	159	d0	d0	NOUN
fuelectenerg-1427	968	160	d1	d1	PROPN
fuelectenerg-1427	968	161	d	d	X
fuelectenerg-1427	968	162	1	1	NUM
fuelectenerg-1427	968	163	(	(	PUNCT
fuelectenerg-1427	968	164	a	a	PRON
fuelectenerg-1427	968	165	,	,	PUNCT
fuelectenerg-1427	968	166	)	)	PUNCT
fuelectenerg-1427	968	167	2	2	NUM
fuelectenerg-1427	968	168	a	a	PRON
fuelectenerg-1427	968	169	,	,	PUNCT
fuelectenerg-1427	968	170	n=1	n=1	PROPN
fuelectenerg-1427	968	171	n=81	n=81	PRON
fuelectenerg-1427	968	172	n=729	n=729	PROPN
fuelectenerg-1427	968	173	n=59049	n=59049	PROPN
fuelectenerg-1427	968	174	n=9	n=9	PROPN
fuelectenerg-1427	968	175	n=81	n=81	VERB
fuelectenerg-1427	968	176	n=6561	n=6561	PROPN
fuelectenerg-1427	968	177	n=59049	n=59049	PROPN
fuelectenerg-1427	968	178	n=9	n=9	PROPN
fuelectenerg-1427	968	179	n=81	n=81	ADP
fuelectenerg-1427	968	180	n=6561	n=6561	PROPN
fuelectenerg-1427	968	181	n=59049	n=59049	PROPN
fuelectenerg-1427	968	182	n=9	n=9	PROPN
fuelectenerg-1427	968	183	n=729	n=729	X
fuelectenerg-1427	968	184	n=6561	n=6561	PROPN
fuelectenerg-1427	969	1	n=531441	n=531441	ADV
fuelectenerg-1427	969	2	0	0	PUNCT
fuelectenerg-1427	970	1	a	a	DET
fuelectenerg-1427	970	2	0	0	NUM
fuelectenerg-1427	970	3	a	a	DET
fuelectenerg-1427	970	4	0	0	NUM
fuelectenerg-1427	970	5	b	b	NOUN
fuelectenerg-1427	970	6	0	0	NUM
fuelectenerg-1427	970	7	b	b	NOUN
fuelectenerg-1427	970	8	0	0	NUM
fuelectenerg-1427	970	9	a	a	DET
fuelectenerg-1427	970	10	0	0	NUM
fuelectenerg-1427	970	11	a	a	DET
fuelectenerg-1427	970	12	0	0	NUM
fuelectenerg-1427	970	13	a	a	DET
fuelectenerg-1427	970	14	0	0	NUM
fuelectenerg-1427	970	15	a	a	DET
fuelectenerg-1427	970	16	0	0	NUM
fuelectenerg-1427	970	17	a	a	DET
fuelectenerg-1427	970	18	0	0	NUM
fuelectenerg-1427	970	19	a	a	DET
fuelectenerg-1427	970	20	1	1	NUM
fuelectenerg-1427	970	21	a	a	DET
fuelectenerg-1427	970	22	1	1	NUM
fuelectenerg-1427	970	23	a	a	DET
fuelectenerg-1427	970	24	1	1	NUM
fuelectenerg-1427	970	25	b	b	SYM
fuelectenerg-1427	970	26	1	1	NUM
fuelectenerg-1427	970	27	b	b	SYM
fuelectenerg-1427	970	28	1	1	NUM
fuelectenerg-1427	970	29	a	a	DET
fuelectenerg-1427	970	30	1	1	NUM
fuelectenerg-1427	970	31	a	a	DET
fuelectenerg-1427	970	32	1	1	NUM
fuelectenerg-1427	970	33	a	a	DET
fuelectenerg-1427	970	34	1	1	NUM
fuelectenerg-1427	970	35	a	a	DET
fuelectenerg-1427	970	36	1	1	NUM
fuelectenerg-1427	970	37	a	a	DET
fuelectenerg-1427	970	38	1	1	NUM
fuelectenerg-1427	970	39	a	a	DET
fuelectenerg-1427	970	40	2	2	NUM
fuelectenerg-1427	970	41	a	a	DET
fuelectenerg-1427	970	42	2	2	NUM
fuelectenerg-1427	970	43	a	a	DET
fuelectenerg-1427	970	44	2	2	NUM
fuelectenerg-1427	970	45	b	b	SYM
fuelectenerg-1427	970	46	2	2	NUM
fuelectenerg-1427	970	47	b	b	SYM
fuelectenerg-1427	970	48	2	2	NUM
fuelectenerg-1427	970	49	a	a	DET
fuelectenerg-1427	970	50	2	2	NUM
fuelectenerg-1427	970	51	a	a	DET
fuelectenerg-1427	970	52	2	2	NUM
fuelectenerg-1427	970	53	a	a	DET
fuelectenerg-1427	970	54	2	2	NUM
fuelectenerg-1427	970	55	a	a	DET
fuelectenerg-1427	970	56	2	2	NUM
fuelectenerg-1427	970	57	a	a	DET
fuelectenerg-1427	970	58	2	2	NUM
fuelectenerg-1427	970	59	a	a	DET
fuelectenerg-1427	970	60	(	(	PUNCT
fuelectenerg-1427	970	61	a	a	PRON
fuelectenerg-1427	970	62	)	)	PUNCT
fuelectenerg-1427	970	63	figure	figure	NOUN
fuelectenerg-1427	970	64	5	5	NUM
fuelectenerg-1427	970	65	:	:	PUNCT
fuelectenerg-1427	970	66	ternary	ternary	ADJ
fuelectenerg-1427	970	67	if	if	SCONJ
fuelectenerg-1427	970	68	(	(	PUNCT
fuelectenerg-1427	970	69	tif	tif	PROPN
fuelectenerg-1427	970	70	)	)	PUNCT
fuelectenerg-1427	970	71	s	s	PROPN
fuelectenerg-1427	970	72	/	/	SYM
fuelectenerg-1427	970	73	d	d	NOUN
fuelectenerg-1427	970	74	trees	tree	NOUN
fuelectenerg-1427	970	75	and	and	CCONJ
fuelectenerg-1427	970	76	their	their	PRON
fuelectenerg-1427	970	77	numbers	number	NOUN
fuelectenerg-1427	970	78	:	:	PUNCT
fuelectenerg-1427	970	79	(	(	PUNCT
fuelectenerg-1427	970	80	a	a	X
fuelectenerg-1427	970	81	)	)	PUNCT
fuelectenerg-1427	970	82	2	2	NUM
fuelectenerg-1427	970	83	-	-	PUNCT
fuelectenerg-1427	970	84	variable	variable	ADJ
fuelectenerg-1427	970	85	order	order	NOUN
fuelectenerg-1427	970	86	{	{	PUNCT
fuelectenerg-1427	970	87	a	a	DET
fuelectenerg-1427	970	88	,	,	PUNCT
fuelectenerg-1427	970	89	b	b	NOUN
fuelectenerg-1427	970	90	}	}	PUNCT
fuelectenerg-1427	970	91	and	and	CCONJ
fuelectenerg-1427	970	92	(	(	PUNCT
fuelectenerg-1427	970	93	b	b	X
fuelectenerg-1427	970	94	)	)	PUNCT
fuelectenerg-1427	970	95	2variable	2variable	NUM
fuelectenerg-1427	970	96	order	order	NOUN
fuelectenerg-1427	970	97	{	{	PUNCT
fuelectenerg-1427	970	98	b	b	NOUN
fuelectenerg-1427	970	99	,	,	PUNCT
fuelectenerg-1427	970	100	a	a	PRON
fuelectenerg-1427	970	101	}	}	PUNCT
fuelectenerg-1427	970	102	.	.	PUNCT
fuelectenerg-1427	971	1	variables	variable	NOUN
fuelectenerg-1427	971	2	{	{	PUNCT
fuelectenerg-1427	971	3	a	a	DET
fuelectenerg-1427	971	4	,	,	PUNCT
fuelectenerg-1427	971	5	b	b	NOUN
fuelectenerg-1427	971	6	}	}	PUNCT
fuelectenerg-1427	971	7	are	be	AUX
fuelectenerg-1427	971	8	defined	define	VERB
fuelectenerg-1427	971	9	as	as	ADP
fuelectenerg-1427	971	10	in	in	ADP
fuelectenerg-1427	971	11	eq	eq	ADP
fuelectenerg-1427	971	12	.	.	PUNCT
fuelectenerg-1427	972	1	(	(	PUNCT
fuelectenerg-1427	972	2	28	28	NUM
fuelectenerg-1427	972	3	)	)	PUNCT
fuelectenerg-1427	972	4	for	for	ADP
fuelectenerg-1427	972	5	generalized	generalized	ADJ
fuelectenerg-1427	972	6	davio	davio	NOUN
fuelectenerg-1427	972	7	(	(	PUNCT
fuelectenerg-1427	972	8	d	d	NOUN
fuelectenerg-1427	972	9	)	)	PUNCT
fuelectenerg-1427	972	10	where	where	SCONJ
fuelectenerg-1427	972	11	in	in	ADP
fuelectenerg-1427	972	12	this	this	DET
fuelectenerg-1427	972	13	figure	figure	NOUN
fuelectenerg-1427	972	14	(	(	PUNCT
fuelectenerg-1427	972	15	a,≡	a,≡	NOUN
fuelectenerg-1427	972	16	a	a	X
fuelectenerg-1427	972	17	)	)	PUNCT
fuelectenerg-1427	972	18	and	and	CCONJ
fuelectenerg-1427	972	19	(	(	PUNCT
fuelectenerg-1427	972	20	b,≡	b,≡	X
fuelectenerg-1427	972	21	b	b	X
fuelectenerg-1427	972	22	)	)	PUNCT
fuelectenerg-1427	972	23	.	.	PUNCT
fuelectenerg-1427	973	1	theorem	theorem	NOUN
fuelectenerg-1427	973	2	2	2	NUM
fuelectenerg-1427	973	3	.	.	PUNCT
fuelectenerg-1427	974	1	the	the	DET
fuelectenerg-1427	974	2	total	total	ADJ
fuelectenerg-1427	974	3	number	number	NOUN
fuelectenerg-1427	974	4	of	of	ADP
fuelectenerg-1427	974	5	the	the	DET
fuelectenerg-1427	974	6	ternary	ternary	ADJ
fuelectenerg-1427	974	7	ifs	ifs	PROPN
fuelectenerg-1427	974	8	,	,	PUNCT
fuelectenerg-1427	974	9	for	for	ADP
fuelectenerg-1427	974	10	two	two	NUM
fuelectenerg-1427	974	11	variables	variable	NOUN
fuelectenerg-1427	974	12	and	and	CCONJ
fuelectenerg-1427	974	13	for	for	ADP
fuelectenerg-1427	974	14	orders	order	NOUN
fuelectenerg-1427	974	15	{	{	PUNCT
fuelectenerg-1427	974	16	a	a	DET
fuelectenerg-1427	974	17	,	,	PUNCT
fuelectenerg-1427	974	18	b	b	NOUN
fuelectenerg-1427	974	19	}	}	PUNCT
fuelectenerg-1427	974	20	and	and	CCONJ
fuelectenerg-1427	974	21	{	{	PUNCT
fuelectenerg-1427	974	22	b	b	NOUN
fuelectenerg-1427	974	23	,	,	PUNCT
fuelectenerg-1427	974	24	a	a	PRON
fuelectenerg-1427	974	25	}	}	PUNCT
fuelectenerg-1427	974	26	,	,	PUNCT
fuelectenerg-1427	974	27	and	and	CCONJ
fuelectenerg-1427	974	28	the	the	DET
fuelectenerg-1427	974	29	total	total	ADJ
fuelectenerg-1427	974	30	number	number	NOUN
fuelectenerg-1427	974	31	of	of	ADP
fuelectenerg-1427	974	32	ternary	ternary	ADJ
fuelectenerg-1427	974	33	generalized	generalize	VERB
fuelectenerg-1427	974	34	ifs	ifs	PROPN
fuelectenerg-1427	974	35	,	,	PUNCT
fuelectenerg-1427	974	36	for	for	ADP
fuelectenerg-1427	974	37	two	two	NUM
fuelectenerg-1427	974	38	variables	variable	NOUN
fuelectenerg-1427	974	39	,	,	PUNCT
fuelectenerg-1427	974	40	are	be	AUX
fuelectenerg-1427	974	41	respectively	respectively	ADV
fuelectenerg-1427	974	42	:	:	PUNCT
fuelectenerg-1427	974	43	#	#	SYM
fuelectenerg-1427	974	44	tifa	tifa	NOUN
fuelectenerg-1427	974	45	,	,	PUNCT
fuelectenerg-1427	974	46	b	b	NOUN
fuelectenerg-1427	974	47	=	=	SYM
fuelectenerg-1427	974	48	1	1	NUM
fuelectenerg-1427	974	49	·	·	PUNCT
fuelectenerg-1427	974	50	(	(	PUNCT
fuelectenerg-1427	974	51	3)0	3)0	NUM
fuelectenerg-1427	974	52	+	+	CCONJ
fuelectenerg-1427	974	53	3	3	NUM
fuelectenerg-1427	974	54	·	·	PUNCT
fuelectenerg-1427	974	55	(	(	PUNCT
fuelectenerg-1427	974	56	3)2	3)2	NUM
fuelectenerg-1427	974	57	+	+	SYM
fuelectenerg-1427	974	58	3	3	NUM
fuelectenerg-1427	974	59	·	·	PUNCT
fuelectenerg-1427	974	60	(	(	PUNCT
fuelectenerg-1427	974	61	3)4	3)4	NUM
fuelectenerg-1427	974	62	+	+	NOUN
fuelectenerg-1427	974	63	2	2	NUM
fuelectenerg-1427	974	64	·	·	PUNCT
fuelectenerg-1427	974	65	(	(	PUNCT
fuelectenerg-1427	974	66	3)6	3)6	NUM
fuelectenerg-1427	974	67	+	+	SYM
fuelectenerg-1427	974	68	3	3	NUM
fuelectenerg-1427	974	69	·	·	PUNCT
fuelectenerg-1427	974	70	(	(	PUNCT
fuelectenerg-1427	974	71	3)8	3)8	NUM
fuelectenerg-1427	974	72	+	+	SYM
fuelectenerg-1427	974	73	3	3	NUM
fuelectenerg-1427	974	74	·	·	PUNCT
fuelectenerg-1427	974	75	(	(	PUNCT
fuelectenerg-1427	974	76	3)10	3)10	NUM
fuelectenerg-1427	974	77	+	+	ADJ
fuelectenerg-1427	974	78	1	1	NUM
fuelectenerg-1427	974	79	·	·	PUNCT
fuelectenerg-1427	974	80	(	(	PUNCT
fuelectenerg-1427	974	81	3)12	3)12	NUM
fuelectenerg-1427	974	82	=	=	SYM
fuelectenerg-1427	974	83	730,000	730,000	NUM
fuelectenerg-1427	974	84	,	,	PUNCT
fuelectenerg-1427	974	85	(	(	PUNCT
fuelectenerg-1427	974	86	33	33	NUM
fuelectenerg-1427	974	87	)	)	PUNCT
fuelectenerg-1427	974	88	#	#	SYM
fuelectenerg-1427	974	89	tifb	tifb	NOUN
fuelectenerg-1427	974	90	,	,	PUNCT
fuelectenerg-1427	974	91	a	a	DET
fuelectenerg-1427	974	92	=	=	SYM
fuelectenerg-1427	974	93	1	1	NUM
fuelectenerg-1427	974	94	·	·	PUNCT
fuelectenerg-1427	974	95	(	(	PUNCT
fuelectenerg-1427	974	96	3)0	3)0	NUM
fuelectenerg-1427	974	97	+	+	CCONJ
fuelectenerg-1427	974	98	3	3	NUM
fuelectenerg-1427	974	99	·	·	PUNCT
fuelectenerg-1427	974	100	(	(	PUNCT
fuelectenerg-1427	974	101	3)2	3)2	NUM
fuelectenerg-1427	974	102	+	+	SYM
fuelectenerg-1427	974	103	3	3	NUM
fuelectenerg-1427	974	104	·	·	PUNCT
fuelectenerg-1427	974	105	(	(	PUNCT
fuelectenerg-1427	974	106	3)4	3)4	NUM
fuelectenerg-1427	974	107	+	+	NOUN
fuelectenerg-1427	974	108	2	2	NUM
fuelectenerg-1427	974	109	·	·	PUNCT
fuelectenerg-1427	974	110	(	(	PUNCT
fuelectenerg-1427	974	111	3)6	3)6	NUM
fuelectenerg-1427	974	112	+	+	SYM
fuelectenerg-1427	974	113	3	3	NUM
fuelectenerg-1427	974	114	·	·	PUNCT
fuelectenerg-1427	974	115	(	(	PUNCT
fuelectenerg-1427	974	116	3)8	3)8	NUM
fuelectenerg-1427	974	117	+	+	SYM
fuelectenerg-1427	974	118	3	3	NUM
fuelectenerg-1427	974	119	·	·	PUNCT
fuelectenerg-1427	974	120	(	(	PUNCT
fuelectenerg-1427	974	121	3)10	3)10	NUM
fuelectenerg-1427	974	122	+	+	ADJ
fuelectenerg-1427	974	123	1	1	NUM
fuelectenerg-1427	974	124	·	·	PUNCT
fuelectenerg-1427	974	125	(	(	PUNCT
fuelectenerg-1427	974	126	3)12	3)12	NUM
fuelectenerg-1427	974	127	=	=	SYM
fuelectenerg-1427	974	128	730,000	730,000	NUM
fuelectenerg-1427	974	129	,	,	PUNCT
fuelectenerg-1427	974	130	(	(	PUNCT
fuelectenerg-1427	974	131	34	34	NUM
fuelectenerg-1427	974	132	)	)	PUNCT
fuelectenerg-1427	974	133	#	#	NOUN
fuelectenerg-1427	974	134	tgif	tgif	NOUN
fuelectenerg-1427	974	135	=	=	PUNCT
fuelectenerg-1427	974	136	#	#	NUM
fuelectenerg-1427	974	137	tifa	tifa	NOUN
fuelectenerg-1427	974	138	,	,	PUNCT
fuelectenerg-1427	974	139	b	b	NOUN
fuelectenerg-1427	974	140	+	+	CCONJ
fuelectenerg-1427	974	141	#	#	SYM
fuelectenerg-1427	974	142	tifb	tifb	NOUN
fuelectenerg-1427	974	143	,	,	PUNCT
fuelectenerg-1427	974	144	a−#(tifa	a−#(tifa	PROPN
fuelectenerg-1427	974	145	,	,	PUNCT
fuelectenerg-1427	974	146	b	b	NOUN
fuelectenerg-1427	974	147	∩tifb	∩tifb	NOUN
fuelectenerg-1427	974	148	,	,	PUNCT
fuelectenerg-1427	974	149	a	a	PRON
fuelectenerg-1427	974	150	)	)	PUNCT
fuelectenerg-1427	974	151	=	=	SYM
fuelectenerg-1427	974	152	2	2	NUM
fuelectenerg-1427	974	153	·	·	SYM
fuelectenerg-1427	974	154	#	#	NOUN
fuelectenerg-1427	974	155	tif−#(tifa	tif−#(tifa	NUM
fuelectenerg-1427	974	156	,	,	PUNCT
fuelectenerg-1427	974	157	b	b	NOUN
fuelectenerg-1427	974	158	∩tifb	∩tifb	NOUN
fuelectenerg-1427	974	159	,	,	PUNCT
fuelectenerg-1427	974	160	a	a	PRON
fuelectenerg-1427	974	161	)	)	PUNCT
fuelectenerg-1427	974	162	=	=	SYM
fuelectenerg-1427	974	163	2	2	NUM
fuelectenerg-1427	974	164	·	·	PUNCT
fuelectenerg-1427	974	165	(	(	PUNCT
fuelectenerg-1427	974	166	730,000)−	730,000)−	NUM
fuelectenerg-1427	974	167	(	(	PUNCT
fuelectenerg-1427	974	168	1	1	NUM
fuelectenerg-1427	974	169	·	·	PUNCT
fuelectenerg-1427	974	170	(	(	PUNCT
fuelectenerg-1427	974	171	3)0	3)0	NUM
fuelectenerg-1427	974	172	+	+	PROPN
fuelectenerg-1427	974	173	2	2	NUM
fuelectenerg-1427	974	174	·	·	PUNCT
fuelectenerg-1427	974	175	(	(	PUNCT
fuelectenerg-1427	974	176	3)6	3)6	NUM
fuelectenerg-1427	974	177	+	+	SYM
fuelectenerg-1427	974	178	1	1	NUM
fuelectenerg-1427	974	179	·	·	PUNCT
fuelectenerg-1427	974	180	(	(	PUNCT
fuelectenerg-1427	974	181	3)12	3)12	NUM
fuelectenerg-1427	974	182	)	)	PUNCT
fuelectenerg-1427	974	183	=	=	SYM
fuelectenerg-1427	975	1	927,100	927,100	NUM
fuelectenerg-1427	975	2	.	.	PUNCT
fuelectenerg-1427	976	1	(	(	PUNCT
fuelectenerg-1427	976	2	35	35	NUM
fuelectenerg-1427	976	3	)	)	PUNCT
fuelectenerg-1427	976	4	proof	proof	NOUN
fuelectenerg-1427	976	5	.	.	PUNCT
fuelectenerg-1427	977	1	by	by	ADP
fuelectenerg-1427	977	2	observing	observe	VERB
fuelectenerg-1427	977	3	figure	figure	NOUN
fuelectenerg-1427	977	4	5	5	NUM
fuelectenerg-1427	977	5	,	,	PUNCT
fuelectenerg-1427	977	6	we	we	PRON
fuelectenerg-1427	977	7	note	note	VERB
fuelectenerg-1427	977	8	that	that	SCONJ
fuelectenerg-1427	977	9	the	the	DET
fuelectenerg-1427	977	10	total	total	ADJ
fuelectenerg-1427	977	11	number	number	NOUN
fuelectenerg-1427	977	12	of	of	ADP
fuelectenerg-1427	977	13	tifs	tifs	PROPN
fuelectenerg-1427	977	14	for	for	ADP
fuelectenerg-1427	977	15	orders	order	NOUN
fuelectenerg-1427	977	16	{	{	PUNCT
fuelectenerg-1427	977	17	a	a	DET
fuelectenerg-1427	977	18	,	,	PUNCT
fuelectenerg-1427	977	19	b	b	NOUN
fuelectenerg-1427	977	20	}	}	PUNCT
fuelectenerg-1427	977	21	and	and	CCONJ
fuelectenerg-1427	977	22	{	{	PUNCT
fuelectenerg-1427	977	23	b	b	NOUN
fuelectenerg-1427	977	24	,	,	PUNCT
fuelectenerg-1427	977	25	a	a	PRON
fuelectenerg-1427	977	26	}	}	PUNCT
fuelectenerg-1427	977	27	is	be	AUX
fuelectenerg-1427	977	28	the	the	DET
fuelectenerg-1427	977	29	sum	sum	NOUN
fuelectenerg-1427	977	30	of	of	ADP
fuelectenerg-1427	977	31	the	the	DET
fuelectenerg-1427	977	32	numbers	number	NOUN
fuelectenerg-1427	977	33	on	on	ADP
fuelectenerg-1427	977	34	top	top	NOUN
fuelectenerg-1427	977	35	of	of	ADP
fuelectenerg-1427	977	36	s	s	PROPN
fuelectenerg-1427	977	37	/	/	SYM
fuelectenerg-1427	977	38	d	d	NOUN
fuelectenerg-1427	977	39	trees	tree	NOUN
fuelectenerg-1427	977	40	that	that	PRON
fuelectenerg-1427	977	41	leads	lead	VERB
fuelectenerg-1427	977	42	to	to	ADP
fuelectenerg-1427	977	43	equations	equation	NOUN
fuelectenerg-1427	977	44	(	(	PUNCT
fuelectenerg-1427	977	45	33	33	NUM
fuelectenerg-1427	977	46	)	)	PUNCT
fuelectenerg-1427	977	47	(	(	PUNCT
fuelectenerg-1427	977	48	35	35	NUM
fuelectenerg-1427	977	49	)	)	PUNCT
fuelectenerg-1427	977	50	,	,	PUNCT
fuelectenerg-1427	977	51	respectively	respectively	ADV
fuelectenerg-1427	977	52	.	.	PUNCT
fuelectenerg-1427	978	1	2.2	2.2	NUM
fuelectenerg-1427	978	2	properties	property	NOUN
fuelectenerg-1427	978	3	of	of	ADP
fuelectenerg-1427	978	4	tifs	tifs	PROPN
fuelectenerg-1427	978	5	and	and	CCONJ
fuelectenerg-1427	978	6	tgifs	tgif	VERB
fuelectenerg-1427	978	7	the	the	DET
fuelectenerg-1427	978	8	following	follow	VERB
fuelectenerg-1427	978	9	present	present	ADJ
fuelectenerg-1427	978	10	basic	basic	ADJ
fuelectenerg-1427	978	11	properties	property	NOUN
fuelectenerg-1427	978	12	of	of	ADP
fuelectenerg-1427	978	13	the	the	DET
fuelectenerg-1427	978	14	presented	present	VERB
fuelectenerg-1427	978	15	tifs	tifs	PROPN
fuelectenerg-1427	978	16	and	and	CCONJ
fuelectenerg-1427	978	17	tgifs	tgif	NOUN
fuelectenerg-1427	978	18	.	.	PUNCT
fuelectenerg-1427	978	19	theorem	theorem	NOUN
fuelectenerg-1427	978	20	3	3	NUM
fuelectenerg-1427	978	21	.	.	PUNCT
fuelectenerg-1427	979	1	each	each	DET
fuelectenerg-1427	979	2	ternary	ternary	ADJ
fuelectenerg-1427	979	3	inclusive	inclusive	ADJ
fuelectenerg-1427	979	4	form	form	NOUN
fuelectenerg-1427	979	5	(	(	PUNCT
fuelectenerg-1427	979	6	tif	tif	PROPN
fuelectenerg-1427	979	7	)	)	PUNCT
fuelectenerg-1427	979	8	is	be	AUX
fuelectenerg-1427	979	9	canonical	canonical	ADJ
fuelectenerg-1427	979	10	.	.	PUNCT
fuelectenerg-1427	980	1	110	110	NUM
fuelectenerg-1427	980	2	an	an	DET
fuelectenerg-1427	980	3	extended	extend	VERB
fuelectenerg-1427	980	4	green	green	ADJ
fuelectenerg-1427	980	5	sasao	sasao	PROPN
fuelectenerg-1427	980	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	980	7	of	of	ADP
fuelectenerg-1427	980	8	canonical	canonical	ADJ
fuelectenerg-1427	980	9	ternary	ternary	ADJ
fuelectenerg-1427	980	10	galois	galois	NOUN
fuelectenerg-1427	980	11	forms	form	NOUN
fuelectenerg-1427	980	12	...	...	PUNCT
fuelectenerg-1427	981	1	s	s	PART
fuelectenerg-1427	981	2	s	s	X
fuelectenerg-1427	981	3	s	s	X
fuelectenerg-1427	981	4	s	s	NOUN
fuelectenerg-1427	981	5	0	0	NUM
fuelectenerg-1427	981	6	b	b	SYM
fuelectenerg-1427	981	7	1	1	NUM
fuelectenerg-1427	981	8	b	b	SYM
fuelectenerg-1427	981	9	2	2	NUM
fuelectenerg-1427	981	10	b	b	NOUN
fuelectenerg-1427	981	11	s	s	X
fuelectenerg-1427	981	12	s	s	NOUN
fuelectenerg-1427	981	13	d	d	X
fuelectenerg-1427	981	14	d	d	X
fuelectenerg-1427	981	15	s	s	X
fuelectenerg-1427	981	16	s	s	X
fuelectenerg-1427	981	17	s	s	X
fuelectenerg-1427	981	18	d	d	NOUN
fuelectenerg-1427	981	19	1	1	NUM
fuelectenerg-1427	981	20	(	(	PUNCT
fuelectenerg-1427	981	21	a	a	PRON
fuelectenerg-1427	981	22	,	,	PUNCT
fuelectenerg-1427	981	23	)	)	PUNCT
fuelectenerg-1427	981	24	2	2	NUM
fuelectenerg-1427	981	25	a	a	PRON
fuelectenerg-1427	981	26	,	,	PUNCT
fuelectenerg-1427	981	27	s	s	NOUN
fuelectenerg-1427	981	28	d	d	X
fuelectenerg-1427	981	29	d	d	PROPN
fuelectenerg-1427	981	30	d	d	PROPN
fuelectenerg-1427	981	31	1	1	NUM
fuelectenerg-1427	981	32	(	(	PUNCT
fuelectenerg-1427	981	33	a	a	PRON
fuelectenerg-1427	981	34	,	,	PUNCT
fuelectenerg-1427	981	35	)	)	PUNCT
fuelectenerg-1427	981	36	2	2	NUM
fuelectenerg-1427	981	37	a	a	PRON
fuelectenerg-1427	981	38	,	,	PUNCT
fuelectenerg-1427	981	39	s	s	X
fuelectenerg-1427	981	40	s	s	NOUN
fuelectenerg-1427	981	41	s	s	NOUN
fuelectenerg-1427	981	42	0	0	NUM
fuelectenerg-1427	981	43	b	b	NOUN
fuelectenerg-1427	981	44	0	0	NUM
fuelectenerg-1427	981	45	b	b	SYM
fuelectenerg-1427	981	46	1	1	NUM
fuelectenerg-1427	981	47	b	b	SYM
fuelectenerg-1427	981	48	1	1	NUM
fuelectenerg-1427	981	49	b	b	SYM
fuelectenerg-1427	981	50	2	2	NUM
fuelectenerg-1427	981	51	b	b	SYM
fuelectenerg-1427	981	52	2	2	NUM
fuelectenerg-1427	981	53	b	b	NOUN
fuelectenerg-1427	981	54	d	d	SYM
fuelectenerg-1427	981	55	1	1	NUM
fuelectenerg-1427	981	56	1	1	NUM
fuelectenerg-1427	981	57	1	1	NUM
fuelectenerg-1427	981	58	1	1	NUM
fuelectenerg-1427	981	59	1	1	NUM
fuelectenerg-1427	981	60	1	1	NUM
fuelectenerg-1427	981	61	1	1	NUM
fuelectenerg-1427	981	62	1	1	NUM
fuelectenerg-1427	981	63	1	1	NUM
fuelectenerg-1427	981	64	1	1	NUM
fuelectenerg-1427	981	65	11	11	NUM
fuelectenerg-1427	981	66	1	1	NUM
fuelectenerg-1427	981	67	1	1	NUM
fuelectenerg-1427	981	68	1	1	NUM
fuelectenerg-1427	981	69	1	1	NUM
fuelectenerg-1427	981	70	1	1	NUM
fuelectenerg-1427	981	71	1	1	NUM
fuelectenerg-1427	981	72	1	1	NUM
fuelectenerg-1427	981	73	1	1	NUM
fuelectenerg-1427	981	74	1	1	NUM
fuelectenerg-1427	981	75	1	1	NUM
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fuelectenerg-1427	981	79	2	2	NUM
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fuelectenerg-1427	981	81	b	b	NOUN
fuelectenerg-1427	981	82	,	,	PUNCT
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fuelectenerg-1427	981	84	2	2	NUM
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fuelectenerg-1427	981	86	b	b	NOUN
fuelectenerg-1427	981	87	,	,	PUNCT
fuelectenerg-1427	981	88	)	)	PUNCT
fuelectenerg-1427	981	89	2	2	NUM
fuelectenerg-1427	981	90	(	(	PUNCT
fuelectenerg-1427	981	91	b	b	NOUN
fuelectenerg-1427	981	92	,	,	PUNCT
fuelectenerg-1427	981	93	)	)	PUNCT
fuelectenerg-1427	981	94	2	2	NUM
fuelectenerg-1427	981	95	(	(	PUNCT
fuelectenerg-1427	981	96	b	b	NOUN
fuelectenerg-1427	981	97	,	,	PUNCT
fuelectenerg-1427	981	98	)	)	PUNCT
fuelectenerg-1427	981	99	2	2	NUM
fuelectenerg-1427	981	100	(	(	PUNCT
fuelectenerg-1427	981	101	b	b	NOUN
fuelectenerg-1427	981	102	,	,	PUNCT
fuelectenerg-1427	981	103	)	)	PUNCT
fuelectenerg-1427	981	104	2	2	NUM
fuelectenerg-1427	981	105	(	(	PUNCT
fuelectenerg-1427	981	106	b	b	NOUN
fuelectenerg-1427	981	107	,	,	PUNCT
fuelectenerg-1427	981	108	)	)	PUNCT
fuelectenerg-1427	981	109	2	2	NUM
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fuelectenerg-1427	981	114	2	2	NUM
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fuelectenerg-1427	981	119	2	2	NUM
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fuelectenerg-1427	981	121	b	b	NOUN
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fuelectenerg-1427	981	124	2	2	NUM
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fuelectenerg-1427	981	126	b	b	NOUN
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fuelectenerg-1427	981	129	2	2	NUM
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fuelectenerg-1427	981	131	b	b	NOUN
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fuelectenerg-1427	981	134	2	2	NUM
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fuelectenerg-1427	981	139	2	2	NUM
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fuelectenerg-1427	981	144	2	2	NUM
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fuelectenerg-1427	981	149	2	2	NUM
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fuelectenerg-1427	981	154	2	2	NUM
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fuelectenerg-1427	981	156	b	b	NOUN
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fuelectenerg-1427	981	158	)	)	PUNCT
fuelectenerg-1427	981	159	2	2	NUM
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fuelectenerg-1427	981	164	2	2	NUM
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fuelectenerg-1427	981	166	b	b	NOUN
fuelectenerg-1427	981	167	,	,	PUNCT
fuelectenerg-1427	981	168	)	)	PUNCT
fuelectenerg-1427	981	169	2	2	NUM
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fuelectenerg-1427	981	171	b	b	NOUN
fuelectenerg-1427	981	172	,	,	PUNCT
fuelectenerg-1427	981	173	)	)	PUNCT
fuelectenerg-1427	981	174	2	2	NUM
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fuelectenerg-1427	981	177	,	,	PUNCT
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fuelectenerg-1427	981	179	2	2	NUM
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fuelectenerg-1427	981	184	2	2	NUM
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fuelectenerg-1427	981	189	2	2	NUM
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fuelectenerg-1427	981	224	,	,	PUNCT
fuelectenerg-1427	981	225	b	b	PROPN
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fuelectenerg-1427	982	23	b	b	NOUN
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fuelectenerg-1427	982	25	b	b	NOUN
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fuelectenerg-1427	982	34	b	b	SYM
fuelectenerg-1427	982	35	1	1	NUM
fuelectenerg-1427	982	36	b	b	SYM
fuelectenerg-1427	982	37	1	1	NUM
fuelectenerg-1427	982	38	b	b	SYM
fuelectenerg-1427	982	39	1	1	NUM
fuelectenerg-1427	982	40	b	b	SYM
fuelectenerg-1427	982	41	1	1	NUM
fuelectenerg-1427	982	42	b	b	SYM
fuelectenerg-1427	982	43	1	1	NUM
fuelectenerg-1427	982	44	b	b	SYM
fuelectenerg-1427	982	45	1	1	NUM
fuelectenerg-1427	982	46	b	b	SYM
fuelectenerg-1427	982	47	1	1	NUM
fuelectenerg-1427	982	48	b	b	SYM
fuelectenerg-1427	982	49	1	1	NUM
fuelectenerg-1427	982	50	b	b	SYM
fuelectenerg-1427	982	51	1	1	NUM
fuelectenerg-1427	982	52	b	b	SYM
fuelectenerg-1427	982	53	1	1	NUM
fuelectenerg-1427	982	54	b	b	SYM
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fuelectenerg-1427	982	56	b	b	SYM
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fuelectenerg-1427	982	58	b	b	SYM
fuelectenerg-1427	982	59	1	1	NUM
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fuelectenerg-1427	982	126	2	2	NUM
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fuelectenerg-1427	982	140	,	,	PUNCT
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fuelectenerg-1427	982	147	dd	dd	NOUN
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fuelectenerg-1427	982	169	,	,	PUNCT
fuelectenerg-1427	982	170	n=1	n=1	PROPN
fuelectenerg-1427	982	171	n=81	n=81	PRON
fuelectenerg-1427	982	172	n=729	n=729	PROPN
fuelectenerg-1427	982	173	n=59049	n=59049	PROPN
fuelectenerg-1427	982	174	n=9	n=9	PROPN
fuelectenerg-1427	982	175	n=81	n=81	VERB
fuelectenerg-1427	982	176	n=6561	n=6561	PROPN
fuelectenerg-1427	982	177	n=59049	n=59049	PROPN
fuelectenerg-1427	982	178	n=9	n=9	PROPN
fuelectenerg-1427	982	179	n=81	n=81	ADP
fuelectenerg-1427	982	180	n=6561	n=6561	PROPN
fuelectenerg-1427	982	181	n=59049	n=59049	PROPN
fuelectenerg-1427	982	182	n=9	n=9	PROPN
fuelectenerg-1427	982	183	n=729	n=729	X
fuelectenerg-1427	982	184	n=6561	n=6561	PROPN
fuelectenerg-1427	983	1	n=531441	n=531441	ADV
fuelectenerg-1427	983	2	0	0	PUNCT
fuelectenerg-1427	984	1	a	a	DET
fuelectenerg-1427	984	2	0	0	NUM
fuelectenerg-1427	984	3	a	a	DET
fuelectenerg-1427	984	4	0	0	NUM
fuelectenerg-1427	984	5	b	b	NOUN
fuelectenerg-1427	984	6	0	0	NUM
fuelectenerg-1427	984	7	b	b	NOUN
fuelectenerg-1427	984	8	0	0	NUM
fuelectenerg-1427	984	9	a	a	DET
fuelectenerg-1427	984	10	0	0	NUM
fuelectenerg-1427	984	11	a	a	DET
fuelectenerg-1427	984	12	0	0	NUM
fuelectenerg-1427	984	13	a	a	DET
fuelectenerg-1427	984	14	0	0	NUM
fuelectenerg-1427	984	15	a	a	DET
fuelectenerg-1427	984	16	0	0	NUM
fuelectenerg-1427	984	17	a	a	DET
fuelectenerg-1427	984	18	0	0	NUM
fuelectenerg-1427	984	19	a	a	DET
fuelectenerg-1427	984	20	1	1	NUM
fuelectenerg-1427	984	21	a	a	DET
fuelectenerg-1427	984	22	1	1	NUM
fuelectenerg-1427	984	23	a	a	DET
fuelectenerg-1427	984	24	1	1	NUM
fuelectenerg-1427	984	25	b	b	SYM
fuelectenerg-1427	984	26	1	1	NUM
fuelectenerg-1427	984	27	b	b	SYM
fuelectenerg-1427	984	28	1	1	NUM
fuelectenerg-1427	984	29	a	a	DET
fuelectenerg-1427	984	30	1	1	NUM
fuelectenerg-1427	984	31	a	a	DET
fuelectenerg-1427	984	32	1	1	NUM
fuelectenerg-1427	984	33	a	a	DET
fuelectenerg-1427	984	34	1	1	NUM
fuelectenerg-1427	984	35	a	a	DET
fuelectenerg-1427	984	36	1	1	NUM
fuelectenerg-1427	984	37	a	a	DET
fuelectenerg-1427	984	38	1	1	NUM
fuelectenerg-1427	984	39	a	a	DET
fuelectenerg-1427	984	40	2	2	NUM
fuelectenerg-1427	984	41	a	a	DET
fuelectenerg-1427	984	42	2	2	NUM
fuelectenerg-1427	984	43	a	a	DET
fuelectenerg-1427	984	44	2	2	NUM
fuelectenerg-1427	984	45	b	b	SYM
fuelectenerg-1427	984	46	2	2	NUM
fuelectenerg-1427	984	47	b	b	SYM
fuelectenerg-1427	984	48	2	2	NUM
fuelectenerg-1427	984	49	a	a	DET
fuelectenerg-1427	984	50	2	2	NUM
fuelectenerg-1427	984	51	a	a	DET
fuelectenerg-1427	984	52	2	2	NUM
fuelectenerg-1427	984	53	a	a	DET
fuelectenerg-1427	984	54	2	2	NUM
fuelectenerg-1427	984	55	a	a	DET
fuelectenerg-1427	984	56	2	2	NUM
fuelectenerg-1427	984	57	a	a	DET
fuelectenerg-1427	984	58	2	2	NUM
fuelectenerg-1427	984	59	a	a	DET
fuelectenerg-1427	984	60	(	(	PUNCT
fuelectenerg-1427	984	61	a	a	PRON
fuelectenerg-1427	984	62	)	)	PUNCT
fuelectenerg-1427	984	63	figure	figure	NOUN
fuelectenerg-1427	984	64	5	5	NUM
fuelectenerg-1427	984	65	:	:	PUNCT
fuelectenerg-1427	984	66	ternary	ternary	ADJ
fuelectenerg-1427	984	67	if	if	SCONJ
fuelectenerg-1427	984	68	(	(	PUNCT
fuelectenerg-1427	984	69	tif	tif	PROPN
fuelectenerg-1427	984	70	)	)	PUNCT
fuelectenerg-1427	984	71	s	s	PROPN
fuelectenerg-1427	984	72	/	/	SYM
fuelectenerg-1427	984	73	d	d	NOUN
fuelectenerg-1427	984	74	trees	tree	NOUN
fuelectenerg-1427	984	75	and	and	CCONJ
fuelectenerg-1427	984	76	their	their	PRON
fuelectenerg-1427	984	77	numbers	number	NOUN
fuelectenerg-1427	984	78	:	:	PUNCT
fuelectenerg-1427	984	79	(	(	PUNCT
fuelectenerg-1427	984	80	a	a	X
fuelectenerg-1427	984	81	)	)	PUNCT
fuelectenerg-1427	984	82	2	2	NUM
fuelectenerg-1427	984	83	-	-	PUNCT
fuelectenerg-1427	984	84	variable	variable	ADJ
fuelectenerg-1427	984	85	order	order	NOUN
fuelectenerg-1427	984	86	{	{	PUNCT
fuelectenerg-1427	984	87	a	a	DET
fuelectenerg-1427	984	88	,	,	PUNCT
fuelectenerg-1427	984	89	b	b	NOUN
fuelectenerg-1427	984	90	}	}	PUNCT
fuelectenerg-1427	984	91	and	and	CCONJ
fuelectenerg-1427	984	92	(	(	PUNCT
fuelectenerg-1427	984	93	b	b	X
fuelectenerg-1427	984	94	)	)	PUNCT
fuelectenerg-1427	984	95	2variable	2variable	NUM
fuelectenerg-1427	984	96	order	order	NOUN
fuelectenerg-1427	984	97	{	{	PUNCT
fuelectenerg-1427	984	98	b	b	NOUN
fuelectenerg-1427	984	99	,	,	PUNCT
fuelectenerg-1427	984	100	a	a	PRON
fuelectenerg-1427	984	101	}	}	PUNCT
fuelectenerg-1427	984	102	.	.	PUNCT
fuelectenerg-1427	985	1	variables	variable	NOUN
fuelectenerg-1427	985	2	{	{	PUNCT
fuelectenerg-1427	985	3	a	a	DET
fuelectenerg-1427	985	4	,	,	PUNCT
fuelectenerg-1427	985	5	b	b	NOUN
fuelectenerg-1427	985	6	}	}	PUNCT
fuelectenerg-1427	985	7	are	be	AUX
fuelectenerg-1427	985	8	defined	define	VERB
fuelectenerg-1427	985	9	as	as	ADP
fuelectenerg-1427	985	10	in	in	ADP
fuelectenerg-1427	985	11	eq	eq	ADP
fuelectenerg-1427	985	12	.	.	PUNCT
fuelectenerg-1427	986	1	(	(	PUNCT
fuelectenerg-1427	986	2	28	28	NUM
fuelectenerg-1427	986	3	)	)	PUNCT
fuelectenerg-1427	986	4	for	for	ADP
fuelectenerg-1427	986	5	generalized	generalized	ADJ
fuelectenerg-1427	986	6	davio	davio	NOUN
fuelectenerg-1427	986	7	(	(	PUNCT
fuelectenerg-1427	986	8	d	d	NOUN
fuelectenerg-1427	986	9	)	)	PUNCT
fuelectenerg-1427	986	10	where	where	SCONJ
fuelectenerg-1427	986	11	in	in	ADP
fuelectenerg-1427	986	12	this	this	DET
fuelectenerg-1427	986	13	figure	figure	NOUN
fuelectenerg-1427	986	14	(	(	PUNCT
fuelectenerg-1427	986	15	a,≡	a,≡	NOUN
fuelectenerg-1427	986	16	a	a	X
fuelectenerg-1427	986	17	)	)	PUNCT
fuelectenerg-1427	986	18	and	and	CCONJ
fuelectenerg-1427	986	19	(	(	PUNCT
fuelectenerg-1427	986	20	b,≡	b,≡	X
fuelectenerg-1427	986	21	b	b	X
fuelectenerg-1427	986	22	)	)	PUNCT
fuelectenerg-1427	986	23	.	.	PUNCT
fuelectenerg-1427	987	1	theorem	theorem	NOUN
fuelectenerg-1427	987	2	2	2	NUM
fuelectenerg-1427	987	3	.	.	PUNCT
fuelectenerg-1427	988	1	the	the	DET
fuelectenerg-1427	988	2	total	total	ADJ
fuelectenerg-1427	988	3	number	number	NOUN
fuelectenerg-1427	988	4	of	of	ADP
fuelectenerg-1427	988	5	the	the	DET
fuelectenerg-1427	988	6	ternary	ternary	ADJ
fuelectenerg-1427	988	7	ifs	ifs	PROPN
fuelectenerg-1427	988	8	,	,	PUNCT
fuelectenerg-1427	988	9	for	for	ADP
fuelectenerg-1427	988	10	two	two	NUM
fuelectenerg-1427	988	11	variables	variable	NOUN
fuelectenerg-1427	988	12	and	and	CCONJ
fuelectenerg-1427	988	13	for	for	ADP
fuelectenerg-1427	988	14	orders	order	NOUN
fuelectenerg-1427	988	15	{	{	PUNCT
fuelectenerg-1427	988	16	a	a	DET
fuelectenerg-1427	988	17	,	,	PUNCT
fuelectenerg-1427	988	18	b	b	NOUN
fuelectenerg-1427	988	19	}	}	PUNCT
fuelectenerg-1427	988	20	and	and	CCONJ
fuelectenerg-1427	988	21	{	{	PUNCT
fuelectenerg-1427	988	22	b	b	NOUN
fuelectenerg-1427	988	23	,	,	PUNCT
fuelectenerg-1427	988	24	a	a	PRON
fuelectenerg-1427	988	25	}	}	PUNCT
fuelectenerg-1427	988	26	,	,	PUNCT
fuelectenerg-1427	988	27	and	and	CCONJ
fuelectenerg-1427	988	28	the	the	DET
fuelectenerg-1427	988	29	total	total	ADJ
fuelectenerg-1427	988	30	number	number	NOUN
fuelectenerg-1427	988	31	of	of	ADP
fuelectenerg-1427	988	32	ternary	ternary	ADJ
fuelectenerg-1427	988	33	generalized	generalize	VERB
fuelectenerg-1427	988	34	ifs	ifs	PROPN
fuelectenerg-1427	988	35	,	,	PUNCT
fuelectenerg-1427	988	36	for	for	ADP
fuelectenerg-1427	988	37	two	two	NUM
fuelectenerg-1427	988	38	variables	variable	NOUN
fuelectenerg-1427	988	39	,	,	PUNCT
fuelectenerg-1427	988	40	are	be	AUX
fuelectenerg-1427	988	41	respectively	respectively	ADV
fuelectenerg-1427	988	42	:	:	PUNCT
fuelectenerg-1427	988	43	#	#	SYM
fuelectenerg-1427	988	44	tifa	tifa	NOUN
fuelectenerg-1427	988	45	,	,	PUNCT
fuelectenerg-1427	988	46	b	b	NOUN
fuelectenerg-1427	988	47	=	=	SYM
fuelectenerg-1427	988	48	1	1	NUM
fuelectenerg-1427	988	49	·	·	PUNCT
fuelectenerg-1427	988	50	(	(	PUNCT
fuelectenerg-1427	988	51	3)0	3)0	NUM
fuelectenerg-1427	988	52	+	+	CCONJ
fuelectenerg-1427	988	53	3	3	NUM
fuelectenerg-1427	988	54	·	·	PUNCT
fuelectenerg-1427	988	55	(	(	PUNCT
fuelectenerg-1427	988	56	3)2	3)2	NUM
fuelectenerg-1427	988	57	+	+	SYM
fuelectenerg-1427	988	58	3	3	NUM
fuelectenerg-1427	988	59	·	·	PUNCT
fuelectenerg-1427	988	60	(	(	PUNCT
fuelectenerg-1427	988	61	3)4	3)4	NUM
fuelectenerg-1427	988	62	+	+	NOUN
fuelectenerg-1427	988	63	2	2	NUM
fuelectenerg-1427	988	64	·	·	PUNCT
fuelectenerg-1427	988	65	(	(	PUNCT
fuelectenerg-1427	988	66	3)6	3)6	NUM
fuelectenerg-1427	988	67	+	+	SYM
fuelectenerg-1427	988	68	3	3	NUM
fuelectenerg-1427	988	69	·	·	PUNCT
fuelectenerg-1427	988	70	(	(	PUNCT
fuelectenerg-1427	988	71	3)8	3)8	NUM
fuelectenerg-1427	988	72	+	+	SYM
fuelectenerg-1427	988	73	3	3	NUM
fuelectenerg-1427	988	74	·	·	PUNCT
fuelectenerg-1427	988	75	(	(	PUNCT
fuelectenerg-1427	988	76	3)10	3)10	NUM
fuelectenerg-1427	988	77	+	+	ADJ
fuelectenerg-1427	988	78	1	1	NUM
fuelectenerg-1427	988	79	·	·	PUNCT
fuelectenerg-1427	988	80	(	(	PUNCT
fuelectenerg-1427	988	81	3)12	3)12	NUM
fuelectenerg-1427	988	82	=	=	SYM
fuelectenerg-1427	988	83	730,000	730,000	NUM
fuelectenerg-1427	988	84	,	,	PUNCT
fuelectenerg-1427	988	85	(	(	PUNCT
fuelectenerg-1427	988	86	33	33	NUM
fuelectenerg-1427	988	87	)	)	PUNCT
fuelectenerg-1427	988	88	#	#	SYM
fuelectenerg-1427	988	89	tifb	tifb	NOUN
fuelectenerg-1427	988	90	,	,	PUNCT
fuelectenerg-1427	988	91	a	a	DET
fuelectenerg-1427	988	92	=	=	SYM
fuelectenerg-1427	988	93	1	1	NUM
fuelectenerg-1427	988	94	·	·	PUNCT
fuelectenerg-1427	988	95	(	(	PUNCT
fuelectenerg-1427	988	96	3)0	3)0	NUM
fuelectenerg-1427	988	97	+	+	CCONJ
fuelectenerg-1427	988	98	3	3	NUM
fuelectenerg-1427	988	99	·	·	PUNCT
fuelectenerg-1427	988	100	(	(	PUNCT
fuelectenerg-1427	988	101	3)2	3)2	NUM
fuelectenerg-1427	988	102	+	+	SYM
fuelectenerg-1427	988	103	3	3	NUM
fuelectenerg-1427	988	104	·	·	PUNCT
fuelectenerg-1427	988	105	(	(	PUNCT
fuelectenerg-1427	988	106	3)4	3)4	NUM
fuelectenerg-1427	988	107	+	+	NOUN
fuelectenerg-1427	988	108	2	2	NUM
fuelectenerg-1427	988	109	·	·	PUNCT
fuelectenerg-1427	988	110	(	(	PUNCT
fuelectenerg-1427	988	111	3)6	3)6	NUM
fuelectenerg-1427	988	112	+	+	SYM
fuelectenerg-1427	988	113	3	3	NUM
fuelectenerg-1427	988	114	·	·	PUNCT
fuelectenerg-1427	988	115	(	(	PUNCT
fuelectenerg-1427	988	116	3)8	3)8	NUM
fuelectenerg-1427	988	117	+	+	SYM
fuelectenerg-1427	988	118	3	3	NUM
fuelectenerg-1427	988	119	·	·	PUNCT
fuelectenerg-1427	988	120	(	(	PUNCT
fuelectenerg-1427	988	121	3)10	3)10	NUM
fuelectenerg-1427	988	122	+	+	ADJ
fuelectenerg-1427	988	123	1	1	NUM
fuelectenerg-1427	988	124	·	·	PUNCT
fuelectenerg-1427	988	125	(	(	PUNCT
fuelectenerg-1427	988	126	3)12	3)12	NUM
fuelectenerg-1427	988	127	=	=	SYM
fuelectenerg-1427	988	128	730,000	730,000	NUM
fuelectenerg-1427	988	129	,	,	PUNCT
fuelectenerg-1427	988	130	(	(	PUNCT
fuelectenerg-1427	988	131	34	34	NUM
fuelectenerg-1427	988	132	)	)	PUNCT
fuelectenerg-1427	988	133	#	#	NOUN
fuelectenerg-1427	988	134	tgif	tgif	NOUN
fuelectenerg-1427	988	135	=	=	PUNCT
fuelectenerg-1427	988	136	#	#	NUM
fuelectenerg-1427	988	137	tifa	tifa	NOUN
fuelectenerg-1427	988	138	,	,	PUNCT
fuelectenerg-1427	988	139	b	b	NOUN
fuelectenerg-1427	988	140	+	+	CCONJ
fuelectenerg-1427	988	141	#	#	SYM
fuelectenerg-1427	988	142	tifb	tifb	NOUN
fuelectenerg-1427	988	143	,	,	PUNCT
fuelectenerg-1427	988	144	a−#(tifa	a−#(tifa	PROPN
fuelectenerg-1427	988	145	,	,	PUNCT
fuelectenerg-1427	988	146	b	b	NOUN
fuelectenerg-1427	988	147	∩tifb	∩tifb	NOUN
fuelectenerg-1427	988	148	,	,	PUNCT
fuelectenerg-1427	988	149	a	a	PRON
fuelectenerg-1427	988	150	)	)	PUNCT
fuelectenerg-1427	988	151	=	=	SYM
fuelectenerg-1427	988	152	2	2	NUM
fuelectenerg-1427	988	153	·	·	SYM
fuelectenerg-1427	988	154	#	#	NOUN
fuelectenerg-1427	988	155	tif−#(tifa	tif−#(tifa	NUM
fuelectenerg-1427	988	156	,	,	PUNCT
fuelectenerg-1427	988	157	b	b	NOUN
fuelectenerg-1427	988	158	∩tifb	∩tifb	NOUN
fuelectenerg-1427	988	159	,	,	PUNCT
fuelectenerg-1427	988	160	a	a	PRON
fuelectenerg-1427	988	161	)	)	PUNCT
fuelectenerg-1427	988	162	=	=	SYM
fuelectenerg-1427	988	163	2	2	NUM
fuelectenerg-1427	988	164	·	·	PUNCT
fuelectenerg-1427	988	165	(	(	PUNCT
fuelectenerg-1427	988	166	730,000)−	730,000)−	NUM
fuelectenerg-1427	988	167	(	(	PUNCT
fuelectenerg-1427	988	168	1	1	NUM
fuelectenerg-1427	988	169	·	·	PUNCT
fuelectenerg-1427	988	170	(	(	PUNCT
fuelectenerg-1427	988	171	3)0	3)0	NUM
fuelectenerg-1427	988	172	+	+	PROPN
fuelectenerg-1427	988	173	2	2	NUM
fuelectenerg-1427	988	174	·	·	PUNCT
fuelectenerg-1427	988	175	(	(	PUNCT
fuelectenerg-1427	988	176	3)6	3)6	NUM
fuelectenerg-1427	988	177	+	+	SYM
fuelectenerg-1427	988	178	1	1	NUM
fuelectenerg-1427	988	179	·	·	PUNCT
fuelectenerg-1427	988	180	(	(	PUNCT
fuelectenerg-1427	988	181	3)12	3)12	NUM
fuelectenerg-1427	988	182	)	)	PUNCT
fuelectenerg-1427	988	183	=	=	SYM
fuelectenerg-1427	989	1	927,100	927,100	NUM
fuelectenerg-1427	989	2	.	.	PUNCT
fuelectenerg-1427	990	1	(	(	PUNCT
fuelectenerg-1427	990	2	35	35	NUM
fuelectenerg-1427	990	3	)	)	PUNCT
fuelectenerg-1427	990	4	proof	proof	NOUN
fuelectenerg-1427	990	5	.	.	PUNCT
fuelectenerg-1427	991	1	by	by	ADP
fuelectenerg-1427	991	2	observing	observe	VERB
fuelectenerg-1427	991	3	figure	figure	NOUN
fuelectenerg-1427	991	4	5	5	NUM
fuelectenerg-1427	991	5	,	,	PUNCT
fuelectenerg-1427	991	6	we	we	PRON
fuelectenerg-1427	991	7	note	note	VERB
fuelectenerg-1427	991	8	that	that	SCONJ
fuelectenerg-1427	991	9	the	the	DET
fuelectenerg-1427	991	10	total	total	ADJ
fuelectenerg-1427	991	11	number	number	NOUN
fuelectenerg-1427	991	12	of	of	ADP
fuelectenerg-1427	991	13	tifs	tifs	PROPN
fuelectenerg-1427	991	14	for	for	ADP
fuelectenerg-1427	991	15	orders	order	NOUN
fuelectenerg-1427	991	16	{	{	PUNCT
fuelectenerg-1427	991	17	a	a	DET
fuelectenerg-1427	991	18	,	,	PUNCT
fuelectenerg-1427	991	19	b	b	NOUN
fuelectenerg-1427	991	20	}	}	PUNCT
fuelectenerg-1427	991	21	and	and	CCONJ
fuelectenerg-1427	991	22	{	{	PUNCT
fuelectenerg-1427	991	23	b	b	NOUN
fuelectenerg-1427	991	24	,	,	PUNCT
fuelectenerg-1427	991	25	a	a	PRON
fuelectenerg-1427	991	26	}	}	PUNCT
fuelectenerg-1427	991	27	is	be	AUX
fuelectenerg-1427	991	28	the	the	DET
fuelectenerg-1427	991	29	sum	sum	NOUN
fuelectenerg-1427	991	30	of	of	ADP
fuelectenerg-1427	991	31	the	the	DET
fuelectenerg-1427	991	32	numbers	number	NOUN
fuelectenerg-1427	991	33	on	on	ADP
fuelectenerg-1427	991	34	top	top	NOUN
fuelectenerg-1427	991	35	of	of	ADP
fuelectenerg-1427	991	36	s	s	PROPN
fuelectenerg-1427	991	37	/	/	SYM
fuelectenerg-1427	991	38	d	d	NOUN
fuelectenerg-1427	991	39	trees	tree	NOUN
fuelectenerg-1427	991	40	that	that	PRON
fuelectenerg-1427	991	41	leads	lead	VERB
fuelectenerg-1427	991	42	to	to	ADP
fuelectenerg-1427	991	43	equations	equation	NOUN
fuelectenerg-1427	991	44	(	(	PUNCT
fuelectenerg-1427	991	45	33	33	NUM
fuelectenerg-1427	991	46	)	)	PUNCT
fuelectenerg-1427	991	47	(	(	PUNCT
fuelectenerg-1427	991	48	35	35	NUM
fuelectenerg-1427	991	49	)	)	PUNCT
fuelectenerg-1427	991	50	,	,	PUNCT
fuelectenerg-1427	991	51	respectively	respectively	ADV
fuelectenerg-1427	991	52	.	.	PUNCT
fuelectenerg-1427	992	1	2.2	2.2	NUM
fuelectenerg-1427	992	2	properties	property	NOUN
fuelectenerg-1427	992	3	of	of	ADP
fuelectenerg-1427	992	4	tifs	tifs	PROPN
fuelectenerg-1427	992	5	and	and	CCONJ
fuelectenerg-1427	992	6	tgifs	tgif	VERB
fuelectenerg-1427	992	7	the	the	DET
fuelectenerg-1427	992	8	following	follow	VERB
fuelectenerg-1427	992	9	present	present	ADJ
fuelectenerg-1427	992	10	basic	basic	ADJ
fuelectenerg-1427	992	11	properties	property	NOUN
fuelectenerg-1427	992	12	of	of	ADP
fuelectenerg-1427	992	13	the	the	DET
fuelectenerg-1427	992	14	presented	present	VERB
fuelectenerg-1427	992	15	tifs	tifs	PROPN
fuelectenerg-1427	992	16	and	and	CCONJ
fuelectenerg-1427	992	17	tgifs	tgif	NOUN
fuelectenerg-1427	992	18	.	.	PUNCT
fuelectenerg-1427	992	19	theorem	theorem	NOUN
fuelectenerg-1427	992	20	3	3	NUM
fuelectenerg-1427	992	21	.	.	PUNCT
fuelectenerg-1427	993	1	each	each	DET
fuelectenerg-1427	993	2	ternary	ternary	ADJ
fuelectenerg-1427	993	3	inclusive	inclusive	ADJ
fuelectenerg-1427	993	4	form	form	NOUN
fuelectenerg-1427	993	5	(	(	PUNCT
fuelectenerg-1427	993	6	tif	tif	PROPN
fuelectenerg-1427	993	7	)	)	PUNCT
fuelectenerg-1427	993	8	is	be	AUX
fuelectenerg-1427	993	9	canonical	canonical	ADJ
fuelectenerg-1427	993	10	.	.	PUNCT
fuelectenerg-1427	994	1	110	110	NUM
fuelectenerg-1427	994	2	58	58	NUM
fuelectenerg-1427	994	3	a.	a.	NOUN
fuelectenerg-1427	994	4	n.	n.	PROPN
fuelectenerg-1427	994	5	al	al	PROPN
fuelectenerg-1427	994	6	-	-	PUNCT
fuelectenerg-1427	994	7	rabadi	rabadi	VERB
fuelectenerg-1427	994	8	an	an	DET
fuelectenerg-1427	994	9	extended	extended	ADJ
fuelectenerg-1427	994	10	green	green	ADJ
fuelectenerg-1427	994	11	sasao	sasao	PROPN
fuelectenerg-1427	994	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	994	13	of	of	ADP
fuelectenerg-1427	994	14	canonical	canonical	ADJ
fuelectenerg-1427	994	15	ternary	ternary	ADJ
fuelectenerg-1427	994	16	galois	galois	NOUN
fuelectenerg-1427	994	17	forms	form	NOUN
fuelectenerg-1427	994	18	and	and	CCONJ
fuelectenerg-1427	994	19	universal	universal	ADJ
fuelectenerg-1427	994	20	logic	logic	NOUN
fuelectenerg-1427	994	21	modules	module	VERB
fuelectenerg-1427	994	22	59	59	NUM
fuelectenerg-1427	994	23	an	an	DET
fuelectenerg-1427	994	24	extended	extended	ADJ
fuelectenerg-1427	994	25	green	green	ADJ
fuelectenerg-1427	994	26	sasao	sasao	PROPN
fuelectenerg-1427	994	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	994	28	of	of	ADP
fuelectenerg-1427	994	29	canonical	canonical	ADJ
fuelectenerg-1427	994	30	ternary	ternary	ADJ
fuelectenerg-1427	994	31	galois	galois	NOUN
fuelectenerg-1427	994	32	forms	form	NOUN
fuelectenerg-1427	994	33	...	...	PUNCT
fuelectenerg-1427	995	1	s	s	PART
fuelectenerg-1427	995	2	s	s	X
fuelectenerg-1427	995	3	s	s	X
fuelectenerg-1427	995	4	s	s	NOUN
fuelectenerg-1427	995	5	0	0	NUM
fuelectenerg-1427	995	6	a	a	DET
fuelectenerg-1427	995	7	1	1	NUM
fuelectenerg-1427	995	8	a	a	DET
fuelectenerg-1427	995	9	2	2	NUM
fuelectenerg-1427	995	10	a	a	DET
fuelectenerg-1427	995	11	s	s	NOUN
fuelectenerg-1427	995	12	s	s	X
fuelectenerg-1427	995	13	d	d	X
fuelectenerg-1427	995	14	d	d	X
fuelectenerg-1427	995	15	s	s	X
fuelectenerg-1427	995	16	s	s	X
fuelectenerg-1427	995	17	s	s	X
fuelectenerg-1427	995	18	d	d	X
fuelectenerg-1427	995	19	1	1	NUM
fuelectenerg-1427	995	20	(	(	PUNCT
fuelectenerg-1427	995	21	b	b	NOUN
fuelectenerg-1427	995	22	,	,	PUNCT
fuelectenerg-1427	995	23	)	)	PUNCT
fuelectenerg-1427	995	24	2	2	NUM
fuelectenerg-1427	995	25	b	b	NOUN
fuelectenerg-1427	995	26	,	,	PUNCT
fuelectenerg-1427	995	27	s	s	NOUN
fuelectenerg-1427	995	28	d	d	X
fuelectenerg-1427	995	29	d	d	PROPN
fuelectenerg-1427	995	30	d	d	PROPN
fuelectenerg-1427	995	31	1	1	NUM
fuelectenerg-1427	995	32	(	(	PUNCT
fuelectenerg-1427	995	33	b	b	NOUN
fuelectenerg-1427	995	34	,	,	PUNCT
fuelectenerg-1427	995	35	)	)	PUNCT
fuelectenerg-1427	995	36	2	2	NUM
fuelectenerg-1427	995	37	b	b	NOUN
fuelectenerg-1427	995	38	,	,	PUNCT
fuelectenerg-1427	995	39	s	s	X
fuelectenerg-1427	995	40	s	s	NOUN
fuelectenerg-1427	995	41	s	s	NOUN
fuelectenerg-1427	995	42	0	0	NUM
fuelectenerg-1427	995	43	a	a	DET
fuelectenerg-1427	995	44	0	0	NUM
fuelectenerg-1427	995	45	a	a	DET
fuelectenerg-1427	995	46	1	1	NUM
fuelectenerg-1427	995	47	a	a	DET
fuelectenerg-1427	995	48	1	1	NUM
fuelectenerg-1427	995	49	a	a	DET
fuelectenerg-1427	995	50	2	2	NUM
fuelectenerg-1427	995	51	a	a	DET
fuelectenerg-1427	995	52	2	2	NUM
fuelectenerg-1427	995	53	a	a	DET
fuelectenerg-1427	995	54	d	d	PROPN
fuelectenerg-1427	995	55	1	1	NUM
fuelectenerg-1427	995	56	1	1	NUM
fuelectenerg-1427	995	57	1	1	NUM
fuelectenerg-1427	995	58	1	1	NUM
fuelectenerg-1427	995	59	1	1	NUM
fuelectenerg-1427	995	60	1	1	NUM
fuelectenerg-1427	995	61	1	1	NUM
fuelectenerg-1427	995	62	1	1	NUM
fuelectenerg-1427	995	63	1	1	NUM
fuelectenerg-1427	995	64	1	1	NUM
fuelectenerg-1427	995	65	11	11	NUM
fuelectenerg-1427	995	66	1	1	NUM
fuelectenerg-1427	995	67	1	1	NUM
fuelectenerg-1427	995	68	1	1	NUM
fuelectenerg-1427	995	69	1	1	NUM
fuelectenerg-1427	995	70	1	1	NUM
fuelectenerg-1427	995	71	1	1	NUM
fuelectenerg-1427	995	72	1	1	NUM
fuelectenerg-1427	995	73	1	1	NUM
fuelectenerg-1427	995	74	1	1	NUM
fuelectenerg-1427	995	75	1	1	NUM
fuelectenerg-1427	995	76	1(a	1(a	NUM
fuelectenerg-1427	995	77	,	,	PUNCT
fuelectenerg-1427	995	78	)	)	PUNCT
fuelectenerg-1427	995	79	2	2	NUM
fuelectenerg-1427	995	80	(	(	PUNCT
fuelectenerg-1427	995	81	a	a	PRON
fuelectenerg-1427	995	82	,	,	PUNCT
fuelectenerg-1427	995	83	)	)	PUNCT
fuelectenerg-1427	995	84	2	2	NUM
fuelectenerg-1427	995	85	(	(	PUNCT
fuelectenerg-1427	995	86	a	a	PRON
fuelectenerg-1427	995	87	,	,	PUNCT
fuelectenerg-1427	995	88	)	)	PUNCT
fuelectenerg-1427	995	89	2	2	NUM
fuelectenerg-1427	995	90	(	(	PUNCT
fuelectenerg-1427	995	91	a	a	PRON
fuelectenerg-1427	995	92	,	,	PUNCT
fuelectenerg-1427	995	93	)	)	PUNCT
fuelectenerg-1427	995	94	2	2	NUM
fuelectenerg-1427	995	95	(	(	PUNCT
fuelectenerg-1427	995	96	a	a	PRON
fuelectenerg-1427	995	97	,	,	PUNCT
fuelectenerg-1427	995	98	)	)	PUNCT
fuelectenerg-1427	995	99	2	2	NUM
fuelectenerg-1427	995	100	(	(	PUNCT
fuelectenerg-1427	995	101	a	a	PRON
fuelectenerg-1427	995	102	,	,	PUNCT
fuelectenerg-1427	995	103	)	)	PUNCT
fuelectenerg-1427	995	104	2	2	NUM
fuelectenerg-1427	995	105	(	(	PUNCT
fuelectenerg-1427	995	106	a	a	PRON
fuelectenerg-1427	995	107	,	,	PUNCT
fuelectenerg-1427	995	108	)	)	PUNCT
fuelectenerg-1427	995	109	2	2	NUM
fuelectenerg-1427	995	110	(	(	PUNCT
fuelectenerg-1427	995	111	a	a	PRON
fuelectenerg-1427	995	112	,	,	PUNCT
fuelectenerg-1427	995	113	)	)	PUNCT
fuelectenerg-1427	995	114	2	2	NUM
fuelectenerg-1427	995	115	(	(	PUNCT
fuelectenerg-1427	995	116	a	a	PRON
fuelectenerg-1427	995	117	,	,	PUNCT
fuelectenerg-1427	995	118	)	)	PUNCT
fuelectenerg-1427	995	119	2	2	NUM
fuelectenerg-1427	995	120	(	(	PUNCT
fuelectenerg-1427	995	121	a	a	PRON
fuelectenerg-1427	995	122	,	,	PUNCT
fuelectenerg-1427	995	123	)	)	PUNCT
fuelectenerg-1427	995	124	2	2	NUM
fuelectenerg-1427	995	125	(	(	PUNCT
fuelectenerg-1427	995	126	a	a	PRON
fuelectenerg-1427	995	127	,	,	PUNCT
fuelectenerg-1427	995	128	)	)	PUNCT
fuelectenerg-1427	995	129	2	2	NUM
fuelectenerg-1427	995	130	(	(	PUNCT
fuelectenerg-1427	995	131	a	a	PRON
fuelectenerg-1427	995	132	,	,	PUNCT
fuelectenerg-1427	995	133	)	)	PUNCT
fuelectenerg-1427	995	134	2	2	NUM
fuelectenerg-1427	995	135	(	(	PUNCT
fuelectenerg-1427	995	136	a	a	PRON
fuelectenerg-1427	995	137	,	,	PUNCT
fuelectenerg-1427	995	138	)	)	PUNCT
fuelectenerg-1427	995	139	2	2	NUM
fuelectenerg-1427	995	140	(	(	PUNCT
fuelectenerg-1427	995	141	a	a	PRON
fuelectenerg-1427	995	142	,	,	PUNCT
fuelectenerg-1427	995	143	)	)	PUNCT
fuelectenerg-1427	995	144	2	2	NUM
fuelectenerg-1427	995	145	(	(	PUNCT
fuelectenerg-1427	995	146	a	a	PRON
fuelectenerg-1427	995	147	,	,	PUNCT
fuelectenerg-1427	995	148	)	)	PUNCT
fuelectenerg-1427	995	149	2	2	NUM
fuelectenerg-1427	995	150	(	(	PUNCT
fuelectenerg-1427	995	151	a	a	PRON
fuelectenerg-1427	995	152	,	,	PUNCT
fuelectenerg-1427	995	153	)	)	PUNCT
fuelectenerg-1427	995	154	2	2	NUM
fuelectenerg-1427	995	155	(	(	PUNCT
fuelectenerg-1427	995	156	a	a	PRON
fuelectenerg-1427	995	157	,	,	PUNCT
fuelectenerg-1427	995	158	)	)	PUNCT
fuelectenerg-1427	995	159	2	2	NUM
fuelectenerg-1427	995	160	(	(	PUNCT
fuelectenerg-1427	995	161	a	a	PRON
fuelectenerg-1427	995	162	,	,	PUNCT
fuelectenerg-1427	995	163	)	)	PUNCT
fuelectenerg-1427	995	164	2	2	NUM
fuelectenerg-1427	995	165	(	(	PUNCT
fuelectenerg-1427	995	166	a	a	PRON
fuelectenerg-1427	995	167	,	,	PUNCT
fuelectenerg-1427	995	168	)	)	PUNCT
fuelectenerg-1427	995	169	2	2	NUM
fuelectenerg-1427	995	170	(	(	PUNCT
fuelectenerg-1427	995	171	a	a	PRON
fuelectenerg-1427	995	172	,	,	PUNCT
fuelectenerg-1427	995	173	)	)	PUNCT
fuelectenerg-1427	995	174	2	2	NUM
fuelectenerg-1427	995	175	(	(	PUNCT
fuelectenerg-1427	995	176	a	a	PRON
fuelectenerg-1427	995	177	,	,	PUNCT
fuelectenerg-1427	995	178	)	)	PUNCT
fuelectenerg-1427	995	179	2	2	NUM
fuelectenerg-1427	995	180	(	(	PUNCT
fuelectenerg-1427	995	181	a	a	PRON
fuelectenerg-1427	995	182	,	,	PUNCT
fuelectenerg-1427	995	183	)	)	PUNCT
fuelectenerg-1427	995	184	2	2	NUM
fuelectenerg-1427	995	185	(	(	PUNCT
fuelectenerg-1427	995	186	a	a	PRON
fuelectenerg-1427	995	187	,	,	PUNCT
fuelectenerg-1427	995	188	)	)	PUNCT
fuelectenerg-1427	995	189	2	2	NUM
fuelectenerg-1427	995	190	(	(	PUNCT
fuelectenerg-1427	995	191	a	a	PRON
fuelectenerg-1427	995	192	,	,	PUNCT
fuelectenerg-1427	995	193	)	)	PUNCT
fuelectenerg-1427	995	194	2	2	NUM
fuelectenerg-1427	995	195	a	a	PRON
fuelectenerg-1427	995	196	,	,	PUNCT
fuelectenerg-1427	995	197	a	a	PRON
fuelectenerg-1427	995	198	,	,	PUNCT
fuelectenerg-1427	995	199	a	a	PRON
fuelectenerg-1427	995	200	,	,	PUNCT
fuelectenerg-1427	995	201	a	a	PRON
fuelectenerg-1427	995	202	,	,	PUNCT
fuelectenerg-1427	995	203	a	a	PRON
fuelectenerg-1427	995	204	,	,	PUNCT
fuelectenerg-1427	995	205	a	a	PRON
fuelectenerg-1427	995	206	,	,	PUNCT
fuelectenerg-1427	995	207	a	a	PRON
fuelectenerg-1427	995	208	,	,	PUNCT
fuelectenerg-1427	995	209	a	a	PRON
fuelectenerg-1427	995	210	,	,	PUNCT
fuelectenerg-1427	995	211	a	a	PRON
fuelectenerg-1427	995	212	,	,	PUNCT
fuelectenerg-1427	995	213	a	a	PRON
fuelectenerg-1427	995	214	,	,	PUNCT
fuelectenerg-1427	995	215	a	a	PRON
fuelectenerg-1427	995	216	,	,	PUNCT
fuelectenerg-1427	995	217	a	a	PRON
fuelectenerg-1427	995	218	,	,	PUNCT
fuelectenerg-1427	995	219	a	a	PRON
fuelectenerg-1427	995	220	,	,	PUNCT
fuelectenerg-1427	995	221	a	a	PRON
fuelectenerg-1427	995	222	,	,	PUNCT
fuelectenerg-1427	995	223	a	a	PRON
fuelectenerg-1427	995	224	,	,	PUNCT
fuelectenerg-1427	995	225	a	a	PRON
fuelectenerg-1427	995	226	,	,	PUNCT
fuelectenerg-1427	995	227	a	a	PRON
fuelectenerg-1427	995	228	,	,	PUNCT
fuelectenerg-1427	995	229	a	a	PRON
fuelectenerg-1427	995	230	,	,	PUNCT
fuelectenerg-1427	995	231	a	a	PRON
fuelectenerg-1427	995	232	,	,	PUNCT
fuelectenerg-1427	995	233	a	a	PRON
fuelectenerg-1427	995	234	,	,	PUNCT
fuelectenerg-1427	995	235	a	a	PRON
fuelectenerg-1427	995	236	,	,	PUNCT
fuelectenerg-1427	995	237	a	a	PRON
fuelectenerg-1427	995	238	,	,	PUNCT
fuelectenerg-1427	995	239	a	a	PRON
fuelectenerg-1427	995	240	,	,	PUNCT
fuelectenerg-1427	995	241	s	s	NOUN
fuelectenerg-1427	995	242	s	s	X
fuelectenerg-1427	995	243	d	d	X
fuelectenerg-1427	995	244	d	d	X
fuelectenerg-1427	995	245	s	s	X
fuelectenerg-1427	995	246	s	s	X
fuelectenerg-1427	995	247	d	d	X
fuelectenerg-1427	995	248	d	d	SYM
fuelectenerg-1427	995	249	1	1	NUM
fuelectenerg-1427	995	250	(	(	PUNCT
fuelectenerg-1427	995	251	b	b	NOUN
fuelectenerg-1427	995	252	,	,	PUNCT
fuelectenerg-1427	995	253	)	)	PUNCT
fuelectenerg-1427	995	254	2	2	NUM
fuelectenerg-1427	995	255	b	b	NOUN
fuelectenerg-1427	995	256	,	,	PUNCT
fuelectenerg-1427	995	257	sd	sd	ADP
fuelectenerg-1427	995	258	d	d	PROPN
fuelectenerg-1427	995	259	d	d	PROPN
fuelectenerg-1427	995	260	1	1	NUM
fuelectenerg-1427	995	261	(	(	PUNCT
fuelectenerg-1427	995	262	b	b	NOUN
fuelectenerg-1427	995	263	,	,	PUNCT
fuelectenerg-1427	995	264	)	)	PUNCT
fuelectenerg-1427	995	265	2	2	NUM
fuelectenerg-1427	995	266	b	b	NOUN
fuelectenerg-1427	995	267	,	,	PUNCT
fuelectenerg-1427	995	268	s	s	X
fuelectenerg-1427	995	269	s	s	NOUN
fuelectenerg-1427	995	270	s	s	NOUN
fuelectenerg-1427	995	271	0	0	NUM
fuelectenerg-1427	995	272	a	a	DET
fuelectenerg-1427	995	273	0	0	NUM
fuelectenerg-1427	995	274	a	a	DET
fuelectenerg-1427	995	275	0	0	NUM
fuelectenerg-1427	996	1	a	a	DET
fuelectenerg-1427	996	2	0	0	NUM
fuelectenerg-1427	996	3	a	a	DET
fuelectenerg-1427	996	4	0	0	NUM
fuelectenerg-1427	996	5	a	a	DET
fuelectenerg-1427	996	6	0	0	NUM
fuelectenerg-1427	996	7	a	a	DET
fuelectenerg-1427	996	8	0	0	NUM
fuelectenerg-1427	996	9	a	a	DET
fuelectenerg-1427	996	10	0	0	NUM
fuelectenerg-1427	996	11	a	a	DET
fuelectenerg-1427	996	12	0	0	NUM
fuelectenerg-1427	996	13	a	a	DET
fuelectenerg-1427	996	14	0	0	NUM
fuelectenerg-1427	996	15	a	a	DET
fuelectenerg-1427	996	16	0	0	NUM
fuelectenerg-1427	996	17	a	a	DET
fuelectenerg-1427	996	18	0	0	NUM
fuelectenerg-1427	996	19	a	a	DET
fuelectenerg-1427	996	20	0	0	NUM
fuelectenerg-1427	996	21	a	a	DET
fuelectenerg-1427	996	22	0	0	NUM
fuelectenerg-1427	996	23	a	a	DET
fuelectenerg-1427	996	24	0	0	NUM
fuelectenerg-1427	996	25	a	a	DET
fuelectenerg-1427	996	26	0	0	NUM
fuelectenerg-1427	996	27	a0	a0	NOUN
fuelectenerg-1427	996	28	a	a	DET
fuelectenerg-1427	996	29	0	0	NUM
fuelectenerg-1427	996	30	a	a	DET
fuelectenerg-1427	996	31	0	0	NUM
fuelectenerg-1427	996	32	a	a	DET
fuelectenerg-1427	996	33	1	1	NUM
fuelectenerg-1427	996	34	a	a	DET
fuelectenerg-1427	996	35	1	1	NUM
fuelectenerg-1427	996	36	a	a	DET
fuelectenerg-1427	996	37	1	1	NUM
fuelectenerg-1427	996	38	a	a	DET
fuelectenerg-1427	996	39	1	1	NUM
fuelectenerg-1427	996	40	a	a	DET
fuelectenerg-1427	996	41	1	1	NUM
fuelectenerg-1427	996	42	a	a	DET
fuelectenerg-1427	996	43	1	1	NUM
fuelectenerg-1427	996	44	a	a	DET
fuelectenerg-1427	996	45	1	1	NUM
fuelectenerg-1427	996	46	a	a	DET
fuelectenerg-1427	996	47	1	1	NUM
fuelectenerg-1427	996	48	a	a	DET
fuelectenerg-1427	996	49	1	1	NUM
fuelectenerg-1427	996	50	a	a	DET
fuelectenerg-1427	996	51	1	1	NUM
fuelectenerg-1427	996	52	a	a	DET
fuelectenerg-1427	996	53	1	1	NUM
fuelectenerg-1427	996	54	a	a	DET
fuelectenerg-1427	996	55	1	1	NUM
fuelectenerg-1427	996	56	a	a	DET
fuelectenerg-1427	996	57	1	1	NUM
fuelectenerg-1427	996	58	a	a	DET
fuelectenerg-1427	996	59	1	1	NUM
fuelectenerg-1427	996	60	a	a	DET
fuelectenerg-1427	996	61	1	1	NUM
fuelectenerg-1427	996	62	a	a	DET
fuelectenerg-1427	996	63	1	1	NUM
fuelectenerg-1427	996	64	a1	a1	NOUN
fuelectenerg-1427	996	65	a	a	DET
fuelectenerg-1427	996	66	1	1	NUM
fuelectenerg-1427	996	67	a	a	DET
fuelectenerg-1427	996	68	1	1	NUM
fuelectenerg-1427	996	69	a	a	DET
fuelectenerg-1427	996	70	2	2	NUM
fuelectenerg-1427	996	71	a	a	DET
fuelectenerg-1427	996	72	2	2	NUM
fuelectenerg-1427	996	73	a	a	DET
fuelectenerg-1427	996	74	2	2	NUM
fuelectenerg-1427	996	75	a	a	DET
fuelectenerg-1427	996	76	2	2	NUM
fuelectenerg-1427	996	77	a	a	DET
fuelectenerg-1427	996	78	2	2	NUM
fuelectenerg-1427	996	79	a	a	DET
fuelectenerg-1427	996	80	2	2	NUM
fuelectenerg-1427	996	81	a	a	DET
fuelectenerg-1427	996	82	2	2	NUM
fuelectenerg-1427	996	83	a	a	DET
fuelectenerg-1427	996	84	2	2	NUM
fuelectenerg-1427	996	85	a	a	DET
fuelectenerg-1427	996	86	2	2	NUM
fuelectenerg-1427	996	87	a	a	DET
fuelectenerg-1427	996	88	2	2	NUM
fuelectenerg-1427	996	89	a	a	DET
fuelectenerg-1427	996	90	2	2	NUM
fuelectenerg-1427	996	91	a	a	DET
fuelectenerg-1427	996	92	2	2	NUM
fuelectenerg-1427	996	93	a	a	DET
fuelectenerg-1427	996	94	2	2	NUM
fuelectenerg-1427	996	95	a	a	DET
fuelectenerg-1427	996	96	2	2	NUM
fuelectenerg-1427	996	97	a	a	DET
fuelectenerg-1427	996	98	2	2	NUM
fuelectenerg-1427	996	99	a	a	DET
fuelectenerg-1427	996	100	2	2	NUM
fuelectenerg-1427	996	101	a2	a2	NOUN
fuelectenerg-1427	996	102	a	a	DET
fuelectenerg-1427	996	103	2	2	NUM
fuelectenerg-1427	996	104	a	a	DET
fuelectenerg-1427	996	105	2	2	NUM
fuelectenerg-1427	996	106	a	a	PRON
fuelectenerg-1427	996	107	d	d	PROPN
fuelectenerg-1427	996	108	1	1	NUM
fuelectenerg-1427	996	109	a	a	PRON
fuelectenerg-1427	996	110	,	,	PUNCT
fuelectenerg-1427	996	111	s	s	PART
fuelectenerg-1427	996	112	sd	sd	NOUN
fuelectenerg-1427	996	113	d	d	PROPN
fuelectenerg-1427	996	114	s	s	AUX
fuelectenerg-1427	996	115	s	s	X
fuelectenerg-1427	996	116	s	s	X
fuelectenerg-1427	996	117	sd	sd	NOUN
fuelectenerg-1427	996	118	d	d	NOUN
fuelectenerg-1427	996	119	1	1	NUM
fuelectenerg-1427	996	120	(	(	PUNCT
fuelectenerg-1427	996	121	b	b	NOUN
fuelectenerg-1427	996	122	,	,	PUNCT
fuelectenerg-1427	996	123	)	)	PUNCT
fuelectenerg-1427	996	124	2	2	NUM
fuelectenerg-1427	996	125	b	b	NOUN
fuelectenerg-1427	996	126	,	,	PUNCT
fuelectenerg-1427	996	127	d	d	PROPN
fuelectenerg-1427	996	128	d	d	PROPN
fuelectenerg-1427	996	129	d	d	PROPN
fuelectenerg-1427	996	130	d	d	PROPN
fuelectenerg-1427	996	131	1	1	NUM
fuelectenerg-1427	996	132	(	(	PUNCT
fuelectenerg-1427	996	133	b	b	NOUN
fuelectenerg-1427	996	134	,	,	PUNCT
fuelectenerg-1427	996	135	)	)	PUNCT
fuelectenerg-1427	996	136	2	2	NUM
fuelectenerg-1427	996	137	b	b	NOUN
fuelectenerg-1427	996	138	,	,	PUNCT
fuelectenerg-1427	996	139	s	s	X
fuelectenerg-1427	996	140	s	s	NOUN
fuelectenerg-1427	996	141	s	s	X
fuelectenerg-1427	996	142	d	d	X
fuelectenerg-1427	996	143	s	s	X
fuelectenerg-1427	996	144	d	d	X
fuelectenerg-1427	996	145	dd	dd	NOUN
fuelectenerg-1427	996	146	d	d	PROPN
fuelectenerg-1427	996	147	d	d	PROPN
fuelectenerg-1427	996	148	1	1	NUM
fuelectenerg-1427	996	149	(	(	PUNCT
fuelectenerg-1427	996	150	b	b	NOUN
fuelectenerg-1427	996	151	,	,	PUNCT
fuelectenerg-1427	996	152	)	)	PUNCT
fuelectenerg-1427	996	153	2	2	NUM
fuelectenerg-1427	996	154	b	b	NOUN
fuelectenerg-1427	996	155	,	,	PUNCT
fuelectenerg-1427	996	156	s	s	NOUN
fuelectenerg-1427	996	157	d	d	X
fuelectenerg-1427	996	158	d	d	PROPN
fuelectenerg-1427	996	159	d	d	PROPN
fuelectenerg-1427	996	160	1	1	NUM
fuelectenerg-1427	996	161	(	(	PUNCT
fuelectenerg-1427	996	162	b	b	NOUN
fuelectenerg-1427	996	163	,	,	PUNCT
fuelectenerg-1427	996	164	)	)	PUNCT
fuelectenerg-1427	996	165	2	2	NUM
fuelectenerg-1427	996	166	b	b	NOUN
fuelectenerg-1427	996	167	,	,	PUNCT
fuelectenerg-1427	996	168	n=1	n=1	PROPN
fuelectenerg-1427	996	169	n=81	n=81	VERB
fuelectenerg-1427	996	170	n=729	n=729	PROPN
fuelectenerg-1427	996	171	n=59049	n=59049	PROPN
fuelectenerg-1427	996	172	n=9	n=9	PROPN
fuelectenerg-1427	996	173	n=81	n=81	VERB
fuelectenerg-1427	996	174	n=6561	n=6561	PROPN
fuelectenerg-1427	996	175	n=59049	n=59049	PROPN
fuelectenerg-1427	996	176	n=9	n=9	PROPN
fuelectenerg-1427	996	177	n=81	n=81	ADP
fuelectenerg-1427	996	178	n=6561	n=6561	PROPN
fuelectenerg-1427	996	179	n=59049	n=59049	PROPN
fuelectenerg-1427	996	180	n=9	n=9	PROPN
fuelectenerg-1427	996	181	n=729	n=729	X
fuelectenerg-1427	996	182	n=6561	n=6561	PROPN
fuelectenerg-1427	997	1	n=531441	n=531441	ADV
fuelectenerg-1427	997	2	0	0	NUM
fuelectenerg-1427	997	3	b	b	X
fuelectenerg-1427	997	4	0	0	NUM
fuelectenerg-1427	997	5	b	b	NOUN
fuelectenerg-1427	997	6	0	0	NUM
fuelectenerg-1427	997	7	a	a	DET
fuelectenerg-1427	997	8	0	0	NUM
fuelectenerg-1427	997	9	a	a	DET
fuelectenerg-1427	997	10	0	0	NUM
fuelectenerg-1427	997	11	b	b	NOUN
fuelectenerg-1427	997	12	0	0	NUM
fuelectenerg-1427	997	13	b	b	NOUN
fuelectenerg-1427	997	14	0	0	NUM
fuelectenerg-1427	997	15	b	b	NOUN
fuelectenerg-1427	997	16	0	0	NUM
fuelectenerg-1427	997	17	b	b	NOUN
fuelectenerg-1427	997	18	0	0	NUM
fuelectenerg-1427	997	19	b	b	NOUN
fuelectenerg-1427	997	20	0	0	NUM
fuelectenerg-1427	997	21	b	b	SYM
fuelectenerg-1427	997	22	1	1	NUM
fuelectenerg-1427	997	23	b	b	SYM
fuelectenerg-1427	997	24	1	1	NUM
fuelectenerg-1427	997	25	b	b	SYM
fuelectenerg-1427	997	26	1	1	NUM
fuelectenerg-1427	997	27	a	a	DET
fuelectenerg-1427	997	28	1	1	NUM
fuelectenerg-1427	997	29	a	a	DET
fuelectenerg-1427	997	30	1	1	NUM
fuelectenerg-1427	997	31	b	b	SYM
fuelectenerg-1427	997	32	1	1	NUM
fuelectenerg-1427	997	33	b	b	SYM
fuelectenerg-1427	997	34	1	1	NUM
fuelectenerg-1427	997	35	b	b	SYM
fuelectenerg-1427	997	36	1	1	NUM
fuelectenerg-1427	997	37	b	b	SYM
fuelectenerg-1427	997	38	1	1	NUM
fuelectenerg-1427	997	39	b	b	SYM
fuelectenerg-1427	997	40	1	1	NUM
fuelectenerg-1427	997	41	b	b	SYM
fuelectenerg-1427	997	42	2	2	NUM
fuelectenerg-1427	997	43	b	b	SYM
fuelectenerg-1427	997	44	2	2	NUM
fuelectenerg-1427	997	45	b	b	SYM
fuelectenerg-1427	997	46	2	2	NUM
fuelectenerg-1427	997	47	a	a	DET
fuelectenerg-1427	997	48	2	2	NUM
fuelectenerg-1427	997	49	a	a	DET
fuelectenerg-1427	997	50	2	2	NUM
fuelectenerg-1427	997	51	b	b	SYM
fuelectenerg-1427	997	52	2	2	NUM
fuelectenerg-1427	997	53	b	b	SYM
fuelectenerg-1427	997	54	2	2	NUM
fuelectenerg-1427	997	55	b	b	SYM
fuelectenerg-1427	997	56	2	2	NUM
fuelectenerg-1427	997	57	b	b	SYM
fuelectenerg-1427	997	58	2	2	NUM
fuelectenerg-1427	997	59	b	b	SYM
fuelectenerg-1427	997	60	2	2	NUM
fuelectenerg-1427	997	61	b	b	PROPN
fuelectenerg-1427	997	62	(	(	PUNCT
fuelectenerg-1427	997	63	b	b	NOUN
fuelectenerg-1427	997	64	)	)	PUNCT
fuelectenerg-1427	997	65	figure	figure	NOUN
fuelectenerg-1427	997	66	5	5	NUM
fuelectenerg-1427	997	67	:	:	PUNCT
fuelectenerg-1427	997	68	(	(	PUNCT
fuelectenerg-1427	997	69	continued	continued	ADJ
fuelectenerg-1427	997	70	)	)	PUNCT
fuelectenerg-1427	997	71	.	.	PUNCT
fuelectenerg-1427	998	1	proof	proof	NOUN
fuelectenerg-1427	998	2	.	.	PUNCT
fuelectenerg-1427	999	1	an	an	DET
fuelectenerg-1427	999	2	expansion	expansion	NOUN
fuelectenerg-1427	999	3	is	be	AUX
fuelectenerg-1427	999	4	canonical	canonical	ADJ
fuelectenerg-1427	999	5	iff	iff	VERB
fuelectenerg-1427	999	6	its	its	PRON
fuelectenerg-1427	999	7	terms	term	NOUN
fuelectenerg-1427	999	8	are	be	AUX
fuelectenerg-1427	999	9	linearly	linearly	ADV
fuelectenerg-1427	999	10	independent	independent	ADJ
fuelectenerg-1427	999	11	;	;	PUNCT
fuelectenerg-1427	999	12	none	none	NOUN
fuelectenerg-1427	999	13	of	of	ADP
fuelectenerg-1427	999	14	the	the	DET
fuelectenerg-1427	999	15	terms	term	NOUN
fuelectenerg-1427	999	16	is	be	AUX
fuelectenerg-1427	999	17	equal	equal	ADJ
fuelectenerg-1427	999	18	to	to	ADP
fuelectenerg-1427	999	19	a	a	DET
fuelectenerg-1427	999	20	linear	linear	ADJ
fuelectenerg-1427	999	21	combination	combination	NOUN
fuelectenerg-1427	999	22	of	of	ADP
fuelectenerg-1427	999	23	other	other	ADJ
fuelectenerg-1427	999	24	terms	term	NOUN
fuelectenerg-1427	999	25	.	.	PUNCT
fuelectenerg-1427	1000	1	using	use	VERB
fuelectenerg-1427	1000	2	this	this	DET
fuelectenerg-1427	1000	3	fact	fact	NOUN
fuelectenerg-1427	1000	4	,	,	PUNCT
fuelectenerg-1427	1000	5	it	it	PRON
fuelectenerg-1427	1000	6	was	be	AUX
fuelectenerg-1427	1000	7	proven	prove	VERB
fuelectenerg-1427	1000	8	that	that	SCONJ
fuelectenerg-1427	1000	9	all	all	DET
fuelectenerg-1427	1000	10	gf(2	gf(2	PROPN
fuelectenerg-1427	1000	11	)	)	PUNCT
fuelectenerg-1427	1000	12	ifs	if	NOUN
fuelectenerg-1427	1000	13	are	be	AUX
fuelectenerg-1427	1000	14	canonical	canonical	ADJ
fuelectenerg-1427	1000	15	.	.	PUNCT
fuelectenerg-1427	1001	1	analogously	analogously	ADV
fuelectenerg-1427	1001	2	over	over	ADP
fuelectenerg-1427	1001	3	gf(3	gf(3	PROPN
fuelectenerg-1427	1001	4	)	)	PUNCT
fuelectenerg-1427	1001	5	,	,	PUNCT
fuelectenerg-1427	1001	6	for	for	ADP
fuelectenerg-1427	1001	7	any	any	DET
fuelectenerg-1427	1001	8	function	function	NOUN
fuelectenerg-1427	1001	9	f	f	PROPN
fuelectenerg-1427	1001	10	of	of	ADP
fuelectenerg-1427	1001	11	the	the	DET
fuelectenerg-1427	1001	12	same	same	ADJ
fuelectenerg-1427	1001	13	number	number	NOUN
fuelectenerg-1427	1001	14	of	of	ADP
fuelectenerg-1427	1001	15	variables	variable	NOUN
fuelectenerg-1427	1001	16	,	,	PUNCT
fuelectenerg-1427	1001	17	there	there	PRON
fuelectenerg-1427	1001	18	exists	exist	VERB
fuelectenerg-1427	1001	19	one	one	NUM
fuelectenerg-1427	1001	20	and	and	CCONJ
fuelectenerg-1427	1001	21	only	only	ADV
fuelectenerg-1427	1001	22	one	one	NUM
fuelectenerg-1427	1001	23	set	set	NOUN
fuelectenerg-1427	1001	24	of	of	ADP
fuelectenerg-1427	1001	25	coefficients	coefficient	NOUN
fuelectenerg-1427	1001	26	ai	ai	VERB
fuelectenerg-1427	1001	27	such	such	ADJ
fuelectenerg-1427	1001	28	that	that	SCONJ
fuelectenerg-1427	1001	29	f	f	PROPN
fuelectenerg-1427	1001	30	is	be	AUX
fuelectenerg-1427	1001	31	uniquely	uniquely	ADV
fuelectenerg-1427	1001	32	tif	tif	NOUN
fuelectenerg-1427	1001	33	-	-	PUNCT
fuelectenerg-1427	1001	34	expandable	expandable	ADJ
fuelectenerg-1427	1001	35	using	using	NOUN
fuelectenerg-1427	1001	36	ai	ai	NOUN
fuelectenerg-1427	1001	37	and	and	CCONJ
fuelectenerg-1427	1001	38	thus	thus	ADV
fuelectenerg-1427	1001	39	the	the	DET
fuelectenerg-1427	1001	40	resulting	result	VERB
fuelectenerg-1427	1001	41	expression	expression	NOUN
fuelectenerg-1427	1001	42	is	be	AUX
fuelectenerg-1427	1001	43	canonical	canonical	ADJ
fuelectenerg-1427	1001	44	.	.	PUNCT
fuelectenerg-1427	1002	1	by	by	ADP
fuelectenerg-1427	1002	2	induction	induction	NOUN
fuelectenerg-1427	1002	3	on	on	ADP
fuelectenerg-1427	1002	4	number	number	NOUN
fuelectenerg-1427	1002	5	of	of	ADP
fuelectenerg-1427	1002	6	variables	variable	NOUN
fuelectenerg-1427	1002	7	,	,	PUNCT
fuelectenerg-1427	1002	8	terms	term	NOUN
fuelectenerg-1427	1002	9	in	in	ADP
fuelectenerg-1427	1002	10	tifs	tifs	PROPN
fuelectenerg-1427	1002	11	will	will	AUX
fuelectenerg-1427	1002	12	be	be	AUX
fuelectenerg-1427	1002	13	linearly	linearly	ADV
fuelectenerg-1427	1002	14	independent	independent	ADJ
fuelectenerg-1427	1002	15	and	and	CCONJ
fuelectenerg-1427	1002	16	thus	thus	ADV
fuelectenerg-1427	1002	17	canonical	canonical	ADJ
fuelectenerg-1427	1002	18	.	.	PUNCT
fuelectenerg-1427	1003	1	theorem	theorem	VERB
fuelectenerg-1427	1003	2	4	4	NUM
fuelectenerg-1427	1003	3	.	.	PUNCT
fuelectenerg-1427	1003	4	ternary	ternary	ADJ
fuelectenerg-1427	1003	5	generalized	generalize	VERB
fuelectenerg-1427	1003	6	inclusive	inclusive	ADJ
fuelectenerg-1427	1003	7	forms	form	NOUN
fuelectenerg-1427	1003	8	(	(	PUNCT
fuelectenerg-1427	1003	9	tgifs	tgif	NOUN
fuelectenerg-1427	1003	10	)	)	PUNCT
fuelectenerg-1427	1003	11	are	be	AUX
fuelectenerg-1427	1003	12	canonical	canonical	ADJ
fuelectenerg-1427	1003	13	with	with	ADP
fuelectenerg-1427	1003	14	respect	respect	NOUN
fuelectenerg-1427	1003	15	to	to	ADP
fuelectenerg-1427	1003	16	given	give	VERB
fuelectenerg-1427	1003	17	variable	variable	ADJ
fuelectenerg-1427	1003	18	order	order	NOUN
fuelectenerg-1427	1003	19	.	.	PUNCT
fuelectenerg-1427	1004	1	proof	proof	NOUN
fuelectenerg-1427	1004	2	.	.	PUNCT
fuelectenerg-1427	1005	1	since	since	SCONJ
fuelectenerg-1427	1005	2	tgif	tgif	NOUN
fuelectenerg-1427	1005	3	is	be	AUX
fuelectenerg-1427	1005	4	the	the	DET
fuelectenerg-1427	1005	5	union	union	NOUN
fuelectenerg-1427	1005	6	of	of	ADP
fuelectenerg-1427	1005	7	the	the	DET
fuelectenerg-1427	1005	8	corresponding	corresponding	ADJ
fuelectenerg-1427	1005	9	tifs	tifs	PROPN
fuelectenerg-1427	1005	10	,	,	PUNCT
fuelectenerg-1427	1005	11	and	and	CCONJ
fuelectenerg-1427	1005	12	since	since	SCONJ
fuelectenerg-1427	1005	13	each	each	DET
fuelectenerg-1427	1005	14	tif	tif	PROPN
fuelectenerg-1427	1005	15	is	be	AUX
fuelectenerg-1427	1005	16	canonical	canonical	ADJ
fuelectenerg-1427	1005	17	,	,	PUNCT
fuelectenerg-1427	1005	18	then	then	ADV
fuelectenerg-1427	1005	19	the	the	DET
fuelectenerg-1427	1005	20	resulting	result	VERB
fuelectenerg-1427	1005	21	union	union	NOUN
fuelectenerg-1427	1005	22	of	of	ADP
fuelectenerg-1427	1005	23	the	the	DET
fuelectenerg-1427	1005	24	corresponding	corresponding	ADJ
fuelectenerg-1427	1005	25	canonical	canonical	ADJ
fuelectenerg-1427	1005	26	tifs	tif	NOUN
fuelectenerg-1427	1005	27	will	will	AUX
fuelectenerg-1427	1005	28	be	be	AUX
fuelectenerg-1427	1005	29	also	also	ADV
fuelectenerg-1427	1005	30	canonical	canonical	ADJ
fuelectenerg-1427	1005	31	.	.	PUNCT
fuelectenerg-1427	1006	1	for	for	ADP
fuelectenerg-1427	1006	2	different	different	ADJ
fuelectenerg-1427	1006	3	variable	variable	ADJ
fuelectenerg-1427	1006	4	orderings	ordering	NOUN
fuelectenerg-1427	1006	5	,	,	PUNCT
fuelectenerg-1427	1006	6	some	some	DET
fuelectenerg-1427	1006	7	forms	form	NOUN
fuelectenerg-1427	1006	8	are	be	AUX
fuelectenerg-1427	1006	9	not	not	PART
fuelectenerg-1427	1006	10	repeated	repeat	VERB
fuelectenerg-1427	1006	11	while	while	SCONJ
fuelectenerg-1427	1006	12	other	other	ADJ
fuelectenerg-1427	1006	13	forms	form	NOUN
fuelectenerg-1427	1006	14	are	be	AUX
fuelectenerg-1427	1006	15	.	.	PUNCT
fuelectenerg-1427	1007	1	therefore	therefore	ADV
fuelectenerg-1427	1007	2	the	the	DET
fuelectenerg-1427	1007	3	union	union	NOUN
fuelectenerg-1427	1007	4	of	of	ADP
fuelectenerg-1427	1007	5	sets	set	NOUN
fuelectenerg-1427	1007	6	of	of	ADP
fuelectenerg-1427	1007	7	tifs	tif	NOUN
fuelectenerg-1427	1007	8	for	for	ADP
fuelectenerg-1427	1007	9	all	all	DET
fuelectenerg-1427	1007	10	variable	variable	ADJ
fuelectenerg-1427	1007	11	orders	order	NOUN
fuelectenerg-1427	1007	12	contains	contain	VERB
fuelectenerg-1427	1007	13	more	more	ADJ
fuelectenerg-1427	1007	14	forms	form	NOUN
fuelectenerg-1427	1007	15	than	than	ADP
fuelectenerg-1427	1007	16	any	any	PRON
fuelectenerg-1427	1007	17	of	of	ADP
fuelectenerg-1427	1007	18	the	the	DET
fuelectenerg-1427	1007	19	tif	tif	PROPN
fuelectenerg-1427	1007	20	sets	set	NOUN
fuelectenerg-1427	1007	21	taken	take	VERB
fuelectenerg-1427	1007	22	separately	separately	ADV
fuelectenerg-1427	1007	23	and	and	CCONJ
fuelectenerg-1427	1007	24	less	less	ADJ
fuelectenerg-1427	1007	25	forms	form	NOUN
fuelectenerg-1427	1007	26	than	than	ADP
fuelectenerg-1427	1007	27	total	total	ADJ
fuelectenerg-1427	1007	28	sum	sum	NOUN
fuelectenerg-1427	1007	29	of	of	ADP
fuelectenerg-1427	1007	30	all	all	DET
fuelectenerg-1427	1007	31	tifs	tif	NOUN
fuelectenerg-1427	1007	32	.	.	PUNCT
fuelectenerg-1427	1008	1	generalized	generalized	ADJ
fuelectenerg-1427	1008	2	inclusive	inclusive	ADJ
fuelectenerg-1427	1008	3	forms	form	NOUN
fuelectenerg-1427	1008	4	include	include	VERB
fuelectenerg-1427	1008	5	other	other	ADJ
fuelectenerg-1427	1008	6	forms	form	NOUN
fuelectenerg-1427	1008	7	such	such	ADJ
fuelectenerg-1427	1008	8	as	as	ADP
fuelectenerg-1427	1008	9	grms	grm	NOUN
fuelectenerg-1427	1008	10	over	over	ADP
fuelectenerg-1427	1008	11	gf(3	gf(3	PROPN
fuelectenerg-1427	1008	12	)	)	PUNCT
fuelectenerg-1427	1008	13	as	as	SCONJ
fuelectenerg-1427	1008	14	can	can	AUX
fuelectenerg-1427	1008	15	be	be	AUX
fuelectenerg-1427	1008	16	shown	show	VERB
fuelectenerg-1427	1008	17	by	by	ADP
fuelectenerg-1427	1008	18	considering	consider	VERB
fuelectenerg-1427	1008	19	all	all	DET
fuelectenerg-1427	1008	20	possible	possible	ADJ
fuelectenerg-1427	1008	21	combinations	combination	NOUN
fuelectenerg-1427	1008	22	of	of	ADP
fuelectenerg-1427	1008	23	literals	literal	NOUN
fuelectenerg-1427	1008	24	for	for	ADP
fuelectenerg-1427	1008	25	all	all	DET
fuelectenerg-1427	1008	26	possible	possible	ADJ
fuelectenerg-1427	1008	27	orders	order	NOUN
fuelectenerg-1427	1008	28	of	of	ADP
fuelectenerg-1427	1008	29	variables	variable	NOUN
fuelectenerg-1427	1008	30	.	.	PUNCT
fuelectenerg-1427	1009	1	if	if	SCONJ
fuelectenerg-1427	1009	2	we	we	PRON
fuelectenerg-1427	1009	3	relax	relax	VERB
fuelectenerg-1427	1009	4	the	the	DET
fuelectenerg-1427	1009	5	requirement	requirement	NOUN
fuelectenerg-1427	1009	6	of	of	ADP
fuelectenerg-1427	1009	7	fixed	fix	VERB
fuelectenerg-1427	1009	8	variable	variable	ADJ
fuelectenerg-1427	1009	9	ordering	ordering	NOUN
fuelectenerg-1427	1009	10	,	,	PUNCT
fuelectenerg-1427	1009	11	and	and	CCONJ
fuelectenerg-1427	1009	12	allow	allow	VERB
fuelectenerg-1427	1009	13	any	any	DET
fuelectenerg-1427	1009	14	ordering	ordering	NOUN
fuelectenerg-1427	1009	15	of	of	ADP
fuelectenerg-1427	1009	16	variables	variable	NOUN
fuelectenerg-1427	1009	17	in	in	ADP
fuelectenerg-1427	1009	18	branches	branch	NOUN
fuelectenerg-1427	1009	19	of	of	ADP
fuelectenerg-1427	1009	20	the	the	DET
fuelectenerg-1427	1009	21	tree	tree	NOUN
fuelectenerg-1427	1009	22	but	but	CCONJ
fuelectenerg-1427	1009	23	do	do	AUX
fuelectenerg-1427	1009	24	not	not	PART
fuelectenerg-1427	1009	25	allow	allow	VERB
fuelectenerg-1427	1009	26	repetitions	repetition	NOUN
fuelectenerg-1427	1009	27	of	of	ADP
fuelectenerg-1427	1009	28	variables	variable	NOUN
fuelectenerg-1427	1009	29	in	in	ADP
fuelectenerg-1427	1009	30	the	the	DET
fuelectenerg-1427	1009	31	branches	branch	NOUN
fuelectenerg-1427	1009	32	,	,	PUNCT
fuelectenerg-1427	1009	33	we	we	PRON
fuelectenerg-1427	1009	34	generate	generate	VERB
fuelectenerg-1427	1009	35	more	more	ADJ
fuelectenerg-1427	1009	36	general	general	ADJ
fuelectenerg-1427	1009	37	gf(3	gf(3	PROPN
fuelectenerg-1427	1009	38	)	)	PUNCT
fuelectenerg-1427	1009	39	family	family	NOUN
fuelectenerg-1427	1009	40	of	of	ADP
fuelectenerg-1427	1009	41	forms	form	NOUN
fuelectenerg-1427	1009	42	.	.	PUNCT
fuelectenerg-1427	1010	1	111	111	NUM
fuelectenerg-1427	1010	2	an	an	DET
fuelectenerg-1427	1010	3	extended	extend	VERB
fuelectenerg-1427	1010	4	green	green	ADJ
fuelectenerg-1427	1010	5	sasao	sasao	PROPN
fuelectenerg-1427	1010	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1010	7	of	of	ADP
fuelectenerg-1427	1010	8	canonical	canonical	ADJ
fuelectenerg-1427	1010	9	ternary	ternary	ADJ
fuelectenerg-1427	1010	10	galois	galois	NOUN
fuelectenerg-1427	1010	11	forms	form	NOUN
fuelectenerg-1427	1010	12	...	...	PUNCT
fuelectenerg-1427	1011	1	s	s	PART
fuelectenerg-1427	1011	2	s	s	X
fuelectenerg-1427	1011	3	s	s	X
fuelectenerg-1427	1011	4	s	s	NOUN
fuelectenerg-1427	1011	5	0	0	NUM
fuelectenerg-1427	1011	6	a	a	DET
fuelectenerg-1427	1011	7	1	1	NUM
fuelectenerg-1427	1011	8	a	a	DET
fuelectenerg-1427	1011	9	2	2	NUM
fuelectenerg-1427	1011	10	a	a	DET
fuelectenerg-1427	1011	11	s	s	NOUN
fuelectenerg-1427	1011	12	s	s	X
fuelectenerg-1427	1011	13	d	d	X
fuelectenerg-1427	1011	14	d	d	X
fuelectenerg-1427	1011	15	s	s	X
fuelectenerg-1427	1011	16	s	s	X
fuelectenerg-1427	1011	17	s	s	X
fuelectenerg-1427	1011	18	d	d	X
fuelectenerg-1427	1011	19	1	1	NUM
fuelectenerg-1427	1011	20	(	(	PUNCT
fuelectenerg-1427	1011	21	b	b	NOUN
fuelectenerg-1427	1011	22	,	,	PUNCT
fuelectenerg-1427	1011	23	)	)	PUNCT
fuelectenerg-1427	1011	24	2	2	NUM
fuelectenerg-1427	1011	25	b	b	NOUN
fuelectenerg-1427	1011	26	,	,	PUNCT
fuelectenerg-1427	1011	27	s	s	NOUN
fuelectenerg-1427	1011	28	d	d	X
fuelectenerg-1427	1011	29	d	d	PROPN
fuelectenerg-1427	1011	30	d	d	PROPN
fuelectenerg-1427	1011	31	1	1	NUM
fuelectenerg-1427	1011	32	(	(	PUNCT
fuelectenerg-1427	1011	33	b	b	NOUN
fuelectenerg-1427	1011	34	,	,	PUNCT
fuelectenerg-1427	1011	35	)	)	PUNCT
fuelectenerg-1427	1011	36	2	2	NUM
fuelectenerg-1427	1011	37	b	b	NOUN
fuelectenerg-1427	1011	38	,	,	PUNCT
fuelectenerg-1427	1011	39	s	s	X
fuelectenerg-1427	1011	40	s	s	NOUN
fuelectenerg-1427	1011	41	s	s	NOUN
fuelectenerg-1427	1011	42	0	0	NUM
fuelectenerg-1427	1011	43	a	a	DET
fuelectenerg-1427	1011	44	0	0	NUM
fuelectenerg-1427	1011	45	a	a	DET
fuelectenerg-1427	1011	46	1	1	NUM
fuelectenerg-1427	1011	47	a	a	DET
fuelectenerg-1427	1011	48	1	1	NUM
fuelectenerg-1427	1011	49	a	a	DET
fuelectenerg-1427	1011	50	2	2	NUM
fuelectenerg-1427	1011	51	a	a	DET
fuelectenerg-1427	1011	52	2	2	NUM
fuelectenerg-1427	1011	53	a	a	DET
fuelectenerg-1427	1011	54	d	d	PROPN
fuelectenerg-1427	1011	55	1	1	NUM
fuelectenerg-1427	1011	56	1	1	NUM
fuelectenerg-1427	1011	57	1	1	NUM
fuelectenerg-1427	1011	58	1	1	NUM
fuelectenerg-1427	1011	59	1	1	NUM
fuelectenerg-1427	1011	60	1	1	NUM
fuelectenerg-1427	1011	61	1	1	NUM
fuelectenerg-1427	1011	62	1	1	NUM
fuelectenerg-1427	1011	63	1	1	NUM
fuelectenerg-1427	1011	64	1	1	NUM
fuelectenerg-1427	1011	65	11	11	NUM
fuelectenerg-1427	1011	66	1	1	NUM
fuelectenerg-1427	1011	67	1	1	NUM
fuelectenerg-1427	1011	68	1	1	NUM
fuelectenerg-1427	1011	69	1	1	NUM
fuelectenerg-1427	1011	70	1	1	NUM
fuelectenerg-1427	1011	71	1	1	NUM
fuelectenerg-1427	1011	72	1	1	NUM
fuelectenerg-1427	1011	73	1	1	NUM
fuelectenerg-1427	1011	74	1	1	NUM
fuelectenerg-1427	1011	75	1	1	NUM
fuelectenerg-1427	1011	76	1(a	1(a	NUM
fuelectenerg-1427	1011	77	,	,	PUNCT
fuelectenerg-1427	1011	78	)	)	PUNCT
fuelectenerg-1427	1011	79	2	2	NUM
fuelectenerg-1427	1011	80	(	(	PUNCT
fuelectenerg-1427	1011	81	a	a	PRON
fuelectenerg-1427	1011	82	,	,	PUNCT
fuelectenerg-1427	1011	83	)	)	PUNCT
fuelectenerg-1427	1011	84	2	2	NUM
fuelectenerg-1427	1011	85	(	(	PUNCT
fuelectenerg-1427	1011	86	a	a	PRON
fuelectenerg-1427	1011	87	,	,	PUNCT
fuelectenerg-1427	1011	88	)	)	PUNCT
fuelectenerg-1427	1011	89	2	2	NUM
fuelectenerg-1427	1011	90	(	(	PUNCT
fuelectenerg-1427	1011	91	a	a	PRON
fuelectenerg-1427	1011	92	,	,	PUNCT
fuelectenerg-1427	1011	93	)	)	PUNCT
fuelectenerg-1427	1011	94	2	2	NUM
fuelectenerg-1427	1011	95	(	(	PUNCT
fuelectenerg-1427	1011	96	a	a	PRON
fuelectenerg-1427	1011	97	,	,	PUNCT
fuelectenerg-1427	1011	98	)	)	PUNCT
fuelectenerg-1427	1011	99	2	2	NUM
fuelectenerg-1427	1011	100	(	(	PUNCT
fuelectenerg-1427	1011	101	a	a	PRON
fuelectenerg-1427	1011	102	,	,	PUNCT
fuelectenerg-1427	1011	103	)	)	PUNCT
fuelectenerg-1427	1011	104	2	2	NUM
fuelectenerg-1427	1011	105	(	(	PUNCT
fuelectenerg-1427	1011	106	a	a	PRON
fuelectenerg-1427	1011	107	,	,	PUNCT
fuelectenerg-1427	1011	108	)	)	PUNCT
fuelectenerg-1427	1011	109	2	2	NUM
fuelectenerg-1427	1011	110	(	(	PUNCT
fuelectenerg-1427	1011	111	a	a	PRON
fuelectenerg-1427	1011	112	,	,	PUNCT
fuelectenerg-1427	1011	113	)	)	PUNCT
fuelectenerg-1427	1011	114	2	2	NUM
fuelectenerg-1427	1011	115	(	(	PUNCT
fuelectenerg-1427	1011	116	a	a	PRON
fuelectenerg-1427	1011	117	,	,	PUNCT
fuelectenerg-1427	1011	118	)	)	PUNCT
fuelectenerg-1427	1011	119	2	2	NUM
fuelectenerg-1427	1011	120	(	(	PUNCT
fuelectenerg-1427	1011	121	a	a	PRON
fuelectenerg-1427	1011	122	,	,	PUNCT
fuelectenerg-1427	1011	123	)	)	PUNCT
fuelectenerg-1427	1011	124	2	2	NUM
fuelectenerg-1427	1011	125	(	(	PUNCT
fuelectenerg-1427	1011	126	a	a	PRON
fuelectenerg-1427	1011	127	,	,	PUNCT
fuelectenerg-1427	1011	128	)	)	PUNCT
fuelectenerg-1427	1011	129	2	2	NUM
fuelectenerg-1427	1011	130	(	(	PUNCT
fuelectenerg-1427	1011	131	a	a	PRON
fuelectenerg-1427	1011	132	,	,	PUNCT
fuelectenerg-1427	1011	133	)	)	PUNCT
fuelectenerg-1427	1011	134	2	2	NUM
fuelectenerg-1427	1011	135	(	(	PUNCT
fuelectenerg-1427	1011	136	a	a	PRON
fuelectenerg-1427	1011	137	,	,	PUNCT
fuelectenerg-1427	1011	138	)	)	PUNCT
fuelectenerg-1427	1011	139	2	2	NUM
fuelectenerg-1427	1011	140	(	(	PUNCT
fuelectenerg-1427	1011	141	a	a	PRON
fuelectenerg-1427	1011	142	,	,	PUNCT
fuelectenerg-1427	1011	143	)	)	PUNCT
fuelectenerg-1427	1011	144	2	2	NUM
fuelectenerg-1427	1011	145	(	(	PUNCT
fuelectenerg-1427	1011	146	a	a	PRON
fuelectenerg-1427	1011	147	,	,	PUNCT
fuelectenerg-1427	1011	148	)	)	PUNCT
fuelectenerg-1427	1011	149	2	2	NUM
fuelectenerg-1427	1011	150	(	(	PUNCT
fuelectenerg-1427	1011	151	a	a	PRON
fuelectenerg-1427	1011	152	,	,	PUNCT
fuelectenerg-1427	1011	153	)	)	PUNCT
fuelectenerg-1427	1011	154	2	2	NUM
fuelectenerg-1427	1011	155	(	(	PUNCT
fuelectenerg-1427	1011	156	a	a	PRON
fuelectenerg-1427	1011	157	,	,	PUNCT
fuelectenerg-1427	1011	158	)	)	PUNCT
fuelectenerg-1427	1011	159	2	2	NUM
fuelectenerg-1427	1011	160	(	(	PUNCT
fuelectenerg-1427	1011	161	a	a	PRON
fuelectenerg-1427	1011	162	,	,	PUNCT
fuelectenerg-1427	1011	163	)	)	PUNCT
fuelectenerg-1427	1011	164	2	2	NUM
fuelectenerg-1427	1011	165	(	(	PUNCT
fuelectenerg-1427	1011	166	a	a	PRON
fuelectenerg-1427	1011	167	,	,	PUNCT
fuelectenerg-1427	1011	168	)	)	PUNCT
fuelectenerg-1427	1011	169	2	2	NUM
fuelectenerg-1427	1011	170	(	(	PUNCT
fuelectenerg-1427	1011	171	a	a	PRON
fuelectenerg-1427	1011	172	,	,	PUNCT
fuelectenerg-1427	1011	173	)	)	PUNCT
fuelectenerg-1427	1011	174	2	2	NUM
fuelectenerg-1427	1011	175	(	(	PUNCT
fuelectenerg-1427	1011	176	a	a	PRON
fuelectenerg-1427	1011	177	,	,	PUNCT
fuelectenerg-1427	1011	178	)	)	PUNCT
fuelectenerg-1427	1011	179	2	2	NUM
fuelectenerg-1427	1011	180	(	(	PUNCT
fuelectenerg-1427	1011	181	a	a	PRON
fuelectenerg-1427	1011	182	,	,	PUNCT
fuelectenerg-1427	1011	183	)	)	PUNCT
fuelectenerg-1427	1011	184	2	2	NUM
fuelectenerg-1427	1011	185	(	(	PUNCT
fuelectenerg-1427	1011	186	a	a	PRON
fuelectenerg-1427	1011	187	,	,	PUNCT
fuelectenerg-1427	1011	188	)	)	PUNCT
fuelectenerg-1427	1011	189	2	2	NUM
fuelectenerg-1427	1011	190	(	(	PUNCT
fuelectenerg-1427	1011	191	a	a	PRON
fuelectenerg-1427	1011	192	,	,	PUNCT
fuelectenerg-1427	1011	193	)	)	PUNCT
fuelectenerg-1427	1011	194	2	2	NUM
fuelectenerg-1427	1011	195	a	a	PRON
fuelectenerg-1427	1011	196	,	,	PUNCT
fuelectenerg-1427	1011	197	a	a	PRON
fuelectenerg-1427	1011	198	,	,	PUNCT
fuelectenerg-1427	1011	199	a	a	PRON
fuelectenerg-1427	1011	200	,	,	PUNCT
fuelectenerg-1427	1011	201	a	a	PRON
fuelectenerg-1427	1011	202	,	,	PUNCT
fuelectenerg-1427	1011	203	a	a	PRON
fuelectenerg-1427	1011	204	,	,	PUNCT
fuelectenerg-1427	1011	205	a	a	PRON
fuelectenerg-1427	1011	206	,	,	PUNCT
fuelectenerg-1427	1011	207	a	a	PRON
fuelectenerg-1427	1011	208	,	,	PUNCT
fuelectenerg-1427	1011	209	a	a	PRON
fuelectenerg-1427	1011	210	,	,	PUNCT
fuelectenerg-1427	1011	211	a	a	PRON
fuelectenerg-1427	1011	212	,	,	PUNCT
fuelectenerg-1427	1011	213	a	a	PRON
fuelectenerg-1427	1011	214	,	,	PUNCT
fuelectenerg-1427	1011	215	a	a	PRON
fuelectenerg-1427	1011	216	,	,	PUNCT
fuelectenerg-1427	1011	217	a	a	PRON
fuelectenerg-1427	1011	218	,	,	PUNCT
fuelectenerg-1427	1011	219	a	a	PRON
fuelectenerg-1427	1011	220	,	,	PUNCT
fuelectenerg-1427	1011	221	a	a	PRON
fuelectenerg-1427	1011	222	,	,	PUNCT
fuelectenerg-1427	1011	223	a	a	PRON
fuelectenerg-1427	1011	224	,	,	PUNCT
fuelectenerg-1427	1011	225	a	a	PRON
fuelectenerg-1427	1011	226	,	,	PUNCT
fuelectenerg-1427	1011	227	a	a	PRON
fuelectenerg-1427	1011	228	,	,	PUNCT
fuelectenerg-1427	1011	229	a	a	PRON
fuelectenerg-1427	1011	230	,	,	PUNCT
fuelectenerg-1427	1011	231	a	a	PRON
fuelectenerg-1427	1011	232	,	,	PUNCT
fuelectenerg-1427	1011	233	a	a	PRON
fuelectenerg-1427	1011	234	,	,	PUNCT
fuelectenerg-1427	1011	235	a	a	PRON
fuelectenerg-1427	1011	236	,	,	PUNCT
fuelectenerg-1427	1011	237	a	a	PRON
fuelectenerg-1427	1011	238	,	,	PUNCT
fuelectenerg-1427	1011	239	a	a	PRON
fuelectenerg-1427	1011	240	,	,	PUNCT
fuelectenerg-1427	1011	241	s	s	NOUN
fuelectenerg-1427	1011	242	s	s	X
fuelectenerg-1427	1011	243	d	d	X
fuelectenerg-1427	1011	244	d	d	X
fuelectenerg-1427	1011	245	s	s	X
fuelectenerg-1427	1011	246	s	s	X
fuelectenerg-1427	1011	247	d	d	X
fuelectenerg-1427	1011	248	d	d	SYM
fuelectenerg-1427	1011	249	1	1	NUM
fuelectenerg-1427	1011	250	(	(	PUNCT
fuelectenerg-1427	1011	251	b	b	NOUN
fuelectenerg-1427	1011	252	,	,	PUNCT
fuelectenerg-1427	1011	253	)	)	PUNCT
fuelectenerg-1427	1011	254	2	2	NUM
fuelectenerg-1427	1011	255	b	b	NOUN
fuelectenerg-1427	1011	256	,	,	PUNCT
fuelectenerg-1427	1011	257	sd	sd	ADP
fuelectenerg-1427	1011	258	d	d	PROPN
fuelectenerg-1427	1011	259	d	d	PROPN
fuelectenerg-1427	1011	260	1	1	NUM
fuelectenerg-1427	1011	261	(	(	PUNCT
fuelectenerg-1427	1011	262	b	b	NOUN
fuelectenerg-1427	1011	263	,	,	PUNCT
fuelectenerg-1427	1011	264	)	)	PUNCT
fuelectenerg-1427	1011	265	2	2	NUM
fuelectenerg-1427	1011	266	b	b	NOUN
fuelectenerg-1427	1011	267	,	,	PUNCT
fuelectenerg-1427	1011	268	s	s	X
fuelectenerg-1427	1011	269	s	s	NOUN
fuelectenerg-1427	1011	270	s	s	NOUN
fuelectenerg-1427	1011	271	0	0	NUM
fuelectenerg-1427	1011	272	a	a	DET
fuelectenerg-1427	1011	273	0	0	NUM
fuelectenerg-1427	1011	274	a	a	DET
fuelectenerg-1427	1011	275	0	0	NUM
fuelectenerg-1427	1012	1	a	a	DET
fuelectenerg-1427	1012	2	0	0	NUM
fuelectenerg-1427	1012	3	a	a	DET
fuelectenerg-1427	1012	4	0	0	NUM
fuelectenerg-1427	1012	5	a	a	DET
fuelectenerg-1427	1012	6	0	0	NUM
fuelectenerg-1427	1012	7	a	a	DET
fuelectenerg-1427	1012	8	0	0	NUM
fuelectenerg-1427	1012	9	a	a	DET
fuelectenerg-1427	1012	10	0	0	NUM
fuelectenerg-1427	1012	11	a	a	DET
fuelectenerg-1427	1012	12	0	0	NUM
fuelectenerg-1427	1012	13	a	a	DET
fuelectenerg-1427	1012	14	0	0	NUM
fuelectenerg-1427	1012	15	a	a	DET
fuelectenerg-1427	1012	16	0	0	NUM
fuelectenerg-1427	1012	17	a	a	DET
fuelectenerg-1427	1012	18	0	0	NUM
fuelectenerg-1427	1012	19	a	a	DET
fuelectenerg-1427	1012	20	0	0	NUM
fuelectenerg-1427	1012	21	a	a	DET
fuelectenerg-1427	1012	22	0	0	NUM
fuelectenerg-1427	1012	23	a	a	DET
fuelectenerg-1427	1012	24	0	0	NUM
fuelectenerg-1427	1012	25	a	a	DET
fuelectenerg-1427	1012	26	0	0	NUM
fuelectenerg-1427	1012	27	a0	a0	NOUN
fuelectenerg-1427	1012	28	a	a	DET
fuelectenerg-1427	1012	29	0	0	NUM
fuelectenerg-1427	1012	30	a	a	DET
fuelectenerg-1427	1012	31	0	0	NUM
fuelectenerg-1427	1012	32	a	a	DET
fuelectenerg-1427	1012	33	1	1	NUM
fuelectenerg-1427	1012	34	a	a	DET
fuelectenerg-1427	1012	35	1	1	NUM
fuelectenerg-1427	1012	36	a	a	DET
fuelectenerg-1427	1012	37	1	1	NUM
fuelectenerg-1427	1012	38	a	a	DET
fuelectenerg-1427	1012	39	1	1	NUM
fuelectenerg-1427	1012	40	a	a	DET
fuelectenerg-1427	1012	41	1	1	NUM
fuelectenerg-1427	1012	42	a	a	DET
fuelectenerg-1427	1012	43	1	1	NUM
fuelectenerg-1427	1012	44	a	a	DET
fuelectenerg-1427	1012	45	1	1	NUM
fuelectenerg-1427	1012	46	a	a	DET
fuelectenerg-1427	1012	47	1	1	NUM
fuelectenerg-1427	1012	48	a	a	DET
fuelectenerg-1427	1012	49	1	1	NUM
fuelectenerg-1427	1012	50	a	a	DET
fuelectenerg-1427	1012	51	1	1	NUM
fuelectenerg-1427	1012	52	a	a	DET
fuelectenerg-1427	1012	53	1	1	NUM
fuelectenerg-1427	1012	54	a	a	DET
fuelectenerg-1427	1012	55	1	1	NUM
fuelectenerg-1427	1012	56	a	a	DET
fuelectenerg-1427	1012	57	1	1	NUM
fuelectenerg-1427	1012	58	a	a	DET
fuelectenerg-1427	1012	59	1	1	NUM
fuelectenerg-1427	1012	60	a	a	DET
fuelectenerg-1427	1012	61	1	1	NUM
fuelectenerg-1427	1012	62	a	a	DET
fuelectenerg-1427	1012	63	1	1	NUM
fuelectenerg-1427	1012	64	a1	a1	NOUN
fuelectenerg-1427	1012	65	a	a	DET
fuelectenerg-1427	1012	66	1	1	NUM
fuelectenerg-1427	1012	67	a	a	DET
fuelectenerg-1427	1012	68	1	1	NUM
fuelectenerg-1427	1012	69	a	a	DET
fuelectenerg-1427	1012	70	2	2	NUM
fuelectenerg-1427	1012	71	a	a	DET
fuelectenerg-1427	1012	72	2	2	NUM
fuelectenerg-1427	1012	73	a	a	DET
fuelectenerg-1427	1012	74	2	2	NUM
fuelectenerg-1427	1012	75	a	a	DET
fuelectenerg-1427	1012	76	2	2	NUM
fuelectenerg-1427	1012	77	a	a	DET
fuelectenerg-1427	1012	78	2	2	NUM
fuelectenerg-1427	1012	79	a	a	DET
fuelectenerg-1427	1012	80	2	2	NUM
fuelectenerg-1427	1012	81	a	a	DET
fuelectenerg-1427	1012	82	2	2	NUM
fuelectenerg-1427	1012	83	a	a	DET
fuelectenerg-1427	1012	84	2	2	NUM
fuelectenerg-1427	1012	85	a	a	DET
fuelectenerg-1427	1012	86	2	2	NUM
fuelectenerg-1427	1012	87	a	a	DET
fuelectenerg-1427	1012	88	2	2	NUM
fuelectenerg-1427	1012	89	a	a	DET
fuelectenerg-1427	1012	90	2	2	NUM
fuelectenerg-1427	1012	91	a	a	DET
fuelectenerg-1427	1012	92	2	2	NUM
fuelectenerg-1427	1012	93	a	a	DET
fuelectenerg-1427	1012	94	2	2	NUM
fuelectenerg-1427	1012	95	a	a	DET
fuelectenerg-1427	1012	96	2	2	NUM
fuelectenerg-1427	1012	97	a	a	DET
fuelectenerg-1427	1012	98	2	2	NUM
fuelectenerg-1427	1012	99	a	a	DET
fuelectenerg-1427	1012	100	2	2	NUM
fuelectenerg-1427	1012	101	a2	a2	NOUN
fuelectenerg-1427	1012	102	a	a	DET
fuelectenerg-1427	1012	103	2	2	NUM
fuelectenerg-1427	1012	104	a	a	DET
fuelectenerg-1427	1012	105	2	2	NUM
fuelectenerg-1427	1012	106	a	a	PRON
fuelectenerg-1427	1012	107	d	d	PROPN
fuelectenerg-1427	1012	108	1	1	NUM
fuelectenerg-1427	1012	109	a	a	PRON
fuelectenerg-1427	1012	110	,	,	PUNCT
fuelectenerg-1427	1012	111	s	s	PART
fuelectenerg-1427	1012	112	sd	sd	NOUN
fuelectenerg-1427	1012	113	d	d	PROPN
fuelectenerg-1427	1012	114	s	s	AUX
fuelectenerg-1427	1012	115	s	s	X
fuelectenerg-1427	1012	116	s	s	X
fuelectenerg-1427	1012	117	sd	sd	NOUN
fuelectenerg-1427	1012	118	d	d	NOUN
fuelectenerg-1427	1012	119	1	1	NUM
fuelectenerg-1427	1012	120	(	(	PUNCT
fuelectenerg-1427	1012	121	b	b	NOUN
fuelectenerg-1427	1012	122	,	,	PUNCT
fuelectenerg-1427	1012	123	)	)	PUNCT
fuelectenerg-1427	1012	124	2	2	NUM
fuelectenerg-1427	1012	125	b	b	NOUN
fuelectenerg-1427	1012	126	,	,	PUNCT
fuelectenerg-1427	1012	127	d	d	PROPN
fuelectenerg-1427	1012	128	d	d	PROPN
fuelectenerg-1427	1012	129	d	d	PROPN
fuelectenerg-1427	1012	130	d	d	PROPN
fuelectenerg-1427	1012	131	1	1	NUM
fuelectenerg-1427	1012	132	(	(	PUNCT
fuelectenerg-1427	1012	133	b	b	NOUN
fuelectenerg-1427	1012	134	,	,	PUNCT
fuelectenerg-1427	1012	135	)	)	PUNCT
fuelectenerg-1427	1012	136	2	2	NUM
fuelectenerg-1427	1012	137	b	b	NOUN
fuelectenerg-1427	1012	138	,	,	PUNCT
fuelectenerg-1427	1012	139	s	s	X
fuelectenerg-1427	1012	140	s	s	NOUN
fuelectenerg-1427	1012	141	s	s	X
fuelectenerg-1427	1012	142	d	d	X
fuelectenerg-1427	1012	143	s	s	X
fuelectenerg-1427	1012	144	d	d	X
fuelectenerg-1427	1012	145	dd	dd	NOUN
fuelectenerg-1427	1012	146	d	d	PROPN
fuelectenerg-1427	1012	147	d	d	PROPN
fuelectenerg-1427	1012	148	1	1	NUM
fuelectenerg-1427	1012	149	(	(	PUNCT
fuelectenerg-1427	1012	150	b	b	NOUN
fuelectenerg-1427	1012	151	,	,	PUNCT
fuelectenerg-1427	1012	152	)	)	PUNCT
fuelectenerg-1427	1012	153	2	2	NUM
fuelectenerg-1427	1012	154	b	b	NOUN
fuelectenerg-1427	1012	155	,	,	PUNCT
fuelectenerg-1427	1012	156	s	s	NOUN
fuelectenerg-1427	1012	157	d	d	X
fuelectenerg-1427	1012	158	d	d	PROPN
fuelectenerg-1427	1012	159	d	d	PROPN
fuelectenerg-1427	1012	160	1	1	NUM
fuelectenerg-1427	1012	161	(	(	PUNCT
fuelectenerg-1427	1012	162	b	b	NOUN
fuelectenerg-1427	1012	163	,	,	PUNCT
fuelectenerg-1427	1012	164	)	)	PUNCT
fuelectenerg-1427	1012	165	2	2	NUM
fuelectenerg-1427	1012	166	b	b	NOUN
fuelectenerg-1427	1012	167	,	,	PUNCT
fuelectenerg-1427	1012	168	n=1	n=1	PROPN
fuelectenerg-1427	1012	169	n=81	n=81	VERB
fuelectenerg-1427	1012	170	n=729	n=729	PROPN
fuelectenerg-1427	1012	171	n=59049	n=59049	PROPN
fuelectenerg-1427	1012	172	n=9	n=9	PROPN
fuelectenerg-1427	1012	173	n=81	n=81	VERB
fuelectenerg-1427	1012	174	n=6561	n=6561	PROPN
fuelectenerg-1427	1012	175	n=59049	n=59049	PROPN
fuelectenerg-1427	1012	176	n=9	n=9	PROPN
fuelectenerg-1427	1012	177	n=81	n=81	ADP
fuelectenerg-1427	1012	178	n=6561	n=6561	PROPN
fuelectenerg-1427	1012	179	n=59049	n=59049	PROPN
fuelectenerg-1427	1012	180	n=9	n=9	PROPN
fuelectenerg-1427	1012	181	n=729	n=729	X
fuelectenerg-1427	1012	182	n=6561	n=6561	PROPN
fuelectenerg-1427	1013	1	n=531441	n=531441	ADV
fuelectenerg-1427	1013	2	0	0	NUM
fuelectenerg-1427	1013	3	b	b	X
fuelectenerg-1427	1013	4	0	0	NUM
fuelectenerg-1427	1013	5	b	b	NOUN
fuelectenerg-1427	1013	6	0	0	NUM
fuelectenerg-1427	1013	7	a	a	DET
fuelectenerg-1427	1013	8	0	0	NUM
fuelectenerg-1427	1013	9	a	a	DET
fuelectenerg-1427	1013	10	0	0	NUM
fuelectenerg-1427	1013	11	b	b	NOUN
fuelectenerg-1427	1013	12	0	0	NUM
fuelectenerg-1427	1013	13	b	b	NOUN
fuelectenerg-1427	1013	14	0	0	NUM
fuelectenerg-1427	1013	15	b	b	NOUN
fuelectenerg-1427	1013	16	0	0	NUM
fuelectenerg-1427	1013	17	b	b	NOUN
fuelectenerg-1427	1013	18	0	0	NUM
fuelectenerg-1427	1013	19	b	b	NOUN
fuelectenerg-1427	1013	20	0	0	NUM
fuelectenerg-1427	1013	21	b	b	SYM
fuelectenerg-1427	1013	22	1	1	NUM
fuelectenerg-1427	1013	23	b	b	SYM
fuelectenerg-1427	1013	24	1	1	NUM
fuelectenerg-1427	1013	25	b	b	SYM
fuelectenerg-1427	1013	26	1	1	NUM
fuelectenerg-1427	1013	27	a	a	DET
fuelectenerg-1427	1013	28	1	1	NUM
fuelectenerg-1427	1013	29	a	a	DET
fuelectenerg-1427	1013	30	1	1	NUM
fuelectenerg-1427	1013	31	b	b	SYM
fuelectenerg-1427	1013	32	1	1	NUM
fuelectenerg-1427	1013	33	b	b	SYM
fuelectenerg-1427	1013	34	1	1	NUM
fuelectenerg-1427	1013	35	b	b	SYM
fuelectenerg-1427	1013	36	1	1	NUM
fuelectenerg-1427	1013	37	b	b	SYM
fuelectenerg-1427	1013	38	1	1	NUM
fuelectenerg-1427	1013	39	b	b	SYM
fuelectenerg-1427	1013	40	1	1	NUM
fuelectenerg-1427	1013	41	b	b	SYM
fuelectenerg-1427	1013	42	2	2	NUM
fuelectenerg-1427	1013	43	b	b	SYM
fuelectenerg-1427	1013	44	2	2	NUM
fuelectenerg-1427	1013	45	b	b	SYM
fuelectenerg-1427	1013	46	2	2	NUM
fuelectenerg-1427	1013	47	a	a	DET
fuelectenerg-1427	1013	48	2	2	NUM
fuelectenerg-1427	1013	49	a	a	DET
fuelectenerg-1427	1013	50	2	2	NUM
fuelectenerg-1427	1013	51	b	b	SYM
fuelectenerg-1427	1013	52	2	2	NUM
fuelectenerg-1427	1013	53	b	b	SYM
fuelectenerg-1427	1013	54	2	2	NUM
fuelectenerg-1427	1013	55	b	b	SYM
fuelectenerg-1427	1013	56	2	2	NUM
fuelectenerg-1427	1013	57	b	b	SYM
fuelectenerg-1427	1013	58	2	2	NUM
fuelectenerg-1427	1013	59	b	b	SYM
fuelectenerg-1427	1013	60	2	2	NUM
fuelectenerg-1427	1013	61	b	b	PROPN
fuelectenerg-1427	1013	62	(	(	PUNCT
fuelectenerg-1427	1013	63	b	b	NOUN
fuelectenerg-1427	1013	64	)	)	PUNCT
fuelectenerg-1427	1013	65	figure	figure	NOUN
fuelectenerg-1427	1013	66	5	5	NUM
fuelectenerg-1427	1013	67	:	:	PUNCT
fuelectenerg-1427	1013	68	(	(	PUNCT
fuelectenerg-1427	1013	69	continued	continued	ADJ
fuelectenerg-1427	1013	70	)	)	PUNCT
fuelectenerg-1427	1013	71	.	.	PUNCT
fuelectenerg-1427	1014	1	proof	proof	NOUN
fuelectenerg-1427	1014	2	.	.	PUNCT
fuelectenerg-1427	1015	1	an	an	DET
fuelectenerg-1427	1015	2	expansion	expansion	NOUN
fuelectenerg-1427	1015	3	is	be	AUX
fuelectenerg-1427	1015	4	canonical	canonical	ADJ
fuelectenerg-1427	1015	5	iff	iff	VERB
fuelectenerg-1427	1015	6	its	its	PRON
fuelectenerg-1427	1015	7	terms	term	NOUN
fuelectenerg-1427	1015	8	are	be	AUX
fuelectenerg-1427	1015	9	linearly	linearly	ADV
fuelectenerg-1427	1015	10	independent	independent	ADJ
fuelectenerg-1427	1015	11	;	;	PUNCT
fuelectenerg-1427	1015	12	none	none	NOUN
fuelectenerg-1427	1015	13	of	of	ADP
fuelectenerg-1427	1015	14	the	the	DET
fuelectenerg-1427	1015	15	terms	term	NOUN
fuelectenerg-1427	1015	16	is	be	AUX
fuelectenerg-1427	1015	17	equal	equal	ADJ
fuelectenerg-1427	1015	18	to	to	ADP
fuelectenerg-1427	1015	19	a	a	DET
fuelectenerg-1427	1015	20	linear	linear	ADJ
fuelectenerg-1427	1015	21	combination	combination	NOUN
fuelectenerg-1427	1015	22	of	of	ADP
fuelectenerg-1427	1015	23	other	other	ADJ
fuelectenerg-1427	1015	24	terms	term	NOUN
fuelectenerg-1427	1015	25	.	.	PUNCT
fuelectenerg-1427	1016	1	using	use	VERB
fuelectenerg-1427	1016	2	this	this	DET
fuelectenerg-1427	1016	3	fact	fact	NOUN
fuelectenerg-1427	1016	4	,	,	PUNCT
fuelectenerg-1427	1016	5	it	it	PRON
fuelectenerg-1427	1016	6	was	be	AUX
fuelectenerg-1427	1016	7	proven	prove	VERB
fuelectenerg-1427	1016	8	that	that	SCONJ
fuelectenerg-1427	1016	9	all	all	DET
fuelectenerg-1427	1016	10	gf(2	gf(2	PROPN
fuelectenerg-1427	1016	11	)	)	PUNCT
fuelectenerg-1427	1016	12	ifs	if	NOUN
fuelectenerg-1427	1016	13	are	be	AUX
fuelectenerg-1427	1016	14	canonical	canonical	ADJ
fuelectenerg-1427	1016	15	.	.	PUNCT
fuelectenerg-1427	1017	1	analogously	analogously	ADV
fuelectenerg-1427	1017	2	over	over	ADP
fuelectenerg-1427	1017	3	gf(3	gf(3	PROPN
fuelectenerg-1427	1017	4	)	)	PUNCT
fuelectenerg-1427	1017	5	,	,	PUNCT
fuelectenerg-1427	1017	6	for	for	ADP
fuelectenerg-1427	1017	7	any	any	DET
fuelectenerg-1427	1017	8	function	function	NOUN
fuelectenerg-1427	1017	9	f	f	PROPN
fuelectenerg-1427	1017	10	of	of	ADP
fuelectenerg-1427	1017	11	the	the	DET
fuelectenerg-1427	1017	12	same	same	ADJ
fuelectenerg-1427	1017	13	number	number	NOUN
fuelectenerg-1427	1017	14	of	of	ADP
fuelectenerg-1427	1017	15	variables	variable	NOUN
fuelectenerg-1427	1017	16	,	,	PUNCT
fuelectenerg-1427	1017	17	there	there	PRON
fuelectenerg-1427	1017	18	exists	exist	VERB
fuelectenerg-1427	1017	19	one	one	NUM
fuelectenerg-1427	1017	20	and	and	CCONJ
fuelectenerg-1427	1017	21	only	only	ADV
fuelectenerg-1427	1017	22	one	one	NUM
fuelectenerg-1427	1017	23	set	set	NOUN
fuelectenerg-1427	1017	24	of	of	ADP
fuelectenerg-1427	1017	25	coefficients	coefficient	NOUN
fuelectenerg-1427	1017	26	ai	ai	VERB
fuelectenerg-1427	1017	27	such	such	ADJ
fuelectenerg-1427	1017	28	that	that	SCONJ
fuelectenerg-1427	1017	29	f	f	PROPN
fuelectenerg-1427	1017	30	is	be	AUX
fuelectenerg-1427	1017	31	uniquely	uniquely	ADV
fuelectenerg-1427	1017	32	tif	tif	NOUN
fuelectenerg-1427	1017	33	-	-	PUNCT
fuelectenerg-1427	1017	34	expandable	expandable	ADJ
fuelectenerg-1427	1017	35	using	using	NOUN
fuelectenerg-1427	1017	36	ai	ai	NOUN
fuelectenerg-1427	1017	37	and	and	CCONJ
fuelectenerg-1427	1017	38	thus	thus	ADV
fuelectenerg-1427	1017	39	the	the	DET
fuelectenerg-1427	1017	40	resulting	result	VERB
fuelectenerg-1427	1017	41	expression	expression	NOUN
fuelectenerg-1427	1017	42	is	be	AUX
fuelectenerg-1427	1017	43	canonical	canonical	ADJ
fuelectenerg-1427	1017	44	.	.	PUNCT
fuelectenerg-1427	1018	1	by	by	ADP
fuelectenerg-1427	1018	2	induction	induction	NOUN
fuelectenerg-1427	1018	3	on	on	ADP
fuelectenerg-1427	1018	4	number	number	NOUN
fuelectenerg-1427	1018	5	of	of	ADP
fuelectenerg-1427	1018	6	variables	variable	NOUN
fuelectenerg-1427	1018	7	,	,	PUNCT
fuelectenerg-1427	1018	8	terms	term	NOUN
fuelectenerg-1427	1018	9	in	in	ADP
fuelectenerg-1427	1018	10	tifs	tifs	PROPN
fuelectenerg-1427	1018	11	will	will	AUX
fuelectenerg-1427	1018	12	be	be	AUX
fuelectenerg-1427	1018	13	linearly	linearly	ADV
fuelectenerg-1427	1018	14	independent	independent	ADJ
fuelectenerg-1427	1018	15	and	and	CCONJ
fuelectenerg-1427	1018	16	thus	thus	ADV
fuelectenerg-1427	1018	17	canonical	canonical	ADJ
fuelectenerg-1427	1018	18	.	.	PUNCT
fuelectenerg-1427	1019	1	theorem	theorem	VERB
fuelectenerg-1427	1019	2	4	4	NUM
fuelectenerg-1427	1019	3	.	.	PUNCT
fuelectenerg-1427	1019	4	ternary	ternary	ADJ
fuelectenerg-1427	1019	5	generalized	generalize	VERB
fuelectenerg-1427	1019	6	inclusive	inclusive	ADJ
fuelectenerg-1427	1019	7	forms	form	NOUN
fuelectenerg-1427	1019	8	(	(	PUNCT
fuelectenerg-1427	1019	9	tgifs	tgif	NOUN
fuelectenerg-1427	1019	10	)	)	PUNCT
fuelectenerg-1427	1019	11	are	be	AUX
fuelectenerg-1427	1019	12	canonical	canonical	ADJ
fuelectenerg-1427	1019	13	with	with	ADP
fuelectenerg-1427	1019	14	respect	respect	NOUN
fuelectenerg-1427	1019	15	to	to	ADP
fuelectenerg-1427	1019	16	given	give	VERB
fuelectenerg-1427	1019	17	variable	variable	ADJ
fuelectenerg-1427	1019	18	order	order	NOUN
fuelectenerg-1427	1019	19	.	.	PUNCT
fuelectenerg-1427	1020	1	proof	proof	NOUN
fuelectenerg-1427	1020	2	.	.	PUNCT
fuelectenerg-1427	1021	1	since	since	SCONJ
fuelectenerg-1427	1021	2	tgif	tgif	NOUN
fuelectenerg-1427	1021	3	is	be	AUX
fuelectenerg-1427	1021	4	the	the	DET
fuelectenerg-1427	1021	5	union	union	NOUN
fuelectenerg-1427	1021	6	of	of	ADP
fuelectenerg-1427	1021	7	the	the	DET
fuelectenerg-1427	1021	8	corresponding	corresponding	ADJ
fuelectenerg-1427	1021	9	tifs	tifs	PROPN
fuelectenerg-1427	1021	10	,	,	PUNCT
fuelectenerg-1427	1021	11	and	and	CCONJ
fuelectenerg-1427	1021	12	since	since	SCONJ
fuelectenerg-1427	1021	13	each	each	DET
fuelectenerg-1427	1021	14	tif	tif	PROPN
fuelectenerg-1427	1021	15	is	be	AUX
fuelectenerg-1427	1021	16	canonical	canonical	ADJ
fuelectenerg-1427	1021	17	,	,	PUNCT
fuelectenerg-1427	1021	18	then	then	ADV
fuelectenerg-1427	1021	19	the	the	DET
fuelectenerg-1427	1021	20	resulting	result	VERB
fuelectenerg-1427	1021	21	union	union	NOUN
fuelectenerg-1427	1021	22	of	of	ADP
fuelectenerg-1427	1021	23	the	the	DET
fuelectenerg-1427	1021	24	corresponding	corresponding	ADJ
fuelectenerg-1427	1021	25	canonical	canonical	ADJ
fuelectenerg-1427	1021	26	tifs	tif	NOUN
fuelectenerg-1427	1021	27	will	will	AUX
fuelectenerg-1427	1021	28	be	be	AUX
fuelectenerg-1427	1021	29	also	also	ADV
fuelectenerg-1427	1021	30	canonical	canonical	ADJ
fuelectenerg-1427	1021	31	.	.	PUNCT
fuelectenerg-1427	1022	1	for	for	ADP
fuelectenerg-1427	1022	2	different	different	ADJ
fuelectenerg-1427	1022	3	variable	variable	ADJ
fuelectenerg-1427	1022	4	orderings	ordering	NOUN
fuelectenerg-1427	1022	5	,	,	PUNCT
fuelectenerg-1427	1022	6	some	some	DET
fuelectenerg-1427	1022	7	forms	form	NOUN
fuelectenerg-1427	1022	8	are	be	AUX
fuelectenerg-1427	1022	9	not	not	PART
fuelectenerg-1427	1022	10	repeated	repeat	VERB
fuelectenerg-1427	1022	11	while	while	SCONJ
fuelectenerg-1427	1022	12	other	other	ADJ
fuelectenerg-1427	1022	13	forms	form	NOUN
fuelectenerg-1427	1022	14	are	be	AUX
fuelectenerg-1427	1022	15	.	.	PUNCT
fuelectenerg-1427	1023	1	therefore	therefore	ADV
fuelectenerg-1427	1023	2	the	the	DET
fuelectenerg-1427	1023	3	union	union	NOUN
fuelectenerg-1427	1023	4	of	of	ADP
fuelectenerg-1427	1023	5	sets	set	NOUN
fuelectenerg-1427	1023	6	of	of	ADP
fuelectenerg-1427	1023	7	tifs	tif	NOUN
fuelectenerg-1427	1023	8	for	for	ADP
fuelectenerg-1427	1023	9	all	all	DET
fuelectenerg-1427	1023	10	variable	variable	ADJ
fuelectenerg-1427	1023	11	orders	order	NOUN
fuelectenerg-1427	1023	12	contains	contain	VERB
fuelectenerg-1427	1023	13	more	more	ADJ
fuelectenerg-1427	1023	14	forms	form	NOUN
fuelectenerg-1427	1023	15	than	than	ADP
fuelectenerg-1427	1023	16	any	any	PRON
fuelectenerg-1427	1023	17	of	of	ADP
fuelectenerg-1427	1023	18	the	the	DET
fuelectenerg-1427	1023	19	tif	tif	PROPN
fuelectenerg-1427	1023	20	sets	set	NOUN
fuelectenerg-1427	1023	21	taken	take	VERB
fuelectenerg-1427	1023	22	separately	separately	ADV
fuelectenerg-1427	1023	23	and	and	CCONJ
fuelectenerg-1427	1023	24	less	less	ADJ
fuelectenerg-1427	1023	25	forms	form	NOUN
fuelectenerg-1427	1023	26	than	than	ADP
fuelectenerg-1427	1023	27	total	total	ADJ
fuelectenerg-1427	1023	28	sum	sum	NOUN
fuelectenerg-1427	1023	29	of	of	ADP
fuelectenerg-1427	1023	30	all	all	DET
fuelectenerg-1427	1023	31	tifs	tif	NOUN
fuelectenerg-1427	1023	32	.	.	PUNCT
fuelectenerg-1427	1024	1	generalized	generalized	ADJ
fuelectenerg-1427	1024	2	inclusive	inclusive	ADJ
fuelectenerg-1427	1024	3	forms	form	NOUN
fuelectenerg-1427	1024	4	include	include	VERB
fuelectenerg-1427	1024	5	other	other	ADJ
fuelectenerg-1427	1024	6	forms	form	NOUN
fuelectenerg-1427	1024	7	such	such	ADJ
fuelectenerg-1427	1024	8	as	as	ADP
fuelectenerg-1427	1024	9	grms	grm	NOUN
fuelectenerg-1427	1024	10	over	over	ADP
fuelectenerg-1427	1024	11	gf(3	gf(3	PROPN
fuelectenerg-1427	1024	12	)	)	PUNCT
fuelectenerg-1427	1024	13	as	as	SCONJ
fuelectenerg-1427	1024	14	can	can	AUX
fuelectenerg-1427	1024	15	be	be	AUX
fuelectenerg-1427	1024	16	shown	show	VERB
fuelectenerg-1427	1024	17	by	by	ADP
fuelectenerg-1427	1024	18	considering	consider	VERB
fuelectenerg-1427	1024	19	all	all	DET
fuelectenerg-1427	1024	20	possible	possible	ADJ
fuelectenerg-1427	1024	21	combinations	combination	NOUN
fuelectenerg-1427	1024	22	of	of	ADP
fuelectenerg-1427	1024	23	literals	literal	NOUN
fuelectenerg-1427	1024	24	for	for	ADP
fuelectenerg-1427	1024	25	all	all	DET
fuelectenerg-1427	1024	26	possible	possible	ADJ
fuelectenerg-1427	1024	27	orders	order	NOUN
fuelectenerg-1427	1024	28	of	of	ADP
fuelectenerg-1427	1024	29	variables	variable	NOUN
fuelectenerg-1427	1024	30	.	.	PUNCT
fuelectenerg-1427	1025	1	if	if	SCONJ
fuelectenerg-1427	1025	2	we	we	PRON
fuelectenerg-1427	1025	3	relax	relax	VERB
fuelectenerg-1427	1025	4	the	the	DET
fuelectenerg-1427	1025	5	requirement	requirement	NOUN
fuelectenerg-1427	1025	6	of	of	ADP
fuelectenerg-1427	1025	7	fixed	fix	VERB
fuelectenerg-1427	1025	8	variable	variable	ADJ
fuelectenerg-1427	1025	9	ordering	ordering	NOUN
fuelectenerg-1427	1025	10	,	,	PUNCT
fuelectenerg-1427	1025	11	and	and	CCONJ
fuelectenerg-1427	1025	12	allow	allow	VERB
fuelectenerg-1427	1025	13	any	any	DET
fuelectenerg-1427	1025	14	ordering	ordering	NOUN
fuelectenerg-1427	1025	15	of	of	ADP
fuelectenerg-1427	1025	16	variables	variable	NOUN
fuelectenerg-1427	1025	17	in	in	ADP
fuelectenerg-1427	1025	18	branches	branch	NOUN
fuelectenerg-1427	1025	19	of	of	ADP
fuelectenerg-1427	1025	20	the	the	DET
fuelectenerg-1427	1025	21	tree	tree	NOUN
fuelectenerg-1427	1025	22	but	but	CCONJ
fuelectenerg-1427	1025	23	do	do	AUX
fuelectenerg-1427	1025	24	not	not	PART
fuelectenerg-1427	1025	25	allow	allow	VERB
fuelectenerg-1427	1025	26	repetitions	repetition	NOUN
fuelectenerg-1427	1025	27	of	of	ADP
fuelectenerg-1427	1025	28	variables	variable	NOUN
fuelectenerg-1427	1025	29	in	in	ADP
fuelectenerg-1427	1025	30	the	the	DET
fuelectenerg-1427	1025	31	branches	branch	NOUN
fuelectenerg-1427	1025	32	,	,	PUNCT
fuelectenerg-1427	1025	33	we	we	PRON
fuelectenerg-1427	1025	34	generate	generate	VERB
fuelectenerg-1427	1025	35	more	more	ADJ
fuelectenerg-1427	1025	36	general	general	ADJ
fuelectenerg-1427	1025	37	gf(3	gf(3	PROPN
fuelectenerg-1427	1025	38	)	)	PUNCT
fuelectenerg-1427	1025	39	family	family	NOUN
fuelectenerg-1427	1025	40	of	of	ADP
fuelectenerg-1427	1025	41	forms	form	NOUN
fuelectenerg-1427	1025	42	.	.	PUNCT
fuelectenerg-1427	1026	1	111	111	NUM
fuelectenerg-1427	1026	2	an	an	DET
fuelectenerg-1427	1026	3	extended	extend	VERB
fuelectenerg-1427	1026	4	green	green	ADJ
fuelectenerg-1427	1026	5	sasao	sasao	PROPN
fuelectenerg-1427	1026	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1026	7	of	of	ADP
fuelectenerg-1427	1026	8	canonical	canonical	ADJ
fuelectenerg-1427	1026	9	ternary	ternary	ADJ
fuelectenerg-1427	1026	10	galois	galois	NOUN
fuelectenerg-1427	1026	11	forms	form	NOUN
fuelectenerg-1427	1026	12	...	...	PUNCT
fuelectenerg-1427	1027	1	s	s	PART
fuelectenerg-1427	1027	2	s	s	X
fuelectenerg-1427	1027	3	s	s	X
fuelectenerg-1427	1027	4	s	s	NOUN
fuelectenerg-1427	1027	5	0	0	NUM
fuelectenerg-1427	1027	6	a	a	DET
fuelectenerg-1427	1027	7	1	1	NUM
fuelectenerg-1427	1027	8	a	a	DET
fuelectenerg-1427	1027	9	2	2	NUM
fuelectenerg-1427	1027	10	a	a	DET
fuelectenerg-1427	1027	11	s	s	NOUN
fuelectenerg-1427	1027	12	s	s	X
fuelectenerg-1427	1027	13	d	d	X
fuelectenerg-1427	1027	14	d	d	X
fuelectenerg-1427	1027	15	s	s	X
fuelectenerg-1427	1027	16	s	s	X
fuelectenerg-1427	1027	17	s	s	X
fuelectenerg-1427	1027	18	d	d	X
fuelectenerg-1427	1027	19	1	1	NUM
fuelectenerg-1427	1027	20	(	(	PUNCT
fuelectenerg-1427	1027	21	b	b	NOUN
fuelectenerg-1427	1027	22	,	,	PUNCT
fuelectenerg-1427	1027	23	)	)	PUNCT
fuelectenerg-1427	1027	24	2	2	NUM
fuelectenerg-1427	1027	25	b	b	NOUN
fuelectenerg-1427	1027	26	,	,	PUNCT
fuelectenerg-1427	1027	27	s	s	NOUN
fuelectenerg-1427	1027	28	d	d	X
fuelectenerg-1427	1027	29	d	d	PROPN
fuelectenerg-1427	1027	30	d	d	PROPN
fuelectenerg-1427	1027	31	1	1	NUM
fuelectenerg-1427	1027	32	(	(	PUNCT
fuelectenerg-1427	1027	33	b	b	NOUN
fuelectenerg-1427	1027	34	,	,	PUNCT
fuelectenerg-1427	1027	35	)	)	PUNCT
fuelectenerg-1427	1027	36	2	2	NUM
fuelectenerg-1427	1027	37	b	b	NOUN
fuelectenerg-1427	1027	38	,	,	PUNCT
fuelectenerg-1427	1027	39	s	s	X
fuelectenerg-1427	1027	40	s	s	NOUN
fuelectenerg-1427	1027	41	s	s	NOUN
fuelectenerg-1427	1027	42	0	0	NUM
fuelectenerg-1427	1027	43	a	a	DET
fuelectenerg-1427	1027	44	0	0	NUM
fuelectenerg-1427	1027	45	a	a	DET
fuelectenerg-1427	1027	46	1	1	NUM
fuelectenerg-1427	1027	47	a	a	DET
fuelectenerg-1427	1027	48	1	1	NUM
fuelectenerg-1427	1027	49	a	a	DET
fuelectenerg-1427	1027	50	2	2	NUM
fuelectenerg-1427	1027	51	a	a	DET
fuelectenerg-1427	1027	52	2	2	NUM
fuelectenerg-1427	1027	53	a	a	DET
fuelectenerg-1427	1027	54	d	d	PROPN
fuelectenerg-1427	1027	55	1	1	NUM
fuelectenerg-1427	1027	56	1	1	NUM
fuelectenerg-1427	1027	57	1	1	NUM
fuelectenerg-1427	1027	58	1	1	NUM
fuelectenerg-1427	1027	59	1	1	NUM
fuelectenerg-1427	1027	60	1	1	NUM
fuelectenerg-1427	1027	61	1	1	NUM
fuelectenerg-1427	1027	62	1	1	NUM
fuelectenerg-1427	1027	63	1	1	NUM
fuelectenerg-1427	1027	64	1	1	NUM
fuelectenerg-1427	1027	65	11	11	NUM
fuelectenerg-1427	1027	66	1	1	NUM
fuelectenerg-1427	1027	67	1	1	NUM
fuelectenerg-1427	1027	68	1	1	NUM
fuelectenerg-1427	1027	69	1	1	NUM
fuelectenerg-1427	1027	70	1	1	NUM
fuelectenerg-1427	1027	71	1	1	NUM
fuelectenerg-1427	1027	72	1	1	NUM
fuelectenerg-1427	1027	73	1	1	NUM
fuelectenerg-1427	1027	74	1	1	NUM
fuelectenerg-1427	1027	75	1	1	NUM
fuelectenerg-1427	1027	76	1(a	1(a	NUM
fuelectenerg-1427	1027	77	,	,	PUNCT
fuelectenerg-1427	1027	78	)	)	PUNCT
fuelectenerg-1427	1027	79	2	2	NUM
fuelectenerg-1427	1027	80	(	(	PUNCT
fuelectenerg-1427	1027	81	a	a	PRON
fuelectenerg-1427	1027	82	,	,	PUNCT
fuelectenerg-1427	1027	83	)	)	PUNCT
fuelectenerg-1427	1027	84	2	2	NUM
fuelectenerg-1427	1027	85	(	(	PUNCT
fuelectenerg-1427	1027	86	a	a	PRON
fuelectenerg-1427	1027	87	,	,	PUNCT
fuelectenerg-1427	1027	88	)	)	PUNCT
fuelectenerg-1427	1027	89	2	2	NUM
fuelectenerg-1427	1027	90	(	(	PUNCT
fuelectenerg-1427	1027	91	a	a	PRON
fuelectenerg-1427	1027	92	,	,	PUNCT
fuelectenerg-1427	1027	93	)	)	PUNCT
fuelectenerg-1427	1027	94	2	2	NUM
fuelectenerg-1427	1027	95	(	(	PUNCT
fuelectenerg-1427	1027	96	a	a	PRON
fuelectenerg-1427	1027	97	,	,	PUNCT
fuelectenerg-1427	1027	98	)	)	PUNCT
fuelectenerg-1427	1027	99	2	2	NUM
fuelectenerg-1427	1027	100	(	(	PUNCT
fuelectenerg-1427	1027	101	a	a	PRON
fuelectenerg-1427	1027	102	,	,	PUNCT
fuelectenerg-1427	1027	103	)	)	PUNCT
fuelectenerg-1427	1027	104	2	2	NUM
fuelectenerg-1427	1027	105	(	(	PUNCT
fuelectenerg-1427	1027	106	a	a	PRON
fuelectenerg-1427	1027	107	,	,	PUNCT
fuelectenerg-1427	1027	108	)	)	PUNCT
fuelectenerg-1427	1027	109	2	2	NUM
fuelectenerg-1427	1027	110	(	(	PUNCT
fuelectenerg-1427	1027	111	a	a	PRON
fuelectenerg-1427	1027	112	,	,	PUNCT
fuelectenerg-1427	1027	113	)	)	PUNCT
fuelectenerg-1427	1027	114	2	2	NUM
fuelectenerg-1427	1027	115	(	(	PUNCT
fuelectenerg-1427	1027	116	a	a	PRON
fuelectenerg-1427	1027	117	,	,	PUNCT
fuelectenerg-1427	1027	118	)	)	PUNCT
fuelectenerg-1427	1027	119	2	2	NUM
fuelectenerg-1427	1027	120	(	(	PUNCT
fuelectenerg-1427	1027	121	a	a	PRON
fuelectenerg-1427	1027	122	,	,	PUNCT
fuelectenerg-1427	1027	123	)	)	PUNCT
fuelectenerg-1427	1027	124	2	2	NUM
fuelectenerg-1427	1027	125	(	(	PUNCT
fuelectenerg-1427	1027	126	a	a	PRON
fuelectenerg-1427	1027	127	,	,	PUNCT
fuelectenerg-1427	1027	128	)	)	PUNCT
fuelectenerg-1427	1027	129	2	2	NUM
fuelectenerg-1427	1027	130	(	(	PUNCT
fuelectenerg-1427	1027	131	a	a	PRON
fuelectenerg-1427	1027	132	,	,	PUNCT
fuelectenerg-1427	1027	133	)	)	PUNCT
fuelectenerg-1427	1027	134	2	2	NUM
fuelectenerg-1427	1027	135	(	(	PUNCT
fuelectenerg-1427	1027	136	a	a	PRON
fuelectenerg-1427	1027	137	,	,	PUNCT
fuelectenerg-1427	1027	138	)	)	PUNCT
fuelectenerg-1427	1027	139	2	2	NUM
fuelectenerg-1427	1027	140	(	(	PUNCT
fuelectenerg-1427	1027	141	a	a	PRON
fuelectenerg-1427	1027	142	,	,	PUNCT
fuelectenerg-1427	1027	143	)	)	PUNCT
fuelectenerg-1427	1027	144	2	2	NUM
fuelectenerg-1427	1027	145	(	(	PUNCT
fuelectenerg-1427	1027	146	a	a	PRON
fuelectenerg-1427	1027	147	,	,	PUNCT
fuelectenerg-1427	1027	148	)	)	PUNCT
fuelectenerg-1427	1027	149	2	2	NUM
fuelectenerg-1427	1027	150	(	(	PUNCT
fuelectenerg-1427	1027	151	a	a	PRON
fuelectenerg-1427	1027	152	,	,	PUNCT
fuelectenerg-1427	1027	153	)	)	PUNCT
fuelectenerg-1427	1027	154	2	2	NUM
fuelectenerg-1427	1027	155	(	(	PUNCT
fuelectenerg-1427	1027	156	a	a	PRON
fuelectenerg-1427	1027	157	,	,	PUNCT
fuelectenerg-1427	1027	158	)	)	PUNCT
fuelectenerg-1427	1027	159	2	2	NUM
fuelectenerg-1427	1027	160	(	(	PUNCT
fuelectenerg-1427	1027	161	a	a	PRON
fuelectenerg-1427	1027	162	,	,	PUNCT
fuelectenerg-1427	1027	163	)	)	PUNCT
fuelectenerg-1427	1027	164	2	2	NUM
fuelectenerg-1427	1027	165	(	(	PUNCT
fuelectenerg-1427	1027	166	a	a	PRON
fuelectenerg-1427	1027	167	,	,	PUNCT
fuelectenerg-1427	1027	168	)	)	PUNCT
fuelectenerg-1427	1027	169	2	2	NUM
fuelectenerg-1427	1027	170	(	(	PUNCT
fuelectenerg-1427	1027	171	a	a	PRON
fuelectenerg-1427	1027	172	,	,	PUNCT
fuelectenerg-1427	1027	173	)	)	PUNCT
fuelectenerg-1427	1027	174	2	2	NUM
fuelectenerg-1427	1027	175	(	(	PUNCT
fuelectenerg-1427	1027	176	a	a	PRON
fuelectenerg-1427	1027	177	,	,	PUNCT
fuelectenerg-1427	1027	178	)	)	PUNCT
fuelectenerg-1427	1027	179	2	2	NUM
fuelectenerg-1427	1027	180	(	(	PUNCT
fuelectenerg-1427	1027	181	a	a	PRON
fuelectenerg-1427	1027	182	,	,	PUNCT
fuelectenerg-1427	1027	183	)	)	PUNCT
fuelectenerg-1427	1027	184	2	2	NUM
fuelectenerg-1427	1027	185	(	(	PUNCT
fuelectenerg-1427	1027	186	a	a	PRON
fuelectenerg-1427	1027	187	,	,	PUNCT
fuelectenerg-1427	1027	188	)	)	PUNCT
fuelectenerg-1427	1027	189	2	2	NUM
fuelectenerg-1427	1027	190	(	(	PUNCT
fuelectenerg-1427	1027	191	a	a	PRON
fuelectenerg-1427	1027	192	,	,	PUNCT
fuelectenerg-1427	1027	193	)	)	PUNCT
fuelectenerg-1427	1027	194	2	2	NUM
fuelectenerg-1427	1027	195	a	a	PRON
fuelectenerg-1427	1027	196	,	,	PUNCT
fuelectenerg-1427	1027	197	a	a	PRON
fuelectenerg-1427	1027	198	,	,	PUNCT
fuelectenerg-1427	1027	199	a	a	PRON
fuelectenerg-1427	1027	200	,	,	PUNCT
fuelectenerg-1427	1027	201	a	a	PRON
fuelectenerg-1427	1027	202	,	,	PUNCT
fuelectenerg-1427	1027	203	a	a	PRON
fuelectenerg-1427	1027	204	,	,	PUNCT
fuelectenerg-1427	1027	205	a	a	PRON
fuelectenerg-1427	1027	206	,	,	PUNCT
fuelectenerg-1427	1027	207	a	a	PRON
fuelectenerg-1427	1027	208	,	,	PUNCT
fuelectenerg-1427	1027	209	a	a	PRON
fuelectenerg-1427	1027	210	,	,	PUNCT
fuelectenerg-1427	1027	211	a	a	PRON
fuelectenerg-1427	1027	212	,	,	PUNCT
fuelectenerg-1427	1027	213	a	a	PRON
fuelectenerg-1427	1027	214	,	,	PUNCT
fuelectenerg-1427	1027	215	a	a	PRON
fuelectenerg-1427	1027	216	,	,	PUNCT
fuelectenerg-1427	1027	217	a	a	PRON
fuelectenerg-1427	1027	218	,	,	PUNCT
fuelectenerg-1427	1027	219	a	a	PRON
fuelectenerg-1427	1027	220	,	,	PUNCT
fuelectenerg-1427	1027	221	a	a	PRON
fuelectenerg-1427	1027	222	,	,	PUNCT
fuelectenerg-1427	1027	223	a	a	PRON
fuelectenerg-1427	1027	224	,	,	PUNCT
fuelectenerg-1427	1027	225	a	a	PRON
fuelectenerg-1427	1027	226	,	,	PUNCT
fuelectenerg-1427	1027	227	a	a	PRON
fuelectenerg-1427	1027	228	,	,	PUNCT
fuelectenerg-1427	1027	229	a	a	PRON
fuelectenerg-1427	1027	230	,	,	PUNCT
fuelectenerg-1427	1027	231	a	a	PRON
fuelectenerg-1427	1027	232	,	,	PUNCT
fuelectenerg-1427	1027	233	a	a	PRON
fuelectenerg-1427	1027	234	,	,	PUNCT
fuelectenerg-1427	1027	235	a	a	PRON
fuelectenerg-1427	1027	236	,	,	PUNCT
fuelectenerg-1427	1027	237	a	a	PRON
fuelectenerg-1427	1027	238	,	,	PUNCT
fuelectenerg-1427	1027	239	a	a	PRON
fuelectenerg-1427	1027	240	,	,	PUNCT
fuelectenerg-1427	1027	241	s	s	NOUN
fuelectenerg-1427	1027	242	s	s	X
fuelectenerg-1427	1027	243	d	d	X
fuelectenerg-1427	1027	244	d	d	X
fuelectenerg-1427	1027	245	s	s	X
fuelectenerg-1427	1027	246	s	s	X
fuelectenerg-1427	1027	247	d	d	X
fuelectenerg-1427	1027	248	d	d	SYM
fuelectenerg-1427	1027	249	1	1	NUM
fuelectenerg-1427	1027	250	(	(	PUNCT
fuelectenerg-1427	1027	251	b	b	NOUN
fuelectenerg-1427	1027	252	,	,	PUNCT
fuelectenerg-1427	1027	253	)	)	PUNCT
fuelectenerg-1427	1027	254	2	2	NUM
fuelectenerg-1427	1027	255	b	b	NOUN
fuelectenerg-1427	1027	256	,	,	PUNCT
fuelectenerg-1427	1027	257	sd	sd	ADP
fuelectenerg-1427	1027	258	d	d	PROPN
fuelectenerg-1427	1027	259	d	d	PROPN
fuelectenerg-1427	1027	260	1	1	NUM
fuelectenerg-1427	1027	261	(	(	PUNCT
fuelectenerg-1427	1027	262	b	b	NOUN
fuelectenerg-1427	1027	263	,	,	PUNCT
fuelectenerg-1427	1027	264	)	)	PUNCT
fuelectenerg-1427	1027	265	2	2	NUM
fuelectenerg-1427	1027	266	b	b	NOUN
fuelectenerg-1427	1027	267	,	,	PUNCT
fuelectenerg-1427	1027	268	s	s	X
fuelectenerg-1427	1027	269	s	s	NOUN
fuelectenerg-1427	1027	270	s	s	NOUN
fuelectenerg-1427	1027	271	0	0	NUM
fuelectenerg-1427	1027	272	a	a	DET
fuelectenerg-1427	1027	273	0	0	NUM
fuelectenerg-1427	1027	274	a	a	DET
fuelectenerg-1427	1027	275	0	0	NUM
fuelectenerg-1427	1028	1	a	a	DET
fuelectenerg-1427	1028	2	0	0	NUM
fuelectenerg-1427	1028	3	a	a	DET
fuelectenerg-1427	1028	4	0	0	NUM
fuelectenerg-1427	1028	5	a	a	DET
fuelectenerg-1427	1028	6	0	0	NUM
fuelectenerg-1427	1028	7	a	a	DET
fuelectenerg-1427	1028	8	0	0	NUM
fuelectenerg-1427	1028	9	a	a	DET
fuelectenerg-1427	1028	10	0	0	NUM
fuelectenerg-1427	1028	11	a	a	DET
fuelectenerg-1427	1028	12	0	0	NUM
fuelectenerg-1427	1028	13	a	a	DET
fuelectenerg-1427	1028	14	0	0	NUM
fuelectenerg-1427	1028	15	a	a	DET
fuelectenerg-1427	1028	16	0	0	NUM
fuelectenerg-1427	1028	17	a	a	DET
fuelectenerg-1427	1028	18	0	0	NUM
fuelectenerg-1427	1028	19	a	a	DET
fuelectenerg-1427	1028	20	0	0	NUM
fuelectenerg-1427	1028	21	a	a	DET
fuelectenerg-1427	1028	22	0	0	NUM
fuelectenerg-1427	1028	23	a	a	DET
fuelectenerg-1427	1028	24	0	0	NUM
fuelectenerg-1427	1028	25	a	a	DET
fuelectenerg-1427	1028	26	0	0	NUM
fuelectenerg-1427	1028	27	a0	a0	NOUN
fuelectenerg-1427	1028	28	a	a	DET
fuelectenerg-1427	1028	29	0	0	NUM
fuelectenerg-1427	1028	30	a	a	DET
fuelectenerg-1427	1028	31	0	0	NUM
fuelectenerg-1427	1028	32	a	a	DET
fuelectenerg-1427	1028	33	1	1	NUM
fuelectenerg-1427	1028	34	a	a	DET
fuelectenerg-1427	1028	35	1	1	NUM
fuelectenerg-1427	1028	36	a	a	DET
fuelectenerg-1427	1028	37	1	1	NUM
fuelectenerg-1427	1028	38	a	a	DET
fuelectenerg-1427	1028	39	1	1	NUM
fuelectenerg-1427	1028	40	a	a	DET
fuelectenerg-1427	1028	41	1	1	NUM
fuelectenerg-1427	1028	42	a	a	DET
fuelectenerg-1427	1028	43	1	1	NUM
fuelectenerg-1427	1028	44	a	a	DET
fuelectenerg-1427	1028	45	1	1	NUM
fuelectenerg-1427	1028	46	a	a	DET
fuelectenerg-1427	1028	47	1	1	NUM
fuelectenerg-1427	1028	48	a	a	DET
fuelectenerg-1427	1028	49	1	1	NUM
fuelectenerg-1427	1028	50	a	a	DET
fuelectenerg-1427	1028	51	1	1	NUM
fuelectenerg-1427	1028	52	a	a	DET
fuelectenerg-1427	1028	53	1	1	NUM
fuelectenerg-1427	1028	54	a	a	DET
fuelectenerg-1427	1028	55	1	1	NUM
fuelectenerg-1427	1028	56	a	a	DET
fuelectenerg-1427	1028	57	1	1	NUM
fuelectenerg-1427	1028	58	a	a	DET
fuelectenerg-1427	1028	59	1	1	NUM
fuelectenerg-1427	1028	60	a	a	DET
fuelectenerg-1427	1028	61	1	1	NUM
fuelectenerg-1427	1028	62	a	a	DET
fuelectenerg-1427	1028	63	1	1	NUM
fuelectenerg-1427	1028	64	a1	a1	NOUN
fuelectenerg-1427	1028	65	a	a	DET
fuelectenerg-1427	1028	66	1	1	NUM
fuelectenerg-1427	1028	67	a	a	DET
fuelectenerg-1427	1028	68	1	1	NUM
fuelectenerg-1427	1028	69	a	a	DET
fuelectenerg-1427	1028	70	2	2	NUM
fuelectenerg-1427	1028	71	a	a	DET
fuelectenerg-1427	1028	72	2	2	NUM
fuelectenerg-1427	1028	73	a	a	DET
fuelectenerg-1427	1028	74	2	2	NUM
fuelectenerg-1427	1028	75	a	a	DET
fuelectenerg-1427	1028	76	2	2	NUM
fuelectenerg-1427	1028	77	a	a	DET
fuelectenerg-1427	1028	78	2	2	NUM
fuelectenerg-1427	1028	79	a	a	DET
fuelectenerg-1427	1028	80	2	2	NUM
fuelectenerg-1427	1028	81	a	a	DET
fuelectenerg-1427	1028	82	2	2	NUM
fuelectenerg-1427	1028	83	a	a	DET
fuelectenerg-1427	1028	84	2	2	NUM
fuelectenerg-1427	1028	85	a	a	DET
fuelectenerg-1427	1028	86	2	2	NUM
fuelectenerg-1427	1028	87	a	a	DET
fuelectenerg-1427	1028	88	2	2	NUM
fuelectenerg-1427	1028	89	a	a	DET
fuelectenerg-1427	1028	90	2	2	NUM
fuelectenerg-1427	1028	91	a	a	DET
fuelectenerg-1427	1028	92	2	2	NUM
fuelectenerg-1427	1028	93	a	a	DET
fuelectenerg-1427	1028	94	2	2	NUM
fuelectenerg-1427	1028	95	a	a	DET
fuelectenerg-1427	1028	96	2	2	NUM
fuelectenerg-1427	1028	97	a	a	DET
fuelectenerg-1427	1028	98	2	2	NUM
fuelectenerg-1427	1028	99	a	a	DET
fuelectenerg-1427	1028	100	2	2	NUM
fuelectenerg-1427	1028	101	a2	a2	NOUN
fuelectenerg-1427	1028	102	a	a	DET
fuelectenerg-1427	1028	103	2	2	NUM
fuelectenerg-1427	1028	104	a	a	DET
fuelectenerg-1427	1028	105	2	2	NUM
fuelectenerg-1427	1028	106	a	a	PRON
fuelectenerg-1427	1028	107	d	d	PROPN
fuelectenerg-1427	1028	108	1	1	NUM
fuelectenerg-1427	1028	109	a	a	PRON
fuelectenerg-1427	1028	110	,	,	PUNCT
fuelectenerg-1427	1028	111	s	s	PART
fuelectenerg-1427	1028	112	sd	sd	NOUN
fuelectenerg-1427	1028	113	d	d	PROPN
fuelectenerg-1427	1028	114	s	s	AUX
fuelectenerg-1427	1028	115	s	s	X
fuelectenerg-1427	1028	116	s	s	X
fuelectenerg-1427	1028	117	sd	sd	NOUN
fuelectenerg-1427	1028	118	d	d	NOUN
fuelectenerg-1427	1028	119	1	1	NUM
fuelectenerg-1427	1028	120	(	(	PUNCT
fuelectenerg-1427	1028	121	b	b	NOUN
fuelectenerg-1427	1028	122	,	,	PUNCT
fuelectenerg-1427	1028	123	)	)	PUNCT
fuelectenerg-1427	1028	124	2	2	NUM
fuelectenerg-1427	1028	125	b	b	NOUN
fuelectenerg-1427	1028	126	,	,	PUNCT
fuelectenerg-1427	1028	127	d	d	PROPN
fuelectenerg-1427	1028	128	d	d	PROPN
fuelectenerg-1427	1028	129	d	d	PROPN
fuelectenerg-1427	1028	130	d	d	PROPN
fuelectenerg-1427	1028	131	1	1	NUM
fuelectenerg-1427	1028	132	(	(	PUNCT
fuelectenerg-1427	1028	133	b	b	NOUN
fuelectenerg-1427	1028	134	,	,	PUNCT
fuelectenerg-1427	1028	135	)	)	PUNCT
fuelectenerg-1427	1028	136	2	2	NUM
fuelectenerg-1427	1028	137	b	b	NOUN
fuelectenerg-1427	1028	138	,	,	PUNCT
fuelectenerg-1427	1028	139	s	s	X
fuelectenerg-1427	1028	140	s	s	NOUN
fuelectenerg-1427	1028	141	s	s	X
fuelectenerg-1427	1028	142	d	d	X
fuelectenerg-1427	1028	143	s	s	X
fuelectenerg-1427	1028	144	d	d	X
fuelectenerg-1427	1028	145	dd	dd	NOUN
fuelectenerg-1427	1028	146	d	d	PROPN
fuelectenerg-1427	1028	147	d	d	PROPN
fuelectenerg-1427	1028	148	1	1	NUM
fuelectenerg-1427	1028	149	(	(	PUNCT
fuelectenerg-1427	1028	150	b	b	NOUN
fuelectenerg-1427	1028	151	,	,	PUNCT
fuelectenerg-1427	1028	152	)	)	PUNCT
fuelectenerg-1427	1028	153	2	2	NUM
fuelectenerg-1427	1028	154	b	b	NOUN
fuelectenerg-1427	1028	155	,	,	PUNCT
fuelectenerg-1427	1028	156	s	s	NOUN
fuelectenerg-1427	1028	157	d	d	X
fuelectenerg-1427	1028	158	d	d	PROPN
fuelectenerg-1427	1028	159	d	d	PROPN
fuelectenerg-1427	1028	160	1	1	NUM
fuelectenerg-1427	1028	161	(	(	PUNCT
fuelectenerg-1427	1028	162	b	b	NOUN
fuelectenerg-1427	1028	163	,	,	PUNCT
fuelectenerg-1427	1028	164	)	)	PUNCT
fuelectenerg-1427	1028	165	2	2	NUM
fuelectenerg-1427	1028	166	b	b	NOUN
fuelectenerg-1427	1028	167	,	,	PUNCT
fuelectenerg-1427	1028	168	n=1	n=1	PROPN
fuelectenerg-1427	1028	169	n=81	n=81	VERB
fuelectenerg-1427	1028	170	n=729	n=729	PROPN
fuelectenerg-1427	1028	171	n=59049	n=59049	PROPN
fuelectenerg-1427	1028	172	n=9	n=9	PROPN
fuelectenerg-1427	1028	173	n=81	n=81	VERB
fuelectenerg-1427	1028	174	n=6561	n=6561	PROPN
fuelectenerg-1427	1028	175	n=59049	n=59049	PROPN
fuelectenerg-1427	1028	176	n=9	n=9	PROPN
fuelectenerg-1427	1028	177	n=81	n=81	ADP
fuelectenerg-1427	1028	178	n=6561	n=6561	PROPN
fuelectenerg-1427	1028	179	n=59049	n=59049	PROPN
fuelectenerg-1427	1028	180	n=9	n=9	PROPN
fuelectenerg-1427	1028	181	n=729	n=729	X
fuelectenerg-1427	1028	182	n=6561	n=6561	PROPN
fuelectenerg-1427	1029	1	n=531441	n=531441	ADV
fuelectenerg-1427	1029	2	0	0	NUM
fuelectenerg-1427	1029	3	b	b	X
fuelectenerg-1427	1029	4	0	0	NUM
fuelectenerg-1427	1029	5	b	b	NOUN
fuelectenerg-1427	1029	6	0	0	NUM
fuelectenerg-1427	1029	7	a	a	DET
fuelectenerg-1427	1029	8	0	0	NUM
fuelectenerg-1427	1029	9	a	a	DET
fuelectenerg-1427	1029	10	0	0	NUM
fuelectenerg-1427	1029	11	b	b	NOUN
fuelectenerg-1427	1029	12	0	0	NUM
fuelectenerg-1427	1029	13	b	b	NOUN
fuelectenerg-1427	1029	14	0	0	NUM
fuelectenerg-1427	1029	15	b	b	NOUN
fuelectenerg-1427	1029	16	0	0	NUM
fuelectenerg-1427	1029	17	b	b	NOUN
fuelectenerg-1427	1029	18	0	0	NUM
fuelectenerg-1427	1029	19	b	b	NOUN
fuelectenerg-1427	1029	20	0	0	NUM
fuelectenerg-1427	1029	21	b	b	SYM
fuelectenerg-1427	1029	22	1	1	NUM
fuelectenerg-1427	1029	23	b	b	SYM
fuelectenerg-1427	1029	24	1	1	NUM
fuelectenerg-1427	1029	25	b	b	SYM
fuelectenerg-1427	1029	26	1	1	NUM
fuelectenerg-1427	1029	27	a	a	DET
fuelectenerg-1427	1029	28	1	1	NUM
fuelectenerg-1427	1029	29	a	a	DET
fuelectenerg-1427	1029	30	1	1	NUM
fuelectenerg-1427	1029	31	b	b	SYM
fuelectenerg-1427	1029	32	1	1	NUM
fuelectenerg-1427	1029	33	b	b	SYM
fuelectenerg-1427	1029	34	1	1	NUM
fuelectenerg-1427	1029	35	b	b	SYM
fuelectenerg-1427	1029	36	1	1	NUM
fuelectenerg-1427	1029	37	b	b	SYM
fuelectenerg-1427	1029	38	1	1	NUM
fuelectenerg-1427	1029	39	b	b	SYM
fuelectenerg-1427	1029	40	1	1	NUM
fuelectenerg-1427	1029	41	b	b	SYM
fuelectenerg-1427	1029	42	2	2	NUM
fuelectenerg-1427	1029	43	b	b	SYM
fuelectenerg-1427	1029	44	2	2	NUM
fuelectenerg-1427	1029	45	b	b	SYM
fuelectenerg-1427	1029	46	2	2	NUM
fuelectenerg-1427	1029	47	a	a	DET
fuelectenerg-1427	1029	48	2	2	NUM
fuelectenerg-1427	1029	49	a	a	DET
fuelectenerg-1427	1029	50	2	2	NUM
fuelectenerg-1427	1029	51	b	b	SYM
fuelectenerg-1427	1029	52	2	2	NUM
fuelectenerg-1427	1029	53	b	b	SYM
fuelectenerg-1427	1029	54	2	2	NUM
fuelectenerg-1427	1029	55	b	b	SYM
fuelectenerg-1427	1029	56	2	2	NUM
fuelectenerg-1427	1029	57	b	b	SYM
fuelectenerg-1427	1029	58	2	2	NUM
fuelectenerg-1427	1029	59	b	b	SYM
fuelectenerg-1427	1029	60	2	2	NUM
fuelectenerg-1427	1029	61	b	b	PROPN
fuelectenerg-1427	1029	62	(	(	PUNCT
fuelectenerg-1427	1029	63	b	b	NOUN
fuelectenerg-1427	1029	64	)	)	PUNCT
fuelectenerg-1427	1029	65	figure	figure	NOUN
fuelectenerg-1427	1029	66	5	5	NUM
fuelectenerg-1427	1029	67	:	:	PUNCT
fuelectenerg-1427	1029	68	(	(	PUNCT
fuelectenerg-1427	1029	69	continued	continued	ADJ
fuelectenerg-1427	1029	70	)	)	PUNCT
fuelectenerg-1427	1029	71	.	.	PUNCT
fuelectenerg-1427	1030	1	proof	proof	NOUN
fuelectenerg-1427	1030	2	.	.	PUNCT
fuelectenerg-1427	1031	1	an	an	DET
fuelectenerg-1427	1031	2	expansion	expansion	NOUN
fuelectenerg-1427	1031	3	is	be	AUX
fuelectenerg-1427	1031	4	canonical	canonical	ADJ
fuelectenerg-1427	1031	5	iff	iff	VERB
fuelectenerg-1427	1031	6	its	its	PRON
fuelectenerg-1427	1031	7	terms	term	NOUN
fuelectenerg-1427	1031	8	are	be	AUX
fuelectenerg-1427	1031	9	linearly	linearly	ADV
fuelectenerg-1427	1031	10	independent	independent	ADJ
fuelectenerg-1427	1031	11	;	;	PUNCT
fuelectenerg-1427	1031	12	none	none	NOUN
fuelectenerg-1427	1031	13	of	of	ADP
fuelectenerg-1427	1031	14	the	the	DET
fuelectenerg-1427	1031	15	terms	term	NOUN
fuelectenerg-1427	1031	16	is	be	AUX
fuelectenerg-1427	1031	17	equal	equal	ADJ
fuelectenerg-1427	1031	18	to	to	ADP
fuelectenerg-1427	1031	19	a	a	DET
fuelectenerg-1427	1031	20	linear	linear	ADJ
fuelectenerg-1427	1031	21	combination	combination	NOUN
fuelectenerg-1427	1031	22	of	of	ADP
fuelectenerg-1427	1031	23	other	other	ADJ
fuelectenerg-1427	1031	24	terms	term	NOUN
fuelectenerg-1427	1031	25	.	.	PUNCT
fuelectenerg-1427	1032	1	using	use	VERB
fuelectenerg-1427	1032	2	this	this	DET
fuelectenerg-1427	1032	3	fact	fact	NOUN
fuelectenerg-1427	1032	4	,	,	PUNCT
fuelectenerg-1427	1032	5	it	it	PRON
fuelectenerg-1427	1032	6	was	be	AUX
fuelectenerg-1427	1032	7	proven	prove	VERB
fuelectenerg-1427	1032	8	that	that	SCONJ
fuelectenerg-1427	1032	9	all	all	DET
fuelectenerg-1427	1032	10	gf(2	gf(2	PROPN
fuelectenerg-1427	1032	11	)	)	PUNCT
fuelectenerg-1427	1032	12	ifs	if	NOUN
fuelectenerg-1427	1032	13	are	be	AUX
fuelectenerg-1427	1032	14	canonical	canonical	ADJ
fuelectenerg-1427	1032	15	.	.	PUNCT
fuelectenerg-1427	1033	1	analogously	analogously	ADV
fuelectenerg-1427	1033	2	over	over	ADP
fuelectenerg-1427	1033	3	gf(3	gf(3	PROPN
fuelectenerg-1427	1033	4	)	)	PUNCT
fuelectenerg-1427	1033	5	,	,	PUNCT
fuelectenerg-1427	1033	6	for	for	ADP
fuelectenerg-1427	1033	7	any	any	DET
fuelectenerg-1427	1033	8	function	function	NOUN
fuelectenerg-1427	1033	9	f	f	PROPN
fuelectenerg-1427	1033	10	of	of	ADP
fuelectenerg-1427	1033	11	the	the	DET
fuelectenerg-1427	1033	12	same	same	ADJ
fuelectenerg-1427	1033	13	number	number	NOUN
fuelectenerg-1427	1033	14	of	of	ADP
fuelectenerg-1427	1033	15	variables	variable	NOUN
fuelectenerg-1427	1033	16	,	,	PUNCT
fuelectenerg-1427	1033	17	there	there	PRON
fuelectenerg-1427	1033	18	exists	exist	VERB
fuelectenerg-1427	1033	19	one	one	NUM
fuelectenerg-1427	1033	20	and	and	CCONJ
fuelectenerg-1427	1033	21	only	only	ADV
fuelectenerg-1427	1033	22	one	one	NUM
fuelectenerg-1427	1033	23	set	set	NOUN
fuelectenerg-1427	1033	24	of	of	ADP
fuelectenerg-1427	1033	25	coefficients	coefficient	NOUN
fuelectenerg-1427	1033	26	ai	ai	VERB
fuelectenerg-1427	1033	27	such	such	ADJ
fuelectenerg-1427	1033	28	that	that	SCONJ
fuelectenerg-1427	1033	29	f	f	PROPN
fuelectenerg-1427	1033	30	is	be	AUX
fuelectenerg-1427	1033	31	uniquely	uniquely	ADV
fuelectenerg-1427	1033	32	tif	tif	NOUN
fuelectenerg-1427	1033	33	-	-	PUNCT
fuelectenerg-1427	1033	34	expandable	expandable	ADJ
fuelectenerg-1427	1033	35	using	using	NOUN
fuelectenerg-1427	1033	36	ai	ai	NOUN
fuelectenerg-1427	1033	37	and	and	CCONJ
fuelectenerg-1427	1033	38	thus	thus	ADV
fuelectenerg-1427	1033	39	the	the	DET
fuelectenerg-1427	1033	40	resulting	result	VERB
fuelectenerg-1427	1033	41	expression	expression	NOUN
fuelectenerg-1427	1033	42	is	be	AUX
fuelectenerg-1427	1033	43	canonical	canonical	ADJ
fuelectenerg-1427	1033	44	.	.	PUNCT
fuelectenerg-1427	1034	1	by	by	ADP
fuelectenerg-1427	1034	2	induction	induction	NOUN
fuelectenerg-1427	1034	3	on	on	ADP
fuelectenerg-1427	1034	4	number	number	NOUN
fuelectenerg-1427	1034	5	of	of	ADP
fuelectenerg-1427	1034	6	variables	variable	NOUN
fuelectenerg-1427	1034	7	,	,	PUNCT
fuelectenerg-1427	1034	8	terms	term	NOUN
fuelectenerg-1427	1034	9	in	in	ADP
fuelectenerg-1427	1034	10	tifs	tifs	PROPN
fuelectenerg-1427	1034	11	will	will	AUX
fuelectenerg-1427	1034	12	be	be	AUX
fuelectenerg-1427	1034	13	linearly	linearly	ADV
fuelectenerg-1427	1034	14	independent	independent	ADJ
fuelectenerg-1427	1034	15	and	and	CCONJ
fuelectenerg-1427	1034	16	thus	thus	ADV
fuelectenerg-1427	1034	17	canonical	canonical	ADJ
fuelectenerg-1427	1034	18	.	.	PUNCT
fuelectenerg-1427	1035	1	theorem	theorem	VERB
fuelectenerg-1427	1035	2	4	4	NUM
fuelectenerg-1427	1035	3	.	.	PUNCT
fuelectenerg-1427	1035	4	ternary	ternary	ADJ
fuelectenerg-1427	1035	5	generalized	generalize	VERB
fuelectenerg-1427	1035	6	inclusive	inclusive	ADJ
fuelectenerg-1427	1035	7	forms	form	NOUN
fuelectenerg-1427	1035	8	(	(	PUNCT
fuelectenerg-1427	1035	9	tgifs	tgif	NOUN
fuelectenerg-1427	1035	10	)	)	PUNCT
fuelectenerg-1427	1035	11	are	be	AUX
fuelectenerg-1427	1035	12	canonical	canonical	ADJ
fuelectenerg-1427	1035	13	with	with	ADP
fuelectenerg-1427	1035	14	respect	respect	NOUN
fuelectenerg-1427	1035	15	to	to	ADP
fuelectenerg-1427	1035	16	given	give	VERB
fuelectenerg-1427	1035	17	variable	variable	ADJ
fuelectenerg-1427	1035	18	order	order	NOUN
fuelectenerg-1427	1035	19	.	.	PUNCT
fuelectenerg-1427	1036	1	proof	proof	NOUN
fuelectenerg-1427	1036	2	.	.	PUNCT
fuelectenerg-1427	1037	1	since	since	SCONJ
fuelectenerg-1427	1037	2	tgif	tgif	NOUN
fuelectenerg-1427	1037	3	is	be	AUX
fuelectenerg-1427	1037	4	the	the	DET
fuelectenerg-1427	1037	5	union	union	NOUN
fuelectenerg-1427	1037	6	of	of	ADP
fuelectenerg-1427	1037	7	the	the	DET
fuelectenerg-1427	1037	8	corresponding	corresponding	ADJ
fuelectenerg-1427	1037	9	tifs	tifs	PROPN
fuelectenerg-1427	1037	10	,	,	PUNCT
fuelectenerg-1427	1037	11	and	and	CCONJ
fuelectenerg-1427	1037	12	since	since	SCONJ
fuelectenerg-1427	1037	13	each	each	DET
fuelectenerg-1427	1037	14	tif	tif	PROPN
fuelectenerg-1427	1037	15	is	be	AUX
fuelectenerg-1427	1037	16	canonical	canonical	ADJ
fuelectenerg-1427	1037	17	,	,	PUNCT
fuelectenerg-1427	1037	18	then	then	ADV
fuelectenerg-1427	1037	19	the	the	DET
fuelectenerg-1427	1037	20	resulting	result	VERB
fuelectenerg-1427	1037	21	union	union	NOUN
fuelectenerg-1427	1037	22	of	of	ADP
fuelectenerg-1427	1037	23	the	the	DET
fuelectenerg-1427	1037	24	corresponding	corresponding	ADJ
fuelectenerg-1427	1037	25	canonical	canonical	ADJ
fuelectenerg-1427	1037	26	tifs	tif	NOUN
fuelectenerg-1427	1037	27	will	will	AUX
fuelectenerg-1427	1037	28	be	be	AUX
fuelectenerg-1427	1037	29	also	also	ADV
fuelectenerg-1427	1037	30	canonical	canonical	ADJ
fuelectenerg-1427	1037	31	.	.	PUNCT
fuelectenerg-1427	1038	1	for	for	ADP
fuelectenerg-1427	1038	2	different	different	ADJ
fuelectenerg-1427	1038	3	variable	variable	ADJ
fuelectenerg-1427	1038	4	orderings	ordering	NOUN
fuelectenerg-1427	1038	5	,	,	PUNCT
fuelectenerg-1427	1038	6	some	some	DET
fuelectenerg-1427	1038	7	forms	form	NOUN
fuelectenerg-1427	1038	8	are	be	AUX
fuelectenerg-1427	1038	9	not	not	PART
fuelectenerg-1427	1038	10	repeated	repeat	VERB
fuelectenerg-1427	1038	11	while	while	SCONJ
fuelectenerg-1427	1038	12	other	other	ADJ
fuelectenerg-1427	1038	13	forms	form	NOUN
fuelectenerg-1427	1038	14	are	be	AUX
fuelectenerg-1427	1038	15	.	.	PUNCT
fuelectenerg-1427	1039	1	therefore	therefore	ADV
fuelectenerg-1427	1039	2	the	the	DET
fuelectenerg-1427	1039	3	union	union	NOUN
fuelectenerg-1427	1039	4	of	of	ADP
fuelectenerg-1427	1039	5	sets	set	NOUN
fuelectenerg-1427	1039	6	of	of	ADP
fuelectenerg-1427	1039	7	tifs	tif	NOUN
fuelectenerg-1427	1039	8	for	for	ADP
fuelectenerg-1427	1039	9	all	all	DET
fuelectenerg-1427	1039	10	variable	variable	ADJ
fuelectenerg-1427	1039	11	orders	order	NOUN
fuelectenerg-1427	1039	12	contains	contain	VERB
fuelectenerg-1427	1039	13	more	more	ADJ
fuelectenerg-1427	1039	14	forms	form	NOUN
fuelectenerg-1427	1039	15	than	than	ADP
fuelectenerg-1427	1039	16	any	any	PRON
fuelectenerg-1427	1039	17	of	of	ADP
fuelectenerg-1427	1039	18	the	the	DET
fuelectenerg-1427	1039	19	tif	tif	PROPN
fuelectenerg-1427	1039	20	sets	set	NOUN
fuelectenerg-1427	1039	21	taken	take	VERB
fuelectenerg-1427	1039	22	separately	separately	ADV
fuelectenerg-1427	1039	23	and	and	CCONJ
fuelectenerg-1427	1039	24	less	less	ADJ
fuelectenerg-1427	1039	25	forms	form	NOUN
fuelectenerg-1427	1039	26	than	than	ADP
fuelectenerg-1427	1039	27	total	total	ADJ
fuelectenerg-1427	1039	28	sum	sum	NOUN
fuelectenerg-1427	1039	29	of	of	ADP
fuelectenerg-1427	1039	30	all	all	DET
fuelectenerg-1427	1039	31	tifs	tif	NOUN
fuelectenerg-1427	1039	32	.	.	PUNCT
fuelectenerg-1427	1040	1	generalized	generalized	ADJ
fuelectenerg-1427	1040	2	inclusive	inclusive	ADJ
fuelectenerg-1427	1040	3	forms	form	NOUN
fuelectenerg-1427	1040	4	include	include	VERB
fuelectenerg-1427	1040	5	other	other	ADJ
fuelectenerg-1427	1040	6	forms	form	NOUN
fuelectenerg-1427	1040	7	such	such	ADJ
fuelectenerg-1427	1040	8	as	as	ADP
fuelectenerg-1427	1040	9	grms	grm	NOUN
fuelectenerg-1427	1040	10	over	over	ADP
fuelectenerg-1427	1040	11	gf(3	gf(3	PROPN
fuelectenerg-1427	1040	12	)	)	PUNCT
fuelectenerg-1427	1040	13	as	as	SCONJ
fuelectenerg-1427	1040	14	can	can	AUX
fuelectenerg-1427	1040	15	be	be	AUX
fuelectenerg-1427	1040	16	shown	show	VERB
fuelectenerg-1427	1040	17	by	by	ADP
fuelectenerg-1427	1040	18	considering	consider	VERB
fuelectenerg-1427	1040	19	all	all	DET
fuelectenerg-1427	1040	20	possible	possible	ADJ
fuelectenerg-1427	1040	21	combinations	combination	NOUN
fuelectenerg-1427	1040	22	of	of	ADP
fuelectenerg-1427	1040	23	literals	literal	NOUN
fuelectenerg-1427	1040	24	for	for	ADP
fuelectenerg-1427	1040	25	all	all	DET
fuelectenerg-1427	1040	26	possible	possible	ADJ
fuelectenerg-1427	1040	27	orders	order	NOUN
fuelectenerg-1427	1040	28	of	of	ADP
fuelectenerg-1427	1040	29	variables	variable	NOUN
fuelectenerg-1427	1040	30	.	.	PUNCT
fuelectenerg-1427	1041	1	if	if	SCONJ
fuelectenerg-1427	1041	2	we	we	PRON
fuelectenerg-1427	1041	3	relax	relax	VERB
fuelectenerg-1427	1041	4	the	the	DET
fuelectenerg-1427	1041	5	requirement	requirement	NOUN
fuelectenerg-1427	1041	6	of	of	ADP
fuelectenerg-1427	1041	7	fixed	fix	VERB
fuelectenerg-1427	1041	8	variable	variable	ADJ
fuelectenerg-1427	1041	9	ordering	ordering	NOUN
fuelectenerg-1427	1041	10	,	,	PUNCT
fuelectenerg-1427	1041	11	and	and	CCONJ
fuelectenerg-1427	1041	12	allow	allow	VERB
fuelectenerg-1427	1041	13	any	any	DET
fuelectenerg-1427	1041	14	ordering	ordering	NOUN
fuelectenerg-1427	1041	15	of	of	ADP
fuelectenerg-1427	1041	16	variables	variable	NOUN
fuelectenerg-1427	1041	17	in	in	ADP
fuelectenerg-1427	1041	18	branches	branch	NOUN
fuelectenerg-1427	1041	19	of	of	ADP
fuelectenerg-1427	1041	20	the	the	DET
fuelectenerg-1427	1041	21	tree	tree	NOUN
fuelectenerg-1427	1041	22	but	but	CCONJ
fuelectenerg-1427	1041	23	do	do	AUX
fuelectenerg-1427	1041	24	not	not	PART
fuelectenerg-1427	1041	25	allow	allow	VERB
fuelectenerg-1427	1041	26	repetitions	repetition	NOUN
fuelectenerg-1427	1041	27	of	of	ADP
fuelectenerg-1427	1041	28	variables	variable	NOUN
fuelectenerg-1427	1041	29	in	in	ADP
fuelectenerg-1427	1041	30	the	the	DET
fuelectenerg-1427	1041	31	branches	branch	NOUN
fuelectenerg-1427	1041	32	,	,	PUNCT
fuelectenerg-1427	1041	33	we	we	PRON
fuelectenerg-1427	1041	34	generate	generate	VERB
fuelectenerg-1427	1041	35	more	more	ADJ
fuelectenerg-1427	1041	36	general	general	ADJ
fuelectenerg-1427	1041	37	gf(3	gf(3	PROPN
fuelectenerg-1427	1041	38	)	)	PUNCT
fuelectenerg-1427	1041	39	family	family	NOUN
fuelectenerg-1427	1041	40	of	of	ADP
fuelectenerg-1427	1041	41	forms	form	NOUN
fuelectenerg-1427	1041	42	.	.	PUNCT
fuelectenerg-1427	1042	1	111	111	NUM
fuelectenerg-1427	1042	2	an	an	DET
fuelectenerg-1427	1042	3	extended	extend	VERB
fuelectenerg-1427	1042	4	green	green	ADJ
fuelectenerg-1427	1042	5	sasao	sasao	PROPN
fuelectenerg-1427	1042	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1042	7	of	of	ADP
fuelectenerg-1427	1042	8	canonical	canonical	ADJ
fuelectenerg-1427	1042	9	ternary	ternary	ADJ
fuelectenerg-1427	1042	10	galois	galois	NOUN
fuelectenerg-1427	1042	11	forms	form	NOUN
fuelectenerg-1427	1042	12	...	...	PUNCT
fuelectenerg-1427	1043	1	s	s	PART
fuelectenerg-1427	1043	2	s	s	X
fuelectenerg-1427	1043	3	s	s	X
fuelectenerg-1427	1043	4	s	s	NOUN
fuelectenerg-1427	1043	5	0	0	NUM
fuelectenerg-1427	1043	6	a	a	DET
fuelectenerg-1427	1043	7	1	1	NUM
fuelectenerg-1427	1043	8	a	a	DET
fuelectenerg-1427	1043	9	2	2	NUM
fuelectenerg-1427	1043	10	a	a	DET
fuelectenerg-1427	1043	11	s	s	NOUN
fuelectenerg-1427	1043	12	s	s	X
fuelectenerg-1427	1043	13	d	d	X
fuelectenerg-1427	1043	14	d	d	X
fuelectenerg-1427	1043	15	s	s	X
fuelectenerg-1427	1043	16	s	s	X
fuelectenerg-1427	1043	17	s	s	X
fuelectenerg-1427	1043	18	d	d	X
fuelectenerg-1427	1043	19	1	1	NUM
fuelectenerg-1427	1043	20	(	(	PUNCT
fuelectenerg-1427	1043	21	b	b	NOUN
fuelectenerg-1427	1043	22	,	,	PUNCT
fuelectenerg-1427	1043	23	)	)	PUNCT
fuelectenerg-1427	1043	24	2	2	NUM
fuelectenerg-1427	1043	25	b	b	NOUN
fuelectenerg-1427	1043	26	,	,	PUNCT
fuelectenerg-1427	1043	27	s	s	NOUN
fuelectenerg-1427	1043	28	d	d	X
fuelectenerg-1427	1043	29	d	d	PROPN
fuelectenerg-1427	1043	30	d	d	PROPN
fuelectenerg-1427	1043	31	1	1	NUM
fuelectenerg-1427	1043	32	(	(	PUNCT
fuelectenerg-1427	1043	33	b	b	NOUN
fuelectenerg-1427	1043	34	,	,	PUNCT
fuelectenerg-1427	1043	35	)	)	PUNCT
fuelectenerg-1427	1043	36	2	2	NUM
fuelectenerg-1427	1043	37	b	b	NOUN
fuelectenerg-1427	1043	38	,	,	PUNCT
fuelectenerg-1427	1043	39	s	s	X
fuelectenerg-1427	1043	40	s	s	NOUN
fuelectenerg-1427	1043	41	s	s	NOUN
fuelectenerg-1427	1043	42	0	0	NUM
fuelectenerg-1427	1043	43	a	a	DET
fuelectenerg-1427	1043	44	0	0	NUM
fuelectenerg-1427	1043	45	a	a	DET
fuelectenerg-1427	1043	46	1	1	NUM
fuelectenerg-1427	1043	47	a	a	DET
fuelectenerg-1427	1043	48	1	1	NUM
fuelectenerg-1427	1043	49	a	a	DET
fuelectenerg-1427	1043	50	2	2	NUM
fuelectenerg-1427	1043	51	a	a	DET
fuelectenerg-1427	1043	52	2	2	NUM
fuelectenerg-1427	1043	53	a	a	DET
fuelectenerg-1427	1043	54	d	d	PROPN
fuelectenerg-1427	1043	55	1	1	NUM
fuelectenerg-1427	1043	56	1	1	NUM
fuelectenerg-1427	1043	57	1	1	NUM
fuelectenerg-1427	1043	58	1	1	NUM
fuelectenerg-1427	1043	59	1	1	NUM
fuelectenerg-1427	1043	60	1	1	NUM
fuelectenerg-1427	1043	61	1	1	NUM
fuelectenerg-1427	1043	62	1	1	NUM
fuelectenerg-1427	1043	63	1	1	NUM
fuelectenerg-1427	1043	64	1	1	NUM
fuelectenerg-1427	1043	65	11	11	NUM
fuelectenerg-1427	1043	66	1	1	NUM
fuelectenerg-1427	1043	67	1	1	NUM
fuelectenerg-1427	1043	68	1	1	NUM
fuelectenerg-1427	1043	69	1	1	NUM
fuelectenerg-1427	1043	70	1	1	NUM
fuelectenerg-1427	1043	71	1	1	NUM
fuelectenerg-1427	1043	72	1	1	NUM
fuelectenerg-1427	1043	73	1	1	NUM
fuelectenerg-1427	1043	74	1	1	NUM
fuelectenerg-1427	1043	75	1	1	NUM
fuelectenerg-1427	1043	76	1(a	1(a	NUM
fuelectenerg-1427	1043	77	,	,	PUNCT
fuelectenerg-1427	1043	78	)	)	PUNCT
fuelectenerg-1427	1043	79	2	2	NUM
fuelectenerg-1427	1043	80	(	(	PUNCT
fuelectenerg-1427	1043	81	a	a	PRON
fuelectenerg-1427	1043	82	,	,	PUNCT
fuelectenerg-1427	1043	83	)	)	PUNCT
fuelectenerg-1427	1043	84	2	2	NUM
fuelectenerg-1427	1043	85	(	(	PUNCT
fuelectenerg-1427	1043	86	a	a	PRON
fuelectenerg-1427	1043	87	,	,	PUNCT
fuelectenerg-1427	1043	88	)	)	PUNCT
fuelectenerg-1427	1043	89	2	2	NUM
fuelectenerg-1427	1043	90	(	(	PUNCT
fuelectenerg-1427	1043	91	a	a	PRON
fuelectenerg-1427	1043	92	,	,	PUNCT
fuelectenerg-1427	1043	93	)	)	PUNCT
fuelectenerg-1427	1043	94	2	2	NUM
fuelectenerg-1427	1043	95	(	(	PUNCT
fuelectenerg-1427	1043	96	a	a	PRON
fuelectenerg-1427	1043	97	,	,	PUNCT
fuelectenerg-1427	1043	98	)	)	PUNCT
fuelectenerg-1427	1043	99	2	2	NUM
fuelectenerg-1427	1043	100	(	(	PUNCT
fuelectenerg-1427	1043	101	a	a	PRON
fuelectenerg-1427	1043	102	,	,	PUNCT
fuelectenerg-1427	1043	103	)	)	PUNCT
fuelectenerg-1427	1043	104	2	2	NUM
fuelectenerg-1427	1043	105	(	(	PUNCT
fuelectenerg-1427	1043	106	a	a	PRON
fuelectenerg-1427	1043	107	,	,	PUNCT
fuelectenerg-1427	1043	108	)	)	PUNCT
fuelectenerg-1427	1043	109	2	2	NUM
fuelectenerg-1427	1043	110	(	(	PUNCT
fuelectenerg-1427	1043	111	a	a	PRON
fuelectenerg-1427	1043	112	,	,	PUNCT
fuelectenerg-1427	1043	113	)	)	PUNCT
fuelectenerg-1427	1043	114	2	2	NUM
fuelectenerg-1427	1043	115	(	(	PUNCT
fuelectenerg-1427	1043	116	a	a	PRON
fuelectenerg-1427	1043	117	,	,	PUNCT
fuelectenerg-1427	1043	118	)	)	PUNCT
fuelectenerg-1427	1043	119	2	2	NUM
fuelectenerg-1427	1043	120	(	(	PUNCT
fuelectenerg-1427	1043	121	a	a	PRON
fuelectenerg-1427	1043	122	,	,	PUNCT
fuelectenerg-1427	1043	123	)	)	PUNCT
fuelectenerg-1427	1043	124	2	2	NUM
fuelectenerg-1427	1043	125	(	(	PUNCT
fuelectenerg-1427	1043	126	a	a	PRON
fuelectenerg-1427	1043	127	,	,	PUNCT
fuelectenerg-1427	1043	128	)	)	PUNCT
fuelectenerg-1427	1043	129	2	2	NUM
fuelectenerg-1427	1043	130	(	(	PUNCT
fuelectenerg-1427	1043	131	a	a	PRON
fuelectenerg-1427	1043	132	,	,	PUNCT
fuelectenerg-1427	1043	133	)	)	PUNCT
fuelectenerg-1427	1043	134	2	2	NUM
fuelectenerg-1427	1043	135	(	(	PUNCT
fuelectenerg-1427	1043	136	a	a	PRON
fuelectenerg-1427	1043	137	,	,	PUNCT
fuelectenerg-1427	1043	138	)	)	PUNCT
fuelectenerg-1427	1043	139	2	2	NUM
fuelectenerg-1427	1043	140	(	(	PUNCT
fuelectenerg-1427	1043	141	a	a	PRON
fuelectenerg-1427	1043	142	,	,	PUNCT
fuelectenerg-1427	1043	143	)	)	PUNCT
fuelectenerg-1427	1043	144	2	2	NUM
fuelectenerg-1427	1043	145	(	(	PUNCT
fuelectenerg-1427	1043	146	a	a	PRON
fuelectenerg-1427	1043	147	,	,	PUNCT
fuelectenerg-1427	1043	148	)	)	PUNCT
fuelectenerg-1427	1043	149	2	2	NUM
fuelectenerg-1427	1043	150	(	(	PUNCT
fuelectenerg-1427	1043	151	a	a	PRON
fuelectenerg-1427	1043	152	,	,	PUNCT
fuelectenerg-1427	1043	153	)	)	PUNCT
fuelectenerg-1427	1043	154	2	2	NUM
fuelectenerg-1427	1043	155	(	(	PUNCT
fuelectenerg-1427	1043	156	a	a	PRON
fuelectenerg-1427	1043	157	,	,	PUNCT
fuelectenerg-1427	1043	158	)	)	PUNCT
fuelectenerg-1427	1043	159	2	2	NUM
fuelectenerg-1427	1043	160	(	(	PUNCT
fuelectenerg-1427	1043	161	a	a	PRON
fuelectenerg-1427	1043	162	,	,	PUNCT
fuelectenerg-1427	1043	163	)	)	PUNCT
fuelectenerg-1427	1043	164	2	2	NUM
fuelectenerg-1427	1043	165	(	(	PUNCT
fuelectenerg-1427	1043	166	a	a	PRON
fuelectenerg-1427	1043	167	,	,	PUNCT
fuelectenerg-1427	1043	168	)	)	PUNCT
fuelectenerg-1427	1043	169	2	2	NUM
fuelectenerg-1427	1043	170	(	(	PUNCT
fuelectenerg-1427	1043	171	a	a	PRON
fuelectenerg-1427	1043	172	,	,	PUNCT
fuelectenerg-1427	1043	173	)	)	PUNCT
fuelectenerg-1427	1043	174	2	2	NUM
fuelectenerg-1427	1043	175	(	(	PUNCT
fuelectenerg-1427	1043	176	a	a	PRON
fuelectenerg-1427	1043	177	,	,	PUNCT
fuelectenerg-1427	1043	178	)	)	PUNCT
fuelectenerg-1427	1043	179	2	2	NUM
fuelectenerg-1427	1043	180	(	(	PUNCT
fuelectenerg-1427	1043	181	a	a	PRON
fuelectenerg-1427	1043	182	,	,	PUNCT
fuelectenerg-1427	1043	183	)	)	PUNCT
fuelectenerg-1427	1043	184	2	2	NUM
fuelectenerg-1427	1043	185	(	(	PUNCT
fuelectenerg-1427	1043	186	a	a	PRON
fuelectenerg-1427	1043	187	,	,	PUNCT
fuelectenerg-1427	1043	188	)	)	PUNCT
fuelectenerg-1427	1043	189	2	2	NUM
fuelectenerg-1427	1043	190	(	(	PUNCT
fuelectenerg-1427	1043	191	a	a	PRON
fuelectenerg-1427	1043	192	,	,	PUNCT
fuelectenerg-1427	1043	193	)	)	PUNCT
fuelectenerg-1427	1043	194	2	2	NUM
fuelectenerg-1427	1043	195	a	a	PRON
fuelectenerg-1427	1043	196	,	,	PUNCT
fuelectenerg-1427	1043	197	a	a	PRON
fuelectenerg-1427	1043	198	,	,	PUNCT
fuelectenerg-1427	1043	199	a	a	PRON
fuelectenerg-1427	1043	200	,	,	PUNCT
fuelectenerg-1427	1043	201	a	a	PRON
fuelectenerg-1427	1043	202	,	,	PUNCT
fuelectenerg-1427	1043	203	a	a	PRON
fuelectenerg-1427	1043	204	,	,	PUNCT
fuelectenerg-1427	1043	205	a	a	PRON
fuelectenerg-1427	1043	206	,	,	PUNCT
fuelectenerg-1427	1043	207	a	a	PRON
fuelectenerg-1427	1043	208	,	,	PUNCT
fuelectenerg-1427	1043	209	a	a	PRON
fuelectenerg-1427	1043	210	,	,	PUNCT
fuelectenerg-1427	1043	211	a	a	PRON
fuelectenerg-1427	1043	212	,	,	PUNCT
fuelectenerg-1427	1043	213	a	a	PRON
fuelectenerg-1427	1043	214	,	,	PUNCT
fuelectenerg-1427	1043	215	a	a	PRON
fuelectenerg-1427	1043	216	,	,	PUNCT
fuelectenerg-1427	1043	217	a	a	PRON
fuelectenerg-1427	1043	218	,	,	PUNCT
fuelectenerg-1427	1043	219	a	a	PRON
fuelectenerg-1427	1043	220	,	,	PUNCT
fuelectenerg-1427	1043	221	a	a	PRON
fuelectenerg-1427	1043	222	,	,	PUNCT
fuelectenerg-1427	1043	223	a	a	PRON
fuelectenerg-1427	1043	224	,	,	PUNCT
fuelectenerg-1427	1043	225	a	a	PRON
fuelectenerg-1427	1043	226	,	,	PUNCT
fuelectenerg-1427	1043	227	a	a	PRON
fuelectenerg-1427	1043	228	,	,	PUNCT
fuelectenerg-1427	1043	229	a	a	PRON
fuelectenerg-1427	1043	230	,	,	PUNCT
fuelectenerg-1427	1043	231	a	a	PRON
fuelectenerg-1427	1043	232	,	,	PUNCT
fuelectenerg-1427	1043	233	a	a	PRON
fuelectenerg-1427	1043	234	,	,	PUNCT
fuelectenerg-1427	1043	235	a	a	PRON
fuelectenerg-1427	1043	236	,	,	PUNCT
fuelectenerg-1427	1043	237	a	a	PRON
fuelectenerg-1427	1043	238	,	,	PUNCT
fuelectenerg-1427	1043	239	a	a	PRON
fuelectenerg-1427	1043	240	,	,	PUNCT
fuelectenerg-1427	1043	241	s	s	NOUN
fuelectenerg-1427	1043	242	s	s	X
fuelectenerg-1427	1043	243	d	d	X
fuelectenerg-1427	1043	244	d	d	X
fuelectenerg-1427	1043	245	s	s	X
fuelectenerg-1427	1043	246	s	s	X
fuelectenerg-1427	1043	247	d	d	X
fuelectenerg-1427	1043	248	d	d	SYM
fuelectenerg-1427	1043	249	1	1	NUM
fuelectenerg-1427	1043	250	(	(	PUNCT
fuelectenerg-1427	1043	251	b	b	NOUN
fuelectenerg-1427	1043	252	,	,	PUNCT
fuelectenerg-1427	1043	253	)	)	PUNCT
fuelectenerg-1427	1043	254	2	2	NUM
fuelectenerg-1427	1043	255	b	b	NOUN
fuelectenerg-1427	1043	256	,	,	PUNCT
fuelectenerg-1427	1043	257	sd	sd	ADP
fuelectenerg-1427	1043	258	d	d	PROPN
fuelectenerg-1427	1043	259	d	d	PROPN
fuelectenerg-1427	1043	260	1	1	NUM
fuelectenerg-1427	1043	261	(	(	PUNCT
fuelectenerg-1427	1043	262	b	b	NOUN
fuelectenerg-1427	1043	263	,	,	PUNCT
fuelectenerg-1427	1043	264	)	)	PUNCT
fuelectenerg-1427	1043	265	2	2	NUM
fuelectenerg-1427	1043	266	b	b	NOUN
fuelectenerg-1427	1043	267	,	,	PUNCT
fuelectenerg-1427	1043	268	s	s	X
fuelectenerg-1427	1043	269	s	s	NOUN
fuelectenerg-1427	1043	270	s	s	NOUN
fuelectenerg-1427	1043	271	0	0	NUM
fuelectenerg-1427	1043	272	a	a	DET
fuelectenerg-1427	1043	273	0	0	NUM
fuelectenerg-1427	1043	274	a	a	DET
fuelectenerg-1427	1043	275	0	0	NUM
fuelectenerg-1427	1044	1	a	a	DET
fuelectenerg-1427	1044	2	0	0	NUM
fuelectenerg-1427	1044	3	a	a	DET
fuelectenerg-1427	1044	4	0	0	NUM
fuelectenerg-1427	1044	5	a	a	DET
fuelectenerg-1427	1044	6	0	0	NUM
fuelectenerg-1427	1044	7	a	a	DET
fuelectenerg-1427	1044	8	0	0	NUM
fuelectenerg-1427	1044	9	a	a	DET
fuelectenerg-1427	1044	10	0	0	NUM
fuelectenerg-1427	1044	11	a	a	DET
fuelectenerg-1427	1044	12	0	0	NUM
fuelectenerg-1427	1044	13	a	a	DET
fuelectenerg-1427	1044	14	0	0	NUM
fuelectenerg-1427	1044	15	a	a	DET
fuelectenerg-1427	1044	16	0	0	NUM
fuelectenerg-1427	1044	17	a	a	DET
fuelectenerg-1427	1044	18	0	0	NUM
fuelectenerg-1427	1044	19	a	a	DET
fuelectenerg-1427	1044	20	0	0	NUM
fuelectenerg-1427	1044	21	a	a	DET
fuelectenerg-1427	1044	22	0	0	NUM
fuelectenerg-1427	1044	23	a	a	DET
fuelectenerg-1427	1044	24	0	0	NUM
fuelectenerg-1427	1044	25	a	a	DET
fuelectenerg-1427	1044	26	0	0	NUM
fuelectenerg-1427	1044	27	a0	a0	NOUN
fuelectenerg-1427	1044	28	a	a	DET
fuelectenerg-1427	1044	29	0	0	NUM
fuelectenerg-1427	1044	30	a	a	DET
fuelectenerg-1427	1044	31	0	0	NUM
fuelectenerg-1427	1044	32	a	a	DET
fuelectenerg-1427	1044	33	1	1	NUM
fuelectenerg-1427	1044	34	a	a	DET
fuelectenerg-1427	1044	35	1	1	NUM
fuelectenerg-1427	1044	36	a	a	DET
fuelectenerg-1427	1044	37	1	1	NUM
fuelectenerg-1427	1044	38	a	a	DET
fuelectenerg-1427	1044	39	1	1	NUM
fuelectenerg-1427	1044	40	a	a	DET
fuelectenerg-1427	1044	41	1	1	NUM
fuelectenerg-1427	1044	42	a	a	DET
fuelectenerg-1427	1044	43	1	1	NUM
fuelectenerg-1427	1044	44	a	a	DET
fuelectenerg-1427	1044	45	1	1	NUM
fuelectenerg-1427	1044	46	a	a	DET
fuelectenerg-1427	1044	47	1	1	NUM
fuelectenerg-1427	1044	48	a	a	DET
fuelectenerg-1427	1044	49	1	1	NUM
fuelectenerg-1427	1044	50	a	a	DET
fuelectenerg-1427	1044	51	1	1	NUM
fuelectenerg-1427	1044	52	a	a	DET
fuelectenerg-1427	1044	53	1	1	NUM
fuelectenerg-1427	1044	54	a	a	DET
fuelectenerg-1427	1044	55	1	1	NUM
fuelectenerg-1427	1044	56	a	a	DET
fuelectenerg-1427	1044	57	1	1	NUM
fuelectenerg-1427	1044	58	a	a	DET
fuelectenerg-1427	1044	59	1	1	NUM
fuelectenerg-1427	1044	60	a	a	DET
fuelectenerg-1427	1044	61	1	1	NUM
fuelectenerg-1427	1044	62	a	a	DET
fuelectenerg-1427	1044	63	1	1	NUM
fuelectenerg-1427	1044	64	a1	a1	NOUN
fuelectenerg-1427	1044	65	a	a	DET
fuelectenerg-1427	1044	66	1	1	NUM
fuelectenerg-1427	1044	67	a	a	DET
fuelectenerg-1427	1044	68	1	1	NUM
fuelectenerg-1427	1044	69	a	a	DET
fuelectenerg-1427	1044	70	2	2	NUM
fuelectenerg-1427	1044	71	a	a	DET
fuelectenerg-1427	1044	72	2	2	NUM
fuelectenerg-1427	1044	73	a	a	DET
fuelectenerg-1427	1044	74	2	2	NUM
fuelectenerg-1427	1044	75	a	a	DET
fuelectenerg-1427	1044	76	2	2	NUM
fuelectenerg-1427	1044	77	a	a	DET
fuelectenerg-1427	1044	78	2	2	NUM
fuelectenerg-1427	1044	79	a	a	DET
fuelectenerg-1427	1044	80	2	2	NUM
fuelectenerg-1427	1044	81	a	a	DET
fuelectenerg-1427	1044	82	2	2	NUM
fuelectenerg-1427	1044	83	a	a	DET
fuelectenerg-1427	1044	84	2	2	NUM
fuelectenerg-1427	1044	85	a	a	DET
fuelectenerg-1427	1044	86	2	2	NUM
fuelectenerg-1427	1044	87	a	a	DET
fuelectenerg-1427	1044	88	2	2	NUM
fuelectenerg-1427	1044	89	a	a	DET
fuelectenerg-1427	1044	90	2	2	NUM
fuelectenerg-1427	1044	91	a	a	DET
fuelectenerg-1427	1044	92	2	2	NUM
fuelectenerg-1427	1044	93	a	a	DET
fuelectenerg-1427	1044	94	2	2	NUM
fuelectenerg-1427	1044	95	a	a	DET
fuelectenerg-1427	1044	96	2	2	NUM
fuelectenerg-1427	1044	97	a	a	DET
fuelectenerg-1427	1044	98	2	2	NUM
fuelectenerg-1427	1044	99	a	a	DET
fuelectenerg-1427	1044	100	2	2	NUM
fuelectenerg-1427	1044	101	a2	a2	NOUN
fuelectenerg-1427	1044	102	a	a	DET
fuelectenerg-1427	1044	103	2	2	NUM
fuelectenerg-1427	1044	104	a	a	DET
fuelectenerg-1427	1044	105	2	2	NUM
fuelectenerg-1427	1044	106	a	a	PRON
fuelectenerg-1427	1044	107	d	d	PROPN
fuelectenerg-1427	1044	108	1	1	NUM
fuelectenerg-1427	1044	109	a	a	PRON
fuelectenerg-1427	1044	110	,	,	PUNCT
fuelectenerg-1427	1044	111	s	s	PART
fuelectenerg-1427	1044	112	sd	sd	NOUN
fuelectenerg-1427	1044	113	d	d	PROPN
fuelectenerg-1427	1044	114	s	s	AUX
fuelectenerg-1427	1044	115	s	s	X
fuelectenerg-1427	1044	116	s	s	X
fuelectenerg-1427	1044	117	sd	sd	NOUN
fuelectenerg-1427	1044	118	d	d	NOUN
fuelectenerg-1427	1044	119	1	1	NUM
fuelectenerg-1427	1044	120	(	(	PUNCT
fuelectenerg-1427	1044	121	b	b	NOUN
fuelectenerg-1427	1044	122	,	,	PUNCT
fuelectenerg-1427	1044	123	)	)	PUNCT
fuelectenerg-1427	1044	124	2	2	NUM
fuelectenerg-1427	1044	125	b	b	NOUN
fuelectenerg-1427	1044	126	,	,	PUNCT
fuelectenerg-1427	1044	127	d	d	PROPN
fuelectenerg-1427	1044	128	d	d	PROPN
fuelectenerg-1427	1044	129	d	d	PROPN
fuelectenerg-1427	1044	130	d	d	PROPN
fuelectenerg-1427	1044	131	1	1	NUM
fuelectenerg-1427	1044	132	(	(	PUNCT
fuelectenerg-1427	1044	133	b	b	NOUN
fuelectenerg-1427	1044	134	,	,	PUNCT
fuelectenerg-1427	1044	135	)	)	PUNCT
fuelectenerg-1427	1044	136	2	2	NUM
fuelectenerg-1427	1044	137	b	b	NOUN
fuelectenerg-1427	1044	138	,	,	PUNCT
fuelectenerg-1427	1044	139	s	s	X
fuelectenerg-1427	1044	140	s	s	NOUN
fuelectenerg-1427	1044	141	s	s	X
fuelectenerg-1427	1044	142	d	d	X
fuelectenerg-1427	1044	143	s	s	X
fuelectenerg-1427	1044	144	d	d	X
fuelectenerg-1427	1044	145	dd	dd	NOUN
fuelectenerg-1427	1044	146	d	d	PROPN
fuelectenerg-1427	1044	147	d	d	PROPN
fuelectenerg-1427	1044	148	1	1	NUM
fuelectenerg-1427	1044	149	(	(	PUNCT
fuelectenerg-1427	1044	150	b	b	NOUN
fuelectenerg-1427	1044	151	,	,	PUNCT
fuelectenerg-1427	1044	152	)	)	PUNCT
fuelectenerg-1427	1044	153	2	2	NUM
fuelectenerg-1427	1044	154	b	b	NOUN
fuelectenerg-1427	1044	155	,	,	PUNCT
fuelectenerg-1427	1044	156	s	s	NOUN
fuelectenerg-1427	1044	157	d	d	X
fuelectenerg-1427	1044	158	d	d	PROPN
fuelectenerg-1427	1044	159	d	d	PROPN
fuelectenerg-1427	1044	160	1	1	NUM
fuelectenerg-1427	1044	161	(	(	PUNCT
fuelectenerg-1427	1044	162	b	b	NOUN
fuelectenerg-1427	1044	163	,	,	PUNCT
fuelectenerg-1427	1044	164	)	)	PUNCT
fuelectenerg-1427	1044	165	2	2	NUM
fuelectenerg-1427	1044	166	b	b	NOUN
fuelectenerg-1427	1044	167	,	,	PUNCT
fuelectenerg-1427	1044	168	n=1	n=1	PROPN
fuelectenerg-1427	1044	169	n=81	n=81	VERB
fuelectenerg-1427	1044	170	n=729	n=729	PROPN
fuelectenerg-1427	1044	171	n=59049	n=59049	PROPN
fuelectenerg-1427	1044	172	n=9	n=9	PROPN
fuelectenerg-1427	1044	173	n=81	n=81	VERB
fuelectenerg-1427	1044	174	n=6561	n=6561	PROPN
fuelectenerg-1427	1044	175	n=59049	n=59049	PROPN
fuelectenerg-1427	1044	176	n=9	n=9	PROPN
fuelectenerg-1427	1044	177	n=81	n=81	ADP
fuelectenerg-1427	1044	178	n=6561	n=6561	PROPN
fuelectenerg-1427	1044	179	n=59049	n=59049	PROPN
fuelectenerg-1427	1044	180	n=9	n=9	PROPN
fuelectenerg-1427	1044	181	n=729	n=729	X
fuelectenerg-1427	1044	182	n=6561	n=6561	PROPN
fuelectenerg-1427	1045	1	n=531441	n=531441	ADV
fuelectenerg-1427	1045	2	0	0	NUM
fuelectenerg-1427	1045	3	b	b	X
fuelectenerg-1427	1045	4	0	0	NUM
fuelectenerg-1427	1045	5	b	b	NOUN
fuelectenerg-1427	1045	6	0	0	NUM
fuelectenerg-1427	1045	7	a	a	DET
fuelectenerg-1427	1045	8	0	0	NUM
fuelectenerg-1427	1045	9	a	a	DET
fuelectenerg-1427	1045	10	0	0	NUM
fuelectenerg-1427	1045	11	b	b	NOUN
fuelectenerg-1427	1045	12	0	0	NUM
fuelectenerg-1427	1045	13	b	b	NOUN
fuelectenerg-1427	1045	14	0	0	NUM
fuelectenerg-1427	1045	15	b	b	NOUN
fuelectenerg-1427	1045	16	0	0	NUM
fuelectenerg-1427	1045	17	b	b	NOUN
fuelectenerg-1427	1045	18	0	0	NUM
fuelectenerg-1427	1045	19	b	b	NOUN
fuelectenerg-1427	1045	20	0	0	NUM
fuelectenerg-1427	1045	21	b	b	SYM
fuelectenerg-1427	1045	22	1	1	NUM
fuelectenerg-1427	1045	23	b	b	SYM
fuelectenerg-1427	1045	24	1	1	NUM
fuelectenerg-1427	1045	25	b	b	SYM
fuelectenerg-1427	1045	26	1	1	NUM
fuelectenerg-1427	1045	27	a	a	DET
fuelectenerg-1427	1045	28	1	1	NUM
fuelectenerg-1427	1045	29	a	a	DET
fuelectenerg-1427	1045	30	1	1	NUM
fuelectenerg-1427	1045	31	b	b	SYM
fuelectenerg-1427	1045	32	1	1	NUM
fuelectenerg-1427	1045	33	b	b	SYM
fuelectenerg-1427	1045	34	1	1	NUM
fuelectenerg-1427	1045	35	b	b	SYM
fuelectenerg-1427	1045	36	1	1	NUM
fuelectenerg-1427	1045	37	b	b	SYM
fuelectenerg-1427	1045	38	1	1	NUM
fuelectenerg-1427	1045	39	b	b	SYM
fuelectenerg-1427	1045	40	1	1	NUM
fuelectenerg-1427	1045	41	b	b	SYM
fuelectenerg-1427	1045	42	2	2	NUM
fuelectenerg-1427	1045	43	b	b	SYM
fuelectenerg-1427	1045	44	2	2	NUM
fuelectenerg-1427	1045	45	b	b	SYM
fuelectenerg-1427	1045	46	2	2	NUM
fuelectenerg-1427	1045	47	a	a	DET
fuelectenerg-1427	1045	48	2	2	NUM
fuelectenerg-1427	1045	49	a	a	DET
fuelectenerg-1427	1045	50	2	2	NUM
fuelectenerg-1427	1045	51	b	b	SYM
fuelectenerg-1427	1045	52	2	2	NUM
fuelectenerg-1427	1045	53	b	b	SYM
fuelectenerg-1427	1045	54	2	2	NUM
fuelectenerg-1427	1045	55	b	b	SYM
fuelectenerg-1427	1045	56	2	2	NUM
fuelectenerg-1427	1045	57	b	b	SYM
fuelectenerg-1427	1045	58	2	2	NUM
fuelectenerg-1427	1045	59	b	b	SYM
fuelectenerg-1427	1045	60	2	2	NUM
fuelectenerg-1427	1045	61	b	b	PROPN
fuelectenerg-1427	1045	62	(	(	PUNCT
fuelectenerg-1427	1045	63	b	b	NOUN
fuelectenerg-1427	1045	64	)	)	PUNCT
fuelectenerg-1427	1045	65	figure	figure	NOUN
fuelectenerg-1427	1045	66	5	5	NUM
fuelectenerg-1427	1045	67	:	:	PUNCT
fuelectenerg-1427	1045	68	(	(	PUNCT
fuelectenerg-1427	1045	69	continued	continued	ADJ
fuelectenerg-1427	1045	70	)	)	PUNCT
fuelectenerg-1427	1045	71	.	.	PUNCT
fuelectenerg-1427	1046	1	proof	proof	NOUN
fuelectenerg-1427	1046	2	.	.	PUNCT
fuelectenerg-1427	1047	1	an	an	DET
fuelectenerg-1427	1047	2	expansion	expansion	NOUN
fuelectenerg-1427	1047	3	is	be	AUX
fuelectenerg-1427	1047	4	canonical	canonical	ADJ
fuelectenerg-1427	1047	5	iff	iff	VERB
fuelectenerg-1427	1047	6	its	its	PRON
fuelectenerg-1427	1047	7	terms	term	NOUN
fuelectenerg-1427	1047	8	are	be	AUX
fuelectenerg-1427	1047	9	linearly	linearly	ADV
fuelectenerg-1427	1047	10	independent	independent	ADJ
fuelectenerg-1427	1047	11	;	;	PUNCT
fuelectenerg-1427	1047	12	none	none	NOUN
fuelectenerg-1427	1047	13	of	of	ADP
fuelectenerg-1427	1047	14	the	the	DET
fuelectenerg-1427	1047	15	terms	term	NOUN
fuelectenerg-1427	1047	16	is	be	AUX
fuelectenerg-1427	1047	17	equal	equal	ADJ
fuelectenerg-1427	1047	18	to	to	ADP
fuelectenerg-1427	1047	19	a	a	DET
fuelectenerg-1427	1047	20	linear	linear	ADJ
fuelectenerg-1427	1047	21	combination	combination	NOUN
fuelectenerg-1427	1047	22	of	of	ADP
fuelectenerg-1427	1047	23	other	other	ADJ
fuelectenerg-1427	1047	24	terms	term	NOUN
fuelectenerg-1427	1047	25	.	.	PUNCT
fuelectenerg-1427	1048	1	using	use	VERB
fuelectenerg-1427	1048	2	this	this	DET
fuelectenerg-1427	1048	3	fact	fact	NOUN
fuelectenerg-1427	1048	4	,	,	PUNCT
fuelectenerg-1427	1048	5	it	it	PRON
fuelectenerg-1427	1048	6	was	be	AUX
fuelectenerg-1427	1048	7	proven	prove	VERB
fuelectenerg-1427	1048	8	that	that	SCONJ
fuelectenerg-1427	1048	9	all	all	DET
fuelectenerg-1427	1048	10	gf(2	gf(2	PROPN
fuelectenerg-1427	1048	11	)	)	PUNCT
fuelectenerg-1427	1048	12	ifs	if	NOUN
fuelectenerg-1427	1048	13	are	be	AUX
fuelectenerg-1427	1048	14	canonical	canonical	ADJ
fuelectenerg-1427	1048	15	.	.	PUNCT
fuelectenerg-1427	1049	1	analogously	analogously	ADV
fuelectenerg-1427	1049	2	over	over	ADP
fuelectenerg-1427	1049	3	gf(3	gf(3	PROPN
fuelectenerg-1427	1049	4	)	)	PUNCT
fuelectenerg-1427	1049	5	,	,	PUNCT
fuelectenerg-1427	1049	6	for	for	ADP
fuelectenerg-1427	1049	7	any	any	DET
fuelectenerg-1427	1049	8	function	function	NOUN
fuelectenerg-1427	1049	9	f	f	PROPN
fuelectenerg-1427	1049	10	of	of	ADP
fuelectenerg-1427	1049	11	the	the	DET
fuelectenerg-1427	1049	12	same	same	ADJ
fuelectenerg-1427	1049	13	number	number	NOUN
fuelectenerg-1427	1049	14	of	of	ADP
fuelectenerg-1427	1049	15	variables	variable	NOUN
fuelectenerg-1427	1049	16	,	,	PUNCT
fuelectenerg-1427	1049	17	there	there	PRON
fuelectenerg-1427	1049	18	exists	exist	VERB
fuelectenerg-1427	1049	19	one	one	NUM
fuelectenerg-1427	1049	20	and	and	CCONJ
fuelectenerg-1427	1049	21	only	only	ADV
fuelectenerg-1427	1049	22	one	one	NUM
fuelectenerg-1427	1049	23	set	set	NOUN
fuelectenerg-1427	1049	24	of	of	ADP
fuelectenerg-1427	1049	25	coefficients	coefficient	NOUN
fuelectenerg-1427	1049	26	ai	ai	VERB
fuelectenerg-1427	1049	27	such	such	ADJ
fuelectenerg-1427	1049	28	that	that	SCONJ
fuelectenerg-1427	1049	29	f	f	PROPN
fuelectenerg-1427	1049	30	is	be	AUX
fuelectenerg-1427	1049	31	uniquely	uniquely	ADV
fuelectenerg-1427	1049	32	tif	tif	NOUN
fuelectenerg-1427	1049	33	-	-	PUNCT
fuelectenerg-1427	1049	34	expandable	expandable	ADJ
fuelectenerg-1427	1049	35	using	using	NOUN
fuelectenerg-1427	1049	36	ai	ai	NOUN
fuelectenerg-1427	1049	37	and	and	CCONJ
fuelectenerg-1427	1049	38	thus	thus	ADV
fuelectenerg-1427	1049	39	the	the	DET
fuelectenerg-1427	1049	40	resulting	result	VERB
fuelectenerg-1427	1049	41	expression	expression	NOUN
fuelectenerg-1427	1049	42	is	be	AUX
fuelectenerg-1427	1049	43	canonical	canonical	ADJ
fuelectenerg-1427	1049	44	.	.	PUNCT
fuelectenerg-1427	1050	1	by	by	ADP
fuelectenerg-1427	1050	2	induction	induction	NOUN
fuelectenerg-1427	1050	3	on	on	ADP
fuelectenerg-1427	1050	4	number	number	NOUN
fuelectenerg-1427	1050	5	of	of	ADP
fuelectenerg-1427	1050	6	variables	variable	NOUN
fuelectenerg-1427	1050	7	,	,	PUNCT
fuelectenerg-1427	1050	8	terms	term	NOUN
fuelectenerg-1427	1050	9	in	in	ADP
fuelectenerg-1427	1050	10	tifs	tifs	PROPN
fuelectenerg-1427	1050	11	will	will	AUX
fuelectenerg-1427	1050	12	be	be	AUX
fuelectenerg-1427	1050	13	linearly	linearly	ADV
fuelectenerg-1427	1050	14	independent	independent	ADJ
fuelectenerg-1427	1050	15	and	and	CCONJ
fuelectenerg-1427	1050	16	thus	thus	ADV
fuelectenerg-1427	1050	17	canonical	canonical	ADJ
fuelectenerg-1427	1050	18	.	.	PUNCT
fuelectenerg-1427	1051	1	theorem	theorem	VERB
fuelectenerg-1427	1051	2	4	4	NUM
fuelectenerg-1427	1051	3	.	.	PUNCT
fuelectenerg-1427	1051	4	ternary	ternary	ADJ
fuelectenerg-1427	1051	5	generalized	generalize	VERB
fuelectenerg-1427	1051	6	inclusive	inclusive	ADJ
fuelectenerg-1427	1051	7	forms	form	NOUN
fuelectenerg-1427	1051	8	(	(	PUNCT
fuelectenerg-1427	1051	9	tgifs	tgif	NOUN
fuelectenerg-1427	1051	10	)	)	PUNCT
fuelectenerg-1427	1051	11	are	be	AUX
fuelectenerg-1427	1051	12	canonical	canonical	ADJ
fuelectenerg-1427	1051	13	with	with	ADP
fuelectenerg-1427	1051	14	respect	respect	NOUN
fuelectenerg-1427	1051	15	to	to	ADP
fuelectenerg-1427	1051	16	given	give	VERB
fuelectenerg-1427	1051	17	variable	variable	ADJ
fuelectenerg-1427	1051	18	order	order	NOUN
fuelectenerg-1427	1051	19	.	.	PUNCT
fuelectenerg-1427	1052	1	proof	proof	NOUN
fuelectenerg-1427	1052	2	.	.	PUNCT
fuelectenerg-1427	1053	1	since	since	SCONJ
fuelectenerg-1427	1053	2	tgif	tgif	NOUN
fuelectenerg-1427	1053	3	is	be	AUX
fuelectenerg-1427	1053	4	the	the	DET
fuelectenerg-1427	1053	5	union	union	NOUN
fuelectenerg-1427	1053	6	of	of	ADP
fuelectenerg-1427	1053	7	the	the	DET
fuelectenerg-1427	1053	8	corresponding	corresponding	ADJ
fuelectenerg-1427	1053	9	tifs	tifs	PROPN
fuelectenerg-1427	1053	10	,	,	PUNCT
fuelectenerg-1427	1053	11	and	and	CCONJ
fuelectenerg-1427	1053	12	since	since	SCONJ
fuelectenerg-1427	1053	13	each	each	DET
fuelectenerg-1427	1053	14	tif	tif	PROPN
fuelectenerg-1427	1053	15	is	be	AUX
fuelectenerg-1427	1053	16	canonical	canonical	ADJ
fuelectenerg-1427	1053	17	,	,	PUNCT
fuelectenerg-1427	1053	18	then	then	ADV
fuelectenerg-1427	1053	19	the	the	DET
fuelectenerg-1427	1053	20	resulting	result	VERB
fuelectenerg-1427	1053	21	union	union	NOUN
fuelectenerg-1427	1053	22	of	of	ADP
fuelectenerg-1427	1053	23	the	the	DET
fuelectenerg-1427	1053	24	corresponding	corresponding	ADJ
fuelectenerg-1427	1053	25	canonical	canonical	ADJ
fuelectenerg-1427	1053	26	tifs	tif	NOUN
fuelectenerg-1427	1053	27	will	will	AUX
fuelectenerg-1427	1053	28	be	be	AUX
fuelectenerg-1427	1053	29	also	also	ADV
fuelectenerg-1427	1053	30	canonical	canonical	ADJ
fuelectenerg-1427	1053	31	.	.	PUNCT
fuelectenerg-1427	1054	1	for	for	ADP
fuelectenerg-1427	1054	2	different	different	ADJ
fuelectenerg-1427	1054	3	variable	variable	ADJ
fuelectenerg-1427	1054	4	orderings	ordering	NOUN
fuelectenerg-1427	1054	5	,	,	PUNCT
fuelectenerg-1427	1054	6	some	some	DET
fuelectenerg-1427	1054	7	forms	form	NOUN
fuelectenerg-1427	1054	8	are	be	AUX
fuelectenerg-1427	1054	9	not	not	PART
fuelectenerg-1427	1054	10	repeated	repeat	VERB
fuelectenerg-1427	1054	11	while	while	SCONJ
fuelectenerg-1427	1054	12	other	other	ADJ
fuelectenerg-1427	1054	13	forms	form	NOUN
fuelectenerg-1427	1054	14	are	be	AUX
fuelectenerg-1427	1054	15	.	.	PUNCT
fuelectenerg-1427	1055	1	therefore	therefore	ADV
fuelectenerg-1427	1055	2	the	the	DET
fuelectenerg-1427	1055	3	union	union	NOUN
fuelectenerg-1427	1055	4	of	of	ADP
fuelectenerg-1427	1055	5	sets	set	NOUN
fuelectenerg-1427	1055	6	of	of	ADP
fuelectenerg-1427	1055	7	tifs	tif	NOUN
fuelectenerg-1427	1055	8	for	for	ADP
fuelectenerg-1427	1055	9	all	all	DET
fuelectenerg-1427	1055	10	variable	variable	ADJ
fuelectenerg-1427	1055	11	orders	order	NOUN
fuelectenerg-1427	1055	12	contains	contain	VERB
fuelectenerg-1427	1055	13	more	more	ADJ
fuelectenerg-1427	1055	14	forms	form	NOUN
fuelectenerg-1427	1055	15	than	than	ADP
fuelectenerg-1427	1055	16	any	any	PRON
fuelectenerg-1427	1055	17	of	of	ADP
fuelectenerg-1427	1055	18	the	the	DET
fuelectenerg-1427	1055	19	tif	tif	PROPN
fuelectenerg-1427	1055	20	sets	set	NOUN
fuelectenerg-1427	1055	21	taken	take	VERB
fuelectenerg-1427	1055	22	separately	separately	ADV
fuelectenerg-1427	1055	23	and	and	CCONJ
fuelectenerg-1427	1055	24	less	less	ADJ
fuelectenerg-1427	1055	25	forms	form	NOUN
fuelectenerg-1427	1055	26	than	than	ADP
fuelectenerg-1427	1055	27	total	total	ADJ
fuelectenerg-1427	1055	28	sum	sum	NOUN
fuelectenerg-1427	1055	29	of	of	ADP
fuelectenerg-1427	1055	30	all	all	DET
fuelectenerg-1427	1055	31	tifs	tif	NOUN
fuelectenerg-1427	1055	32	.	.	PUNCT
fuelectenerg-1427	1056	1	generalized	generalized	ADJ
fuelectenerg-1427	1056	2	inclusive	inclusive	ADJ
fuelectenerg-1427	1056	3	forms	form	NOUN
fuelectenerg-1427	1056	4	include	include	VERB
fuelectenerg-1427	1056	5	other	other	ADJ
fuelectenerg-1427	1056	6	forms	form	NOUN
fuelectenerg-1427	1056	7	such	such	ADJ
fuelectenerg-1427	1056	8	as	as	ADP
fuelectenerg-1427	1056	9	grms	grm	NOUN
fuelectenerg-1427	1056	10	over	over	ADP
fuelectenerg-1427	1056	11	gf(3	gf(3	PROPN
fuelectenerg-1427	1056	12	)	)	PUNCT
fuelectenerg-1427	1056	13	as	as	SCONJ
fuelectenerg-1427	1056	14	can	can	AUX
fuelectenerg-1427	1056	15	be	be	AUX
fuelectenerg-1427	1056	16	shown	show	VERB
fuelectenerg-1427	1056	17	by	by	ADP
fuelectenerg-1427	1056	18	considering	consider	VERB
fuelectenerg-1427	1056	19	all	all	DET
fuelectenerg-1427	1056	20	possible	possible	ADJ
fuelectenerg-1427	1056	21	combinations	combination	NOUN
fuelectenerg-1427	1056	22	of	of	ADP
fuelectenerg-1427	1056	23	literals	literal	NOUN
fuelectenerg-1427	1056	24	for	for	ADP
fuelectenerg-1427	1056	25	all	all	DET
fuelectenerg-1427	1056	26	possible	possible	ADJ
fuelectenerg-1427	1056	27	orders	order	NOUN
fuelectenerg-1427	1056	28	of	of	ADP
fuelectenerg-1427	1056	29	variables	variable	NOUN
fuelectenerg-1427	1056	30	.	.	PUNCT
fuelectenerg-1427	1057	1	if	if	SCONJ
fuelectenerg-1427	1057	2	we	we	PRON
fuelectenerg-1427	1057	3	relax	relax	VERB
fuelectenerg-1427	1057	4	the	the	DET
fuelectenerg-1427	1057	5	requirement	requirement	NOUN
fuelectenerg-1427	1057	6	of	of	ADP
fuelectenerg-1427	1057	7	fixed	fix	VERB
fuelectenerg-1427	1057	8	variable	variable	ADJ
fuelectenerg-1427	1057	9	ordering	ordering	NOUN
fuelectenerg-1427	1057	10	,	,	PUNCT
fuelectenerg-1427	1057	11	and	and	CCONJ
fuelectenerg-1427	1057	12	allow	allow	VERB
fuelectenerg-1427	1057	13	any	any	DET
fuelectenerg-1427	1057	14	ordering	ordering	NOUN
fuelectenerg-1427	1057	15	of	of	ADP
fuelectenerg-1427	1057	16	variables	variable	NOUN
fuelectenerg-1427	1057	17	in	in	ADP
fuelectenerg-1427	1057	18	branches	branch	NOUN
fuelectenerg-1427	1057	19	of	of	ADP
fuelectenerg-1427	1057	20	the	the	DET
fuelectenerg-1427	1057	21	tree	tree	NOUN
fuelectenerg-1427	1057	22	but	but	CCONJ
fuelectenerg-1427	1057	23	do	do	AUX
fuelectenerg-1427	1057	24	not	not	PART
fuelectenerg-1427	1057	25	allow	allow	VERB
fuelectenerg-1427	1057	26	repetitions	repetition	NOUN
fuelectenerg-1427	1057	27	of	of	ADP
fuelectenerg-1427	1057	28	variables	variable	NOUN
fuelectenerg-1427	1057	29	in	in	ADP
fuelectenerg-1427	1057	30	the	the	DET
fuelectenerg-1427	1057	31	branches	branch	NOUN
fuelectenerg-1427	1057	32	,	,	PUNCT
fuelectenerg-1427	1057	33	we	we	PRON
fuelectenerg-1427	1057	34	generate	generate	VERB
fuelectenerg-1427	1057	35	more	more	ADJ
fuelectenerg-1427	1057	36	general	general	ADJ
fuelectenerg-1427	1057	37	gf(3	gf(3	PROPN
fuelectenerg-1427	1057	38	)	)	PUNCT
fuelectenerg-1427	1057	39	family	family	NOUN
fuelectenerg-1427	1057	40	of	of	ADP
fuelectenerg-1427	1057	41	forms	form	NOUN
fuelectenerg-1427	1057	42	.	.	PUNCT
fuelectenerg-1427	1058	1	111	111	NUM
fuelectenerg-1427	1058	2	60	60	NUM
fuelectenerg-1427	1058	3	a.	a.	NOUN
fuelectenerg-1427	1058	4	n.	n.	PROPN
fuelectenerg-1427	1058	5	al	al	PROPN
fuelectenerg-1427	1058	6	-	-	PUNCT
fuelectenerg-1427	1058	7	rabadi	rabadi	VERB
fuelectenerg-1427	1058	8	an	an	DET
fuelectenerg-1427	1058	9	extended	extended	ADJ
fuelectenerg-1427	1058	10	green	green	ADJ
fuelectenerg-1427	1058	11	sasao	sasao	PROPN
fuelectenerg-1427	1058	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1058	13	of	of	ADP
fuelectenerg-1427	1058	14	canonical	canonical	ADJ
fuelectenerg-1427	1058	15	ternary	ternary	ADJ
fuelectenerg-1427	1058	16	galois	galois	NOUN
fuelectenerg-1427	1058	17	forms	form	NOUN
fuelectenerg-1427	1058	18	and	and	CCONJ
fuelectenerg-1427	1058	19	universal	universal	ADJ
fuelectenerg-1427	1058	20	logic	logic	NOUN
fuelectenerg-1427	1058	21	modules	module	VERB
fuelectenerg-1427	1058	22	61	61	NUM
fuelectenerg-1427	1058	23	an	an	DET
fuelectenerg-1427	1058	24	extended	extended	ADJ
fuelectenerg-1427	1058	25	green	green	ADJ
fuelectenerg-1427	1058	26	sasao	sasao	PROPN
fuelectenerg-1427	1058	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1058	28	of	of	ADP
fuelectenerg-1427	1058	29	canonical	canonical	ADJ
fuelectenerg-1427	1058	30	ternary	ternary	ADJ
fuelectenerg-1427	1058	31	galois	galois	NOUN
fuelectenerg-1427	1058	32	forms	form	NOUN
fuelectenerg-1427	1058	33	...	...	PUNCT
fuelectenerg-1427	1059	1	definition	definition	NOUN
fuelectenerg-1427	1059	2	4	4	NUM
fuelectenerg-1427	1059	3	.	.	PUNCT
fuelectenerg-1427	1060	1	the	the	DET
fuelectenerg-1427	1060	2	family	family	NOUN
fuelectenerg-1427	1060	3	of	of	ADP
fuelectenerg-1427	1060	4	forms	form	NOUN
fuelectenerg-1427	1060	5	,	,	PUNCT
fuelectenerg-1427	1060	6	generated	generate	VERB
fuelectenerg-1427	1060	7	by	by	ADP
fuelectenerg-1427	1060	8	s	s	PROPN
fuelectenerg-1427	1060	9	/	/	SYM
fuelectenerg-1427	1060	10	d	d	NOUN
fuelectenerg-1427	1060	11	tree	tree	NOUN
fuelectenerg-1427	1060	12	with	with	ADP
fuelectenerg-1427	1060	13	no	no	DET
fuelectenerg-1427	1060	14	fixed	fix	VERB
fuelectenerg-1427	1060	15	ordering	ordering	NOUN
fuelectenerg-1427	1060	16	of	of	ADP
fuelectenerg-1427	1060	17	variables	variable	NOUN
fuelectenerg-1427	1060	18	,	,	PUNCT
fuelectenerg-1427	1060	19	with	with	ADP
fuelectenerg-1427	1060	20	variables	variable	NOUN
fuelectenerg-1427	1060	21	not	not	PART
fuelectenerg-1427	1060	22	repeated	repeat	VERB
fuelectenerg-1427	1060	23	along	along	ADP
fuelectenerg-1427	1060	24	same	same	ADJ
fuelectenerg-1427	1060	25	branches	branch	NOUN
fuelectenerg-1427	1060	26	,	,	PUNCT
fuelectenerg-1427	1060	27	is	be	AUX
fuelectenerg-1427	1060	28	called	call	VERB
fuelectenerg-1427	1060	29	ternary	ternary	ADJ
fuelectenerg-1427	1060	30	free	free	ADJ
fuelectenerg-1427	1060	31	generalized	generalize	VERB
fuelectenerg-1427	1060	32	inclusive	inclusive	ADJ
fuelectenerg-1427	1060	33	forms	form	NOUN
fuelectenerg-1427	1060	34	(	(	PUNCT
fuelectenerg-1427	1060	35	tfgifs	tfgifs	PROPN
fuelectenerg-1427	1060	36	)	)	PUNCT
fuelectenerg-1427	1060	37	.	.	PUNCT
fuelectenerg-1427	1061	1	2.3	2.3	NUM
fuelectenerg-1427	1061	2	an	an	DET
fuelectenerg-1427	1061	3	extended	extended	ADJ
fuelectenerg-1427	1061	4	green	green	ADJ
fuelectenerg-1427	1061	5	-	-	PUNCT
fuelectenerg-1427	1061	6	sasao	sasao	NOUN
fuelectenerg-1427	1061	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1061	8	with	with	ADP
fuelectenerg-1427	1061	9	a	a	DET
fuelectenerg-1427	1061	10	new	new	ADJ
fuelectenerg-1427	1061	11	sub	sub	NOUN
fuelectenerg-1427	1061	12	-	-	NOUN
fuelectenerg-1427	1061	13	family	family	NOUN
fuelectenerg-1427	1061	14	for	for	ADP
fuelectenerg-1427	1061	15	ternary	ternary	ADJ
fuelectenerg-1427	1061	16	reed	reed	NOUN
fuelectenerg-1427	1061	17	-	-	PUNCT
fuelectenerg-1427	1061	18	muller	muller	NOUN
fuelectenerg-1427	1061	19	logic	logic	NOUN
fuelectenerg-1427	1061	20	the	the	DET
fuelectenerg-1427	1061	21	green	green	PROPN
fuelectenerg-1427	1061	22	-	-	PUNCT
fuelectenerg-1427	1061	23	sasao	sasao	PROPN
fuelectenerg-1427	1061	24	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1061	25	of	of	ADP
fuelectenerg-1427	1061	26	families	family	NOUN
fuelectenerg-1427	1061	27	of	of	ADP
fuelectenerg-1427	1061	28	canonical	canonical	ADJ
fuelectenerg-1427	1061	29	forms	form	NOUN
fuelectenerg-1427	1061	30	[	[	X
fuelectenerg-1427	1061	31	1	1	NUM
fuelectenerg-1427	1061	32	,	,	PUNCT
fuelectenerg-1427	1061	33	10	10	NUM
fuelectenerg-1427	1061	34	-	-	SYM
fuelectenerg-1427	1061	35	13	13	NUM
fuelectenerg-1427	1061	36	,	,	PUNCT
fuelectenerg-1427	1061	37	17	17	NUM
fuelectenerg-1427	1061	38	,	,	PUNCT
fuelectenerg-1427	1061	39	24	24	NUM
fuelectenerg-1427	1061	40	,	,	PUNCT
fuelectenerg-1427	1061	41	26	26	NUM
fuelectenerg-1427	1061	42	]	]	PUNCT
fuelectenerg-1427	1061	43	and	and	CCONJ
fuelectenerg-1427	1061	44	the	the	DET
fuelectenerg-1427	1061	45	corresponding	correspond	VERB
fuelectenerg-1427	1061	46	decision	decision	NOUN
fuelectenerg-1427	1061	47	trees	tree	NOUN
fuelectenerg-1427	1061	48	and	and	CCONJ
fuelectenerg-1427	1061	49	diagrams	diagram	NOUN
fuelectenerg-1427	1061	50	is	be	AUX
fuelectenerg-1427	1061	51	based	base	VERB
fuelectenerg-1427	1061	52	on	on	ADP
fuelectenerg-1427	1061	53	three	three	NUM
fuelectenerg-1427	1061	54	generic	generic	ADJ
fuelectenerg-1427	1061	55	expansions	expansion	NOUN
fuelectenerg-1427	1061	56	,	,	PUNCT
fuelectenerg-1427	1061	57	shannon	shannon	PROPN
fuelectenerg-1427	1061	58	,	,	PUNCT
fuelectenerg-1427	1061	59	positive	positive	ADJ
fuelectenerg-1427	1061	60	and	and	CCONJ
fuelectenerg-1427	1061	61	negative	negative	ADJ
fuelectenerg-1427	1061	62	davio	davio	NOUN
fuelectenerg-1427	1061	63	expansions	expansion	NOUN
fuelectenerg-1427	1061	64	.	.	PUNCT
fuelectenerg-1427	1062	1	for	for	ADP
fuelectenerg-1427	1062	2	example	example	NOUN
fuelectenerg-1427	1062	3	,	,	PUNCT
fuelectenerg-1427	1062	4	this	this	PRON
fuelectenerg-1427	1062	5	includes	include	VERB
fuelectenerg-1427	1062	6	shannon	shannon	ADJ
fuelectenerg-1427	1062	7	decision	decision	NOUN
fuelectenerg-1427	1062	8	trees	tree	NOUN
fuelectenerg-1427	1062	9	and	and	CCONJ
fuelectenerg-1427	1062	10	diagrams	diagram	NOUN
fuelectenerg-1427	1062	11	,	,	PUNCT
fuelectenerg-1427	1062	12	positive	positive	ADJ
fuelectenerg-1427	1062	13	and	and	CCONJ
fuelectenerg-1427	1062	14	negative	negative	ADJ
fuelectenerg-1427	1062	15	davio	davio	NOUN
fuelectenerg-1427	1062	16	decision	decision	NOUN
fuelectenerg-1427	1062	17	trees	tree	NOUN
fuelectenerg-1427	1062	18	and	and	CCONJ
fuelectenerg-1427	1062	19	diagrams	diagram	NOUN
fuelectenerg-1427	1062	20	,	,	PUNCT
fuelectenerg-1427	1062	21	fixed	fix	VERB
fuelectenerg-1427	1062	22	polarity	polarity	NOUN
fuelectenerg-1427	1062	23	reed	reed	NOUN
fuelectenerg-1427	1062	24	-	-	PUNCT
fuelectenerg-1427	1062	25	muller	muller	NOUN
fuelectenerg-1427	1062	26	decision	decision	NOUN
fuelectenerg-1427	1062	27	trees	tree	NOUN
fuelectenerg-1427	1062	28	and	and	CCONJ
fuelectenerg-1427	1062	29	diagrams	diagram	NOUN
fuelectenerg-1427	1062	30	,	,	PUNCT
fuelectenerg-1427	1062	31	kronecker	kronecker	NOUN
fuelectenerg-1427	1062	32	decision	decision	NOUN
fuelectenerg-1427	1062	33	trees	tree	NOUN
fuelectenerg-1427	1062	34	and	and	CCONJ
fuelectenerg-1427	1062	35	diagrams	diagram	NOUN
fuelectenerg-1427	1062	36	,	,	PUNCT
fuelectenerg-1427	1062	37	pseudo	pseudo	NOUN
fuelectenerg-1427	1062	38	reed	reed	NOUN
fuelectenerg-1427	1062	39	-	-	PUNCT
fuelectenerg-1427	1062	40	muller	muller	NOUN
fuelectenerg-1427	1062	41	decision	decision	NOUN
fuelectenerg-1427	1062	42	trees	tree	NOUN
fuelectenerg-1427	1062	43	and	and	CCONJ
fuelectenerg-1427	1062	44	diagrams	diagram	NOUN
fuelectenerg-1427	1062	45	,	,	PUNCT
fuelectenerg-1427	1062	46	pseudo	pseudo	NOUN
fuelectenerg-1427	1062	47	kronecker	kronecker	NOUN
fuelectenerg-1427	1062	48	decision	decision	NOUN
fuelectenerg-1427	1062	49	trees	tree	NOUN
fuelectenerg-1427	1062	50	and	and	CCONJ
fuelectenerg-1427	1062	51	diagrams	diagram	NOUN
fuelectenerg-1427	1062	52	,	,	PUNCT
fuelectenerg-1427	1062	53	and	and	CCONJ
fuelectenerg-1427	1062	54	linearly	linearly	ADV
fuelectenerg-1427	1062	55	-	-	PUNCT
fuelectenerg-1427	1062	56	independent	independent	ADJ
fuelectenerg-1427	1062	57	decision	decision	NOUN
fuelectenerg-1427	1062	58	trees	tree	NOUN
fuelectenerg-1427	1062	59	and	and	CCONJ
fuelectenerg-1427	1062	60	diagrams	diagram	NOUN
fuelectenerg-1427	1063	1	[	[	X
fuelectenerg-1427	1063	2	1	1	NUM
fuelectenerg-1427	1063	3	,	,	PUNCT
fuelectenerg-1427	1063	4	17	17	NUM
fuelectenerg-1427	1063	5	,	,	PUNCT
fuelectenerg-1427	1063	6	24	24	NUM
fuelectenerg-1427	1063	7	]	]	PUNCT
fuelectenerg-1427	1063	8	.	.	PUNCT
fuelectenerg-1427	1064	1	a	a	DET
fuelectenerg-1427	1064	2	set	set	VERB
fuelectenerg-1427	1064	3	-	-	PUNCT
fuelectenerg-1427	1064	4	theoretic	theoretic	NOUN
fuelectenerg-1427	1064	5	relationship	relationship	NOUN
fuelectenerg-1427	1064	6	between	between	ADP
fuelectenerg-1427	1064	7	families	family	NOUN
fuelectenerg-1427	1064	8	of	of	ADP
fuelectenerg-1427	1064	9	canonical	canonical	ADJ
fuelectenerg-1427	1064	10	forms	form	NOUN
fuelectenerg-1427	1064	11	over	over	ADP
fuelectenerg-1427	1064	12	gf(2	gf(2	PROPN
fuelectenerg-1427	1064	13	)	)	PUNCT
fuelectenerg-1427	1064	14	was	be	AUX
fuelectenerg-1427	1064	15	proposed	propose	VERB
fuelectenerg-1427	1064	16	and	and	CCONJ
fuelectenerg-1427	1064	17	extended	extend	VERB
fuelectenerg-1427	1064	18	by	by	ADP
fuelectenerg-1427	1064	19	introducing	introduce	VERB
fuelectenerg-1427	1064	20	binary	binary	NOUN
fuelectenerg-1427	1064	21	if	if	SCONJ
fuelectenerg-1427	1064	22	,	,	PUNCT
fuelectenerg-1427	1064	23	gif	gif	NOUN
fuelectenerg-1427	1064	24	and	and	CCONJ
fuelectenerg-1427	1064	25	free	free	ADJ
fuelectenerg-1427	1064	26	gif	gif	NOUN
fuelectenerg-1427	1064	27	(	(	PUNCT
fuelectenerg-1427	1064	28	fgif	fgif	NOUN
fuelectenerg-1427	1064	29	)	)	PUNCT
fuelectenerg-1427	1064	30	forms	form	NOUN
fuelectenerg-1427	1064	31	where	where	SCONJ
fuelectenerg-1427	1064	32	figure	figure	NOUN
fuelectenerg-1427	1064	33	6(a	6(a	NUM
fuelectenerg-1427	1064	34	)	)	PUNCT
fuelectenerg-1427	1064	35	illustrates	illustrate	VERB
fuelectenerg-1427	1064	36	set	set	VERB
fuelectenerg-1427	1064	37	-	-	PUNCT
fuelectenerg-1427	1064	38	theoretic	theoretic	NOUN
fuelectenerg-1427	1064	39	relationship	relationship	NOUN
fuelectenerg-1427	1064	40	between	between	ADP
fuelectenerg-1427	1064	41	the	the	DET
fuelectenerg-1427	1064	42	various	various	ADJ
fuelectenerg-1427	1064	43	families	family	NOUN
fuelectenerg-1427	1064	44	of	of	ADP
fuelectenerg-1427	1064	45	canonical	canonical	ADJ
fuelectenerg-1427	1064	46	forms	form	NOUN
fuelectenerg-1427	1064	47	over	over	ADP
fuelectenerg-1427	1064	48	gf(2	gf(2	PROPN
fuelectenerg-1427	1064	49	)	)	PUNCT
fuelectenerg-1427	1064	50	.	.	PUNCT
fuelectenerg-1427	1065	1	analogously	analogously	ADV
fuelectenerg-1427	1065	2	to	to	ADP
fuelectenerg-1427	1065	3	the	the	DET
fuelectenerg-1427	1065	4	green	green	ADJ
fuelectenerg-1427	1065	5	-	-	PUNCT
fuelectenerg-1427	1065	6	sasao	sasao	PROPN
fuelectenerg-1427	1065	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1065	8	of	of	ADP
fuelectenerg-1427	1065	9	binary	binary	PROPN
fuelectenerg-1427	1065	10	reed	reed	PROPN
fuelectenerg-1427	1065	11	-	-	PUNCT
fuelectenerg-1427	1065	12	muller	muller	NOUN
fuelectenerg-1427	1065	13	families	family	NOUN
fuelectenerg-1427	1065	14	of	of	ADP
fuelectenerg-1427	1065	15	spectral	spectral	ADJ
fuelectenerg-1427	1065	16	transforms	transform	VERB
fuelectenerg-1427	1065	17	over	over	ADP
fuelectenerg-1427	1065	18	gf(2	gf(2	PROPN
fuelectenerg-1427	1065	19	)	)	PUNCT
fuelectenerg-1427	1065	20	that	that	PRON
fuelectenerg-1427	1065	21	is	be	AUX
fuelectenerg-1427	1065	22	shown	show	VERB
fuelectenerg-1427	1065	23	in	in	ADP
fuelectenerg-1427	1065	24	figure	figure	NOUN
fuelectenerg-1427	1065	25	6(a	6(a	NUM
fuelectenerg-1427	1065	26	)	)	PUNCT
fuelectenerg-1427	1065	27	,	,	PUNCT
fuelectenerg-1427	1065	28	we	we	PRON
fuelectenerg-1427	1065	29	will	will	AUX
fuelectenerg-1427	1065	30	introduce	introduce	VERB
fuelectenerg-1427	1065	31	the	the	DET
fuelectenerg-1427	1065	32	extended	extended	ADJ
fuelectenerg-1427	1065	33	green	green	ADJ
fuelectenerg-1427	1065	34	-	-	PUNCT
fuelectenerg-1427	1065	35	sasao	sasao	NOUN
fuelectenerg-1427	1065	36	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1065	37	of	of	ADP
fuelectenerg-1427	1065	38	spectral	spectral	ADJ
fuelectenerg-1427	1065	39	transforms	transform	NOUN
fuelectenerg-1427	1065	40	,	,	PUNCT
fuelectenerg-1427	1065	41	with	with	ADP
fuelectenerg-1427	1065	42	a	a	DET
fuelectenerg-1427	1065	43	new	new	ADJ
fuelectenerg-1427	1065	44	sub	sub	NOUN
fuelectenerg-1427	1065	45	-	-	NOUN
fuelectenerg-1427	1065	46	family	family	NOUN
fuelectenerg-1427	1065	47	for	for	ADP
fuelectenerg-1427	1065	48	ternary	ternary	ADJ
fuelectenerg-1427	1065	49	reedmuller	reedmuller	NOUN
fuelectenerg-1427	1065	50	logic	logic	NOUN
fuelectenerg-1427	1065	51	over	over	ADP
fuelectenerg-1427	1065	52	gf(3	gf(3	PROPN
fuelectenerg-1427	1065	53	)	)	PUNCT
fuelectenerg-1427	1065	54	.	.	PUNCT
fuelectenerg-1427	1066	1	while	while	SCONJ
fuelectenerg-1427	1066	2	definitions	definition	NOUN
fuelectenerg-1427	1066	3	2	2	NUM
fuelectenerg-1427	1066	4	4	4	NUM
fuelectenerg-1427	1066	5	defined	define	VERB
fuelectenerg-1427	1066	6	the	the	DET
fuelectenerg-1427	1066	7	ternary	ternary	ADJ
fuelectenerg-1427	1066	8	inclusive	inclusive	ADJ
fuelectenerg-1427	1066	9	forms	form	NOUN
fuelectenerg-1427	1066	10	,	,	PUNCT
fuelectenerg-1427	1066	11	ternary	ternary	ADJ
fuelectenerg-1427	1066	12	generalized	generalize	VERB
fuelectenerg-1427	1066	13	inclusive	inclusive	ADJ
fuelectenerg-1427	1066	14	forms	form	NOUN
fuelectenerg-1427	1066	15	and	and	CCONJ
fuelectenerg-1427	1066	16	ternary	ternary	ADJ
fuelectenerg-1427	1066	17	free	free	ADJ
fuelectenerg-1427	1066	18	generalized	generalized	ADJ
fuelectenerg-1427	1066	19	inclusive	inclusive	ADJ
fuelectenerg-1427	1066	20	forms	form	NOUN
fuelectenerg-1427	1066	21	,	,	PUNCT
fuelectenerg-1427	1066	22	respectively	respectively	ADV
fuelectenerg-1427	1066	23	,	,	PUNCT
fuelectenerg-1427	1066	24	and	and	CCONJ
fuelectenerg-1427	1066	25	analogously	analogously	ADV
fuelectenerg-1427	1066	26	to	to	ADP
fuelectenerg-1427	1066	27	the	the	DET
fuelectenerg-1427	1066	28	binary	binary	PROPN
fuelectenerg-1427	1066	29	reed	reed	PROPN
fuelectenerg-1427	1066	30	-	-	PUNCT
fuelectenerg-1427	1066	31	muller	muller	NOUN
fuelectenerg-1427	1066	32	case	case	NOUN
fuelectenerg-1427	1066	33	,	,	PUNCT
fuelectenerg-1427	1066	34	the	the	DET
fuelectenerg-1427	1066	35	following	follow	VERB
fuelectenerg-1427	1066	36	definitions	definition	NOUN
fuelectenerg-1427	1066	37	are	be	AUX
fuelectenerg-1427	1066	38	introduced	introduce	VERB
fuelectenerg-1427	1066	39	for	for	ADP
fuelectenerg-1427	1066	40	the	the	DET
fuelectenerg-1427	1066	41	corresponding	corresponding	ADJ
fuelectenerg-1427	1066	42	canonical	canonical	ADJ
fuelectenerg-1427	1066	43	expressions	expression	NOUN
fuelectenerg-1427	1066	44	over	over	ADP
fuelectenerg-1427	1066	45	gf(3	gf(3	PROPN
fuelectenerg-1427	1066	46	)	)	PUNCT
fuelectenerg-1427	1066	47	.	.	PUNCT
fuelectenerg-1427	1067	1	definition	definition	NOUN
fuelectenerg-1427	1067	2	5	5	NUM
fuelectenerg-1427	1067	3	.	.	PUNCT
fuelectenerg-1427	1068	1	the	the	DET
fuelectenerg-1427	1068	2	decision	decision	NOUN
fuelectenerg-1427	1068	3	tree	tree	NOUN
fuelectenerg-1427	1068	4	that	that	PRON
fuelectenerg-1427	1068	5	results	result	VERB
fuelectenerg-1427	1068	6	from	from	ADP
fuelectenerg-1427	1068	7	applying	apply	VERB
fuelectenerg-1427	1068	8	the	the	DET
fuelectenerg-1427	1068	9	ternary	ternary	ADJ
fuelectenerg-1427	1068	10	shannon	shannon	NOUN
fuelectenerg-1427	1068	11	expansion	expansion	NOUN
fuelectenerg-1427	1068	12	in	in	ADP
fuelectenerg-1427	1068	13	equation	equation	NOUN
fuelectenerg-1427	1068	14	(	(	PUNCT
fuelectenerg-1427	1068	15	23	23	NUM
fuelectenerg-1427	1068	16	)	)	PUNCT
fuelectenerg-1427	1068	17	recursively	recursively	ADV
fuelectenerg-1427	1068	18	to	to	ADP
fuelectenerg-1427	1068	19	a	a	DET
fuelectenerg-1427	1068	20	ternary	ternary	ADJ
fuelectenerg-1427	1068	21	input	input	NOUN
fuelectenerg-1427	1068	22	-	-	PUNCT
fuelectenerg-1427	1068	23	ternary	ternary	ADJ
fuelectenerg-1427	1068	24	output	output	NOUN
fuelectenerg-1427	1068	25	logic	logic	NOUN
fuelectenerg-1427	1068	26	function	function	NOUN
fuelectenerg-1427	1068	27	(	(	PUNCT
fuelectenerg-1427	1068	28	i.e.	i.e.	X
fuelectenerg-1427	1068	29	,	,	PUNCT
fuelectenerg-1427	1068	30	all	all	DET
fuelectenerg-1427	1068	31	levels	level	NOUN
fuelectenerg-1427	1068	32	in	in	ADP
fuelectenerg-1427	1068	33	a	a	DET
fuelectenerg-1427	1068	34	dt	dt	NOUN
fuelectenerg-1427	1068	35	)	)	PUNCT
fuelectenerg-1427	1068	36	is	be	AUX
fuelectenerg-1427	1068	37	called	call	VERB
fuelectenerg-1427	1068	38	ternary	ternary	ADJ
fuelectenerg-1427	1068	39	shannon	shannon	PROPN
fuelectenerg-1427	1068	40	decision	decision	NOUN
fuelectenerg-1427	1068	41	tree	tree	NOUN
fuelectenerg-1427	1068	42	(	(	PUNCT
fuelectenerg-1427	1068	43	tsdt	tsdt	NOUN
fuelectenerg-1427	1068	44	)	)	PUNCT
fuelectenerg-1427	1068	45	.	.	PUNCT
fuelectenerg-1427	1069	1	the	the	DET
fuelectenerg-1427	1069	2	result	result	NOUN
fuelectenerg-1427	1069	3	expression	expression	NOUN
fuelectenerg-1427	1069	4	(	(	PUNCT
fuelectenerg-1427	1069	5	flattened	flatten	VERB
fuelectenerg-1427	1069	6	form	form	NOUN
fuelectenerg-1427	1069	7	)	)	PUNCT
fuelectenerg-1427	1069	8	from	from	ADP
fuelectenerg-1427	1069	9	the	the	DET
fuelectenerg-1427	1069	10	tsdt	tsdt	NOUN
fuelectenerg-1427	1069	11	is	be	AUX
fuelectenerg-1427	1069	12	called	call	VERB
fuelectenerg-1427	1069	13	ternary	ternary	ADJ
fuelectenerg-1427	1069	14	shannon	shannon	NOUN
fuelectenerg-1427	1069	15	expression	expression	NOUN
fuelectenerg-1427	1069	16	.	.	PUNCT
fuelectenerg-1427	1070	1	definition	definition	NOUN
fuelectenerg-1427	1070	2	6	6	NUM
fuelectenerg-1427	1070	3	.	.	PUNCT
fuelectenerg-1427	1071	1	the	the	DET
fuelectenerg-1427	1071	2	decision	decision	NOUN
fuelectenerg-1427	1071	3	trees	tree	NOUN
fuelectenerg-1427	1071	4	that	that	PRON
fuelectenerg-1427	1071	5	result	result	VERB
fuelectenerg-1427	1071	6	from	from	ADP
fuelectenerg-1427	1071	7	applying	apply	VERB
fuelectenerg-1427	1071	8	the	the	DET
fuelectenerg-1427	1071	9	ternary	ternary	ADJ
fuelectenerg-1427	1071	10	davio	davio	NOUN
fuelectenerg-1427	1071	11	expansions	expansion	NOUN
fuelectenerg-1427	1071	12	in	in	ADP
fuelectenerg-1427	1071	13	equations	equation	NOUN
fuelectenerg-1427	1071	14	(	(	PUNCT
fuelectenerg-1427	1071	15	24	24	NUM
fuelectenerg-1427	1071	16	)	)	PUNCT
fuelectenerg-1427	1071	17	(	(	PUNCT
fuelectenerg-1427	1071	18	26	26	NUM
fuelectenerg-1427	1071	19	)	)	PUNCT
fuelectenerg-1427	1071	20	recursively	recursively	ADV
fuelectenerg-1427	1071	21	to	to	ADP
fuelectenerg-1427	1071	22	a	a	DET
fuelectenerg-1427	1071	23	ternary	ternary	ADJ
fuelectenerg-1427	1071	24	-	-	PUNCT
fuelectenerg-1427	1071	25	input	input	NOUN
fuelectenerg-1427	1071	26	ternary	ternary	ADJ
fuelectenerg-1427	1071	27	-	-	PUNCT
fuelectenerg-1427	1071	28	output	output	NOUN
fuelectenerg-1427	1071	29	logic	logic	NOUN
fuelectenerg-1427	1071	30	function	function	NOUN
fuelectenerg-1427	1071	31	(	(	PUNCT
fuelectenerg-1427	1071	32	i.e.	i.e.	X
fuelectenerg-1427	1071	33	,	,	PUNCT
fuelectenerg-1427	1071	34	all	all	DET
fuelectenerg-1427	1071	35	levels	level	NOUN
fuelectenerg-1427	1071	36	in	in	ADP
fuelectenerg-1427	1071	37	a	a	DET
fuelectenerg-1427	1071	38	dt	dt	NOUN
fuelectenerg-1427	1071	39	)	)	PUNCT
fuelectenerg-1427	1071	40	are	be	AUX
fuelectenerg-1427	1071	41	called	call	VERB
fuelectenerg-1427	1071	42	:	:	PUNCT
fuelectenerg-1427	1071	43	ternary	ternary	ADJ
fuelectenerg-1427	1071	44	zero	zero	NUM
fuelectenerg-1427	1071	45	-	-	PUNCT
fuelectenerg-1427	1071	46	polarity	polarity	NOUN
fuelectenerg-1427	1071	47	davio	davio	NOUN
fuelectenerg-1427	1071	48	decision	decision	NOUN
fuelectenerg-1427	1071	49	tree	tree	NOUN
fuelectenerg-1427	1071	50	(	(	PUNCT
fuelectenerg-1427	1071	51	td0dt	td0dt	NOUN
fuelectenerg-1427	1071	52	)	)	PUNCT
fuelectenerg-1427	1071	53	,	,	PUNCT
fuelectenerg-1427	1071	54	ternary	ternary	ADJ
fuelectenerg-1427	1071	55	first	first	ADJ
fuelectenerg-1427	1071	56	-	-	PUNCT
fuelectenerg-1427	1071	57	polarity	polarity	NOUN
fuelectenerg-1427	1071	58	davio	davio	NOUN
fuelectenerg-1427	1071	59	decision	decision	NOUN
fuelectenerg-1427	1071	60	tree	tree	NOUN
fuelectenerg-1427	1071	61	(	(	PUNCT
fuelectenerg-1427	1071	62	td1dt	td1dt	NUM
fuelectenerg-1427	1071	63	)	)	PUNCT
fuelectenerg-1427	1071	64	and	and	CCONJ
fuelectenerg-1427	1071	65	ternary	ternary	ADJ
fuelectenerg-1427	1071	66	secondpolarity	secondpolarity	NOUN
fuelectenerg-1427	1071	67	davio	davio	NOUN
fuelectenerg-1427	1071	68	decision	decision	NOUN
fuelectenerg-1427	1071	69	tree	tree	NOUN
fuelectenerg-1427	1071	70	(	(	PUNCT
fuelectenerg-1427	1071	71	td2dt	td2dt	NUM
fuelectenerg-1427	1071	72	)	)	PUNCT
fuelectenerg-1427	1071	73	,	,	PUNCT
fuelectenerg-1427	1071	74	respectively	respectively	ADV
fuelectenerg-1427	1071	75	.	.	PUNCT
fuelectenerg-1427	1072	1	the	the	DET
fuelectenerg-1427	1072	2	resulting	result	VERB
fuelectenerg-1427	1072	3	expressions	expression	NOUN
fuelectenerg-1427	1072	4	(	(	PUNCT
fuelectenerg-1427	1072	5	flattened	flatten	VERB
fuelectenerg-1427	1072	6	forms	form	NOUN
fuelectenerg-1427	1072	7	)	)	PUNCT
fuelectenerg-1427	1072	8	from	from	ADP
fuelectenerg-1427	1072	9	td0dt	td0dt	PROPN
fuelectenerg-1427	1072	10	,	,	PUNCT
fuelectenerg-1427	1072	11	td1dt	td1dt	NUM
fuelectenerg-1427	1072	12	and	and	CCONJ
fuelectenerg-1427	1072	13	td2dt	td2dt	NUM
fuelectenerg-1427	1072	14	are	be	AUX
fuelectenerg-1427	1072	15	called	call	VERB
fuelectenerg-1427	1072	16	td0	td0	NOUN
fuelectenerg-1427	1072	17	,	,	PUNCT
fuelectenerg-1427	1072	18	td1	td1	PROPN
fuelectenerg-1427	1072	19	and	and	CCONJ
fuelectenerg-1427	1072	20	td2	td2	PROPN
fuelectenerg-1427	1072	21	expressions	expression	NOUN
fuelectenerg-1427	1072	22	,	,	PUNCT
fuelectenerg-1427	1072	23	respectively	respectively	ADV
fuelectenerg-1427	1072	24	.	.	PUNCT
fuelectenerg-1427	1073	1	definition	definition	NOUN
fuelectenerg-1427	1073	2	7	7	NUM
fuelectenerg-1427	1073	3	.	.	PUNCT
fuelectenerg-1427	1074	1	the	the	DET
fuelectenerg-1427	1074	2	decision	decision	NOUN
fuelectenerg-1427	1074	3	tree	tree	NOUN
fuelectenerg-1427	1074	4	that	that	PRON
fuelectenerg-1427	1074	5	results	result	VERB
fuelectenerg-1427	1074	6	from	from	ADP
fuelectenerg-1427	1074	7	applying	apply	VERB
fuelectenerg-1427	1074	8	any	any	PRON
fuelectenerg-1427	1074	9	of	of	ADP
fuelectenerg-1427	1074	10	the	the	DET
fuelectenerg-1427	1074	11	ternary	ternary	ADJ
fuelectenerg-1427	1074	12	davio	davio	NOUN
fuelectenerg-1427	1074	13	expansions	expansion	NOUN
fuelectenerg-1427	1074	14	(	(	PUNCT
fuelectenerg-1427	1074	15	nodes	node	NOUN
fuelectenerg-1427	1074	16	)	)	PUNCT
fuelectenerg-1427	1074	17	for	for	ADP
fuelectenerg-1427	1074	18	all	all	DET
fuelectenerg-1427	1074	19	nodes	node	NOUN
fuelectenerg-1427	1074	20	in	in	ADP
fuelectenerg-1427	1074	21	each	each	DET
fuelectenerg-1427	1074	22	level	level	NOUN
fuelectenerg-1427	1074	23	(	(	PUNCT
fuelectenerg-1427	1074	24	variable	variable	NOUN
fuelectenerg-1427	1074	25	)	)	PUNCT
fuelectenerg-1427	1074	26	in	in	ADP
fuelectenerg-1427	1074	27	the	the	DET
fuelectenerg-1427	1074	28	dt	dt	NOUN
fuelectenerg-1427	1074	29	is	be	AUX
fuelectenerg-1427	1074	30	called	call	VERB
fuelectenerg-1427	1074	31	ternary	ternary	ADJ
fuelectenerg-1427	1074	32	reed	reed	NOUN
fuelectenerg-1427	1074	33	-	-	PUNCT
fuelectenerg-1427	1074	34	muller	muller	NOUN
fuelectenerg-1427	1074	35	decision	decision	NOUN
fuelectenerg-1427	1074	36	tree	tree	NOUN
fuelectenerg-1427	1074	37	(	(	PUNCT
fuelectenerg-1427	1074	38	trmdt	trmdt	NOUN
fuelectenerg-1427	1074	39	)	)	PUNCT
fuelectenerg-1427	1074	40	.	.	PUNCT
fuelectenerg-1427	1075	1	the	the	DET
fuelectenerg-1427	1075	2	corresponding	corresponding	ADJ
fuelectenerg-1427	1075	3	expression	expression	NOUN
fuelectenerg-1427	1075	4	is	be	AUX
fuelectenerg-1427	1075	5	called	call	VERB
fuelectenerg-1427	1075	6	ternary	ternary	ADJ
fuelectenerg-1427	1075	7	fixed	fix	VERB
fuelectenerg-1427	1075	8	polarity	polarity	NOUN
fuelectenerg-1427	1075	9	reed	reed	NOUN
fuelectenerg-1427	1075	10	-	-	PUNCT
fuelectenerg-1427	1075	11	muller	muller	NOUN
fuelectenerg-1427	1075	12	(	(	PUNCT
fuelectenerg-1427	1075	13	tfprm	tfprm	ADJ
fuelectenerg-1427	1075	14	)	)	PUNCT
fuelectenerg-1427	1075	15	expression	expression	NOUN
fuelectenerg-1427	1075	16	.	.	PUNCT
fuelectenerg-1427	1076	1	definition	definition	NOUN
fuelectenerg-1427	1076	2	8	8	NUM
fuelectenerg-1427	1076	3	.	.	PUNCT
fuelectenerg-1427	1077	1	the	the	DET
fuelectenerg-1427	1077	2	decision	decision	NOUN
fuelectenerg-1427	1077	3	tree	tree	NOUN
fuelectenerg-1427	1077	4	that	that	PRON
fuelectenerg-1427	1077	5	results	result	VERB
fuelectenerg-1427	1077	6	from	from	ADP
fuelectenerg-1427	1077	7	using	use	VERB
fuelectenerg-1427	1077	8	any	any	PRON
fuelectenerg-1427	1077	9	of	of	ADP
fuelectenerg-1427	1077	10	the	the	DET
fuelectenerg-1427	1077	11	ternary	ternary	ADJ
fuelectenerg-1427	1077	12	shannon	shannon	NOUN
fuelectenerg-1427	1077	13	(	(	PUNCT
fuelectenerg-1427	1077	14	s	s	NOUN
fuelectenerg-1427	1077	15	)	)	PUNCT
fuelectenerg-1427	1077	16	or	or	CCONJ
fuelectenerg-1427	1077	17	davio	davio	NOUN
fuelectenerg-1427	1077	18	(	(	PUNCT
fuelectenerg-1427	1077	19	d0	d0	NOUN
fuelectenerg-1427	1077	20	,	,	PUNCT
fuelectenerg-1427	1077	21	d1	d1	PROPN
fuelectenerg-1427	1077	22	or	or	CCONJ
fuelectenerg-1427	1077	23	d2	d2	PROPN
fuelectenerg-1427	1077	24	)	)	PUNCT
fuelectenerg-1427	1077	25	expansions	expansion	NOUN
fuelectenerg-1427	1077	26	(	(	PUNCT
fuelectenerg-1427	1077	27	nodes	node	NOUN
fuelectenerg-1427	1077	28	)	)	PUNCT
fuelectenerg-1427	1077	29	for	for	ADP
fuelectenerg-1427	1077	30	all	all	DET
fuelectenerg-1427	1077	31	nodes	node	NOUN
fuelectenerg-1427	1077	32	in	in	ADP
fuelectenerg-1427	1077	33	each	each	DET
fuelectenerg-1427	1077	34	level	level	NOUN
fuelectenerg-1427	1077	35	(	(	PUNCT
fuelectenerg-1427	1077	36	variable	variable	NOUN
fuelectenerg-1427	1077	37	)	)	PUNCT
fuelectenerg-1427	1077	38	in	in	ADP
fuelectenerg-1427	1077	39	the	the	DET
fuelectenerg-1427	1077	40	dt	dt	X
fuelectenerg-1427	1077	41	(	(	PUNCT
fuelectenerg-1427	1077	42	that	that	PRON
fuelectenerg-1427	1077	43	has	have	AUX
fuelectenerg-1427	1077	44	fixed	fix	VERB
fuelectenerg-1427	1077	45	order	order	NOUN
fuelectenerg-1427	1077	46	of	of	ADP
fuelectenerg-1427	1077	47	variables	variable	NOUN
fuelectenerg-1427	1077	48	)	)	PUNCT
fuelectenerg-1427	1077	49	is	be	AUX
fuelectenerg-1427	1077	50	called	call	VERB
fuelectenerg-1427	1077	51	ternary	ternary	ADJ
fuelectenerg-1427	1077	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1077	53	decision	decision	NOUN
fuelectenerg-1427	1077	54	tree	tree	NOUN
fuelectenerg-1427	1077	55	(	(	PUNCT
fuelectenerg-1427	1077	56	tkrodt	tkrodt	NOUN
fuelectenerg-1427	1077	57	)	)	PUNCT
fuelectenerg-1427	1077	58	.	.	PUNCT
fuelectenerg-1427	1078	1	the	the	DET
fuelectenerg-1427	1078	2	resulting	result	VERB
fuelectenerg-1427	1078	3	expression	expression	NOUN
fuelectenerg-1427	1078	4	is	be	AUX
fuelectenerg-1427	1078	5	called	call	VERB
fuelectenerg-1427	1078	6	ternary	ternary	ADJ
fuelectenerg-1427	1078	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1078	8	expression	expression	NOUN
fuelectenerg-1427	1078	9	.	.	PUNCT
fuelectenerg-1427	1079	1	definition	definition	NOUN
fuelectenerg-1427	1079	2	9	9	NUM
fuelectenerg-1427	1079	3	.	.	PUNCT
fuelectenerg-1427	1080	1	the	the	DET
fuelectenerg-1427	1080	2	decision	decision	NOUN
fuelectenerg-1427	1080	3	tree	tree	NOUN
fuelectenerg-1427	1080	4	that	that	PRON
fuelectenerg-1427	1080	5	results	result	VERB
fuelectenerg-1427	1080	6	from	from	ADP
fuelectenerg-1427	1080	7	using	use	VERB
fuelectenerg-1427	1080	8	any	any	PRON
fuelectenerg-1427	1080	9	of	of	ADP
fuelectenerg-1427	1080	10	the	the	DET
fuelectenerg-1427	1080	11	ternary	ternary	ADJ
fuelectenerg-1427	1080	12	davio	davio	NOUN
fuelectenerg-1427	1080	13	expansions	expansion	NOUN
fuelectenerg-1427	1080	14	(	(	PUNCT
fuelectenerg-1427	1080	15	nodes	node	NOUN
fuelectenerg-1427	1080	16	)	)	PUNCT
fuelectenerg-1427	1080	17	for	for	ADP
fuelectenerg-1427	1080	18	each	each	DET
fuelectenerg-1427	1080	19	node	node	NOUN
fuelectenerg-1427	1080	20	(	(	PUNCT
fuelectenerg-1427	1080	21	per	per	ADP
fuelectenerg-1427	1080	22	level	level	NOUN
fuelectenerg-1427	1080	23	)	)	PUNCT
fuelectenerg-1427	1080	24	of	of	ADP
fuelectenerg-1427	1080	25	the	the	DET
fuelectenerg-1427	1080	26	dt	dt	NOUN
fuelectenerg-1427	1080	27	is	be	AUX
fuelectenerg-1427	1080	28	called	call	VERB
fuelectenerg-1427	1080	29	ternary	ternary	ADJ
fuelectenerg-1427	1080	30	pseudo	pseudo	NOUN
fuelectenerg-1427	1080	31	-	-	NOUN
fuelectenerg-1427	1080	32	reed112	reed112	VERB
fuelectenerg-1427	1080	33	an	an	DET
fuelectenerg-1427	1080	34	extended	extend	VERB
fuelectenerg-1427	1080	35	green	green	PROPN
fuelectenerg-1427	1080	36	sasao	sasao	PROPN
fuelectenerg-1427	1080	37	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1080	38	of	of	ADP
fuelectenerg-1427	1080	39	canonical	canonical	ADJ
fuelectenerg-1427	1080	40	ternary	ternary	ADJ
fuelectenerg-1427	1080	41	galois	galois	NOUN
fuelectenerg-1427	1080	42	forms	form	NOUN
fuelectenerg-1427	1080	43	...	...	PUNCT
fuelectenerg-1427	1080	44	definition	definition	NOUN
fuelectenerg-1427	1080	45	4	4	NUM
fuelectenerg-1427	1080	46	.	.	PUNCT
fuelectenerg-1427	1081	1	the	the	DET
fuelectenerg-1427	1081	2	family	family	NOUN
fuelectenerg-1427	1081	3	of	of	ADP
fuelectenerg-1427	1081	4	forms	form	NOUN
fuelectenerg-1427	1081	5	,	,	PUNCT
fuelectenerg-1427	1081	6	generated	generate	VERB
fuelectenerg-1427	1081	7	by	by	ADP
fuelectenerg-1427	1081	8	s	s	PROPN
fuelectenerg-1427	1081	9	/	/	SYM
fuelectenerg-1427	1081	10	d	d	NOUN
fuelectenerg-1427	1081	11	tree	tree	NOUN
fuelectenerg-1427	1081	12	with	with	ADP
fuelectenerg-1427	1081	13	no	no	DET
fuelectenerg-1427	1081	14	fixed	fix	VERB
fuelectenerg-1427	1081	15	ordering	ordering	NOUN
fuelectenerg-1427	1081	16	of	of	ADP
fuelectenerg-1427	1081	17	variables	variable	NOUN
fuelectenerg-1427	1081	18	,	,	PUNCT
fuelectenerg-1427	1081	19	with	with	ADP
fuelectenerg-1427	1081	20	variables	variable	NOUN
fuelectenerg-1427	1081	21	not	not	PART
fuelectenerg-1427	1081	22	repeated	repeat	VERB
fuelectenerg-1427	1081	23	along	along	ADP
fuelectenerg-1427	1081	24	same	same	ADJ
fuelectenerg-1427	1081	25	branches	branch	NOUN
fuelectenerg-1427	1081	26	,	,	PUNCT
fuelectenerg-1427	1081	27	is	be	AUX
fuelectenerg-1427	1081	28	called	call	VERB
fuelectenerg-1427	1081	29	ternary	ternary	ADJ
fuelectenerg-1427	1081	30	free	free	ADJ
fuelectenerg-1427	1081	31	generalized	generalize	VERB
fuelectenerg-1427	1081	32	inclusive	inclusive	ADJ
fuelectenerg-1427	1081	33	forms	form	NOUN
fuelectenerg-1427	1081	34	(	(	PUNCT
fuelectenerg-1427	1081	35	tfgifs	tfgifs	PROPN
fuelectenerg-1427	1081	36	)	)	PUNCT
fuelectenerg-1427	1081	37	.	.	PUNCT
fuelectenerg-1427	1082	1	2.3	2.3	NUM
fuelectenerg-1427	1082	2	an	an	DET
fuelectenerg-1427	1082	3	extended	extended	ADJ
fuelectenerg-1427	1082	4	green	green	ADJ
fuelectenerg-1427	1082	5	-	-	PUNCT
fuelectenerg-1427	1082	6	sasao	sasao	NOUN
fuelectenerg-1427	1082	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1082	8	with	with	ADP
fuelectenerg-1427	1082	9	a	a	DET
fuelectenerg-1427	1082	10	new	new	ADJ
fuelectenerg-1427	1082	11	sub	sub	NOUN
fuelectenerg-1427	1082	12	-	-	NOUN
fuelectenerg-1427	1082	13	family	family	NOUN
fuelectenerg-1427	1082	14	for	for	ADP
fuelectenerg-1427	1082	15	ternary	ternary	ADJ
fuelectenerg-1427	1082	16	reed	reed	NOUN
fuelectenerg-1427	1082	17	-	-	PUNCT
fuelectenerg-1427	1082	18	muller	muller	NOUN
fuelectenerg-1427	1082	19	logic	logic	NOUN
fuelectenerg-1427	1082	20	the	the	DET
fuelectenerg-1427	1082	21	green	green	PROPN
fuelectenerg-1427	1082	22	-	-	PUNCT
fuelectenerg-1427	1082	23	sasao	sasao	PROPN
fuelectenerg-1427	1082	24	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1082	25	of	of	ADP
fuelectenerg-1427	1082	26	families	family	NOUN
fuelectenerg-1427	1082	27	of	of	ADP
fuelectenerg-1427	1082	28	canonical	canonical	ADJ
fuelectenerg-1427	1082	29	forms	form	NOUN
fuelectenerg-1427	1082	30	[	[	X
fuelectenerg-1427	1082	31	1	1	NUM
fuelectenerg-1427	1082	32	,	,	PUNCT
fuelectenerg-1427	1082	33	10	10	NUM
fuelectenerg-1427	1082	34	-	-	SYM
fuelectenerg-1427	1082	35	13	13	NUM
fuelectenerg-1427	1082	36	,	,	PUNCT
fuelectenerg-1427	1082	37	17	17	NUM
fuelectenerg-1427	1082	38	,	,	PUNCT
fuelectenerg-1427	1082	39	24	24	NUM
fuelectenerg-1427	1082	40	,	,	PUNCT
fuelectenerg-1427	1082	41	26	26	NUM
fuelectenerg-1427	1082	42	]	]	PUNCT
fuelectenerg-1427	1082	43	and	and	CCONJ
fuelectenerg-1427	1082	44	the	the	DET
fuelectenerg-1427	1082	45	corresponding	correspond	VERB
fuelectenerg-1427	1082	46	decision	decision	NOUN
fuelectenerg-1427	1082	47	trees	tree	NOUN
fuelectenerg-1427	1082	48	and	and	CCONJ
fuelectenerg-1427	1082	49	diagrams	diagram	NOUN
fuelectenerg-1427	1082	50	is	be	AUX
fuelectenerg-1427	1082	51	based	base	VERB
fuelectenerg-1427	1082	52	on	on	ADP
fuelectenerg-1427	1082	53	three	three	NUM
fuelectenerg-1427	1082	54	generic	generic	ADJ
fuelectenerg-1427	1082	55	expansions	expansion	NOUN
fuelectenerg-1427	1082	56	,	,	PUNCT
fuelectenerg-1427	1082	57	shannon	shannon	PROPN
fuelectenerg-1427	1082	58	,	,	PUNCT
fuelectenerg-1427	1082	59	positive	positive	ADJ
fuelectenerg-1427	1082	60	and	and	CCONJ
fuelectenerg-1427	1082	61	negative	negative	ADJ
fuelectenerg-1427	1082	62	davio	davio	NOUN
fuelectenerg-1427	1082	63	expansions	expansion	NOUN
fuelectenerg-1427	1082	64	.	.	PUNCT
fuelectenerg-1427	1083	1	for	for	ADP
fuelectenerg-1427	1083	2	example	example	NOUN
fuelectenerg-1427	1083	3	,	,	PUNCT
fuelectenerg-1427	1083	4	this	this	PRON
fuelectenerg-1427	1083	5	includes	include	VERB
fuelectenerg-1427	1083	6	shannon	shannon	ADJ
fuelectenerg-1427	1083	7	decision	decision	NOUN
fuelectenerg-1427	1083	8	trees	tree	NOUN
fuelectenerg-1427	1083	9	and	and	CCONJ
fuelectenerg-1427	1083	10	diagrams	diagram	NOUN
fuelectenerg-1427	1083	11	,	,	PUNCT
fuelectenerg-1427	1083	12	positive	positive	ADJ
fuelectenerg-1427	1083	13	and	and	CCONJ
fuelectenerg-1427	1083	14	negative	negative	ADJ
fuelectenerg-1427	1083	15	davio	davio	NOUN
fuelectenerg-1427	1083	16	decision	decision	NOUN
fuelectenerg-1427	1083	17	trees	tree	NOUN
fuelectenerg-1427	1083	18	and	and	CCONJ
fuelectenerg-1427	1083	19	diagrams	diagram	NOUN
fuelectenerg-1427	1083	20	,	,	PUNCT
fuelectenerg-1427	1083	21	fixed	fix	VERB
fuelectenerg-1427	1083	22	polarity	polarity	NOUN
fuelectenerg-1427	1083	23	reed	reed	NOUN
fuelectenerg-1427	1083	24	-	-	PUNCT
fuelectenerg-1427	1083	25	muller	muller	NOUN
fuelectenerg-1427	1083	26	decision	decision	NOUN
fuelectenerg-1427	1083	27	trees	tree	NOUN
fuelectenerg-1427	1083	28	and	and	CCONJ
fuelectenerg-1427	1083	29	diagrams	diagram	NOUN
fuelectenerg-1427	1083	30	,	,	PUNCT
fuelectenerg-1427	1083	31	kronecker	kronecker	NOUN
fuelectenerg-1427	1083	32	decision	decision	NOUN
fuelectenerg-1427	1083	33	trees	tree	NOUN
fuelectenerg-1427	1083	34	and	and	CCONJ
fuelectenerg-1427	1083	35	diagrams	diagram	NOUN
fuelectenerg-1427	1083	36	,	,	PUNCT
fuelectenerg-1427	1083	37	pseudo	pseudo	NOUN
fuelectenerg-1427	1083	38	reed	reed	NOUN
fuelectenerg-1427	1083	39	-	-	PUNCT
fuelectenerg-1427	1083	40	muller	muller	NOUN
fuelectenerg-1427	1083	41	decision	decision	NOUN
fuelectenerg-1427	1083	42	trees	tree	NOUN
fuelectenerg-1427	1083	43	and	and	CCONJ
fuelectenerg-1427	1083	44	diagrams	diagram	NOUN
fuelectenerg-1427	1083	45	,	,	PUNCT
fuelectenerg-1427	1083	46	pseudo	pseudo	NOUN
fuelectenerg-1427	1083	47	kronecker	kronecker	NOUN
fuelectenerg-1427	1083	48	decision	decision	NOUN
fuelectenerg-1427	1083	49	trees	tree	NOUN
fuelectenerg-1427	1083	50	and	and	CCONJ
fuelectenerg-1427	1083	51	diagrams	diagram	NOUN
fuelectenerg-1427	1083	52	,	,	PUNCT
fuelectenerg-1427	1083	53	and	and	CCONJ
fuelectenerg-1427	1083	54	linearly	linearly	ADV
fuelectenerg-1427	1083	55	-	-	PUNCT
fuelectenerg-1427	1083	56	independent	independent	ADJ
fuelectenerg-1427	1083	57	decision	decision	NOUN
fuelectenerg-1427	1083	58	trees	tree	NOUN
fuelectenerg-1427	1083	59	and	and	CCONJ
fuelectenerg-1427	1083	60	diagrams	diagram	NOUN
fuelectenerg-1427	1084	1	[	[	X
fuelectenerg-1427	1084	2	1	1	NUM
fuelectenerg-1427	1084	3	,	,	PUNCT
fuelectenerg-1427	1084	4	17	17	NUM
fuelectenerg-1427	1084	5	,	,	PUNCT
fuelectenerg-1427	1084	6	24	24	NUM
fuelectenerg-1427	1084	7	]	]	PUNCT
fuelectenerg-1427	1084	8	.	.	PUNCT
fuelectenerg-1427	1085	1	a	a	DET
fuelectenerg-1427	1085	2	set	set	VERB
fuelectenerg-1427	1085	3	-	-	PUNCT
fuelectenerg-1427	1085	4	theoretic	theoretic	NOUN
fuelectenerg-1427	1085	5	relationship	relationship	NOUN
fuelectenerg-1427	1085	6	between	between	ADP
fuelectenerg-1427	1085	7	families	family	NOUN
fuelectenerg-1427	1085	8	of	of	ADP
fuelectenerg-1427	1085	9	canonical	canonical	ADJ
fuelectenerg-1427	1085	10	forms	form	NOUN
fuelectenerg-1427	1085	11	over	over	ADP
fuelectenerg-1427	1085	12	gf(2	gf(2	PROPN
fuelectenerg-1427	1085	13	)	)	PUNCT
fuelectenerg-1427	1085	14	was	be	AUX
fuelectenerg-1427	1085	15	proposed	propose	VERB
fuelectenerg-1427	1085	16	and	and	CCONJ
fuelectenerg-1427	1085	17	extended	extend	VERB
fuelectenerg-1427	1085	18	by	by	ADP
fuelectenerg-1427	1085	19	introducing	introduce	VERB
fuelectenerg-1427	1085	20	binary	binary	NOUN
fuelectenerg-1427	1085	21	if	if	SCONJ
fuelectenerg-1427	1085	22	,	,	PUNCT
fuelectenerg-1427	1085	23	gif	gif	NOUN
fuelectenerg-1427	1085	24	and	and	CCONJ
fuelectenerg-1427	1085	25	free	free	ADJ
fuelectenerg-1427	1085	26	gif	gif	NOUN
fuelectenerg-1427	1085	27	(	(	PUNCT
fuelectenerg-1427	1085	28	fgif	fgif	NOUN
fuelectenerg-1427	1085	29	)	)	PUNCT
fuelectenerg-1427	1085	30	forms	form	NOUN
fuelectenerg-1427	1085	31	where	where	SCONJ
fuelectenerg-1427	1085	32	figure	figure	NOUN
fuelectenerg-1427	1085	33	6(a	6(a	NUM
fuelectenerg-1427	1085	34	)	)	PUNCT
fuelectenerg-1427	1085	35	illustrates	illustrate	VERB
fuelectenerg-1427	1085	36	set	set	VERB
fuelectenerg-1427	1085	37	-	-	PUNCT
fuelectenerg-1427	1085	38	theoretic	theoretic	NOUN
fuelectenerg-1427	1085	39	relationship	relationship	NOUN
fuelectenerg-1427	1085	40	between	between	ADP
fuelectenerg-1427	1085	41	the	the	DET
fuelectenerg-1427	1085	42	various	various	ADJ
fuelectenerg-1427	1085	43	families	family	NOUN
fuelectenerg-1427	1085	44	of	of	ADP
fuelectenerg-1427	1085	45	canonical	canonical	ADJ
fuelectenerg-1427	1085	46	forms	form	NOUN
fuelectenerg-1427	1085	47	over	over	ADP
fuelectenerg-1427	1085	48	gf(2	gf(2	PROPN
fuelectenerg-1427	1085	49	)	)	PUNCT
fuelectenerg-1427	1085	50	.	.	PUNCT
fuelectenerg-1427	1086	1	analogously	analogously	ADV
fuelectenerg-1427	1086	2	to	to	ADP
fuelectenerg-1427	1086	3	the	the	DET
fuelectenerg-1427	1086	4	green	green	ADJ
fuelectenerg-1427	1086	5	-	-	PUNCT
fuelectenerg-1427	1086	6	sasao	sasao	PROPN
fuelectenerg-1427	1086	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1086	8	of	of	ADP
fuelectenerg-1427	1086	9	binary	binary	PROPN
fuelectenerg-1427	1086	10	reed	reed	PROPN
fuelectenerg-1427	1086	11	-	-	PUNCT
fuelectenerg-1427	1086	12	muller	muller	NOUN
fuelectenerg-1427	1086	13	families	family	NOUN
fuelectenerg-1427	1086	14	of	of	ADP
fuelectenerg-1427	1086	15	spectral	spectral	ADJ
fuelectenerg-1427	1086	16	transforms	transform	VERB
fuelectenerg-1427	1086	17	over	over	ADP
fuelectenerg-1427	1086	18	gf(2	gf(2	PROPN
fuelectenerg-1427	1086	19	)	)	PUNCT
fuelectenerg-1427	1086	20	that	that	PRON
fuelectenerg-1427	1086	21	is	be	AUX
fuelectenerg-1427	1086	22	shown	show	VERB
fuelectenerg-1427	1086	23	in	in	ADP
fuelectenerg-1427	1086	24	figure	figure	NOUN
fuelectenerg-1427	1086	25	6(a	6(a	NUM
fuelectenerg-1427	1086	26	)	)	PUNCT
fuelectenerg-1427	1086	27	,	,	PUNCT
fuelectenerg-1427	1086	28	we	we	PRON
fuelectenerg-1427	1086	29	will	will	AUX
fuelectenerg-1427	1086	30	introduce	introduce	VERB
fuelectenerg-1427	1086	31	the	the	DET
fuelectenerg-1427	1086	32	extended	extended	ADJ
fuelectenerg-1427	1086	33	green	green	ADJ
fuelectenerg-1427	1086	34	-	-	PUNCT
fuelectenerg-1427	1086	35	sasao	sasao	NOUN
fuelectenerg-1427	1086	36	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1086	37	of	of	ADP
fuelectenerg-1427	1086	38	spectral	spectral	ADJ
fuelectenerg-1427	1086	39	transforms	transform	NOUN
fuelectenerg-1427	1086	40	,	,	PUNCT
fuelectenerg-1427	1086	41	with	with	ADP
fuelectenerg-1427	1086	42	a	a	DET
fuelectenerg-1427	1086	43	new	new	ADJ
fuelectenerg-1427	1086	44	sub	sub	NOUN
fuelectenerg-1427	1086	45	-	-	NOUN
fuelectenerg-1427	1086	46	family	family	NOUN
fuelectenerg-1427	1086	47	for	for	ADP
fuelectenerg-1427	1086	48	ternary	ternary	ADJ
fuelectenerg-1427	1086	49	reedmuller	reedmuller	NOUN
fuelectenerg-1427	1086	50	logic	logic	NOUN
fuelectenerg-1427	1086	51	over	over	ADP
fuelectenerg-1427	1086	52	gf(3	gf(3	PROPN
fuelectenerg-1427	1086	53	)	)	PUNCT
fuelectenerg-1427	1086	54	.	.	PUNCT
fuelectenerg-1427	1087	1	while	while	SCONJ
fuelectenerg-1427	1087	2	definitions	definition	NOUN
fuelectenerg-1427	1087	3	2	2	NUM
fuelectenerg-1427	1087	4	4	4	NUM
fuelectenerg-1427	1087	5	defined	define	VERB
fuelectenerg-1427	1087	6	the	the	DET
fuelectenerg-1427	1087	7	ternary	ternary	ADJ
fuelectenerg-1427	1087	8	inclusive	inclusive	ADJ
fuelectenerg-1427	1087	9	forms	form	NOUN
fuelectenerg-1427	1087	10	,	,	PUNCT
fuelectenerg-1427	1087	11	ternary	ternary	ADJ
fuelectenerg-1427	1087	12	generalized	generalize	VERB
fuelectenerg-1427	1087	13	inclusive	inclusive	ADJ
fuelectenerg-1427	1087	14	forms	form	NOUN
fuelectenerg-1427	1087	15	and	and	CCONJ
fuelectenerg-1427	1087	16	ternary	ternary	ADJ
fuelectenerg-1427	1087	17	free	free	ADJ
fuelectenerg-1427	1087	18	generalized	generalized	ADJ
fuelectenerg-1427	1087	19	inclusive	inclusive	ADJ
fuelectenerg-1427	1087	20	forms	form	NOUN
fuelectenerg-1427	1087	21	,	,	PUNCT
fuelectenerg-1427	1087	22	respectively	respectively	ADV
fuelectenerg-1427	1087	23	,	,	PUNCT
fuelectenerg-1427	1087	24	and	and	CCONJ
fuelectenerg-1427	1087	25	analogously	analogously	ADV
fuelectenerg-1427	1087	26	to	to	ADP
fuelectenerg-1427	1087	27	the	the	DET
fuelectenerg-1427	1087	28	binary	binary	PROPN
fuelectenerg-1427	1087	29	reed	reed	PROPN
fuelectenerg-1427	1087	30	-	-	PUNCT
fuelectenerg-1427	1087	31	muller	muller	NOUN
fuelectenerg-1427	1087	32	case	case	NOUN
fuelectenerg-1427	1087	33	,	,	PUNCT
fuelectenerg-1427	1087	34	the	the	DET
fuelectenerg-1427	1087	35	following	follow	VERB
fuelectenerg-1427	1087	36	definitions	definition	NOUN
fuelectenerg-1427	1087	37	are	be	AUX
fuelectenerg-1427	1087	38	introduced	introduce	VERB
fuelectenerg-1427	1087	39	for	for	ADP
fuelectenerg-1427	1087	40	the	the	DET
fuelectenerg-1427	1087	41	corresponding	corresponding	ADJ
fuelectenerg-1427	1087	42	canonical	canonical	ADJ
fuelectenerg-1427	1087	43	expressions	expression	NOUN
fuelectenerg-1427	1087	44	over	over	ADP
fuelectenerg-1427	1087	45	gf(3	gf(3	PROPN
fuelectenerg-1427	1087	46	)	)	PUNCT
fuelectenerg-1427	1087	47	.	.	PUNCT
fuelectenerg-1427	1088	1	definition	definition	NOUN
fuelectenerg-1427	1088	2	5	5	NUM
fuelectenerg-1427	1088	3	.	.	PUNCT
fuelectenerg-1427	1089	1	the	the	DET
fuelectenerg-1427	1089	2	decision	decision	NOUN
fuelectenerg-1427	1089	3	tree	tree	NOUN
fuelectenerg-1427	1089	4	that	that	PRON
fuelectenerg-1427	1089	5	results	result	VERB
fuelectenerg-1427	1089	6	from	from	ADP
fuelectenerg-1427	1089	7	applying	apply	VERB
fuelectenerg-1427	1089	8	the	the	DET
fuelectenerg-1427	1089	9	ternary	ternary	ADJ
fuelectenerg-1427	1089	10	shannon	shannon	NOUN
fuelectenerg-1427	1089	11	expansion	expansion	NOUN
fuelectenerg-1427	1089	12	in	in	ADP
fuelectenerg-1427	1089	13	equation	equation	NOUN
fuelectenerg-1427	1089	14	(	(	PUNCT
fuelectenerg-1427	1089	15	23	23	NUM
fuelectenerg-1427	1089	16	)	)	PUNCT
fuelectenerg-1427	1089	17	recursively	recursively	ADV
fuelectenerg-1427	1089	18	to	to	ADP
fuelectenerg-1427	1089	19	a	a	DET
fuelectenerg-1427	1089	20	ternary	ternary	ADJ
fuelectenerg-1427	1089	21	input	input	NOUN
fuelectenerg-1427	1089	22	-	-	PUNCT
fuelectenerg-1427	1089	23	ternary	ternary	ADJ
fuelectenerg-1427	1089	24	output	output	NOUN
fuelectenerg-1427	1089	25	logic	logic	NOUN
fuelectenerg-1427	1089	26	function	function	NOUN
fuelectenerg-1427	1089	27	(	(	PUNCT
fuelectenerg-1427	1089	28	i.e.	i.e.	X
fuelectenerg-1427	1089	29	,	,	PUNCT
fuelectenerg-1427	1089	30	all	all	DET
fuelectenerg-1427	1089	31	levels	level	NOUN
fuelectenerg-1427	1089	32	in	in	ADP
fuelectenerg-1427	1089	33	a	a	DET
fuelectenerg-1427	1089	34	dt	dt	NOUN
fuelectenerg-1427	1089	35	)	)	PUNCT
fuelectenerg-1427	1089	36	is	be	AUX
fuelectenerg-1427	1089	37	called	call	VERB
fuelectenerg-1427	1089	38	ternary	ternary	ADJ
fuelectenerg-1427	1089	39	shannon	shannon	PROPN
fuelectenerg-1427	1089	40	decision	decision	NOUN
fuelectenerg-1427	1089	41	tree	tree	NOUN
fuelectenerg-1427	1089	42	(	(	PUNCT
fuelectenerg-1427	1089	43	tsdt	tsdt	NOUN
fuelectenerg-1427	1089	44	)	)	PUNCT
fuelectenerg-1427	1089	45	.	.	PUNCT
fuelectenerg-1427	1090	1	the	the	DET
fuelectenerg-1427	1090	2	result	result	NOUN
fuelectenerg-1427	1090	3	expression	expression	NOUN
fuelectenerg-1427	1090	4	(	(	PUNCT
fuelectenerg-1427	1090	5	flattened	flatten	VERB
fuelectenerg-1427	1090	6	form	form	NOUN
fuelectenerg-1427	1090	7	)	)	PUNCT
fuelectenerg-1427	1090	8	from	from	ADP
fuelectenerg-1427	1090	9	the	the	DET
fuelectenerg-1427	1090	10	tsdt	tsdt	NOUN
fuelectenerg-1427	1090	11	is	be	AUX
fuelectenerg-1427	1090	12	called	call	VERB
fuelectenerg-1427	1090	13	ternary	ternary	ADJ
fuelectenerg-1427	1090	14	shannon	shannon	NOUN
fuelectenerg-1427	1090	15	expression	expression	NOUN
fuelectenerg-1427	1090	16	.	.	PUNCT
fuelectenerg-1427	1091	1	definition	definition	NOUN
fuelectenerg-1427	1091	2	6	6	NUM
fuelectenerg-1427	1091	3	.	.	PUNCT
fuelectenerg-1427	1092	1	the	the	DET
fuelectenerg-1427	1092	2	decision	decision	NOUN
fuelectenerg-1427	1092	3	trees	tree	NOUN
fuelectenerg-1427	1092	4	that	that	PRON
fuelectenerg-1427	1092	5	result	result	VERB
fuelectenerg-1427	1092	6	from	from	ADP
fuelectenerg-1427	1092	7	applying	apply	VERB
fuelectenerg-1427	1092	8	the	the	DET
fuelectenerg-1427	1092	9	ternary	ternary	ADJ
fuelectenerg-1427	1092	10	davio	davio	NOUN
fuelectenerg-1427	1092	11	expansions	expansion	NOUN
fuelectenerg-1427	1092	12	in	in	ADP
fuelectenerg-1427	1092	13	equations	equation	NOUN
fuelectenerg-1427	1092	14	(	(	PUNCT
fuelectenerg-1427	1092	15	24	24	NUM
fuelectenerg-1427	1092	16	)	)	PUNCT
fuelectenerg-1427	1092	17	(	(	PUNCT
fuelectenerg-1427	1092	18	26	26	NUM
fuelectenerg-1427	1092	19	)	)	PUNCT
fuelectenerg-1427	1092	20	recursively	recursively	ADV
fuelectenerg-1427	1092	21	to	to	ADP
fuelectenerg-1427	1092	22	a	a	DET
fuelectenerg-1427	1092	23	ternary	ternary	ADJ
fuelectenerg-1427	1092	24	-	-	PUNCT
fuelectenerg-1427	1092	25	input	input	NOUN
fuelectenerg-1427	1092	26	ternary	ternary	ADJ
fuelectenerg-1427	1092	27	-	-	PUNCT
fuelectenerg-1427	1092	28	output	output	NOUN
fuelectenerg-1427	1092	29	logic	logic	NOUN
fuelectenerg-1427	1092	30	function	function	NOUN
fuelectenerg-1427	1092	31	(	(	PUNCT
fuelectenerg-1427	1092	32	i.e.	i.e.	X
fuelectenerg-1427	1092	33	,	,	PUNCT
fuelectenerg-1427	1092	34	all	all	DET
fuelectenerg-1427	1092	35	levels	level	NOUN
fuelectenerg-1427	1092	36	in	in	ADP
fuelectenerg-1427	1092	37	a	a	DET
fuelectenerg-1427	1092	38	dt	dt	NOUN
fuelectenerg-1427	1092	39	)	)	PUNCT
fuelectenerg-1427	1092	40	are	be	AUX
fuelectenerg-1427	1092	41	called	call	VERB
fuelectenerg-1427	1092	42	:	:	PUNCT
fuelectenerg-1427	1092	43	ternary	ternary	ADJ
fuelectenerg-1427	1092	44	zero	zero	NUM
fuelectenerg-1427	1092	45	-	-	PUNCT
fuelectenerg-1427	1092	46	polarity	polarity	NOUN
fuelectenerg-1427	1092	47	davio	davio	NOUN
fuelectenerg-1427	1092	48	decision	decision	NOUN
fuelectenerg-1427	1092	49	tree	tree	NOUN
fuelectenerg-1427	1092	50	(	(	PUNCT
fuelectenerg-1427	1092	51	td0dt	td0dt	NOUN
fuelectenerg-1427	1092	52	)	)	PUNCT
fuelectenerg-1427	1092	53	,	,	PUNCT
fuelectenerg-1427	1092	54	ternary	ternary	ADJ
fuelectenerg-1427	1092	55	first	first	ADJ
fuelectenerg-1427	1092	56	-	-	PUNCT
fuelectenerg-1427	1092	57	polarity	polarity	NOUN
fuelectenerg-1427	1092	58	davio	davio	NOUN
fuelectenerg-1427	1092	59	decision	decision	NOUN
fuelectenerg-1427	1092	60	tree	tree	NOUN
fuelectenerg-1427	1092	61	(	(	PUNCT
fuelectenerg-1427	1092	62	td1dt	td1dt	NUM
fuelectenerg-1427	1092	63	)	)	PUNCT
fuelectenerg-1427	1092	64	and	and	CCONJ
fuelectenerg-1427	1092	65	ternary	ternary	ADJ
fuelectenerg-1427	1092	66	secondpolarity	secondpolarity	NOUN
fuelectenerg-1427	1092	67	davio	davio	NOUN
fuelectenerg-1427	1092	68	decision	decision	NOUN
fuelectenerg-1427	1092	69	tree	tree	NOUN
fuelectenerg-1427	1092	70	(	(	PUNCT
fuelectenerg-1427	1092	71	td2dt	td2dt	NUM
fuelectenerg-1427	1092	72	)	)	PUNCT
fuelectenerg-1427	1092	73	,	,	PUNCT
fuelectenerg-1427	1092	74	respectively	respectively	ADV
fuelectenerg-1427	1092	75	.	.	PUNCT
fuelectenerg-1427	1093	1	the	the	DET
fuelectenerg-1427	1093	2	resulting	result	VERB
fuelectenerg-1427	1093	3	expressions	expression	NOUN
fuelectenerg-1427	1093	4	(	(	PUNCT
fuelectenerg-1427	1093	5	flattened	flatten	VERB
fuelectenerg-1427	1093	6	forms	form	NOUN
fuelectenerg-1427	1093	7	)	)	PUNCT
fuelectenerg-1427	1093	8	from	from	ADP
fuelectenerg-1427	1093	9	td0dt	td0dt	PROPN
fuelectenerg-1427	1093	10	,	,	PUNCT
fuelectenerg-1427	1093	11	td1dt	td1dt	NUM
fuelectenerg-1427	1093	12	and	and	CCONJ
fuelectenerg-1427	1093	13	td2dt	td2dt	NUM
fuelectenerg-1427	1093	14	are	be	AUX
fuelectenerg-1427	1093	15	called	call	VERB
fuelectenerg-1427	1093	16	td0	td0	NOUN
fuelectenerg-1427	1093	17	,	,	PUNCT
fuelectenerg-1427	1093	18	td1	td1	PROPN
fuelectenerg-1427	1093	19	and	and	CCONJ
fuelectenerg-1427	1093	20	td2	td2	PROPN
fuelectenerg-1427	1093	21	expressions	expression	NOUN
fuelectenerg-1427	1093	22	,	,	PUNCT
fuelectenerg-1427	1093	23	respectively	respectively	ADV
fuelectenerg-1427	1093	24	.	.	PUNCT
fuelectenerg-1427	1094	1	definition	definition	NOUN
fuelectenerg-1427	1094	2	7	7	NUM
fuelectenerg-1427	1094	3	.	.	PUNCT
fuelectenerg-1427	1095	1	the	the	DET
fuelectenerg-1427	1095	2	decision	decision	NOUN
fuelectenerg-1427	1095	3	tree	tree	NOUN
fuelectenerg-1427	1095	4	that	that	PRON
fuelectenerg-1427	1095	5	results	result	VERB
fuelectenerg-1427	1095	6	from	from	ADP
fuelectenerg-1427	1095	7	applying	apply	VERB
fuelectenerg-1427	1095	8	any	any	PRON
fuelectenerg-1427	1095	9	of	of	ADP
fuelectenerg-1427	1095	10	the	the	DET
fuelectenerg-1427	1095	11	ternary	ternary	ADJ
fuelectenerg-1427	1095	12	davio	davio	NOUN
fuelectenerg-1427	1095	13	expansions	expansion	NOUN
fuelectenerg-1427	1095	14	(	(	PUNCT
fuelectenerg-1427	1095	15	nodes	node	NOUN
fuelectenerg-1427	1095	16	)	)	PUNCT
fuelectenerg-1427	1095	17	for	for	ADP
fuelectenerg-1427	1095	18	all	all	DET
fuelectenerg-1427	1095	19	nodes	node	NOUN
fuelectenerg-1427	1095	20	in	in	ADP
fuelectenerg-1427	1095	21	each	each	DET
fuelectenerg-1427	1095	22	level	level	NOUN
fuelectenerg-1427	1095	23	(	(	PUNCT
fuelectenerg-1427	1095	24	variable	variable	NOUN
fuelectenerg-1427	1095	25	)	)	PUNCT
fuelectenerg-1427	1095	26	in	in	ADP
fuelectenerg-1427	1095	27	the	the	DET
fuelectenerg-1427	1095	28	dt	dt	NOUN
fuelectenerg-1427	1095	29	is	be	AUX
fuelectenerg-1427	1095	30	called	call	VERB
fuelectenerg-1427	1095	31	ternary	ternary	ADJ
fuelectenerg-1427	1095	32	reed	reed	NOUN
fuelectenerg-1427	1095	33	-	-	PUNCT
fuelectenerg-1427	1095	34	muller	muller	NOUN
fuelectenerg-1427	1095	35	decision	decision	NOUN
fuelectenerg-1427	1095	36	tree	tree	NOUN
fuelectenerg-1427	1095	37	(	(	PUNCT
fuelectenerg-1427	1095	38	trmdt	trmdt	NOUN
fuelectenerg-1427	1095	39	)	)	PUNCT
fuelectenerg-1427	1095	40	.	.	PUNCT
fuelectenerg-1427	1096	1	the	the	DET
fuelectenerg-1427	1096	2	corresponding	corresponding	ADJ
fuelectenerg-1427	1096	3	expression	expression	NOUN
fuelectenerg-1427	1096	4	is	be	AUX
fuelectenerg-1427	1096	5	called	call	VERB
fuelectenerg-1427	1096	6	ternary	ternary	ADJ
fuelectenerg-1427	1096	7	fixed	fix	VERB
fuelectenerg-1427	1096	8	polarity	polarity	NOUN
fuelectenerg-1427	1096	9	reed	reed	NOUN
fuelectenerg-1427	1096	10	-	-	PUNCT
fuelectenerg-1427	1096	11	muller	muller	NOUN
fuelectenerg-1427	1096	12	(	(	PUNCT
fuelectenerg-1427	1096	13	tfprm	tfprm	ADJ
fuelectenerg-1427	1096	14	)	)	PUNCT
fuelectenerg-1427	1096	15	expression	expression	NOUN
fuelectenerg-1427	1096	16	.	.	PUNCT
fuelectenerg-1427	1097	1	definition	definition	NOUN
fuelectenerg-1427	1097	2	8	8	NUM
fuelectenerg-1427	1097	3	.	.	PUNCT
fuelectenerg-1427	1098	1	the	the	DET
fuelectenerg-1427	1098	2	decision	decision	NOUN
fuelectenerg-1427	1098	3	tree	tree	NOUN
fuelectenerg-1427	1098	4	that	that	PRON
fuelectenerg-1427	1098	5	results	result	VERB
fuelectenerg-1427	1098	6	from	from	ADP
fuelectenerg-1427	1098	7	using	use	VERB
fuelectenerg-1427	1098	8	any	any	PRON
fuelectenerg-1427	1098	9	of	of	ADP
fuelectenerg-1427	1098	10	the	the	DET
fuelectenerg-1427	1098	11	ternary	ternary	ADJ
fuelectenerg-1427	1098	12	shannon	shannon	NOUN
fuelectenerg-1427	1098	13	(	(	PUNCT
fuelectenerg-1427	1098	14	s	s	NOUN
fuelectenerg-1427	1098	15	)	)	PUNCT
fuelectenerg-1427	1098	16	or	or	CCONJ
fuelectenerg-1427	1098	17	davio	davio	NOUN
fuelectenerg-1427	1098	18	(	(	PUNCT
fuelectenerg-1427	1098	19	d0	d0	NOUN
fuelectenerg-1427	1098	20	,	,	PUNCT
fuelectenerg-1427	1098	21	d1	d1	PROPN
fuelectenerg-1427	1098	22	or	or	CCONJ
fuelectenerg-1427	1098	23	d2	d2	PROPN
fuelectenerg-1427	1098	24	)	)	PUNCT
fuelectenerg-1427	1098	25	expansions	expansion	NOUN
fuelectenerg-1427	1098	26	(	(	PUNCT
fuelectenerg-1427	1098	27	nodes	node	NOUN
fuelectenerg-1427	1098	28	)	)	PUNCT
fuelectenerg-1427	1098	29	for	for	ADP
fuelectenerg-1427	1098	30	all	all	DET
fuelectenerg-1427	1098	31	nodes	node	NOUN
fuelectenerg-1427	1098	32	in	in	ADP
fuelectenerg-1427	1098	33	each	each	DET
fuelectenerg-1427	1098	34	level	level	NOUN
fuelectenerg-1427	1098	35	(	(	PUNCT
fuelectenerg-1427	1098	36	variable	variable	NOUN
fuelectenerg-1427	1098	37	)	)	PUNCT
fuelectenerg-1427	1098	38	in	in	ADP
fuelectenerg-1427	1098	39	the	the	DET
fuelectenerg-1427	1098	40	dt	dt	X
fuelectenerg-1427	1098	41	(	(	PUNCT
fuelectenerg-1427	1098	42	that	that	PRON
fuelectenerg-1427	1098	43	has	have	AUX
fuelectenerg-1427	1098	44	fixed	fix	VERB
fuelectenerg-1427	1098	45	order	order	NOUN
fuelectenerg-1427	1098	46	of	of	ADP
fuelectenerg-1427	1098	47	variables	variable	NOUN
fuelectenerg-1427	1098	48	)	)	PUNCT
fuelectenerg-1427	1098	49	is	be	AUX
fuelectenerg-1427	1098	50	called	call	VERB
fuelectenerg-1427	1098	51	ternary	ternary	ADJ
fuelectenerg-1427	1098	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1098	53	decision	decision	NOUN
fuelectenerg-1427	1098	54	tree	tree	NOUN
fuelectenerg-1427	1098	55	(	(	PUNCT
fuelectenerg-1427	1098	56	tkrodt	tkrodt	NOUN
fuelectenerg-1427	1098	57	)	)	PUNCT
fuelectenerg-1427	1098	58	.	.	PUNCT
fuelectenerg-1427	1099	1	the	the	DET
fuelectenerg-1427	1099	2	resulting	result	VERB
fuelectenerg-1427	1099	3	expression	expression	NOUN
fuelectenerg-1427	1099	4	is	be	AUX
fuelectenerg-1427	1099	5	called	call	VERB
fuelectenerg-1427	1099	6	ternary	ternary	ADJ
fuelectenerg-1427	1099	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1099	8	expression	expression	NOUN
fuelectenerg-1427	1099	9	.	.	PUNCT
fuelectenerg-1427	1100	1	definition	definition	NOUN
fuelectenerg-1427	1100	2	9	9	NUM
fuelectenerg-1427	1100	3	.	.	PUNCT
fuelectenerg-1427	1101	1	the	the	DET
fuelectenerg-1427	1101	2	decision	decision	NOUN
fuelectenerg-1427	1101	3	tree	tree	NOUN
fuelectenerg-1427	1101	4	that	that	PRON
fuelectenerg-1427	1101	5	results	result	VERB
fuelectenerg-1427	1101	6	from	from	ADP
fuelectenerg-1427	1101	7	using	use	VERB
fuelectenerg-1427	1101	8	any	any	PRON
fuelectenerg-1427	1101	9	of	of	ADP
fuelectenerg-1427	1101	10	the	the	DET
fuelectenerg-1427	1101	11	ternary	ternary	ADJ
fuelectenerg-1427	1101	12	davio	davio	NOUN
fuelectenerg-1427	1101	13	expansions	expansion	NOUN
fuelectenerg-1427	1101	14	(	(	PUNCT
fuelectenerg-1427	1101	15	nodes	node	NOUN
fuelectenerg-1427	1101	16	)	)	PUNCT
fuelectenerg-1427	1101	17	for	for	ADP
fuelectenerg-1427	1101	18	each	each	DET
fuelectenerg-1427	1101	19	node	node	NOUN
fuelectenerg-1427	1101	20	(	(	PUNCT
fuelectenerg-1427	1101	21	per	per	ADP
fuelectenerg-1427	1101	22	level	level	NOUN
fuelectenerg-1427	1101	23	)	)	PUNCT
fuelectenerg-1427	1101	24	of	of	ADP
fuelectenerg-1427	1101	25	the	the	DET
fuelectenerg-1427	1101	26	dt	dt	NOUN
fuelectenerg-1427	1101	27	is	be	AUX
fuelectenerg-1427	1101	28	called	call	VERB
fuelectenerg-1427	1101	29	ternary	ternary	ADJ
fuelectenerg-1427	1101	30	pseudo	pseudo	NOUN
fuelectenerg-1427	1101	31	-	-	NOUN
fuelectenerg-1427	1101	32	reed112	reed112	VERB
fuelectenerg-1427	1101	33	an	an	DET
fuelectenerg-1427	1101	34	extended	extend	VERB
fuelectenerg-1427	1101	35	green	green	PROPN
fuelectenerg-1427	1101	36	sasao	sasao	PROPN
fuelectenerg-1427	1101	37	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1101	38	of	of	ADP
fuelectenerg-1427	1101	39	canonical	canonical	ADJ
fuelectenerg-1427	1101	40	ternary	ternary	ADJ
fuelectenerg-1427	1101	41	galois	galois	NOUN
fuelectenerg-1427	1101	42	forms	form	NOUN
fuelectenerg-1427	1101	43	...	...	PUNCT
fuelectenerg-1427	1101	44	definition	definition	NOUN
fuelectenerg-1427	1101	45	4	4	NUM
fuelectenerg-1427	1101	46	.	.	PUNCT
fuelectenerg-1427	1102	1	the	the	DET
fuelectenerg-1427	1102	2	family	family	NOUN
fuelectenerg-1427	1102	3	of	of	ADP
fuelectenerg-1427	1102	4	forms	form	NOUN
fuelectenerg-1427	1102	5	,	,	PUNCT
fuelectenerg-1427	1102	6	generated	generate	VERB
fuelectenerg-1427	1102	7	by	by	ADP
fuelectenerg-1427	1102	8	s	s	PROPN
fuelectenerg-1427	1102	9	/	/	SYM
fuelectenerg-1427	1102	10	d	d	NOUN
fuelectenerg-1427	1102	11	tree	tree	NOUN
fuelectenerg-1427	1102	12	with	with	ADP
fuelectenerg-1427	1102	13	no	no	DET
fuelectenerg-1427	1102	14	fixed	fix	VERB
fuelectenerg-1427	1102	15	ordering	ordering	NOUN
fuelectenerg-1427	1102	16	of	of	ADP
fuelectenerg-1427	1102	17	variables	variable	NOUN
fuelectenerg-1427	1102	18	,	,	PUNCT
fuelectenerg-1427	1102	19	with	with	ADP
fuelectenerg-1427	1102	20	variables	variable	NOUN
fuelectenerg-1427	1102	21	not	not	PART
fuelectenerg-1427	1102	22	repeated	repeat	VERB
fuelectenerg-1427	1102	23	along	along	ADP
fuelectenerg-1427	1102	24	same	same	ADJ
fuelectenerg-1427	1102	25	branches	branch	NOUN
fuelectenerg-1427	1102	26	,	,	PUNCT
fuelectenerg-1427	1102	27	is	be	AUX
fuelectenerg-1427	1102	28	called	call	VERB
fuelectenerg-1427	1102	29	ternary	ternary	ADJ
fuelectenerg-1427	1102	30	free	free	ADJ
fuelectenerg-1427	1102	31	generalized	generalize	VERB
fuelectenerg-1427	1102	32	inclusive	inclusive	ADJ
fuelectenerg-1427	1102	33	forms	form	NOUN
fuelectenerg-1427	1102	34	(	(	PUNCT
fuelectenerg-1427	1102	35	tfgifs	tfgifs	PROPN
fuelectenerg-1427	1102	36	)	)	PUNCT
fuelectenerg-1427	1102	37	.	.	PUNCT
fuelectenerg-1427	1103	1	2.3	2.3	NUM
fuelectenerg-1427	1103	2	an	an	DET
fuelectenerg-1427	1103	3	extended	extended	ADJ
fuelectenerg-1427	1103	4	green	green	ADJ
fuelectenerg-1427	1103	5	-	-	PUNCT
fuelectenerg-1427	1103	6	sasao	sasao	NOUN
fuelectenerg-1427	1103	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1103	8	with	with	ADP
fuelectenerg-1427	1103	9	a	a	DET
fuelectenerg-1427	1103	10	new	new	ADJ
fuelectenerg-1427	1103	11	sub	sub	NOUN
fuelectenerg-1427	1103	12	-	-	NOUN
fuelectenerg-1427	1103	13	family	family	NOUN
fuelectenerg-1427	1103	14	for	for	ADP
fuelectenerg-1427	1103	15	ternary	ternary	ADJ
fuelectenerg-1427	1103	16	reed	reed	NOUN
fuelectenerg-1427	1103	17	-	-	PUNCT
fuelectenerg-1427	1103	18	muller	muller	NOUN
fuelectenerg-1427	1103	19	logic	logic	NOUN
fuelectenerg-1427	1103	20	the	the	DET
fuelectenerg-1427	1103	21	green	green	PROPN
fuelectenerg-1427	1103	22	-	-	PUNCT
fuelectenerg-1427	1103	23	sasao	sasao	PROPN
fuelectenerg-1427	1103	24	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1103	25	of	of	ADP
fuelectenerg-1427	1103	26	families	family	NOUN
fuelectenerg-1427	1103	27	of	of	ADP
fuelectenerg-1427	1103	28	canonical	canonical	ADJ
fuelectenerg-1427	1103	29	forms	form	NOUN
fuelectenerg-1427	1103	30	[	[	X
fuelectenerg-1427	1103	31	1	1	NUM
fuelectenerg-1427	1103	32	,	,	PUNCT
fuelectenerg-1427	1103	33	10	10	NUM
fuelectenerg-1427	1103	34	-	-	SYM
fuelectenerg-1427	1103	35	13	13	NUM
fuelectenerg-1427	1103	36	,	,	PUNCT
fuelectenerg-1427	1103	37	17	17	NUM
fuelectenerg-1427	1103	38	,	,	PUNCT
fuelectenerg-1427	1103	39	24	24	NUM
fuelectenerg-1427	1103	40	,	,	PUNCT
fuelectenerg-1427	1103	41	26	26	NUM
fuelectenerg-1427	1103	42	]	]	PUNCT
fuelectenerg-1427	1103	43	and	and	CCONJ
fuelectenerg-1427	1103	44	the	the	DET
fuelectenerg-1427	1103	45	corresponding	correspond	VERB
fuelectenerg-1427	1103	46	decision	decision	NOUN
fuelectenerg-1427	1103	47	trees	tree	NOUN
fuelectenerg-1427	1103	48	and	and	CCONJ
fuelectenerg-1427	1103	49	diagrams	diagram	NOUN
fuelectenerg-1427	1103	50	is	be	AUX
fuelectenerg-1427	1103	51	based	base	VERB
fuelectenerg-1427	1103	52	on	on	ADP
fuelectenerg-1427	1103	53	three	three	NUM
fuelectenerg-1427	1103	54	generic	generic	ADJ
fuelectenerg-1427	1103	55	expansions	expansion	NOUN
fuelectenerg-1427	1103	56	,	,	PUNCT
fuelectenerg-1427	1103	57	shannon	shannon	PROPN
fuelectenerg-1427	1103	58	,	,	PUNCT
fuelectenerg-1427	1103	59	positive	positive	ADJ
fuelectenerg-1427	1103	60	and	and	CCONJ
fuelectenerg-1427	1103	61	negative	negative	ADJ
fuelectenerg-1427	1103	62	davio	davio	NOUN
fuelectenerg-1427	1103	63	expansions	expansion	NOUN
fuelectenerg-1427	1103	64	.	.	PUNCT
fuelectenerg-1427	1104	1	for	for	ADP
fuelectenerg-1427	1104	2	example	example	NOUN
fuelectenerg-1427	1104	3	,	,	PUNCT
fuelectenerg-1427	1104	4	this	this	PRON
fuelectenerg-1427	1104	5	includes	include	VERB
fuelectenerg-1427	1104	6	shannon	shannon	ADJ
fuelectenerg-1427	1104	7	decision	decision	NOUN
fuelectenerg-1427	1104	8	trees	tree	NOUN
fuelectenerg-1427	1104	9	and	and	CCONJ
fuelectenerg-1427	1104	10	diagrams	diagram	NOUN
fuelectenerg-1427	1104	11	,	,	PUNCT
fuelectenerg-1427	1104	12	positive	positive	ADJ
fuelectenerg-1427	1104	13	and	and	CCONJ
fuelectenerg-1427	1104	14	negative	negative	ADJ
fuelectenerg-1427	1104	15	davio	davio	NOUN
fuelectenerg-1427	1104	16	decision	decision	NOUN
fuelectenerg-1427	1104	17	trees	tree	NOUN
fuelectenerg-1427	1104	18	and	and	CCONJ
fuelectenerg-1427	1104	19	diagrams	diagram	NOUN
fuelectenerg-1427	1104	20	,	,	PUNCT
fuelectenerg-1427	1104	21	fixed	fix	VERB
fuelectenerg-1427	1104	22	polarity	polarity	NOUN
fuelectenerg-1427	1104	23	reed	reed	NOUN
fuelectenerg-1427	1104	24	-	-	PUNCT
fuelectenerg-1427	1104	25	muller	muller	NOUN
fuelectenerg-1427	1104	26	decision	decision	NOUN
fuelectenerg-1427	1104	27	trees	tree	NOUN
fuelectenerg-1427	1104	28	and	and	CCONJ
fuelectenerg-1427	1104	29	diagrams	diagram	NOUN
fuelectenerg-1427	1104	30	,	,	PUNCT
fuelectenerg-1427	1104	31	kronecker	kronecker	NOUN
fuelectenerg-1427	1104	32	decision	decision	NOUN
fuelectenerg-1427	1104	33	trees	tree	NOUN
fuelectenerg-1427	1104	34	and	and	CCONJ
fuelectenerg-1427	1104	35	diagrams	diagram	NOUN
fuelectenerg-1427	1104	36	,	,	PUNCT
fuelectenerg-1427	1104	37	pseudo	pseudo	NOUN
fuelectenerg-1427	1104	38	reed	reed	NOUN
fuelectenerg-1427	1104	39	-	-	PUNCT
fuelectenerg-1427	1104	40	muller	muller	NOUN
fuelectenerg-1427	1104	41	decision	decision	NOUN
fuelectenerg-1427	1104	42	trees	tree	NOUN
fuelectenerg-1427	1104	43	and	and	CCONJ
fuelectenerg-1427	1104	44	diagrams	diagram	NOUN
fuelectenerg-1427	1104	45	,	,	PUNCT
fuelectenerg-1427	1104	46	pseudo	pseudo	NOUN
fuelectenerg-1427	1104	47	kronecker	kronecker	NOUN
fuelectenerg-1427	1104	48	decision	decision	NOUN
fuelectenerg-1427	1104	49	trees	tree	NOUN
fuelectenerg-1427	1104	50	and	and	CCONJ
fuelectenerg-1427	1104	51	diagrams	diagram	NOUN
fuelectenerg-1427	1104	52	,	,	PUNCT
fuelectenerg-1427	1104	53	and	and	CCONJ
fuelectenerg-1427	1104	54	linearly	linearly	ADV
fuelectenerg-1427	1104	55	-	-	PUNCT
fuelectenerg-1427	1104	56	independent	independent	ADJ
fuelectenerg-1427	1104	57	decision	decision	NOUN
fuelectenerg-1427	1104	58	trees	tree	NOUN
fuelectenerg-1427	1104	59	and	and	CCONJ
fuelectenerg-1427	1104	60	diagrams	diagram	NOUN
fuelectenerg-1427	1105	1	[	[	X
fuelectenerg-1427	1105	2	1	1	NUM
fuelectenerg-1427	1105	3	,	,	PUNCT
fuelectenerg-1427	1105	4	17	17	NUM
fuelectenerg-1427	1105	5	,	,	PUNCT
fuelectenerg-1427	1105	6	24	24	NUM
fuelectenerg-1427	1105	7	]	]	PUNCT
fuelectenerg-1427	1105	8	.	.	PUNCT
fuelectenerg-1427	1106	1	a	a	DET
fuelectenerg-1427	1106	2	set	set	VERB
fuelectenerg-1427	1106	3	-	-	PUNCT
fuelectenerg-1427	1106	4	theoretic	theoretic	NOUN
fuelectenerg-1427	1106	5	relationship	relationship	NOUN
fuelectenerg-1427	1106	6	between	between	ADP
fuelectenerg-1427	1106	7	families	family	NOUN
fuelectenerg-1427	1106	8	of	of	ADP
fuelectenerg-1427	1106	9	canonical	canonical	ADJ
fuelectenerg-1427	1106	10	forms	form	NOUN
fuelectenerg-1427	1106	11	over	over	ADP
fuelectenerg-1427	1106	12	gf(2	gf(2	PROPN
fuelectenerg-1427	1106	13	)	)	PUNCT
fuelectenerg-1427	1106	14	was	be	AUX
fuelectenerg-1427	1106	15	proposed	propose	VERB
fuelectenerg-1427	1106	16	and	and	CCONJ
fuelectenerg-1427	1106	17	extended	extend	VERB
fuelectenerg-1427	1106	18	by	by	ADP
fuelectenerg-1427	1106	19	introducing	introduce	VERB
fuelectenerg-1427	1106	20	binary	binary	NOUN
fuelectenerg-1427	1106	21	if	if	SCONJ
fuelectenerg-1427	1106	22	,	,	PUNCT
fuelectenerg-1427	1106	23	gif	gif	NOUN
fuelectenerg-1427	1106	24	and	and	CCONJ
fuelectenerg-1427	1106	25	free	free	ADJ
fuelectenerg-1427	1106	26	gif	gif	NOUN
fuelectenerg-1427	1106	27	(	(	PUNCT
fuelectenerg-1427	1106	28	fgif	fgif	NOUN
fuelectenerg-1427	1106	29	)	)	PUNCT
fuelectenerg-1427	1106	30	forms	form	NOUN
fuelectenerg-1427	1106	31	where	where	SCONJ
fuelectenerg-1427	1106	32	figure	figure	NOUN
fuelectenerg-1427	1106	33	6(a	6(a	NUM
fuelectenerg-1427	1106	34	)	)	PUNCT
fuelectenerg-1427	1106	35	illustrates	illustrate	VERB
fuelectenerg-1427	1106	36	set	set	VERB
fuelectenerg-1427	1106	37	-	-	PUNCT
fuelectenerg-1427	1106	38	theoretic	theoretic	NOUN
fuelectenerg-1427	1106	39	relationship	relationship	NOUN
fuelectenerg-1427	1106	40	between	between	ADP
fuelectenerg-1427	1106	41	the	the	DET
fuelectenerg-1427	1106	42	various	various	ADJ
fuelectenerg-1427	1106	43	families	family	NOUN
fuelectenerg-1427	1106	44	of	of	ADP
fuelectenerg-1427	1106	45	canonical	canonical	ADJ
fuelectenerg-1427	1106	46	forms	form	NOUN
fuelectenerg-1427	1106	47	over	over	ADP
fuelectenerg-1427	1106	48	gf(2	gf(2	PROPN
fuelectenerg-1427	1106	49	)	)	PUNCT
fuelectenerg-1427	1106	50	.	.	PUNCT
fuelectenerg-1427	1107	1	analogously	analogously	ADV
fuelectenerg-1427	1107	2	to	to	ADP
fuelectenerg-1427	1107	3	the	the	DET
fuelectenerg-1427	1107	4	green	green	ADJ
fuelectenerg-1427	1107	5	-	-	PUNCT
fuelectenerg-1427	1107	6	sasao	sasao	PROPN
fuelectenerg-1427	1107	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1107	8	of	of	ADP
fuelectenerg-1427	1107	9	binary	binary	PROPN
fuelectenerg-1427	1107	10	reed	reed	PROPN
fuelectenerg-1427	1107	11	-	-	PUNCT
fuelectenerg-1427	1107	12	muller	muller	NOUN
fuelectenerg-1427	1107	13	families	family	NOUN
fuelectenerg-1427	1107	14	of	of	ADP
fuelectenerg-1427	1107	15	spectral	spectral	ADJ
fuelectenerg-1427	1107	16	transforms	transform	VERB
fuelectenerg-1427	1107	17	over	over	ADP
fuelectenerg-1427	1107	18	gf(2	gf(2	PROPN
fuelectenerg-1427	1107	19	)	)	PUNCT
fuelectenerg-1427	1107	20	that	that	PRON
fuelectenerg-1427	1107	21	is	be	AUX
fuelectenerg-1427	1107	22	shown	show	VERB
fuelectenerg-1427	1107	23	in	in	ADP
fuelectenerg-1427	1107	24	figure	figure	NOUN
fuelectenerg-1427	1107	25	6(a	6(a	NUM
fuelectenerg-1427	1107	26	)	)	PUNCT
fuelectenerg-1427	1107	27	,	,	PUNCT
fuelectenerg-1427	1107	28	we	we	PRON
fuelectenerg-1427	1107	29	will	will	AUX
fuelectenerg-1427	1107	30	introduce	introduce	VERB
fuelectenerg-1427	1107	31	the	the	DET
fuelectenerg-1427	1107	32	extended	extended	ADJ
fuelectenerg-1427	1107	33	green	green	ADJ
fuelectenerg-1427	1107	34	-	-	PUNCT
fuelectenerg-1427	1107	35	sasao	sasao	NOUN
fuelectenerg-1427	1107	36	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1107	37	of	of	ADP
fuelectenerg-1427	1107	38	spectral	spectral	ADJ
fuelectenerg-1427	1107	39	transforms	transform	NOUN
fuelectenerg-1427	1107	40	,	,	PUNCT
fuelectenerg-1427	1107	41	with	with	ADP
fuelectenerg-1427	1107	42	a	a	DET
fuelectenerg-1427	1107	43	new	new	ADJ
fuelectenerg-1427	1107	44	sub	sub	NOUN
fuelectenerg-1427	1107	45	-	-	NOUN
fuelectenerg-1427	1107	46	family	family	NOUN
fuelectenerg-1427	1107	47	for	for	ADP
fuelectenerg-1427	1107	48	ternary	ternary	ADJ
fuelectenerg-1427	1107	49	reedmuller	reedmuller	NOUN
fuelectenerg-1427	1107	50	logic	logic	NOUN
fuelectenerg-1427	1107	51	over	over	ADP
fuelectenerg-1427	1107	52	gf(3	gf(3	PROPN
fuelectenerg-1427	1107	53	)	)	PUNCT
fuelectenerg-1427	1107	54	.	.	PUNCT
fuelectenerg-1427	1108	1	while	while	SCONJ
fuelectenerg-1427	1108	2	definitions	definition	NOUN
fuelectenerg-1427	1108	3	2	2	NUM
fuelectenerg-1427	1108	4	4	4	NUM
fuelectenerg-1427	1108	5	defined	define	VERB
fuelectenerg-1427	1108	6	the	the	DET
fuelectenerg-1427	1108	7	ternary	ternary	ADJ
fuelectenerg-1427	1108	8	inclusive	inclusive	ADJ
fuelectenerg-1427	1108	9	forms	form	NOUN
fuelectenerg-1427	1108	10	,	,	PUNCT
fuelectenerg-1427	1108	11	ternary	ternary	ADJ
fuelectenerg-1427	1108	12	generalized	generalize	VERB
fuelectenerg-1427	1108	13	inclusive	inclusive	ADJ
fuelectenerg-1427	1108	14	forms	form	NOUN
fuelectenerg-1427	1108	15	and	and	CCONJ
fuelectenerg-1427	1108	16	ternary	ternary	ADJ
fuelectenerg-1427	1108	17	free	free	ADJ
fuelectenerg-1427	1108	18	generalized	generalized	ADJ
fuelectenerg-1427	1108	19	inclusive	inclusive	ADJ
fuelectenerg-1427	1108	20	forms	form	NOUN
fuelectenerg-1427	1108	21	,	,	PUNCT
fuelectenerg-1427	1108	22	respectively	respectively	ADV
fuelectenerg-1427	1108	23	,	,	PUNCT
fuelectenerg-1427	1108	24	and	and	CCONJ
fuelectenerg-1427	1108	25	analogously	analogously	ADV
fuelectenerg-1427	1108	26	to	to	ADP
fuelectenerg-1427	1108	27	the	the	DET
fuelectenerg-1427	1108	28	binary	binary	PROPN
fuelectenerg-1427	1108	29	reed	reed	PROPN
fuelectenerg-1427	1108	30	-	-	PUNCT
fuelectenerg-1427	1108	31	muller	muller	NOUN
fuelectenerg-1427	1108	32	case	case	NOUN
fuelectenerg-1427	1108	33	,	,	PUNCT
fuelectenerg-1427	1108	34	the	the	DET
fuelectenerg-1427	1108	35	following	follow	VERB
fuelectenerg-1427	1108	36	definitions	definition	NOUN
fuelectenerg-1427	1108	37	are	be	AUX
fuelectenerg-1427	1108	38	introduced	introduce	VERB
fuelectenerg-1427	1108	39	for	for	ADP
fuelectenerg-1427	1108	40	the	the	DET
fuelectenerg-1427	1108	41	corresponding	corresponding	ADJ
fuelectenerg-1427	1108	42	canonical	canonical	ADJ
fuelectenerg-1427	1108	43	expressions	expression	NOUN
fuelectenerg-1427	1108	44	over	over	ADP
fuelectenerg-1427	1108	45	gf(3	gf(3	PROPN
fuelectenerg-1427	1108	46	)	)	PUNCT
fuelectenerg-1427	1108	47	.	.	PUNCT
fuelectenerg-1427	1109	1	definition	definition	NOUN
fuelectenerg-1427	1109	2	5	5	NUM
fuelectenerg-1427	1109	3	.	.	PUNCT
fuelectenerg-1427	1110	1	the	the	DET
fuelectenerg-1427	1110	2	decision	decision	NOUN
fuelectenerg-1427	1110	3	tree	tree	NOUN
fuelectenerg-1427	1110	4	that	that	PRON
fuelectenerg-1427	1110	5	results	result	VERB
fuelectenerg-1427	1110	6	from	from	ADP
fuelectenerg-1427	1110	7	applying	apply	VERB
fuelectenerg-1427	1110	8	the	the	DET
fuelectenerg-1427	1110	9	ternary	ternary	ADJ
fuelectenerg-1427	1110	10	shannon	shannon	NOUN
fuelectenerg-1427	1110	11	expansion	expansion	NOUN
fuelectenerg-1427	1110	12	in	in	ADP
fuelectenerg-1427	1110	13	equation	equation	NOUN
fuelectenerg-1427	1110	14	(	(	PUNCT
fuelectenerg-1427	1110	15	23	23	NUM
fuelectenerg-1427	1110	16	)	)	PUNCT
fuelectenerg-1427	1110	17	recursively	recursively	ADV
fuelectenerg-1427	1110	18	to	to	ADP
fuelectenerg-1427	1110	19	a	a	DET
fuelectenerg-1427	1110	20	ternary	ternary	ADJ
fuelectenerg-1427	1110	21	input	input	NOUN
fuelectenerg-1427	1110	22	-	-	PUNCT
fuelectenerg-1427	1110	23	ternary	ternary	ADJ
fuelectenerg-1427	1110	24	output	output	NOUN
fuelectenerg-1427	1110	25	logic	logic	NOUN
fuelectenerg-1427	1110	26	function	function	NOUN
fuelectenerg-1427	1110	27	(	(	PUNCT
fuelectenerg-1427	1110	28	i.e.	i.e.	X
fuelectenerg-1427	1110	29	,	,	PUNCT
fuelectenerg-1427	1110	30	all	all	DET
fuelectenerg-1427	1110	31	levels	level	NOUN
fuelectenerg-1427	1110	32	in	in	ADP
fuelectenerg-1427	1110	33	a	a	DET
fuelectenerg-1427	1110	34	dt	dt	NOUN
fuelectenerg-1427	1110	35	)	)	PUNCT
fuelectenerg-1427	1110	36	is	be	AUX
fuelectenerg-1427	1110	37	called	call	VERB
fuelectenerg-1427	1110	38	ternary	ternary	ADJ
fuelectenerg-1427	1110	39	shannon	shannon	PROPN
fuelectenerg-1427	1110	40	decision	decision	NOUN
fuelectenerg-1427	1110	41	tree	tree	NOUN
fuelectenerg-1427	1110	42	(	(	PUNCT
fuelectenerg-1427	1110	43	tsdt	tsdt	NOUN
fuelectenerg-1427	1110	44	)	)	PUNCT
fuelectenerg-1427	1110	45	.	.	PUNCT
fuelectenerg-1427	1111	1	the	the	DET
fuelectenerg-1427	1111	2	result	result	NOUN
fuelectenerg-1427	1111	3	expression	expression	NOUN
fuelectenerg-1427	1111	4	(	(	PUNCT
fuelectenerg-1427	1111	5	flattened	flatten	VERB
fuelectenerg-1427	1111	6	form	form	NOUN
fuelectenerg-1427	1111	7	)	)	PUNCT
fuelectenerg-1427	1111	8	from	from	ADP
fuelectenerg-1427	1111	9	the	the	DET
fuelectenerg-1427	1111	10	tsdt	tsdt	NOUN
fuelectenerg-1427	1111	11	is	be	AUX
fuelectenerg-1427	1111	12	called	call	VERB
fuelectenerg-1427	1111	13	ternary	ternary	ADJ
fuelectenerg-1427	1111	14	shannon	shannon	NOUN
fuelectenerg-1427	1111	15	expression	expression	NOUN
fuelectenerg-1427	1111	16	.	.	PUNCT
fuelectenerg-1427	1112	1	definition	definition	NOUN
fuelectenerg-1427	1112	2	6	6	NUM
fuelectenerg-1427	1112	3	.	.	PUNCT
fuelectenerg-1427	1113	1	the	the	DET
fuelectenerg-1427	1113	2	decision	decision	NOUN
fuelectenerg-1427	1113	3	trees	tree	NOUN
fuelectenerg-1427	1113	4	that	that	PRON
fuelectenerg-1427	1113	5	result	result	VERB
fuelectenerg-1427	1113	6	from	from	ADP
fuelectenerg-1427	1113	7	applying	apply	VERB
fuelectenerg-1427	1113	8	the	the	DET
fuelectenerg-1427	1113	9	ternary	ternary	ADJ
fuelectenerg-1427	1113	10	davio	davio	NOUN
fuelectenerg-1427	1113	11	expansions	expansion	NOUN
fuelectenerg-1427	1113	12	in	in	ADP
fuelectenerg-1427	1113	13	equations	equation	NOUN
fuelectenerg-1427	1113	14	(	(	PUNCT
fuelectenerg-1427	1113	15	24	24	NUM
fuelectenerg-1427	1113	16	)	)	PUNCT
fuelectenerg-1427	1113	17	(	(	PUNCT
fuelectenerg-1427	1113	18	26	26	NUM
fuelectenerg-1427	1113	19	)	)	PUNCT
fuelectenerg-1427	1113	20	recursively	recursively	ADV
fuelectenerg-1427	1113	21	to	to	ADP
fuelectenerg-1427	1113	22	a	a	DET
fuelectenerg-1427	1113	23	ternary	ternary	ADJ
fuelectenerg-1427	1113	24	-	-	PUNCT
fuelectenerg-1427	1113	25	input	input	NOUN
fuelectenerg-1427	1113	26	ternary	ternary	ADJ
fuelectenerg-1427	1113	27	-	-	PUNCT
fuelectenerg-1427	1113	28	output	output	NOUN
fuelectenerg-1427	1113	29	logic	logic	NOUN
fuelectenerg-1427	1113	30	function	function	NOUN
fuelectenerg-1427	1113	31	(	(	PUNCT
fuelectenerg-1427	1113	32	i.e.	i.e.	X
fuelectenerg-1427	1113	33	,	,	PUNCT
fuelectenerg-1427	1113	34	all	all	DET
fuelectenerg-1427	1113	35	levels	level	NOUN
fuelectenerg-1427	1113	36	in	in	ADP
fuelectenerg-1427	1113	37	a	a	DET
fuelectenerg-1427	1113	38	dt	dt	NOUN
fuelectenerg-1427	1113	39	)	)	PUNCT
fuelectenerg-1427	1113	40	are	be	AUX
fuelectenerg-1427	1113	41	called	call	VERB
fuelectenerg-1427	1113	42	:	:	PUNCT
fuelectenerg-1427	1113	43	ternary	ternary	ADJ
fuelectenerg-1427	1113	44	zero	zero	NUM
fuelectenerg-1427	1113	45	-	-	PUNCT
fuelectenerg-1427	1113	46	polarity	polarity	NOUN
fuelectenerg-1427	1113	47	davio	davio	NOUN
fuelectenerg-1427	1113	48	decision	decision	NOUN
fuelectenerg-1427	1113	49	tree	tree	NOUN
fuelectenerg-1427	1113	50	(	(	PUNCT
fuelectenerg-1427	1113	51	td0dt	td0dt	NOUN
fuelectenerg-1427	1113	52	)	)	PUNCT
fuelectenerg-1427	1113	53	,	,	PUNCT
fuelectenerg-1427	1113	54	ternary	ternary	ADJ
fuelectenerg-1427	1113	55	first	first	ADJ
fuelectenerg-1427	1113	56	-	-	PUNCT
fuelectenerg-1427	1113	57	polarity	polarity	NOUN
fuelectenerg-1427	1113	58	davio	davio	NOUN
fuelectenerg-1427	1113	59	decision	decision	NOUN
fuelectenerg-1427	1113	60	tree	tree	NOUN
fuelectenerg-1427	1113	61	(	(	PUNCT
fuelectenerg-1427	1113	62	td1dt	td1dt	NUM
fuelectenerg-1427	1113	63	)	)	PUNCT
fuelectenerg-1427	1113	64	and	and	CCONJ
fuelectenerg-1427	1113	65	ternary	ternary	ADJ
fuelectenerg-1427	1113	66	secondpolarity	secondpolarity	NOUN
fuelectenerg-1427	1113	67	davio	davio	NOUN
fuelectenerg-1427	1113	68	decision	decision	NOUN
fuelectenerg-1427	1113	69	tree	tree	NOUN
fuelectenerg-1427	1113	70	(	(	PUNCT
fuelectenerg-1427	1113	71	td2dt	td2dt	NUM
fuelectenerg-1427	1113	72	)	)	PUNCT
fuelectenerg-1427	1113	73	,	,	PUNCT
fuelectenerg-1427	1113	74	respectively	respectively	ADV
fuelectenerg-1427	1113	75	.	.	PUNCT
fuelectenerg-1427	1114	1	the	the	DET
fuelectenerg-1427	1114	2	resulting	result	VERB
fuelectenerg-1427	1114	3	expressions	expression	NOUN
fuelectenerg-1427	1114	4	(	(	PUNCT
fuelectenerg-1427	1114	5	flattened	flatten	VERB
fuelectenerg-1427	1114	6	forms	form	NOUN
fuelectenerg-1427	1114	7	)	)	PUNCT
fuelectenerg-1427	1114	8	from	from	ADP
fuelectenerg-1427	1114	9	td0dt	td0dt	PROPN
fuelectenerg-1427	1114	10	,	,	PUNCT
fuelectenerg-1427	1114	11	td1dt	td1dt	NUM
fuelectenerg-1427	1114	12	and	and	CCONJ
fuelectenerg-1427	1114	13	td2dt	td2dt	NUM
fuelectenerg-1427	1114	14	are	be	AUX
fuelectenerg-1427	1114	15	called	call	VERB
fuelectenerg-1427	1114	16	td0	td0	NOUN
fuelectenerg-1427	1114	17	,	,	PUNCT
fuelectenerg-1427	1114	18	td1	td1	PROPN
fuelectenerg-1427	1114	19	and	and	CCONJ
fuelectenerg-1427	1114	20	td2	td2	PROPN
fuelectenerg-1427	1114	21	expressions	expression	NOUN
fuelectenerg-1427	1114	22	,	,	PUNCT
fuelectenerg-1427	1114	23	respectively	respectively	ADV
fuelectenerg-1427	1114	24	.	.	PUNCT
fuelectenerg-1427	1115	1	definition	definition	NOUN
fuelectenerg-1427	1115	2	7	7	NUM
fuelectenerg-1427	1115	3	.	.	PUNCT
fuelectenerg-1427	1116	1	the	the	DET
fuelectenerg-1427	1116	2	decision	decision	NOUN
fuelectenerg-1427	1116	3	tree	tree	NOUN
fuelectenerg-1427	1116	4	that	that	PRON
fuelectenerg-1427	1116	5	results	result	VERB
fuelectenerg-1427	1116	6	from	from	ADP
fuelectenerg-1427	1116	7	applying	apply	VERB
fuelectenerg-1427	1116	8	any	any	PRON
fuelectenerg-1427	1116	9	of	of	ADP
fuelectenerg-1427	1116	10	the	the	DET
fuelectenerg-1427	1116	11	ternary	ternary	ADJ
fuelectenerg-1427	1116	12	davio	davio	NOUN
fuelectenerg-1427	1116	13	expansions	expansion	NOUN
fuelectenerg-1427	1116	14	(	(	PUNCT
fuelectenerg-1427	1116	15	nodes	node	NOUN
fuelectenerg-1427	1116	16	)	)	PUNCT
fuelectenerg-1427	1116	17	for	for	ADP
fuelectenerg-1427	1116	18	all	all	DET
fuelectenerg-1427	1116	19	nodes	node	NOUN
fuelectenerg-1427	1116	20	in	in	ADP
fuelectenerg-1427	1116	21	each	each	DET
fuelectenerg-1427	1116	22	level	level	NOUN
fuelectenerg-1427	1116	23	(	(	PUNCT
fuelectenerg-1427	1116	24	variable	variable	NOUN
fuelectenerg-1427	1116	25	)	)	PUNCT
fuelectenerg-1427	1116	26	in	in	ADP
fuelectenerg-1427	1116	27	the	the	DET
fuelectenerg-1427	1116	28	dt	dt	NOUN
fuelectenerg-1427	1116	29	is	be	AUX
fuelectenerg-1427	1116	30	called	call	VERB
fuelectenerg-1427	1116	31	ternary	ternary	ADJ
fuelectenerg-1427	1116	32	reed	reed	NOUN
fuelectenerg-1427	1116	33	-	-	PUNCT
fuelectenerg-1427	1116	34	muller	muller	NOUN
fuelectenerg-1427	1116	35	decision	decision	NOUN
fuelectenerg-1427	1116	36	tree	tree	NOUN
fuelectenerg-1427	1116	37	(	(	PUNCT
fuelectenerg-1427	1116	38	trmdt	trmdt	NOUN
fuelectenerg-1427	1116	39	)	)	PUNCT
fuelectenerg-1427	1116	40	.	.	PUNCT
fuelectenerg-1427	1117	1	the	the	DET
fuelectenerg-1427	1117	2	corresponding	corresponding	ADJ
fuelectenerg-1427	1117	3	expression	expression	NOUN
fuelectenerg-1427	1117	4	is	be	AUX
fuelectenerg-1427	1117	5	called	call	VERB
fuelectenerg-1427	1117	6	ternary	ternary	ADJ
fuelectenerg-1427	1117	7	fixed	fix	VERB
fuelectenerg-1427	1117	8	polarity	polarity	NOUN
fuelectenerg-1427	1117	9	reed	reed	NOUN
fuelectenerg-1427	1117	10	-	-	PUNCT
fuelectenerg-1427	1117	11	muller	muller	NOUN
fuelectenerg-1427	1117	12	(	(	PUNCT
fuelectenerg-1427	1117	13	tfprm	tfprm	ADJ
fuelectenerg-1427	1117	14	)	)	PUNCT
fuelectenerg-1427	1117	15	expression	expression	NOUN
fuelectenerg-1427	1117	16	.	.	PUNCT
fuelectenerg-1427	1118	1	definition	definition	NOUN
fuelectenerg-1427	1118	2	8	8	NUM
fuelectenerg-1427	1118	3	.	.	PUNCT
fuelectenerg-1427	1119	1	the	the	DET
fuelectenerg-1427	1119	2	decision	decision	NOUN
fuelectenerg-1427	1119	3	tree	tree	NOUN
fuelectenerg-1427	1119	4	that	that	PRON
fuelectenerg-1427	1119	5	results	result	VERB
fuelectenerg-1427	1119	6	from	from	ADP
fuelectenerg-1427	1119	7	using	use	VERB
fuelectenerg-1427	1119	8	any	any	PRON
fuelectenerg-1427	1119	9	of	of	ADP
fuelectenerg-1427	1119	10	the	the	DET
fuelectenerg-1427	1119	11	ternary	ternary	ADJ
fuelectenerg-1427	1119	12	shannon	shannon	NOUN
fuelectenerg-1427	1119	13	(	(	PUNCT
fuelectenerg-1427	1119	14	s	s	NOUN
fuelectenerg-1427	1119	15	)	)	PUNCT
fuelectenerg-1427	1119	16	or	or	CCONJ
fuelectenerg-1427	1119	17	davio	davio	NOUN
fuelectenerg-1427	1119	18	(	(	PUNCT
fuelectenerg-1427	1119	19	d0	d0	NOUN
fuelectenerg-1427	1119	20	,	,	PUNCT
fuelectenerg-1427	1119	21	d1	d1	PROPN
fuelectenerg-1427	1119	22	or	or	CCONJ
fuelectenerg-1427	1119	23	d2	d2	PROPN
fuelectenerg-1427	1119	24	)	)	PUNCT
fuelectenerg-1427	1119	25	expansions	expansion	NOUN
fuelectenerg-1427	1119	26	(	(	PUNCT
fuelectenerg-1427	1119	27	nodes	node	NOUN
fuelectenerg-1427	1119	28	)	)	PUNCT
fuelectenerg-1427	1119	29	for	for	ADP
fuelectenerg-1427	1119	30	all	all	DET
fuelectenerg-1427	1119	31	nodes	node	NOUN
fuelectenerg-1427	1119	32	in	in	ADP
fuelectenerg-1427	1119	33	each	each	DET
fuelectenerg-1427	1119	34	level	level	NOUN
fuelectenerg-1427	1119	35	(	(	PUNCT
fuelectenerg-1427	1119	36	variable	variable	NOUN
fuelectenerg-1427	1119	37	)	)	PUNCT
fuelectenerg-1427	1119	38	in	in	ADP
fuelectenerg-1427	1119	39	the	the	DET
fuelectenerg-1427	1119	40	dt	dt	X
fuelectenerg-1427	1119	41	(	(	PUNCT
fuelectenerg-1427	1119	42	that	that	PRON
fuelectenerg-1427	1119	43	has	have	AUX
fuelectenerg-1427	1119	44	fixed	fix	VERB
fuelectenerg-1427	1119	45	order	order	NOUN
fuelectenerg-1427	1119	46	of	of	ADP
fuelectenerg-1427	1119	47	variables	variable	NOUN
fuelectenerg-1427	1119	48	)	)	PUNCT
fuelectenerg-1427	1119	49	is	be	AUX
fuelectenerg-1427	1119	50	called	call	VERB
fuelectenerg-1427	1119	51	ternary	ternary	ADJ
fuelectenerg-1427	1119	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1119	53	decision	decision	NOUN
fuelectenerg-1427	1119	54	tree	tree	NOUN
fuelectenerg-1427	1119	55	(	(	PUNCT
fuelectenerg-1427	1119	56	tkrodt	tkrodt	NOUN
fuelectenerg-1427	1119	57	)	)	PUNCT
fuelectenerg-1427	1119	58	.	.	PUNCT
fuelectenerg-1427	1120	1	the	the	DET
fuelectenerg-1427	1120	2	resulting	result	VERB
fuelectenerg-1427	1120	3	expression	expression	NOUN
fuelectenerg-1427	1120	4	is	be	AUX
fuelectenerg-1427	1120	5	called	call	VERB
fuelectenerg-1427	1120	6	ternary	ternary	ADJ
fuelectenerg-1427	1120	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1120	8	expression	expression	NOUN
fuelectenerg-1427	1120	9	.	.	PUNCT
fuelectenerg-1427	1121	1	definition	definition	NOUN
fuelectenerg-1427	1121	2	9	9	NUM
fuelectenerg-1427	1121	3	.	.	PUNCT
fuelectenerg-1427	1122	1	the	the	DET
fuelectenerg-1427	1122	2	decision	decision	NOUN
fuelectenerg-1427	1122	3	tree	tree	NOUN
fuelectenerg-1427	1122	4	that	that	PRON
fuelectenerg-1427	1122	5	results	result	VERB
fuelectenerg-1427	1122	6	from	from	ADP
fuelectenerg-1427	1122	7	using	use	VERB
fuelectenerg-1427	1122	8	any	any	PRON
fuelectenerg-1427	1122	9	of	of	ADP
fuelectenerg-1427	1122	10	the	the	DET
fuelectenerg-1427	1122	11	ternary	ternary	ADJ
fuelectenerg-1427	1122	12	davio	davio	NOUN
fuelectenerg-1427	1122	13	expansions	expansion	NOUN
fuelectenerg-1427	1122	14	(	(	PUNCT
fuelectenerg-1427	1122	15	nodes	node	NOUN
fuelectenerg-1427	1122	16	)	)	PUNCT
fuelectenerg-1427	1122	17	for	for	ADP
fuelectenerg-1427	1122	18	each	each	DET
fuelectenerg-1427	1122	19	node	node	NOUN
fuelectenerg-1427	1122	20	(	(	PUNCT
fuelectenerg-1427	1122	21	per	per	ADP
fuelectenerg-1427	1122	22	level	level	NOUN
fuelectenerg-1427	1122	23	)	)	PUNCT
fuelectenerg-1427	1122	24	of	of	ADP
fuelectenerg-1427	1122	25	the	the	DET
fuelectenerg-1427	1122	26	dt	dt	NOUN
fuelectenerg-1427	1122	27	is	be	AUX
fuelectenerg-1427	1122	28	called	call	VERB
fuelectenerg-1427	1122	29	ternary	ternary	ADJ
fuelectenerg-1427	1122	30	pseudo	pseudo	NOUN
fuelectenerg-1427	1122	31	-	-	NOUN
fuelectenerg-1427	1122	32	reed112	reed112	VERB
fuelectenerg-1427	1122	33	an	an	DET
fuelectenerg-1427	1122	34	extended	extend	VERB
fuelectenerg-1427	1122	35	green	green	PROPN
fuelectenerg-1427	1122	36	sasao	sasao	PROPN
fuelectenerg-1427	1122	37	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1122	38	of	of	ADP
fuelectenerg-1427	1122	39	canonical	canonical	ADJ
fuelectenerg-1427	1122	40	ternary	ternary	ADJ
fuelectenerg-1427	1122	41	galois	galois	NOUN
fuelectenerg-1427	1122	42	forms	form	NOUN
fuelectenerg-1427	1122	43	...	...	PUNCT
fuelectenerg-1427	1122	44	definition	definition	NOUN
fuelectenerg-1427	1122	45	4	4	NUM
fuelectenerg-1427	1122	46	.	.	PUNCT
fuelectenerg-1427	1123	1	the	the	DET
fuelectenerg-1427	1123	2	family	family	NOUN
fuelectenerg-1427	1123	3	of	of	ADP
fuelectenerg-1427	1123	4	forms	form	NOUN
fuelectenerg-1427	1123	5	,	,	PUNCT
fuelectenerg-1427	1123	6	generated	generate	VERB
fuelectenerg-1427	1123	7	by	by	ADP
fuelectenerg-1427	1123	8	s	s	PROPN
fuelectenerg-1427	1123	9	/	/	SYM
fuelectenerg-1427	1123	10	d	d	NOUN
fuelectenerg-1427	1123	11	tree	tree	NOUN
fuelectenerg-1427	1123	12	with	with	ADP
fuelectenerg-1427	1123	13	no	no	DET
fuelectenerg-1427	1123	14	fixed	fix	VERB
fuelectenerg-1427	1123	15	ordering	ordering	NOUN
fuelectenerg-1427	1123	16	of	of	ADP
fuelectenerg-1427	1123	17	variables	variable	NOUN
fuelectenerg-1427	1123	18	,	,	PUNCT
fuelectenerg-1427	1123	19	with	with	ADP
fuelectenerg-1427	1123	20	variables	variable	NOUN
fuelectenerg-1427	1123	21	not	not	PART
fuelectenerg-1427	1123	22	repeated	repeat	VERB
fuelectenerg-1427	1123	23	along	along	ADP
fuelectenerg-1427	1123	24	same	same	ADJ
fuelectenerg-1427	1123	25	branches	branch	NOUN
fuelectenerg-1427	1123	26	,	,	PUNCT
fuelectenerg-1427	1123	27	is	be	AUX
fuelectenerg-1427	1123	28	called	call	VERB
fuelectenerg-1427	1123	29	ternary	ternary	ADJ
fuelectenerg-1427	1123	30	free	free	ADJ
fuelectenerg-1427	1123	31	generalized	generalize	VERB
fuelectenerg-1427	1123	32	inclusive	inclusive	ADJ
fuelectenerg-1427	1123	33	forms	form	NOUN
fuelectenerg-1427	1123	34	(	(	PUNCT
fuelectenerg-1427	1123	35	tfgifs	tfgifs	PROPN
fuelectenerg-1427	1123	36	)	)	PUNCT
fuelectenerg-1427	1123	37	.	.	PUNCT
fuelectenerg-1427	1124	1	2.3	2.3	NUM
fuelectenerg-1427	1124	2	an	an	DET
fuelectenerg-1427	1124	3	extended	extended	ADJ
fuelectenerg-1427	1124	4	green	green	ADJ
fuelectenerg-1427	1124	5	-	-	PUNCT
fuelectenerg-1427	1124	6	sasao	sasao	NOUN
fuelectenerg-1427	1124	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1124	8	with	with	ADP
fuelectenerg-1427	1124	9	a	a	DET
fuelectenerg-1427	1124	10	new	new	ADJ
fuelectenerg-1427	1124	11	sub	sub	NOUN
fuelectenerg-1427	1124	12	-	-	NOUN
fuelectenerg-1427	1124	13	family	family	NOUN
fuelectenerg-1427	1124	14	for	for	ADP
fuelectenerg-1427	1124	15	ternary	ternary	ADJ
fuelectenerg-1427	1124	16	reed	reed	NOUN
fuelectenerg-1427	1124	17	-	-	PUNCT
fuelectenerg-1427	1124	18	muller	muller	NOUN
fuelectenerg-1427	1124	19	logic	logic	NOUN
fuelectenerg-1427	1124	20	the	the	DET
fuelectenerg-1427	1124	21	green	green	PROPN
fuelectenerg-1427	1124	22	-	-	PUNCT
fuelectenerg-1427	1124	23	sasao	sasao	PROPN
fuelectenerg-1427	1124	24	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1124	25	of	of	ADP
fuelectenerg-1427	1124	26	families	family	NOUN
fuelectenerg-1427	1124	27	of	of	ADP
fuelectenerg-1427	1124	28	canonical	canonical	ADJ
fuelectenerg-1427	1124	29	forms	form	NOUN
fuelectenerg-1427	1124	30	[	[	X
fuelectenerg-1427	1124	31	1	1	NUM
fuelectenerg-1427	1124	32	,	,	PUNCT
fuelectenerg-1427	1124	33	10	10	NUM
fuelectenerg-1427	1124	34	-	-	SYM
fuelectenerg-1427	1124	35	13	13	NUM
fuelectenerg-1427	1124	36	,	,	PUNCT
fuelectenerg-1427	1124	37	17	17	NUM
fuelectenerg-1427	1124	38	,	,	PUNCT
fuelectenerg-1427	1124	39	24	24	NUM
fuelectenerg-1427	1124	40	,	,	PUNCT
fuelectenerg-1427	1124	41	26	26	NUM
fuelectenerg-1427	1124	42	]	]	PUNCT
fuelectenerg-1427	1124	43	and	and	CCONJ
fuelectenerg-1427	1124	44	the	the	DET
fuelectenerg-1427	1124	45	corresponding	correspond	VERB
fuelectenerg-1427	1124	46	decision	decision	NOUN
fuelectenerg-1427	1124	47	trees	tree	NOUN
fuelectenerg-1427	1124	48	and	and	CCONJ
fuelectenerg-1427	1124	49	diagrams	diagram	NOUN
fuelectenerg-1427	1124	50	is	be	AUX
fuelectenerg-1427	1124	51	based	base	VERB
fuelectenerg-1427	1124	52	on	on	ADP
fuelectenerg-1427	1124	53	three	three	NUM
fuelectenerg-1427	1124	54	generic	generic	ADJ
fuelectenerg-1427	1124	55	expansions	expansion	NOUN
fuelectenerg-1427	1124	56	,	,	PUNCT
fuelectenerg-1427	1124	57	shannon	shannon	PROPN
fuelectenerg-1427	1124	58	,	,	PUNCT
fuelectenerg-1427	1124	59	positive	positive	ADJ
fuelectenerg-1427	1124	60	and	and	CCONJ
fuelectenerg-1427	1124	61	negative	negative	ADJ
fuelectenerg-1427	1124	62	davio	davio	NOUN
fuelectenerg-1427	1124	63	expansions	expansion	NOUN
fuelectenerg-1427	1124	64	.	.	PUNCT
fuelectenerg-1427	1125	1	for	for	ADP
fuelectenerg-1427	1125	2	example	example	NOUN
fuelectenerg-1427	1125	3	,	,	PUNCT
fuelectenerg-1427	1125	4	this	this	PRON
fuelectenerg-1427	1125	5	includes	include	VERB
fuelectenerg-1427	1125	6	shannon	shannon	ADJ
fuelectenerg-1427	1125	7	decision	decision	NOUN
fuelectenerg-1427	1125	8	trees	tree	NOUN
fuelectenerg-1427	1125	9	and	and	CCONJ
fuelectenerg-1427	1125	10	diagrams	diagram	NOUN
fuelectenerg-1427	1125	11	,	,	PUNCT
fuelectenerg-1427	1125	12	positive	positive	ADJ
fuelectenerg-1427	1125	13	and	and	CCONJ
fuelectenerg-1427	1125	14	negative	negative	ADJ
fuelectenerg-1427	1125	15	davio	davio	NOUN
fuelectenerg-1427	1125	16	decision	decision	NOUN
fuelectenerg-1427	1125	17	trees	tree	NOUN
fuelectenerg-1427	1125	18	and	and	CCONJ
fuelectenerg-1427	1125	19	diagrams	diagram	NOUN
fuelectenerg-1427	1125	20	,	,	PUNCT
fuelectenerg-1427	1125	21	fixed	fix	VERB
fuelectenerg-1427	1125	22	polarity	polarity	NOUN
fuelectenerg-1427	1125	23	reed	reed	NOUN
fuelectenerg-1427	1125	24	-	-	PUNCT
fuelectenerg-1427	1125	25	muller	muller	NOUN
fuelectenerg-1427	1125	26	decision	decision	NOUN
fuelectenerg-1427	1125	27	trees	tree	NOUN
fuelectenerg-1427	1125	28	and	and	CCONJ
fuelectenerg-1427	1125	29	diagrams	diagram	NOUN
fuelectenerg-1427	1125	30	,	,	PUNCT
fuelectenerg-1427	1125	31	kronecker	kronecker	NOUN
fuelectenerg-1427	1125	32	decision	decision	NOUN
fuelectenerg-1427	1125	33	trees	tree	NOUN
fuelectenerg-1427	1125	34	and	and	CCONJ
fuelectenerg-1427	1125	35	diagrams	diagram	NOUN
fuelectenerg-1427	1125	36	,	,	PUNCT
fuelectenerg-1427	1125	37	pseudo	pseudo	NOUN
fuelectenerg-1427	1125	38	reed	reed	NOUN
fuelectenerg-1427	1125	39	-	-	PUNCT
fuelectenerg-1427	1125	40	muller	muller	NOUN
fuelectenerg-1427	1125	41	decision	decision	NOUN
fuelectenerg-1427	1125	42	trees	tree	NOUN
fuelectenerg-1427	1125	43	and	and	CCONJ
fuelectenerg-1427	1125	44	diagrams	diagram	NOUN
fuelectenerg-1427	1125	45	,	,	PUNCT
fuelectenerg-1427	1125	46	pseudo	pseudo	NOUN
fuelectenerg-1427	1125	47	kronecker	kronecker	NOUN
fuelectenerg-1427	1125	48	decision	decision	NOUN
fuelectenerg-1427	1125	49	trees	tree	NOUN
fuelectenerg-1427	1125	50	and	and	CCONJ
fuelectenerg-1427	1125	51	diagrams	diagram	NOUN
fuelectenerg-1427	1125	52	,	,	PUNCT
fuelectenerg-1427	1125	53	and	and	CCONJ
fuelectenerg-1427	1125	54	linearly	linearly	ADV
fuelectenerg-1427	1125	55	-	-	PUNCT
fuelectenerg-1427	1125	56	independent	independent	ADJ
fuelectenerg-1427	1125	57	decision	decision	NOUN
fuelectenerg-1427	1125	58	trees	tree	NOUN
fuelectenerg-1427	1125	59	and	and	CCONJ
fuelectenerg-1427	1125	60	diagrams	diagram	NOUN
fuelectenerg-1427	1126	1	[	[	X
fuelectenerg-1427	1126	2	1	1	NUM
fuelectenerg-1427	1126	3	,	,	PUNCT
fuelectenerg-1427	1126	4	17	17	NUM
fuelectenerg-1427	1126	5	,	,	PUNCT
fuelectenerg-1427	1126	6	24	24	NUM
fuelectenerg-1427	1126	7	]	]	PUNCT
fuelectenerg-1427	1126	8	.	.	PUNCT
fuelectenerg-1427	1127	1	a	a	DET
fuelectenerg-1427	1127	2	set	set	VERB
fuelectenerg-1427	1127	3	-	-	PUNCT
fuelectenerg-1427	1127	4	theoretic	theoretic	NOUN
fuelectenerg-1427	1127	5	relationship	relationship	NOUN
fuelectenerg-1427	1127	6	between	between	ADP
fuelectenerg-1427	1127	7	families	family	NOUN
fuelectenerg-1427	1127	8	of	of	ADP
fuelectenerg-1427	1127	9	canonical	canonical	ADJ
fuelectenerg-1427	1127	10	forms	form	NOUN
fuelectenerg-1427	1127	11	over	over	ADP
fuelectenerg-1427	1127	12	gf(2	gf(2	PROPN
fuelectenerg-1427	1127	13	)	)	PUNCT
fuelectenerg-1427	1127	14	was	be	AUX
fuelectenerg-1427	1127	15	proposed	propose	VERB
fuelectenerg-1427	1127	16	and	and	CCONJ
fuelectenerg-1427	1127	17	extended	extend	VERB
fuelectenerg-1427	1127	18	by	by	ADP
fuelectenerg-1427	1127	19	introducing	introduce	VERB
fuelectenerg-1427	1127	20	binary	binary	NOUN
fuelectenerg-1427	1127	21	if	if	SCONJ
fuelectenerg-1427	1127	22	,	,	PUNCT
fuelectenerg-1427	1127	23	gif	gif	NOUN
fuelectenerg-1427	1127	24	and	and	CCONJ
fuelectenerg-1427	1127	25	free	free	ADJ
fuelectenerg-1427	1127	26	gif	gif	NOUN
fuelectenerg-1427	1127	27	(	(	PUNCT
fuelectenerg-1427	1127	28	fgif	fgif	NOUN
fuelectenerg-1427	1127	29	)	)	PUNCT
fuelectenerg-1427	1127	30	forms	form	NOUN
fuelectenerg-1427	1127	31	where	where	SCONJ
fuelectenerg-1427	1127	32	figure	figure	NOUN
fuelectenerg-1427	1127	33	6(a	6(a	NUM
fuelectenerg-1427	1127	34	)	)	PUNCT
fuelectenerg-1427	1127	35	illustrates	illustrate	VERB
fuelectenerg-1427	1127	36	set	set	VERB
fuelectenerg-1427	1127	37	-	-	PUNCT
fuelectenerg-1427	1127	38	theoretic	theoretic	NOUN
fuelectenerg-1427	1127	39	relationship	relationship	NOUN
fuelectenerg-1427	1127	40	between	between	ADP
fuelectenerg-1427	1127	41	the	the	DET
fuelectenerg-1427	1127	42	various	various	ADJ
fuelectenerg-1427	1127	43	families	family	NOUN
fuelectenerg-1427	1127	44	of	of	ADP
fuelectenerg-1427	1127	45	canonical	canonical	ADJ
fuelectenerg-1427	1127	46	forms	form	NOUN
fuelectenerg-1427	1127	47	over	over	ADP
fuelectenerg-1427	1127	48	gf(2	gf(2	PROPN
fuelectenerg-1427	1127	49	)	)	PUNCT
fuelectenerg-1427	1127	50	.	.	PUNCT
fuelectenerg-1427	1128	1	analogously	analogously	ADV
fuelectenerg-1427	1128	2	to	to	ADP
fuelectenerg-1427	1128	3	the	the	DET
fuelectenerg-1427	1128	4	green	green	ADJ
fuelectenerg-1427	1128	5	-	-	PUNCT
fuelectenerg-1427	1128	6	sasao	sasao	PROPN
fuelectenerg-1427	1128	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1128	8	of	of	ADP
fuelectenerg-1427	1128	9	binary	binary	PROPN
fuelectenerg-1427	1128	10	reed	reed	PROPN
fuelectenerg-1427	1128	11	-	-	PUNCT
fuelectenerg-1427	1128	12	muller	muller	NOUN
fuelectenerg-1427	1128	13	families	family	NOUN
fuelectenerg-1427	1128	14	of	of	ADP
fuelectenerg-1427	1128	15	spectral	spectral	ADJ
fuelectenerg-1427	1128	16	transforms	transform	VERB
fuelectenerg-1427	1128	17	over	over	ADP
fuelectenerg-1427	1128	18	gf(2	gf(2	PROPN
fuelectenerg-1427	1128	19	)	)	PUNCT
fuelectenerg-1427	1128	20	that	that	PRON
fuelectenerg-1427	1128	21	is	be	AUX
fuelectenerg-1427	1128	22	shown	show	VERB
fuelectenerg-1427	1128	23	in	in	ADP
fuelectenerg-1427	1128	24	figure	figure	NOUN
fuelectenerg-1427	1128	25	6(a	6(a	NUM
fuelectenerg-1427	1128	26	)	)	PUNCT
fuelectenerg-1427	1128	27	,	,	PUNCT
fuelectenerg-1427	1128	28	we	we	PRON
fuelectenerg-1427	1128	29	will	will	AUX
fuelectenerg-1427	1128	30	introduce	introduce	VERB
fuelectenerg-1427	1128	31	the	the	DET
fuelectenerg-1427	1128	32	extended	extended	ADJ
fuelectenerg-1427	1128	33	green	green	ADJ
fuelectenerg-1427	1128	34	-	-	PUNCT
fuelectenerg-1427	1128	35	sasao	sasao	NOUN
fuelectenerg-1427	1128	36	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1128	37	of	of	ADP
fuelectenerg-1427	1128	38	spectral	spectral	ADJ
fuelectenerg-1427	1128	39	transforms	transform	NOUN
fuelectenerg-1427	1128	40	,	,	PUNCT
fuelectenerg-1427	1128	41	with	with	ADP
fuelectenerg-1427	1128	42	a	a	DET
fuelectenerg-1427	1128	43	new	new	ADJ
fuelectenerg-1427	1128	44	sub	sub	NOUN
fuelectenerg-1427	1128	45	-	-	NOUN
fuelectenerg-1427	1128	46	family	family	NOUN
fuelectenerg-1427	1128	47	for	for	ADP
fuelectenerg-1427	1128	48	ternary	ternary	ADJ
fuelectenerg-1427	1128	49	reedmuller	reedmuller	NOUN
fuelectenerg-1427	1128	50	logic	logic	NOUN
fuelectenerg-1427	1128	51	over	over	ADP
fuelectenerg-1427	1128	52	gf(3	gf(3	PROPN
fuelectenerg-1427	1128	53	)	)	PUNCT
fuelectenerg-1427	1128	54	.	.	PUNCT
fuelectenerg-1427	1129	1	while	while	SCONJ
fuelectenerg-1427	1129	2	definitions	definition	NOUN
fuelectenerg-1427	1129	3	2	2	NUM
fuelectenerg-1427	1129	4	4	4	NUM
fuelectenerg-1427	1129	5	defined	define	VERB
fuelectenerg-1427	1129	6	the	the	DET
fuelectenerg-1427	1129	7	ternary	ternary	ADJ
fuelectenerg-1427	1129	8	inclusive	inclusive	ADJ
fuelectenerg-1427	1129	9	forms	form	NOUN
fuelectenerg-1427	1129	10	,	,	PUNCT
fuelectenerg-1427	1129	11	ternary	ternary	ADJ
fuelectenerg-1427	1129	12	generalized	generalize	VERB
fuelectenerg-1427	1129	13	inclusive	inclusive	ADJ
fuelectenerg-1427	1129	14	forms	form	NOUN
fuelectenerg-1427	1129	15	and	and	CCONJ
fuelectenerg-1427	1129	16	ternary	ternary	ADJ
fuelectenerg-1427	1129	17	free	free	ADJ
fuelectenerg-1427	1129	18	generalized	generalized	ADJ
fuelectenerg-1427	1129	19	inclusive	inclusive	ADJ
fuelectenerg-1427	1129	20	forms	form	NOUN
fuelectenerg-1427	1129	21	,	,	PUNCT
fuelectenerg-1427	1129	22	respectively	respectively	ADV
fuelectenerg-1427	1129	23	,	,	PUNCT
fuelectenerg-1427	1129	24	and	and	CCONJ
fuelectenerg-1427	1129	25	analogously	analogously	ADV
fuelectenerg-1427	1129	26	to	to	ADP
fuelectenerg-1427	1129	27	the	the	DET
fuelectenerg-1427	1129	28	binary	binary	PROPN
fuelectenerg-1427	1129	29	reed	reed	PROPN
fuelectenerg-1427	1129	30	-	-	PUNCT
fuelectenerg-1427	1129	31	muller	muller	NOUN
fuelectenerg-1427	1129	32	case	case	NOUN
fuelectenerg-1427	1129	33	,	,	PUNCT
fuelectenerg-1427	1129	34	the	the	DET
fuelectenerg-1427	1129	35	following	follow	VERB
fuelectenerg-1427	1129	36	definitions	definition	NOUN
fuelectenerg-1427	1129	37	are	be	AUX
fuelectenerg-1427	1129	38	introduced	introduce	VERB
fuelectenerg-1427	1129	39	for	for	ADP
fuelectenerg-1427	1129	40	the	the	DET
fuelectenerg-1427	1129	41	corresponding	corresponding	ADJ
fuelectenerg-1427	1129	42	canonical	canonical	ADJ
fuelectenerg-1427	1129	43	expressions	expression	NOUN
fuelectenerg-1427	1129	44	over	over	ADP
fuelectenerg-1427	1129	45	gf(3	gf(3	PROPN
fuelectenerg-1427	1129	46	)	)	PUNCT
fuelectenerg-1427	1129	47	.	.	PUNCT
fuelectenerg-1427	1130	1	definition	definition	NOUN
fuelectenerg-1427	1130	2	5	5	NUM
fuelectenerg-1427	1130	3	.	.	PUNCT
fuelectenerg-1427	1131	1	the	the	DET
fuelectenerg-1427	1131	2	decision	decision	NOUN
fuelectenerg-1427	1131	3	tree	tree	NOUN
fuelectenerg-1427	1131	4	that	that	PRON
fuelectenerg-1427	1131	5	results	result	VERB
fuelectenerg-1427	1131	6	from	from	ADP
fuelectenerg-1427	1131	7	applying	apply	VERB
fuelectenerg-1427	1131	8	the	the	DET
fuelectenerg-1427	1131	9	ternary	ternary	ADJ
fuelectenerg-1427	1131	10	shannon	shannon	NOUN
fuelectenerg-1427	1131	11	expansion	expansion	NOUN
fuelectenerg-1427	1131	12	in	in	ADP
fuelectenerg-1427	1131	13	equation	equation	NOUN
fuelectenerg-1427	1131	14	(	(	PUNCT
fuelectenerg-1427	1131	15	23	23	NUM
fuelectenerg-1427	1131	16	)	)	PUNCT
fuelectenerg-1427	1131	17	recursively	recursively	ADV
fuelectenerg-1427	1131	18	to	to	ADP
fuelectenerg-1427	1131	19	a	a	DET
fuelectenerg-1427	1131	20	ternary	ternary	ADJ
fuelectenerg-1427	1131	21	input	input	NOUN
fuelectenerg-1427	1131	22	-	-	PUNCT
fuelectenerg-1427	1131	23	ternary	ternary	ADJ
fuelectenerg-1427	1131	24	output	output	NOUN
fuelectenerg-1427	1131	25	logic	logic	NOUN
fuelectenerg-1427	1131	26	function	function	NOUN
fuelectenerg-1427	1131	27	(	(	PUNCT
fuelectenerg-1427	1131	28	i.e.	i.e.	X
fuelectenerg-1427	1131	29	,	,	PUNCT
fuelectenerg-1427	1131	30	all	all	DET
fuelectenerg-1427	1131	31	levels	level	NOUN
fuelectenerg-1427	1131	32	in	in	ADP
fuelectenerg-1427	1131	33	a	a	DET
fuelectenerg-1427	1131	34	dt	dt	NOUN
fuelectenerg-1427	1131	35	)	)	PUNCT
fuelectenerg-1427	1131	36	is	be	AUX
fuelectenerg-1427	1131	37	called	call	VERB
fuelectenerg-1427	1131	38	ternary	ternary	ADJ
fuelectenerg-1427	1131	39	shannon	shannon	PROPN
fuelectenerg-1427	1131	40	decision	decision	NOUN
fuelectenerg-1427	1131	41	tree	tree	NOUN
fuelectenerg-1427	1131	42	(	(	PUNCT
fuelectenerg-1427	1131	43	tsdt	tsdt	NOUN
fuelectenerg-1427	1131	44	)	)	PUNCT
fuelectenerg-1427	1131	45	.	.	PUNCT
fuelectenerg-1427	1132	1	the	the	DET
fuelectenerg-1427	1132	2	result	result	NOUN
fuelectenerg-1427	1132	3	expression	expression	NOUN
fuelectenerg-1427	1132	4	(	(	PUNCT
fuelectenerg-1427	1132	5	flattened	flatten	VERB
fuelectenerg-1427	1132	6	form	form	NOUN
fuelectenerg-1427	1132	7	)	)	PUNCT
fuelectenerg-1427	1132	8	from	from	ADP
fuelectenerg-1427	1132	9	the	the	DET
fuelectenerg-1427	1132	10	tsdt	tsdt	NOUN
fuelectenerg-1427	1132	11	is	be	AUX
fuelectenerg-1427	1132	12	called	call	VERB
fuelectenerg-1427	1132	13	ternary	ternary	ADJ
fuelectenerg-1427	1132	14	shannon	shannon	NOUN
fuelectenerg-1427	1132	15	expression	expression	NOUN
fuelectenerg-1427	1132	16	.	.	PUNCT
fuelectenerg-1427	1133	1	definition	definition	NOUN
fuelectenerg-1427	1133	2	6	6	NUM
fuelectenerg-1427	1133	3	.	.	PUNCT
fuelectenerg-1427	1134	1	the	the	DET
fuelectenerg-1427	1134	2	decision	decision	NOUN
fuelectenerg-1427	1134	3	trees	tree	NOUN
fuelectenerg-1427	1134	4	that	that	PRON
fuelectenerg-1427	1134	5	result	result	VERB
fuelectenerg-1427	1134	6	from	from	ADP
fuelectenerg-1427	1134	7	applying	apply	VERB
fuelectenerg-1427	1134	8	the	the	DET
fuelectenerg-1427	1134	9	ternary	ternary	ADJ
fuelectenerg-1427	1134	10	davio	davio	NOUN
fuelectenerg-1427	1134	11	expansions	expansion	NOUN
fuelectenerg-1427	1134	12	in	in	ADP
fuelectenerg-1427	1134	13	equations	equation	NOUN
fuelectenerg-1427	1134	14	(	(	PUNCT
fuelectenerg-1427	1134	15	24	24	NUM
fuelectenerg-1427	1134	16	)	)	PUNCT
fuelectenerg-1427	1134	17	(	(	PUNCT
fuelectenerg-1427	1134	18	26	26	NUM
fuelectenerg-1427	1134	19	)	)	PUNCT
fuelectenerg-1427	1134	20	recursively	recursively	ADV
fuelectenerg-1427	1134	21	to	to	ADP
fuelectenerg-1427	1134	22	a	a	DET
fuelectenerg-1427	1134	23	ternary	ternary	ADJ
fuelectenerg-1427	1134	24	-	-	PUNCT
fuelectenerg-1427	1134	25	input	input	NOUN
fuelectenerg-1427	1134	26	ternary	ternary	ADJ
fuelectenerg-1427	1134	27	-	-	PUNCT
fuelectenerg-1427	1134	28	output	output	NOUN
fuelectenerg-1427	1134	29	logic	logic	NOUN
fuelectenerg-1427	1134	30	function	function	NOUN
fuelectenerg-1427	1134	31	(	(	PUNCT
fuelectenerg-1427	1134	32	i.e.	i.e.	X
fuelectenerg-1427	1134	33	,	,	PUNCT
fuelectenerg-1427	1134	34	all	all	DET
fuelectenerg-1427	1134	35	levels	level	NOUN
fuelectenerg-1427	1134	36	in	in	ADP
fuelectenerg-1427	1134	37	a	a	DET
fuelectenerg-1427	1134	38	dt	dt	NOUN
fuelectenerg-1427	1134	39	)	)	PUNCT
fuelectenerg-1427	1134	40	are	be	AUX
fuelectenerg-1427	1134	41	called	call	VERB
fuelectenerg-1427	1134	42	:	:	PUNCT
fuelectenerg-1427	1134	43	ternary	ternary	ADJ
fuelectenerg-1427	1134	44	zero	zero	NUM
fuelectenerg-1427	1134	45	-	-	PUNCT
fuelectenerg-1427	1134	46	polarity	polarity	NOUN
fuelectenerg-1427	1134	47	davio	davio	NOUN
fuelectenerg-1427	1134	48	decision	decision	NOUN
fuelectenerg-1427	1134	49	tree	tree	NOUN
fuelectenerg-1427	1134	50	(	(	PUNCT
fuelectenerg-1427	1134	51	td0dt	td0dt	NOUN
fuelectenerg-1427	1134	52	)	)	PUNCT
fuelectenerg-1427	1134	53	,	,	PUNCT
fuelectenerg-1427	1134	54	ternary	ternary	ADJ
fuelectenerg-1427	1134	55	first	first	ADJ
fuelectenerg-1427	1134	56	-	-	PUNCT
fuelectenerg-1427	1134	57	polarity	polarity	NOUN
fuelectenerg-1427	1134	58	davio	davio	NOUN
fuelectenerg-1427	1134	59	decision	decision	NOUN
fuelectenerg-1427	1134	60	tree	tree	NOUN
fuelectenerg-1427	1134	61	(	(	PUNCT
fuelectenerg-1427	1134	62	td1dt	td1dt	NUM
fuelectenerg-1427	1134	63	)	)	PUNCT
fuelectenerg-1427	1134	64	and	and	CCONJ
fuelectenerg-1427	1134	65	ternary	ternary	ADJ
fuelectenerg-1427	1134	66	secondpolarity	secondpolarity	NOUN
fuelectenerg-1427	1134	67	davio	davio	NOUN
fuelectenerg-1427	1134	68	decision	decision	NOUN
fuelectenerg-1427	1134	69	tree	tree	NOUN
fuelectenerg-1427	1134	70	(	(	PUNCT
fuelectenerg-1427	1134	71	td2dt	td2dt	NUM
fuelectenerg-1427	1134	72	)	)	PUNCT
fuelectenerg-1427	1134	73	,	,	PUNCT
fuelectenerg-1427	1134	74	respectively	respectively	ADV
fuelectenerg-1427	1134	75	.	.	PUNCT
fuelectenerg-1427	1135	1	the	the	DET
fuelectenerg-1427	1135	2	resulting	result	VERB
fuelectenerg-1427	1135	3	expressions	expression	NOUN
fuelectenerg-1427	1135	4	(	(	PUNCT
fuelectenerg-1427	1135	5	flattened	flatten	VERB
fuelectenerg-1427	1135	6	forms	form	NOUN
fuelectenerg-1427	1135	7	)	)	PUNCT
fuelectenerg-1427	1135	8	from	from	ADP
fuelectenerg-1427	1135	9	td0dt	td0dt	PROPN
fuelectenerg-1427	1135	10	,	,	PUNCT
fuelectenerg-1427	1135	11	td1dt	td1dt	NUM
fuelectenerg-1427	1135	12	and	and	CCONJ
fuelectenerg-1427	1135	13	td2dt	td2dt	NUM
fuelectenerg-1427	1135	14	are	be	AUX
fuelectenerg-1427	1135	15	called	call	VERB
fuelectenerg-1427	1135	16	td0	td0	NOUN
fuelectenerg-1427	1135	17	,	,	PUNCT
fuelectenerg-1427	1135	18	td1	td1	PROPN
fuelectenerg-1427	1135	19	and	and	CCONJ
fuelectenerg-1427	1135	20	td2	td2	PROPN
fuelectenerg-1427	1135	21	expressions	expression	NOUN
fuelectenerg-1427	1135	22	,	,	PUNCT
fuelectenerg-1427	1135	23	respectively	respectively	ADV
fuelectenerg-1427	1135	24	.	.	PUNCT
fuelectenerg-1427	1136	1	definition	definition	NOUN
fuelectenerg-1427	1136	2	7	7	NUM
fuelectenerg-1427	1136	3	.	.	PUNCT
fuelectenerg-1427	1137	1	the	the	DET
fuelectenerg-1427	1137	2	decision	decision	NOUN
fuelectenerg-1427	1137	3	tree	tree	NOUN
fuelectenerg-1427	1137	4	that	that	PRON
fuelectenerg-1427	1137	5	results	result	VERB
fuelectenerg-1427	1137	6	from	from	ADP
fuelectenerg-1427	1137	7	applying	apply	VERB
fuelectenerg-1427	1137	8	any	any	PRON
fuelectenerg-1427	1137	9	of	of	ADP
fuelectenerg-1427	1137	10	the	the	DET
fuelectenerg-1427	1137	11	ternary	ternary	ADJ
fuelectenerg-1427	1137	12	davio	davio	NOUN
fuelectenerg-1427	1137	13	expansions	expansion	NOUN
fuelectenerg-1427	1137	14	(	(	PUNCT
fuelectenerg-1427	1137	15	nodes	node	NOUN
fuelectenerg-1427	1137	16	)	)	PUNCT
fuelectenerg-1427	1137	17	for	for	ADP
fuelectenerg-1427	1137	18	all	all	DET
fuelectenerg-1427	1137	19	nodes	node	NOUN
fuelectenerg-1427	1137	20	in	in	ADP
fuelectenerg-1427	1137	21	each	each	DET
fuelectenerg-1427	1137	22	level	level	NOUN
fuelectenerg-1427	1137	23	(	(	PUNCT
fuelectenerg-1427	1137	24	variable	variable	NOUN
fuelectenerg-1427	1137	25	)	)	PUNCT
fuelectenerg-1427	1137	26	in	in	ADP
fuelectenerg-1427	1137	27	the	the	DET
fuelectenerg-1427	1137	28	dt	dt	NOUN
fuelectenerg-1427	1137	29	is	be	AUX
fuelectenerg-1427	1137	30	called	call	VERB
fuelectenerg-1427	1137	31	ternary	ternary	ADJ
fuelectenerg-1427	1137	32	reed	reed	NOUN
fuelectenerg-1427	1137	33	-	-	PUNCT
fuelectenerg-1427	1137	34	muller	muller	NOUN
fuelectenerg-1427	1137	35	decision	decision	NOUN
fuelectenerg-1427	1137	36	tree	tree	NOUN
fuelectenerg-1427	1137	37	(	(	PUNCT
fuelectenerg-1427	1137	38	trmdt	trmdt	NOUN
fuelectenerg-1427	1137	39	)	)	PUNCT
fuelectenerg-1427	1137	40	.	.	PUNCT
fuelectenerg-1427	1138	1	the	the	DET
fuelectenerg-1427	1138	2	corresponding	corresponding	ADJ
fuelectenerg-1427	1138	3	expression	expression	NOUN
fuelectenerg-1427	1138	4	is	be	AUX
fuelectenerg-1427	1138	5	called	call	VERB
fuelectenerg-1427	1138	6	ternary	ternary	ADJ
fuelectenerg-1427	1138	7	fixed	fix	VERB
fuelectenerg-1427	1138	8	polarity	polarity	NOUN
fuelectenerg-1427	1138	9	reed	reed	NOUN
fuelectenerg-1427	1138	10	-	-	PUNCT
fuelectenerg-1427	1138	11	muller	muller	NOUN
fuelectenerg-1427	1138	12	(	(	PUNCT
fuelectenerg-1427	1138	13	tfprm	tfprm	ADJ
fuelectenerg-1427	1138	14	)	)	PUNCT
fuelectenerg-1427	1138	15	expression	expression	NOUN
fuelectenerg-1427	1138	16	.	.	PUNCT
fuelectenerg-1427	1139	1	definition	definition	NOUN
fuelectenerg-1427	1139	2	8	8	NUM
fuelectenerg-1427	1139	3	.	.	PUNCT
fuelectenerg-1427	1140	1	the	the	DET
fuelectenerg-1427	1140	2	decision	decision	NOUN
fuelectenerg-1427	1140	3	tree	tree	NOUN
fuelectenerg-1427	1140	4	that	that	PRON
fuelectenerg-1427	1140	5	results	result	VERB
fuelectenerg-1427	1140	6	from	from	ADP
fuelectenerg-1427	1140	7	using	use	VERB
fuelectenerg-1427	1140	8	any	any	PRON
fuelectenerg-1427	1140	9	of	of	ADP
fuelectenerg-1427	1140	10	the	the	DET
fuelectenerg-1427	1140	11	ternary	ternary	ADJ
fuelectenerg-1427	1140	12	shannon	shannon	NOUN
fuelectenerg-1427	1140	13	(	(	PUNCT
fuelectenerg-1427	1140	14	s	s	NOUN
fuelectenerg-1427	1140	15	)	)	PUNCT
fuelectenerg-1427	1140	16	or	or	CCONJ
fuelectenerg-1427	1140	17	davio	davio	NOUN
fuelectenerg-1427	1140	18	(	(	PUNCT
fuelectenerg-1427	1140	19	d0	d0	NOUN
fuelectenerg-1427	1140	20	,	,	PUNCT
fuelectenerg-1427	1140	21	d1	d1	PROPN
fuelectenerg-1427	1140	22	or	or	CCONJ
fuelectenerg-1427	1140	23	d2	d2	PROPN
fuelectenerg-1427	1140	24	)	)	PUNCT
fuelectenerg-1427	1140	25	expansions	expansion	NOUN
fuelectenerg-1427	1140	26	(	(	PUNCT
fuelectenerg-1427	1140	27	nodes	node	NOUN
fuelectenerg-1427	1140	28	)	)	PUNCT
fuelectenerg-1427	1140	29	for	for	ADP
fuelectenerg-1427	1140	30	all	all	DET
fuelectenerg-1427	1140	31	nodes	node	NOUN
fuelectenerg-1427	1140	32	in	in	ADP
fuelectenerg-1427	1140	33	each	each	DET
fuelectenerg-1427	1140	34	level	level	NOUN
fuelectenerg-1427	1140	35	(	(	PUNCT
fuelectenerg-1427	1140	36	variable	variable	NOUN
fuelectenerg-1427	1140	37	)	)	PUNCT
fuelectenerg-1427	1140	38	in	in	ADP
fuelectenerg-1427	1140	39	the	the	DET
fuelectenerg-1427	1140	40	dt	dt	X
fuelectenerg-1427	1140	41	(	(	PUNCT
fuelectenerg-1427	1140	42	that	that	PRON
fuelectenerg-1427	1140	43	has	have	AUX
fuelectenerg-1427	1140	44	fixed	fix	VERB
fuelectenerg-1427	1140	45	order	order	NOUN
fuelectenerg-1427	1140	46	of	of	ADP
fuelectenerg-1427	1140	47	variables	variable	NOUN
fuelectenerg-1427	1140	48	)	)	PUNCT
fuelectenerg-1427	1140	49	is	be	AUX
fuelectenerg-1427	1140	50	called	call	VERB
fuelectenerg-1427	1140	51	ternary	ternary	ADJ
fuelectenerg-1427	1140	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1140	53	decision	decision	NOUN
fuelectenerg-1427	1140	54	tree	tree	NOUN
fuelectenerg-1427	1140	55	(	(	PUNCT
fuelectenerg-1427	1140	56	tkrodt	tkrodt	NOUN
fuelectenerg-1427	1140	57	)	)	PUNCT
fuelectenerg-1427	1140	58	.	.	PUNCT
fuelectenerg-1427	1141	1	the	the	DET
fuelectenerg-1427	1141	2	resulting	result	VERB
fuelectenerg-1427	1141	3	expression	expression	NOUN
fuelectenerg-1427	1141	4	is	be	AUX
fuelectenerg-1427	1141	5	called	call	VERB
fuelectenerg-1427	1141	6	ternary	ternary	ADJ
fuelectenerg-1427	1141	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1141	8	expression	expression	NOUN
fuelectenerg-1427	1141	9	.	.	PUNCT
fuelectenerg-1427	1142	1	definition	definition	NOUN
fuelectenerg-1427	1142	2	9	9	NUM
fuelectenerg-1427	1142	3	.	.	PUNCT
fuelectenerg-1427	1143	1	the	the	DET
fuelectenerg-1427	1143	2	decision	decision	NOUN
fuelectenerg-1427	1143	3	tree	tree	NOUN
fuelectenerg-1427	1143	4	that	that	PRON
fuelectenerg-1427	1143	5	results	result	VERB
fuelectenerg-1427	1143	6	from	from	ADP
fuelectenerg-1427	1143	7	using	use	VERB
fuelectenerg-1427	1143	8	any	any	PRON
fuelectenerg-1427	1143	9	of	of	ADP
fuelectenerg-1427	1143	10	the	the	DET
fuelectenerg-1427	1143	11	ternary	ternary	ADJ
fuelectenerg-1427	1143	12	davio	davio	NOUN
fuelectenerg-1427	1143	13	expansions	expansion	NOUN
fuelectenerg-1427	1143	14	(	(	PUNCT
fuelectenerg-1427	1143	15	nodes	node	NOUN
fuelectenerg-1427	1143	16	)	)	PUNCT
fuelectenerg-1427	1143	17	for	for	ADP
fuelectenerg-1427	1143	18	each	each	DET
fuelectenerg-1427	1143	19	node	node	NOUN
fuelectenerg-1427	1143	20	(	(	PUNCT
fuelectenerg-1427	1143	21	per	per	ADP
fuelectenerg-1427	1143	22	level	level	NOUN
fuelectenerg-1427	1143	23	)	)	PUNCT
fuelectenerg-1427	1143	24	of	of	ADP
fuelectenerg-1427	1143	25	the	the	DET
fuelectenerg-1427	1143	26	dt	dt	NOUN
fuelectenerg-1427	1143	27	is	be	AUX
fuelectenerg-1427	1143	28	called	call	VERB
fuelectenerg-1427	1143	29	ternary	ternary	ADJ
fuelectenerg-1427	1143	30	pseudo	pseudo	NOUN
fuelectenerg-1427	1143	31	-	-	NOUN
fuelectenerg-1427	1143	32	reed112	reed112	ADJ
fuelectenerg-1427	1143	33	60	60	NUM
fuelectenerg-1427	1143	34	a.	a.	NOUN
fuelectenerg-1427	1143	35	n.	n.	PROPN
fuelectenerg-1427	1143	36	al	al	PROPN
fuelectenerg-1427	1143	37	-	-	PUNCT
fuelectenerg-1427	1143	38	rabadi	rabadi	VERB
fuelectenerg-1427	1143	39	an	an	DET
fuelectenerg-1427	1143	40	extended	extended	ADJ
fuelectenerg-1427	1143	41	green	green	ADJ
fuelectenerg-1427	1143	42	sasao	sasao	PROPN
fuelectenerg-1427	1143	43	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1143	44	of	of	ADP
fuelectenerg-1427	1143	45	canonical	canonical	ADJ
fuelectenerg-1427	1143	46	ternary	ternary	ADJ
fuelectenerg-1427	1143	47	galois	galois	NOUN
fuelectenerg-1427	1143	48	forms	form	NOUN
fuelectenerg-1427	1143	49	and	and	CCONJ
fuelectenerg-1427	1143	50	universal	universal	ADJ
fuelectenerg-1427	1143	51	logic	logic	NOUN
fuelectenerg-1427	1143	52	modules	module	VERB
fuelectenerg-1427	1143	53	61	61	NUM
fuelectenerg-1427	1143	54	an	an	DET
fuelectenerg-1427	1143	55	extended	extended	ADJ
fuelectenerg-1427	1143	56	green	green	ADJ
fuelectenerg-1427	1143	57	sasao	sasao	PROPN
fuelectenerg-1427	1143	58	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1143	59	of	of	ADP
fuelectenerg-1427	1143	60	canonical	canonical	ADJ
fuelectenerg-1427	1143	61	ternary	ternary	ADJ
fuelectenerg-1427	1143	62	galois	galois	NOUN
fuelectenerg-1427	1143	63	forms	form	NOUN
fuelectenerg-1427	1143	64	...	...	PUNCT
fuelectenerg-1427	1144	1	muller	muller	NOUN
fuelectenerg-1427	1144	2	decision	decision	NOUN
fuelectenerg-1427	1144	3	tree	tree	NOUN
fuelectenerg-1427	1144	4	(	(	PUNCT
fuelectenerg-1427	1144	5	tprmdt	tprmdt	NOUN
fuelectenerg-1427	1144	6	)	)	PUNCT
fuelectenerg-1427	1144	7	.	.	PUNCT
fuelectenerg-1427	1145	1	the	the	DET
fuelectenerg-1427	1145	2	resulting	result	VERB
fuelectenerg-1427	1145	3	expression	expression	NOUN
fuelectenerg-1427	1145	4	is	be	AUX
fuelectenerg-1427	1145	5	called	call	VERB
fuelectenerg-1427	1145	6	ternary	ternary	ADJ
fuelectenerg-1427	1145	7	pseudoreed	pseudoreed	NOUN
fuelectenerg-1427	1145	8	-	-	PUNCT
fuelectenerg-1427	1145	9	muller	muller	NOUN
fuelectenerg-1427	1145	10	expression	expression	NOUN
fuelectenerg-1427	1145	11	.	.	PUNCT
fuelectenerg-1427	1146	1	definition	definition	NOUN
fuelectenerg-1427	1146	2	10	10	NUM
fuelectenerg-1427	1146	3	.	.	PUNCT
fuelectenerg-1427	1147	1	the	the	DET
fuelectenerg-1427	1147	2	decision	decision	NOUN
fuelectenerg-1427	1147	3	tree	tree	NOUN
fuelectenerg-1427	1147	4	that	that	PRON
fuelectenerg-1427	1147	5	results	result	VERB
fuelectenerg-1427	1147	6	from	from	ADP
fuelectenerg-1427	1147	7	using	use	VERB
fuelectenerg-1427	1147	8	any	any	PRON
fuelectenerg-1427	1147	9	of	of	ADP
fuelectenerg-1427	1147	10	the	the	DET
fuelectenerg-1427	1147	11	ternary	ternary	ADJ
fuelectenerg-1427	1147	12	shannon	shannon	NOUN
fuelectenerg-1427	1147	13	expansion	expansion	NOUN
fuelectenerg-1427	1147	14	or	or	CCONJ
fuelectenerg-1427	1147	15	ternary	ternary	ADJ
fuelectenerg-1427	1147	16	davio	davio	NOUN
fuelectenerg-1427	1147	17	expansions	expansion	NOUN
fuelectenerg-1427	1147	18	(	(	PUNCT
fuelectenerg-1427	1147	19	nodes	node	NOUN
fuelectenerg-1427	1147	20	)	)	PUNCT
fuelectenerg-1427	1147	21	for	for	ADP
fuelectenerg-1427	1147	22	each	each	DET
fuelectenerg-1427	1147	23	node	node	NOUN
fuelectenerg-1427	1147	24	(	(	PUNCT
fuelectenerg-1427	1147	25	per	per	ADP
fuelectenerg-1427	1147	26	level	level	NOUN
fuelectenerg-1427	1147	27	)	)	PUNCT
fuelectenerg-1427	1147	28	of	of	ADP
fuelectenerg-1427	1147	29	the	the	DET
fuelectenerg-1427	1147	30	dt	dt	NOUN
fuelectenerg-1427	1147	31	is	be	AUX
fuelectenerg-1427	1147	32	called	call	VERB
fuelectenerg-1427	1147	33	ternary	ternary	ADJ
fuelectenerg-1427	1147	34	pseudo	pseudo	NOUN
fuelectenerg-1427	1147	35	-	-	NOUN
fuelectenerg-1427	1147	36	kronecker	kronecker	NOUN
fuelectenerg-1427	1147	37	decision	decision	NOUN
fuelectenerg-1427	1147	38	tree	tree	NOUN
fuelectenerg-1427	1147	39	(	(	PUNCT
fuelectenerg-1427	1147	40	tpkrodt	tpkrodt	PROPN
fuelectenerg-1427	1147	41	)	)	PUNCT
fuelectenerg-1427	1147	42	.	.	PUNCT
fuelectenerg-1427	1148	1	the	the	DET
fuelectenerg-1427	1148	2	resulting	result	VERB
fuelectenerg-1427	1148	3	expression	expression	NOUN
fuelectenerg-1427	1148	4	is	be	AUX
fuelectenerg-1427	1148	5	called	call	VERB
fuelectenerg-1427	1148	6	ternary	ternary	ADJ
fuelectenerg-1427	1148	7	pseudo	pseudo	NOUN
fuelectenerg-1427	1148	8	-	-	NOUN
fuelectenerg-1427	1148	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1148	10	expression	expression	NOUN
fuelectenerg-1427	1148	11	.	.	PUNCT
fuelectenerg-1427	1149	1	definition	definition	NOUN
fuelectenerg-1427	1149	2	11	11	NUM
fuelectenerg-1427	1149	3	.	.	PUNCT
fuelectenerg-1427	1150	1	the	the	DET
fuelectenerg-1427	1150	2	decision	decision	NOUN
fuelectenerg-1427	1150	3	tree	tree	NOUN
fuelectenerg-1427	1150	4	that	that	PRON
fuelectenerg-1427	1150	5	results	result	VERB
fuelectenerg-1427	1150	6	from	from	ADP
fuelectenerg-1427	1150	7	using	use	VERB
fuelectenerg-1427	1150	8	any	any	PRON
fuelectenerg-1427	1150	9	of	of	ADP
fuelectenerg-1427	1150	10	the	the	DET
fuelectenerg-1427	1150	11	ternary	ternary	ADJ
fuelectenerg-1427	1150	12	shannon	shannon	NOUN
fuelectenerg-1427	1150	13	expansion	expansion	NOUN
fuelectenerg-1427	1150	14	or	or	CCONJ
fuelectenerg-1427	1150	15	ternary	ternary	ADJ
fuelectenerg-1427	1150	16	davio	davio	NOUN
fuelectenerg-1427	1150	17	expansions	expansion	NOUN
fuelectenerg-1427	1150	18	(	(	PUNCT
fuelectenerg-1427	1150	19	nodes	node	NOUN
fuelectenerg-1427	1150	20	)	)	PUNCT
fuelectenerg-1427	1150	21	for	for	ADP
fuelectenerg-1427	1150	22	each	each	DET
fuelectenerg-1427	1150	23	node	node	NOUN
fuelectenerg-1427	1150	24	(	(	PUNCT
fuelectenerg-1427	1150	25	per	per	ADP
fuelectenerg-1427	1150	26	level	level	NOUN
fuelectenerg-1427	1150	27	)	)	PUNCT
fuelectenerg-1427	1150	28	of	of	ADP
fuelectenerg-1427	1150	29	the	the	DET
fuelectenerg-1427	1150	30	dt	dt	PROPN
fuelectenerg-1427	1150	31	,	,	PUNCT
fuelectenerg-1427	1150	32	disregarding	disregard	VERB
fuelectenerg-1427	1150	33	order	order	NOUN
fuelectenerg-1427	1150	34	of	of	ADP
fuelectenerg-1427	1150	35	variables	variable	NOUN
fuelectenerg-1427	1150	36	,	,	PUNCT
fuelectenerg-1427	1150	37	provided	provide	VERB
fuelectenerg-1427	1150	38	that	that	SCONJ
fuelectenerg-1427	1150	39	variables	variable	NOUN
fuelectenerg-1427	1150	40	are	be	AUX
fuelectenerg-1427	1150	41	not	not	PART
fuelectenerg-1427	1150	42	repeated	repeat	VERB
fuelectenerg-1427	1150	43	along	along	ADP
fuelectenerg-1427	1150	44	the	the	DET
fuelectenerg-1427	1150	45	same	same	ADJ
fuelectenerg-1427	1150	46	branches	branch	NOUN
fuelectenerg-1427	1150	47	,	,	PUNCT
fuelectenerg-1427	1150	48	is	be	AUX
fuelectenerg-1427	1150	49	called	call	VERB
fuelectenerg-1427	1150	50	ternary	ternary	ADJ
fuelectenerg-1427	1150	51	free	free	ADJ
fuelectenerg-1427	1150	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1150	53	decision	decision	NOUN
fuelectenerg-1427	1150	54	tree	tree	NOUN
fuelectenerg-1427	1150	55	(	(	PUNCT
fuelectenerg-1427	1150	56	tfkrodt	tfkrodt	PROPN
fuelectenerg-1427	1150	57	)	)	PUNCT
fuelectenerg-1427	1150	58	.	.	PUNCT
fuelectenerg-1427	1151	1	the	the	DET
fuelectenerg-1427	1151	2	result	result	NOUN
fuelectenerg-1427	1151	3	is	be	AUX
fuelectenerg-1427	1151	4	called	call	VERB
fuelectenerg-1427	1151	5	ternary	ternary	ADJ
fuelectenerg-1427	1151	6	free	free	ADJ
fuelectenerg-1427	1151	7	-	-	PUNCT
fuelectenerg-1427	1151	8	kronecker	kronecker	NOUN
fuelectenerg-1427	1151	9	expression	expression	NOUN
fuelectenerg-1427	1151	10	.	.	PUNCT
fuelectenerg-1427	1152	1	definition	definition	NOUN
fuelectenerg-1427	1152	2	12	12	NUM
fuelectenerg-1427	1152	3	.	.	PUNCT
fuelectenerg-1427	1153	1	the	the	DET
fuelectenerg-1427	1153	2	ternary	ternary	ADJ
fuelectenerg-1427	1153	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1153	4	dt	dt	NOUN
fuelectenerg-1427	1153	5	that	that	PRON
fuelectenerg-1427	1153	6	has	have	VERB
fuelectenerg-1427	1153	7	at	at	ADV
fuelectenerg-1427	1153	8	least	least	ADV
fuelectenerg-1427	1153	9	one	one	NUM
fuelectenerg-1427	1153	10	ternary	ternary	ADJ
fuelectenerg-1427	1153	11	generalized	generalize	VERB
fuelectenerg-1427	1153	12	reed	reed	NOUN
fuelectenerg-1427	1153	13	-	-	PUNCT
fuelectenerg-1427	1153	14	muller	muller	NOUN
fuelectenerg-1427	1153	15	expansion	expansion	NOUN
fuelectenerg-1427	1153	16	node	node	NOUN
fuelectenerg-1427	1153	17	is	be	AUX
fuelectenerg-1427	1153	18	called	call	VERB
fuelectenerg-1427	1153	19	ternary	ternary	ADJ
fuelectenerg-1427	1153	20	generalized	generalize	VERB
fuelectenerg-1427	1153	21	kronecker	kronecker	NOUN
fuelectenerg-1427	1153	22	decision	decision	NOUN
fuelectenerg-1427	1153	23	tree	tree	NOUN
fuelectenerg-1427	1153	24	(	(	PUNCT
fuelectenerg-1427	1153	25	tgkdt	tgkdt	ADJ
fuelectenerg-1427	1153	26	)	)	PUNCT
fuelectenerg-1427	1153	27	.	.	PUNCT
fuelectenerg-1427	1154	1	the	the	DET
fuelectenerg-1427	1154	2	result	result	NOUN
fuelectenerg-1427	1154	3	is	be	AUX
fuelectenerg-1427	1154	4	called	call	VERB
fuelectenerg-1427	1154	5	ternary	ternary	ADJ
fuelectenerg-1427	1154	6	generalized	generalized	ADJ
fuelectenerg-1427	1154	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1154	8	expression	expression	NOUN
fuelectenerg-1427	1154	9	.	.	PUNCT
fuelectenerg-1427	1155	1	definition	definition	NOUN
fuelectenerg-1427	1155	2	13	13	NUM
fuelectenerg-1427	1155	3	.	.	PUNCT
fuelectenerg-1427	1156	1	the	the	DET
fuelectenerg-1427	1156	2	ternary	ternary	ADJ
fuelectenerg-1427	1156	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1156	4	dt	dt	NOUN
fuelectenerg-1427	1156	5	that	that	PRON
fuelectenerg-1427	1156	6	has	have	VERB
fuelectenerg-1427	1156	7	at	at	ADV
fuelectenerg-1427	1156	8	least	least	ADJ
fuelectenerg-1427	1156	9	one	one	NUM
fuelectenerg-1427	1156	10	tgif	tgif	NOUN
fuelectenerg-1427	1156	11	node	node	NOUN
fuelectenerg-1427	1156	12	is	be	AUX
fuelectenerg-1427	1156	13	called	call	VERB
fuelectenerg-1427	1156	14	ternary	ternary	ADJ
fuelectenerg-1427	1156	15	generalized	generalize	VERB
fuelectenerg-1427	1156	16	inclusive	inclusive	ADJ
fuelectenerg-1427	1156	17	forms	form	NOUN
fuelectenerg-1427	1156	18	kronecker	kronecker	NOUN
fuelectenerg-1427	1156	19	(	(	PUNCT
fuelectenerg-1427	1156	20	tgifk	tgifk	NOUN
fuelectenerg-1427	1156	21	)	)	PUNCT
fuelectenerg-1427	1156	22	decision	decision	NOUN
fuelectenerg-1427	1156	23	tree	tree	NOUN
fuelectenerg-1427	1156	24	.	.	PUNCT
fuelectenerg-1427	1157	1	the	the	DET
fuelectenerg-1427	1157	2	result	result	NOUN
fuelectenerg-1427	1157	3	is	be	AUX
fuelectenerg-1427	1157	4	called	call	VERB
fuelectenerg-1427	1157	5	ternary	ternary	ADJ
fuelectenerg-1427	1157	6	generalized	generalized	ADJ
fuelectenerg-1427	1157	7	inclusive	inclusive	ADJ
fuelectenerg-1427	1157	8	form	form	NOUN
fuelectenerg-1427	1157	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1157	10	expression	expression	NOUN
fuelectenerg-1427	1157	11	.	.	PUNCT
fuelectenerg-1427	1158	1	figure	figure	NOUN
fuelectenerg-1427	1158	2	6(b	6(b	NUM
fuelectenerg-1427	1158	3	)	)	PUNCT
fuelectenerg-1427	1158	4	illustrates	illustrate	VERB
fuelectenerg-1427	1158	5	the	the	DET
fuelectenerg-1427	1158	6	extended	extended	ADJ
fuelectenerg-1427	1158	7	gf(3	gf(3	PROPN
fuelectenerg-1427	1158	8	)	)	PUNCT
fuelectenerg-1427	1158	9	green	green	ADJ
fuelectenerg-1427	1158	10	-	-	PUNCT
fuelectenerg-1427	1158	11	sasao	sasao	PROPN
fuelectenerg-1427	1158	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1158	13	with	with	ADP
fuelectenerg-1427	1158	14	the	the	DET
fuelectenerg-1427	1158	15	new	new	ADJ
fuelectenerg-1427	1158	16	subfamily	subfamily	ADV
fuelectenerg-1427	1158	17	(	(	PUNCT
fuelectenerg-1427	1158	18	tgifk	tgifk	NOUN
fuelectenerg-1427	1158	19	)	)	PUNCT
fuelectenerg-1427	1158	20	.	.	PUNCT
fuelectenerg-1427	1159	1	the	the	DET
fuelectenerg-1427	1159	2	presented	present	VERB
fuelectenerg-1427	1159	3	tgif	tgif	NOUN
fuelectenerg-1427	1159	4	nodes	node	NOUN
fuelectenerg-1427	1159	5	can	can	AUX
fuelectenerg-1427	1159	6	be	be	AUX
fuelectenerg-1427	1159	7	realized	realize	VERB
fuelectenerg-1427	1159	8	with	with	ADP
fuelectenerg-1427	1159	9	universal	universal	ADJ
fuelectenerg-1427	1159	10	logic	logic	NOUN
fuelectenerg-1427	1159	11	modules	module	NOUN
fuelectenerg-1427	1159	12	(	(	PUNCT
fuelectenerg-1427	1159	13	ulms	ulm	NOUN
fuelectenerg-1427	1159	14	)	)	PUNCT
fuelectenerg-1427	1159	15	for	for	ADP
fuelectenerg-1427	1159	16	pairs	pair	NOUN
fuelectenerg-1427	1159	17	of	of	ADP
fuelectenerg-1427	1159	18	variables	variable	NOUN
fuelectenerg-1427	1159	19	,	,	PUNCT
fuelectenerg-1427	1159	20	as	as	SCONJ
fuelectenerg-1427	1159	21	will	will	AUX
fuelectenerg-1427	1159	22	be	be	AUX
fuelectenerg-1427	1159	23	shown	show	VERB
fuelectenerg-1427	1159	24	in	in	ADP
fuelectenerg-1427	1159	25	section	section	NOUN
fuelectenerg-1427	1159	26	3	3	NUM
fuelectenerg-1427	1159	27	,	,	PUNCT
fuelectenerg-1427	1159	28	which	which	PRON
fuelectenerg-1427	1159	29	is	be	AUX
fuelectenerg-1427	1159	30	analogous	analogous	ADJ
fuelectenerg-1427	1159	31	to	to	ADP
fuelectenerg-1427	1159	32	what	what	PRON
fuelectenerg-1427	1159	33	was	be	AUX
fuelectenerg-1427	1159	34	done	do	VERB
fuelectenerg-1427	1159	35	for	for	ADP
fuelectenerg-1427	1159	36	the	the	DET
fuelectenerg-1427	1159	37	binary	binary	ADJ
fuelectenerg-1427	1159	38	case	case	NOUN
fuelectenerg-1427	1159	39	.	.	PUNCT
fuelectenerg-1427	1160	1	although	although	SCONJ
fuelectenerg-1427	1160	2	the	the	DET
fuelectenerg-1427	1160	3	s	s	PROPN
fuelectenerg-1427	1160	4	/	/	SYM
fuelectenerg-1427	1160	5	d	d	NOUN
fuelectenerg-1427	1160	6	trees	tree	NOUN
fuelectenerg-1427	1160	7	that	that	PRON
fuelectenerg-1427	1160	8	have	have	AUX
fuelectenerg-1427	1160	9	been	be	AUX
fuelectenerg-1427	1160	10	developed	develop	VERB
fuelectenerg-1427	1160	11	so	so	ADV
fuelectenerg-1427	1160	12	far	far	ADV
fuelectenerg-1427	1160	13	are	be	AUX
fuelectenerg-1427	1160	14	for	for	ADP
fuelectenerg-1427	1160	15	the	the	DET
fuelectenerg-1427	1160	16	ternary	ternary	ADJ
fuelectenerg-1427	1160	17	radix	radix	NOUN
fuelectenerg-1427	1160	18	,	,	PUNCT
fuelectenerg-1427	1160	19	similar	similar	ADJ
fuelectenerg-1427	1160	20	s	s	NOUN
fuelectenerg-1427	1160	21	/	/	SYM
fuelectenerg-1427	1160	22	d	d	NOUN
fuelectenerg-1427	1160	23	trees	tree	NOUN
fuelectenerg-1427	1160	24	can	can	AUX
fuelectenerg-1427	1160	25	be	be	AUX
fuelectenerg-1427	1160	26	developed	develop	VERB
fuelectenerg-1427	1160	27	as	as	ADV
fuelectenerg-1427	1160	28	well	well	ADV
fuelectenerg-1427	1160	29	for	for	ADP
fuelectenerg-1427	1160	30	higher	high	ADJ
fuelectenerg-1427	1160	31	galois	galois	PROPN
fuelectenerg-1427	1160	32	radices	radix	NOUN
fuelectenerg-1427	1160	33	of	of	ADP
fuelectenerg-1427	1160	34	gf(pk	gf(pk	NOUN
fuelectenerg-1427	1160	35	)	)	PUNCT
fuelectenerg-1427	1160	36	where	where	SCONJ
fuelectenerg-1427	1160	37	p	p	NOUN
fuelectenerg-1427	1160	38	is	be	AUX
fuelectenerg-1427	1160	39	a	a	DET
fuelectenerg-1427	1160	40	prime	prime	ADJ
fuelectenerg-1427	1160	41	number	number	NOUN
fuelectenerg-1427	1160	42	and	and	CCONJ
fuelectenerg-1427	1160	43	k	k	PROPN
fuelectenerg-1427	1160	44	is	be	AUX
fuelectenerg-1427	1160	45	a	a	DET
fuelectenerg-1427	1160	46	natural	natural	ADJ
fuelectenerg-1427	1160	47	number	number	NOUN
fuelectenerg-1427	1160	48	≥	≥	NOUN
fuelectenerg-1427	1160	49	1	1	NUM
fuelectenerg-1427	1160	50	.	.	PUNCT
fuelectenerg-1427	1161	1	tgrm	tgrm	ADJ
fuelectenerg-1427	1161	2	ternary	ternary	ADJ
fuelectenerg-1427	1161	3	gfsop	gfsop	NOUN
fuelectenerg-1427	1161	4	ternary	ternary	ADJ
fuelectenerg-1427	1161	5	canonical	canonical	ADJ
fuelectenerg-1427	1161	6	forms	form	NOUN
fuelectenerg-1427	1161	7	tfgif	tfgif	PROPN
fuelectenerg-1427	1161	8	tgif	tgif	PROPN
fuelectenerg-1427	1161	9	tif	tif	PROPN
fuelectenerg-1427	1161	10	tpgk	tpgk	PROPN
fuelectenerg-1427	1161	11	tgk	tgk	PROPN
fuelectenerg-1427	1161	12	tpkro	tpkro	PROPN
fuelectenerg-1427	1161	13	tkrotfprm	tkrotfprm	PROPN
fuelectenerg-1427	1162	1	tgifk	tgifk	PROPN
fuelectenerg-1427	1162	2	esop	esop	X
fuelectenerg-1427	1162	3	canonical	canonical	ADJ
fuelectenerg-1427	1162	4	forms	form	NOUN
fuelectenerg-1427	1162	5	fgif	fgif	INTJ
fuelectenerg-1427	1162	6	gif	gif	PROPN
fuelectenerg-1427	1162	7	if	if	SCONJ
fuelectenerg-1427	1162	8	pgk	pgk	NOUN
fuelectenerg-1427	1162	9	gk	gk	PROPN
fuelectenerg-1427	1162	10	grm	grm	PROPN
fuelectenerg-1427	1162	11	pkro	pkro	PROPN
fuelectenerg-1427	1162	12	krofprm	krofprm	PROPN
fuelectenerg-1427	1162	13	(	(	PUNCT
fuelectenerg-1427	1162	14	a	a	NOUN
fuelectenerg-1427	1162	15	)	)	PUNCT
fuelectenerg-1427	1162	16	(	(	PUNCT
fuelectenerg-1427	1162	17	b	b	X
fuelectenerg-1427	1162	18	)	)	PUNCT
fuelectenerg-1427	1162	19	figure	figure	NOUN
fuelectenerg-1427	1162	20	6	6	NUM
fuelectenerg-1427	1162	21	:	:	PUNCT
fuelectenerg-1427	1162	22	green	green	ADJ
fuelectenerg-1427	1162	23	-	-	PUNCT
fuelectenerg-1427	1162	24	sasao	sasao	PROPN
fuelectenerg-1427	1162	25	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1162	26	:	:	PUNCT
fuelectenerg-1427	1162	27	(	(	PUNCT
fuelectenerg-1427	1162	28	a	a	X
fuelectenerg-1427	1162	29	)	)	PUNCT
fuelectenerg-1427	1162	30	set	set	NOUN
fuelectenerg-1427	1162	31	-	-	PUNCT
fuelectenerg-1427	1162	32	theoretic	theoretic	NOUN
fuelectenerg-1427	1162	33	relationship	relationship	NOUN
fuelectenerg-1427	1162	34	between	between	ADP
fuelectenerg-1427	1162	35	gf(2	gf(2	PROPN
fuelectenerg-1427	1162	36	)	)	PUNCT
fuelectenerg-1427	1162	37	families	family	NOUN
fuelectenerg-1427	1162	38	of	of	ADP
fuelectenerg-1427	1162	39	canonical	canonical	ADJ
fuelectenerg-1427	1162	40	forms	form	NOUN
fuelectenerg-1427	1162	41	,	,	PUNCT
fuelectenerg-1427	1162	42	and	and	CCONJ
fuelectenerg-1427	1162	43	(	(	PUNCT
fuelectenerg-1427	1162	44	b	b	X
fuelectenerg-1427	1162	45	)	)	PUNCT
fuelectenerg-1427	1162	46	the	the	DET
fuelectenerg-1427	1162	47	extended	extend	VERB
fuelectenerg-1427	1162	48	green	green	ADJ
fuelectenerg-1427	1162	49	-	-	PUNCT
fuelectenerg-1427	1162	50	sasao	sasao	NOUN
fuelectenerg-1427	1162	51	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1162	52	with	with	ADP
fuelectenerg-1427	1162	53	a	a	DET
fuelectenerg-1427	1162	54	new	new	ADJ
fuelectenerg-1427	1162	55	sub	sub	NOUN
fuelectenerg-1427	1162	56	-	-	NOUN
fuelectenerg-1427	1162	57	family	family	ADJ
fuelectenerg-1427	1162	58	(	(	PUNCT
fuelectenerg-1427	1162	59	tgifk	tgifk	NOUN
fuelectenerg-1427	1162	60	)	)	PUNCT
fuelectenerg-1427	1162	61	for	for	ADP
fuelectenerg-1427	1162	62	gf(3	gf(3	PROPN
fuelectenerg-1427	1162	63	)	)	PUNCT
fuelectenerg-1427	1162	64	reed	reed	NOUN
fuelectenerg-1427	1162	65	-	-	PUNCT
fuelectenerg-1427	1162	66	muller	muller	NOUN
fuelectenerg-1427	1162	67	logic	logic	NOUN
fuelectenerg-1427	1162	68	.	.	PUNCT
fuelectenerg-1427	1163	1	113	113	NUM
fuelectenerg-1427	1163	2	an	an	DET
fuelectenerg-1427	1163	3	extended	extend	VERB
fuelectenerg-1427	1163	4	green	green	ADJ
fuelectenerg-1427	1163	5	sasao	sasao	PROPN
fuelectenerg-1427	1163	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1163	7	of	of	ADP
fuelectenerg-1427	1163	8	canonical	canonical	ADJ
fuelectenerg-1427	1163	9	ternary	ternary	ADJ
fuelectenerg-1427	1163	10	galois	galois	NOUN
fuelectenerg-1427	1163	11	forms	form	NOUN
fuelectenerg-1427	1163	12	...	...	PUNCT
fuelectenerg-1427	1163	13	muller	muller	NOUN
fuelectenerg-1427	1163	14	decision	decision	NOUN
fuelectenerg-1427	1163	15	tree	tree	NOUN
fuelectenerg-1427	1163	16	(	(	PUNCT
fuelectenerg-1427	1163	17	tprmdt	tprmdt	NOUN
fuelectenerg-1427	1163	18	)	)	PUNCT
fuelectenerg-1427	1163	19	.	.	PUNCT
fuelectenerg-1427	1164	1	the	the	DET
fuelectenerg-1427	1164	2	resulting	result	VERB
fuelectenerg-1427	1164	3	expression	expression	NOUN
fuelectenerg-1427	1164	4	is	be	AUX
fuelectenerg-1427	1164	5	called	call	VERB
fuelectenerg-1427	1164	6	ternary	ternary	ADJ
fuelectenerg-1427	1164	7	pseudoreed	pseudoreed	NOUN
fuelectenerg-1427	1164	8	-	-	PUNCT
fuelectenerg-1427	1164	9	muller	muller	NOUN
fuelectenerg-1427	1164	10	expression	expression	NOUN
fuelectenerg-1427	1164	11	.	.	PUNCT
fuelectenerg-1427	1165	1	definition	definition	NOUN
fuelectenerg-1427	1165	2	10	10	NUM
fuelectenerg-1427	1165	3	.	.	PUNCT
fuelectenerg-1427	1166	1	the	the	DET
fuelectenerg-1427	1166	2	decision	decision	NOUN
fuelectenerg-1427	1166	3	tree	tree	NOUN
fuelectenerg-1427	1166	4	that	that	PRON
fuelectenerg-1427	1166	5	results	result	VERB
fuelectenerg-1427	1166	6	from	from	ADP
fuelectenerg-1427	1166	7	using	use	VERB
fuelectenerg-1427	1166	8	any	any	PRON
fuelectenerg-1427	1166	9	of	of	ADP
fuelectenerg-1427	1166	10	the	the	DET
fuelectenerg-1427	1166	11	ternary	ternary	ADJ
fuelectenerg-1427	1166	12	shannon	shannon	NOUN
fuelectenerg-1427	1166	13	expansion	expansion	NOUN
fuelectenerg-1427	1166	14	or	or	CCONJ
fuelectenerg-1427	1166	15	ternary	ternary	ADJ
fuelectenerg-1427	1166	16	davio	davio	NOUN
fuelectenerg-1427	1166	17	expansions	expansion	NOUN
fuelectenerg-1427	1166	18	(	(	PUNCT
fuelectenerg-1427	1166	19	nodes	node	NOUN
fuelectenerg-1427	1166	20	)	)	PUNCT
fuelectenerg-1427	1166	21	for	for	ADP
fuelectenerg-1427	1166	22	each	each	DET
fuelectenerg-1427	1166	23	node	node	NOUN
fuelectenerg-1427	1166	24	(	(	PUNCT
fuelectenerg-1427	1166	25	per	per	ADP
fuelectenerg-1427	1166	26	level	level	NOUN
fuelectenerg-1427	1166	27	)	)	PUNCT
fuelectenerg-1427	1166	28	of	of	ADP
fuelectenerg-1427	1166	29	the	the	DET
fuelectenerg-1427	1166	30	dt	dt	NOUN
fuelectenerg-1427	1166	31	is	be	AUX
fuelectenerg-1427	1166	32	called	call	VERB
fuelectenerg-1427	1166	33	ternary	ternary	ADJ
fuelectenerg-1427	1166	34	pseudo	pseudo	NOUN
fuelectenerg-1427	1166	35	-	-	NOUN
fuelectenerg-1427	1166	36	kronecker	kronecker	NOUN
fuelectenerg-1427	1166	37	decision	decision	NOUN
fuelectenerg-1427	1166	38	tree	tree	NOUN
fuelectenerg-1427	1166	39	(	(	PUNCT
fuelectenerg-1427	1166	40	tpkrodt	tpkrodt	PROPN
fuelectenerg-1427	1166	41	)	)	PUNCT
fuelectenerg-1427	1166	42	.	.	PUNCT
fuelectenerg-1427	1167	1	the	the	DET
fuelectenerg-1427	1167	2	resulting	result	VERB
fuelectenerg-1427	1167	3	expression	expression	NOUN
fuelectenerg-1427	1167	4	is	be	AUX
fuelectenerg-1427	1167	5	called	call	VERB
fuelectenerg-1427	1167	6	ternary	ternary	ADJ
fuelectenerg-1427	1167	7	pseudo	pseudo	NOUN
fuelectenerg-1427	1167	8	-	-	NOUN
fuelectenerg-1427	1167	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1167	10	expression	expression	NOUN
fuelectenerg-1427	1167	11	.	.	PUNCT
fuelectenerg-1427	1168	1	definition	definition	NOUN
fuelectenerg-1427	1168	2	11	11	NUM
fuelectenerg-1427	1168	3	.	.	PUNCT
fuelectenerg-1427	1169	1	the	the	DET
fuelectenerg-1427	1169	2	decision	decision	NOUN
fuelectenerg-1427	1169	3	tree	tree	NOUN
fuelectenerg-1427	1169	4	that	that	PRON
fuelectenerg-1427	1169	5	results	result	VERB
fuelectenerg-1427	1169	6	from	from	ADP
fuelectenerg-1427	1169	7	using	use	VERB
fuelectenerg-1427	1169	8	any	any	PRON
fuelectenerg-1427	1169	9	of	of	ADP
fuelectenerg-1427	1169	10	the	the	DET
fuelectenerg-1427	1169	11	ternary	ternary	ADJ
fuelectenerg-1427	1169	12	shannon	shannon	NOUN
fuelectenerg-1427	1169	13	expansion	expansion	NOUN
fuelectenerg-1427	1169	14	or	or	CCONJ
fuelectenerg-1427	1169	15	ternary	ternary	ADJ
fuelectenerg-1427	1169	16	davio	davio	NOUN
fuelectenerg-1427	1169	17	expansions	expansion	NOUN
fuelectenerg-1427	1169	18	(	(	PUNCT
fuelectenerg-1427	1169	19	nodes	node	NOUN
fuelectenerg-1427	1169	20	)	)	PUNCT
fuelectenerg-1427	1169	21	for	for	ADP
fuelectenerg-1427	1169	22	each	each	DET
fuelectenerg-1427	1169	23	node	node	NOUN
fuelectenerg-1427	1169	24	(	(	PUNCT
fuelectenerg-1427	1169	25	per	per	ADP
fuelectenerg-1427	1169	26	level	level	NOUN
fuelectenerg-1427	1169	27	)	)	PUNCT
fuelectenerg-1427	1169	28	of	of	ADP
fuelectenerg-1427	1169	29	the	the	DET
fuelectenerg-1427	1169	30	dt	dt	PROPN
fuelectenerg-1427	1169	31	,	,	PUNCT
fuelectenerg-1427	1169	32	disregarding	disregard	VERB
fuelectenerg-1427	1169	33	order	order	NOUN
fuelectenerg-1427	1169	34	of	of	ADP
fuelectenerg-1427	1169	35	variables	variable	NOUN
fuelectenerg-1427	1169	36	,	,	PUNCT
fuelectenerg-1427	1169	37	provided	provide	VERB
fuelectenerg-1427	1169	38	that	that	SCONJ
fuelectenerg-1427	1169	39	variables	variable	NOUN
fuelectenerg-1427	1169	40	are	be	AUX
fuelectenerg-1427	1169	41	not	not	PART
fuelectenerg-1427	1169	42	repeated	repeat	VERB
fuelectenerg-1427	1169	43	along	along	ADP
fuelectenerg-1427	1169	44	the	the	DET
fuelectenerg-1427	1169	45	same	same	ADJ
fuelectenerg-1427	1169	46	branches	branch	NOUN
fuelectenerg-1427	1169	47	,	,	PUNCT
fuelectenerg-1427	1169	48	is	be	AUX
fuelectenerg-1427	1169	49	called	call	VERB
fuelectenerg-1427	1169	50	ternary	ternary	ADJ
fuelectenerg-1427	1169	51	free	free	ADJ
fuelectenerg-1427	1169	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1169	53	decision	decision	NOUN
fuelectenerg-1427	1169	54	tree	tree	NOUN
fuelectenerg-1427	1169	55	(	(	PUNCT
fuelectenerg-1427	1169	56	tfkrodt	tfkrodt	PROPN
fuelectenerg-1427	1169	57	)	)	PUNCT
fuelectenerg-1427	1169	58	.	.	PUNCT
fuelectenerg-1427	1170	1	the	the	DET
fuelectenerg-1427	1170	2	result	result	NOUN
fuelectenerg-1427	1170	3	is	be	AUX
fuelectenerg-1427	1170	4	called	call	VERB
fuelectenerg-1427	1170	5	ternary	ternary	ADJ
fuelectenerg-1427	1170	6	free	free	ADJ
fuelectenerg-1427	1170	7	-	-	PUNCT
fuelectenerg-1427	1170	8	kronecker	kronecker	NOUN
fuelectenerg-1427	1170	9	expression	expression	NOUN
fuelectenerg-1427	1170	10	.	.	PUNCT
fuelectenerg-1427	1171	1	definition	definition	NOUN
fuelectenerg-1427	1171	2	12	12	NUM
fuelectenerg-1427	1171	3	.	.	PUNCT
fuelectenerg-1427	1172	1	the	the	DET
fuelectenerg-1427	1172	2	ternary	ternary	ADJ
fuelectenerg-1427	1172	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1172	4	dt	dt	NOUN
fuelectenerg-1427	1172	5	that	that	PRON
fuelectenerg-1427	1172	6	has	have	VERB
fuelectenerg-1427	1172	7	at	at	ADV
fuelectenerg-1427	1172	8	least	least	ADV
fuelectenerg-1427	1172	9	one	one	NUM
fuelectenerg-1427	1172	10	ternary	ternary	ADJ
fuelectenerg-1427	1172	11	generalized	generalize	VERB
fuelectenerg-1427	1172	12	reed	reed	NOUN
fuelectenerg-1427	1172	13	-	-	PUNCT
fuelectenerg-1427	1172	14	muller	muller	NOUN
fuelectenerg-1427	1172	15	expansion	expansion	NOUN
fuelectenerg-1427	1172	16	node	node	NOUN
fuelectenerg-1427	1172	17	is	be	AUX
fuelectenerg-1427	1172	18	called	call	VERB
fuelectenerg-1427	1172	19	ternary	ternary	ADJ
fuelectenerg-1427	1172	20	generalized	generalize	VERB
fuelectenerg-1427	1172	21	kronecker	kronecker	NOUN
fuelectenerg-1427	1172	22	decision	decision	NOUN
fuelectenerg-1427	1172	23	tree	tree	NOUN
fuelectenerg-1427	1172	24	(	(	PUNCT
fuelectenerg-1427	1172	25	tgkdt	tgkdt	ADJ
fuelectenerg-1427	1172	26	)	)	PUNCT
fuelectenerg-1427	1172	27	.	.	PUNCT
fuelectenerg-1427	1173	1	the	the	DET
fuelectenerg-1427	1173	2	result	result	NOUN
fuelectenerg-1427	1173	3	is	be	AUX
fuelectenerg-1427	1173	4	called	call	VERB
fuelectenerg-1427	1173	5	ternary	ternary	ADJ
fuelectenerg-1427	1173	6	generalized	generalized	ADJ
fuelectenerg-1427	1173	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1173	8	expression	expression	NOUN
fuelectenerg-1427	1173	9	.	.	PUNCT
fuelectenerg-1427	1174	1	definition	definition	NOUN
fuelectenerg-1427	1174	2	13	13	NUM
fuelectenerg-1427	1174	3	.	.	PUNCT
fuelectenerg-1427	1175	1	the	the	DET
fuelectenerg-1427	1175	2	ternary	ternary	ADJ
fuelectenerg-1427	1175	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1175	4	dt	dt	NOUN
fuelectenerg-1427	1175	5	that	that	PRON
fuelectenerg-1427	1175	6	has	have	VERB
fuelectenerg-1427	1175	7	at	at	ADV
fuelectenerg-1427	1175	8	least	least	ADJ
fuelectenerg-1427	1175	9	one	one	NUM
fuelectenerg-1427	1175	10	tgif	tgif	NOUN
fuelectenerg-1427	1175	11	node	node	NOUN
fuelectenerg-1427	1175	12	is	be	AUX
fuelectenerg-1427	1175	13	called	call	VERB
fuelectenerg-1427	1175	14	ternary	ternary	ADJ
fuelectenerg-1427	1175	15	generalized	generalize	VERB
fuelectenerg-1427	1175	16	inclusive	inclusive	ADJ
fuelectenerg-1427	1175	17	forms	form	NOUN
fuelectenerg-1427	1175	18	kronecker	kronecker	NOUN
fuelectenerg-1427	1175	19	(	(	PUNCT
fuelectenerg-1427	1175	20	tgifk	tgifk	NOUN
fuelectenerg-1427	1175	21	)	)	PUNCT
fuelectenerg-1427	1175	22	decision	decision	NOUN
fuelectenerg-1427	1175	23	tree	tree	NOUN
fuelectenerg-1427	1175	24	.	.	PUNCT
fuelectenerg-1427	1176	1	the	the	DET
fuelectenerg-1427	1176	2	result	result	NOUN
fuelectenerg-1427	1176	3	is	be	AUX
fuelectenerg-1427	1176	4	called	call	VERB
fuelectenerg-1427	1176	5	ternary	ternary	ADJ
fuelectenerg-1427	1176	6	generalized	generalized	ADJ
fuelectenerg-1427	1176	7	inclusive	inclusive	ADJ
fuelectenerg-1427	1176	8	form	form	NOUN
fuelectenerg-1427	1176	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1176	10	expression	expression	NOUN
fuelectenerg-1427	1176	11	.	.	PUNCT
fuelectenerg-1427	1177	1	figure	figure	NOUN
fuelectenerg-1427	1177	2	6(b	6(b	NUM
fuelectenerg-1427	1177	3	)	)	PUNCT
fuelectenerg-1427	1177	4	illustrates	illustrate	VERB
fuelectenerg-1427	1177	5	the	the	DET
fuelectenerg-1427	1177	6	extended	extended	ADJ
fuelectenerg-1427	1177	7	gf(3	gf(3	PROPN
fuelectenerg-1427	1177	8	)	)	PUNCT
fuelectenerg-1427	1177	9	green	green	ADJ
fuelectenerg-1427	1177	10	-	-	PUNCT
fuelectenerg-1427	1177	11	sasao	sasao	PROPN
fuelectenerg-1427	1177	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1177	13	with	with	ADP
fuelectenerg-1427	1177	14	the	the	DET
fuelectenerg-1427	1177	15	new	new	ADJ
fuelectenerg-1427	1177	16	subfamily	subfamily	ADV
fuelectenerg-1427	1177	17	(	(	PUNCT
fuelectenerg-1427	1177	18	tgifk	tgifk	NOUN
fuelectenerg-1427	1177	19	)	)	PUNCT
fuelectenerg-1427	1177	20	.	.	PUNCT
fuelectenerg-1427	1178	1	the	the	DET
fuelectenerg-1427	1178	2	presented	present	VERB
fuelectenerg-1427	1178	3	tgif	tgif	NOUN
fuelectenerg-1427	1178	4	nodes	node	NOUN
fuelectenerg-1427	1178	5	can	can	AUX
fuelectenerg-1427	1178	6	be	be	AUX
fuelectenerg-1427	1178	7	realized	realize	VERB
fuelectenerg-1427	1178	8	with	with	ADP
fuelectenerg-1427	1178	9	universal	universal	ADJ
fuelectenerg-1427	1178	10	logic	logic	NOUN
fuelectenerg-1427	1178	11	modules	module	NOUN
fuelectenerg-1427	1178	12	(	(	PUNCT
fuelectenerg-1427	1178	13	ulms	ulm	NOUN
fuelectenerg-1427	1178	14	)	)	PUNCT
fuelectenerg-1427	1178	15	for	for	ADP
fuelectenerg-1427	1178	16	pairs	pair	NOUN
fuelectenerg-1427	1178	17	of	of	ADP
fuelectenerg-1427	1178	18	variables	variable	NOUN
fuelectenerg-1427	1178	19	,	,	PUNCT
fuelectenerg-1427	1178	20	as	as	SCONJ
fuelectenerg-1427	1178	21	will	will	AUX
fuelectenerg-1427	1178	22	be	be	AUX
fuelectenerg-1427	1178	23	shown	show	VERB
fuelectenerg-1427	1178	24	in	in	ADP
fuelectenerg-1427	1178	25	section	section	NOUN
fuelectenerg-1427	1178	26	3	3	NUM
fuelectenerg-1427	1178	27	,	,	PUNCT
fuelectenerg-1427	1178	28	which	which	PRON
fuelectenerg-1427	1178	29	is	be	AUX
fuelectenerg-1427	1178	30	analogous	analogous	ADJ
fuelectenerg-1427	1178	31	to	to	ADP
fuelectenerg-1427	1178	32	what	what	PRON
fuelectenerg-1427	1178	33	was	be	AUX
fuelectenerg-1427	1178	34	done	do	VERB
fuelectenerg-1427	1178	35	for	for	ADP
fuelectenerg-1427	1178	36	the	the	DET
fuelectenerg-1427	1178	37	binary	binary	ADJ
fuelectenerg-1427	1178	38	case	case	NOUN
fuelectenerg-1427	1178	39	.	.	PUNCT
fuelectenerg-1427	1179	1	although	although	SCONJ
fuelectenerg-1427	1179	2	the	the	DET
fuelectenerg-1427	1179	3	s	s	PROPN
fuelectenerg-1427	1179	4	/	/	SYM
fuelectenerg-1427	1179	5	d	d	NOUN
fuelectenerg-1427	1179	6	trees	tree	NOUN
fuelectenerg-1427	1179	7	that	that	PRON
fuelectenerg-1427	1179	8	have	have	AUX
fuelectenerg-1427	1179	9	been	be	AUX
fuelectenerg-1427	1179	10	developed	develop	VERB
fuelectenerg-1427	1179	11	so	so	ADV
fuelectenerg-1427	1179	12	far	far	ADV
fuelectenerg-1427	1179	13	are	be	AUX
fuelectenerg-1427	1179	14	for	for	ADP
fuelectenerg-1427	1179	15	the	the	DET
fuelectenerg-1427	1179	16	ternary	ternary	ADJ
fuelectenerg-1427	1179	17	radix	radix	NOUN
fuelectenerg-1427	1179	18	,	,	PUNCT
fuelectenerg-1427	1179	19	similar	similar	ADJ
fuelectenerg-1427	1179	20	s	s	NOUN
fuelectenerg-1427	1179	21	/	/	SYM
fuelectenerg-1427	1179	22	d	d	NOUN
fuelectenerg-1427	1179	23	trees	tree	NOUN
fuelectenerg-1427	1179	24	can	can	AUX
fuelectenerg-1427	1179	25	be	be	AUX
fuelectenerg-1427	1179	26	developed	develop	VERB
fuelectenerg-1427	1179	27	as	as	ADV
fuelectenerg-1427	1179	28	well	well	ADV
fuelectenerg-1427	1179	29	for	for	ADP
fuelectenerg-1427	1179	30	higher	high	ADJ
fuelectenerg-1427	1179	31	galois	galois	PROPN
fuelectenerg-1427	1179	32	radices	radix	NOUN
fuelectenerg-1427	1179	33	of	of	ADP
fuelectenerg-1427	1179	34	gf(pk	gf(pk	NOUN
fuelectenerg-1427	1179	35	)	)	PUNCT
fuelectenerg-1427	1179	36	where	where	SCONJ
fuelectenerg-1427	1179	37	p	p	NOUN
fuelectenerg-1427	1179	38	is	be	AUX
fuelectenerg-1427	1179	39	a	a	DET
fuelectenerg-1427	1179	40	prime	prime	ADJ
fuelectenerg-1427	1179	41	number	number	NOUN
fuelectenerg-1427	1179	42	and	and	CCONJ
fuelectenerg-1427	1179	43	k	k	PROPN
fuelectenerg-1427	1179	44	is	be	AUX
fuelectenerg-1427	1179	45	a	a	DET
fuelectenerg-1427	1179	46	natural	natural	ADJ
fuelectenerg-1427	1179	47	number	number	NOUN
fuelectenerg-1427	1179	48	≥	≥	NOUN
fuelectenerg-1427	1179	49	1	1	NUM
fuelectenerg-1427	1179	50	.	.	PUNCT
fuelectenerg-1427	1180	1	tgrm	tgrm	ADJ
fuelectenerg-1427	1180	2	ternary	ternary	ADJ
fuelectenerg-1427	1180	3	gfsop	gfsop	NOUN
fuelectenerg-1427	1180	4	ternary	ternary	ADJ
fuelectenerg-1427	1180	5	canonical	canonical	ADJ
fuelectenerg-1427	1180	6	forms	form	NOUN
fuelectenerg-1427	1180	7	tfgif	tfgif	PROPN
fuelectenerg-1427	1180	8	tgif	tgif	PROPN
fuelectenerg-1427	1180	9	tif	tif	PROPN
fuelectenerg-1427	1180	10	tpgk	tpgk	PROPN
fuelectenerg-1427	1180	11	tgk	tgk	PROPN
fuelectenerg-1427	1180	12	tpkro	tpkro	PROPN
fuelectenerg-1427	1180	13	tkrotfprm	tkrotfprm	PROPN
fuelectenerg-1427	1181	1	tgifk	tgifk	PROPN
fuelectenerg-1427	1181	2	esop	esop	X
fuelectenerg-1427	1181	3	canonical	canonical	ADJ
fuelectenerg-1427	1181	4	forms	form	NOUN
fuelectenerg-1427	1181	5	fgif	fgif	INTJ
fuelectenerg-1427	1181	6	gif	gif	PROPN
fuelectenerg-1427	1181	7	if	if	SCONJ
fuelectenerg-1427	1181	8	pgk	pgk	NOUN
fuelectenerg-1427	1181	9	gk	gk	PROPN
fuelectenerg-1427	1181	10	grm	grm	PROPN
fuelectenerg-1427	1181	11	pkro	pkro	PROPN
fuelectenerg-1427	1181	12	krofprm	krofprm	PROPN
fuelectenerg-1427	1181	13	(	(	PUNCT
fuelectenerg-1427	1181	14	a	a	NOUN
fuelectenerg-1427	1181	15	)	)	PUNCT
fuelectenerg-1427	1181	16	(	(	PUNCT
fuelectenerg-1427	1181	17	b	b	X
fuelectenerg-1427	1181	18	)	)	PUNCT
fuelectenerg-1427	1181	19	figure	figure	NOUN
fuelectenerg-1427	1181	20	6	6	NUM
fuelectenerg-1427	1181	21	:	:	PUNCT
fuelectenerg-1427	1181	22	green	green	ADJ
fuelectenerg-1427	1181	23	-	-	PUNCT
fuelectenerg-1427	1181	24	sasao	sasao	PROPN
fuelectenerg-1427	1181	25	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1181	26	:	:	PUNCT
fuelectenerg-1427	1181	27	(	(	PUNCT
fuelectenerg-1427	1181	28	a	a	X
fuelectenerg-1427	1181	29	)	)	PUNCT
fuelectenerg-1427	1181	30	set	set	NOUN
fuelectenerg-1427	1181	31	-	-	PUNCT
fuelectenerg-1427	1181	32	theoretic	theoretic	NOUN
fuelectenerg-1427	1181	33	relationship	relationship	NOUN
fuelectenerg-1427	1181	34	between	between	ADP
fuelectenerg-1427	1181	35	gf(2	gf(2	PROPN
fuelectenerg-1427	1181	36	)	)	PUNCT
fuelectenerg-1427	1181	37	families	family	NOUN
fuelectenerg-1427	1181	38	of	of	ADP
fuelectenerg-1427	1181	39	canonical	canonical	ADJ
fuelectenerg-1427	1181	40	forms	form	NOUN
fuelectenerg-1427	1181	41	,	,	PUNCT
fuelectenerg-1427	1181	42	and	and	CCONJ
fuelectenerg-1427	1181	43	(	(	PUNCT
fuelectenerg-1427	1181	44	b	b	X
fuelectenerg-1427	1181	45	)	)	PUNCT
fuelectenerg-1427	1181	46	the	the	DET
fuelectenerg-1427	1181	47	extended	extend	VERB
fuelectenerg-1427	1181	48	green	green	ADJ
fuelectenerg-1427	1181	49	-	-	PUNCT
fuelectenerg-1427	1181	50	sasao	sasao	NOUN
fuelectenerg-1427	1181	51	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1181	52	with	with	ADP
fuelectenerg-1427	1181	53	a	a	DET
fuelectenerg-1427	1181	54	new	new	ADJ
fuelectenerg-1427	1181	55	sub	sub	NOUN
fuelectenerg-1427	1181	56	-	-	NOUN
fuelectenerg-1427	1181	57	family	family	ADJ
fuelectenerg-1427	1181	58	(	(	PUNCT
fuelectenerg-1427	1181	59	tgifk	tgifk	NOUN
fuelectenerg-1427	1181	60	)	)	PUNCT
fuelectenerg-1427	1181	61	for	for	ADP
fuelectenerg-1427	1181	62	gf(3	gf(3	PROPN
fuelectenerg-1427	1181	63	)	)	PUNCT
fuelectenerg-1427	1181	64	reed	reed	NOUN
fuelectenerg-1427	1181	65	-	-	PUNCT
fuelectenerg-1427	1181	66	muller	muller	NOUN
fuelectenerg-1427	1181	67	logic	logic	NOUN
fuelectenerg-1427	1181	68	.	.	PUNCT
fuelectenerg-1427	1182	1	113	113	NUM
fuelectenerg-1427	1182	2	an	an	DET
fuelectenerg-1427	1182	3	extended	extend	VERB
fuelectenerg-1427	1182	4	green	green	ADJ
fuelectenerg-1427	1182	5	sasao	sasao	PROPN
fuelectenerg-1427	1182	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1182	7	of	of	ADP
fuelectenerg-1427	1182	8	canonical	canonical	ADJ
fuelectenerg-1427	1182	9	ternary	ternary	ADJ
fuelectenerg-1427	1182	10	galois	galois	NOUN
fuelectenerg-1427	1182	11	forms	form	NOUN
fuelectenerg-1427	1182	12	...	...	PUNCT
fuelectenerg-1427	1182	13	muller	muller	NOUN
fuelectenerg-1427	1182	14	decision	decision	NOUN
fuelectenerg-1427	1182	15	tree	tree	NOUN
fuelectenerg-1427	1182	16	(	(	PUNCT
fuelectenerg-1427	1182	17	tprmdt	tprmdt	NOUN
fuelectenerg-1427	1182	18	)	)	PUNCT
fuelectenerg-1427	1182	19	.	.	PUNCT
fuelectenerg-1427	1183	1	the	the	DET
fuelectenerg-1427	1183	2	resulting	result	VERB
fuelectenerg-1427	1183	3	expression	expression	NOUN
fuelectenerg-1427	1183	4	is	be	AUX
fuelectenerg-1427	1183	5	called	call	VERB
fuelectenerg-1427	1183	6	ternary	ternary	ADJ
fuelectenerg-1427	1183	7	pseudoreed	pseudoreed	NOUN
fuelectenerg-1427	1183	8	-	-	PUNCT
fuelectenerg-1427	1183	9	muller	muller	NOUN
fuelectenerg-1427	1183	10	expression	expression	NOUN
fuelectenerg-1427	1183	11	.	.	PUNCT
fuelectenerg-1427	1184	1	definition	definition	NOUN
fuelectenerg-1427	1184	2	10	10	NUM
fuelectenerg-1427	1184	3	.	.	PUNCT
fuelectenerg-1427	1185	1	the	the	DET
fuelectenerg-1427	1185	2	decision	decision	NOUN
fuelectenerg-1427	1185	3	tree	tree	NOUN
fuelectenerg-1427	1185	4	that	that	PRON
fuelectenerg-1427	1185	5	results	result	VERB
fuelectenerg-1427	1185	6	from	from	ADP
fuelectenerg-1427	1185	7	using	use	VERB
fuelectenerg-1427	1185	8	any	any	PRON
fuelectenerg-1427	1185	9	of	of	ADP
fuelectenerg-1427	1185	10	the	the	DET
fuelectenerg-1427	1185	11	ternary	ternary	ADJ
fuelectenerg-1427	1185	12	shannon	shannon	NOUN
fuelectenerg-1427	1185	13	expansion	expansion	NOUN
fuelectenerg-1427	1185	14	or	or	CCONJ
fuelectenerg-1427	1185	15	ternary	ternary	ADJ
fuelectenerg-1427	1185	16	davio	davio	NOUN
fuelectenerg-1427	1185	17	expansions	expansion	NOUN
fuelectenerg-1427	1185	18	(	(	PUNCT
fuelectenerg-1427	1185	19	nodes	node	NOUN
fuelectenerg-1427	1185	20	)	)	PUNCT
fuelectenerg-1427	1185	21	for	for	ADP
fuelectenerg-1427	1185	22	each	each	DET
fuelectenerg-1427	1185	23	node	node	NOUN
fuelectenerg-1427	1185	24	(	(	PUNCT
fuelectenerg-1427	1185	25	per	per	ADP
fuelectenerg-1427	1185	26	level	level	NOUN
fuelectenerg-1427	1185	27	)	)	PUNCT
fuelectenerg-1427	1185	28	of	of	ADP
fuelectenerg-1427	1185	29	the	the	DET
fuelectenerg-1427	1185	30	dt	dt	NOUN
fuelectenerg-1427	1185	31	is	be	AUX
fuelectenerg-1427	1185	32	called	call	VERB
fuelectenerg-1427	1185	33	ternary	ternary	ADJ
fuelectenerg-1427	1185	34	pseudo	pseudo	NOUN
fuelectenerg-1427	1185	35	-	-	NOUN
fuelectenerg-1427	1185	36	kronecker	kronecker	NOUN
fuelectenerg-1427	1185	37	decision	decision	NOUN
fuelectenerg-1427	1185	38	tree	tree	NOUN
fuelectenerg-1427	1185	39	(	(	PUNCT
fuelectenerg-1427	1185	40	tpkrodt	tpkrodt	PROPN
fuelectenerg-1427	1185	41	)	)	PUNCT
fuelectenerg-1427	1185	42	.	.	PUNCT
fuelectenerg-1427	1186	1	the	the	DET
fuelectenerg-1427	1186	2	resulting	result	VERB
fuelectenerg-1427	1186	3	expression	expression	NOUN
fuelectenerg-1427	1186	4	is	be	AUX
fuelectenerg-1427	1186	5	called	call	VERB
fuelectenerg-1427	1186	6	ternary	ternary	ADJ
fuelectenerg-1427	1186	7	pseudo	pseudo	NOUN
fuelectenerg-1427	1186	8	-	-	NOUN
fuelectenerg-1427	1186	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1186	10	expression	expression	NOUN
fuelectenerg-1427	1186	11	.	.	PUNCT
fuelectenerg-1427	1187	1	definition	definition	NOUN
fuelectenerg-1427	1187	2	11	11	NUM
fuelectenerg-1427	1187	3	.	.	PUNCT
fuelectenerg-1427	1188	1	the	the	DET
fuelectenerg-1427	1188	2	decision	decision	NOUN
fuelectenerg-1427	1188	3	tree	tree	NOUN
fuelectenerg-1427	1188	4	that	that	PRON
fuelectenerg-1427	1188	5	results	result	VERB
fuelectenerg-1427	1188	6	from	from	ADP
fuelectenerg-1427	1188	7	using	use	VERB
fuelectenerg-1427	1188	8	any	any	PRON
fuelectenerg-1427	1188	9	of	of	ADP
fuelectenerg-1427	1188	10	the	the	DET
fuelectenerg-1427	1188	11	ternary	ternary	ADJ
fuelectenerg-1427	1188	12	shannon	shannon	NOUN
fuelectenerg-1427	1188	13	expansion	expansion	NOUN
fuelectenerg-1427	1188	14	or	or	CCONJ
fuelectenerg-1427	1188	15	ternary	ternary	ADJ
fuelectenerg-1427	1188	16	davio	davio	NOUN
fuelectenerg-1427	1188	17	expansions	expansion	NOUN
fuelectenerg-1427	1188	18	(	(	PUNCT
fuelectenerg-1427	1188	19	nodes	node	NOUN
fuelectenerg-1427	1188	20	)	)	PUNCT
fuelectenerg-1427	1188	21	for	for	ADP
fuelectenerg-1427	1188	22	each	each	DET
fuelectenerg-1427	1188	23	node	node	NOUN
fuelectenerg-1427	1188	24	(	(	PUNCT
fuelectenerg-1427	1188	25	per	per	ADP
fuelectenerg-1427	1188	26	level	level	NOUN
fuelectenerg-1427	1188	27	)	)	PUNCT
fuelectenerg-1427	1188	28	of	of	ADP
fuelectenerg-1427	1188	29	the	the	DET
fuelectenerg-1427	1188	30	dt	dt	PROPN
fuelectenerg-1427	1188	31	,	,	PUNCT
fuelectenerg-1427	1188	32	disregarding	disregard	VERB
fuelectenerg-1427	1188	33	order	order	NOUN
fuelectenerg-1427	1188	34	of	of	ADP
fuelectenerg-1427	1188	35	variables	variable	NOUN
fuelectenerg-1427	1188	36	,	,	PUNCT
fuelectenerg-1427	1188	37	provided	provide	VERB
fuelectenerg-1427	1188	38	that	that	SCONJ
fuelectenerg-1427	1188	39	variables	variable	NOUN
fuelectenerg-1427	1188	40	are	be	AUX
fuelectenerg-1427	1188	41	not	not	PART
fuelectenerg-1427	1188	42	repeated	repeat	VERB
fuelectenerg-1427	1188	43	along	along	ADP
fuelectenerg-1427	1188	44	the	the	DET
fuelectenerg-1427	1188	45	same	same	ADJ
fuelectenerg-1427	1188	46	branches	branch	NOUN
fuelectenerg-1427	1188	47	,	,	PUNCT
fuelectenerg-1427	1188	48	is	be	AUX
fuelectenerg-1427	1188	49	called	call	VERB
fuelectenerg-1427	1188	50	ternary	ternary	ADJ
fuelectenerg-1427	1188	51	free	free	ADJ
fuelectenerg-1427	1188	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1188	53	decision	decision	NOUN
fuelectenerg-1427	1188	54	tree	tree	NOUN
fuelectenerg-1427	1188	55	(	(	PUNCT
fuelectenerg-1427	1188	56	tfkrodt	tfkrodt	PROPN
fuelectenerg-1427	1188	57	)	)	PUNCT
fuelectenerg-1427	1188	58	.	.	PUNCT
fuelectenerg-1427	1189	1	the	the	DET
fuelectenerg-1427	1189	2	result	result	NOUN
fuelectenerg-1427	1189	3	is	be	AUX
fuelectenerg-1427	1189	4	called	call	VERB
fuelectenerg-1427	1189	5	ternary	ternary	ADJ
fuelectenerg-1427	1189	6	free	free	ADJ
fuelectenerg-1427	1189	7	-	-	PUNCT
fuelectenerg-1427	1189	8	kronecker	kronecker	NOUN
fuelectenerg-1427	1189	9	expression	expression	NOUN
fuelectenerg-1427	1189	10	.	.	PUNCT
fuelectenerg-1427	1190	1	definition	definition	NOUN
fuelectenerg-1427	1190	2	12	12	NUM
fuelectenerg-1427	1190	3	.	.	PUNCT
fuelectenerg-1427	1191	1	the	the	DET
fuelectenerg-1427	1191	2	ternary	ternary	ADJ
fuelectenerg-1427	1191	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1191	4	dt	dt	NOUN
fuelectenerg-1427	1191	5	that	that	PRON
fuelectenerg-1427	1191	6	has	have	VERB
fuelectenerg-1427	1191	7	at	at	ADV
fuelectenerg-1427	1191	8	least	least	ADV
fuelectenerg-1427	1191	9	one	one	NUM
fuelectenerg-1427	1191	10	ternary	ternary	ADJ
fuelectenerg-1427	1191	11	generalized	generalize	VERB
fuelectenerg-1427	1191	12	reed	reed	NOUN
fuelectenerg-1427	1191	13	-	-	PUNCT
fuelectenerg-1427	1191	14	muller	muller	NOUN
fuelectenerg-1427	1191	15	expansion	expansion	NOUN
fuelectenerg-1427	1191	16	node	node	NOUN
fuelectenerg-1427	1191	17	is	be	AUX
fuelectenerg-1427	1191	18	called	call	VERB
fuelectenerg-1427	1191	19	ternary	ternary	ADJ
fuelectenerg-1427	1191	20	generalized	generalize	VERB
fuelectenerg-1427	1191	21	kronecker	kronecker	NOUN
fuelectenerg-1427	1191	22	decision	decision	NOUN
fuelectenerg-1427	1191	23	tree	tree	NOUN
fuelectenerg-1427	1191	24	(	(	PUNCT
fuelectenerg-1427	1191	25	tgkdt	tgkdt	ADJ
fuelectenerg-1427	1191	26	)	)	PUNCT
fuelectenerg-1427	1191	27	.	.	PUNCT
fuelectenerg-1427	1192	1	the	the	DET
fuelectenerg-1427	1192	2	result	result	NOUN
fuelectenerg-1427	1192	3	is	be	AUX
fuelectenerg-1427	1192	4	called	call	VERB
fuelectenerg-1427	1192	5	ternary	ternary	ADJ
fuelectenerg-1427	1192	6	generalized	generalized	ADJ
fuelectenerg-1427	1192	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1192	8	expression	expression	NOUN
fuelectenerg-1427	1192	9	.	.	PUNCT
fuelectenerg-1427	1193	1	definition	definition	NOUN
fuelectenerg-1427	1193	2	13	13	NUM
fuelectenerg-1427	1193	3	.	.	PUNCT
fuelectenerg-1427	1194	1	the	the	DET
fuelectenerg-1427	1194	2	ternary	ternary	ADJ
fuelectenerg-1427	1194	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1194	4	dt	dt	NOUN
fuelectenerg-1427	1194	5	that	that	PRON
fuelectenerg-1427	1194	6	has	have	VERB
fuelectenerg-1427	1194	7	at	at	ADV
fuelectenerg-1427	1194	8	least	least	ADJ
fuelectenerg-1427	1194	9	one	one	NUM
fuelectenerg-1427	1194	10	tgif	tgif	NOUN
fuelectenerg-1427	1194	11	node	node	NOUN
fuelectenerg-1427	1194	12	is	be	AUX
fuelectenerg-1427	1194	13	called	call	VERB
fuelectenerg-1427	1194	14	ternary	ternary	ADJ
fuelectenerg-1427	1194	15	generalized	generalize	VERB
fuelectenerg-1427	1194	16	inclusive	inclusive	ADJ
fuelectenerg-1427	1194	17	forms	form	NOUN
fuelectenerg-1427	1194	18	kronecker	kronecker	NOUN
fuelectenerg-1427	1194	19	(	(	PUNCT
fuelectenerg-1427	1194	20	tgifk	tgifk	NOUN
fuelectenerg-1427	1194	21	)	)	PUNCT
fuelectenerg-1427	1194	22	decision	decision	NOUN
fuelectenerg-1427	1194	23	tree	tree	NOUN
fuelectenerg-1427	1194	24	.	.	PUNCT
fuelectenerg-1427	1195	1	the	the	DET
fuelectenerg-1427	1195	2	result	result	NOUN
fuelectenerg-1427	1195	3	is	be	AUX
fuelectenerg-1427	1195	4	called	call	VERB
fuelectenerg-1427	1195	5	ternary	ternary	ADJ
fuelectenerg-1427	1195	6	generalized	generalized	ADJ
fuelectenerg-1427	1195	7	inclusive	inclusive	ADJ
fuelectenerg-1427	1195	8	form	form	NOUN
fuelectenerg-1427	1195	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1195	10	expression	expression	NOUN
fuelectenerg-1427	1195	11	.	.	PUNCT
fuelectenerg-1427	1196	1	figure	figure	NOUN
fuelectenerg-1427	1196	2	6(b	6(b	NUM
fuelectenerg-1427	1196	3	)	)	PUNCT
fuelectenerg-1427	1196	4	illustrates	illustrate	VERB
fuelectenerg-1427	1196	5	the	the	DET
fuelectenerg-1427	1196	6	extended	extended	ADJ
fuelectenerg-1427	1196	7	gf(3	gf(3	PROPN
fuelectenerg-1427	1196	8	)	)	PUNCT
fuelectenerg-1427	1196	9	green	green	ADJ
fuelectenerg-1427	1196	10	-	-	PUNCT
fuelectenerg-1427	1196	11	sasao	sasao	PROPN
fuelectenerg-1427	1196	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1196	13	with	with	ADP
fuelectenerg-1427	1196	14	the	the	DET
fuelectenerg-1427	1196	15	new	new	ADJ
fuelectenerg-1427	1196	16	subfamily	subfamily	ADV
fuelectenerg-1427	1196	17	(	(	PUNCT
fuelectenerg-1427	1196	18	tgifk	tgifk	NOUN
fuelectenerg-1427	1196	19	)	)	PUNCT
fuelectenerg-1427	1196	20	.	.	PUNCT
fuelectenerg-1427	1197	1	the	the	DET
fuelectenerg-1427	1197	2	presented	present	VERB
fuelectenerg-1427	1197	3	tgif	tgif	NOUN
fuelectenerg-1427	1197	4	nodes	node	NOUN
fuelectenerg-1427	1197	5	can	can	AUX
fuelectenerg-1427	1197	6	be	be	AUX
fuelectenerg-1427	1197	7	realized	realize	VERB
fuelectenerg-1427	1197	8	with	with	ADP
fuelectenerg-1427	1197	9	universal	universal	ADJ
fuelectenerg-1427	1197	10	logic	logic	NOUN
fuelectenerg-1427	1197	11	modules	module	NOUN
fuelectenerg-1427	1197	12	(	(	PUNCT
fuelectenerg-1427	1197	13	ulms	ulm	NOUN
fuelectenerg-1427	1197	14	)	)	PUNCT
fuelectenerg-1427	1197	15	for	for	ADP
fuelectenerg-1427	1197	16	pairs	pair	NOUN
fuelectenerg-1427	1197	17	of	of	ADP
fuelectenerg-1427	1197	18	variables	variable	NOUN
fuelectenerg-1427	1197	19	,	,	PUNCT
fuelectenerg-1427	1197	20	as	as	SCONJ
fuelectenerg-1427	1197	21	will	will	AUX
fuelectenerg-1427	1197	22	be	be	AUX
fuelectenerg-1427	1197	23	shown	show	VERB
fuelectenerg-1427	1197	24	in	in	ADP
fuelectenerg-1427	1197	25	section	section	NOUN
fuelectenerg-1427	1197	26	3	3	NUM
fuelectenerg-1427	1197	27	,	,	PUNCT
fuelectenerg-1427	1197	28	which	which	PRON
fuelectenerg-1427	1197	29	is	be	AUX
fuelectenerg-1427	1197	30	analogous	analogous	ADJ
fuelectenerg-1427	1197	31	to	to	ADP
fuelectenerg-1427	1197	32	what	what	PRON
fuelectenerg-1427	1197	33	was	be	AUX
fuelectenerg-1427	1197	34	done	do	VERB
fuelectenerg-1427	1197	35	for	for	ADP
fuelectenerg-1427	1197	36	the	the	DET
fuelectenerg-1427	1197	37	binary	binary	ADJ
fuelectenerg-1427	1197	38	case	case	NOUN
fuelectenerg-1427	1197	39	.	.	PUNCT
fuelectenerg-1427	1198	1	although	although	SCONJ
fuelectenerg-1427	1198	2	the	the	DET
fuelectenerg-1427	1198	3	s	s	PROPN
fuelectenerg-1427	1198	4	/	/	SYM
fuelectenerg-1427	1198	5	d	d	NOUN
fuelectenerg-1427	1198	6	trees	tree	NOUN
fuelectenerg-1427	1198	7	that	that	PRON
fuelectenerg-1427	1198	8	have	have	AUX
fuelectenerg-1427	1198	9	been	be	AUX
fuelectenerg-1427	1198	10	developed	develop	VERB
fuelectenerg-1427	1198	11	so	so	ADV
fuelectenerg-1427	1198	12	far	far	ADV
fuelectenerg-1427	1198	13	are	be	AUX
fuelectenerg-1427	1198	14	for	for	ADP
fuelectenerg-1427	1198	15	the	the	DET
fuelectenerg-1427	1198	16	ternary	ternary	ADJ
fuelectenerg-1427	1198	17	radix	radix	NOUN
fuelectenerg-1427	1198	18	,	,	PUNCT
fuelectenerg-1427	1198	19	similar	similar	ADJ
fuelectenerg-1427	1198	20	s	s	NOUN
fuelectenerg-1427	1198	21	/	/	SYM
fuelectenerg-1427	1198	22	d	d	NOUN
fuelectenerg-1427	1198	23	trees	tree	NOUN
fuelectenerg-1427	1198	24	can	can	AUX
fuelectenerg-1427	1198	25	be	be	AUX
fuelectenerg-1427	1198	26	developed	develop	VERB
fuelectenerg-1427	1198	27	as	as	ADV
fuelectenerg-1427	1198	28	well	well	ADV
fuelectenerg-1427	1198	29	for	for	ADP
fuelectenerg-1427	1198	30	higher	high	ADJ
fuelectenerg-1427	1198	31	galois	galois	PROPN
fuelectenerg-1427	1198	32	radices	radix	NOUN
fuelectenerg-1427	1198	33	of	of	ADP
fuelectenerg-1427	1198	34	gf(pk	gf(pk	NOUN
fuelectenerg-1427	1198	35	)	)	PUNCT
fuelectenerg-1427	1198	36	where	where	SCONJ
fuelectenerg-1427	1198	37	p	p	NOUN
fuelectenerg-1427	1198	38	is	be	AUX
fuelectenerg-1427	1198	39	a	a	DET
fuelectenerg-1427	1198	40	prime	prime	ADJ
fuelectenerg-1427	1198	41	number	number	NOUN
fuelectenerg-1427	1198	42	and	and	CCONJ
fuelectenerg-1427	1198	43	k	k	PROPN
fuelectenerg-1427	1198	44	is	be	AUX
fuelectenerg-1427	1198	45	a	a	DET
fuelectenerg-1427	1198	46	natural	natural	ADJ
fuelectenerg-1427	1198	47	number	number	NOUN
fuelectenerg-1427	1198	48	≥	≥	NOUN
fuelectenerg-1427	1198	49	1	1	NUM
fuelectenerg-1427	1198	50	.	.	PUNCT
fuelectenerg-1427	1199	1	tgrm	tgrm	ADJ
fuelectenerg-1427	1199	2	ternary	ternary	ADJ
fuelectenerg-1427	1199	3	gfsop	gfsop	NOUN
fuelectenerg-1427	1199	4	ternary	ternary	ADJ
fuelectenerg-1427	1199	5	canonical	canonical	ADJ
fuelectenerg-1427	1199	6	forms	form	NOUN
fuelectenerg-1427	1199	7	tfgif	tfgif	PROPN
fuelectenerg-1427	1199	8	tgif	tgif	PROPN
fuelectenerg-1427	1199	9	tif	tif	PROPN
fuelectenerg-1427	1199	10	tpgk	tpgk	PROPN
fuelectenerg-1427	1199	11	tgk	tgk	PROPN
fuelectenerg-1427	1199	12	tpkro	tpkro	PROPN
fuelectenerg-1427	1199	13	tkrotfprm	tkrotfprm	PROPN
fuelectenerg-1427	1200	1	tgifk	tgifk	PROPN
fuelectenerg-1427	1200	2	esop	esop	X
fuelectenerg-1427	1200	3	canonical	canonical	ADJ
fuelectenerg-1427	1200	4	forms	form	NOUN
fuelectenerg-1427	1200	5	fgif	fgif	INTJ
fuelectenerg-1427	1200	6	gif	gif	PROPN
fuelectenerg-1427	1200	7	if	if	SCONJ
fuelectenerg-1427	1200	8	pgk	pgk	NOUN
fuelectenerg-1427	1200	9	gk	gk	PROPN
fuelectenerg-1427	1200	10	grm	grm	PROPN
fuelectenerg-1427	1200	11	pkro	pkro	PROPN
fuelectenerg-1427	1200	12	krofprm	krofprm	PROPN
fuelectenerg-1427	1200	13	(	(	PUNCT
fuelectenerg-1427	1200	14	a	a	NOUN
fuelectenerg-1427	1200	15	)	)	PUNCT
fuelectenerg-1427	1200	16	(	(	PUNCT
fuelectenerg-1427	1200	17	b	b	X
fuelectenerg-1427	1200	18	)	)	PUNCT
fuelectenerg-1427	1200	19	figure	figure	NOUN
fuelectenerg-1427	1200	20	6	6	NUM
fuelectenerg-1427	1200	21	:	:	PUNCT
fuelectenerg-1427	1200	22	green	green	ADJ
fuelectenerg-1427	1200	23	-	-	PUNCT
fuelectenerg-1427	1200	24	sasao	sasao	PROPN
fuelectenerg-1427	1200	25	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1200	26	:	:	PUNCT
fuelectenerg-1427	1200	27	(	(	PUNCT
fuelectenerg-1427	1200	28	a	a	X
fuelectenerg-1427	1200	29	)	)	PUNCT
fuelectenerg-1427	1200	30	set	set	NOUN
fuelectenerg-1427	1200	31	-	-	PUNCT
fuelectenerg-1427	1200	32	theoretic	theoretic	NOUN
fuelectenerg-1427	1200	33	relationship	relationship	NOUN
fuelectenerg-1427	1200	34	between	between	ADP
fuelectenerg-1427	1200	35	gf(2	gf(2	PROPN
fuelectenerg-1427	1200	36	)	)	PUNCT
fuelectenerg-1427	1200	37	families	family	NOUN
fuelectenerg-1427	1200	38	of	of	ADP
fuelectenerg-1427	1200	39	canonical	canonical	ADJ
fuelectenerg-1427	1200	40	forms	form	NOUN
fuelectenerg-1427	1200	41	,	,	PUNCT
fuelectenerg-1427	1200	42	and	and	CCONJ
fuelectenerg-1427	1200	43	(	(	PUNCT
fuelectenerg-1427	1200	44	b	b	X
fuelectenerg-1427	1200	45	)	)	PUNCT
fuelectenerg-1427	1200	46	the	the	DET
fuelectenerg-1427	1200	47	extended	extend	VERB
fuelectenerg-1427	1200	48	green	green	ADJ
fuelectenerg-1427	1200	49	-	-	PUNCT
fuelectenerg-1427	1200	50	sasao	sasao	NOUN
fuelectenerg-1427	1200	51	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1200	52	with	with	ADP
fuelectenerg-1427	1200	53	a	a	DET
fuelectenerg-1427	1200	54	new	new	ADJ
fuelectenerg-1427	1200	55	sub	sub	NOUN
fuelectenerg-1427	1200	56	-	-	NOUN
fuelectenerg-1427	1200	57	family	family	ADJ
fuelectenerg-1427	1200	58	(	(	PUNCT
fuelectenerg-1427	1200	59	tgifk	tgifk	NOUN
fuelectenerg-1427	1200	60	)	)	PUNCT
fuelectenerg-1427	1200	61	for	for	ADP
fuelectenerg-1427	1200	62	gf(3	gf(3	PROPN
fuelectenerg-1427	1200	63	)	)	PUNCT
fuelectenerg-1427	1200	64	reed	reed	NOUN
fuelectenerg-1427	1200	65	-	-	PUNCT
fuelectenerg-1427	1200	66	muller	muller	NOUN
fuelectenerg-1427	1200	67	logic	logic	NOUN
fuelectenerg-1427	1200	68	.	.	PUNCT
fuelectenerg-1427	1201	1	113	113	NUM
fuelectenerg-1427	1201	2	an	an	DET
fuelectenerg-1427	1201	3	extended	extend	VERB
fuelectenerg-1427	1201	4	green	green	ADJ
fuelectenerg-1427	1201	5	sasao	sasao	PROPN
fuelectenerg-1427	1201	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1201	7	of	of	ADP
fuelectenerg-1427	1201	8	canonical	canonical	ADJ
fuelectenerg-1427	1201	9	ternary	ternary	ADJ
fuelectenerg-1427	1201	10	galois	galois	NOUN
fuelectenerg-1427	1201	11	forms	form	NOUN
fuelectenerg-1427	1201	12	...	...	PUNCT
fuelectenerg-1427	1202	1	definition	definition	NOUN
fuelectenerg-1427	1202	2	4	4	NUM
fuelectenerg-1427	1202	3	.	.	PUNCT
fuelectenerg-1427	1203	1	the	the	DET
fuelectenerg-1427	1203	2	family	family	NOUN
fuelectenerg-1427	1203	3	of	of	ADP
fuelectenerg-1427	1203	4	forms	form	NOUN
fuelectenerg-1427	1203	5	,	,	PUNCT
fuelectenerg-1427	1203	6	generated	generate	VERB
fuelectenerg-1427	1203	7	by	by	ADP
fuelectenerg-1427	1203	8	s	s	PROPN
fuelectenerg-1427	1203	9	/	/	SYM
fuelectenerg-1427	1203	10	d	d	NOUN
fuelectenerg-1427	1203	11	tree	tree	NOUN
fuelectenerg-1427	1203	12	with	with	ADP
fuelectenerg-1427	1203	13	no	no	DET
fuelectenerg-1427	1203	14	fixed	fix	VERB
fuelectenerg-1427	1203	15	ordering	ordering	NOUN
fuelectenerg-1427	1203	16	of	of	ADP
fuelectenerg-1427	1203	17	variables	variable	NOUN
fuelectenerg-1427	1203	18	,	,	PUNCT
fuelectenerg-1427	1203	19	with	with	ADP
fuelectenerg-1427	1203	20	variables	variable	NOUN
fuelectenerg-1427	1203	21	not	not	PART
fuelectenerg-1427	1203	22	repeated	repeat	VERB
fuelectenerg-1427	1203	23	along	along	ADP
fuelectenerg-1427	1203	24	same	same	ADJ
fuelectenerg-1427	1203	25	branches	branch	NOUN
fuelectenerg-1427	1203	26	,	,	PUNCT
fuelectenerg-1427	1203	27	is	be	AUX
fuelectenerg-1427	1203	28	called	call	VERB
fuelectenerg-1427	1203	29	ternary	ternary	ADJ
fuelectenerg-1427	1203	30	free	free	ADJ
fuelectenerg-1427	1203	31	generalized	generalize	VERB
fuelectenerg-1427	1203	32	inclusive	inclusive	ADJ
fuelectenerg-1427	1203	33	forms	form	NOUN
fuelectenerg-1427	1203	34	(	(	PUNCT
fuelectenerg-1427	1203	35	tfgifs	tfgifs	PROPN
fuelectenerg-1427	1203	36	)	)	PUNCT
fuelectenerg-1427	1203	37	.	.	PUNCT
fuelectenerg-1427	1204	1	2.3	2.3	NUM
fuelectenerg-1427	1204	2	an	an	DET
fuelectenerg-1427	1204	3	extended	extended	ADJ
fuelectenerg-1427	1204	4	green	green	ADJ
fuelectenerg-1427	1204	5	-	-	PUNCT
fuelectenerg-1427	1204	6	sasao	sasao	NOUN
fuelectenerg-1427	1204	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1204	8	with	with	ADP
fuelectenerg-1427	1204	9	a	a	DET
fuelectenerg-1427	1204	10	new	new	ADJ
fuelectenerg-1427	1204	11	sub	sub	NOUN
fuelectenerg-1427	1204	12	-	-	NOUN
fuelectenerg-1427	1204	13	family	family	NOUN
fuelectenerg-1427	1204	14	for	for	ADP
fuelectenerg-1427	1204	15	ternary	ternary	ADJ
fuelectenerg-1427	1204	16	reed	reed	NOUN
fuelectenerg-1427	1204	17	-	-	PUNCT
fuelectenerg-1427	1204	18	muller	muller	NOUN
fuelectenerg-1427	1204	19	logic	logic	NOUN
fuelectenerg-1427	1204	20	the	the	DET
fuelectenerg-1427	1204	21	green	green	PROPN
fuelectenerg-1427	1204	22	-	-	PUNCT
fuelectenerg-1427	1204	23	sasao	sasao	PROPN
fuelectenerg-1427	1204	24	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1204	25	of	of	ADP
fuelectenerg-1427	1204	26	families	family	NOUN
fuelectenerg-1427	1204	27	of	of	ADP
fuelectenerg-1427	1204	28	canonical	canonical	ADJ
fuelectenerg-1427	1204	29	forms	form	NOUN
fuelectenerg-1427	1204	30	[	[	X
fuelectenerg-1427	1204	31	1	1	NUM
fuelectenerg-1427	1204	32	,	,	PUNCT
fuelectenerg-1427	1204	33	10	10	NUM
fuelectenerg-1427	1204	34	-	-	SYM
fuelectenerg-1427	1204	35	13	13	NUM
fuelectenerg-1427	1204	36	,	,	PUNCT
fuelectenerg-1427	1204	37	17	17	NUM
fuelectenerg-1427	1204	38	,	,	PUNCT
fuelectenerg-1427	1204	39	24	24	NUM
fuelectenerg-1427	1204	40	,	,	PUNCT
fuelectenerg-1427	1204	41	26	26	NUM
fuelectenerg-1427	1204	42	]	]	PUNCT
fuelectenerg-1427	1204	43	and	and	CCONJ
fuelectenerg-1427	1204	44	the	the	DET
fuelectenerg-1427	1204	45	corresponding	correspond	VERB
fuelectenerg-1427	1204	46	decision	decision	NOUN
fuelectenerg-1427	1204	47	trees	tree	NOUN
fuelectenerg-1427	1204	48	and	and	CCONJ
fuelectenerg-1427	1204	49	diagrams	diagram	NOUN
fuelectenerg-1427	1204	50	is	be	AUX
fuelectenerg-1427	1204	51	based	base	VERB
fuelectenerg-1427	1204	52	on	on	ADP
fuelectenerg-1427	1204	53	three	three	NUM
fuelectenerg-1427	1204	54	generic	generic	ADJ
fuelectenerg-1427	1204	55	expansions	expansion	NOUN
fuelectenerg-1427	1204	56	,	,	PUNCT
fuelectenerg-1427	1204	57	shannon	shannon	PROPN
fuelectenerg-1427	1204	58	,	,	PUNCT
fuelectenerg-1427	1204	59	positive	positive	ADJ
fuelectenerg-1427	1204	60	and	and	CCONJ
fuelectenerg-1427	1204	61	negative	negative	ADJ
fuelectenerg-1427	1204	62	davio	davio	NOUN
fuelectenerg-1427	1204	63	expansions	expansion	NOUN
fuelectenerg-1427	1204	64	.	.	PUNCT
fuelectenerg-1427	1205	1	for	for	ADP
fuelectenerg-1427	1205	2	example	example	NOUN
fuelectenerg-1427	1205	3	,	,	PUNCT
fuelectenerg-1427	1205	4	this	this	PRON
fuelectenerg-1427	1205	5	includes	include	VERB
fuelectenerg-1427	1205	6	shannon	shannon	ADJ
fuelectenerg-1427	1205	7	decision	decision	NOUN
fuelectenerg-1427	1205	8	trees	tree	NOUN
fuelectenerg-1427	1205	9	and	and	CCONJ
fuelectenerg-1427	1205	10	diagrams	diagram	NOUN
fuelectenerg-1427	1205	11	,	,	PUNCT
fuelectenerg-1427	1205	12	positive	positive	ADJ
fuelectenerg-1427	1205	13	and	and	CCONJ
fuelectenerg-1427	1205	14	negative	negative	ADJ
fuelectenerg-1427	1205	15	davio	davio	NOUN
fuelectenerg-1427	1205	16	decision	decision	NOUN
fuelectenerg-1427	1205	17	trees	tree	NOUN
fuelectenerg-1427	1205	18	and	and	CCONJ
fuelectenerg-1427	1205	19	diagrams	diagram	NOUN
fuelectenerg-1427	1205	20	,	,	PUNCT
fuelectenerg-1427	1205	21	fixed	fix	VERB
fuelectenerg-1427	1205	22	polarity	polarity	NOUN
fuelectenerg-1427	1205	23	reed	reed	NOUN
fuelectenerg-1427	1205	24	-	-	PUNCT
fuelectenerg-1427	1205	25	muller	muller	NOUN
fuelectenerg-1427	1205	26	decision	decision	NOUN
fuelectenerg-1427	1205	27	trees	tree	NOUN
fuelectenerg-1427	1205	28	and	and	CCONJ
fuelectenerg-1427	1205	29	diagrams	diagram	NOUN
fuelectenerg-1427	1205	30	,	,	PUNCT
fuelectenerg-1427	1205	31	kronecker	kronecker	NOUN
fuelectenerg-1427	1205	32	decision	decision	NOUN
fuelectenerg-1427	1205	33	trees	tree	NOUN
fuelectenerg-1427	1205	34	and	and	CCONJ
fuelectenerg-1427	1205	35	diagrams	diagram	NOUN
fuelectenerg-1427	1205	36	,	,	PUNCT
fuelectenerg-1427	1205	37	pseudo	pseudo	NOUN
fuelectenerg-1427	1205	38	reed	reed	NOUN
fuelectenerg-1427	1205	39	-	-	PUNCT
fuelectenerg-1427	1205	40	muller	muller	NOUN
fuelectenerg-1427	1205	41	decision	decision	NOUN
fuelectenerg-1427	1205	42	trees	tree	NOUN
fuelectenerg-1427	1205	43	and	and	CCONJ
fuelectenerg-1427	1205	44	diagrams	diagram	NOUN
fuelectenerg-1427	1205	45	,	,	PUNCT
fuelectenerg-1427	1205	46	pseudo	pseudo	NOUN
fuelectenerg-1427	1205	47	kronecker	kronecker	NOUN
fuelectenerg-1427	1205	48	decision	decision	NOUN
fuelectenerg-1427	1205	49	trees	tree	NOUN
fuelectenerg-1427	1205	50	and	and	CCONJ
fuelectenerg-1427	1205	51	diagrams	diagram	NOUN
fuelectenerg-1427	1205	52	,	,	PUNCT
fuelectenerg-1427	1205	53	and	and	CCONJ
fuelectenerg-1427	1205	54	linearly	linearly	ADV
fuelectenerg-1427	1205	55	-	-	PUNCT
fuelectenerg-1427	1205	56	independent	independent	ADJ
fuelectenerg-1427	1205	57	decision	decision	NOUN
fuelectenerg-1427	1205	58	trees	tree	NOUN
fuelectenerg-1427	1205	59	and	and	CCONJ
fuelectenerg-1427	1205	60	diagrams	diagram	NOUN
fuelectenerg-1427	1206	1	[	[	X
fuelectenerg-1427	1206	2	1	1	NUM
fuelectenerg-1427	1206	3	,	,	PUNCT
fuelectenerg-1427	1206	4	17	17	NUM
fuelectenerg-1427	1206	5	,	,	PUNCT
fuelectenerg-1427	1206	6	24	24	NUM
fuelectenerg-1427	1206	7	]	]	PUNCT
fuelectenerg-1427	1206	8	.	.	PUNCT
fuelectenerg-1427	1207	1	a	a	DET
fuelectenerg-1427	1207	2	set	set	VERB
fuelectenerg-1427	1207	3	-	-	PUNCT
fuelectenerg-1427	1207	4	theoretic	theoretic	NOUN
fuelectenerg-1427	1207	5	relationship	relationship	NOUN
fuelectenerg-1427	1207	6	between	between	ADP
fuelectenerg-1427	1207	7	families	family	NOUN
fuelectenerg-1427	1207	8	of	of	ADP
fuelectenerg-1427	1207	9	canonical	canonical	ADJ
fuelectenerg-1427	1207	10	forms	form	NOUN
fuelectenerg-1427	1207	11	over	over	ADP
fuelectenerg-1427	1207	12	gf(2	gf(2	PROPN
fuelectenerg-1427	1207	13	)	)	PUNCT
fuelectenerg-1427	1207	14	was	be	AUX
fuelectenerg-1427	1207	15	proposed	propose	VERB
fuelectenerg-1427	1207	16	and	and	CCONJ
fuelectenerg-1427	1207	17	extended	extend	VERB
fuelectenerg-1427	1207	18	by	by	ADP
fuelectenerg-1427	1207	19	introducing	introduce	VERB
fuelectenerg-1427	1207	20	binary	binary	NOUN
fuelectenerg-1427	1207	21	if	if	SCONJ
fuelectenerg-1427	1207	22	,	,	PUNCT
fuelectenerg-1427	1207	23	gif	gif	NOUN
fuelectenerg-1427	1207	24	and	and	CCONJ
fuelectenerg-1427	1207	25	free	free	ADJ
fuelectenerg-1427	1207	26	gif	gif	NOUN
fuelectenerg-1427	1207	27	(	(	PUNCT
fuelectenerg-1427	1207	28	fgif	fgif	NOUN
fuelectenerg-1427	1207	29	)	)	PUNCT
fuelectenerg-1427	1207	30	forms	form	NOUN
fuelectenerg-1427	1207	31	where	where	SCONJ
fuelectenerg-1427	1207	32	figure	figure	NOUN
fuelectenerg-1427	1207	33	6(a	6(a	NUM
fuelectenerg-1427	1207	34	)	)	PUNCT
fuelectenerg-1427	1207	35	illustrates	illustrate	VERB
fuelectenerg-1427	1207	36	set	set	VERB
fuelectenerg-1427	1207	37	-	-	PUNCT
fuelectenerg-1427	1207	38	theoretic	theoretic	NOUN
fuelectenerg-1427	1207	39	relationship	relationship	NOUN
fuelectenerg-1427	1207	40	between	between	ADP
fuelectenerg-1427	1207	41	the	the	DET
fuelectenerg-1427	1207	42	various	various	ADJ
fuelectenerg-1427	1207	43	families	family	NOUN
fuelectenerg-1427	1207	44	of	of	ADP
fuelectenerg-1427	1207	45	canonical	canonical	ADJ
fuelectenerg-1427	1207	46	forms	form	NOUN
fuelectenerg-1427	1207	47	over	over	ADP
fuelectenerg-1427	1207	48	gf(2	gf(2	PROPN
fuelectenerg-1427	1207	49	)	)	PUNCT
fuelectenerg-1427	1207	50	.	.	PUNCT
fuelectenerg-1427	1208	1	analogously	analogously	ADV
fuelectenerg-1427	1208	2	to	to	ADP
fuelectenerg-1427	1208	3	the	the	DET
fuelectenerg-1427	1208	4	green	green	ADJ
fuelectenerg-1427	1208	5	-	-	PUNCT
fuelectenerg-1427	1208	6	sasao	sasao	PROPN
fuelectenerg-1427	1208	7	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1208	8	of	of	ADP
fuelectenerg-1427	1208	9	binary	binary	PROPN
fuelectenerg-1427	1208	10	reed	reed	PROPN
fuelectenerg-1427	1208	11	-	-	PUNCT
fuelectenerg-1427	1208	12	muller	muller	NOUN
fuelectenerg-1427	1208	13	families	family	NOUN
fuelectenerg-1427	1208	14	of	of	ADP
fuelectenerg-1427	1208	15	spectral	spectral	ADJ
fuelectenerg-1427	1208	16	transforms	transform	VERB
fuelectenerg-1427	1208	17	over	over	ADP
fuelectenerg-1427	1208	18	gf(2	gf(2	PROPN
fuelectenerg-1427	1208	19	)	)	PUNCT
fuelectenerg-1427	1208	20	that	that	PRON
fuelectenerg-1427	1208	21	is	be	AUX
fuelectenerg-1427	1208	22	shown	show	VERB
fuelectenerg-1427	1208	23	in	in	ADP
fuelectenerg-1427	1208	24	figure	figure	NOUN
fuelectenerg-1427	1208	25	6(a	6(a	NUM
fuelectenerg-1427	1208	26	)	)	PUNCT
fuelectenerg-1427	1208	27	,	,	PUNCT
fuelectenerg-1427	1208	28	we	we	PRON
fuelectenerg-1427	1208	29	will	will	AUX
fuelectenerg-1427	1208	30	introduce	introduce	VERB
fuelectenerg-1427	1208	31	the	the	DET
fuelectenerg-1427	1208	32	extended	extended	ADJ
fuelectenerg-1427	1208	33	green	green	ADJ
fuelectenerg-1427	1208	34	-	-	PUNCT
fuelectenerg-1427	1208	35	sasao	sasao	NOUN
fuelectenerg-1427	1208	36	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1208	37	of	of	ADP
fuelectenerg-1427	1208	38	spectral	spectral	ADJ
fuelectenerg-1427	1208	39	transforms	transform	NOUN
fuelectenerg-1427	1208	40	,	,	PUNCT
fuelectenerg-1427	1208	41	with	with	ADP
fuelectenerg-1427	1208	42	a	a	DET
fuelectenerg-1427	1208	43	new	new	ADJ
fuelectenerg-1427	1208	44	sub	sub	NOUN
fuelectenerg-1427	1208	45	-	-	NOUN
fuelectenerg-1427	1208	46	family	family	NOUN
fuelectenerg-1427	1208	47	for	for	ADP
fuelectenerg-1427	1208	48	ternary	ternary	ADJ
fuelectenerg-1427	1208	49	reedmuller	reedmuller	NOUN
fuelectenerg-1427	1208	50	logic	logic	NOUN
fuelectenerg-1427	1208	51	over	over	ADP
fuelectenerg-1427	1208	52	gf(3	gf(3	PROPN
fuelectenerg-1427	1208	53	)	)	PUNCT
fuelectenerg-1427	1208	54	.	.	PUNCT
fuelectenerg-1427	1209	1	while	while	SCONJ
fuelectenerg-1427	1209	2	definitions	definition	NOUN
fuelectenerg-1427	1209	3	2	2	NUM
fuelectenerg-1427	1209	4	4	4	NUM
fuelectenerg-1427	1209	5	defined	define	VERB
fuelectenerg-1427	1209	6	the	the	DET
fuelectenerg-1427	1209	7	ternary	ternary	ADJ
fuelectenerg-1427	1209	8	inclusive	inclusive	ADJ
fuelectenerg-1427	1209	9	forms	form	NOUN
fuelectenerg-1427	1209	10	,	,	PUNCT
fuelectenerg-1427	1209	11	ternary	ternary	ADJ
fuelectenerg-1427	1209	12	generalized	generalize	VERB
fuelectenerg-1427	1209	13	inclusive	inclusive	ADJ
fuelectenerg-1427	1209	14	forms	form	NOUN
fuelectenerg-1427	1209	15	and	and	CCONJ
fuelectenerg-1427	1209	16	ternary	ternary	ADJ
fuelectenerg-1427	1209	17	free	free	ADJ
fuelectenerg-1427	1209	18	generalized	generalized	ADJ
fuelectenerg-1427	1209	19	inclusive	inclusive	ADJ
fuelectenerg-1427	1209	20	forms	form	NOUN
fuelectenerg-1427	1209	21	,	,	PUNCT
fuelectenerg-1427	1209	22	respectively	respectively	ADV
fuelectenerg-1427	1209	23	,	,	PUNCT
fuelectenerg-1427	1209	24	and	and	CCONJ
fuelectenerg-1427	1209	25	analogously	analogously	ADV
fuelectenerg-1427	1209	26	to	to	ADP
fuelectenerg-1427	1209	27	the	the	DET
fuelectenerg-1427	1209	28	binary	binary	PROPN
fuelectenerg-1427	1209	29	reed	reed	PROPN
fuelectenerg-1427	1209	30	-	-	PUNCT
fuelectenerg-1427	1209	31	muller	muller	NOUN
fuelectenerg-1427	1209	32	case	case	NOUN
fuelectenerg-1427	1209	33	,	,	PUNCT
fuelectenerg-1427	1209	34	the	the	DET
fuelectenerg-1427	1209	35	following	follow	VERB
fuelectenerg-1427	1209	36	definitions	definition	NOUN
fuelectenerg-1427	1209	37	are	be	AUX
fuelectenerg-1427	1209	38	introduced	introduce	VERB
fuelectenerg-1427	1209	39	for	for	ADP
fuelectenerg-1427	1209	40	the	the	DET
fuelectenerg-1427	1209	41	corresponding	corresponding	ADJ
fuelectenerg-1427	1209	42	canonical	canonical	ADJ
fuelectenerg-1427	1209	43	expressions	expression	NOUN
fuelectenerg-1427	1209	44	over	over	ADP
fuelectenerg-1427	1209	45	gf(3	gf(3	PROPN
fuelectenerg-1427	1209	46	)	)	PUNCT
fuelectenerg-1427	1209	47	.	.	PUNCT
fuelectenerg-1427	1210	1	definition	definition	NOUN
fuelectenerg-1427	1210	2	5	5	NUM
fuelectenerg-1427	1210	3	.	.	PUNCT
fuelectenerg-1427	1211	1	the	the	DET
fuelectenerg-1427	1211	2	decision	decision	NOUN
fuelectenerg-1427	1211	3	tree	tree	NOUN
fuelectenerg-1427	1211	4	that	that	PRON
fuelectenerg-1427	1211	5	results	result	VERB
fuelectenerg-1427	1211	6	from	from	ADP
fuelectenerg-1427	1211	7	applying	apply	VERB
fuelectenerg-1427	1211	8	the	the	DET
fuelectenerg-1427	1211	9	ternary	ternary	ADJ
fuelectenerg-1427	1211	10	shannon	shannon	NOUN
fuelectenerg-1427	1211	11	expansion	expansion	NOUN
fuelectenerg-1427	1211	12	in	in	ADP
fuelectenerg-1427	1211	13	equation	equation	NOUN
fuelectenerg-1427	1211	14	(	(	PUNCT
fuelectenerg-1427	1211	15	23	23	NUM
fuelectenerg-1427	1211	16	)	)	PUNCT
fuelectenerg-1427	1211	17	recursively	recursively	ADV
fuelectenerg-1427	1211	18	to	to	ADP
fuelectenerg-1427	1211	19	a	a	DET
fuelectenerg-1427	1211	20	ternary	ternary	ADJ
fuelectenerg-1427	1211	21	input	input	NOUN
fuelectenerg-1427	1211	22	-	-	PUNCT
fuelectenerg-1427	1211	23	ternary	ternary	ADJ
fuelectenerg-1427	1211	24	output	output	NOUN
fuelectenerg-1427	1211	25	logic	logic	NOUN
fuelectenerg-1427	1211	26	function	function	NOUN
fuelectenerg-1427	1211	27	(	(	PUNCT
fuelectenerg-1427	1211	28	i.e.	i.e.	X
fuelectenerg-1427	1211	29	,	,	PUNCT
fuelectenerg-1427	1211	30	all	all	DET
fuelectenerg-1427	1211	31	levels	level	NOUN
fuelectenerg-1427	1211	32	in	in	ADP
fuelectenerg-1427	1211	33	a	a	DET
fuelectenerg-1427	1211	34	dt	dt	NOUN
fuelectenerg-1427	1211	35	)	)	PUNCT
fuelectenerg-1427	1211	36	is	be	AUX
fuelectenerg-1427	1211	37	called	call	VERB
fuelectenerg-1427	1211	38	ternary	ternary	ADJ
fuelectenerg-1427	1211	39	shannon	shannon	PROPN
fuelectenerg-1427	1211	40	decision	decision	NOUN
fuelectenerg-1427	1211	41	tree	tree	NOUN
fuelectenerg-1427	1211	42	(	(	PUNCT
fuelectenerg-1427	1211	43	tsdt	tsdt	NOUN
fuelectenerg-1427	1211	44	)	)	PUNCT
fuelectenerg-1427	1211	45	.	.	PUNCT
fuelectenerg-1427	1212	1	the	the	DET
fuelectenerg-1427	1212	2	result	result	NOUN
fuelectenerg-1427	1212	3	expression	expression	NOUN
fuelectenerg-1427	1212	4	(	(	PUNCT
fuelectenerg-1427	1212	5	flattened	flatten	VERB
fuelectenerg-1427	1212	6	form	form	NOUN
fuelectenerg-1427	1212	7	)	)	PUNCT
fuelectenerg-1427	1212	8	from	from	ADP
fuelectenerg-1427	1212	9	the	the	DET
fuelectenerg-1427	1212	10	tsdt	tsdt	NOUN
fuelectenerg-1427	1212	11	is	be	AUX
fuelectenerg-1427	1212	12	called	call	VERB
fuelectenerg-1427	1212	13	ternary	ternary	ADJ
fuelectenerg-1427	1212	14	shannon	shannon	NOUN
fuelectenerg-1427	1212	15	expression	expression	NOUN
fuelectenerg-1427	1212	16	.	.	PUNCT
fuelectenerg-1427	1213	1	definition	definition	NOUN
fuelectenerg-1427	1213	2	6	6	NUM
fuelectenerg-1427	1213	3	.	.	PUNCT
fuelectenerg-1427	1214	1	the	the	DET
fuelectenerg-1427	1214	2	decision	decision	NOUN
fuelectenerg-1427	1214	3	trees	tree	NOUN
fuelectenerg-1427	1214	4	that	that	PRON
fuelectenerg-1427	1214	5	result	result	VERB
fuelectenerg-1427	1214	6	from	from	ADP
fuelectenerg-1427	1214	7	applying	apply	VERB
fuelectenerg-1427	1214	8	the	the	DET
fuelectenerg-1427	1214	9	ternary	ternary	ADJ
fuelectenerg-1427	1214	10	davio	davio	NOUN
fuelectenerg-1427	1214	11	expansions	expansion	NOUN
fuelectenerg-1427	1214	12	in	in	ADP
fuelectenerg-1427	1214	13	equations	equation	NOUN
fuelectenerg-1427	1214	14	(	(	PUNCT
fuelectenerg-1427	1214	15	24	24	NUM
fuelectenerg-1427	1214	16	)	)	PUNCT
fuelectenerg-1427	1214	17	(	(	PUNCT
fuelectenerg-1427	1214	18	26	26	NUM
fuelectenerg-1427	1214	19	)	)	PUNCT
fuelectenerg-1427	1214	20	recursively	recursively	ADV
fuelectenerg-1427	1214	21	to	to	ADP
fuelectenerg-1427	1214	22	a	a	DET
fuelectenerg-1427	1214	23	ternary	ternary	ADJ
fuelectenerg-1427	1214	24	-	-	PUNCT
fuelectenerg-1427	1214	25	input	input	NOUN
fuelectenerg-1427	1214	26	ternary	ternary	ADJ
fuelectenerg-1427	1214	27	-	-	PUNCT
fuelectenerg-1427	1214	28	output	output	NOUN
fuelectenerg-1427	1214	29	logic	logic	NOUN
fuelectenerg-1427	1214	30	function	function	NOUN
fuelectenerg-1427	1214	31	(	(	PUNCT
fuelectenerg-1427	1214	32	i.e.	i.e.	X
fuelectenerg-1427	1214	33	,	,	PUNCT
fuelectenerg-1427	1214	34	all	all	DET
fuelectenerg-1427	1214	35	levels	level	NOUN
fuelectenerg-1427	1214	36	in	in	ADP
fuelectenerg-1427	1214	37	a	a	DET
fuelectenerg-1427	1214	38	dt	dt	NOUN
fuelectenerg-1427	1214	39	)	)	PUNCT
fuelectenerg-1427	1214	40	are	be	AUX
fuelectenerg-1427	1214	41	called	call	VERB
fuelectenerg-1427	1214	42	:	:	PUNCT
fuelectenerg-1427	1214	43	ternary	ternary	ADJ
fuelectenerg-1427	1214	44	zero	zero	NUM
fuelectenerg-1427	1214	45	-	-	PUNCT
fuelectenerg-1427	1214	46	polarity	polarity	NOUN
fuelectenerg-1427	1214	47	davio	davio	NOUN
fuelectenerg-1427	1214	48	decision	decision	NOUN
fuelectenerg-1427	1214	49	tree	tree	NOUN
fuelectenerg-1427	1214	50	(	(	PUNCT
fuelectenerg-1427	1214	51	td0dt	td0dt	NOUN
fuelectenerg-1427	1214	52	)	)	PUNCT
fuelectenerg-1427	1214	53	,	,	PUNCT
fuelectenerg-1427	1214	54	ternary	ternary	ADJ
fuelectenerg-1427	1214	55	first	first	ADJ
fuelectenerg-1427	1214	56	-	-	PUNCT
fuelectenerg-1427	1214	57	polarity	polarity	NOUN
fuelectenerg-1427	1214	58	davio	davio	NOUN
fuelectenerg-1427	1214	59	decision	decision	NOUN
fuelectenerg-1427	1214	60	tree	tree	NOUN
fuelectenerg-1427	1214	61	(	(	PUNCT
fuelectenerg-1427	1214	62	td1dt	td1dt	NUM
fuelectenerg-1427	1214	63	)	)	PUNCT
fuelectenerg-1427	1214	64	and	and	CCONJ
fuelectenerg-1427	1214	65	ternary	ternary	ADJ
fuelectenerg-1427	1214	66	secondpolarity	secondpolarity	NOUN
fuelectenerg-1427	1214	67	davio	davio	NOUN
fuelectenerg-1427	1214	68	decision	decision	NOUN
fuelectenerg-1427	1214	69	tree	tree	NOUN
fuelectenerg-1427	1214	70	(	(	PUNCT
fuelectenerg-1427	1214	71	td2dt	td2dt	NUM
fuelectenerg-1427	1214	72	)	)	PUNCT
fuelectenerg-1427	1214	73	,	,	PUNCT
fuelectenerg-1427	1214	74	respectively	respectively	ADV
fuelectenerg-1427	1214	75	.	.	PUNCT
fuelectenerg-1427	1215	1	the	the	DET
fuelectenerg-1427	1215	2	resulting	result	VERB
fuelectenerg-1427	1215	3	expressions	expression	NOUN
fuelectenerg-1427	1215	4	(	(	PUNCT
fuelectenerg-1427	1215	5	flattened	flatten	VERB
fuelectenerg-1427	1215	6	forms	form	NOUN
fuelectenerg-1427	1215	7	)	)	PUNCT
fuelectenerg-1427	1215	8	from	from	ADP
fuelectenerg-1427	1215	9	td0dt	td0dt	PROPN
fuelectenerg-1427	1215	10	,	,	PUNCT
fuelectenerg-1427	1215	11	td1dt	td1dt	NUM
fuelectenerg-1427	1215	12	and	and	CCONJ
fuelectenerg-1427	1215	13	td2dt	td2dt	NUM
fuelectenerg-1427	1215	14	are	be	AUX
fuelectenerg-1427	1215	15	called	call	VERB
fuelectenerg-1427	1215	16	td0	td0	NOUN
fuelectenerg-1427	1215	17	,	,	PUNCT
fuelectenerg-1427	1215	18	td1	td1	PROPN
fuelectenerg-1427	1215	19	and	and	CCONJ
fuelectenerg-1427	1215	20	td2	td2	PROPN
fuelectenerg-1427	1215	21	expressions	expression	NOUN
fuelectenerg-1427	1215	22	,	,	PUNCT
fuelectenerg-1427	1215	23	respectively	respectively	ADV
fuelectenerg-1427	1215	24	.	.	PUNCT
fuelectenerg-1427	1216	1	definition	definition	NOUN
fuelectenerg-1427	1216	2	7	7	NUM
fuelectenerg-1427	1216	3	.	.	PUNCT
fuelectenerg-1427	1217	1	the	the	DET
fuelectenerg-1427	1217	2	decision	decision	NOUN
fuelectenerg-1427	1217	3	tree	tree	NOUN
fuelectenerg-1427	1217	4	that	that	PRON
fuelectenerg-1427	1217	5	results	result	VERB
fuelectenerg-1427	1217	6	from	from	ADP
fuelectenerg-1427	1217	7	applying	apply	VERB
fuelectenerg-1427	1217	8	any	any	PRON
fuelectenerg-1427	1217	9	of	of	ADP
fuelectenerg-1427	1217	10	the	the	DET
fuelectenerg-1427	1217	11	ternary	ternary	ADJ
fuelectenerg-1427	1217	12	davio	davio	NOUN
fuelectenerg-1427	1217	13	expansions	expansion	NOUN
fuelectenerg-1427	1217	14	(	(	PUNCT
fuelectenerg-1427	1217	15	nodes	node	NOUN
fuelectenerg-1427	1217	16	)	)	PUNCT
fuelectenerg-1427	1217	17	for	for	ADP
fuelectenerg-1427	1217	18	all	all	DET
fuelectenerg-1427	1217	19	nodes	node	NOUN
fuelectenerg-1427	1217	20	in	in	ADP
fuelectenerg-1427	1217	21	each	each	DET
fuelectenerg-1427	1217	22	level	level	NOUN
fuelectenerg-1427	1217	23	(	(	PUNCT
fuelectenerg-1427	1217	24	variable	variable	NOUN
fuelectenerg-1427	1217	25	)	)	PUNCT
fuelectenerg-1427	1217	26	in	in	ADP
fuelectenerg-1427	1217	27	the	the	DET
fuelectenerg-1427	1217	28	dt	dt	NOUN
fuelectenerg-1427	1217	29	is	be	AUX
fuelectenerg-1427	1217	30	called	call	VERB
fuelectenerg-1427	1217	31	ternary	ternary	ADJ
fuelectenerg-1427	1217	32	reed	reed	NOUN
fuelectenerg-1427	1217	33	-	-	PUNCT
fuelectenerg-1427	1217	34	muller	muller	NOUN
fuelectenerg-1427	1217	35	decision	decision	NOUN
fuelectenerg-1427	1217	36	tree	tree	NOUN
fuelectenerg-1427	1217	37	(	(	PUNCT
fuelectenerg-1427	1217	38	trmdt	trmdt	NOUN
fuelectenerg-1427	1217	39	)	)	PUNCT
fuelectenerg-1427	1217	40	.	.	PUNCT
fuelectenerg-1427	1218	1	the	the	DET
fuelectenerg-1427	1218	2	corresponding	corresponding	ADJ
fuelectenerg-1427	1218	3	expression	expression	NOUN
fuelectenerg-1427	1218	4	is	be	AUX
fuelectenerg-1427	1218	5	called	call	VERB
fuelectenerg-1427	1218	6	ternary	ternary	ADJ
fuelectenerg-1427	1218	7	fixed	fix	VERB
fuelectenerg-1427	1218	8	polarity	polarity	NOUN
fuelectenerg-1427	1218	9	reed	reed	NOUN
fuelectenerg-1427	1218	10	-	-	PUNCT
fuelectenerg-1427	1218	11	muller	muller	NOUN
fuelectenerg-1427	1218	12	(	(	PUNCT
fuelectenerg-1427	1218	13	tfprm	tfprm	ADJ
fuelectenerg-1427	1218	14	)	)	PUNCT
fuelectenerg-1427	1218	15	expression	expression	NOUN
fuelectenerg-1427	1218	16	.	.	PUNCT
fuelectenerg-1427	1219	1	definition	definition	NOUN
fuelectenerg-1427	1219	2	8	8	NUM
fuelectenerg-1427	1219	3	.	.	PUNCT
fuelectenerg-1427	1220	1	the	the	DET
fuelectenerg-1427	1220	2	decision	decision	NOUN
fuelectenerg-1427	1220	3	tree	tree	NOUN
fuelectenerg-1427	1220	4	that	that	PRON
fuelectenerg-1427	1220	5	results	result	VERB
fuelectenerg-1427	1220	6	from	from	ADP
fuelectenerg-1427	1220	7	using	use	VERB
fuelectenerg-1427	1220	8	any	any	PRON
fuelectenerg-1427	1220	9	of	of	ADP
fuelectenerg-1427	1220	10	the	the	DET
fuelectenerg-1427	1220	11	ternary	ternary	ADJ
fuelectenerg-1427	1220	12	shannon	shannon	NOUN
fuelectenerg-1427	1220	13	(	(	PUNCT
fuelectenerg-1427	1220	14	s	s	NOUN
fuelectenerg-1427	1220	15	)	)	PUNCT
fuelectenerg-1427	1220	16	or	or	CCONJ
fuelectenerg-1427	1220	17	davio	davio	NOUN
fuelectenerg-1427	1220	18	(	(	PUNCT
fuelectenerg-1427	1220	19	d0	d0	NOUN
fuelectenerg-1427	1220	20	,	,	PUNCT
fuelectenerg-1427	1220	21	d1	d1	PROPN
fuelectenerg-1427	1220	22	or	or	CCONJ
fuelectenerg-1427	1220	23	d2	d2	PROPN
fuelectenerg-1427	1220	24	)	)	PUNCT
fuelectenerg-1427	1220	25	expansions	expansion	NOUN
fuelectenerg-1427	1220	26	(	(	PUNCT
fuelectenerg-1427	1220	27	nodes	node	NOUN
fuelectenerg-1427	1220	28	)	)	PUNCT
fuelectenerg-1427	1220	29	for	for	ADP
fuelectenerg-1427	1220	30	all	all	DET
fuelectenerg-1427	1220	31	nodes	node	NOUN
fuelectenerg-1427	1220	32	in	in	ADP
fuelectenerg-1427	1220	33	each	each	DET
fuelectenerg-1427	1220	34	level	level	NOUN
fuelectenerg-1427	1220	35	(	(	PUNCT
fuelectenerg-1427	1220	36	variable	variable	NOUN
fuelectenerg-1427	1220	37	)	)	PUNCT
fuelectenerg-1427	1220	38	in	in	ADP
fuelectenerg-1427	1220	39	the	the	DET
fuelectenerg-1427	1220	40	dt	dt	X
fuelectenerg-1427	1220	41	(	(	PUNCT
fuelectenerg-1427	1220	42	that	that	PRON
fuelectenerg-1427	1220	43	has	have	AUX
fuelectenerg-1427	1220	44	fixed	fix	VERB
fuelectenerg-1427	1220	45	order	order	NOUN
fuelectenerg-1427	1220	46	of	of	ADP
fuelectenerg-1427	1220	47	variables	variable	NOUN
fuelectenerg-1427	1220	48	)	)	PUNCT
fuelectenerg-1427	1220	49	is	be	AUX
fuelectenerg-1427	1220	50	called	call	VERB
fuelectenerg-1427	1220	51	ternary	ternary	ADJ
fuelectenerg-1427	1220	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1220	53	decision	decision	NOUN
fuelectenerg-1427	1220	54	tree	tree	NOUN
fuelectenerg-1427	1220	55	(	(	PUNCT
fuelectenerg-1427	1220	56	tkrodt	tkrodt	NOUN
fuelectenerg-1427	1220	57	)	)	PUNCT
fuelectenerg-1427	1220	58	.	.	PUNCT
fuelectenerg-1427	1221	1	the	the	DET
fuelectenerg-1427	1221	2	resulting	result	VERB
fuelectenerg-1427	1221	3	expression	expression	NOUN
fuelectenerg-1427	1221	4	is	be	AUX
fuelectenerg-1427	1221	5	called	call	VERB
fuelectenerg-1427	1221	6	ternary	ternary	ADJ
fuelectenerg-1427	1221	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1221	8	expression	expression	NOUN
fuelectenerg-1427	1221	9	.	.	PUNCT
fuelectenerg-1427	1222	1	definition	definition	NOUN
fuelectenerg-1427	1222	2	9	9	NUM
fuelectenerg-1427	1222	3	.	.	PUNCT
fuelectenerg-1427	1223	1	the	the	DET
fuelectenerg-1427	1223	2	decision	decision	NOUN
fuelectenerg-1427	1223	3	tree	tree	NOUN
fuelectenerg-1427	1223	4	that	that	PRON
fuelectenerg-1427	1223	5	results	result	VERB
fuelectenerg-1427	1223	6	from	from	ADP
fuelectenerg-1427	1223	7	using	use	VERB
fuelectenerg-1427	1223	8	any	any	PRON
fuelectenerg-1427	1223	9	of	of	ADP
fuelectenerg-1427	1223	10	the	the	DET
fuelectenerg-1427	1223	11	ternary	ternary	ADJ
fuelectenerg-1427	1223	12	davio	davio	NOUN
fuelectenerg-1427	1223	13	expansions	expansion	NOUN
fuelectenerg-1427	1223	14	(	(	PUNCT
fuelectenerg-1427	1223	15	nodes	node	NOUN
fuelectenerg-1427	1223	16	)	)	PUNCT
fuelectenerg-1427	1223	17	for	for	ADP
fuelectenerg-1427	1223	18	each	each	DET
fuelectenerg-1427	1223	19	node	node	NOUN
fuelectenerg-1427	1223	20	(	(	PUNCT
fuelectenerg-1427	1223	21	per	per	ADP
fuelectenerg-1427	1223	22	level	level	NOUN
fuelectenerg-1427	1223	23	)	)	PUNCT
fuelectenerg-1427	1223	24	of	of	ADP
fuelectenerg-1427	1223	25	the	the	DET
fuelectenerg-1427	1223	26	dt	dt	NOUN
fuelectenerg-1427	1223	27	is	be	AUX
fuelectenerg-1427	1223	28	called	call	VERB
fuelectenerg-1427	1223	29	ternary	ternary	ADJ
fuelectenerg-1427	1223	30	pseudo	pseudo	NOUN
fuelectenerg-1427	1223	31	-	-	NOUN
fuelectenerg-1427	1223	32	reed112	reed112	VERB
fuelectenerg-1427	1223	33	an	an	DET
fuelectenerg-1427	1223	34	extended	extend	VERB
fuelectenerg-1427	1223	35	green	green	PROPN
fuelectenerg-1427	1223	36	sasao	sasao	PROPN
fuelectenerg-1427	1223	37	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1223	38	of	of	ADP
fuelectenerg-1427	1223	39	canonical	canonical	ADJ
fuelectenerg-1427	1223	40	ternary	ternary	ADJ
fuelectenerg-1427	1223	41	galois	galois	NOUN
fuelectenerg-1427	1223	42	forms	form	NOUN
fuelectenerg-1427	1223	43	...	...	PUNCT
fuelectenerg-1427	1224	1	muller	muller	NOUN
fuelectenerg-1427	1224	2	decision	decision	NOUN
fuelectenerg-1427	1224	3	tree	tree	NOUN
fuelectenerg-1427	1224	4	(	(	PUNCT
fuelectenerg-1427	1224	5	tprmdt	tprmdt	NOUN
fuelectenerg-1427	1224	6	)	)	PUNCT
fuelectenerg-1427	1224	7	.	.	PUNCT
fuelectenerg-1427	1225	1	the	the	DET
fuelectenerg-1427	1225	2	resulting	result	VERB
fuelectenerg-1427	1225	3	expression	expression	NOUN
fuelectenerg-1427	1225	4	is	be	AUX
fuelectenerg-1427	1225	5	called	call	VERB
fuelectenerg-1427	1225	6	ternary	ternary	ADJ
fuelectenerg-1427	1225	7	pseudoreed	pseudoreed	NOUN
fuelectenerg-1427	1225	8	-	-	PUNCT
fuelectenerg-1427	1225	9	muller	muller	NOUN
fuelectenerg-1427	1225	10	expression	expression	NOUN
fuelectenerg-1427	1225	11	.	.	PUNCT
fuelectenerg-1427	1226	1	definition	definition	NOUN
fuelectenerg-1427	1226	2	10	10	NUM
fuelectenerg-1427	1226	3	.	.	PUNCT
fuelectenerg-1427	1227	1	the	the	DET
fuelectenerg-1427	1227	2	decision	decision	NOUN
fuelectenerg-1427	1227	3	tree	tree	NOUN
fuelectenerg-1427	1227	4	that	that	PRON
fuelectenerg-1427	1227	5	results	result	VERB
fuelectenerg-1427	1227	6	from	from	ADP
fuelectenerg-1427	1227	7	using	use	VERB
fuelectenerg-1427	1227	8	any	any	PRON
fuelectenerg-1427	1227	9	of	of	ADP
fuelectenerg-1427	1227	10	the	the	DET
fuelectenerg-1427	1227	11	ternary	ternary	ADJ
fuelectenerg-1427	1227	12	shannon	shannon	NOUN
fuelectenerg-1427	1227	13	expansion	expansion	NOUN
fuelectenerg-1427	1227	14	or	or	CCONJ
fuelectenerg-1427	1227	15	ternary	ternary	ADJ
fuelectenerg-1427	1227	16	davio	davio	NOUN
fuelectenerg-1427	1227	17	expansions	expansion	NOUN
fuelectenerg-1427	1227	18	(	(	PUNCT
fuelectenerg-1427	1227	19	nodes	node	NOUN
fuelectenerg-1427	1227	20	)	)	PUNCT
fuelectenerg-1427	1227	21	for	for	ADP
fuelectenerg-1427	1227	22	each	each	DET
fuelectenerg-1427	1227	23	node	node	NOUN
fuelectenerg-1427	1227	24	(	(	PUNCT
fuelectenerg-1427	1227	25	per	per	ADP
fuelectenerg-1427	1227	26	level	level	NOUN
fuelectenerg-1427	1227	27	)	)	PUNCT
fuelectenerg-1427	1227	28	of	of	ADP
fuelectenerg-1427	1227	29	the	the	DET
fuelectenerg-1427	1227	30	dt	dt	NOUN
fuelectenerg-1427	1227	31	is	be	AUX
fuelectenerg-1427	1227	32	called	call	VERB
fuelectenerg-1427	1227	33	ternary	ternary	ADJ
fuelectenerg-1427	1227	34	pseudo	pseudo	NOUN
fuelectenerg-1427	1227	35	-	-	NOUN
fuelectenerg-1427	1227	36	kronecker	kronecker	NOUN
fuelectenerg-1427	1227	37	decision	decision	NOUN
fuelectenerg-1427	1227	38	tree	tree	NOUN
fuelectenerg-1427	1227	39	(	(	PUNCT
fuelectenerg-1427	1227	40	tpkrodt	tpkrodt	PROPN
fuelectenerg-1427	1227	41	)	)	PUNCT
fuelectenerg-1427	1227	42	.	.	PUNCT
fuelectenerg-1427	1228	1	the	the	DET
fuelectenerg-1427	1228	2	resulting	result	VERB
fuelectenerg-1427	1228	3	expression	expression	NOUN
fuelectenerg-1427	1228	4	is	be	AUX
fuelectenerg-1427	1228	5	called	call	VERB
fuelectenerg-1427	1228	6	ternary	ternary	ADJ
fuelectenerg-1427	1228	7	pseudo	pseudo	NOUN
fuelectenerg-1427	1228	8	-	-	NOUN
fuelectenerg-1427	1228	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1228	10	expression	expression	NOUN
fuelectenerg-1427	1228	11	.	.	PUNCT
fuelectenerg-1427	1229	1	definition	definition	NOUN
fuelectenerg-1427	1229	2	11	11	NUM
fuelectenerg-1427	1229	3	.	.	PUNCT
fuelectenerg-1427	1230	1	the	the	DET
fuelectenerg-1427	1230	2	decision	decision	NOUN
fuelectenerg-1427	1230	3	tree	tree	NOUN
fuelectenerg-1427	1230	4	that	that	PRON
fuelectenerg-1427	1230	5	results	result	VERB
fuelectenerg-1427	1230	6	from	from	ADP
fuelectenerg-1427	1230	7	using	use	VERB
fuelectenerg-1427	1230	8	any	any	PRON
fuelectenerg-1427	1230	9	of	of	ADP
fuelectenerg-1427	1230	10	the	the	DET
fuelectenerg-1427	1230	11	ternary	ternary	ADJ
fuelectenerg-1427	1230	12	shannon	shannon	NOUN
fuelectenerg-1427	1230	13	expansion	expansion	NOUN
fuelectenerg-1427	1230	14	or	or	CCONJ
fuelectenerg-1427	1230	15	ternary	ternary	ADJ
fuelectenerg-1427	1230	16	davio	davio	NOUN
fuelectenerg-1427	1230	17	expansions	expansion	NOUN
fuelectenerg-1427	1230	18	(	(	PUNCT
fuelectenerg-1427	1230	19	nodes	node	NOUN
fuelectenerg-1427	1230	20	)	)	PUNCT
fuelectenerg-1427	1230	21	for	for	ADP
fuelectenerg-1427	1230	22	each	each	DET
fuelectenerg-1427	1230	23	node	node	NOUN
fuelectenerg-1427	1230	24	(	(	PUNCT
fuelectenerg-1427	1230	25	per	per	ADP
fuelectenerg-1427	1230	26	level	level	NOUN
fuelectenerg-1427	1230	27	)	)	PUNCT
fuelectenerg-1427	1230	28	of	of	ADP
fuelectenerg-1427	1230	29	the	the	DET
fuelectenerg-1427	1230	30	dt	dt	PROPN
fuelectenerg-1427	1230	31	,	,	PUNCT
fuelectenerg-1427	1230	32	disregarding	disregard	VERB
fuelectenerg-1427	1230	33	order	order	NOUN
fuelectenerg-1427	1230	34	of	of	ADP
fuelectenerg-1427	1230	35	variables	variable	NOUN
fuelectenerg-1427	1230	36	,	,	PUNCT
fuelectenerg-1427	1230	37	provided	provide	VERB
fuelectenerg-1427	1230	38	that	that	SCONJ
fuelectenerg-1427	1230	39	variables	variable	NOUN
fuelectenerg-1427	1230	40	are	be	AUX
fuelectenerg-1427	1230	41	not	not	PART
fuelectenerg-1427	1230	42	repeated	repeat	VERB
fuelectenerg-1427	1230	43	along	along	ADP
fuelectenerg-1427	1230	44	the	the	DET
fuelectenerg-1427	1230	45	same	same	ADJ
fuelectenerg-1427	1230	46	branches	branch	NOUN
fuelectenerg-1427	1230	47	,	,	PUNCT
fuelectenerg-1427	1230	48	is	be	AUX
fuelectenerg-1427	1230	49	called	call	VERB
fuelectenerg-1427	1230	50	ternary	ternary	ADJ
fuelectenerg-1427	1230	51	free	free	ADJ
fuelectenerg-1427	1230	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1230	53	decision	decision	NOUN
fuelectenerg-1427	1230	54	tree	tree	NOUN
fuelectenerg-1427	1230	55	(	(	PUNCT
fuelectenerg-1427	1230	56	tfkrodt	tfkrodt	PROPN
fuelectenerg-1427	1230	57	)	)	PUNCT
fuelectenerg-1427	1230	58	.	.	PUNCT
fuelectenerg-1427	1231	1	the	the	DET
fuelectenerg-1427	1231	2	result	result	NOUN
fuelectenerg-1427	1231	3	is	be	AUX
fuelectenerg-1427	1231	4	called	call	VERB
fuelectenerg-1427	1231	5	ternary	ternary	ADJ
fuelectenerg-1427	1231	6	free	free	ADJ
fuelectenerg-1427	1231	7	-	-	PUNCT
fuelectenerg-1427	1231	8	kronecker	kronecker	NOUN
fuelectenerg-1427	1231	9	expression	expression	NOUN
fuelectenerg-1427	1231	10	.	.	PUNCT
fuelectenerg-1427	1232	1	definition	definition	NOUN
fuelectenerg-1427	1232	2	12	12	NUM
fuelectenerg-1427	1232	3	.	.	PUNCT
fuelectenerg-1427	1233	1	the	the	DET
fuelectenerg-1427	1233	2	ternary	ternary	ADJ
fuelectenerg-1427	1233	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1233	4	dt	dt	NOUN
fuelectenerg-1427	1233	5	that	that	PRON
fuelectenerg-1427	1233	6	has	have	VERB
fuelectenerg-1427	1233	7	at	at	ADV
fuelectenerg-1427	1233	8	least	least	ADV
fuelectenerg-1427	1233	9	one	one	NUM
fuelectenerg-1427	1233	10	ternary	ternary	ADJ
fuelectenerg-1427	1233	11	generalized	generalize	VERB
fuelectenerg-1427	1233	12	reed	reed	NOUN
fuelectenerg-1427	1233	13	-	-	PUNCT
fuelectenerg-1427	1233	14	muller	muller	NOUN
fuelectenerg-1427	1233	15	expansion	expansion	NOUN
fuelectenerg-1427	1233	16	node	node	NOUN
fuelectenerg-1427	1233	17	is	be	AUX
fuelectenerg-1427	1233	18	called	call	VERB
fuelectenerg-1427	1233	19	ternary	ternary	ADJ
fuelectenerg-1427	1233	20	generalized	generalize	VERB
fuelectenerg-1427	1233	21	kronecker	kronecker	NOUN
fuelectenerg-1427	1233	22	decision	decision	NOUN
fuelectenerg-1427	1233	23	tree	tree	NOUN
fuelectenerg-1427	1233	24	(	(	PUNCT
fuelectenerg-1427	1233	25	tgkdt	tgkdt	ADJ
fuelectenerg-1427	1233	26	)	)	PUNCT
fuelectenerg-1427	1233	27	.	.	PUNCT
fuelectenerg-1427	1234	1	the	the	DET
fuelectenerg-1427	1234	2	result	result	NOUN
fuelectenerg-1427	1234	3	is	be	AUX
fuelectenerg-1427	1234	4	called	call	VERB
fuelectenerg-1427	1234	5	ternary	ternary	ADJ
fuelectenerg-1427	1234	6	generalized	generalized	ADJ
fuelectenerg-1427	1234	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1234	8	expression	expression	NOUN
fuelectenerg-1427	1234	9	.	.	PUNCT
fuelectenerg-1427	1235	1	definition	definition	NOUN
fuelectenerg-1427	1235	2	13	13	NUM
fuelectenerg-1427	1235	3	.	.	PUNCT
fuelectenerg-1427	1236	1	the	the	DET
fuelectenerg-1427	1236	2	ternary	ternary	ADJ
fuelectenerg-1427	1236	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1236	4	dt	dt	NOUN
fuelectenerg-1427	1236	5	that	that	PRON
fuelectenerg-1427	1236	6	has	have	VERB
fuelectenerg-1427	1236	7	at	at	ADV
fuelectenerg-1427	1236	8	least	least	ADJ
fuelectenerg-1427	1236	9	one	one	NUM
fuelectenerg-1427	1236	10	tgif	tgif	NOUN
fuelectenerg-1427	1236	11	node	node	NOUN
fuelectenerg-1427	1236	12	is	be	AUX
fuelectenerg-1427	1236	13	called	call	VERB
fuelectenerg-1427	1236	14	ternary	ternary	ADJ
fuelectenerg-1427	1236	15	generalized	generalize	VERB
fuelectenerg-1427	1236	16	inclusive	inclusive	ADJ
fuelectenerg-1427	1236	17	forms	form	NOUN
fuelectenerg-1427	1236	18	kronecker	kronecker	NOUN
fuelectenerg-1427	1236	19	(	(	PUNCT
fuelectenerg-1427	1236	20	tgifk	tgifk	NOUN
fuelectenerg-1427	1236	21	)	)	PUNCT
fuelectenerg-1427	1236	22	decision	decision	NOUN
fuelectenerg-1427	1236	23	tree	tree	NOUN
fuelectenerg-1427	1236	24	.	.	PUNCT
fuelectenerg-1427	1237	1	the	the	DET
fuelectenerg-1427	1237	2	result	result	NOUN
fuelectenerg-1427	1237	3	is	be	AUX
fuelectenerg-1427	1237	4	called	call	VERB
fuelectenerg-1427	1237	5	ternary	ternary	ADJ
fuelectenerg-1427	1237	6	generalized	generalized	ADJ
fuelectenerg-1427	1237	7	inclusive	inclusive	ADJ
fuelectenerg-1427	1237	8	form	form	NOUN
fuelectenerg-1427	1237	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1237	10	expression	expression	NOUN
fuelectenerg-1427	1237	11	.	.	PUNCT
fuelectenerg-1427	1238	1	figure	figure	NOUN
fuelectenerg-1427	1238	2	6(b	6(b	NUM
fuelectenerg-1427	1238	3	)	)	PUNCT
fuelectenerg-1427	1238	4	illustrates	illustrate	VERB
fuelectenerg-1427	1238	5	the	the	DET
fuelectenerg-1427	1238	6	extended	extended	ADJ
fuelectenerg-1427	1238	7	gf(3	gf(3	PROPN
fuelectenerg-1427	1238	8	)	)	PUNCT
fuelectenerg-1427	1238	9	green	green	ADJ
fuelectenerg-1427	1238	10	-	-	PUNCT
fuelectenerg-1427	1238	11	sasao	sasao	PROPN
fuelectenerg-1427	1238	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1238	13	with	with	ADP
fuelectenerg-1427	1238	14	the	the	DET
fuelectenerg-1427	1238	15	new	new	ADJ
fuelectenerg-1427	1238	16	subfamily	subfamily	ADV
fuelectenerg-1427	1238	17	(	(	PUNCT
fuelectenerg-1427	1238	18	tgifk	tgifk	NOUN
fuelectenerg-1427	1238	19	)	)	PUNCT
fuelectenerg-1427	1238	20	.	.	PUNCT
fuelectenerg-1427	1239	1	the	the	DET
fuelectenerg-1427	1239	2	presented	present	VERB
fuelectenerg-1427	1239	3	tgif	tgif	NOUN
fuelectenerg-1427	1239	4	nodes	node	NOUN
fuelectenerg-1427	1239	5	can	can	AUX
fuelectenerg-1427	1239	6	be	be	AUX
fuelectenerg-1427	1239	7	realized	realize	VERB
fuelectenerg-1427	1239	8	with	with	ADP
fuelectenerg-1427	1239	9	universal	universal	ADJ
fuelectenerg-1427	1239	10	logic	logic	NOUN
fuelectenerg-1427	1239	11	modules	module	NOUN
fuelectenerg-1427	1239	12	(	(	PUNCT
fuelectenerg-1427	1239	13	ulms	ulm	NOUN
fuelectenerg-1427	1239	14	)	)	PUNCT
fuelectenerg-1427	1239	15	for	for	ADP
fuelectenerg-1427	1239	16	pairs	pair	NOUN
fuelectenerg-1427	1239	17	of	of	ADP
fuelectenerg-1427	1239	18	variables	variable	NOUN
fuelectenerg-1427	1239	19	,	,	PUNCT
fuelectenerg-1427	1239	20	as	as	SCONJ
fuelectenerg-1427	1239	21	will	will	AUX
fuelectenerg-1427	1239	22	be	be	AUX
fuelectenerg-1427	1239	23	shown	show	VERB
fuelectenerg-1427	1239	24	in	in	ADP
fuelectenerg-1427	1239	25	section	section	NOUN
fuelectenerg-1427	1239	26	3	3	NUM
fuelectenerg-1427	1239	27	,	,	PUNCT
fuelectenerg-1427	1239	28	which	which	PRON
fuelectenerg-1427	1239	29	is	be	AUX
fuelectenerg-1427	1239	30	analogous	analogous	ADJ
fuelectenerg-1427	1239	31	to	to	ADP
fuelectenerg-1427	1239	32	what	what	PRON
fuelectenerg-1427	1239	33	was	be	AUX
fuelectenerg-1427	1239	34	done	do	VERB
fuelectenerg-1427	1239	35	for	for	ADP
fuelectenerg-1427	1239	36	the	the	DET
fuelectenerg-1427	1239	37	binary	binary	ADJ
fuelectenerg-1427	1239	38	case	case	NOUN
fuelectenerg-1427	1239	39	.	.	PUNCT
fuelectenerg-1427	1240	1	although	although	SCONJ
fuelectenerg-1427	1240	2	the	the	DET
fuelectenerg-1427	1240	3	s	s	PROPN
fuelectenerg-1427	1240	4	/	/	SYM
fuelectenerg-1427	1240	5	d	d	NOUN
fuelectenerg-1427	1240	6	trees	tree	NOUN
fuelectenerg-1427	1240	7	that	that	PRON
fuelectenerg-1427	1240	8	have	have	AUX
fuelectenerg-1427	1240	9	been	be	AUX
fuelectenerg-1427	1240	10	developed	develop	VERB
fuelectenerg-1427	1240	11	so	so	ADV
fuelectenerg-1427	1240	12	far	far	ADV
fuelectenerg-1427	1240	13	are	be	AUX
fuelectenerg-1427	1240	14	for	for	ADP
fuelectenerg-1427	1240	15	the	the	DET
fuelectenerg-1427	1240	16	ternary	ternary	ADJ
fuelectenerg-1427	1240	17	radix	radix	NOUN
fuelectenerg-1427	1240	18	,	,	PUNCT
fuelectenerg-1427	1240	19	similar	similar	ADJ
fuelectenerg-1427	1240	20	s	s	NOUN
fuelectenerg-1427	1240	21	/	/	SYM
fuelectenerg-1427	1240	22	d	d	NOUN
fuelectenerg-1427	1240	23	trees	tree	NOUN
fuelectenerg-1427	1240	24	can	can	AUX
fuelectenerg-1427	1240	25	be	be	AUX
fuelectenerg-1427	1240	26	developed	develop	VERB
fuelectenerg-1427	1240	27	as	as	ADV
fuelectenerg-1427	1240	28	well	well	ADV
fuelectenerg-1427	1240	29	for	for	ADP
fuelectenerg-1427	1240	30	higher	high	ADJ
fuelectenerg-1427	1240	31	galois	galois	PROPN
fuelectenerg-1427	1240	32	radices	radix	NOUN
fuelectenerg-1427	1240	33	of	of	ADP
fuelectenerg-1427	1240	34	gf(pk	gf(pk	NOUN
fuelectenerg-1427	1240	35	)	)	PUNCT
fuelectenerg-1427	1240	36	where	where	SCONJ
fuelectenerg-1427	1240	37	p	p	NOUN
fuelectenerg-1427	1240	38	is	be	AUX
fuelectenerg-1427	1240	39	a	a	DET
fuelectenerg-1427	1240	40	prime	prime	ADJ
fuelectenerg-1427	1240	41	number	number	NOUN
fuelectenerg-1427	1240	42	and	and	CCONJ
fuelectenerg-1427	1240	43	k	k	PROPN
fuelectenerg-1427	1240	44	is	be	AUX
fuelectenerg-1427	1240	45	a	a	DET
fuelectenerg-1427	1240	46	natural	natural	ADJ
fuelectenerg-1427	1240	47	number	number	NOUN
fuelectenerg-1427	1240	48	≥	≥	NOUN
fuelectenerg-1427	1240	49	1	1	NUM
fuelectenerg-1427	1240	50	.	.	PUNCT
fuelectenerg-1427	1241	1	tgrm	tgrm	ADJ
fuelectenerg-1427	1241	2	ternary	ternary	ADJ
fuelectenerg-1427	1241	3	gfsop	gfsop	NOUN
fuelectenerg-1427	1241	4	ternary	ternary	ADJ
fuelectenerg-1427	1241	5	canonical	canonical	ADJ
fuelectenerg-1427	1241	6	forms	form	NOUN
fuelectenerg-1427	1241	7	tfgif	tfgif	PROPN
fuelectenerg-1427	1241	8	tgif	tgif	PROPN
fuelectenerg-1427	1241	9	tif	tif	PROPN
fuelectenerg-1427	1241	10	tpgk	tpgk	PROPN
fuelectenerg-1427	1241	11	tgk	tgk	PROPN
fuelectenerg-1427	1241	12	tpkro	tpkro	PROPN
fuelectenerg-1427	1241	13	tkrotfprm	tkrotfprm	PROPN
fuelectenerg-1427	1242	1	tgifk	tgifk	PROPN
fuelectenerg-1427	1242	2	esop	esop	X
fuelectenerg-1427	1242	3	canonical	canonical	ADJ
fuelectenerg-1427	1242	4	forms	form	NOUN
fuelectenerg-1427	1242	5	fgif	fgif	INTJ
fuelectenerg-1427	1242	6	gif	gif	PROPN
fuelectenerg-1427	1242	7	if	if	SCONJ
fuelectenerg-1427	1242	8	pgk	pgk	NOUN
fuelectenerg-1427	1242	9	gk	gk	PROPN
fuelectenerg-1427	1242	10	grm	grm	PROPN
fuelectenerg-1427	1242	11	pkro	pkro	PROPN
fuelectenerg-1427	1242	12	krofprm	krofprm	PROPN
fuelectenerg-1427	1242	13	(	(	PUNCT
fuelectenerg-1427	1242	14	a	a	NOUN
fuelectenerg-1427	1242	15	)	)	PUNCT
fuelectenerg-1427	1242	16	(	(	PUNCT
fuelectenerg-1427	1242	17	b	b	X
fuelectenerg-1427	1242	18	)	)	PUNCT
fuelectenerg-1427	1242	19	figure	figure	NOUN
fuelectenerg-1427	1242	20	6	6	NUM
fuelectenerg-1427	1242	21	:	:	PUNCT
fuelectenerg-1427	1242	22	green	green	ADJ
fuelectenerg-1427	1242	23	-	-	PUNCT
fuelectenerg-1427	1242	24	sasao	sasao	PROPN
fuelectenerg-1427	1242	25	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1242	26	:	:	PUNCT
fuelectenerg-1427	1242	27	(	(	PUNCT
fuelectenerg-1427	1242	28	a	a	X
fuelectenerg-1427	1242	29	)	)	PUNCT
fuelectenerg-1427	1242	30	set	set	NOUN
fuelectenerg-1427	1242	31	-	-	PUNCT
fuelectenerg-1427	1242	32	theoretic	theoretic	NOUN
fuelectenerg-1427	1242	33	relationship	relationship	NOUN
fuelectenerg-1427	1242	34	between	between	ADP
fuelectenerg-1427	1242	35	gf(2	gf(2	PROPN
fuelectenerg-1427	1242	36	)	)	PUNCT
fuelectenerg-1427	1242	37	families	family	NOUN
fuelectenerg-1427	1242	38	of	of	ADP
fuelectenerg-1427	1242	39	canonical	canonical	ADJ
fuelectenerg-1427	1242	40	forms	form	NOUN
fuelectenerg-1427	1242	41	,	,	PUNCT
fuelectenerg-1427	1242	42	and	and	CCONJ
fuelectenerg-1427	1242	43	(	(	PUNCT
fuelectenerg-1427	1242	44	b	b	X
fuelectenerg-1427	1242	45	)	)	PUNCT
fuelectenerg-1427	1242	46	the	the	DET
fuelectenerg-1427	1242	47	extended	extend	VERB
fuelectenerg-1427	1242	48	green	green	ADJ
fuelectenerg-1427	1242	49	-	-	PUNCT
fuelectenerg-1427	1242	50	sasao	sasao	NOUN
fuelectenerg-1427	1242	51	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1242	52	with	with	ADP
fuelectenerg-1427	1242	53	a	a	DET
fuelectenerg-1427	1242	54	new	new	ADJ
fuelectenerg-1427	1242	55	sub	sub	NOUN
fuelectenerg-1427	1242	56	-	-	NOUN
fuelectenerg-1427	1242	57	family	family	ADJ
fuelectenerg-1427	1242	58	(	(	PUNCT
fuelectenerg-1427	1242	59	tgifk	tgifk	NOUN
fuelectenerg-1427	1242	60	)	)	PUNCT
fuelectenerg-1427	1242	61	for	for	ADP
fuelectenerg-1427	1242	62	gf(3	gf(3	PROPN
fuelectenerg-1427	1242	63	)	)	PUNCT
fuelectenerg-1427	1242	64	reed	reed	NOUN
fuelectenerg-1427	1242	65	-	-	PUNCT
fuelectenerg-1427	1242	66	muller	muller	NOUN
fuelectenerg-1427	1242	67	logic	logic	NOUN
fuelectenerg-1427	1242	68	.	.	PUNCT
fuelectenerg-1427	1243	1	113	113	NUM
fuelectenerg-1427	1243	2	an	an	DET
fuelectenerg-1427	1243	3	extended	extend	VERB
fuelectenerg-1427	1243	4	green	green	ADJ
fuelectenerg-1427	1243	5	sasao	sasao	PROPN
fuelectenerg-1427	1243	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1243	7	of	of	ADP
fuelectenerg-1427	1243	8	canonical	canonical	ADJ
fuelectenerg-1427	1243	9	ternary	ternary	ADJ
fuelectenerg-1427	1243	10	galois	galois	NOUN
fuelectenerg-1427	1243	11	forms	form	NOUN
fuelectenerg-1427	1243	12	...	...	PUNCT
fuelectenerg-1427	1243	13	muller	muller	NOUN
fuelectenerg-1427	1243	14	decision	decision	NOUN
fuelectenerg-1427	1243	15	tree	tree	NOUN
fuelectenerg-1427	1243	16	(	(	PUNCT
fuelectenerg-1427	1243	17	tprmdt	tprmdt	NOUN
fuelectenerg-1427	1243	18	)	)	PUNCT
fuelectenerg-1427	1243	19	.	.	PUNCT
fuelectenerg-1427	1244	1	the	the	DET
fuelectenerg-1427	1244	2	resulting	result	VERB
fuelectenerg-1427	1244	3	expression	expression	NOUN
fuelectenerg-1427	1244	4	is	be	AUX
fuelectenerg-1427	1244	5	called	call	VERB
fuelectenerg-1427	1244	6	ternary	ternary	ADJ
fuelectenerg-1427	1244	7	pseudoreed	pseudoreed	NOUN
fuelectenerg-1427	1244	8	-	-	PUNCT
fuelectenerg-1427	1244	9	muller	muller	NOUN
fuelectenerg-1427	1244	10	expression	expression	NOUN
fuelectenerg-1427	1244	11	.	.	PUNCT
fuelectenerg-1427	1245	1	definition	definition	NOUN
fuelectenerg-1427	1245	2	10	10	NUM
fuelectenerg-1427	1245	3	.	.	PUNCT
fuelectenerg-1427	1246	1	the	the	DET
fuelectenerg-1427	1246	2	decision	decision	NOUN
fuelectenerg-1427	1246	3	tree	tree	NOUN
fuelectenerg-1427	1246	4	that	that	PRON
fuelectenerg-1427	1246	5	results	result	VERB
fuelectenerg-1427	1246	6	from	from	ADP
fuelectenerg-1427	1246	7	using	use	VERB
fuelectenerg-1427	1246	8	any	any	PRON
fuelectenerg-1427	1246	9	of	of	ADP
fuelectenerg-1427	1246	10	the	the	DET
fuelectenerg-1427	1246	11	ternary	ternary	ADJ
fuelectenerg-1427	1246	12	shannon	shannon	NOUN
fuelectenerg-1427	1246	13	expansion	expansion	NOUN
fuelectenerg-1427	1246	14	or	or	CCONJ
fuelectenerg-1427	1246	15	ternary	ternary	ADJ
fuelectenerg-1427	1246	16	davio	davio	NOUN
fuelectenerg-1427	1246	17	expansions	expansion	NOUN
fuelectenerg-1427	1246	18	(	(	PUNCT
fuelectenerg-1427	1246	19	nodes	node	NOUN
fuelectenerg-1427	1246	20	)	)	PUNCT
fuelectenerg-1427	1246	21	for	for	ADP
fuelectenerg-1427	1246	22	each	each	DET
fuelectenerg-1427	1246	23	node	node	NOUN
fuelectenerg-1427	1246	24	(	(	PUNCT
fuelectenerg-1427	1246	25	per	per	ADP
fuelectenerg-1427	1246	26	level	level	NOUN
fuelectenerg-1427	1246	27	)	)	PUNCT
fuelectenerg-1427	1246	28	of	of	ADP
fuelectenerg-1427	1246	29	the	the	DET
fuelectenerg-1427	1246	30	dt	dt	NOUN
fuelectenerg-1427	1246	31	is	be	AUX
fuelectenerg-1427	1246	32	called	call	VERB
fuelectenerg-1427	1246	33	ternary	ternary	ADJ
fuelectenerg-1427	1246	34	pseudo	pseudo	NOUN
fuelectenerg-1427	1246	35	-	-	NOUN
fuelectenerg-1427	1246	36	kronecker	kronecker	NOUN
fuelectenerg-1427	1246	37	decision	decision	NOUN
fuelectenerg-1427	1246	38	tree	tree	NOUN
fuelectenerg-1427	1246	39	(	(	PUNCT
fuelectenerg-1427	1246	40	tpkrodt	tpkrodt	PROPN
fuelectenerg-1427	1246	41	)	)	PUNCT
fuelectenerg-1427	1246	42	.	.	PUNCT
fuelectenerg-1427	1247	1	the	the	DET
fuelectenerg-1427	1247	2	resulting	result	VERB
fuelectenerg-1427	1247	3	expression	expression	NOUN
fuelectenerg-1427	1247	4	is	be	AUX
fuelectenerg-1427	1247	5	called	call	VERB
fuelectenerg-1427	1247	6	ternary	ternary	ADJ
fuelectenerg-1427	1247	7	pseudo	pseudo	NOUN
fuelectenerg-1427	1247	8	-	-	NOUN
fuelectenerg-1427	1247	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1247	10	expression	expression	NOUN
fuelectenerg-1427	1247	11	.	.	PUNCT
fuelectenerg-1427	1248	1	definition	definition	NOUN
fuelectenerg-1427	1248	2	11	11	NUM
fuelectenerg-1427	1248	3	.	.	PUNCT
fuelectenerg-1427	1249	1	the	the	DET
fuelectenerg-1427	1249	2	decision	decision	NOUN
fuelectenerg-1427	1249	3	tree	tree	NOUN
fuelectenerg-1427	1249	4	that	that	PRON
fuelectenerg-1427	1249	5	results	result	VERB
fuelectenerg-1427	1249	6	from	from	ADP
fuelectenerg-1427	1249	7	using	use	VERB
fuelectenerg-1427	1249	8	any	any	PRON
fuelectenerg-1427	1249	9	of	of	ADP
fuelectenerg-1427	1249	10	the	the	DET
fuelectenerg-1427	1249	11	ternary	ternary	ADJ
fuelectenerg-1427	1249	12	shannon	shannon	NOUN
fuelectenerg-1427	1249	13	expansion	expansion	NOUN
fuelectenerg-1427	1249	14	or	or	CCONJ
fuelectenerg-1427	1249	15	ternary	ternary	ADJ
fuelectenerg-1427	1249	16	davio	davio	NOUN
fuelectenerg-1427	1249	17	expansions	expansion	NOUN
fuelectenerg-1427	1249	18	(	(	PUNCT
fuelectenerg-1427	1249	19	nodes	node	NOUN
fuelectenerg-1427	1249	20	)	)	PUNCT
fuelectenerg-1427	1249	21	for	for	ADP
fuelectenerg-1427	1249	22	each	each	DET
fuelectenerg-1427	1249	23	node	node	NOUN
fuelectenerg-1427	1249	24	(	(	PUNCT
fuelectenerg-1427	1249	25	per	per	ADP
fuelectenerg-1427	1249	26	level	level	NOUN
fuelectenerg-1427	1249	27	)	)	PUNCT
fuelectenerg-1427	1249	28	of	of	ADP
fuelectenerg-1427	1249	29	the	the	DET
fuelectenerg-1427	1249	30	dt	dt	PROPN
fuelectenerg-1427	1249	31	,	,	PUNCT
fuelectenerg-1427	1249	32	disregarding	disregard	VERB
fuelectenerg-1427	1249	33	order	order	NOUN
fuelectenerg-1427	1249	34	of	of	ADP
fuelectenerg-1427	1249	35	variables	variable	NOUN
fuelectenerg-1427	1249	36	,	,	PUNCT
fuelectenerg-1427	1249	37	provided	provide	VERB
fuelectenerg-1427	1249	38	that	that	SCONJ
fuelectenerg-1427	1249	39	variables	variable	NOUN
fuelectenerg-1427	1249	40	are	be	AUX
fuelectenerg-1427	1249	41	not	not	PART
fuelectenerg-1427	1249	42	repeated	repeat	VERB
fuelectenerg-1427	1249	43	along	along	ADP
fuelectenerg-1427	1249	44	the	the	DET
fuelectenerg-1427	1249	45	same	same	ADJ
fuelectenerg-1427	1249	46	branches	branch	NOUN
fuelectenerg-1427	1249	47	,	,	PUNCT
fuelectenerg-1427	1249	48	is	be	AUX
fuelectenerg-1427	1249	49	called	call	VERB
fuelectenerg-1427	1249	50	ternary	ternary	ADJ
fuelectenerg-1427	1249	51	free	free	ADJ
fuelectenerg-1427	1249	52	kronecker	kronecker	NOUN
fuelectenerg-1427	1249	53	decision	decision	NOUN
fuelectenerg-1427	1249	54	tree	tree	NOUN
fuelectenerg-1427	1249	55	(	(	PUNCT
fuelectenerg-1427	1249	56	tfkrodt	tfkrodt	PROPN
fuelectenerg-1427	1249	57	)	)	PUNCT
fuelectenerg-1427	1249	58	.	.	PUNCT
fuelectenerg-1427	1250	1	the	the	DET
fuelectenerg-1427	1250	2	result	result	NOUN
fuelectenerg-1427	1250	3	is	be	AUX
fuelectenerg-1427	1250	4	called	call	VERB
fuelectenerg-1427	1250	5	ternary	ternary	ADJ
fuelectenerg-1427	1250	6	free	free	ADJ
fuelectenerg-1427	1250	7	-	-	PUNCT
fuelectenerg-1427	1250	8	kronecker	kronecker	NOUN
fuelectenerg-1427	1250	9	expression	expression	NOUN
fuelectenerg-1427	1250	10	.	.	PUNCT
fuelectenerg-1427	1251	1	definition	definition	NOUN
fuelectenerg-1427	1251	2	12	12	NUM
fuelectenerg-1427	1251	3	.	.	PUNCT
fuelectenerg-1427	1252	1	the	the	DET
fuelectenerg-1427	1252	2	ternary	ternary	ADJ
fuelectenerg-1427	1252	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1252	4	dt	dt	NOUN
fuelectenerg-1427	1252	5	that	that	PRON
fuelectenerg-1427	1252	6	has	have	VERB
fuelectenerg-1427	1252	7	at	at	ADV
fuelectenerg-1427	1252	8	least	least	ADV
fuelectenerg-1427	1252	9	one	one	NUM
fuelectenerg-1427	1252	10	ternary	ternary	ADJ
fuelectenerg-1427	1252	11	generalized	generalize	VERB
fuelectenerg-1427	1252	12	reed	reed	NOUN
fuelectenerg-1427	1252	13	-	-	PUNCT
fuelectenerg-1427	1252	14	muller	muller	NOUN
fuelectenerg-1427	1252	15	expansion	expansion	NOUN
fuelectenerg-1427	1252	16	node	node	NOUN
fuelectenerg-1427	1252	17	is	be	AUX
fuelectenerg-1427	1252	18	called	call	VERB
fuelectenerg-1427	1252	19	ternary	ternary	ADJ
fuelectenerg-1427	1252	20	generalized	generalize	VERB
fuelectenerg-1427	1252	21	kronecker	kronecker	NOUN
fuelectenerg-1427	1252	22	decision	decision	NOUN
fuelectenerg-1427	1252	23	tree	tree	NOUN
fuelectenerg-1427	1252	24	(	(	PUNCT
fuelectenerg-1427	1252	25	tgkdt	tgkdt	ADJ
fuelectenerg-1427	1252	26	)	)	PUNCT
fuelectenerg-1427	1252	27	.	.	PUNCT
fuelectenerg-1427	1253	1	the	the	DET
fuelectenerg-1427	1253	2	result	result	NOUN
fuelectenerg-1427	1253	3	is	be	AUX
fuelectenerg-1427	1253	4	called	call	VERB
fuelectenerg-1427	1253	5	ternary	ternary	ADJ
fuelectenerg-1427	1253	6	generalized	generalized	ADJ
fuelectenerg-1427	1253	7	kronecker	kronecker	NOUN
fuelectenerg-1427	1253	8	expression	expression	NOUN
fuelectenerg-1427	1253	9	.	.	PUNCT
fuelectenerg-1427	1254	1	definition	definition	NOUN
fuelectenerg-1427	1254	2	13	13	NUM
fuelectenerg-1427	1254	3	.	.	PUNCT
fuelectenerg-1427	1255	1	the	the	DET
fuelectenerg-1427	1255	2	ternary	ternary	ADJ
fuelectenerg-1427	1255	3	kronecker	kronecker	NOUN
fuelectenerg-1427	1255	4	dt	dt	NOUN
fuelectenerg-1427	1255	5	that	that	PRON
fuelectenerg-1427	1255	6	has	have	VERB
fuelectenerg-1427	1255	7	at	at	ADV
fuelectenerg-1427	1255	8	least	least	ADJ
fuelectenerg-1427	1255	9	one	one	NUM
fuelectenerg-1427	1255	10	tgif	tgif	NOUN
fuelectenerg-1427	1255	11	node	node	NOUN
fuelectenerg-1427	1255	12	is	be	AUX
fuelectenerg-1427	1255	13	called	call	VERB
fuelectenerg-1427	1255	14	ternary	ternary	ADJ
fuelectenerg-1427	1255	15	generalized	generalize	VERB
fuelectenerg-1427	1255	16	inclusive	inclusive	ADJ
fuelectenerg-1427	1255	17	forms	form	NOUN
fuelectenerg-1427	1255	18	kronecker	kronecker	NOUN
fuelectenerg-1427	1255	19	(	(	PUNCT
fuelectenerg-1427	1255	20	tgifk	tgifk	NOUN
fuelectenerg-1427	1255	21	)	)	PUNCT
fuelectenerg-1427	1255	22	decision	decision	NOUN
fuelectenerg-1427	1255	23	tree	tree	NOUN
fuelectenerg-1427	1255	24	.	.	PUNCT
fuelectenerg-1427	1256	1	the	the	DET
fuelectenerg-1427	1256	2	result	result	NOUN
fuelectenerg-1427	1256	3	is	be	AUX
fuelectenerg-1427	1256	4	called	call	VERB
fuelectenerg-1427	1256	5	ternary	ternary	ADJ
fuelectenerg-1427	1256	6	generalized	generalized	ADJ
fuelectenerg-1427	1256	7	inclusive	inclusive	ADJ
fuelectenerg-1427	1256	8	form	form	NOUN
fuelectenerg-1427	1256	9	kronecker	kronecker	NOUN
fuelectenerg-1427	1256	10	expression	expression	NOUN
fuelectenerg-1427	1256	11	.	.	PUNCT
fuelectenerg-1427	1257	1	figure	figure	NOUN
fuelectenerg-1427	1257	2	6(b	6(b	NUM
fuelectenerg-1427	1257	3	)	)	PUNCT
fuelectenerg-1427	1257	4	illustrates	illustrate	VERB
fuelectenerg-1427	1257	5	the	the	DET
fuelectenerg-1427	1257	6	extended	extended	ADJ
fuelectenerg-1427	1257	7	gf(3	gf(3	PROPN
fuelectenerg-1427	1257	8	)	)	PUNCT
fuelectenerg-1427	1257	9	green	green	ADJ
fuelectenerg-1427	1257	10	-	-	PUNCT
fuelectenerg-1427	1257	11	sasao	sasao	PROPN
fuelectenerg-1427	1257	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1257	13	with	with	ADP
fuelectenerg-1427	1257	14	the	the	DET
fuelectenerg-1427	1257	15	new	new	ADJ
fuelectenerg-1427	1257	16	subfamily	subfamily	ADV
fuelectenerg-1427	1257	17	(	(	PUNCT
fuelectenerg-1427	1257	18	tgifk	tgifk	NOUN
fuelectenerg-1427	1257	19	)	)	PUNCT
fuelectenerg-1427	1257	20	.	.	PUNCT
fuelectenerg-1427	1258	1	the	the	DET
fuelectenerg-1427	1258	2	presented	present	VERB
fuelectenerg-1427	1258	3	tgif	tgif	NOUN
fuelectenerg-1427	1258	4	nodes	node	NOUN
fuelectenerg-1427	1258	5	can	can	AUX
fuelectenerg-1427	1258	6	be	be	AUX
fuelectenerg-1427	1258	7	realized	realize	VERB
fuelectenerg-1427	1258	8	with	with	ADP
fuelectenerg-1427	1258	9	universal	universal	ADJ
fuelectenerg-1427	1258	10	logic	logic	NOUN
fuelectenerg-1427	1258	11	modules	module	NOUN
fuelectenerg-1427	1258	12	(	(	PUNCT
fuelectenerg-1427	1258	13	ulms	ulm	NOUN
fuelectenerg-1427	1258	14	)	)	PUNCT
fuelectenerg-1427	1258	15	for	for	ADP
fuelectenerg-1427	1258	16	pairs	pair	NOUN
fuelectenerg-1427	1258	17	of	of	ADP
fuelectenerg-1427	1258	18	variables	variable	NOUN
fuelectenerg-1427	1258	19	,	,	PUNCT
fuelectenerg-1427	1258	20	as	as	SCONJ
fuelectenerg-1427	1258	21	will	will	AUX
fuelectenerg-1427	1258	22	be	be	AUX
fuelectenerg-1427	1258	23	shown	show	VERB
fuelectenerg-1427	1258	24	in	in	ADP
fuelectenerg-1427	1258	25	section	section	NOUN
fuelectenerg-1427	1258	26	3	3	NUM
fuelectenerg-1427	1258	27	,	,	PUNCT
fuelectenerg-1427	1258	28	which	which	PRON
fuelectenerg-1427	1258	29	is	be	AUX
fuelectenerg-1427	1258	30	analogous	analogous	ADJ
fuelectenerg-1427	1258	31	to	to	ADP
fuelectenerg-1427	1258	32	what	what	PRON
fuelectenerg-1427	1258	33	was	be	AUX
fuelectenerg-1427	1258	34	done	do	VERB
fuelectenerg-1427	1258	35	for	for	ADP
fuelectenerg-1427	1258	36	the	the	DET
fuelectenerg-1427	1258	37	binary	binary	ADJ
fuelectenerg-1427	1258	38	case	case	NOUN
fuelectenerg-1427	1258	39	.	.	PUNCT
fuelectenerg-1427	1259	1	although	although	SCONJ
fuelectenerg-1427	1259	2	the	the	DET
fuelectenerg-1427	1259	3	s	s	PROPN
fuelectenerg-1427	1259	4	/	/	SYM
fuelectenerg-1427	1259	5	d	d	NOUN
fuelectenerg-1427	1259	6	trees	tree	NOUN
fuelectenerg-1427	1259	7	that	that	PRON
fuelectenerg-1427	1259	8	have	have	AUX
fuelectenerg-1427	1259	9	been	be	AUX
fuelectenerg-1427	1259	10	developed	develop	VERB
fuelectenerg-1427	1259	11	so	so	ADV
fuelectenerg-1427	1259	12	far	far	ADV
fuelectenerg-1427	1259	13	are	be	AUX
fuelectenerg-1427	1259	14	for	for	ADP
fuelectenerg-1427	1259	15	the	the	DET
fuelectenerg-1427	1259	16	ternary	ternary	ADJ
fuelectenerg-1427	1259	17	radix	radix	NOUN
fuelectenerg-1427	1259	18	,	,	PUNCT
fuelectenerg-1427	1259	19	similar	similar	ADJ
fuelectenerg-1427	1259	20	s	s	NOUN
fuelectenerg-1427	1259	21	/	/	SYM
fuelectenerg-1427	1259	22	d	d	NOUN
fuelectenerg-1427	1259	23	trees	tree	NOUN
fuelectenerg-1427	1259	24	can	can	AUX
fuelectenerg-1427	1259	25	be	be	AUX
fuelectenerg-1427	1259	26	developed	develop	VERB
fuelectenerg-1427	1259	27	as	as	ADV
fuelectenerg-1427	1259	28	well	well	ADV
fuelectenerg-1427	1259	29	for	for	ADP
fuelectenerg-1427	1259	30	higher	high	ADJ
fuelectenerg-1427	1259	31	galois	galois	PROPN
fuelectenerg-1427	1259	32	radices	radix	NOUN
fuelectenerg-1427	1259	33	of	of	ADP
fuelectenerg-1427	1259	34	gf(pk	gf(pk	NOUN
fuelectenerg-1427	1259	35	)	)	PUNCT
fuelectenerg-1427	1259	36	where	where	SCONJ
fuelectenerg-1427	1259	37	p	p	NOUN
fuelectenerg-1427	1259	38	is	be	AUX
fuelectenerg-1427	1259	39	a	a	DET
fuelectenerg-1427	1259	40	prime	prime	ADJ
fuelectenerg-1427	1259	41	number	number	NOUN
fuelectenerg-1427	1259	42	and	and	CCONJ
fuelectenerg-1427	1259	43	k	k	PROPN
fuelectenerg-1427	1259	44	is	be	AUX
fuelectenerg-1427	1259	45	a	a	DET
fuelectenerg-1427	1259	46	natural	natural	ADJ
fuelectenerg-1427	1259	47	number	number	NOUN
fuelectenerg-1427	1259	48	≥	≥	NOUN
fuelectenerg-1427	1259	49	1	1	NUM
fuelectenerg-1427	1259	50	.	.	PUNCT
fuelectenerg-1427	1260	1	tgrm	tgrm	ADJ
fuelectenerg-1427	1260	2	ternary	ternary	ADJ
fuelectenerg-1427	1260	3	gfsop	gfsop	NOUN
fuelectenerg-1427	1260	4	ternary	ternary	ADJ
fuelectenerg-1427	1260	5	canonical	canonical	ADJ
fuelectenerg-1427	1260	6	forms	form	NOUN
fuelectenerg-1427	1260	7	tfgif	tfgif	PROPN
fuelectenerg-1427	1260	8	tgif	tgif	PROPN
fuelectenerg-1427	1260	9	tif	tif	PROPN
fuelectenerg-1427	1260	10	tpgk	tpgk	PROPN
fuelectenerg-1427	1260	11	tgk	tgk	PROPN
fuelectenerg-1427	1260	12	tpkro	tpkro	PROPN
fuelectenerg-1427	1260	13	tkrotfprm	tkrotfprm	PROPN
fuelectenerg-1427	1261	1	tgifk	tgifk	PROPN
fuelectenerg-1427	1261	2	esop	esop	X
fuelectenerg-1427	1261	3	canonical	canonical	ADJ
fuelectenerg-1427	1261	4	forms	form	NOUN
fuelectenerg-1427	1261	5	fgif	fgif	INTJ
fuelectenerg-1427	1261	6	gif	gif	PROPN
fuelectenerg-1427	1261	7	if	if	SCONJ
fuelectenerg-1427	1261	8	pgk	pgk	NOUN
fuelectenerg-1427	1261	9	gk	gk	PROPN
fuelectenerg-1427	1261	10	grm	grm	PROPN
fuelectenerg-1427	1261	11	pkro	pkro	PROPN
fuelectenerg-1427	1261	12	krofprm	krofprm	PROPN
fuelectenerg-1427	1261	13	(	(	PUNCT
fuelectenerg-1427	1261	14	a	a	NOUN
fuelectenerg-1427	1261	15	)	)	PUNCT
fuelectenerg-1427	1261	16	(	(	PUNCT
fuelectenerg-1427	1261	17	b	b	X
fuelectenerg-1427	1261	18	)	)	PUNCT
fuelectenerg-1427	1261	19	figure	figure	NOUN
fuelectenerg-1427	1261	20	6	6	NUM
fuelectenerg-1427	1261	21	:	:	PUNCT
fuelectenerg-1427	1261	22	green	green	ADJ
fuelectenerg-1427	1261	23	-	-	PUNCT
fuelectenerg-1427	1261	24	sasao	sasao	PROPN
fuelectenerg-1427	1261	25	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1261	26	:	:	PUNCT
fuelectenerg-1427	1261	27	(	(	PUNCT
fuelectenerg-1427	1261	28	a	a	X
fuelectenerg-1427	1261	29	)	)	PUNCT
fuelectenerg-1427	1261	30	set	set	NOUN
fuelectenerg-1427	1261	31	-	-	PUNCT
fuelectenerg-1427	1261	32	theoretic	theoretic	NOUN
fuelectenerg-1427	1261	33	relationship	relationship	NOUN
fuelectenerg-1427	1261	34	between	between	ADP
fuelectenerg-1427	1261	35	gf(2	gf(2	PROPN
fuelectenerg-1427	1261	36	)	)	PUNCT
fuelectenerg-1427	1261	37	families	family	NOUN
fuelectenerg-1427	1261	38	of	of	ADP
fuelectenerg-1427	1261	39	canonical	canonical	ADJ
fuelectenerg-1427	1261	40	forms	form	NOUN
fuelectenerg-1427	1261	41	,	,	PUNCT
fuelectenerg-1427	1261	42	and	and	CCONJ
fuelectenerg-1427	1261	43	(	(	PUNCT
fuelectenerg-1427	1261	44	b	b	X
fuelectenerg-1427	1261	45	)	)	PUNCT
fuelectenerg-1427	1261	46	the	the	DET
fuelectenerg-1427	1261	47	extended	extend	VERB
fuelectenerg-1427	1261	48	green	green	ADJ
fuelectenerg-1427	1261	49	-	-	PUNCT
fuelectenerg-1427	1261	50	sasao	sasao	NOUN
fuelectenerg-1427	1261	51	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1261	52	with	with	ADP
fuelectenerg-1427	1261	53	a	a	DET
fuelectenerg-1427	1261	54	new	new	ADJ
fuelectenerg-1427	1261	55	sub	sub	NOUN
fuelectenerg-1427	1261	56	-	-	NOUN
fuelectenerg-1427	1261	57	family	family	ADJ
fuelectenerg-1427	1261	58	(	(	PUNCT
fuelectenerg-1427	1261	59	tgifk	tgifk	NOUN
fuelectenerg-1427	1261	60	)	)	PUNCT
fuelectenerg-1427	1261	61	for	for	ADP
fuelectenerg-1427	1261	62	gf(3	gf(3	PROPN
fuelectenerg-1427	1261	63	)	)	PUNCT
fuelectenerg-1427	1261	64	reed	reed	NOUN
fuelectenerg-1427	1261	65	-	-	PUNCT
fuelectenerg-1427	1261	66	muller	muller	NOUN
fuelectenerg-1427	1261	67	logic	logic	NOUN
fuelectenerg-1427	1261	68	.	.	PUNCT
fuelectenerg-1427	1262	1	113	113	NUM
fuelectenerg-1427	1262	2	62	62	NUM
fuelectenerg-1427	1262	3	a.	a.	NOUN
fuelectenerg-1427	1262	4	n.	n.	PROPN
fuelectenerg-1427	1262	5	al	al	PROPN
fuelectenerg-1427	1262	6	-	-	PUNCT
fuelectenerg-1427	1262	7	rabadi	rabadi	VERB
fuelectenerg-1427	1262	8	an	an	DET
fuelectenerg-1427	1262	9	extended	extended	ADJ
fuelectenerg-1427	1262	10	green	green	ADJ
fuelectenerg-1427	1262	11	sasao	sasao	PROPN
fuelectenerg-1427	1262	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1262	13	of	of	ADP
fuelectenerg-1427	1262	14	canonical	canonical	ADJ
fuelectenerg-1427	1262	15	ternary	ternary	ADJ
fuelectenerg-1427	1262	16	galois	galois	NOUN
fuelectenerg-1427	1262	17	forms	form	NOUN
fuelectenerg-1427	1262	18	and	and	CCONJ
fuelectenerg-1427	1262	19	universal	universal	ADJ
fuelectenerg-1427	1262	20	logic	logic	NOUN
fuelectenerg-1427	1262	21	modules	module	NOUN
fuelectenerg-1427	1262	22	63	63	NUM
fuelectenerg-1427	1262	23	an	an	DET
fuelectenerg-1427	1262	24	extended	extended	ADJ
fuelectenerg-1427	1262	25	green	green	ADJ
fuelectenerg-1427	1262	26	sasao	sasao	PROPN
fuelectenerg-1427	1262	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1262	28	of	of	ADP
fuelectenerg-1427	1262	29	canonical	canonical	ADJ
fuelectenerg-1427	1262	30	ternary	ternary	ADJ
fuelectenerg-1427	1262	31	galois	galois	NOUN
fuelectenerg-1427	1262	32	forms	form	NOUN
fuelectenerg-1427	1262	33	...	...	PUNCT
fuelectenerg-1427	1262	34	3	3	NUM
fuelectenerg-1427	1262	35	universal	universal	ADJ
fuelectenerg-1427	1262	36	logic	logic	NOUN
fuelectenerg-1427	1262	37	modules	module	NOUN
fuelectenerg-1427	1262	38	for	for	ADP
fuelectenerg-1427	1262	39	the	the	DET
fuelectenerg-1427	1262	40	circuit	circuit	NOUN
fuelectenerg-1427	1262	41	realization	realization	NOUN
fuelectenerg-1427	1262	42	of	of	ADP
fuelectenerg-1427	1262	43	s	s	PROPN
fuelectenerg-1427	1262	44	/	/	SYM
fuelectenerg-1427	1262	45	d	d	NOUN
fuelectenerg-1427	1262	46	trees	tree	NOUN
fuelectenerg-1427	1262	47	the	the	DET
fuelectenerg-1427	1262	48	nonsingular	nonsingular	ADJ
fuelectenerg-1427	1262	49	expansions	expansion	NOUN
fuelectenerg-1427	1262	50	of	of	ADP
fuelectenerg-1427	1262	51	ternary	ternary	ADJ
fuelectenerg-1427	1262	52	shannon	shannon	NOUN
fuelectenerg-1427	1262	53	(	(	PUNCT
fuelectenerg-1427	1262	54	s	s	NOUN
fuelectenerg-1427	1262	55	)	)	PUNCT
fuelectenerg-1427	1262	56	and	and	CCONJ
fuelectenerg-1427	1262	57	ternary	ternary	ADJ
fuelectenerg-1427	1262	58	davio	davio	NOUN
fuelectenerg-1427	1262	59	(	(	PUNCT
fuelectenerg-1427	1262	60	d0	d0	NOUN
fuelectenerg-1427	1262	61	,	,	PUNCT
fuelectenerg-1427	1262	62	d1	d1	PROPN
fuelectenerg-1427	1262	63	and	and	CCONJ
fuelectenerg-1427	1262	64	d2	d2	PROPN
fuelectenerg-1427	1262	65	)	)	PUNCT
fuelectenerg-1427	1262	66	,	,	PUNCT
fuelectenerg-1427	1262	67	can	can	AUX
fuelectenerg-1427	1262	68	be	be	AUX
fuelectenerg-1427	1262	69	realized	realize	VERB
fuelectenerg-1427	1262	70	using	use	VERB
fuelectenerg-1427	1262	71	a	a	DET
fuelectenerg-1427	1262	72	universal	universal	ADJ
fuelectenerg-1427	1262	73	logic	logic	NOUN
fuelectenerg-1427	1262	74	module	module	NOUN
fuelectenerg-1427	1262	75	(	(	PUNCT
fuelectenerg-1427	1262	76	ulm	ulm	PROPN
fuelectenerg-1427	1262	77	)	)	PUNCT
fuelectenerg-1427	1262	78	with	with	ADP
fuelectenerg-1427	1262	79	control	control	NOUN
fuelectenerg-1427	1262	80	variables	variable	NOUN
fuelectenerg-1427	1262	81	corresponding	correspond	VERB
fuelectenerg-1427	1262	82	to	to	ADP
fuelectenerg-1427	1262	83	the	the	DET
fuelectenerg-1427	1262	84	variables	variable	NOUN
fuelectenerg-1427	1262	85	of	of	ADP
fuelectenerg-1427	1262	86	the	the	DET
fuelectenerg-1427	1262	87	basis	basis	NOUN
fuelectenerg-1427	1262	88	functions	function	NOUN
fuelectenerg-1427	1262	89	which	which	PRON
fuelectenerg-1427	1262	90	are	be	AUX
fuelectenerg-1427	1262	91	the	the	DET
fuelectenerg-1427	1262	92	variables	variable	NOUN
fuelectenerg-1427	1262	93	we	we	PRON
fuelectenerg-1427	1262	94	are	be	AUX
fuelectenerg-1427	1262	95	expanding	expand	VERB
fuelectenerg-1427	1262	96	upon	upon	SCONJ
fuelectenerg-1427	1262	97	.	.	PUNCT
fuelectenerg-1427	1263	1	we	we	PRON
fuelectenerg-1427	1263	2	call	call	VERB
fuelectenerg-1427	1263	3	it	it	PRON
fuelectenerg-1427	1263	4	a	a	DET
fuelectenerg-1427	1263	5	universal	universal	ADJ
fuelectenerg-1427	1263	6	logic	logic	NOUN
fuelectenerg-1427	1263	7	module	module	NOUN
fuelectenerg-1427	1263	8	,	,	PUNCT
fuelectenerg-1427	1263	9	because	because	SCONJ
fuelectenerg-1427	1263	10	similarly	similarly	ADV
fuelectenerg-1427	1263	11	to	to	ADP
fuelectenerg-1427	1263	12	a	a	DET
fuelectenerg-1427	1263	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1263	14	,	,	PUNCT
fuelectenerg-1427	1263	15	all	all	DET
fuelectenerg-1427	1263	16	functions	function	NOUN
fuelectenerg-1427	1263	17	of	of	ADP
fuelectenerg-1427	1263	18	two	two	NUM
fuelectenerg-1427	1263	19	variables	variable	NOUN
fuelectenerg-1427	1263	20	can	can	AUX
fuelectenerg-1427	1263	21	be	be	AUX
fuelectenerg-1427	1263	22	realized	realize	VERB
fuelectenerg-1427	1263	23	with	with	ADP
fuelectenerg-1427	1263	24	two	two	NUM
fuelectenerg-1427	1263	25	-	-	PUNCT
fuelectenerg-1427	1263	26	level	level	NOUN
fuelectenerg-1427	1263	27	trees	tree	NOUN
fuelectenerg-1427	1263	28	of	of	ADP
fuelectenerg-1427	1263	29	such	such	ADJ
fuelectenerg-1427	1263	30	modules	module	NOUN
fuelectenerg-1427	1263	31	using	use	VERB
fuelectenerg-1427	1263	32	constants	constant	NOUN
fuelectenerg-1427	1263	33	on	on	ADP
fuelectenerg-1427	1263	34	the	the	DET
fuelectenerg-1427	1263	35	second	second	ADJ
fuelectenerg-1427	1263	36	-	-	PUNCT
fuelectenerg-1427	1263	37	level	level	NOUN
fuelectenerg-1427	1263	38	data	datum	NOUN
fuelectenerg-1427	1263	39	inputs	input	NOUN
fuelectenerg-1427	1263	40	.	.	PUNCT
fuelectenerg-1427	1264	1	the	the	DET
fuelectenerg-1427	1264	2	presented	present	VERB
fuelectenerg-1427	1264	3	ulms	ulm	NOUN
fuelectenerg-1427	1264	4	are	be	AUX
fuelectenerg-1427	1264	5	complete	complete	ADJ
fuelectenerg-1427	1264	6	systems	system	NOUN
fuelectenerg-1427	1264	7	because	because	SCONJ
fuelectenerg-1427	1264	8	they	they	PRON
fuelectenerg-1427	1264	9	can	can	AUX
fuelectenerg-1427	1264	10	implement	implement	VERB
fuelectenerg-1427	1264	11	all	all	DET
fuelectenerg-1427	1264	12	possible	possible	ADJ
fuelectenerg-1427	1264	13	functions	function	NOUN
fuelectenerg-1427	1264	14	with	with	ADP
fuelectenerg-1427	1264	15	certain	certain	ADJ
fuelectenerg-1427	1264	16	number	number	NOUN
fuelectenerg-1427	1264	17	of	of	ADP
fuelectenerg-1427	1264	18	variables	variable	NOUN
fuelectenerg-1427	1264	19	.	.	PUNCT
fuelectenerg-1427	1265	1	the	the	DET
fuelectenerg-1427	1265	2	concept	concept	NOUN
fuelectenerg-1427	1265	3	of	of	ADP
fuelectenerg-1427	1265	4	the	the	DET
fuelectenerg-1427	1265	5	universal	universal	ADJ
fuelectenerg-1427	1265	6	logic	logic	NOUN
fuelectenerg-1427	1265	7	module	module	NOUN
fuelectenerg-1427	1265	8	was	be	AUX
fuelectenerg-1427	1265	9	used	use	VERB
fuelectenerg-1427	1265	10	for	for	ADP
fuelectenerg-1427	1265	11	binary	binary	PROPN
fuelectenerg-1427	1265	12	rm	rm	PROPN
fuelectenerg-1427	1265	13	logic	logic	PROPN
fuelectenerg-1427	1265	14	over	over	ADP
fuelectenerg-1427	1265	15	gf(2	gf(2	PROPN
fuelectenerg-1427	1265	16	)	)	PUNCT
fuelectenerg-1427	1265	17	,	,	PUNCT
fuelectenerg-1427	1265	18	as	as	ADV
fuelectenerg-1427	1265	19	well	well	ADV
fuelectenerg-1427	1265	20	as	as	ADP
fuelectenerg-1427	1265	21	the	the	DET
fuelectenerg-1427	1265	22	general	general	ADJ
fuelectenerg-1427	1265	23	case	case	NOUN
fuelectenerg-1427	1265	24	of	of	ADP
fuelectenerg-1427	1265	25	linearly	linearly	ADV
fuelectenerg-1427	1265	26	independent	independent	ADJ
fuelectenerg-1427	1265	27	(	(	PUNCT
fuelectenerg-1427	1265	28	li	li	NOUN
fuelectenerg-1427	1265	29	)	)	PUNCT
fuelectenerg-1427	1265	30	logic	logic	NOUN
fuelectenerg-1427	1265	31	that	that	PRON
fuelectenerg-1427	1265	32	includes	include	VERB
fuelectenerg-1427	1265	33	rm	rm	NOUN
fuelectenerg-1427	1265	34	logic	logic	NOUN
fuelectenerg-1427	1265	35	as	as	ADP
fuelectenerg-1427	1265	36	a	a	DET
fuelectenerg-1427	1265	37	special	special	ADJ
fuelectenerg-1427	1265	38	case	case	NOUN
fuelectenerg-1427	1265	39	.	.	PUNCT
fuelectenerg-1427	1266	1	binary	binary	PROPN
fuelectenerg-1427	1266	2	li	li	PROPN
fuelectenerg-1427	1266	3	logic	logic	PROPN
fuelectenerg-1427	1266	4	extended	extend	VERB
fuelectenerg-1427	1266	5	the	the	DET
fuelectenerg-1427	1266	6	universal	universal	ADJ
fuelectenerg-1427	1266	7	logic	logic	NOUN
fuelectenerg-1427	1266	8	module	module	NOUN
fuelectenerg-1427	1266	9	from	from	ADP
fuelectenerg-1427	1266	10	just	just	ADV
fuelectenerg-1427	1266	11	being	be	AUX
fuelectenerg-1427	1266	12	a	a	DET
fuelectenerg-1427	1266	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1266	14	(	(	PUNCT
fuelectenerg-1427	1266	15	shannon	shannon	PROPN
fuelectenerg-1427	1266	16	expansion	expansion	PROPN
fuelectenerg-1427	1266	17	)	)	PUNCT
fuelectenerg-1427	1266	18	,	,	PUNCT
fuelectenerg-1427	1266	19	and	and	CCONJ
fuelectenerg-1427	1266	20	/	/	SYM
fuelectenerg-1427	1266	21	exor	exor	PROPN
fuelectenerg-1427	1266	22	gate	gate	PROPN
fuelectenerg-1427	1266	23	(	(	PUNCT
fuelectenerg-1427	1266	24	positive	positive	ADJ
fuelectenerg-1427	1266	25	davio	davio	NOUN
fuelectenerg-1427	1266	26	expansion	expansion	NOUN
fuelectenerg-1427	1266	27	)	)	PUNCT
fuelectenerg-1427	1266	28	and	and	CCONJ
fuelectenerg-1427	1266	29	and	and	CCONJ
fuelectenerg-1427	1266	30	/	/	SYM
fuelectenerg-1427	1266	31	exor	exor	PROPN
fuelectenerg-1427	1266	32	/	/	SYM
fuelectenerg-1427	1266	33	not	not	PART
fuelectenerg-1427	1266	34	gate	gate	VERB
fuelectenerg-1427	1266	35	with	with	ADP
fuelectenerg-1427	1266	36	inverted	inverted	ADJ
fuelectenerg-1427	1266	37	control	control	NOUN
fuelectenerg-1427	1266	38	variable	variable	NOUN
fuelectenerg-1427	1266	39	(	(	PUNCT
fuelectenerg-1427	1266	40	negative	negative	ADJ
fuelectenerg-1427	1266	41	davio	davio	NOUN
fuelectenerg-1427	1266	42	expansion	expansion	NOUN
fuelectenerg-1427	1266	43	)	)	PUNCT
fuelectenerg-1427	1266	44	,	,	PUNCT
fuelectenerg-1427	1266	45	to	to	ADP
fuelectenerg-1427	1266	46	the	the	DET
fuelectenerg-1427	1266	47	universal	universal	ADJ
fuelectenerg-1427	1266	48	logic	logic	NOUN
fuelectenerg-1427	1266	49	modules	module	NOUN
fuelectenerg-1427	1266	50	for	for	ADP
fuelectenerg-1427	1266	51	any	any	DET
fuelectenerg-1427	1266	52	expansion	expansion	NOUN
fuelectenerg-1427	1266	53	over	over	ADP
fuelectenerg-1427	1266	54	any	any	DET
fuelectenerg-1427	1266	55	linearly	linearly	ADV
fuelectenerg-1427	1266	56	independent	independent	ADJ
fuelectenerg-1427	1266	57	basis	basis	NOUN
fuelectenerg-1427	1266	58	functions	function	NOUN
fuelectenerg-1427	1266	59	.	.	PUNCT
fuelectenerg-1427	1267	1	analogously	analogously	ADV
fuelectenerg-1427	1267	2	to	to	ADP
fuelectenerg-1427	1267	3	the	the	DET
fuelectenerg-1427	1267	4	binary	binary	ADJ
fuelectenerg-1427	1267	5	case	case	NOUN
fuelectenerg-1427	1267	6	,	,	PUNCT
fuelectenerg-1427	1267	7	figure	figure	VERB
fuelectenerg-1427	1267	8	7	7	NUM
fuelectenerg-1427	1267	9	presents	present	VERB
fuelectenerg-1427	1267	10	universal	universal	ADJ
fuelectenerg-1427	1267	11	logic	logic	NOUN
fuelectenerg-1427	1267	12	modules	module	NOUN
fuelectenerg-1427	1267	13	for	for	ADP
fuelectenerg-1427	1267	14	ternary	ternary	ADJ
fuelectenerg-1427	1267	15	shannon	shannon	NOUN
fuelectenerg-1427	1267	16	and	and	CCONJ
fuelectenerg-1427	1267	17	ternary	ternary	ADJ
fuelectenerg-1427	1267	18	davio	davio	NOUN
fuelectenerg-1427	1267	19	,	,	PUNCT
fuelectenerg-1427	1267	20	respectively	respectively	ADV
fuelectenerg-1427	1267	21	.	.	PUNCT
fuelectenerg-1427	1268	1	one	one	PRON
fuelectenerg-1427	1268	2	can	can	AUX
fuelectenerg-1427	1268	3	note	note	VERB
fuelectenerg-1427	1268	4	,	,	PUNCT
fuelectenerg-1427	1268	5	that	that	SCONJ
fuelectenerg-1427	1268	6	any	any	DET
fuelectenerg-1427	1268	7	function	function	NOUN
fuelectenerg-1427	1268	8	f	f	PROPN
fuelectenerg-1427	1268	9	can	can	AUX
fuelectenerg-1427	1268	10	be	be	AUX
fuelectenerg-1427	1268	11	produced	produce	VERB
fuelectenerg-1427	1268	12	by	by	ADP
fuelectenerg-1427	1268	13	the	the	DET
fuelectenerg-1427	1268	14	application	application	NOUN
fuelectenerg-1427	1268	15	of	of	ADP
fuelectenerg-1427	1268	16	the	the	DET
fuelectenerg-1427	1268	17	independent	independent	ADJ
fuelectenerg-1427	1268	18	variable	variable	NOUN
fuelectenerg-1427	1268	19	x	x	PUNCT
fuelectenerg-1427	1268	20	and	and	CCONJ
fuelectenerg-1427	1268	21	the	the	DET
fuelectenerg-1427	1268	22	cofactors	cofactor	NOUN
fuelectenerg-1427	1268	23	{	{	PUNCT
fuelectenerg-1427	1268	24	fi	fi	NOUN
fuelectenerg-1427	1268	25	,	,	PUNCT
fuelectenerg-1427	1268	26	f	f	PROPN
fuelectenerg-1427	1268	27	j	j	PROPN
fuelectenerg-1427	1268	28	and	and	CCONJ
fuelectenerg-1427	1268	29	fk	fk	INTJ
fuelectenerg-1427	1268	30	}	}	PUNCT
fuelectenerg-1427	1268	31	as	as	ADP
fuelectenerg-1427	1268	32	inputs	input	NOUN
fuelectenerg-1427	1268	33	to	to	ADP
fuelectenerg-1427	1268	34	a	a	DET
fuelectenerg-1427	1268	35	ulm	ulm	NOUN
fuelectenerg-1427	1268	36	.	.	PUNCT
fuelectenerg-1427	1269	1	the	the	DET
fuelectenerg-1427	1269	2	form	form	NOUN
fuelectenerg-1427	1269	3	of	of	ADP
fuelectenerg-1427	1269	4	the	the	DET
fuelectenerg-1427	1269	5	resulting	result	VERB
fuelectenerg-1427	1269	6	function	function	NOUN
fuelectenerg-1427	1269	7	depends	depend	VERB
fuelectenerg-1427	1269	8	on	on	ADP
fuelectenerg-1427	1269	9	our	our	PRON
fuelectenerg-1427	1269	10	choice	choice	NOUN
fuelectenerg-1427	1269	11	of	of	ADP
fuelectenerg-1427	1269	12	the	the	DET
fuelectenerg-1427	1269	13	shift	shift	NOUN
fuelectenerg-1427	1269	14	and	and	CCONJ
fuelectenerg-1427	1269	15	power	power	NOUN
fuelectenerg-1427	1269	16	operations	operation	NOUN
fuelectenerg-1427	1269	17	that	that	PRON
fuelectenerg-1427	1269	18	we	we	PRON
fuelectenerg-1427	1269	19	choose	choose	VERB
fuelectenerg-1427	1269	20	inside	inside	ADP
fuelectenerg-1427	1269	21	the	the	DET
fuelectenerg-1427	1269	22	ulm	ulm	NOUN
fuelectenerg-1427	1269	23	for	for	ADP
fuelectenerg-1427	1269	24	the	the	DET
fuelectenerg-1427	1269	25	input	input	NOUN
fuelectenerg-1427	1269	26	independent	independent	ADJ
fuelectenerg-1427	1269	27	variable	variable	NOUN
fuelectenerg-1427	1269	28	,	,	PUNCT
fuelectenerg-1427	1269	29	and	and	CCONJ
fuelectenerg-1427	1269	30	on	on	ADP
fuelectenerg-1427	1269	31	our	our	PRON
fuelectenerg-1427	1269	32	choice	choice	NOUN
fuelectenerg-1427	1269	33	of	of	ADP
fuelectenerg-1427	1269	34	the	the	DET
fuelectenerg-1427	1269	35	weighted	weight	VERB
fuelectenerg-1427	1269	36	combinations	combination	NOUN
fuelectenerg-1427	1269	37	of	of	ADP
fuelectenerg-1427	1269	38	the	the	DET
fuelectenerg-1427	1269	39	input	input	NOUN
fuelectenerg-1427	1269	40	cofactors	cofactor	NOUN
fuelectenerg-1427	1269	41	.	.	PUNCT
fuelectenerg-1427	1270	1	utilizing	utilize	VERB
fuelectenerg-1427	1270	2	this	this	DET
fuelectenerg-1427	1270	3	note	note	NOUN
fuelectenerg-1427	1270	4	,	,	PUNCT
fuelectenerg-1427	1270	5	we	we	PRON
fuelectenerg-1427	1270	6	can	can	AUX
fuelectenerg-1427	1270	7	combine	combine	VERB
fuelectenerg-1427	1270	8	all	all	DET
fuelectenerg-1427	1270	9	davio	davio	NOUN
fuelectenerg-1427	1270	10	ulms	ulm	NOUN
fuelectenerg-1427	1270	11	to	to	PART
fuelectenerg-1427	1270	12	create	create	VERB
fuelectenerg-1427	1270	13	the	the	DET
fuelectenerg-1427	1270	14	single	single	ADJ
fuelectenerg-1427	1270	15	all	all	ADJ
fuelectenerg-1427	1270	16	-	-	PUNCT
fuelectenerg-1427	1270	17	davio	davio	NOUN
fuelectenerg-1427	1270	18	ulm	ulm	NOUN
fuelectenerg-1427	1270	19	,	,	PUNCT
fuelectenerg-1427	1270	20	where	where	SCONJ
fuelectenerg-1427	1270	21	figure	figure	NOUN
fuelectenerg-1427	1270	22	7(c	7(c	NOUN
fuelectenerg-1427	1270	23	)	)	PUNCT
fuelectenerg-1427	1270	24	illustrates	illustrate	VERB
fuelectenerg-1427	1270	25	this	this	DET
fuelectenerg-1427	1270	26	ulm	ulm	NOUN
fuelectenerg-1427	1270	27	.	.	PUNCT
fuelectenerg-1427	1271	1	also	also	ADV
fuelectenerg-1427	1271	2	,	,	PUNCT
fuelectenerg-1427	1271	3	the	the	DET
fuelectenerg-1427	1271	4	more	more	ADV
fuelectenerg-1427	1271	5	general	general	ADJ
fuelectenerg-1427	1271	6	ulm	ulm	NOUN
fuelectenerg-1427	1271	7	as	as	SCONJ
fuelectenerg-1427	1271	8	shown	show	VERB
fuelectenerg-1427	1271	9	in	in	ADP
fuelectenerg-1427	1271	10	figure	figure	NOUN
fuelectenerg-1427	1271	11	7(d	7(d	NUM
fuelectenerg-1427	1271	12	)	)	PUNCT
fuelectenerg-1427	1271	13	,	,	PUNCT
fuelectenerg-1427	1271	14	can	can	AUX
fuelectenerg-1427	1271	15	be	be	AUX
fuelectenerg-1427	1271	16	generated	generate	VERB
fuelectenerg-1427	1271	17	to	to	PART
fuelectenerg-1427	1271	18	implement	implement	VERB
fuelectenerg-1427	1271	19	all	all	DET
fuelectenerg-1427	1271	20	ternary	ternary	ADJ
fuelectenerg-1427	1271	21	gf(3	gf(3	PROPN
fuelectenerg-1427	1271	22	)	)	PUNCT
fuelectenerg-1427	1271	23	shannon	shannon	NOUN
fuelectenerg-1427	1271	24	and	and	CCONJ
fuelectenerg-1427	1271	25	davio	davio	NOUN
fuelectenerg-1427	1271	26	expansions	expansion	NOUN
fuelectenerg-1427	1271	27	.	.	PUNCT
fuelectenerg-1427	1272	1	in	in	ADP
fuelectenerg-1427	1272	2	general	general	ADJ
fuelectenerg-1427	1272	3	,	,	PUNCT
fuelectenerg-1427	1272	4	the	the	DET
fuelectenerg-1427	1272	5	gates	gate	NOUN
fuelectenerg-1427	1272	6	in	in	ADP
fuelectenerg-1427	1272	7	the	the	DET
fuelectenerg-1427	1272	8	ulms	ulm	NOUN
fuelectenerg-1427	1272	9	can	can	AUX
fuelectenerg-1427	1272	10	be	be	AUX
fuelectenerg-1427	1272	11	implemented	implement	VERB
fuelectenerg-1427	1272	12	,	,	PUNCT
fuelectenerg-1427	1272	13	among	among	ADP
fuelectenerg-1427	1272	14	other	other	ADJ
fuelectenerg-1427	1272	15	circuit	circuit	NOUN
fuelectenerg-1427	1272	16	technologies	technology	NOUN
fuelectenerg-1427	1272	17	,	,	PUNCT
fuelectenerg-1427	1272	18	by	by	ADP
fuelectenerg-1427	1272	19	using	use	VERB
fuelectenerg-1427	1272	20	binary	binary	ADJ
fuelectenerg-1427	1272	21	logic	logic	NOUN
fuelectenerg-1427	1272	22	over	over	ADP
fuelectenerg-1427	1272	23	gf(2	gf(2	PROPN
fuelectenerg-1427	1272	24	)	)	PUNCT
fuelectenerg-1427	1272	25	or	or	CCONJ
fuelectenerg-1427	1272	26	using	use	VERB
fuelectenerg-1427	1272	27	multiple	multiple	ADV
fuelectenerg-1427	1272	28	-	-	PUNCT
fuelectenerg-1427	1272	29	valued	value	VERB
fuelectenerg-1427	1272	30	circuit	circuit	NOUN
fuelectenerg-1427	1272	31	gates	gate	NOUN
fuelectenerg-1427	1272	32	.	.	PUNCT
fuelectenerg-1427	1273	1	each	each	DET
fuelectenerg-1427	1273	2	ternary	ternary	ADJ
fuelectenerg-1427	1273	3	ulm	ulm	PROPN
fuelectenerg-1427	1273	4	corresponds	correspond	VERB
fuelectenerg-1427	1273	5	to	to	ADP
fuelectenerg-1427	1273	6	a	a	DET
fuelectenerg-1427	1273	7	single	single	ADJ
fuelectenerg-1427	1273	8	node	node	NOUN
fuelectenerg-1427	1273	9	in	in	ADP
fuelectenerg-1427	1273	10	the	the	DET
fuelectenerg-1427	1273	11	nodes	node	NOUN
fuelectenerg-1427	1273	12	of	of	ADP
fuelectenerg-1427	1273	13	ternary	ternary	ADJ
fuelectenerg-1427	1273	14	dts	dts	NOUN
fuelectenerg-1427	1273	15	that	that	PRON
fuelectenerg-1427	1273	16	were	be	AUX
fuelectenerg-1427	1273	17	illustrated	illustrate	VERB
fuelectenerg-1427	1273	18	previously	previously	ADV
fuelectenerg-1427	1273	19	.	.	PUNCT
fuelectenerg-1427	1274	1	the	the	DET
fuelectenerg-1427	1274	2	main	main	ADJ
fuelectenerg-1427	1274	3	advantage	advantage	NOUN
fuelectenerg-1427	1274	4	of	of	ADP
fuelectenerg-1427	1274	5	such	such	ADJ
fuelectenerg-1427	1274	6	powerful	powerful	ADJ
fuelectenerg-1427	1274	7	ulms	ulm	NOUN
fuelectenerg-1427	1274	8	is	be	AUX
fuelectenerg-1427	1274	9	in	in	ADP
fuelectenerg-1427	1274	10	high	high	ADJ
fuelectenerg-1427	1274	11	layout	layout	NOUN
fuelectenerg-1427	1274	12	regularity	regularity	NOUN
fuelectenerg-1427	1274	13	that	that	PRON
fuelectenerg-1427	1274	14	is	be	AUX
fuelectenerg-1427	1274	15	required	require	VERB
fuelectenerg-1427	1274	16	by	by	ADP
fuelectenerg-1427	1274	17	future	future	ADJ
fuelectenerg-1427	1274	18	nanotechnologies	nanotechnology	NOUN
fuelectenerg-1427	1274	19	,	,	PUNCT
fuelectenerg-1427	1274	20	where	where	SCONJ
fuelectenerg-1427	1274	21	the	the	DET
fuelectenerg-1427	1274	22	trees	tree	NOUN
fuelectenerg-1427	1274	23	can	can	AUX
fuelectenerg-1427	1274	24	be	be	AUX
fuelectenerg-1427	1274	25	realized	realize	VERB
fuelectenerg-1427	1274	26	in	in	ADP
fuelectenerg-1427	1274	27	efficient	efficient	ADJ
fuelectenerg-1427	1274	28	layout	layout	NOUN
fuelectenerg-1427	1274	29	because	because	SCONJ
fuelectenerg-1427	1274	30	they	they	PRON
fuelectenerg-1427	1274	31	do	do	AUX
fuelectenerg-1427	1274	32	not	not	PART
fuelectenerg-1427	1274	33	grow	grow	VERB
fuelectenerg-1427	1274	34	exponentially	exponentially	ADV
fuelectenerg-1427	1274	35	for	for	ADP
fuelectenerg-1427	1274	36	practical	practical	ADJ
fuelectenerg-1427	1274	37	functions	function	NOUN
fuelectenerg-1427	1274	38	.	.	PUNCT
fuelectenerg-1427	1275	1	for	for	ADP
fuelectenerg-1427	1275	2	instance	instance	NOUN
fuelectenerg-1427	1275	3	,	,	PUNCT
fuelectenerg-1427	1275	4	assuming	assume	VERB
fuelectenerg-1427	1275	5	ulm	ulm	NOUN
fuelectenerg-1427	1275	6	from	from	ADP
fuelectenerg-1427	1275	7	figure	figure	NOUN
fuelectenerg-1427	1275	8	7	7	NUM
fuelectenerg-1427	1275	9	,	,	PUNCT
fuelectenerg-1427	1275	10	although	although	SCONJ
fuelectenerg-1427	1275	11	every	every	DET
fuelectenerg-1427	1275	12	two	two	NUM
fuelectenerg-1427	1275	13	-	-	PUNCT
fuelectenerg-1427	1275	14	variable	variable	NOUN
fuelectenerg-1427	1275	15	function	function	NOUN
fuelectenerg-1427	1275	16	can	can	AUX
fuelectenerg-1427	1275	17	be	be	AUX
fuelectenerg-1427	1275	18	realized	realize	VERB
fuelectenerg-1427	1275	19	with	with	ADP
fuelectenerg-1427	1275	20	four	four	NUM
fuelectenerg-1427	1275	21	such	such	ADJ
fuelectenerg-1427	1275	22	modules	module	NOUN
fuelectenerg-1427	1275	23	,	,	PUNCT
fuelectenerg-1427	1275	24	it	it	PRON
fuelectenerg-1427	1275	25	is	be	AUX
fuelectenerg-1427	1275	26	highly	highly	ADV
fuelectenerg-1427	1275	27	probable	probable	ADJ
fuelectenerg-1427	1275	28	that	that	SCONJ
fuelectenerg-1427	1275	29	most	most	ADJ
fuelectenerg-1427	1275	30	of	of	ADP
fuelectenerg-1427	1275	31	two	two	NUM
fuelectenerg-1427	1275	32	-	-	PUNCT
fuelectenerg-1427	1275	33	variable	variable	NOUN
fuelectenerg-1427	1275	34	functions	function	NOUN
fuelectenerg-1427	1275	35	will	will	AUX
fuelectenerg-1427	1275	36	require	require	VERB
fuelectenerg-1427	1275	37	less	less	ADJ
fuelectenerg-1427	1275	38	than	than	ADP
fuelectenerg-1427	1275	39	four	four	NUM
fuelectenerg-1427	1275	40	modules	module	NOUN
fuelectenerg-1427	1275	41	.	.	PUNCT
fuelectenerg-1427	1276	1	because	because	SCONJ
fuelectenerg-1427	1276	2	of	of	ADP
fuelectenerg-1427	1276	3	these	these	DET
fuelectenerg-1427	1276	4	properties	property	NOUN
fuelectenerg-1427	1276	5	,	,	PUNCT
fuelectenerg-1427	1276	6	this	this	DET
fuelectenerg-1427	1276	7	approach	approach	NOUN
fuelectenerg-1427	1276	8	is	be	AUX
fuelectenerg-1427	1276	9	further	far	ADV
fuelectenerg-1427	1276	10	expected	expect	VERB
fuelectenerg-1427	1276	11	to	to	PART
fuelectenerg-1427	1276	12	give	give	VERB
fuelectenerg-1427	1276	13	good	good	ADJ
fuelectenerg-1427	1276	14	results	result	NOUN
fuelectenerg-1427	1276	15	when	when	SCONJ
fuelectenerg-1427	1276	16	applied	apply	VERB
fuelectenerg-1427	1276	17	to	to	ADP
fuelectenerg-1427	1276	18	the	the	DET
fuelectenerg-1427	1276	19	corresponding	corresponding	ADJ
fuelectenerg-1427	1276	20	incompletely	incompletely	ADV
fuelectenerg-1427	1276	21	specified	specify	VERB
fuelectenerg-1427	1276	22	functions	function	NOUN
fuelectenerg-1427	1276	23	and	and	CCONJ
fuelectenerg-1427	1276	24	multiple	multiple	ADV
fuelectenerg-1427	1276	25	-	-	PUNCT
fuelectenerg-1427	1276	26	valued	value	VERB
fuelectenerg-1427	1276	27	relations	relation	NOUN
fuelectenerg-1427	1276	28	.	.	PUNCT
fuelectenerg-1427	1277	1	4	4	NUM
fuelectenerg-1427	1277	2	conclusions	conclusion	NOUN
fuelectenerg-1427	1277	3	and	and	CCONJ
fuelectenerg-1427	1277	4	future	future	ADJ
fuelectenerg-1427	1277	5	work	work	NOUN
fuelectenerg-1427	1277	6	in	in	ADP
fuelectenerg-1427	1277	7	this	this	DET
fuelectenerg-1427	1277	8	paper	paper	NOUN
fuelectenerg-1427	1277	9	,	,	PUNCT
fuelectenerg-1427	1277	10	an	an	DET
fuelectenerg-1427	1277	11	extended	extended	ADJ
fuelectenerg-1427	1277	12	green	green	ADJ
fuelectenerg-1427	1277	13	-	-	PUNCT
fuelectenerg-1427	1277	14	sasao	sasao	NOUN
fuelectenerg-1427	1277	15	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1277	16	of	of	ADP
fuelectenerg-1427	1277	17	families	family	NOUN
fuelectenerg-1427	1277	18	and	and	CCONJ
fuelectenerg-1427	1277	19	forms	form	NOUN
fuelectenerg-1427	1277	20	is	be	AUX
fuelectenerg-1427	1277	21	introduced	introduce	VERB
fuelectenerg-1427	1277	22	.	.	PUNCT
fuelectenerg-1427	1278	1	analogously	analogously	ADV
fuelectenerg-1427	1278	2	to	to	ADP
fuelectenerg-1427	1278	3	the	the	DET
fuelectenerg-1427	1278	4	binary	binary	ADJ
fuelectenerg-1427	1278	5	case	case	NOUN
fuelectenerg-1427	1278	6	,	,	PUNCT
fuelectenerg-1427	1278	7	two	two	NUM
fuelectenerg-1427	1278	8	general	general	ADJ
fuelectenerg-1427	1278	9	families	family	NOUN
fuelectenerg-1427	1278	10	of	of	ADP
fuelectenerg-1427	1278	11	canonical	canonical	ADJ
fuelectenerg-1427	1278	12	ternary	ternary	ADJ
fuelectenerg-1427	1278	13	reed	reed	NOUN
fuelectenerg-1427	1278	14	-	-	PUNCT
fuelectenerg-1427	1278	15	muller	muller	NOUN
fuelectenerg-1427	1278	16	forms	form	NOUN
fuelectenerg-1427	1278	17	,	,	PUNCT
fuelectenerg-1427	1278	18	called	call	VERB
fuelectenerg-1427	1278	19	ternary	ternary	ADJ
fuelectenerg-1427	1278	20	inclusive	inclusive	ADJ
fuelectenerg-1427	1278	21	forms	form	NOUN
fuelectenerg-1427	1278	22	(	(	PUNCT
fuelectenerg-1427	1278	23	tifs	tifs	PROPN
fuelectenerg-1427	1278	24	)	)	PUNCT
fuelectenerg-1427	1278	25	and	and	CCONJ
fuelectenerg-1427	1278	26	their	their	PRON
fuelectenerg-1427	1278	27	generalization	generalization	NOUN
fuelectenerg-1427	1278	28	of	of	ADP
fuelectenerg-1427	1278	29	ternary	ternary	ADJ
fuelectenerg-1427	1278	30	generalized	generalize	VERB
fuelectenerg-1427	1278	31	inclusive	inclusive	ADJ
fuelectenerg-1427	1278	32	forms	form	NOUN
fuelectenerg-1427	1278	33	(	(	PUNCT
fuelectenerg-1427	1278	34	tgifs	tgif	NOUN
fuelectenerg-1427	1278	35	)	)	PUNCT
fuelectenerg-1427	1278	36	,	,	PUNCT
fuelectenerg-1427	1278	37	are	be	AUX
fuelectenerg-1427	1278	38	presented	present	VERB
fuelectenerg-1427	1278	39	.	.	PUNCT
fuelectenerg-1427	1279	1	the	the	DET
fuelectenerg-1427	1279	2	second	second	ADJ
fuelectenerg-1427	1279	3	family	family	NOUN
fuelectenerg-1427	1279	4	includes	include	VERB
fuelectenerg-1427	1279	5	minimum	minimum	ADJ
fuelectenerg-1427	1279	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1279	7	)	)	PUNCT
fuelectenerg-1427	1279	8	galois	galois	PROPN
fuelectenerg-1427	1279	9	field	field	NOUN
fuelectenerg-1427	1279	10	sum	sum	NOUN
fuelectenerg-1427	1279	11	-	-	PUNCT
fuelectenerg-1427	1279	12	of	of	ADP
fuelectenerg-1427	1279	13	-	-	PUNCT
fuelectenerg-1427	1279	14	products	product	NOUN
fuelectenerg-1427	1279	15	(	(	PUNCT
fuelectenerg-1427	1279	16	gfsops	gfsop	NOUN
fuelectenerg-1427	1279	17	)	)	PUNCT
fuelectenerg-1427	1279	18	.	.	PUNCT
fuelectenerg-1427	1280	1	the	the	DET
fuelectenerg-1427	1280	2	multiple	multiple	ADV
fuelectenerg-1427	1280	3	-	-	PUNCT
fuelectenerg-1427	1280	4	valued	value	VERB
fuelectenerg-1427	1280	5	shannon	shannon	NOUN
fuelectenerg-1427	1280	6	-	-	PUNCT
fuelectenerg-1427	1280	7	davio	davio	NOUN
fuelectenerg-1427	1280	8	(	(	PUNCT
fuelectenerg-1427	1280	9	s	s	NOUN
fuelectenerg-1427	1280	10	/	/	SYM
fuelectenerg-1427	1280	11	d	d	NOUN
fuelectenerg-1427	1280	12	)	)	PUNCT
fuelectenerg-1427	1280	13	trees	tree	NOUN
fuelectenerg-1427	1280	14	developed	develop	VERB
fuelectenerg-1427	1280	15	in	in	ADP
fuelectenerg-1427	1280	16	this	this	DET
fuelectenerg-1427	1280	17	paper	paper	NOUN
fuelectenerg-1427	1280	18	provide	provide	VERB
fuelectenerg-1427	1280	19	more	more	ADJ
fuelectenerg-1427	1280	20	general	general	ADJ
fuelectenerg-1427	1280	21	polarity	polarity	NOUN
fuelectenerg-1427	1280	22	with	with	ADP
fuelectenerg-1427	1280	23	regards	regard	NOUN
fuelectenerg-1427	1280	24	to	to	ADP
fuelectenerg-1427	1280	25	the	the	DET
fuelectenerg-1427	1280	26	114	114	NUM
fuelectenerg-1427	1280	27	an	an	DET
fuelectenerg-1427	1280	28	extended	extended	ADJ
fuelectenerg-1427	1280	29	green	green	ADJ
fuelectenerg-1427	1280	30	sasao	sasao	PROPN
fuelectenerg-1427	1280	31	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1280	32	of	of	ADP
fuelectenerg-1427	1280	33	canonical	canonical	ADJ
fuelectenerg-1427	1280	34	ternary	ternary	ADJ
fuelectenerg-1427	1280	35	galois	galois	NOUN
fuelectenerg-1427	1280	36	forms	form	NOUN
fuelectenerg-1427	1280	37	...	...	PUNCT
fuelectenerg-1427	1280	38	3	3	NUM
fuelectenerg-1427	1280	39	universal	universal	ADJ
fuelectenerg-1427	1280	40	logic	logic	NOUN
fuelectenerg-1427	1280	41	modules	module	NOUN
fuelectenerg-1427	1280	42	for	for	ADP
fuelectenerg-1427	1280	43	the	the	DET
fuelectenerg-1427	1280	44	circuit	circuit	NOUN
fuelectenerg-1427	1280	45	realization	realization	NOUN
fuelectenerg-1427	1280	46	of	of	ADP
fuelectenerg-1427	1280	47	s	s	PROPN
fuelectenerg-1427	1280	48	/	/	SYM
fuelectenerg-1427	1280	49	d	d	NOUN
fuelectenerg-1427	1280	50	trees	tree	NOUN
fuelectenerg-1427	1280	51	the	the	DET
fuelectenerg-1427	1280	52	nonsingular	nonsingular	ADJ
fuelectenerg-1427	1280	53	expansions	expansion	NOUN
fuelectenerg-1427	1280	54	of	of	ADP
fuelectenerg-1427	1280	55	ternary	ternary	ADJ
fuelectenerg-1427	1280	56	shannon	shannon	NOUN
fuelectenerg-1427	1280	57	(	(	PUNCT
fuelectenerg-1427	1280	58	s	s	NOUN
fuelectenerg-1427	1280	59	)	)	PUNCT
fuelectenerg-1427	1280	60	and	and	CCONJ
fuelectenerg-1427	1280	61	ternary	ternary	ADJ
fuelectenerg-1427	1280	62	davio	davio	NOUN
fuelectenerg-1427	1280	63	(	(	PUNCT
fuelectenerg-1427	1280	64	d0	d0	NOUN
fuelectenerg-1427	1280	65	,	,	PUNCT
fuelectenerg-1427	1280	66	d1	d1	PROPN
fuelectenerg-1427	1280	67	and	and	CCONJ
fuelectenerg-1427	1280	68	d2	d2	PROPN
fuelectenerg-1427	1280	69	)	)	PUNCT
fuelectenerg-1427	1280	70	,	,	PUNCT
fuelectenerg-1427	1280	71	can	can	AUX
fuelectenerg-1427	1280	72	be	be	AUX
fuelectenerg-1427	1280	73	realized	realize	VERB
fuelectenerg-1427	1280	74	using	use	VERB
fuelectenerg-1427	1280	75	a	a	DET
fuelectenerg-1427	1280	76	universal	universal	ADJ
fuelectenerg-1427	1280	77	logic	logic	NOUN
fuelectenerg-1427	1280	78	module	module	NOUN
fuelectenerg-1427	1280	79	(	(	PUNCT
fuelectenerg-1427	1280	80	ulm	ulm	PROPN
fuelectenerg-1427	1280	81	)	)	PUNCT
fuelectenerg-1427	1280	82	with	with	ADP
fuelectenerg-1427	1280	83	control	control	NOUN
fuelectenerg-1427	1280	84	variables	variable	NOUN
fuelectenerg-1427	1280	85	corresponding	correspond	VERB
fuelectenerg-1427	1280	86	to	to	ADP
fuelectenerg-1427	1280	87	the	the	DET
fuelectenerg-1427	1280	88	variables	variable	NOUN
fuelectenerg-1427	1280	89	of	of	ADP
fuelectenerg-1427	1280	90	the	the	DET
fuelectenerg-1427	1280	91	basis	basis	NOUN
fuelectenerg-1427	1280	92	functions	function	NOUN
fuelectenerg-1427	1280	93	which	which	PRON
fuelectenerg-1427	1280	94	are	be	AUX
fuelectenerg-1427	1280	95	the	the	DET
fuelectenerg-1427	1280	96	variables	variable	NOUN
fuelectenerg-1427	1280	97	we	we	PRON
fuelectenerg-1427	1280	98	are	be	AUX
fuelectenerg-1427	1280	99	expanding	expand	VERB
fuelectenerg-1427	1280	100	upon	upon	SCONJ
fuelectenerg-1427	1280	101	.	.	PUNCT
fuelectenerg-1427	1281	1	we	we	PRON
fuelectenerg-1427	1281	2	call	call	VERB
fuelectenerg-1427	1281	3	it	it	PRON
fuelectenerg-1427	1281	4	a	a	DET
fuelectenerg-1427	1281	5	universal	universal	ADJ
fuelectenerg-1427	1281	6	logic	logic	NOUN
fuelectenerg-1427	1281	7	module	module	NOUN
fuelectenerg-1427	1281	8	,	,	PUNCT
fuelectenerg-1427	1281	9	because	because	SCONJ
fuelectenerg-1427	1281	10	similarly	similarly	ADV
fuelectenerg-1427	1281	11	to	to	ADP
fuelectenerg-1427	1281	12	a	a	DET
fuelectenerg-1427	1281	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1281	14	,	,	PUNCT
fuelectenerg-1427	1281	15	all	all	DET
fuelectenerg-1427	1281	16	functions	function	NOUN
fuelectenerg-1427	1281	17	of	of	ADP
fuelectenerg-1427	1281	18	two	two	NUM
fuelectenerg-1427	1281	19	variables	variable	NOUN
fuelectenerg-1427	1281	20	can	can	AUX
fuelectenerg-1427	1281	21	be	be	AUX
fuelectenerg-1427	1281	22	realized	realize	VERB
fuelectenerg-1427	1281	23	with	with	ADP
fuelectenerg-1427	1281	24	two	two	NUM
fuelectenerg-1427	1281	25	-	-	PUNCT
fuelectenerg-1427	1281	26	level	level	NOUN
fuelectenerg-1427	1281	27	trees	tree	NOUN
fuelectenerg-1427	1281	28	of	of	ADP
fuelectenerg-1427	1281	29	such	such	ADJ
fuelectenerg-1427	1281	30	modules	module	NOUN
fuelectenerg-1427	1281	31	using	use	VERB
fuelectenerg-1427	1281	32	constants	constant	NOUN
fuelectenerg-1427	1281	33	on	on	ADP
fuelectenerg-1427	1281	34	the	the	DET
fuelectenerg-1427	1281	35	second	second	ADJ
fuelectenerg-1427	1281	36	-	-	PUNCT
fuelectenerg-1427	1281	37	level	level	NOUN
fuelectenerg-1427	1281	38	data	datum	NOUN
fuelectenerg-1427	1281	39	inputs	input	NOUN
fuelectenerg-1427	1281	40	.	.	PUNCT
fuelectenerg-1427	1282	1	the	the	DET
fuelectenerg-1427	1282	2	presented	present	VERB
fuelectenerg-1427	1282	3	ulms	ulm	NOUN
fuelectenerg-1427	1282	4	are	be	AUX
fuelectenerg-1427	1282	5	complete	complete	ADJ
fuelectenerg-1427	1282	6	systems	system	NOUN
fuelectenerg-1427	1282	7	because	because	SCONJ
fuelectenerg-1427	1282	8	they	they	PRON
fuelectenerg-1427	1282	9	can	can	AUX
fuelectenerg-1427	1282	10	implement	implement	VERB
fuelectenerg-1427	1282	11	all	all	DET
fuelectenerg-1427	1282	12	possible	possible	ADJ
fuelectenerg-1427	1282	13	functions	function	NOUN
fuelectenerg-1427	1282	14	with	with	ADP
fuelectenerg-1427	1282	15	certain	certain	ADJ
fuelectenerg-1427	1282	16	number	number	NOUN
fuelectenerg-1427	1282	17	of	of	ADP
fuelectenerg-1427	1282	18	variables	variable	NOUN
fuelectenerg-1427	1282	19	.	.	PUNCT
fuelectenerg-1427	1283	1	the	the	DET
fuelectenerg-1427	1283	2	concept	concept	NOUN
fuelectenerg-1427	1283	3	of	of	ADP
fuelectenerg-1427	1283	4	the	the	DET
fuelectenerg-1427	1283	5	universal	universal	ADJ
fuelectenerg-1427	1283	6	logic	logic	NOUN
fuelectenerg-1427	1283	7	module	module	NOUN
fuelectenerg-1427	1283	8	was	be	AUX
fuelectenerg-1427	1283	9	used	use	VERB
fuelectenerg-1427	1283	10	for	for	ADP
fuelectenerg-1427	1283	11	binary	binary	PROPN
fuelectenerg-1427	1283	12	rm	rm	PROPN
fuelectenerg-1427	1283	13	logic	logic	PROPN
fuelectenerg-1427	1283	14	over	over	ADP
fuelectenerg-1427	1283	15	gf(2	gf(2	PROPN
fuelectenerg-1427	1283	16	)	)	PUNCT
fuelectenerg-1427	1283	17	,	,	PUNCT
fuelectenerg-1427	1283	18	as	as	ADV
fuelectenerg-1427	1283	19	well	well	ADV
fuelectenerg-1427	1283	20	as	as	ADP
fuelectenerg-1427	1283	21	the	the	DET
fuelectenerg-1427	1283	22	general	general	ADJ
fuelectenerg-1427	1283	23	case	case	NOUN
fuelectenerg-1427	1283	24	of	of	ADP
fuelectenerg-1427	1283	25	linearly	linearly	ADV
fuelectenerg-1427	1283	26	independent	independent	ADJ
fuelectenerg-1427	1283	27	(	(	PUNCT
fuelectenerg-1427	1283	28	li	li	NOUN
fuelectenerg-1427	1283	29	)	)	PUNCT
fuelectenerg-1427	1283	30	logic	logic	NOUN
fuelectenerg-1427	1283	31	that	that	PRON
fuelectenerg-1427	1283	32	includes	include	VERB
fuelectenerg-1427	1283	33	rm	rm	NOUN
fuelectenerg-1427	1283	34	logic	logic	NOUN
fuelectenerg-1427	1283	35	as	as	ADP
fuelectenerg-1427	1283	36	a	a	DET
fuelectenerg-1427	1283	37	special	special	ADJ
fuelectenerg-1427	1283	38	case	case	NOUN
fuelectenerg-1427	1283	39	.	.	PUNCT
fuelectenerg-1427	1284	1	binary	binary	PROPN
fuelectenerg-1427	1284	2	li	li	PROPN
fuelectenerg-1427	1284	3	logic	logic	PROPN
fuelectenerg-1427	1284	4	extended	extend	VERB
fuelectenerg-1427	1284	5	the	the	DET
fuelectenerg-1427	1284	6	universal	universal	ADJ
fuelectenerg-1427	1284	7	logic	logic	NOUN
fuelectenerg-1427	1284	8	module	module	NOUN
fuelectenerg-1427	1284	9	from	from	ADP
fuelectenerg-1427	1284	10	just	just	ADV
fuelectenerg-1427	1284	11	being	be	AUX
fuelectenerg-1427	1284	12	a	a	DET
fuelectenerg-1427	1284	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1284	14	(	(	PUNCT
fuelectenerg-1427	1284	15	shannon	shannon	PROPN
fuelectenerg-1427	1284	16	expansion	expansion	PROPN
fuelectenerg-1427	1284	17	)	)	PUNCT
fuelectenerg-1427	1284	18	,	,	PUNCT
fuelectenerg-1427	1284	19	and	and	CCONJ
fuelectenerg-1427	1284	20	/	/	SYM
fuelectenerg-1427	1284	21	exor	exor	PROPN
fuelectenerg-1427	1284	22	gate	gate	PROPN
fuelectenerg-1427	1284	23	(	(	PUNCT
fuelectenerg-1427	1284	24	positive	positive	ADJ
fuelectenerg-1427	1284	25	davio	davio	NOUN
fuelectenerg-1427	1284	26	expansion	expansion	NOUN
fuelectenerg-1427	1284	27	)	)	PUNCT
fuelectenerg-1427	1284	28	and	and	CCONJ
fuelectenerg-1427	1284	29	and	and	CCONJ
fuelectenerg-1427	1284	30	/	/	SYM
fuelectenerg-1427	1284	31	exor	exor	PROPN
fuelectenerg-1427	1284	32	/	/	SYM
fuelectenerg-1427	1284	33	not	not	PART
fuelectenerg-1427	1284	34	gate	gate	VERB
fuelectenerg-1427	1284	35	with	with	ADP
fuelectenerg-1427	1284	36	inverted	inverted	ADJ
fuelectenerg-1427	1284	37	control	control	NOUN
fuelectenerg-1427	1284	38	variable	variable	NOUN
fuelectenerg-1427	1284	39	(	(	PUNCT
fuelectenerg-1427	1284	40	negative	negative	ADJ
fuelectenerg-1427	1284	41	davio	davio	NOUN
fuelectenerg-1427	1284	42	expansion	expansion	NOUN
fuelectenerg-1427	1284	43	)	)	PUNCT
fuelectenerg-1427	1284	44	,	,	PUNCT
fuelectenerg-1427	1284	45	to	to	ADP
fuelectenerg-1427	1284	46	the	the	DET
fuelectenerg-1427	1284	47	universal	universal	ADJ
fuelectenerg-1427	1284	48	logic	logic	NOUN
fuelectenerg-1427	1284	49	modules	module	NOUN
fuelectenerg-1427	1284	50	for	for	ADP
fuelectenerg-1427	1284	51	any	any	DET
fuelectenerg-1427	1284	52	expansion	expansion	NOUN
fuelectenerg-1427	1284	53	over	over	ADP
fuelectenerg-1427	1284	54	any	any	DET
fuelectenerg-1427	1284	55	linearly	linearly	ADV
fuelectenerg-1427	1284	56	independent	independent	ADJ
fuelectenerg-1427	1284	57	basis	basis	NOUN
fuelectenerg-1427	1284	58	functions	function	NOUN
fuelectenerg-1427	1284	59	.	.	PUNCT
fuelectenerg-1427	1285	1	analogously	analogously	ADV
fuelectenerg-1427	1285	2	to	to	ADP
fuelectenerg-1427	1285	3	the	the	DET
fuelectenerg-1427	1285	4	binary	binary	ADJ
fuelectenerg-1427	1285	5	case	case	NOUN
fuelectenerg-1427	1285	6	,	,	PUNCT
fuelectenerg-1427	1285	7	figure	figure	VERB
fuelectenerg-1427	1285	8	7	7	NUM
fuelectenerg-1427	1285	9	presents	present	VERB
fuelectenerg-1427	1285	10	universal	universal	ADJ
fuelectenerg-1427	1285	11	logic	logic	NOUN
fuelectenerg-1427	1285	12	modules	module	NOUN
fuelectenerg-1427	1285	13	for	for	ADP
fuelectenerg-1427	1285	14	ternary	ternary	ADJ
fuelectenerg-1427	1285	15	shannon	shannon	NOUN
fuelectenerg-1427	1285	16	and	and	CCONJ
fuelectenerg-1427	1285	17	ternary	ternary	ADJ
fuelectenerg-1427	1285	18	davio	davio	NOUN
fuelectenerg-1427	1285	19	,	,	PUNCT
fuelectenerg-1427	1285	20	respectively	respectively	ADV
fuelectenerg-1427	1285	21	.	.	PUNCT
fuelectenerg-1427	1286	1	one	one	PRON
fuelectenerg-1427	1286	2	can	can	AUX
fuelectenerg-1427	1286	3	note	note	VERB
fuelectenerg-1427	1286	4	,	,	PUNCT
fuelectenerg-1427	1286	5	that	that	SCONJ
fuelectenerg-1427	1286	6	any	any	DET
fuelectenerg-1427	1286	7	function	function	NOUN
fuelectenerg-1427	1286	8	f	f	PROPN
fuelectenerg-1427	1286	9	can	can	AUX
fuelectenerg-1427	1286	10	be	be	AUX
fuelectenerg-1427	1286	11	produced	produce	VERB
fuelectenerg-1427	1286	12	by	by	ADP
fuelectenerg-1427	1286	13	the	the	DET
fuelectenerg-1427	1286	14	application	application	NOUN
fuelectenerg-1427	1286	15	of	of	ADP
fuelectenerg-1427	1286	16	the	the	DET
fuelectenerg-1427	1286	17	independent	independent	ADJ
fuelectenerg-1427	1286	18	variable	variable	NOUN
fuelectenerg-1427	1286	19	x	x	PUNCT
fuelectenerg-1427	1286	20	and	and	CCONJ
fuelectenerg-1427	1286	21	the	the	DET
fuelectenerg-1427	1286	22	cofactors	cofactor	NOUN
fuelectenerg-1427	1286	23	{	{	PUNCT
fuelectenerg-1427	1286	24	fi	fi	NOUN
fuelectenerg-1427	1286	25	,	,	PUNCT
fuelectenerg-1427	1286	26	f	f	PROPN
fuelectenerg-1427	1286	27	j	j	PROPN
fuelectenerg-1427	1286	28	and	and	CCONJ
fuelectenerg-1427	1286	29	fk	fk	INTJ
fuelectenerg-1427	1286	30	}	}	PUNCT
fuelectenerg-1427	1286	31	as	as	ADP
fuelectenerg-1427	1286	32	inputs	input	NOUN
fuelectenerg-1427	1286	33	to	to	ADP
fuelectenerg-1427	1286	34	a	a	DET
fuelectenerg-1427	1286	35	ulm	ulm	NOUN
fuelectenerg-1427	1286	36	.	.	PUNCT
fuelectenerg-1427	1287	1	the	the	DET
fuelectenerg-1427	1287	2	form	form	NOUN
fuelectenerg-1427	1287	3	of	of	ADP
fuelectenerg-1427	1287	4	the	the	DET
fuelectenerg-1427	1287	5	resulting	result	VERB
fuelectenerg-1427	1287	6	function	function	NOUN
fuelectenerg-1427	1287	7	depends	depend	VERB
fuelectenerg-1427	1287	8	on	on	ADP
fuelectenerg-1427	1287	9	our	our	PRON
fuelectenerg-1427	1287	10	choice	choice	NOUN
fuelectenerg-1427	1287	11	of	of	ADP
fuelectenerg-1427	1287	12	the	the	DET
fuelectenerg-1427	1287	13	shift	shift	NOUN
fuelectenerg-1427	1287	14	and	and	CCONJ
fuelectenerg-1427	1287	15	power	power	NOUN
fuelectenerg-1427	1287	16	operations	operation	NOUN
fuelectenerg-1427	1287	17	that	that	PRON
fuelectenerg-1427	1287	18	we	we	PRON
fuelectenerg-1427	1287	19	choose	choose	VERB
fuelectenerg-1427	1287	20	inside	inside	ADP
fuelectenerg-1427	1287	21	the	the	DET
fuelectenerg-1427	1287	22	ulm	ulm	NOUN
fuelectenerg-1427	1287	23	for	for	ADP
fuelectenerg-1427	1287	24	the	the	DET
fuelectenerg-1427	1287	25	input	input	NOUN
fuelectenerg-1427	1287	26	independent	independent	ADJ
fuelectenerg-1427	1287	27	variable	variable	NOUN
fuelectenerg-1427	1287	28	,	,	PUNCT
fuelectenerg-1427	1287	29	and	and	CCONJ
fuelectenerg-1427	1287	30	on	on	ADP
fuelectenerg-1427	1287	31	our	our	PRON
fuelectenerg-1427	1287	32	choice	choice	NOUN
fuelectenerg-1427	1287	33	of	of	ADP
fuelectenerg-1427	1287	34	the	the	DET
fuelectenerg-1427	1287	35	weighted	weight	VERB
fuelectenerg-1427	1287	36	combinations	combination	NOUN
fuelectenerg-1427	1287	37	of	of	ADP
fuelectenerg-1427	1287	38	the	the	DET
fuelectenerg-1427	1287	39	input	input	NOUN
fuelectenerg-1427	1287	40	cofactors	cofactor	NOUN
fuelectenerg-1427	1287	41	.	.	PUNCT
fuelectenerg-1427	1288	1	utilizing	utilize	VERB
fuelectenerg-1427	1288	2	this	this	DET
fuelectenerg-1427	1288	3	note	note	NOUN
fuelectenerg-1427	1288	4	,	,	PUNCT
fuelectenerg-1427	1288	5	we	we	PRON
fuelectenerg-1427	1288	6	can	can	AUX
fuelectenerg-1427	1288	7	combine	combine	VERB
fuelectenerg-1427	1288	8	all	all	DET
fuelectenerg-1427	1288	9	davio	davio	NOUN
fuelectenerg-1427	1288	10	ulms	ulm	NOUN
fuelectenerg-1427	1288	11	to	to	PART
fuelectenerg-1427	1288	12	create	create	VERB
fuelectenerg-1427	1288	13	the	the	DET
fuelectenerg-1427	1288	14	single	single	ADJ
fuelectenerg-1427	1288	15	all	all	ADJ
fuelectenerg-1427	1288	16	-	-	PUNCT
fuelectenerg-1427	1288	17	davio	davio	NOUN
fuelectenerg-1427	1288	18	ulm	ulm	NOUN
fuelectenerg-1427	1288	19	,	,	PUNCT
fuelectenerg-1427	1288	20	where	where	SCONJ
fuelectenerg-1427	1288	21	figure	figure	NOUN
fuelectenerg-1427	1288	22	7(c	7(c	NOUN
fuelectenerg-1427	1288	23	)	)	PUNCT
fuelectenerg-1427	1288	24	illustrates	illustrate	VERB
fuelectenerg-1427	1288	25	this	this	DET
fuelectenerg-1427	1288	26	ulm	ulm	NOUN
fuelectenerg-1427	1288	27	.	.	PUNCT
fuelectenerg-1427	1289	1	also	also	ADV
fuelectenerg-1427	1289	2	,	,	PUNCT
fuelectenerg-1427	1289	3	the	the	DET
fuelectenerg-1427	1289	4	more	more	ADV
fuelectenerg-1427	1289	5	general	general	ADJ
fuelectenerg-1427	1289	6	ulm	ulm	NOUN
fuelectenerg-1427	1289	7	as	as	SCONJ
fuelectenerg-1427	1289	8	shown	show	VERB
fuelectenerg-1427	1289	9	in	in	ADP
fuelectenerg-1427	1289	10	figure	figure	NOUN
fuelectenerg-1427	1289	11	7(d	7(d	NUM
fuelectenerg-1427	1289	12	)	)	PUNCT
fuelectenerg-1427	1289	13	,	,	PUNCT
fuelectenerg-1427	1289	14	can	can	AUX
fuelectenerg-1427	1289	15	be	be	AUX
fuelectenerg-1427	1289	16	generated	generate	VERB
fuelectenerg-1427	1289	17	to	to	PART
fuelectenerg-1427	1289	18	implement	implement	VERB
fuelectenerg-1427	1289	19	all	all	DET
fuelectenerg-1427	1289	20	ternary	ternary	ADJ
fuelectenerg-1427	1289	21	gf(3	gf(3	PROPN
fuelectenerg-1427	1289	22	)	)	PUNCT
fuelectenerg-1427	1289	23	shannon	shannon	NOUN
fuelectenerg-1427	1289	24	and	and	CCONJ
fuelectenerg-1427	1289	25	davio	davio	NOUN
fuelectenerg-1427	1289	26	expansions	expansion	NOUN
fuelectenerg-1427	1289	27	.	.	PUNCT
fuelectenerg-1427	1290	1	in	in	ADP
fuelectenerg-1427	1290	2	general	general	ADJ
fuelectenerg-1427	1290	3	,	,	PUNCT
fuelectenerg-1427	1290	4	the	the	DET
fuelectenerg-1427	1290	5	gates	gate	NOUN
fuelectenerg-1427	1290	6	in	in	ADP
fuelectenerg-1427	1290	7	the	the	DET
fuelectenerg-1427	1290	8	ulms	ulm	NOUN
fuelectenerg-1427	1290	9	can	can	AUX
fuelectenerg-1427	1290	10	be	be	AUX
fuelectenerg-1427	1290	11	implemented	implement	VERB
fuelectenerg-1427	1290	12	,	,	PUNCT
fuelectenerg-1427	1290	13	among	among	ADP
fuelectenerg-1427	1290	14	other	other	ADJ
fuelectenerg-1427	1290	15	circuit	circuit	NOUN
fuelectenerg-1427	1290	16	technologies	technology	NOUN
fuelectenerg-1427	1290	17	,	,	PUNCT
fuelectenerg-1427	1290	18	by	by	ADP
fuelectenerg-1427	1290	19	using	use	VERB
fuelectenerg-1427	1290	20	binary	binary	ADJ
fuelectenerg-1427	1290	21	logic	logic	NOUN
fuelectenerg-1427	1290	22	over	over	ADP
fuelectenerg-1427	1290	23	gf(2	gf(2	PROPN
fuelectenerg-1427	1290	24	)	)	PUNCT
fuelectenerg-1427	1290	25	or	or	CCONJ
fuelectenerg-1427	1290	26	using	use	VERB
fuelectenerg-1427	1290	27	multiple	multiple	ADV
fuelectenerg-1427	1290	28	-	-	PUNCT
fuelectenerg-1427	1290	29	valued	value	VERB
fuelectenerg-1427	1290	30	circuit	circuit	NOUN
fuelectenerg-1427	1290	31	gates	gate	NOUN
fuelectenerg-1427	1290	32	.	.	PUNCT
fuelectenerg-1427	1291	1	each	each	DET
fuelectenerg-1427	1291	2	ternary	ternary	ADJ
fuelectenerg-1427	1291	3	ulm	ulm	PROPN
fuelectenerg-1427	1291	4	corresponds	correspond	VERB
fuelectenerg-1427	1291	5	to	to	ADP
fuelectenerg-1427	1291	6	a	a	DET
fuelectenerg-1427	1291	7	single	single	ADJ
fuelectenerg-1427	1291	8	node	node	NOUN
fuelectenerg-1427	1291	9	in	in	ADP
fuelectenerg-1427	1291	10	the	the	DET
fuelectenerg-1427	1291	11	nodes	node	NOUN
fuelectenerg-1427	1291	12	of	of	ADP
fuelectenerg-1427	1291	13	ternary	ternary	ADJ
fuelectenerg-1427	1291	14	dts	dts	NOUN
fuelectenerg-1427	1291	15	that	that	PRON
fuelectenerg-1427	1291	16	were	be	AUX
fuelectenerg-1427	1291	17	illustrated	illustrate	VERB
fuelectenerg-1427	1291	18	previously	previously	ADV
fuelectenerg-1427	1291	19	.	.	PUNCT
fuelectenerg-1427	1292	1	the	the	DET
fuelectenerg-1427	1292	2	main	main	ADJ
fuelectenerg-1427	1292	3	advantage	advantage	NOUN
fuelectenerg-1427	1292	4	of	of	ADP
fuelectenerg-1427	1292	5	such	such	ADJ
fuelectenerg-1427	1292	6	powerful	powerful	ADJ
fuelectenerg-1427	1292	7	ulms	ulm	NOUN
fuelectenerg-1427	1292	8	is	be	AUX
fuelectenerg-1427	1292	9	in	in	ADP
fuelectenerg-1427	1292	10	high	high	ADJ
fuelectenerg-1427	1292	11	layout	layout	NOUN
fuelectenerg-1427	1292	12	regularity	regularity	NOUN
fuelectenerg-1427	1292	13	that	that	PRON
fuelectenerg-1427	1292	14	is	be	AUX
fuelectenerg-1427	1292	15	required	require	VERB
fuelectenerg-1427	1292	16	by	by	ADP
fuelectenerg-1427	1292	17	future	future	ADJ
fuelectenerg-1427	1292	18	nanotechnologies	nanotechnology	NOUN
fuelectenerg-1427	1292	19	,	,	PUNCT
fuelectenerg-1427	1292	20	where	where	SCONJ
fuelectenerg-1427	1292	21	the	the	DET
fuelectenerg-1427	1292	22	trees	tree	NOUN
fuelectenerg-1427	1292	23	can	can	AUX
fuelectenerg-1427	1292	24	be	be	AUX
fuelectenerg-1427	1292	25	realized	realize	VERB
fuelectenerg-1427	1292	26	in	in	ADP
fuelectenerg-1427	1292	27	efficient	efficient	ADJ
fuelectenerg-1427	1292	28	layout	layout	NOUN
fuelectenerg-1427	1292	29	because	because	SCONJ
fuelectenerg-1427	1292	30	they	they	PRON
fuelectenerg-1427	1292	31	do	do	AUX
fuelectenerg-1427	1292	32	not	not	PART
fuelectenerg-1427	1292	33	grow	grow	VERB
fuelectenerg-1427	1292	34	exponentially	exponentially	ADV
fuelectenerg-1427	1292	35	for	for	ADP
fuelectenerg-1427	1292	36	practical	practical	ADJ
fuelectenerg-1427	1292	37	functions	function	NOUN
fuelectenerg-1427	1292	38	.	.	PUNCT
fuelectenerg-1427	1293	1	for	for	ADP
fuelectenerg-1427	1293	2	instance	instance	NOUN
fuelectenerg-1427	1293	3	,	,	PUNCT
fuelectenerg-1427	1293	4	assuming	assume	VERB
fuelectenerg-1427	1293	5	ulm	ulm	NOUN
fuelectenerg-1427	1293	6	from	from	ADP
fuelectenerg-1427	1293	7	figure	figure	NOUN
fuelectenerg-1427	1293	8	7	7	NUM
fuelectenerg-1427	1293	9	,	,	PUNCT
fuelectenerg-1427	1293	10	although	although	SCONJ
fuelectenerg-1427	1293	11	every	every	DET
fuelectenerg-1427	1293	12	two	two	NUM
fuelectenerg-1427	1293	13	-	-	PUNCT
fuelectenerg-1427	1293	14	variable	variable	NOUN
fuelectenerg-1427	1293	15	function	function	NOUN
fuelectenerg-1427	1293	16	can	can	AUX
fuelectenerg-1427	1293	17	be	be	AUX
fuelectenerg-1427	1293	18	realized	realize	VERB
fuelectenerg-1427	1293	19	with	with	ADP
fuelectenerg-1427	1293	20	four	four	NUM
fuelectenerg-1427	1293	21	such	such	ADJ
fuelectenerg-1427	1293	22	modules	module	NOUN
fuelectenerg-1427	1293	23	,	,	PUNCT
fuelectenerg-1427	1293	24	it	it	PRON
fuelectenerg-1427	1293	25	is	be	AUX
fuelectenerg-1427	1293	26	highly	highly	ADV
fuelectenerg-1427	1293	27	probable	probable	ADJ
fuelectenerg-1427	1293	28	that	that	SCONJ
fuelectenerg-1427	1293	29	most	most	ADJ
fuelectenerg-1427	1293	30	of	of	ADP
fuelectenerg-1427	1293	31	two	two	NUM
fuelectenerg-1427	1293	32	-	-	PUNCT
fuelectenerg-1427	1293	33	variable	variable	NOUN
fuelectenerg-1427	1293	34	functions	function	NOUN
fuelectenerg-1427	1293	35	will	will	AUX
fuelectenerg-1427	1293	36	require	require	VERB
fuelectenerg-1427	1293	37	less	less	ADJ
fuelectenerg-1427	1293	38	than	than	ADP
fuelectenerg-1427	1293	39	four	four	NUM
fuelectenerg-1427	1293	40	modules	module	NOUN
fuelectenerg-1427	1293	41	.	.	PUNCT
fuelectenerg-1427	1294	1	because	because	SCONJ
fuelectenerg-1427	1294	2	of	of	ADP
fuelectenerg-1427	1294	3	these	these	DET
fuelectenerg-1427	1294	4	properties	property	NOUN
fuelectenerg-1427	1294	5	,	,	PUNCT
fuelectenerg-1427	1294	6	this	this	DET
fuelectenerg-1427	1294	7	approach	approach	NOUN
fuelectenerg-1427	1294	8	is	be	AUX
fuelectenerg-1427	1294	9	further	far	ADV
fuelectenerg-1427	1294	10	expected	expect	VERB
fuelectenerg-1427	1294	11	to	to	PART
fuelectenerg-1427	1294	12	give	give	VERB
fuelectenerg-1427	1294	13	good	good	ADJ
fuelectenerg-1427	1294	14	results	result	NOUN
fuelectenerg-1427	1294	15	when	when	SCONJ
fuelectenerg-1427	1294	16	applied	apply	VERB
fuelectenerg-1427	1294	17	to	to	ADP
fuelectenerg-1427	1294	18	the	the	DET
fuelectenerg-1427	1294	19	corresponding	corresponding	ADJ
fuelectenerg-1427	1294	20	incompletely	incompletely	ADV
fuelectenerg-1427	1294	21	specified	specify	VERB
fuelectenerg-1427	1294	22	functions	function	NOUN
fuelectenerg-1427	1294	23	and	and	CCONJ
fuelectenerg-1427	1294	24	multiple	multiple	ADV
fuelectenerg-1427	1294	25	-	-	PUNCT
fuelectenerg-1427	1294	26	valued	value	VERB
fuelectenerg-1427	1294	27	relations	relation	NOUN
fuelectenerg-1427	1294	28	.	.	PUNCT
fuelectenerg-1427	1295	1	4	4	NUM
fuelectenerg-1427	1295	2	conclusions	conclusion	NOUN
fuelectenerg-1427	1295	3	and	and	CCONJ
fuelectenerg-1427	1295	4	future	future	ADJ
fuelectenerg-1427	1295	5	work	work	NOUN
fuelectenerg-1427	1295	6	in	in	ADP
fuelectenerg-1427	1295	7	this	this	DET
fuelectenerg-1427	1295	8	paper	paper	NOUN
fuelectenerg-1427	1295	9	,	,	PUNCT
fuelectenerg-1427	1295	10	an	an	DET
fuelectenerg-1427	1295	11	extended	extended	ADJ
fuelectenerg-1427	1295	12	green	green	ADJ
fuelectenerg-1427	1295	13	-	-	PUNCT
fuelectenerg-1427	1295	14	sasao	sasao	NOUN
fuelectenerg-1427	1295	15	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1295	16	of	of	ADP
fuelectenerg-1427	1295	17	families	family	NOUN
fuelectenerg-1427	1295	18	and	and	CCONJ
fuelectenerg-1427	1295	19	forms	form	NOUN
fuelectenerg-1427	1295	20	is	be	AUX
fuelectenerg-1427	1295	21	introduced	introduce	VERB
fuelectenerg-1427	1295	22	.	.	PUNCT
fuelectenerg-1427	1296	1	analogously	analogously	ADV
fuelectenerg-1427	1296	2	to	to	ADP
fuelectenerg-1427	1296	3	the	the	DET
fuelectenerg-1427	1296	4	binary	binary	ADJ
fuelectenerg-1427	1296	5	case	case	NOUN
fuelectenerg-1427	1296	6	,	,	PUNCT
fuelectenerg-1427	1296	7	two	two	NUM
fuelectenerg-1427	1296	8	general	general	ADJ
fuelectenerg-1427	1296	9	families	family	NOUN
fuelectenerg-1427	1296	10	of	of	ADP
fuelectenerg-1427	1296	11	canonical	canonical	ADJ
fuelectenerg-1427	1296	12	ternary	ternary	ADJ
fuelectenerg-1427	1296	13	reed	reed	NOUN
fuelectenerg-1427	1296	14	-	-	PUNCT
fuelectenerg-1427	1296	15	muller	muller	NOUN
fuelectenerg-1427	1296	16	forms	form	NOUN
fuelectenerg-1427	1296	17	,	,	PUNCT
fuelectenerg-1427	1296	18	called	call	VERB
fuelectenerg-1427	1296	19	ternary	ternary	ADJ
fuelectenerg-1427	1296	20	inclusive	inclusive	ADJ
fuelectenerg-1427	1296	21	forms	form	NOUN
fuelectenerg-1427	1296	22	(	(	PUNCT
fuelectenerg-1427	1296	23	tifs	tifs	PROPN
fuelectenerg-1427	1296	24	)	)	PUNCT
fuelectenerg-1427	1296	25	and	and	CCONJ
fuelectenerg-1427	1296	26	their	their	PRON
fuelectenerg-1427	1296	27	generalization	generalization	NOUN
fuelectenerg-1427	1296	28	of	of	ADP
fuelectenerg-1427	1296	29	ternary	ternary	ADJ
fuelectenerg-1427	1296	30	generalized	generalize	VERB
fuelectenerg-1427	1296	31	inclusive	inclusive	ADJ
fuelectenerg-1427	1296	32	forms	form	NOUN
fuelectenerg-1427	1296	33	(	(	PUNCT
fuelectenerg-1427	1296	34	tgifs	tgif	NOUN
fuelectenerg-1427	1296	35	)	)	PUNCT
fuelectenerg-1427	1296	36	,	,	PUNCT
fuelectenerg-1427	1296	37	are	be	AUX
fuelectenerg-1427	1296	38	presented	present	VERB
fuelectenerg-1427	1296	39	.	.	PUNCT
fuelectenerg-1427	1297	1	the	the	DET
fuelectenerg-1427	1297	2	second	second	ADJ
fuelectenerg-1427	1297	3	family	family	NOUN
fuelectenerg-1427	1297	4	includes	include	VERB
fuelectenerg-1427	1297	5	minimum	minimum	ADJ
fuelectenerg-1427	1297	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1297	7	)	)	PUNCT
fuelectenerg-1427	1297	8	galois	galois	PROPN
fuelectenerg-1427	1297	9	field	field	NOUN
fuelectenerg-1427	1297	10	sum	sum	NOUN
fuelectenerg-1427	1297	11	-	-	PUNCT
fuelectenerg-1427	1297	12	of	of	ADP
fuelectenerg-1427	1297	13	-	-	PUNCT
fuelectenerg-1427	1297	14	products	product	NOUN
fuelectenerg-1427	1297	15	(	(	PUNCT
fuelectenerg-1427	1297	16	gfsops	gfsop	NOUN
fuelectenerg-1427	1297	17	)	)	PUNCT
fuelectenerg-1427	1297	18	.	.	PUNCT
fuelectenerg-1427	1298	1	the	the	DET
fuelectenerg-1427	1298	2	multiple	multiple	ADV
fuelectenerg-1427	1298	3	-	-	PUNCT
fuelectenerg-1427	1298	4	valued	value	VERB
fuelectenerg-1427	1298	5	shannon	shannon	NOUN
fuelectenerg-1427	1298	6	-	-	PUNCT
fuelectenerg-1427	1298	7	davio	davio	NOUN
fuelectenerg-1427	1298	8	(	(	PUNCT
fuelectenerg-1427	1298	9	s	s	NOUN
fuelectenerg-1427	1298	10	/	/	SYM
fuelectenerg-1427	1298	11	d	d	NOUN
fuelectenerg-1427	1298	12	)	)	PUNCT
fuelectenerg-1427	1298	13	trees	tree	NOUN
fuelectenerg-1427	1298	14	developed	develop	VERB
fuelectenerg-1427	1298	15	in	in	ADP
fuelectenerg-1427	1298	16	this	this	DET
fuelectenerg-1427	1298	17	paper	paper	NOUN
fuelectenerg-1427	1298	18	provide	provide	VERB
fuelectenerg-1427	1298	19	more	more	ADJ
fuelectenerg-1427	1298	20	general	general	ADJ
fuelectenerg-1427	1298	21	polarity	polarity	NOUN
fuelectenerg-1427	1298	22	with	with	ADP
fuelectenerg-1427	1298	23	regards	regard	NOUN
fuelectenerg-1427	1298	24	to	to	ADP
fuelectenerg-1427	1298	25	the	the	DET
fuelectenerg-1427	1298	26	114	114	NUM
fuelectenerg-1427	1298	27	an	an	DET
fuelectenerg-1427	1298	28	extended	extended	ADJ
fuelectenerg-1427	1298	29	green	green	ADJ
fuelectenerg-1427	1298	30	sasao	sasao	PROPN
fuelectenerg-1427	1298	31	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1298	32	of	of	ADP
fuelectenerg-1427	1298	33	canonical	canonical	ADJ
fuelectenerg-1427	1298	34	ternary	ternary	ADJ
fuelectenerg-1427	1298	35	galois	galois	NOUN
fuelectenerg-1427	1298	36	forms	form	NOUN
fuelectenerg-1427	1298	37	...	...	PUNCT
fuelectenerg-1427	1298	38	3	3	NUM
fuelectenerg-1427	1298	39	universal	universal	ADJ
fuelectenerg-1427	1298	40	logic	logic	NOUN
fuelectenerg-1427	1298	41	modules	module	NOUN
fuelectenerg-1427	1298	42	for	for	ADP
fuelectenerg-1427	1298	43	the	the	DET
fuelectenerg-1427	1298	44	circuit	circuit	NOUN
fuelectenerg-1427	1298	45	realization	realization	NOUN
fuelectenerg-1427	1298	46	of	of	ADP
fuelectenerg-1427	1298	47	s	s	PROPN
fuelectenerg-1427	1298	48	/	/	SYM
fuelectenerg-1427	1298	49	d	d	NOUN
fuelectenerg-1427	1298	50	trees	tree	NOUN
fuelectenerg-1427	1298	51	the	the	DET
fuelectenerg-1427	1298	52	nonsingular	nonsingular	ADJ
fuelectenerg-1427	1298	53	expansions	expansion	NOUN
fuelectenerg-1427	1298	54	of	of	ADP
fuelectenerg-1427	1298	55	ternary	ternary	ADJ
fuelectenerg-1427	1298	56	shannon	shannon	NOUN
fuelectenerg-1427	1298	57	(	(	PUNCT
fuelectenerg-1427	1298	58	s	s	NOUN
fuelectenerg-1427	1298	59	)	)	PUNCT
fuelectenerg-1427	1298	60	and	and	CCONJ
fuelectenerg-1427	1298	61	ternary	ternary	ADJ
fuelectenerg-1427	1298	62	davio	davio	NOUN
fuelectenerg-1427	1298	63	(	(	PUNCT
fuelectenerg-1427	1298	64	d0	d0	NOUN
fuelectenerg-1427	1298	65	,	,	PUNCT
fuelectenerg-1427	1298	66	d1	d1	PROPN
fuelectenerg-1427	1298	67	and	and	CCONJ
fuelectenerg-1427	1298	68	d2	d2	PROPN
fuelectenerg-1427	1298	69	)	)	PUNCT
fuelectenerg-1427	1298	70	,	,	PUNCT
fuelectenerg-1427	1298	71	can	can	AUX
fuelectenerg-1427	1298	72	be	be	AUX
fuelectenerg-1427	1298	73	realized	realize	VERB
fuelectenerg-1427	1298	74	using	use	VERB
fuelectenerg-1427	1298	75	a	a	DET
fuelectenerg-1427	1298	76	universal	universal	ADJ
fuelectenerg-1427	1298	77	logic	logic	NOUN
fuelectenerg-1427	1298	78	module	module	NOUN
fuelectenerg-1427	1298	79	(	(	PUNCT
fuelectenerg-1427	1298	80	ulm	ulm	PROPN
fuelectenerg-1427	1298	81	)	)	PUNCT
fuelectenerg-1427	1298	82	with	with	ADP
fuelectenerg-1427	1298	83	control	control	NOUN
fuelectenerg-1427	1298	84	variables	variable	NOUN
fuelectenerg-1427	1298	85	corresponding	correspond	VERB
fuelectenerg-1427	1298	86	to	to	ADP
fuelectenerg-1427	1298	87	the	the	DET
fuelectenerg-1427	1298	88	variables	variable	NOUN
fuelectenerg-1427	1298	89	of	of	ADP
fuelectenerg-1427	1298	90	the	the	DET
fuelectenerg-1427	1298	91	basis	basis	NOUN
fuelectenerg-1427	1298	92	functions	function	NOUN
fuelectenerg-1427	1298	93	which	which	PRON
fuelectenerg-1427	1298	94	are	be	AUX
fuelectenerg-1427	1298	95	the	the	DET
fuelectenerg-1427	1298	96	variables	variable	NOUN
fuelectenerg-1427	1298	97	we	we	PRON
fuelectenerg-1427	1298	98	are	be	AUX
fuelectenerg-1427	1298	99	expanding	expand	VERB
fuelectenerg-1427	1298	100	upon	upon	SCONJ
fuelectenerg-1427	1298	101	.	.	PUNCT
fuelectenerg-1427	1299	1	we	we	PRON
fuelectenerg-1427	1299	2	call	call	VERB
fuelectenerg-1427	1299	3	it	it	PRON
fuelectenerg-1427	1299	4	a	a	DET
fuelectenerg-1427	1299	5	universal	universal	ADJ
fuelectenerg-1427	1299	6	logic	logic	NOUN
fuelectenerg-1427	1299	7	module	module	NOUN
fuelectenerg-1427	1299	8	,	,	PUNCT
fuelectenerg-1427	1299	9	because	because	SCONJ
fuelectenerg-1427	1299	10	similarly	similarly	ADV
fuelectenerg-1427	1299	11	to	to	ADP
fuelectenerg-1427	1299	12	a	a	DET
fuelectenerg-1427	1299	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1299	14	,	,	PUNCT
fuelectenerg-1427	1299	15	all	all	DET
fuelectenerg-1427	1299	16	functions	function	NOUN
fuelectenerg-1427	1299	17	of	of	ADP
fuelectenerg-1427	1299	18	two	two	NUM
fuelectenerg-1427	1299	19	variables	variable	NOUN
fuelectenerg-1427	1299	20	can	can	AUX
fuelectenerg-1427	1299	21	be	be	AUX
fuelectenerg-1427	1299	22	realized	realize	VERB
fuelectenerg-1427	1299	23	with	with	ADP
fuelectenerg-1427	1299	24	two	two	NUM
fuelectenerg-1427	1299	25	-	-	PUNCT
fuelectenerg-1427	1299	26	level	level	NOUN
fuelectenerg-1427	1299	27	trees	tree	NOUN
fuelectenerg-1427	1299	28	of	of	ADP
fuelectenerg-1427	1299	29	such	such	ADJ
fuelectenerg-1427	1299	30	modules	module	NOUN
fuelectenerg-1427	1299	31	using	use	VERB
fuelectenerg-1427	1299	32	constants	constant	NOUN
fuelectenerg-1427	1299	33	on	on	ADP
fuelectenerg-1427	1299	34	the	the	DET
fuelectenerg-1427	1299	35	second	second	ADJ
fuelectenerg-1427	1299	36	-	-	PUNCT
fuelectenerg-1427	1299	37	level	level	NOUN
fuelectenerg-1427	1299	38	data	datum	NOUN
fuelectenerg-1427	1299	39	inputs	input	NOUN
fuelectenerg-1427	1299	40	.	.	PUNCT
fuelectenerg-1427	1300	1	the	the	DET
fuelectenerg-1427	1300	2	presented	present	VERB
fuelectenerg-1427	1300	3	ulms	ulm	NOUN
fuelectenerg-1427	1300	4	are	be	AUX
fuelectenerg-1427	1300	5	complete	complete	ADJ
fuelectenerg-1427	1300	6	systems	system	NOUN
fuelectenerg-1427	1300	7	because	because	SCONJ
fuelectenerg-1427	1300	8	they	they	PRON
fuelectenerg-1427	1300	9	can	can	AUX
fuelectenerg-1427	1300	10	implement	implement	VERB
fuelectenerg-1427	1300	11	all	all	DET
fuelectenerg-1427	1300	12	possible	possible	ADJ
fuelectenerg-1427	1300	13	functions	function	NOUN
fuelectenerg-1427	1300	14	with	with	ADP
fuelectenerg-1427	1300	15	certain	certain	ADJ
fuelectenerg-1427	1300	16	number	number	NOUN
fuelectenerg-1427	1300	17	of	of	ADP
fuelectenerg-1427	1300	18	variables	variable	NOUN
fuelectenerg-1427	1300	19	.	.	PUNCT
fuelectenerg-1427	1301	1	the	the	DET
fuelectenerg-1427	1301	2	concept	concept	NOUN
fuelectenerg-1427	1301	3	of	of	ADP
fuelectenerg-1427	1301	4	the	the	DET
fuelectenerg-1427	1301	5	universal	universal	ADJ
fuelectenerg-1427	1301	6	logic	logic	NOUN
fuelectenerg-1427	1301	7	module	module	NOUN
fuelectenerg-1427	1301	8	was	be	AUX
fuelectenerg-1427	1301	9	used	use	VERB
fuelectenerg-1427	1301	10	for	for	ADP
fuelectenerg-1427	1301	11	binary	binary	PROPN
fuelectenerg-1427	1301	12	rm	rm	PROPN
fuelectenerg-1427	1301	13	logic	logic	PROPN
fuelectenerg-1427	1301	14	over	over	ADP
fuelectenerg-1427	1301	15	gf(2	gf(2	PROPN
fuelectenerg-1427	1301	16	)	)	PUNCT
fuelectenerg-1427	1301	17	,	,	PUNCT
fuelectenerg-1427	1301	18	as	as	ADV
fuelectenerg-1427	1301	19	well	well	ADV
fuelectenerg-1427	1301	20	as	as	ADP
fuelectenerg-1427	1301	21	the	the	DET
fuelectenerg-1427	1301	22	general	general	ADJ
fuelectenerg-1427	1301	23	case	case	NOUN
fuelectenerg-1427	1301	24	of	of	ADP
fuelectenerg-1427	1301	25	linearly	linearly	ADV
fuelectenerg-1427	1301	26	independent	independent	ADJ
fuelectenerg-1427	1301	27	(	(	PUNCT
fuelectenerg-1427	1301	28	li	li	NOUN
fuelectenerg-1427	1301	29	)	)	PUNCT
fuelectenerg-1427	1301	30	logic	logic	NOUN
fuelectenerg-1427	1301	31	that	that	PRON
fuelectenerg-1427	1301	32	includes	include	VERB
fuelectenerg-1427	1301	33	rm	rm	NOUN
fuelectenerg-1427	1301	34	logic	logic	NOUN
fuelectenerg-1427	1301	35	as	as	ADP
fuelectenerg-1427	1301	36	a	a	DET
fuelectenerg-1427	1301	37	special	special	ADJ
fuelectenerg-1427	1301	38	case	case	NOUN
fuelectenerg-1427	1301	39	.	.	PUNCT
fuelectenerg-1427	1302	1	binary	binary	PROPN
fuelectenerg-1427	1302	2	li	li	PROPN
fuelectenerg-1427	1302	3	logic	logic	PROPN
fuelectenerg-1427	1302	4	extended	extend	VERB
fuelectenerg-1427	1302	5	the	the	DET
fuelectenerg-1427	1302	6	universal	universal	ADJ
fuelectenerg-1427	1302	7	logic	logic	NOUN
fuelectenerg-1427	1302	8	module	module	NOUN
fuelectenerg-1427	1302	9	from	from	ADP
fuelectenerg-1427	1302	10	just	just	ADV
fuelectenerg-1427	1302	11	being	be	AUX
fuelectenerg-1427	1302	12	a	a	DET
fuelectenerg-1427	1302	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1302	14	(	(	PUNCT
fuelectenerg-1427	1302	15	shannon	shannon	PROPN
fuelectenerg-1427	1302	16	expansion	expansion	PROPN
fuelectenerg-1427	1302	17	)	)	PUNCT
fuelectenerg-1427	1302	18	,	,	PUNCT
fuelectenerg-1427	1302	19	and	and	CCONJ
fuelectenerg-1427	1302	20	/	/	SYM
fuelectenerg-1427	1302	21	exor	exor	PROPN
fuelectenerg-1427	1302	22	gate	gate	PROPN
fuelectenerg-1427	1302	23	(	(	PUNCT
fuelectenerg-1427	1302	24	positive	positive	ADJ
fuelectenerg-1427	1302	25	davio	davio	NOUN
fuelectenerg-1427	1302	26	expansion	expansion	NOUN
fuelectenerg-1427	1302	27	)	)	PUNCT
fuelectenerg-1427	1302	28	and	and	CCONJ
fuelectenerg-1427	1302	29	and	and	CCONJ
fuelectenerg-1427	1302	30	/	/	SYM
fuelectenerg-1427	1302	31	exor	exor	PROPN
fuelectenerg-1427	1302	32	/	/	SYM
fuelectenerg-1427	1302	33	not	not	PART
fuelectenerg-1427	1302	34	gate	gate	VERB
fuelectenerg-1427	1302	35	with	with	ADP
fuelectenerg-1427	1302	36	inverted	inverted	ADJ
fuelectenerg-1427	1302	37	control	control	NOUN
fuelectenerg-1427	1302	38	variable	variable	NOUN
fuelectenerg-1427	1302	39	(	(	PUNCT
fuelectenerg-1427	1302	40	negative	negative	ADJ
fuelectenerg-1427	1302	41	davio	davio	NOUN
fuelectenerg-1427	1302	42	expansion	expansion	NOUN
fuelectenerg-1427	1302	43	)	)	PUNCT
fuelectenerg-1427	1302	44	,	,	PUNCT
fuelectenerg-1427	1302	45	to	to	ADP
fuelectenerg-1427	1302	46	the	the	DET
fuelectenerg-1427	1302	47	universal	universal	ADJ
fuelectenerg-1427	1302	48	logic	logic	NOUN
fuelectenerg-1427	1302	49	modules	module	NOUN
fuelectenerg-1427	1302	50	for	for	ADP
fuelectenerg-1427	1302	51	any	any	DET
fuelectenerg-1427	1302	52	expansion	expansion	NOUN
fuelectenerg-1427	1302	53	over	over	ADP
fuelectenerg-1427	1302	54	any	any	DET
fuelectenerg-1427	1302	55	linearly	linearly	ADV
fuelectenerg-1427	1302	56	independent	independent	ADJ
fuelectenerg-1427	1302	57	basis	basis	NOUN
fuelectenerg-1427	1302	58	functions	function	NOUN
fuelectenerg-1427	1302	59	.	.	PUNCT
fuelectenerg-1427	1303	1	analogously	analogously	ADV
fuelectenerg-1427	1303	2	to	to	ADP
fuelectenerg-1427	1303	3	the	the	DET
fuelectenerg-1427	1303	4	binary	binary	ADJ
fuelectenerg-1427	1303	5	case	case	NOUN
fuelectenerg-1427	1303	6	,	,	PUNCT
fuelectenerg-1427	1303	7	figure	figure	VERB
fuelectenerg-1427	1303	8	7	7	NUM
fuelectenerg-1427	1303	9	presents	present	VERB
fuelectenerg-1427	1303	10	universal	universal	ADJ
fuelectenerg-1427	1303	11	logic	logic	NOUN
fuelectenerg-1427	1303	12	modules	module	NOUN
fuelectenerg-1427	1303	13	for	for	ADP
fuelectenerg-1427	1303	14	ternary	ternary	ADJ
fuelectenerg-1427	1303	15	shannon	shannon	NOUN
fuelectenerg-1427	1303	16	and	and	CCONJ
fuelectenerg-1427	1303	17	ternary	ternary	ADJ
fuelectenerg-1427	1303	18	davio	davio	NOUN
fuelectenerg-1427	1303	19	,	,	PUNCT
fuelectenerg-1427	1303	20	respectively	respectively	ADV
fuelectenerg-1427	1303	21	.	.	PUNCT
fuelectenerg-1427	1304	1	one	one	PRON
fuelectenerg-1427	1304	2	can	can	AUX
fuelectenerg-1427	1304	3	note	note	VERB
fuelectenerg-1427	1304	4	,	,	PUNCT
fuelectenerg-1427	1304	5	that	that	SCONJ
fuelectenerg-1427	1304	6	any	any	DET
fuelectenerg-1427	1304	7	function	function	NOUN
fuelectenerg-1427	1304	8	f	f	PROPN
fuelectenerg-1427	1304	9	can	can	AUX
fuelectenerg-1427	1304	10	be	be	AUX
fuelectenerg-1427	1304	11	produced	produce	VERB
fuelectenerg-1427	1304	12	by	by	ADP
fuelectenerg-1427	1304	13	the	the	DET
fuelectenerg-1427	1304	14	application	application	NOUN
fuelectenerg-1427	1304	15	of	of	ADP
fuelectenerg-1427	1304	16	the	the	DET
fuelectenerg-1427	1304	17	independent	independent	ADJ
fuelectenerg-1427	1304	18	variable	variable	NOUN
fuelectenerg-1427	1304	19	x	x	PUNCT
fuelectenerg-1427	1304	20	and	and	CCONJ
fuelectenerg-1427	1304	21	the	the	DET
fuelectenerg-1427	1304	22	cofactors	cofactor	NOUN
fuelectenerg-1427	1304	23	{	{	PUNCT
fuelectenerg-1427	1304	24	fi	fi	NOUN
fuelectenerg-1427	1304	25	,	,	PUNCT
fuelectenerg-1427	1304	26	f	f	PROPN
fuelectenerg-1427	1304	27	j	j	PROPN
fuelectenerg-1427	1304	28	and	and	CCONJ
fuelectenerg-1427	1304	29	fk	fk	INTJ
fuelectenerg-1427	1304	30	}	}	PUNCT
fuelectenerg-1427	1304	31	as	as	ADP
fuelectenerg-1427	1304	32	inputs	input	NOUN
fuelectenerg-1427	1304	33	to	to	ADP
fuelectenerg-1427	1304	34	a	a	DET
fuelectenerg-1427	1304	35	ulm	ulm	NOUN
fuelectenerg-1427	1304	36	.	.	PUNCT
fuelectenerg-1427	1305	1	the	the	DET
fuelectenerg-1427	1305	2	form	form	NOUN
fuelectenerg-1427	1305	3	of	of	ADP
fuelectenerg-1427	1305	4	the	the	DET
fuelectenerg-1427	1305	5	resulting	result	VERB
fuelectenerg-1427	1305	6	function	function	NOUN
fuelectenerg-1427	1305	7	depends	depend	VERB
fuelectenerg-1427	1305	8	on	on	ADP
fuelectenerg-1427	1305	9	our	our	PRON
fuelectenerg-1427	1305	10	choice	choice	NOUN
fuelectenerg-1427	1305	11	of	of	ADP
fuelectenerg-1427	1305	12	the	the	DET
fuelectenerg-1427	1305	13	shift	shift	NOUN
fuelectenerg-1427	1305	14	and	and	CCONJ
fuelectenerg-1427	1305	15	power	power	NOUN
fuelectenerg-1427	1305	16	operations	operation	NOUN
fuelectenerg-1427	1305	17	that	that	PRON
fuelectenerg-1427	1305	18	we	we	PRON
fuelectenerg-1427	1305	19	choose	choose	VERB
fuelectenerg-1427	1305	20	inside	inside	ADP
fuelectenerg-1427	1305	21	the	the	DET
fuelectenerg-1427	1305	22	ulm	ulm	NOUN
fuelectenerg-1427	1305	23	for	for	ADP
fuelectenerg-1427	1305	24	the	the	DET
fuelectenerg-1427	1305	25	input	input	NOUN
fuelectenerg-1427	1305	26	independent	independent	ADJ
fuelectenerg-1427	1305	27	variable	variable	NOUN
fuelectenerg-1427	1305	28	,	,	PUNCT
fuelectenerg-1427	1305	29	and	and	CCONJ
fuelectenerg-1427	1305	30	on	on	ADP
fuelectenerg-1427	1305	31	our	our	PRON
fuelectenerg-1427	1305	32	choice	choice	NOUN
fuelectenerg-1427	1305	33	of	of	ADP
fuelectenerg-1427	1305	34	the	the	DET
fuelectenerg-1427	1305	35	weighted	weight	VERB
fuelectenerg-1427	1305	36	combinations	combination	NOUN
fuelectenerg-1427	1305	37	of	of	ADP
fuelectenerg-1427	1305	38	the	the	DET
fuelectenerg-1427	1305	39	input	input	NOUN
fuelectenerg-1427	1305	40	cofactors	cofactor	NOUN
fuelectenerg-1427	1305	41	.	.	PUNCT
fuelectenerg-1427	1306	1	utilizing	utilize	VERB
fuelectenerg-1427	1306	2	this	this	DET
fuelectenerg-1427	1306	3	note	note	NOUN
fuelectenerg-1427	1306	4	,	,	PUNCT
fuelectenerg-1427	1306	5	we	we	PRON
fuelectenerg-1427	1306	6	can	can	AUX
fuelectenerg-1427	1306	7	combine	combine	VERB
fuelectenerg-1427	1306	8	all	all	DET
fuelectenerg-1427	1306	9	davio	davio	NOUN
fuelectenerg-1427	1306	10	ulms	ulm	NOUN
fuelectenerg-1427	1306	11	to	to	PART
fuelectenerg-1427	1306	12	create	create	VERB
fuelectenerg-1427	1306	13	the	the	DET
fuelectenerg-1427	1306	14	single	single	ADJ
fuelectenerg-1427	1306	15	all	all	ADJ
fuelectenerg-1427	1306	16	-	-	PUNCT
fuelectenerg-1427	1306	17	davio	davio	NOUN
fuelectenerg-1427	1306	18	ulm	ulm	NOUN
fuelectenerg-1427	1306	19	,	,	PUNCT
fuelectenerg-1427	1306	20	where	where	SCONJ
fuelectenerg-1427	1306	21	figure	figure	NOUN
fuelectenerg-1427	1306	22	7(c	7(c	NOUN
fuelectenerg-1427	1306	23	)	)	PUNCT
fuelectenerg-1427	1306	24	illustrates	illustrate	VERB
fuelectenerg-1427	1306	25	this	this	DET
fuelectenerg-1427	1306	26	ulm	ulm	NOUN
fuelectenerg-1427	1306	27	.	.	PUNCT
fuelectenerg-1427	1307	1	also	also	ADV
fuelectenerg-1427	1307	2	,	,	PUNCT
fuelectenerg-1427	1307	3	the	the	DET
fuelectenerg-1427	1307	4	more	more	ADV
fuelectenerg-1427	1307	5	general	general	ADJ
fuelectenerg-1427	1307	6	ulm	ulm	NOUN
fuelectenerg-1427	1307	7	as	as	SCONJ
fuelectenerg-1427	1307	8	shown	show	VERB
fuelectenerg-1427	1307	9	in	in	ADP
fuelectenerg-1427	1307	10	figure	figure	NOUN
fuelectenerg-1427	1307	11	7(d	7(d	NUM
fuelectenerg-1427	1307	12	)	)	PUNCT
fuelectenerg-1427	1307	13	,	,	PUNCT
fuelectenerg-1427	1307	14	can	can	AUX
fuelectenerg-1427	1307	15	be	be	AUX
fuelectenerg-1427	1307	16	generated	generate	VERB
fuelectenerg-1427	1307	17	to	to	PART
fuelectenerg-1427	1307	18	implement	implement	VERB
fuelectenerg-1427	1307	19	all	all	DET
fuelectenerg-1427	1307	20	ternary	ternary	ADJ
fuelectenerg-1427	1307	21	gf(3	gf(3	PROPN
fuelectenerg-1427	1307	22	)	)	PUNCT
fuelectenerg-1427	1307	23	shannon	shannon	NOUN
fuelectenerg-1427	1307	24	and	and	CCONJ
fuelectenerg-1427	1307	25	davio	davio	NOUN
fuelectenerg-1427	1307	26	expansions	expansion	NOUN
fuelectenerg-1427	1307	27	.	.	PUNCT
fuelectenerg-1427	1308	1	in	in	ADP
fuelectenerg-1427	1308	2	general	general	ADJ
fuelectenerg-1427	1308	3	,	,	PUNCT
fuelectenerg-1427	1308	4	the	the	DET
fuelectenerg-1427	1308	5	gates	gate	NOUN
fuelectenerg-1427	1308	6	in	in	ADP
fuelectenerg-1427	1308	7	the	the	DET
fuelectenerg-1427	1308	8	ulms	ulm	NOUN
fuelectenerg-1427	1308	9	can	can	AUX
fuelectenerg-1427	1308	10	be	be	AUX
fuelectenerg-1427	1308	11	implemented	implement	VERB
fuelectenerg-1427	1308	12	,	,	PUNCT
fuelectenerg-1427	1308	13	among	among	ADP
fuelectenerg-1427	1308	14	other	other	ADJ
fuelectenerg-1427	1308	15	circuit	circuit	NOUN
fuelectenerg-1427	1308	16	technologies	technology	NOUN
fuelectenerg-1427	1308	17	,	,	PUNCT
fuelectenerg-1427	1308	18	by	by	ADP
fuelectenerg-1427	1308	19	using	use	VERB
fuelectenerg-1427	1308	20	binary	binary	ADJ
fuelectenerg-1427	1308	21	logic	logic	NOUN
fuelectenerg-1427	1308	22	over	over	ADP
fuelectenerg-1427	1308	23	gf(2	gf(2	PROPN
fuelectenerg-1427	1308	24	)	)	PUNCT
fuelectenerg-1427	1308	25	or	or	CCONJ
fuelectenerg-1427	1308	26	using	use	VERB
fuelectenerg-1427	1308	27	multiple	multiple	ADV
fuelectenerg-1427	1308	28	-	-	PUNCT
fuelectenerg-1427	1308	29	valued	value	VERB
fuelectenerg-1427	1308	30	circuit	circuit	NOUN
fuelectenerg-1427	1308	31	gates	gate	NOUN
fuelectenerg-1427	1308	32	.	.	PUNCT
fuelectenerg-1427	1309	1	each	each	DET
fuelectenerg-1427	1309	2	ternary	ternary	ADJ
fuelectenerg-1427	1309	3	ulm	ulm	PROPN
fuelectenerg-1427	1309	4	corresponds	correspond	VERB
fuelectenerg-1427	1309	5	to	to	ADP
fuelectenerg-1427	1309	6	a	a	DET
fuelectenerg-1427	1309	7	single	single	ADJ
fuelectenerg-1427	1309	8	node	node	NOUN
fuelectenerg-1427	1309	9	in	in	ADP
fuelectenerg-1427	1309	10	the	the	DET
fuelectenerg-1427	1309	11	nodes	node	NOUN
fuelectenerg-1427	1309	12	of	of	ADP
fuelectenerg-1427	1309	13	ternary	ternary	ADJ
fuelectenerg-1427	1309	14	dts	dts	NOUN
fuelectenerg-1427	1309	15	that	that	PRON
fuelectenerg-1427	1309	16	were	be	AUX
fuelectenerg-1427	1309	17	illustrated	illustrate	VERB
fuelectenerg-1427	1309	18	previously	previously	ADV
fuelectenerg-1427	1309	19	.	.	PUNCT
fuelectenerg-1427	1310	1	the	the	DET
fuelectenerg-1427	1310	2	main	main	ADJ
fuelectenerg-1427	1310	3	advantage	advantage	NOUN
fuelectenerg-1427	1310	4	of	of	ADP
fuelectenerg-1427	1310	5	such	such	ADJ
fuelectenerg-1427	1310	6	powerful	powerful	ADJ
fuelectenerg-1427	1310	7	ulms	ulm	NOUN
fuelectenerg-1427	1310	8	is	be	AUX
fuelectenerg-1427	1310	9	in	in	ADP
fuelectenerg-1427	1310	10	high	high	ADJ
fuelectenerg-1427	1310	11	layout	layout	NOUN
fuelectenerg-1427	1310	12	regularity	regularity	NOUN
fuelectenerg-1427	1310	13	that	that	PRON
fuelectenerg-1427	1310	14	is	be	AUX
fuelectenerg-1427	1310	15	required	require	VERB
fuelectenerg-1427	1310	16	by	by	ADP
fuelectenerg-1427	1310	17	future	future	ADJ
fuelectenerg-1427	1310	18	nanotechnologies	nanotechnology	NOUN
fuelectenerg-1427	1310	19	,	,	PUNCT
fuelectenerg-1427	1310	20	where	where	SCONJ
fuelectenerg-1427	1310	21	the	the	DET
fuelectenerg-1427	1310	22	trees	tree	NOUN
fuelectenerg-1427	1310	23	can	can	AUX
fuelectenerg-1427	1310	24	be	be	AUX
fuelectenerg-1427	1310	25	realized	realize	VERB
fuelectenerg-1427	1310	26	in	in	ADP
fuelectenerg-1427	1310	27	efficient	efficient	ADJ
fuelectenerg-1427	1310	28	layout	layout	NOUN
fuelectenerg-1427	1310	29	because	because	SCONJ
fuelectenerg-1427	1310	30	they	they	PRON
fuelectenerg-1427	1310	31	do	do	AUX
fuelectenerg-1427	1310	32	not	not	PART
fuelectenerg-1427	1310	33	grow	grow	VERB
fuelectenerg-1427	1310	34	exponentially	exponentially	ADV
fuelectenerg-1427	1310	35	for	for	ADP
fuelectenerg-1427	1310	36	practical	practical	ADJ
fuelectenerg-1427	1310	37	functions	function	NOUN
fuelectenerg-1427	1310	38	.	.	PUNCT
fuelectenerg-1427	1311	1	for	for	ADP
fuelectenerg-1427	1311	2	instance	instance	NOUN
fuelectenerg-1427	1311	3	,	,	PUNCT
fuelectenerg-1427	1311	4	assuming	assume	VERB
fuelectenerg-1427	1311	5	ulm	ulm	NOUN
fuelectenerg-1427	1311	6	from	from	ADP
fuelectenerg-1427	1311	7	figure	figure	NOUN
fuelectenerg-1427	1311	8	7	7	NUM
fuelectenerg-1427	1311	9	,	,	PUNCT
fuelectenerg-1427	1311	10	although	although	SCONJ
fuelectenerg-1427	1311	11	every	every	DET
fuelectenerg-1427	1311	12	two	two	NUM
fuelectenerg-1427	1311	13	-	-	PUNCT
fuelectenerg-1427	1311	14	variable	variable	NOUN
fuelectenerg-1427	1311	15	function	function	NOUN
fuelectenerg-1427	1311	16	can	can	AUX
fuelectenerg-1427	1311	17	be	be	AUX
fuelectenerg-1427	1311	18	realized	realize	VERB
fuelectenerg-1427	1311	19	with	with	ADP
fuelectenerg-1427	1311	20	four	four	NUM
fuelectenerg-1427	1311	21	such	such	ADJ
fuelectenerg-1427	1311	22	modules	module	NOUN
fuelectenerg-1427	1311	23	,	,	PUNCT
fuelectenerg-1427	1311	24	it	it	PRON
fuelectenerg-1427	1311	25	is	be	AUX
fuelectenerg-1427	1311	26	highly	highly	ADV
fuelectenerg-1427	1311	27	probable	probable	ADJ
fuelectenerg-1427	1311	28	that	that	SCONJ
fuelectenerg-1427	1311	29	most	most	ADJ
fuelectenerg-1427	1311	30	of	of	ADP
fuelectenerg-1427	1311	31	two	two	NUM
fuelectenerg-1427	1311	32	-	-	PUNCT
fuelectenerg-1427	1311	33	variable	variable	NOUN
fuelectenerg-1427	1311	34	functions	function	NOUN
fuelectenerg-1427	1311	35	will	will	AUX
fuelectenerg-1427	1311	36	require	require	VERB
fuelectenerg-1427	1311	37	less	less	ADJ
fuelectenerg-1427	1311	38	than	than	ADP
fuelectenerg-1427	1311	39	four	four	NUM
fuelectenerg-1427	1311	40	modules	module	NOUN
fuelectenerg-1427	1311	41	.	.	PUNCT
fuelectenerg-1427	1312	1	because	because	SCONJ
fuelectenerg-1427	1312	2	of	of	ADP
fuelectenerg-1427	1312	3	these	these	DET
fuelectenerg-1427	1312	4	properties	property	NOUN
fuelectenerg-1427	1312	5	,	,	PUNCT
fuelectenerg-1427	1312	6	this	this	DET
fuelectenerg-1427	1312	7	approach	approach	NOUN
fuelectenerg-1427	1312	8	is	be	AUX
fuelectenerg-1427	1312	9	further	far	ADV
fuelectenerg-1427	1312	10	expected	expect	VERB
fuelectenerg-1427	1312	11	to	to	PART
fuelectenerg-1427	1312	12	give	give	VERB
fuelectenerg-1427	1312	13	good	good	ADJ
fuelectenerg-1427	1312	14	results	result	NOUN
fuelectenerg-1427	1312	15	when	when	SCONJ
fuelectenerg-1427	1312	16	applied	apply	VERB
fuelectenerg-1427	1312	17	to	to	ADP
fuelectenerg-1427	1312	18	the	the	DET
fuelectenerg-1427	1312	19	corresponding	corresponding	ADJ
fuelectenerg-1427	1312	20	incompletely	incompletely	ADV
fuelectenerg-1427	1312	21	specified	specify	VERB
fuelectenerg-1427	1312	22	functions	function	NOUN
fuelectenerg-1427	1312	23	and	and	CCONJ
fuelectenerg-1427	1312	24	multiple	multiple	ADV
fuelectenerg-1427	1312	25	-	-	PUNCT
fuelectenerg-1427	1312	26	valued	value	VERB
fuelectenerg-1427	1312	27	relations	relation	NOUN
fuelectenerg-1427	1312	28	.	.	PUNCT
fuelectenerg-1427	1313	1	4	4	NUM
fuelectenerg-1427	1313	2	conclusions	conclusion	NOUN
fuelectenerg-1427	1313	3	and	and	CCONJ
fuelectenerg-1427	1313	4	future	future	ADJ
fuelectenerg-1427	1313	5	work	work	NOUN
fuelectenerg-1427	1313	6	in	in	ADP
fuelectenerg-1427	1313	7	this	this	DET
fuelectenerg-1427	1313	8	paper	paper	NOUN
fuelectenerg-1427	1313	9	,	,	PUNCT
fuelectenerg-1427	1313	10	an	an	DET
fuelectenerg-1427	1313	11	extended	extended	ADJ
fuelectenerg-1427	1313	12	green	green	ADJ
fuelectenerg-1427	1313	13	-	-	PUNCT
fuelectenerg-1427	1313	14	sasao	sasao	NOUN
fuelectenerg-1427	1313	15	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1313	16	of	of	ADP
fuelectenerg-1427	1313	17	families	family	NOUN
fuelectenerg-1427	1313	18	and	and	CCONJ
fuelectenerg-1427	1313	19	forms	form	NOUN
fuelectenerg-1427	1313	20	is	be	AUX
fuelectenerg-1427	1313	21	introduced	introduce	VERB
fuelectenerg-1427	1313	22	.	.	PUNCT
fuelectenerg-1427	1314	1	analogously	analogously	ADV
fuelectenerg-1427	1314	2	to	to	ADP
fuelectenerg-1427	1314	3	the	the	DET
fuelectenerg-1427	1314	4	binary	binary	ADJ
fuelectenerg-1427	1314	5	case	case	NOUN
fuelectenerg-1427	1314	6	,	,	PUNCT
fuelectenerg-1427	1314	7	two	two	NUM
fuelectenerg-1427	1314	8	general	general	ADJ
fuelectenerg-1427	1314	9	families	family	NOUN
fuelectenerg-1427	1314	10	of	of	ADP
fuelectenerg-1427	1314	11	canonical	canonical	ADJ
fuelectenerg-1427	1314	12	ternary	ternary	ADJ
fuelectenerg-1427	1314	13	reed	reed	NOUN
fuelectenerg-1427	1314	14	-	-	PUNCT
fuelectenerg-1427	1314	15	muller	muller	NOUN
fuelectenerg-1427	1314	16	forms	form	NOUN
fuelectenerg-1427	1314	17	,	,	PUNCT
fuelectenerg-1427	1314	18	called	call	VERB
fuelectenerg-1427	1314	19	ternary	ternary	ADJ
fuelectenerg-1427	1314	20	inclusive	inclusive	ADJ
fuelectenerg-1427	1314	21	forms	form	NOUN
fuelectenerg-1427	1314	22	(	(	PUNCT
fuelectenerg-1427	1314	23	tifs	tifs	PROPN
fuelectenerg-1427	1314	24	)	)	PUNCT
fuelectenerg-1427	1314	25	and	and	CCONJ
fuelectenerg-1427	1314	26	their	their	PRON
fuelectenerg-1427	1314	27	generalization	generalization	NOUN
fuelectenerg-1427	1314	28	of	of	ADP
fuelectenerg-1427	1314	29	ternary	ternary	ADJ
fuelectenerg-1427	1314	30	generalized	generalize	VERB
fuelectenerg-1427	1314	31	inclusive	inclusive	ADJ
fuelectenerg-1427	1314	32	forms	form	NOUN
fuelectenerg-1427	1314	33	(	(	PUNCT
fuelectenerg-1427	1314	34	tgifs	tgif	NOUN
fuelectenerg-1427	1314	35	)	)	PUNCT
fuelectenerg-1427	1314	36	,	,	PUNCT
fuelectenerg-1427	1314	37	are	be	AUX
fuelectenerg-1427	1314	38	presented	present	VERB
fuelectenerg-1427	1314	39	.	.	PUNCT
fuelectenerg-1427	1315	1	the	the	DET
fuelectenerg-1427	1315	2	second	second	ADJ
fuelectenerg-1427	1315	3	family	family	NOUN
fuelectenerg-1427	1315	4	includes	include	VERB
fuelectenerg-1427	1315	5	minimum	minimum	ADJ
fuelectenerg-1427	1315	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1315	7	)	)	PUNCT
fuelectenerg-1427	1315	8	galois	galois	PROPN
fuelectenerg-1427	1315	9	field	field	NOUN
fuelectenerg-1427	1315	10	sum	sum	NOUN
fuelectenerg-1427	1315	11	-	-	PUNCT
fuelectenerg-1427	1315	12	of	of	ADP
fuelectenerg-1427	1315	13	-	-	PUNCT
fuelectenerg-1427	1315	14	products	product	NOUN
fuelectenerg-1427	1315	15	(	(	PUNCT
fuelectenerg-1427	1315	16	gfsops	gfsop	NOUN
fuelectenerg-1427	1315	17	)	)	PUNCT
fuelectenerg-1427	1315	18	.	.	PUNCT
fuelectenerg-1427	1316	1	the	the	DET
fuelectenerg-1427	1316	2	multiple	multiple	ADV
fuelectenerg-1427	1316	3	-	-	PUNCT
fuelectenerg-1427	1316	4	valued	value	VERB
fuelectenerg-1427	1316	5	shannon	shannon	NOUN
fuelectenerg-1427	1316	6	-	-	PUNCT
fuelectenerg-1427	1316	7	davio	davio	NOUN
fuelectenerg-1427	1316	8	(	(	PUNCT
fuelectenerg-1427	1316	9	s	s	NOUN
fuelectenerg-1427	1316	10	/	/	SYM
fuelectenerg-1427	1316	11	d	d	NOUN
fuelectenerg-1427	1316	12	)	)	PUNCT
fuelectenerg-1427	1316	13	trees	tree	NOUN
fuelectenerg-1427	1316	14	developed	develop	VERB
fuelectenerg-1427	1316	15	in	in	ADP
fuelectenerg-1427	1316	16	this	this	DET
fuelectenerg-1427	1316	17	paper	paper	NOUN
fuelectenerg-1427	1316	18	provide	provide	VERB
fuelectenerg-1427	1316	19	more	more	ADJ
fuelectenerg-1427	1316	20	general	general	ADJ
fuelectenerg-1427	1316	21	polarity	polarity	NOUN
fuelectenerg-1427	1316	22	with	with	ADP
fuelectenerg-1427	1316	23	regards	regard	NOUN
fuelectenerg-1427	1316	24	to	to	ADP
fuelectenerg-1427	1316	25	the	the	DET
fuelectenerg-1427	1316	26	114	114	NUM
fuelectenerg-1427	1316	27	an	an	DET
fuelectenerg-1427	1316	28	extended	extended	ADJ
fuelectenerg-1427	1316	29	green	green	ADJ
fuelectenerg-1427	1316	30	sasao	sasao	PROPN
fuelectenerg-1427	1316	31	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1316	32	of	of	ADP
fuelectenerg-1427	1316	33	canonical	canonical	ADJ
fuelectenerg-1427	1316	34	ternary	ternary	ADJ
fuelectenerg-1427	1316	35	galois	galois	NOUN
fuelectenerg-1427	1316	36	forms	form	NOUN
fuelectenerg-1427	1316	37	...	...	PUNCT
fuelectenerg-1427	1316	38	3	3	NUM
fuelectenerg-1427	1316	39	universal	universal	ADJ
fuelectenerg-1427	1316	40	logic	logic	NOUN
fuelectenerg-1427	1316	41	modules	module	NOUN
fuelectenerg-1427	1316	42	for	for	ADP
fuelectenerg-1427	1316	43	the	the	DET
fuelectenerg-1427	1316	44	circuit	circuit	NOUN
fuelectenerg-1427	1316	45	realization	realization	NOUN
fuelectenerg-1427	1316	46	of	of	ADP
fuelectenerg-1427	1316	47	s	s	PROPN
fuelectenerg-1427	1316	48	/	/	SYM
fuelectenerg-1427	1316	49	d	d	NOUN
fuelectenerg-1427	1316	50	trees	tree	NOUN
fuelectenerg-1427	1316	51	the	the	DET
fuelectenerg-1427	1316	52	nonsingular	nonsingular	ADJ
fuelectenerg-1427	1316	53	expansions	expansion	NOUN
fuelectenerg-1427	1316	54	of	of	ADP
fuelectenerg-1427	1316	55	ternary	ternary	ADJ
fuelectenerg-1427	1316	56	shannon	shannon	NOUN
fuelectenerg-1427	1316	57	(	(	PUNCT
fuelectenerg-1427	1316	58	s	s	NOUN
fuelectenerg-1427	1316	59	)	)	PUNCT
fuelectenerg-1427	1316	60	and	and	CCONJ
fuelectenerg-1427	1316	61	ternary	ternary	ADJ
fuelectenerg-1427	1316	62	davio	davio	NOUN
fuelectenerg-1427	1316	63	(	(	PUNCT
fuelectenerg-1427	1316	64	d0	d0	NOUN
fuelectenerg-1427	1316	65	,	,	PUNCT
fuelectenerg-1427	1316	66	d1	d1	PROPN
fuelectenerg-1427	1316	67	and	and	CCONJ
fuelectenerg-1427	1316	68	d2	d2	PROPN
fuelectenerg-1427	1316	69	)	)	PUNCT
fuelectenerg-1427	1316	70	,	,	PUNCT
fuelectenerg-1427	1316	71	can	can	AUX
fuelectenerg-1427	1316	72	be	be	AUX
fuelectenerg-1427	1316	73	realized	realize	VERB
fuelectenerg-1427	1316	74	using	use	VERB
fuelectenerg-1427	1316	75	a	a	DET
fuelectenerg-1427	1316	76	universal	universal	ADJ
fuelectenerg-1427	1316	77	logic	logic	NOUN
fuelectenerg-1427	1316	78	module	module	NOUN
fuelectenerg-1427	1316	79	(	(	PUNCT
fuelectenerg-1427	1316	80	ulm	ulm	PROPN
fuelectenerg-1427	1316	81	)	)	PUNCT
fuelectenerg-1427	1316	82	with	with	ADP
fuelectenerg-1427	1316	83	control	control	NOUN
fuelectenerg-1427	1316	84	variables	variable	NOUN
fuelectenerg-1427	1316	85	corresponding	correspond	VERB
fuelectenerg-1427	1316	86	to	to	ADP
fuelectenerg-1427	1316	87	the	the	DET
fuelectenerg-1427	1316	88	variables	variable	NOUN
fuelectenerg-1427	1316	89	of	of	ADP
fuelectenerg-1427	1316	90	the	the	DET
fuelectenerg-1427	1316	91	basis	basis	NOUN
fuelectenerg-1427	1316	92	functions	function	NOUN
fuelectenerg-1427	1316	93	which	which	PRON
fuelectenerg-1427	1316	94	are	be	AUX
fuelectenerg-1427	1316	95	the	the	DET
fuelectenerg-1427	1316	96	variables	variable	NOUN
fuelectenerg-1427	1316	97	we	we	PRON
fuelectenerg-1427	1316	98	are	be	AUX
fuelectenerg-1427	1316	99	expanding	expand	VERB
fuelectenerg-1427	1316	100	upon	upon	SCONJ
fuelectenerg-1427	1316	101	.	.	PUNCT
fuelectenerg-1427	1317	1	we	we	PRON
fuelectenerg-1427	1317	2	call	call	VERB
fuelectenerg-1427	1317	3	it	it	PRON
fuelectenerg-1427	1317	4	a	a	DET
fuelectenerg-1427	1317	5	universal	universal	ADJ
fuelectenerg-1427	1317	6	logic	logic	NOUN
fuelectenerg-1427	1317	7	module	module	NOUN
fuelectenerg-1427	1317	8	,	,	PUNCT
fuelectenerg-1427	1317	9	because	because	SCONJ
fuelectenerg-1427	1317	10	similarly	similarly	ADV
fuelectenerg-1427	1317	11	to	to	ADP
fuelectenerg-1427	1317	12	a	a	DET
fuelectenerg-1427	1317	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1317	14	,	,	PUNCT
fuelectenerg-1427	1317	15	all	all	DET
fuelectenerg-1427	1317	16	functions	function	NOUN
fuelectenerg-1427	1317	17	of	of	ADP
fuelectenerg-1427	1317	18	two	two	NUM
fuelectenerg-1427	1317	19	variables	variable	NOUN
fuelectenerg-1427	1317	20	can	can	AUX
fuelectenerg-1427	1317	21	be	be	AUX
fuelectenerg-1427	1317	22	realized	realize	VERB
fuelectenerg-1427	1317	23	with	with	ADP
fuelectenerg-1427	1317	24	two	two	NUM
fuelectenerg-1427	1317	25	-	-	PUNCT
fuelectenerg-1427	1317	26	level	level	NOUN
fuelectenerg-1427	1317	27	trees	tree	NOUN
fuelectenerg-1427	1317	28	of	of	ADP
fuelectenerg-1427	1317	29	such	such	ADJ
fuelectenerg-1427	1317	30	modules	module	NOUN
fuelectenerg-1427	1317	31	using	use	VERB
fuelectenerg-1427	1317	32	constants	constant	NOUN
fuelectenerg-1427	1317	33	on	on	ADP
fuelectenerg-1427	1317	34	the	the	DET
fuelectenerg-1427	1317	35	second	second	ADJ
fuelectenerg-1427	1317	36	-	-	PUNCT
fuelectenerg-1427	1317	37	level	level	NOUN
fuelectenerg-1427	1317	38	data	datum	NOUN
fuelectenerg-1427	1317	39	inputs	input	NOUN
fuelectenerg-1427	1317	40	.	.	PUNCT
fuelectenerg-1427	1318	1	the	the	DET
fuelectenerg-1427	1318	2	presented	present	VERB
fuelectenerg-1427	1318	3	ulms	ulm	NOUN
fuelectenerg-1427	1318	4	are	be	AUX
fuelectenerg-1427	1318	5	complete	complete	ADJ
fuelectenerg-1427	1318	6	systems	system	NOUN
fuelectenerg-1427	1318	7	because	because	SCONJ
fuelectenerg-1427	1318	8	they	they	PRON
fuelectenerg-1427	1318	9	can	can	AUX
fuelectenerg-1427	1318	10	implement	implement	VERB
fuelectenerg-1427	1318	11	all	all	DET
fuelectenerg-1427	1318	12	possible	possible	ADJ
fuelectenerg-1427	1318	13	functions	function	NOUN
fuelectenerg-1427	1318	14	with	with	ADP
fuelectenerg-1427	1318	15	certain	certain	ADJ
fuelectenerg-1427	1318	16	number	number	NOUN
fuelectenerg-1427	1318	17	of	of	ADP
fuelectenerg-1427	1318	18	variables	variable	NOUN
fuelectenerg-1427	1318	19	.	.	PUNCT
fuelectenerg-1427	1319	1	the	the	DET
fuelectenerg-1427	1319	2	concept	concept	NOUN
fuelectenerg-1427	1319	3	of	of	ADP
fuelectenerg-1427	1319	4	the	the	DET
fuelectenerg-1427	1319	5	universal	universal	ADJ
fuelectenerg-1427	1319	6	logic	logic	NOUN
fuelectenerg-1427	1319	7	module	module	NOUN
fuelectenerg-1427	1319	8	was	be	AUX
fuelectenerg-1427	1319	9	used	use	VERB
fuelectenerg-1427	1319	10	for	for	ADP
fuelectenerg-1427	1319	11	binary	binary	PROPN
fuelectenerg-1427	1319	12	rm	rm	PROPN
fuelectenerg-1427	1319	13	logic	logic	PROPN
fuelectenerg-1427	1319	14	over	over	ADP
fuelectenerg-1427	1319	15	gf(2	gf(2	PROPN
fuelectenerg-1427	1319	16	)	)	PUNCT
fuelectenerg-1427	1319	17	,	,	PUNCT
fuelectenerg-1427	1319	18	as	as	ADV
fuelectenerg-1427	1319	19	well	well	ADV
fuelectenerg-1427	1319	20	as	as	ADP
fuelectenerg-1427	1319	21	the	the	DET
fuelectenerg-1427	1319	22	general	general	ADJ
fuelectenerg-1427	1319	23	case	case	NOUN
fuelectenerg-1427	1319	24	of	of	ADP
fuelectenerg-1427	1319	25	linearly	linearly	ADV
fuelectenerg-1427	1319	26	independent	independent	ADJ
fuelectenerg-1427	1319	27	(	(	PUNCT
fuelectenerg-1427	1319	28	li	li	NOUN
fuelectenerg-1427	1319	29	)	)	PUNCT
fuelectenerg-1427	1319	30	logic	logic	NOUN
fuelectenerg-1427	1319	31	that	that	PRON
fuelectenerg-1427	1319	32	includes	include	VERB
fuelectenerg-1427	1319	33	rm	rm	NOUN
fuelectenerg-1427	1319	34	logic	logic	NOUN
fuelectenerg-1427	1319	35	as	as	ADP
fuelectenerg-1427	1319	36	a	a	DET
fuelectenerg-1427	1319	37	special	special	ADJ
fuelectenerg-1427	1319	38	case	case	NOUN
fuelectenerg-1427	1319	39	.	.	PUNCT
fuelectenerg-1427	1320	1	binary	binary	PROPN
fuelectenerg-1427	1320	2	li	li	PROPN
fuelectenerg-1427	1320	3	logic	logic	PROPN
fuelectenerg-1427	1320	4	extended	extend	VERB
fuelectenerg-1427	1320	5	the	the	DET
fuelectenerg-1427	1320	6	universal	universal	ADJ
fuelectenerg-1427	1320	7	logic	logic	NOUN
fuelectenerg-1427	1320	8	module	module	NOUN
fuelectenerg-1427	1320	9	from	from	ADP
fuelectenerg-1427	1320	10	just	just	ADV
fuelectenerg-1427	1320	11	being	be	AUX
fuelectenerg-1427	1320	12	a	a	DET
fuelectenerg-1427	1320	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1320	14	(	(	PUNCT
fuelectenerg-1427	1320	15	shannon	shannon	PROPN
fuelectenerg-1427	1320	16	expansion	expansion	PROPN
fuelectenerg-1427	1320	17	)	)	PUNCT
fuelectenerg-1427	1320	18	,	,	PUNCT
fuelectenerg-1427	1320	19	and	and	CCONJ
fuelectenerg-1427	1320	20	/	/	SYM
fuelectenerg-1427	1320	21	exor	exor	PROPN
fuelectenerg-1427	1320	22	gate	gate	PROPN
fuelectenerg-1427	1320	23	(	(	PUNCT
fuelectenerg-1427	1320	24	positive	positive	ADJ
fuelectenerg-1427	1320	25	davio	davio	NOUN
fuelectenerg-1427	1320	26	expansion	expansion	NOUN
fuelectenerg-1427	1320	27	)	)	PUNCT
fuelectenerg-1427	1320	28	and	and	CCONJ
fuelectenerg-1427	1320	29	and	and	CCONJ
fuelectenerg-1427	1320	30	/	/	SYM
fuelectenerg-1427	1320	31	exor	exor	PROPN
fuelectenerg-1427	1320	32	/	/	SYM
fuelectenerg-1427	1320	33	not	not	PART
fuelectenerg-1427	1320	34	gate	gate	VERB
fuelectenerg-1427	1320	35	with	with	ADP
fuelectenerg-1427	1320	36	inverted	inverted	ADJ
fuelectenerg-1427	1320	37	control	control	NOUN
fuelectenerg-1427	1320	38	variable	variable	NOUN
fuelectenerg-1427	1320	39	(	(	PUNCT
fuelectenerg-1427	1320	40	negative	negative	ADJ
fuelectenerg-1427	1320	41	davio	davio	NOUN
fuelectenerg-1427	1320	42	expansion	expansion	NOUN
fuelectenerg-1427	1320	43	)	)	PUNCT
fuelectenerg-1427	1320	44	,	,	PUNCT
fuelectenerg-1427	1320	45	to	to	ADP
fuelectenerg-1427	1320	46	the	the	DET
fuelectenerg-1427	1320	47	universal	universal	ADJ
fuelectenerg-1427	1320	48	logic	logic	NOUN
fuelectenerg-1427	1320	49	modules	module	NOUN
fuelectenerg-1427	1320	50	for	for	ADP
fuelectenerg-1427	1320	51	any	any	DET
fuelectenerg-1427	1320	52	expansion	expansion	NOUN
fuelectenerg-1427	1320	53	over	over	ADP
fuelectenerg-1427	1320	54	any	any	DET
fuelectenerg-1427	1320	55	linearly	linearly	ADV
fuelectenerg-1427	1320	56	independent	independent	ADJ
fuelectenerg-1427	1320	57	basis	basis	NOUN
fuelectenerg-1427	1320	58	functions	function	NOUN
fuelectenerg-1427	1320	59	.	.	PUNCT
fuelectenerg-1427	1321	1	analogously	analogously	ADV
fuelectenerg-1427	1321	2	to	to	ADP
fuelectenerg-1427	1321	3	the	the	DET
fuelectenerg-1427	1321	4	binary	binary	ADJ
fuelectenerg-1427	1321	5	case	case	NOUN
fuelectenerg-1427	1321	6	,	,	PUNCT
fuelectenerg-1427	1321	7	figure	figure	VERB
fuelectenerg-1427	1321	8	7	7	NUM
fuelectenerg-1427	1321	9	presents	present	VERB
fuelectenerg-1427	1321	10	universal	universal	ADJ
fuelectenerg-1427	1321	11	logic	logic	NOUN
fuelectenerg-1427	1321	12	modules	module	NOUN
fuelectenerg-1427	1321	13	for	for	ADP
fuelectenerg-1427	1321	14	ternary	ternary	ADJ
fuelectenerg-1427	1321	15	shannon	shannon	NOUN
fuelectenerg-1427	1321	16	and	and	CCONJ
fuelectenerg-1427	1321	17	ternary	ternary	ADJ
fuelectenerg-1427	1321	18	davio	davio	NOUN
fuelectenerg-1427	1321	19	,	,	PUNCT
fuelectenerg-1427	1321	20	respectively	respectively	ADV
fuelectenerg-1427	1321	21	.	.	PUNCT
fuelectenerg-1427	1322	1	one	one	PRON
fuelectenerg-1427	1322	2	can	can	AUX
fuelectenerg-1427	1322	3	note	note	VERB
fuelectenerg-1427	1322	4	,	,	PUNCT
fuelectenerg-1427	1322	5	that	that	SCONJ
fuelectenerg-1427	1322	6	any	any	DET
fuelectenerg-1427	1322	7	function	function	NOUN
fuelectenerg-1427	1322	8	f	f	PROPN
fuelectenerg-1427	1322	9	can	can	AUX
fuelectenerg-1427	1322	10	be	be	AUX
fuelectenerg-1427	1322	11	produced	produce	VERB
fuelectenerg-1427	1322	12	by	by	ADP
fuelectenerg-1427	1322	13	the	the	DET
fuelectenerg-1427	1322	14	application	application	NOUN
fuelectenerg-1427	1322	15	of	of	ADP
fuelectenerg-1427	1322	16	the	the	DET
fuelectenerg-1427	1322	17	independent	independent	ADJ
fuelectenerg-1427	1322	18	variable	variable	NOUN
fuelectenerg-1427	1322	19	x	x	PUNCT
fuelectenerg-1427	1322	20	and	and	CCONJ
fuelectenerg-1427	1322	21	the	the	DET
fuelectenerg-1427	1322	22	cofactors	cofactor	NOUN
fuelectenerg-1427	1322	23	{	{	PUNCT
fuelectenerg-1427	1322	24	fi	fi	NOUN
fuelectenerg-1427	1322	25	,	,	PUNCT
fuelectenerg-1427	1322	26	f	f	PROPN
fuelectenerg-1427	1322	27	j	j	PROPN
fuelectenerg-1427	1322	28	and	and	CCONJ
fuelectenerg-1427	1322	29	fk	fk	INTJ
fuelectenerg-1427	1322	30	}	}	PUNCT
fuelectenerg-1427	1322	31	as	as	ADP
fuelectenerg-1427	1322	32	inputs	input	NOUN
fuelectenerg-1427	1322	33	to	to	ADP
fuelectenerg-1427	1322	34	a	a	DET
fuelectenerg-1427	1322	35	ulm	ulm	NOUN
fuelectenerg-1427	1322	36	.	.	PUNCT
fuelectenerg-1427	1323	1	the	the	DET
fuelectenerg-1427	1323	2	form	form	NOUN
fuelectenerg-1427	1323	3	of	of	ADP
fuelectenerg-1427	1323	4	the	the	DET
fuelectenerg-1427	1323	5	resulting	result	VERB
fuelectenerg-1427	1323	6	function	function	NOUN
fuelectenerg-1427	1323	7	depends	depend	VERB
fuelectenerg-1427	1323	8	on	on	ADP
fuelectenerg-1427	1323	9	our	our	PRON
fuelectenerg-1427	1323	10	choice	choice	NOUN
fuelectenerg-1427	1323	11	of	of	ADP
fuelectenerg-1427	1323	12	the	the	DET
fuelectenerg-1427	1323	13	shift	shift	NOUN
fuelectenerg-1427	1323	14	and	and	CCONJ
fuelectenerg-1427	1323	15	power	power	NOUN
fuelectenerg-1427	1323	16	operations	operation	NOUN
fuelectenerg-1427	1323	17	that	that	PRON
fuelectenerg-1427	1323	18	we	we	PRON
fuelectenerg-1427	1323	19	choose	choose	VERB
fuelectenerg-1427	1323	20	inside	inside	ADP
fuelectenerg-1427	1323	21	the	the	DET
fuelectenerg-1427	1323	22	ulm	ulm	NOUN
fuelectenerg-1427	1323	23	for	for	ADP
fuelectenerg-1427	1323	24	the	the	DET
fuelectenerg-1427	1323	25	input	input	NOUN
fuelectenerg-1427	1323	26	independent	independent	ADJ
fuelectenerg-1427	1323	27	variable	variable	NOUN
fuelectenerg-1427	1323	28	,	,	PUNCT
fuelectenerg-1427	1323	29	and	and	CCONJ
fuelectenerg-1427	1323	30	on	on	ADP
fuelectenerg-1427	1323	31	our	our	PRON
fuelectenerg-1427	1323	32	choice	choice	NOUN
fuelectenerg-1427	1323	33	of	of	ADP
fuelectenerg-1427	1323	34	the	the	DET
fuelectenerg-1427	1323	35	weighted	weight	VERB
fuelectenerg-1427	1323	36	combinations	combination	NOUN
fuelectenerg-1427	1323	37	of	of	ADP
fuelectenerg-1427	1323	38	the	the	DET
fuelectenerg-1427	1323	39	input	input	NOUN
fuelectenerg-1427	1323	40	cofactors	cofactor	NOUN
fuelectenerg-1427	1323	41	.	.	PUNCT
fuelectenerg-1427	1324	1	utilizing	utilize	VERB
fuelectenerg-1427	1324	2	this	this	DET
fuelectenerg-1427	1324	3	note	note	NOUN
fuelectenerg-1427	1324	4	,	,	PUNCT
fuelectenerg-1427	1324	5	we	we	PRON
fuelectenerg-1427	1324	6	can	can	AUX
fuelectenerg-1427	1324	7	combine	combine	VERB
fuelectenerg-1427	1324	8	all	all	DET
fuelectenerg-1427	1324	9	davio	davio	NOUN
fuelectenerg-1427	1324	10	ulms	ulm	NOUN
fuelectenerg-1427	1324	11	to	to	PART
fuelectenerg-1427	1324	12	create	create	VERB
fuelectenerg-1427	1324	13	the	the	DET
fuelectenerg-1427	1324	14	single	single	ADJ
fuelectenerg-1427	1324	15	all	all	ADJ
fuelectenerg-1427	1324	16	-	-	PUNCT
fuelectenerg-1427	1324	17	davio	davio	NOUN
fuelectenerg-1427	1324	18	ulm	ulm	NOUN
fuelectenerg-1427	1324	19	,	,	PUNCT
fuelectenerg-1427	1324	20	where	where	SCONJ
fuelectenerg-1427	1324	21	figure	figure	NOUN
fuelectenerg-1427	1324	22	7(c	7(c	NOUN
fuelectenerg-1427	1324	23	)	)	PUNCT
fuelectenerg-1427	1324	24	illustrates	illustrate	VERB
fuelectenerg-1427	1324	25	this	this	DET
fuelectenerg-1427	1324	26	ulm	ulm	NOUN
fuelectenerg-1427	1324	27	.	.	PUNCT
fuelectenerg-1427	1325	1	also	also	ADV
fuelectenerg-1427	1325	2	,	,	PUNCT
fuelectenerg-1427	1325	3	the	the	DET
fuelectenerg-1427	1325	4	more	more	ADV
fuelectenerg-1427	1325	5	general	general	ADJ
fuelectenerg-1427	1325	6	ulm	ulm	NOUN
fuelectenerg-1427	1325	7	as	as	SCONJ
fuelectenerg-1427	1325	8	shown	show	VERB
fuelectenerg-1427	1325	9	in	in	ADP
fuelectenerg-1427	1325	10	figure	figure	NOUN
fuelectenerg-1427	1325	11	7(d	7(d	NUM
fuelectenerg-1427	1325	12	)	)	PUNCT
fuelectenerg-1427	1325	13	,	,	PUNCT
fuelectenerg-1427	1325	14	can	can	AUX
fuelectenerg-1427	1325	15	be	be	AUX
fuelectenerg-1427	1325	16	generated	generate	VERB
fuelectenerg-1427	1325	17	to	to	PART
fuelectenerg-1427	1325	18	implement	implement	VERB
fuelectenerg-1427	1325	19	all	all	DET
fuelectenerg-1427	1325	20	ternary	ternary	ADJ
fuelectenerg-1427	1325	21	gf(3	gf(3	PROPN
fuelectenerg-1427	1325	22	)	)	PUNCT
fuelectenerg-1427	1325	23	shannon	shannon	NOUN
fuelectenerg-1427	1325	24	and	and	CCONJ
fuelectenerg-1427	1325	25	davio	davio	NOUN
fuelectenerg-1427	1325	26	expansions	expansion	NOUN
fuelectenerg-1427	1325	27	.	.	PUNCT
fuelectenerg-1427	1326	1	in	in	ADP
fuelectenerg-1427	1326	2	general	general	ADJ
fuelectenerg-1427	1326	3	,	,	PUNCT
fuelectenerg-1427	1326	4	the	the	DET
fuelectenerg-1427	1326	5	gates	gate	NOUN
fuelectenerg-1427	1326	6	in	in	ADP
fuelectenerg-1427	1326	7	the	the	DET
fuelectenerg-1427	1326	8	ulms	ulm	NOUN
fuelectenerg-1427	1326	9	can	can	AUX
fuelectenerg-1427	1326	10	be	be	AUX
fuelectenerg-1427	1326	11	implemented	implement	VERB
fuelectenerg-1427	1326	12	,	,	PUNCT
fuelectenerg-1427	1326	13	among	among	ADP
fuelectenerg-1427	1326	14	other	other	ADJ
fuelectenerg-1427	1326	15	circuit	circuit	NOUN
fuelectenerg-1427	1326	16	technologies	technology	NOUN
fuelectenerg-1427	1326	17	,	,	PUNCT
fuelectenerg-1427	1326	18	by	by	ADP
fuelectenerg-1427	1326	19	using	use	VERB
fuelectenerg-1427	1326	20	binary	binary	ADJ
fuelectenerg-1427	1326	21	logic	logic	NOUN
fuelectenerg-1427	1326	22	over	over	ADP
fuelectenerg-1427	1326	23	gf(2	gf(2	PROPN
fuelectenerg-1427	1326	24	)	)	PUNCT
fuelectenerg-1427	1326	25	or	or	CCONJ
fuelectenerg-1427	1326	26	using	use	VERB
fuelectenerg-1427	1326	27	multiple	multiple	ADV
fuelectenerg-1427	1326	28	-	-	PUNCT
fuelectenerg-1427	1326	29	valued	value	VERB
fuelectenerg-1427	1326	30	circuit	circuit	NOUN
fuelectenerg-1427	1326	31	gates	gate	NOUN
fuelectenerg-1427	1326	32	.	.	PUNCT
fuelectenerg-1427	1327	1	each	each	DET
fuelectenerg-1427	1327	2	ternary	ternary	ADJ
fuelectenerg-1427	1327	3	ulm	ulm	PROPN
fuelectenerg-1427	1327	4	corresponds	correspond	VERB
fuelectenerg-1427	1327	5	to	to	ADP
fuelectenerg-1427	1327	6	a	a	DET
fuelectenerg-1427	1327	7	single	single	ADJ
fuelectenerg-1427	1327	8	node	node	NOUN
fuelectenerg-1427	1327	9	in	in	ADP
fuelectenerg-1427	1327	10	the	the	DET
fuelectenerg-1427	1327	11	nodes	node	NOUN
fuelectenerg-1427	1327	12	of	of	ADP
fuelectenerg-1427	1327	13	ternary	ternary	ADJ
fuelectenerg-1427	1327	14	dts	dts	NOUN
fuelectenerg-1427	1327	15	that	that	PRON
fuelectenerg-1427	1327	16	were	be	AUX
fuelectenerg-1427	1327	17	illustrated	illustrate	VERB
fuelectenerg-1427	1327	18	previously	previously	ADV
fuelectenerg-1427	1327	19	.	.	PUNCT
fuelectenerg-1427	1328	1	the	the	DET
fuelectenerg-1427	1328	2	main	main	ADJ
fuelectenerg-1427	1328	3	advantage	advantage	NOUN
fuelectenerg-1427	1328	4	of	of	ADP
fuelectenerg-1427	1328	5	such	such	ADJ
fuelectenerg-1427	1328	6	powerful	powerful	ADJ
fuelectenerg-1427	1328	7	ulms	ulm	NOUN
fuelectenerg-1427	1328	8	is	be	AUX
fuelectenerg-1427	1328	9	in	in	ADP
fuelectenerg-1427	1328	10	high	high	ADJ
fuelectenerg-1427	1328	11	layout	layout	NOUN
fuelectenerg-1427	1328	12	regularity	regularity	NOUN
fuelectenerg-1427	1328	13	that	that	PRON
fuelectenerg-1427	1328	14	is	be	AUX
fuelectenerg-1427	1328	15	required	require	VERB
fuelectenerg-1427	1328	16	by	by	ADP
fuelectenerg-1427	1328	17	future	future	ADJ
fuelectenerg-1427	1328	18	nanotechnologies	nanotechnology	NOUN
fuelectenerg-1427	1328	19	,	,	PUNCT
fuelectenerg-1427	1328	20	where	where	SCONJ
fuelectenerg-1427	1328	21	the	the	DET
fuelectenerg-1427	1328	22	trees	tree	NOUN
fuelectenerg-1427	1328	23	can	can	AUX
fuelectenerg-1427	1328	24	be	be	AUX
fuelectenerg-1427	1328	25	realized	realize	VERB
fuelectenerg-1427	1328	26	in	in	ADP
fuelectenerg-1427	1328	27	efficient	efficient	ADJ
fuelectenerg-1427	1328	28	layout	layout	NOUN
fuelectenerg-1427	1328	29	because	because	SCONJ
fuelectenerg-1427	1328	30	they	they	PRON
fuelectenerg-1427	1328	31	do	do	AUX
fuelectenerg-1427	1328	32	not	not	PART
fuelectenerg-1427	1328	33	grow	grow	VERB
fuelectenerg-1427	1328	34	exponentially	exponentially	ADV
fuelectenerg-1427	1328	35	for	for	ADP
fuelectenerg-1427	1328	36	practical	practical	ADJ
fuelectenerg-1427	1328	37	functions	function	NOUN
fuelectenerg-1427	1328	38	.	.	PUNCT
fuelectenerg-1427	1329	1	for	for	ADP
fuelectenerg-1427	1329	2	instance	instance	NOUN
fuelectenerg-1427	1329	3	,	,	PUNCT
fuelectenerg-1427	1329	4	assuming	assume	VERB
fuelectenerg-1427	1329	5	ulm	ulm	NOUN
fuelectenerg-1427	1329	6	from	from	ADP
fuelectenerg-1427	1329	7	figure	figure	NOUN
fuelectenerg-1427	1329	8	7	7	NUM
fuelectenerg-1427	1329	9	,	,	PUNCT
fuelectenerg-1427	1329	10	although	although	SCONJ
fuelectenerg-1427	1329	11	every	every	DET
fuelectenerg-1427	1329	12	two	two	NUM
fuelectenerg-1427	1329	13	-	-	PUNCT
fuelectenerg-1427	1329	14	variable	variable	NOUN
fuelectenerg-1427	1329	15	function	function	NOUN
fuelectenerg-1427	1329	16	can	can	AUX
fuelectenerg-1427	1329	17	be	be	AUX
fuelectenerg-1427	1329	18	realized	realize	VERB
fuelectenerg-1427	1329	19	with	with	ADP
fuelectenerg-1427	1329	20	four	four	NUM
fuelectenerg-1427	1329	21	such	such	ADJ
fuelectenerg-1427	1329	22	modules	module	NOUN
fuelectenerg-1427	1329	23	,	,	PUNCT
fuelectenerg-1427	1329	24	it	it	PRON
fuelectenerg-1427	1329	25	is	be	AUX
fuelectenerg-1427	1329	26	highly	highly	ADV
fuelectenerg-1427	1329	27	probable	probable	ADJ
fuelectenerg-1427	1329	28	that	that	SCONJ
fuelectenerg-1427	1329	29	most	most	ADJ
fuelectenerg-1427	1329	30	of	of	ADP
fuelectenerg-1427	1329	31	two	two	NUM
fuelectenerg-1427	1329	32	-	-	PUNCT
fuelectenerg-1427	1329	33	variable	variable	NOUN
fuelectenerg-1427	1329	34	functions	function	NOUN
fuelectenerg-1427	1329	35	will	will	AUX
fuelectenerg-1427	1329	36	require	require	VERB
fuelectenerg-1427	1329	37	less	less	ADJ
fuelectenerg-1427	1329	38	than	than	ADP
fuelectenerg-1427	1329	39	four	four	NUM
fuelectenerg-1427	1329	40	modules	module	NOUN
fuelectenerg-1427	1329	41	.	.	PUNCT
fuelectenerg-1427	1330	1	because	because	SCONJ
fuelectenerg-1427	1330	2	of	of	ADP
fuelectenerg-1427	1330	3	these	these	DET
fuelectenerg-1427	1330	4	properties	property	NOUN
fuelectenerg-1427	1330	5	,	,	PUNCT
fuelectenerg-1427	1330	6	this	this	DET
fuelectenerg-1427	1330	7	approach	approach	NOUN
fuelectenerg-1427	1330	8	is	be	AUX
fuelectenerg-1427	1330	9	further	far	ADV
fuelectenerg-1427	1330	10	expected	expect	VERB
fuelectenerg-1427	1330	11	to	to	PART
fuelectenerg-1427	1330	12	give	give	VERB
fuelectenerg-1427	1330	13	good	good	ADJ
fuelectenerg-1427	1330	14	results	result	NOUN
fuelectenerg-1427	1330	15	when	when	SCONJ
fuelectenerg-1427	1330	16	applied	apply	VERB
fuelectenerg-1427	1330	17	to	to	ADP
fuelectenerg-1427	1330	18	the	the	DET
fuelectenerg-1427	1330	19	corresponding	corresponding	ADJ
fuelectenerg-1427	1330	20	incompletely	incompletely	ADV
fuelectenerg-1427	1330	21	specified	specify	VERB
fuelectenerg-1427	1330	22	functions	function	NOUN
fuelectenerg-1427	1330	23	and	and	CCONJ
fuelectenerg-1427	1330	24	multiple	multiple	ADV
fuelectenerg-1427	1330	25	-	-	PUNCT
fuelectenerg-1427	1330	26	valued	value	VERB
fuelectenerg-1427	1330	27	relations	relation	NOUN
fuelectenerg-1427	1330	28	.	.	PUNCT
fuelectenerg-1427	1331	1	4	4	NUM
fuelectenerg-1427	1331	2	conclusions	conclusion	NOUN
fuelectenerg-1427	1331	3	and	and	CCONJ
fuelectenerg-1427	1331	4	future	future	ADJ
fuelectenerg-1427	1331	5	work	work	NOUN
fuelectenerg-1427	1331	6	in	in	ADP
fuelectenerg-1427	1331	7	this	this	DET
fuelectenerg-1427	1331	8	paper	paper	NOUN
fuelectenerg-1427	1331	9	,	,	PUNCT
fuelectenerg-1427	1331	10	an	an	DET
fuelectenerg-1427	1331	11	extended	extended	ADJ
fuelectenerg-1427	1331	12	green	green	ADJ
fuelectenerg-1427	1331	13	-	-	PUNCT
fuelectenerg-1427	1331	14	sasao	sasao	NOUN
fuelectenerg-1427	1331	15	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1331	16	of	of	ADP
fuelectenerg-1427	1331	17	families	family	NOUN
fuelectenerg-1427	1331	18	and	and	CCONJ
fuelectenerg-1427	1331	19	forms	form	NOUN
fuelectenerg-1427	1331	20	is	be	AUX
fuelectenerg-1427	1331	21	introduced	introduce	VERB
fuelectenerg-1427	1331	22	.	.	PUNCT
fuelectenerg-1427	1332	1	analogously	analogously	ADV
fuelectenerg-1427	1332	2	to	to	ADP
fuelectenerg-1427	1332	3	the	the	DET
fuelectenerg-1427	1332	4	binary	binary	ADJ
fuelectenerg-1427	1332	5	case	case	NOUN
fuelectenerg-1427	1332	6	,	,	PUNCT
fuelectenerg-1427	1332	7	two	two	NUM
fuelectenerg-1427	1332	8	general	general	ADJ
fuelectenerg-1427	1332	9	families	family	NOUN
fuelectenerg-1427	1332	10	of	of	ADP
fuelectenerg-1427	1332	11	canonical	canonical	ADJ
fuelectenerg-1427	1332	12	ternary	ternary	ADJ
fuelectenerg-1427	1332	13	reed	reed	NOUN
fuelectenerg-1427	1332	14	-	-	PUNCT
fuelectenerg-1427	1332	15	muller	muller	NOUN
fuelectenerg-1427	1332	16	forms	form	NOUN
fuelectenerg-1427	1332	17	,	,	PUNCT
fuelectenerg-1427	1332	18	called	call	VERB
fuelectenerg-1427	1332	19	ternary	ternary	ADJ
fuelectenerg-1427	1332	20	inclusive	inclusive	ADJ
fuelectenerg-1427	1332	21	forms	form	NOUN
fuelectenerg-1427	1332	22	(	(	PUNCT
fuelectenerg-1427	1332	23	tifs	tifs	PROPN
fuelectenerg-1427	1332	24	)	)	PUNCT
fuelectenerg-1427	1332	25	and	and	CCONJ
fuelectenerg-1427	1332	26	their	their	PRON
fuelectenerg-1427	1332	27	generalization	generalization	NOUN
fuelectenerg-1427	1332	28	of	of	ADP
fuelectenerg-1427	1332	29	ternary	ternary	ADJ
fuelectenerg-1427	1332	30	generalized	generalize	VERB
fuelectenerg-1427	1332	31	inclusive	inclusive	ADJ
fuelectenerg-1427	1332	32	forms	form	NOUN
fuelectenerg-1427	1332	33	(	(	PUNCT
fuelectenerg-1427	1332	34	tgifs	tgif	NOUN
fuelectenerg-1427	1332	35	)	)	PUNCT
fuelectenerg-1427	1332	36	,	,	PUNCT
fuelectenerg-1427	1332	37	are	be	AUX
fuelectenerg-1427	1332	38	presented	present	VERB
fuelectenerg-1427	1332	39	.	.	PUNCT
fuelectenerg-1427	1333	1	the	the	DET
fuelectenerg-1427	1333	2	second	second	ADJ
fuelectenerg-1427	1333	3	family	family	NOUN
fuelectenerg-1427	1333	4	includes	include	VERB
fuelectenerg-1427	1333	5	minimum	minimum	ADJ
fuelectenerg-1427	1333	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1333	7	)	)	PUNCT
fuelectenerg-1427	1333	8	galois	galois	PROPN
fuelectenerg-1427	1333	9	field	field	NOUN
fuelectenerg-1427	1333	10	sum	sum	NOUN
fuelectenerg-1427	1333	11	-	-	PUNCT
fuelectenerg-1427	1333	12	of	of	ADP
fuelectenerg-1427	1333	13	-	-	PUNCT
fuelectenerg-1427	1333	14	products	product	NOUN
fuelectenerg-1427	1333	15	(	(	PUNCT
fuelectenerg-1427	1333	16	gfsops	gfsop	NOUN
fuelectenerg-1427	1333	17	)	)	PUNCT
fuelectenerg-1427	1333	18	.	.	PUNCT
fuelectenerg-1427	1334	1	the	the	DET
fuelectenerg-1427	1334	2	multiple	multiple	ADV
fuelectenerg-1427	1334	3	-	-	PUNCT
fuelectenerg-1427	1334	4	valued	value	VERB
fuelectenerg-1427	1334	5	shannon	shannon	NOUN
fuelectenerg-1427	1334	6	-	-	PUNCT
fuelectenerg-1427	1334	7	davio	davio	NOUN
fuelectenerg-1427	1334	8	(	(	PUNCT
fuelectenerg-1427	1334	9	s	s	NOUN
fuelectenerg-1427	1334	10	/	/	SYM
fuelectenerg-1427	1334	11	d	d	NOUN
fuelectenerg-1427	1334	12	)	)	PUNCT
fuelectenerg-1427	1334	13	trees	tree	NOUN
fuelectenerg-1427	1334	14	developed	develop	VERB
fuelectenerg-1427	1334	15	in	in	ADP
fuelectenerg-1427	1334	16	this	this	DET
fuelectenerg-1427	1334	17	paper	paper	NOUN
fuelectenerg-1427	1334	18	provide	provide	VERB
fuelectenerg-1427	1334	19	more	more	ADJ
fuelectenerg-1427	1334	20	general	general	ADJ
fuelectenerg-1427	1334	21	polarity	polarity	NOUN
fuelectenerg-1427	1334	22	with	with	ADP
fuelectenerg-1427	1334	23	regards	regard	NOUN
fuelectenerg-1427	1334	24	to	to	ADP
fuelectenerg-1427	1334	25	the	the	DET
fuelectenerg-1427	1334	26	114	114	NUM
fuelectenerg-1427	1334	27	an	an	DET
fuelectenerg-1427	1334	28	extended	extended	ADJ
fuelectenerg-1427	1334	29	green	green	ADJ
fuelectenerg-1427	1334	30	sasao	sasao	PROPN
fuelectenerg-1427	1334	31	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1334	32	of	of	ADP
fuelectenerg-1427	1334	33	canonical	canonical	ADJ
fuelectenerg-1427	1334	34	ternary	ternary	ADJ
fuelectenerg-1427	1334	35	galois	galois	NOUN
fuelectenerg-1427	1334	36	forms	form	NOUN
fuelectenerg-1427	1334	37	...	...	PUNCT
fuelectenerg-1427	1335	1	•	•	NUM
fuelectenerg-1427	1335	2	•	•	NOUN
fuelectenerg-1427	1335	3	x	x	SYM
fuelectenerg-1427	1335	4	f0	f0	PROPN
fuelectenerg-1427	1335	5	f2	f2	PROPN
fuelectenerg-1427	1335	6	f1	f1	NOUN
fuelectenerg-1427	1335	7	0x	0x	NOUN
fuelectenerg-1427	1335	8	2	2	NUM
fuelectenerg-1427	1335	9	x	x	SYM
fuelectenerg-1427	1335	10	1	1	NUM
fuelectenerg-1427	1335	11	x	x	SYM
fuelectenerg-1427	1335	12	x	x	NOUN
fuelectenerg-1427	1335	13	f1	f1	NOUN
fuelectenerg-1427	1335	14	f0	f0	PROPN
fuelectenerg-1427	1336	1	+	+	PROPN
fuelectenerg-1427	1336	2	f	f	PROPN
fuelectenerg-1427	1336	3	1	1	NUM
fuelectenerg-1427	1336	4	+	+	NOUN
fuelectenerg-1427	1336	5	f	f	PROPN
fuelectenerg-1427	1336	6	2	2	NUM
fuelectenerg-1427	1336	7	2f2	2f2	NUM
fuelectenerg-1427	1337	1	+	+	NOUN
fuelectenerg-1427	1337	2	f	f	NOUN
fuelectenerg-1427	1337	3	0	0	NUM
fuelectenerg-1427	1337	4	1	1	NUM
fuelectenerg-1427	1337	5	2	2	NUM
fuelectenerg-1427	1337	6	(	(	PUNCT
fuelectenerg-1427	1337	7	”	"	PUNCT
fuelectenerg-1427	1337	8	)	)	PUNCT
fuelectenerg-1427	1337	9	x	x	SYM
fuelectenerg-1427	1337	10	2	2	NUM
fuelectenerg-1427	1337	11	x	x	NOUN
fuelectenerg-1427	1337	12	”	"	PUNCT
fuelectenerg-1427	1337	13	x	x	NUM
fuelectenerg-1427	1337	14	f0	f0	NOUN
fuelectenerg-1427	1337	15	f0	f0	PROPN
fuelectenerg-1427	1338	1	+	+	NOUN
fuelectenerg-1427	1338	2	f	f	PROPN
fuelectenerg-1427	1338	3	1	1	NUM
fuelectenerg-1427	1339	1	+	+	NOUN
fuelectenerg-1427	1339	2	f	f	PROPN
fuelectenerg-1427	1339	3	2	2	NUM
fuelectenerg-1427	1339	4	2f1	2f1	NUM
fuelectenerg-1427	1339	5	+	+	NOUN
fuelectenerg-1427	1339	6	f	f	PROPN
fuelectenerg-1427	1339	7	2	2	NUM
fuelectenerg-1427	1339	8	1	1	NUM
fuelectenerg-1427	1339	9	2	2	NUM
fuelectenerg-1427	1339	10	(	(	PUNCT
fuelectenerg-1427	1339	11	)	)	PUNCT
fuelectenerg-1427	1339	12	x	x	SYM
fuelectenerg-1427	1339	13	2	2	NUM
fuelectenerg-1427	1339	14	x	x	SYM
fuelectenerg-1427	1339	15	2	2	NUM
fuelectenerg-1427	1339	16	(	(	PUNCT
fuelectenerg-1427	1339	17	’	'	PUNCT
fuelectenerg-1427	1339	18	)	)	PUNCT
fuelectenerg-1427	1339	19	x	x	SYM
fuelectenerg-1427	1339	20	2	2	NUM
fuelectenerg-1427	1339	21	x	x	SYM
fuelectenerg-1427	1339	22	f2	f2	PROPN
fuelectenerg-1427	1339	23	f0	f0	PROPN
fuelectenerg-1427	1340	1	+	+	PROPN
fuelectenerg-1427	1340	2	f	f	PROPN
fuelectenerg-1427	1340	3	1	1	NUM
fuelectenerg-1427	1340	4	+	+	NOUN
fuelectenerg-1427	1340	5	f	f	PROPN
fuelectenerg-1427	1340	6	2	2	NUM
fuelectenerg-1427	1340	7	2f0	2f0	NUM
fuelectenerg-1427	1340	8	+	+	NOUN
fuelectenerg-1427	1340	9	f	f	NOUN
fuelectenerg-1427	1340	10	1	1	NUM
fuelectenerg-1427	1340	11	1	1	NUM
fuelectenerg-1427	1340	12	x	x	NOUN
fuelectenerg-1427	1340	13	’	'	PUNCT
fuelectenerg-1427	1341	1	+	+	PROPN
fuelectenerg-1427	1342	1	+	+	PUNCT
fuelectenerg-1427	1342	2	+	+	PUNCT
fuelectenerg-1427	1343	1	+	+	PUNCT
fuelectenerg-1427	1343	2	+	+	SYM
fuelectenerg-1427	1343	3	0	0	NUM
fuelectenerg-1427	1343	4	x	x	SYM
fuelectenerg-1427	1343	5	1	1	NUM
fuelectenerg-1427	1343	6	1	1	NUM
fuelectenerg-1427	1343	7	x	x	SYM
fuelectenerg-1427	1343	8	2	2	NUM
fuelectenerg-1427	1343	9	x	x	SYM
fuelectenerg-1427	1343	10	2	2	NUM
fuelectenerg-1427	1343	11	x	x	SYM
fuelectenerg-1427	1343	12	x	x	NOUN
fuelectenerg-1427	1343	13	’	'	PUNCT
fuelectenerg-1427	1343	14	x	x	ADJ
fuelectenerg-1427	1343	15	”	"	PUNCT
fuelectenerg-1427	1343	16	fi	fi	NOUN
fuelectenerg-1427	1343	17	fk	fk	INTJ
fuelectenerg-1427	1344	1	fj	fj	INTJ
fuelectenerg-1427	1344	2	f	f	NOUN
fuelectenerg-1427	1344	3	x	x	SYM
fuelectenerg-1427	1344	4	1	1	NUM
fuelectenerg-1427	1344	5	2	2	NUM
fuelectenerg-1427	1344	6	�	�	PROPN
fuelectenerg-1427	1344	7	�	�	PROPN
fuelectenerg-1427	1344	8	�	�	PROPN
fuelectenerg-1427	1344	9	�	�	PROPN
fuelectenerg-1427	1344	10	�	�	PROPN
fuelectenerg-1427	1344	11	�	�	PROPN
fuelectenerg-1427	1344	12	�	�	PROPN
fuelectenerg-1427	1344	13	+	+	CCONJ
fuelectenerg-1427	1344	14	+1	+1	PROPN
fuelectenerg-1427	1345	1	fi	fi	NOUN
fuelectenerg-1427	1345	2	fk	fk	INTJ
fuelectenerg-1427	1346	1	fj	fj	INTJ
fuelectenerg-1427	1346	2	f	f	PROPN
fuelectenerg-1427	1346	3	+1	+1	PROPN
fuelectenerg-1427	1346	4	(	(	PUNCT
fuelectenerg-1427	1346	5	a	a	NOUN
fuelectenerg-1427	1346	6	)	)	PUNCT
fuelectenerg-1427	1346	7	(	(	PUNCT
fuelectenerg-1427	1346	8	b	b	X
fuelectenerg-1427	1346	9	)	)	PUNCT
fuelectenerg-1427	1346	10	(	(	PUNCT
fuelectenerg-1427	1346	11	c	c	X
fuelectenerg-1427	1346	12	)	)	PUNCT
fuelectenerg-1427	1346	13	(	(	PUNCT
fuelectenerg-1427	1346	14	d	d	X
fuelectenerg-1427	1346	15	)	)	PUNCT
fuelectenerg-1427	1346	16	figure	figure	NOUN
fuelectenerg-1427	1346	17	7	7	NUM
fuelectenerg-1427	1346	18	:	:	PUNCT
fuelectenerg-1427	1346	19	various	various	ADJ
fuelectenerg-1427	1346	20	ternary	ternary	ADJ
fuelectenerg-1427	1346	21	ulms	ulm	NOUN
fuelectenerg-1427	1346	22	:	:	PUNCT
fuelectenerg-1427	1346	23	(	(	PUNCT
fuelectenerg-1427	1346	24	a	a	X
fuelectenerg-1427	1346	25	)	)	PUNCT
fuelectenerg-1427	1346	26	ulm	ulm	NOUN
fuelectenerg-1427	1346	27	of	of	ADP
fuelectenerg-1427	1346	28	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	29	)	)	PUNCT
fuelectenerg-1427	1346	30	shannon	shannon	NOUN
fuelectenerg-1427	1346	31	using	use	VERB
fuelectenerg-1427	1346	32	three	three	NUM
fuelectenerg-1427	1346	33	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	34	)	)	PUNCT
fuelectenerg-1427	1346	35	multiplication	multiplication	NOUN
fuelectenerg-1427	1346	36	gates	gate	NOUN
fuelectenerg-1427	1346	37	and	and	CCONJ
fuelectenerg-1427	1346	38	one	one	NUM
fuelectenerg-1427	1346	39	gf(3	gf(3	NOUN
fuelectenerg-1427	1346	40	)	)	PUNCT
fuelectenerg-1427	1346	41	addition	addition	NOUN
fuelectenerg-1427	1346	42	gate	gate	NOUN
fuelectenerg-1427	1346	43	,	,	PUNCT
fuelectenerg-1427	1346	44	(	(	PUNCT
fuelectenerg-1427	1346	45	b	b	X
fuelectenerg-1427	1346	46	)	)	PUNCT
fuelectenerg-1427	1346	47	ulms	ulm	NOUN
fuelectenerg-1427	1346	48	of	of	ADP
fuelectenerg-1427	1346	49	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	50	)	)	PUNCT
fuelectenerg-1427	1346	51	davio	davio	NOUN
fuelectenerg-1427	1346	52	{	{	PUNCT
fuelectenerg-1427	1346	53	d0,d1,d2	d0,d1,d2	PROPN
fuelectenerg-1427	1346	54	}	}	PUNCT
fuelectenerg-1427	1346	55	using	use	VERB
fuelectenerg-1427	1346	56	three	three	NUM
fuelectenerg-1427	1346	57	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	58	)	)	PUNCT
fuelectenerg-1427	1346	59	multiplication	multiplication	NOUN
fuelectenerg-1427	1346	60	gates	gate	NOUN
fuelectenerg-1427	1346	61	and	and	CCONJ
fuelectenerg-1427	1346	62	one	one	NUM
fuelectenerg-1427	1346	63	gf(3	gf(3	NOUN
fuelectenerg-1427	1346	64	)	)	PUNCT
fuelectenerg-1427	1346	65	addition	addition	NOUN
fuelectenerg-1427	1346	66	gate	gate	NOUN
fuelectenerg-1427	1346	67	,	,	PUNCT
fuelectenerg-1427	1346	68	(	(	PUNCT
fuelectenerg-1427	1346	69	c	c	X
fuelectenerg-1427	1346	70	)	)	PUNCT
fuelectenerg-1427	1346	71	ulm	ulm	NOUN
fuelectenerg-1427	1346	72	for	for	ADP
fuelectenerg-1427	1346	73	all	all	DET
fuelectenerg-1427	1346	74	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	75	)	)	PUNCT
fuelectenerg-1427	1346	76	davio	davio	NOUN
fuelectenerg-1427	1346	77	expansions	expansion	NOUN
fuelectenerg-1427	1346	78	using	use	VERB
fuelectenerg-1427	1346	79	four	four	NUM
fuelectenerg-1427	1346	80	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	81	)	)	PUNCT
fuelectenerg-1427	1346	82	multiplication	multiplication	NOUN
fuelectenerg-1427	1346	83	gates	gate	NOUN
fuelectenerg-1427	1346	84	,	,	PUNCT
fuelectenerg-1427	1346	85	one	one	NUM
fuelectenerg-1427	1346	86	gf(3	gf(3	NOUN
fuelectenerg-1427	1346	87	)	)	PUNCT
fuelectenerg-1427	1346	88	addition	addition	NOUN
fuelectenerg-1427	1346	89	gate	gate	NOUN
fuelectenerg-1427	1346	90	,	,	PUNCT
fuelectenerg-1427	1346	91	two	two	NUM
fuelectenerg-1427	1346	92	shift	shift	NOUN
fuelectenerg-1427	1346	93	operators	operator	NOUN
fuelectenerg-1427	1346	94	,	,	PUNCT
fuelectenerg-1427	1346	95	and	and	CCONJ
fuelectenerg-1427	1346	96	one	one	NUM
fuelectenerg-1427	1346	97	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1346	98	,	,	PUNCT
fuelectenerg-1427	1346	99	and	and	CCONJ
fuelectenerg-1427	1346	100	(	(	PUNCT
fuelectenerg-1427	1346	101	d	d	NOUN
fuelectenerg-1427	1346	102	)	)	PUNCT
fuelectenerg-1427	1346	103	general	general	ADJ
fuelectenerg-1427	1346	104	ulm	ulm	NOUN
fuelectenerg-1427	1346	105	of	of	ADP
fuelectenerg-1427	1346	106	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	107	)	)	PUNCT
fuelectenerg-1427	1346	108	s	s	PROPN
fuelectenerg-1427	1346	109	/	/	SYM
fuelectenerg-1427	1346	110	d	d	NOUN
fuelectenerg-1427	1346	111	node	node	NOUN
fuelectenerg-1427	1346	112	using	use	VERB
fuelectenerg-1427	1346	113	four	four	NUM
fuelectenerg-1427	1346	114	gf(3	gf(3	PROPN
fuelectenerg-1427	1346	115	)	)	PUNCT
fuelectenerg-1427	1346	116	multiplication	multiplication	NOUN
fuelectenerg-1427	1346	117	gates	gate	NOUN
fuelectenerg-1427	1346	118	,	,	PUNCT
fuelectenerg-1427	1346	119	one	one	NUM
fuelectenerg-1427	1346	120	gf(3	gf(3	NOUN
fuelectenerg-1427	1346	121	)	)	PUNCT
fuelectenerg-1427	1346	122	addition	addition	NOUN
fuelectenerg-1427	1346	123	gate	gate	NOUN
fuelectenerg-1427	1346	124	and	and	CCONJ
fuelectenerg-1427	1346	125	four	four	NUM
fuelectenerg-1427	1346	126	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1346	127	.	.	PUNCT
fuelectenerg-1427	1347	1	corresponding	correspond	VERB
fuelectenerg-1427	1347	2	if	if	SCONJ
fuelectenerg-1427	1347	3	polarity	polarity	NOUN
fuelectenerg-1427	1347	4	,	,	PUNCT
fuelectenerg-1427	1347	5	which	which	PRON
fuelectenerg-1427	1347	6	contains	contain	VERB
fuelectenerg-1427	1347	7	the	the	DET
fuelectenerg-1427	1347	8	grm	grm	NOUN
fuelectenerg-1427	1347	9	as	as	ADP
fuelectenerg-1427	1347	10	a	a	DET
fuelectenerg-1427	1347	11	special	special	ADJ
fuelectenerg-1427	1347	12	case	case	NOUN
fuelectenerg-1427	1347	13	.	.	PUNCT
fuelectenerg-1427	1348	1	since	since	SCONJ
fuelectenerg-1427	1348	2	universal	universal	ADJ
fuelectenerg-1427	1348	3	logic	logic	NOUN
fuelectenerg-1427	1348	4	modules	module	NOUN
fuelectenerg-1427	1348	5	(	(	PUNCT
fuelectenerg-1427	1348	6	ulms	ulm	NOUN
fuelectenerg-1427	1348	7	)	)	PUNCT
fuelectenerg-1427	1348	8	are	be	AUX
fuelectenerg-1427	1348	9	complete	complete	ADJ
fuelectenerg-1427	1348	10	systems	system	NOUN
fuelectenerg-1427	1348	11	that	that	PRON
fuelectenerg-1427	1348	12	can	can	AUX
fuelectenerg-1427	1348	13	implement	implement	VERB
fuelectenerg-1427	1348	14	all	all	DET
fuelectenerg-1427	1348	15	possible	possible	ADJ
fuelectenerg-1427	1348	16	logic	logic	NOUN
fuelectenerg-1427	1348	17	functions	function	NOUN
fuelectenerg-1427	1348	18	utilizing	utilize	VERB
fuelectenerg-1427	1348	19	s	s	PART
fuelectenerg-1427	1348	20	/	/	SYM
fuelectenerg-1427	1348	21	d	d	NOUN
fuelectenerg-1427	1348	22	expansions	expansion	NOUN
fuelectenerg-1427	1348	23	of	of	ADP
fuelectenerg-1427	1348	24	multiple	multiple	ADV
fuelectenerg-1427	1348	25	-	-	PUNCT
fuelectenerg-1427	1348	26	valued	value	VERB
fuelectenerg-1427	1348	27	shannon	shannon	NOUN
fuelectenerg-1427	1348	28	and	and	CCONJ
fuelectenerg-1427	1348	29	davio	davio	NOUN
fuelectenerg-1427	1348	30	decompositions	decomposition	NOUN
fuelectenerg-1427	1348	31	,	,	PUNCT
fuelectenerg-1427	1348	32	the	the	DET
fuelectenerg-1427	1348	33	realization	realization	NOUN
fuelectenerg-1427	1348	34	of	of	ADP
fuelectenerg-1427	1348	35	the	the	DET
fuelectenerg-1427	1348	36	presented	present	VERB
fuelectenerg-1427	1348	37	s	s	PROPN
fuelectenerg-1427	1348	38	/	/	SYM
fuelectenerg-1427	1348	39	d	d	NOUN
fuelectenerg-1427	1348	40	trees	tree	NOUN
fuelectenerg-1427	1348	41	utilizing	utilize	VERB
fuelectenerg-1427	1348	42	the	the	DET
fuelectenerg-1427	1348	43	corresponding	corresponding	ADJ
fuelectenerg-1427	1348	44	ulms	ulm	NOUN
fuelectenerg-1427	1348	45	is	be	AUX
fuelectenerg-1427	1348	46	also	also	ADV
fuelectenerg-1427	1348	47	introduced	introduce	VERB
fuelectenerg-1427	1348	48	.	.	PUNCT
fuelectenerg-1427	1349	1	the	the	DET
fuelectenerg-1427	1349	2	application	application	NOUN
fuelectenerg-1427	1349	3	of	of	ADP
fuelectenerg-1427	1349	4	the	the	DET
fuelectenerg-1427	1349	5	presented	present	VERB
fuelectenerg-1427	1349	6	tifs	tif	NOUN
fuelectenerg-1427	1349	7	and	and	CCONJ
fuelectenerg-1427	1349	8	tgifs	tgif	NOUN
fuelectenerg-1427	1349	9	can	can	AUX
fuelectenerg-1427	1349	10	be	be	AUX
fuelectenerg-1427	1349	11	used	use	VERB
fuelectenerg-1427	1349	12	to	to	PART
fuelectenerg-1427	1349	13	find	find	VERB
fuelectenerg-1427	1349	14	minimum	minimum	ADJ
fuelectenerg-1427	1349	15	gfsop	gfsop	NOUN
fuelectenerg-1427	1349	16	for	for	ADP
fuelectenerg-1427	1349	17	multiple	multiple	ADV
fuelectenerg-1427	1349	18	-	-	PUNCT
fuelectenerg-1427	1349	19	valued	value	VERB
fuelectenerg-1427	1349	20	inputs	input	NOUN
fuelectenerg-1427	1349	21	-	-	PUNCT
fuelectenerg-1427	1349	22	outputs	output	NOUN
fuelectenerg-1427	1349	23	within	within	ADP
fuelectenerg-1427	1349	24	logic	logic	NOUN
fuelectenerg-1427	1349	25	synthesis	synthesis	NOUN
fuelectenerg-1427	1349	26	,	,	PUNCT
fuelectenerg-1427	1349	27	where	where	SCONJ
fuelectenerg-1427	1349	28	a	a	DET
fuelectenerg-1427	1349	29	gfsop	gfsop	NOUN
fuelectenerg-1427	1349	30	minimizer	minimizer	NOUN
fuelectenerg-1427	1349	31	based	base	VERB
fuelectenerg-1427	1349	32	on	on	ADP
fuelectenerg-1427	1349	33	if	if	SCONJ
fuelectenerg-1427	1349	34	polarity	polarity	NOUN
fuelectenerg-1427	1349	35	can	can	AUX
fuelectenerg-1427	1349	36	be	be	AUX
fuelectenerg-1427	1349	37	used	use	VERB
fuelectenerg-1427	1349	38	to	to	PART
fuelectenerg-1427	1349	39	minimize	minimize	VERB
fuelectenerg-1427	1349	40	the	the	DET
fuelectenerg-1427	1349	41	corresponding	correspond	VERB
fuelectenerg-1427	1349	42	multiple	multiple	ADV
fuelectenerg-1427	1349	43	-	-	PUNCT
fuelectenerg-1427	1349	44	valued	value	VERB
fuelectenerg-1427	1349	45	gfsop	gfsop	NOUN
fuelectenerg-1427	1349	46	expressions	expression	NOUN
fuelectenerg-1427	1349	47	.	.	PUNCT
fuelectenerg-1427	1350	1	115	115	NUM
fuelectenerg-1427	1350	2	an	an	DET
fuelectenerg-1427	1350	3	extended	extend	VERB
fuelectenerg-1427	1350	4	green	green	ADJ
fuelectenerg-1427	1350	5	sasao	sasao	PROPN
fuelectenerg-1427	1350	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1350	7	of	of	ADP
fuelectenerg-1427	1350	8	canonical	canonical	ADJ
fuelectenerg-1427	1350	9	ternary	ternary	ADJ
fuelectenerg-1427	1350	10	galois	galois	NOUN
fuelectenerg-1427	1350	11	forms	form	NOUN
fuelectenerg-1427	1350	12	...	...	PUNCT
fuelectenerg-1427	1351	1	•	•	NUM
fuelectenerg-1427	1351	2	•	•	NOUN
fuelectenerg-1427	1351	3	x	x	SYM
fuelectenerg-1427	1351	4	f0	f0	PROPN
fuelectenerg-1427	1351	5	f2	f2	PROPN
fuelectenerg-1427	1351	6	f1	f1	NOUN
fuelectenerg-1427	1351	7	0x	0x	NOUN
fuelectenerg-1427	1351	8	2	2	NUM
fuelectenerg-1427	1351	9	x	x	SYM
fuelectenerg-1427	1351	10	1	1	NUM
fuelectenerg-1427	1351	11	x	x	SYM
fuelectenerg-1427	1351	12	x	x	NOUN
fuelectenerg-1427	1351	13	f1	f1	NOUN
fuelectenerg-1427	1351	14	f0	f0	PROPN
fuelectenerg-1427	1352	1	+	+	PROPN
fuelectenerg-1427	1352	2	f	f	PROPN
fuelectenerg-1427	1352	3	1	1	NUM
fuelectenerg-1427	1352	4	+	+	NOUN
fuelectenerg-1427	1352	5	f	f	PROPN
fuelectenerg-1427	1352	6	2	2	NUM
fuelectenerg-1427	1352	7	2f2	2f2	NUM
fuelectenerg-1427	1353	1	+	+	NOUN
fuelectenerg-1427	1353	2	f	f	NOUN
fuelectenerg-1427	1353	3	0	0	NUM
fuelectenerg-1427	1353	4	1	1	NUM
fuelectenerg-1427	1353	5	2	2	NUM
fuelectenerg-1427	1353	6	(	(	PUNCT
fuelectenerg-1427	1353	7	”	"	PUNCT
fuelectenerg-1427	1353	8	)	)	PUNCT
fuelectenerg-1427	1353	9	x	x	SYM
fuelectenerg-1427	1353	10	2	2	NUM
fuelectenerg-1427	1353	11	x	x	NOUN
fuelectenerg-1427	1353	12	”	"	PUNCT
fuelectenerg-1427	1353	13	x	x	NUM
fuelectenerg-1427	1353	14	f0	f0	NOUN
fuelectenerg-1427	1353	15	f0	f0	PROPN
fuelectenerg-1427	1354	1	+	+	NOUN
fuelectenerg-1427	1354	2	f	f	PROPN
fuelectenerg-1427	1354	3	1	1	NUM
fuelectenerg-1427	1355	1	+	+	NOUN
fuelectenerg-1427	1355	2	f	f	PROPN
fuelectenerg-1427	1355	3	2	2	NUM
fuelectenerg-1427	1355	4	2f1	2f1	NUM
fuelectenerg-1427	1355	5	+	+	NOUN
fuelectenerg-1427	1355	6	f	f	PROPN
fuelectenerg-1427	1355	7	2	2	NUM
fuelectenerg-1427	1355	8	1	1	NUM
fuelectenerg-1427	1355	9	2	2	NUM
fuelectenerg-1427	1355	10	(	(	PUNCT
fuelectenerg-1427	1355	11	)	)	PUNCT
fuelectenerg-1427	1355	12	x	x	SYM
fuelectenerg-1427	1355	13	2	2	NUM
fuelectenerg-1427	1355	14	x	x	SYM
fuelectenerg-1427	1355	15	2	2	NUM
fuelectenerg-1427	1355	16	(	(	PUNCT
fuelectenerg-1427	1355	17	’	'	PUNCT
fuelectenerg-1427	1355	18	)	)	PUNCT
fuelectenerg-1427	1355	19	x	x	SYM
fuelectenerg-1427	1355	20	2	2	NUM
fuelectenerg-1427	1355	21	x	x	SYM
fuelectenerg-1427	1355	22	f2	f2	PROPN
fuelectenerg-1427	1355	23	f0	f0	PROPN
fuelectenerg-1427	1356	1	+	+	PROPN
fuelectenerg-1427	1356	2	f	f	PROPN
fuelectenerg-1427	1356	3	1	1	NUM
fuelectenerg-1427	1356	4	+	+	NOUN
fuelectenerg-1427	1356	5	f	f	PROPN
fuelectenerg-1427	1356	6	2	2	NUM
fuelectenerg-1427	1356	7	2f0	2f0	NUM
fuelectenerg-1427	1356	8	+	+	NOUN
fuelectenerg-1427	1356	9	f	f	NOUN
fuelectenerg-1427	1356	10	1	1	NUM
fuelectenerg-1427	1356	11	1	1	NUM
fuelectenerg-1427	1356	12	x	x	NOUN
fuelectenerg-1427	1356	13	’	'	PUNCT
fuelectenerg-1427	1357	1	+	+	PROPN
fuelectenerg-1427	1358	1	+	+	PUNCT
fuelectenerg-1427	1358	2	+	+	PUNCT
fuelectenerg-1427	1359	1	+	+	PUNCT
fuelectenerg-1427	1359	2	+	+	SYM
fuelectenerg-1427	1359	3	0	0	NUM
fuelectenerg-1427	1359	4	x	x	SYM
fuelectenerg-1427	1359	5	1	1	NUM
fuelectenerg-1427	1359	6	1	1	NUM
fuelectenerg-1427	1359	7	x	x	SYM
fuelectenerg-1427	1359	8	2	2	NUM
fuelectenerg-1427	1359	9	x	x	SYM
fuelectenerg-1427	1359	10	2	2	NUM
fuelectenerg-1427	1359	11	x	x	SYM
fuelectenerg-1427	1359	12	x	x	NOUN
fuelectenerg-1427	1359	13	’	'	PUNCT
fuelectenerg-1427	1359	14	x	x	ADJ
fuelectenerg-1427	1359	15	”	"	PUNCT
fuelectenerg-1427	1359	16	fi	fi	NOUN
fuelectenerg-1427	1359	17	fk	fk	INTJ
fuelectenerg-1427	1360	1	fj	fj	INTJ
fuelectenerg-1427	1360	2	f	f	NOUN
fuelectenerg-1427	1360	3	x	x	SYM
fuelectenerg-1427	1360	4	1	1	NUM
fuelectenerg-1427	1360	5	2	2	NUM
fuelectenerg-1427	1360	6	�	�	PROPN
fuelectenerg-1427	1360	7	�	�	PROPN
fuelectenerg-1427	1360	8	�	�	PROPN
fuelectenerg-1427	1360	9	�	�	PROPN
fuelectenerg-1427	1360	10	�	�	PROPN
fuelectenerg-1427	1360	11	�	�	PROPN
fuelectenerg-1427	1360	12	�	�	PROPN
fuelectenerg-1427	1360	13	+	+	CCONJ
fuelectenerg-1427	1360	14	+1	+1	PROPN
fuelectenerg-1427	1361	1	fi	fi	NOUN
fuelectenerg-1427	1361	2	fk	fk	INTJ
fuelectenerg-1427	1362	1	fj	fj	INTJ
fuelectenerg-1427	1362	2	f	f	PROPN
fuelectenerg-1427	1362	3	+1	+1	PROPN
fuelectenerg-1427	1362	4	(	(	PUNCT
fuelectenerg-1427	1362	5	a	a	NOUN
fuelectenerg-1427	1362	6	)	)	PUNCT
fuelectenerg-1427	1362	7	(	(	PUNCT
fuelectenerg-1427	1362	8	b	b	X
fuelectenerg-1427	1362	9	)	)	PUNCT
fuelectenerg-1427	1362	10	(	(	PUNCT
fuelectenerg-1427	1362	11	c	c	X
fuelectenerg-1427	1362	12	)	)	PUNCT
fuelectenerg-1427	1362	13	(	(	PUNCT
fuelectenerg-1427	1362	14	d	d	X
fuelectenerg-1427	1362	15	)	)	PUNCT
fuelectenerg-1427	1362	16	figure	figure	NOUN
fuelectenerg-1427	1362	17	7	7	NUM
fuelectenerg-1427	1362	18	:	:	PUNCT
fuelectenerg-1427	1362	19	various	various	ADJ
fuelectenerg-1427	1362	20	ternary	ternary	ADJ
fuelectenerg-1427	1362	21	ulms	ulm	NOUN
fuelectenerg-1427	1362	22	:	:	PUNCT
fuelectenerg-1427	1362	23	(	(	PUNCT
fuelectenerg-1427	1362	24	a	a	X
fuelectenerg-1427	1362	25	)	)	PUNCT
fuelectenerg-1427	1362	26	ulm	ulm	NOUN
fuelectenerg-1427	1362	27	of	of	ADP
fuelectenerg-1427	1362	28	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	29	)	)	PUNCT
fuelectenerg-1427	1362	30	shannon	shannon	NOUN
fuelectenerg-1427	1362	31	using	use	VERB
fuelectenerg-1427	1362	32	three	three	NUM
fuelectenerg-1427	1362	33	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	34	)	)	PUNCT
fuelectenerg-1427	1362	35	multiplication	multiplication	NOUN
fuelectenerg-1427	1362	36	gates	gate	NOUN
fuelectenerg-1427	1362	37	and	and	CCONJ
fuelectenerg-1427	1362	38	one	one	NUM
fuelectenerg-1427	1362	39	gf(3	gf(3	NOUN
fuelectenerg-1427	1362	40	)	)	PUNCT
fuelectenerg-1427	1362	41	addition	addition	NOUN
fuelectenerg-1427	1362	42	gate	gate	NOUN
fuelectenerg-1427	1362	43	,	,	PUNCT
fuelectenerg-1427	1362	44	(	(	PUNCT
fuelectenerg-1427	1362	45	b	b	X
fuelectenerg-1427	1362	46	)	)	PUNCT
fuelectenerg-1427	1362	47	ulms	ulm	NOUN
fuelectenerg-1427	1362	48	of	of	ADP
fuelectenerg-1427	1362	49	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	50	)	)	PUNCT
fuelectenerg-1427	1362	51	davio	davio	NOUN
fuelectenerg-1427	1362	52	{	{	PUNCT
fuelectenerg-1427	1362	53	d0,d1,d2	d0,d1,d2	PROPN
fuelectenerg-1427	1362	54	}	}	PUNCT
fuelectenerg-1427	1362	55	using	use	VERB
fuelectenerg-1427	1362	56	three	three	NUM
fuelectenerg-1427	1362	57	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	58	)	)	PUNCT
fuelectenerg-1427	1362	59	multiplication	multiplication	NOUN
fuelectenerg-1427	1362	60	gates	gate	NOUN
fuelectenerg-1427	1362	61	and	and	CCONJ
fuelectenerg-1427	1362	62	one	one	NUM
fuelectenerg-1427	1362	63	gf(3	gf(3	NOUN
fuelectenerg-1427	1362	64	)	)	PUNCT
fuelectenerg-1427	1362	65	addition	addition	NOUN
fuelectenerg-1427	1362	66	gate	gate	NOUN
fuelectenerg-1427	1362	67	,	,	PUNCT
fuelectenerg-1427	1362	68	(	(	PUNCT
fuelectenerg-1427	1362	69	c	c	X
fuelectenerg-1427	1362	70	)	)	PUNCT
fuelectenerg-1427	1362	71	ulm	ulm	NOUN
fuelectenerg-1427	1362	72	for	for	ADP
fuelectenerg-1427	1362	73	all	all	DET
fuelectenerg-1427	1362	74	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	75	)	)	PUNCT
fuelectenerg-1427	1362	76	davio	davio	NOUN
fuelectenerg-1427	1362	77	expansions	expansion	NOUN
fuelectenerg-1427	1362	78	using	use	VERB
fuelectenerg-1427	1362	79	four	four	NUM
fuelectenerg-1427	1362	80	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	81	)	)	PUNCT
fuelectenerg-1427	1362	82	multiplication	multiplication	NOUN
fuelectenerg-1427	1362	83	gates	gate	NOUN
fuelectenerg-1427	1362	84	,	,	PUNCT
fuelectenerg-1427	1362	85	one	one	NUM
fuelectenerg-1427	1362	86	gf(3	gf(3	NOUN
fuelectenerg-1427	1362	87	)	)	PUNCT
fuelectenerg-1427	1362	88	addition	addition	NOUN
fuelectenerg-1427	1362	89	gate	gate	NOUN
fuelectenerg-1427	1362	90	,	,	PUNCT
fuelectenerg-1427	1362	91	two	two	NUM
fuelectenerg-1427	1362	92	shift	shift	NOUN
fuelectenerg-1427	1362	93	operators	operator	NOUN
fuelectenerg-1427	1362	94	,	,	PUNCT
fuelectenerg-1427	1362	95	and	and	CCONJ
fuelectenerg-1427	1362	96	one	one	NUM
fuelectenerg-1427	1362	97	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1362	98	,	,	PUNCT
fuelectenerg-1427	1362	99	and	and	CCONJ
fuelectenerg-1427	1362	100	(	(	PUNCT
fuelectenerg-1427	1362	101	d	d	NOUN
fuelectenerg-1427	1362	102	)	)	PUNCT
fuelectenerg-1427	1362	103	general	general	ADJ
fuelectenerg-1427	1362	104	ulm	ulm	NOUN
fuelectenerg-1427	1362	105	of	of	ADP
fuelectenerg-1427	1362	106	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	107	)	)	PUNCT
fuelectenerg-1427	1362	108	s	s	PROPN
fuelectenerg-1427	1362	109	/	/	SYM
fuelectenerg-1427	1362	110	d	d	NOUN
fuelectenerg-1427	1362	111	node	node	NOUN
fuelectenerg-1427	1362	112	using	use	VERB
fuelectenerg-1427	1362	113	four	four	NUM
fuelectenerg-1427	1362	114	gf(3	gf(3	PROPN
fuelectenerg-1427	1362	115	)	)	PUNCT
fuelectenerg-1427	1362	116	multiplication	multiplication	NOUN
fuelectenerg-1427	1362	117	gates	gate	NOUN
fuelectenerg-1427	1362	118	,	,	PUNCT
fuelectenerg-1427	1362	119	one	one	NUM
fuelectenerg-1427	1362	120	gf(3	gf(3	NOUN
fuelectenerg-1427	1362	121	)	)	PUNCT
fuelectenerg-1427	1362	122	addition	addition	NOUN
fuelectenerg-1427	1362	123	gate	gate	NOUN
fuelectenerg-1427	1362	124	and	and	CCONJ
fuelectenerg-1427	1362	125	four	four	NUM
fuelectenerg-1427	1362	126	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1362	127	.	.	PUNCT
fuelectenerg-1427	1363	1	corresponding	correspond	VERB
fuelectenerg-1427	1363	2	if	if	SCONJ
fuelectenerg-1427	1363	3	polarity	polarity	NOUN
fuelectenerg-1427	1363	4	,	,	PUNCT
fuelectenerg-1427	1363	5	which	which	PRON
fuelectenerg-1427	1363	6	contains	contain	VERB
fuelectenerg-1427	1363	7	the	the	DET
fuelectenerg-1427	1363	8	grm	grm	NOUN
fuelectenerg-1427	1363	9	as	as	ADP
fuelectenerg-1427	1363	10	a	a	DET
fuelectenerg-1427	1363	11	special	special	ADJ
fuelectenerg-1427	1363	12	case	case	NOUN
fuelectenerg-1427	1363	13	.	.	PUNCT
fuelectenerg-1427	1364	1	since	since	SCONJ
fuelectenerg-1427	1364	2	universal	universal	ADJ
fuelectenerg-1427	1364	3	logic	logic	NOUN
fuelectenerg-1427	1364	4	modules	module	NOUN
fuelectenerg-1427	1364	5	(	(	PUNCT
fuelectenerg-1427	1364	6	ulms	ulm	NOUN
fuelectenerg-1427	1364	7	)	)	PUNCT
fuelectenerg-1427	1364	8	are	be	AUX
fuelectenerg-1427	1364	9	complete	complete	ADJ
fuelectenerg-1427	1364	10	systems	system	NOUN
fuelectenerg-1427	1364	11	that	that	PRON
fuelectenerg-1427	1364	12	can	can	AUX
fuelectenerg-1427	1364	13	implement	implement	VERB
fuelectenerg-1427	1364	14	all	all	DET
fuelectenerg-1427	1364	15	possible	possible	ADJ
fuelectenerg-1427	1364	16	logic	logic	NOUN
fuelectenerg-1427	1364	17	functions	function	NOUN
fuelectenerg-1427	1364	18	utilizing	utilize	VERB
fuelectenerg-1427	1364	19	s	s	PART
fuelectenerg-1427	1364	20	/	/	SYM
fuelectenerg-1427	1364	21	d	d	NOUN
fuelectenerg-1427	1364	22	expansions	expansion	NOUN
fuelectenerg-1427	1364	23	of	of	ADP
fuelectenerg-1427	1364	24	multiple	multiple	ADV
fuelectenerg-1427	1364	25	-	-	PUNCT
fuelectenerg-1427	1364	26	valued	value	VERB
fuelectenerg-1427	1364	27	shannon	shannon	NOUN
fuelectenerg-1427	1364	28	and	and	CCONJ
fuelectenerg-1427	1364	29	davio	davio	NOUN
fuelectenerg-1427	1364	30	decompositions	decomposition	NOUN
fuelectenerg-1427	1364	31	,	,	PUNCT
fuelectenerg-1427	1364	32	the	the	DET
fuelectenerg-1427	1364	33	realization	realization	NOUN
fuelectenerg-1427	1364	34	of	of	ADP
fuelectenerg-1427	1364	35	the	the	DET
fuelectenerg-1427	1364	36	presented	present	VERB
fuelectenerg-1427	1364	37	s	s	PROPN
fuelectenerg-1427	1364	38	/	/	SYM
fuelectenerg-1427	1364	39	d	d	NOUN
fuelectenerg-1427	1364	40	trees	tree	NOUN
fuelectenerg-1427	1364	41	utilizing	utilize	VERB
fuelectenerg-1427	1364	42	the	the	DET
fuelectenerg-1427	1364	43	corresponding	corresponding	ADJ
fuelectenerg-1427	1364	44	ulms	ulm	NOUN
fuelectenerg-1427	1364	45	is	be	AUX
fuelectenerg-1427	1364	46	also	also	ADV
fuelectenerg-1427	1364	47	introduced	introduce	VERB
fuelectenerg-1427	1364	48	.	.	PUNCT
fuelectenerg-1427	1365	1	the	the	DET
fuelectenerg-1427	1365	2	application	application	NOUN
fuelectenerg-1427	1365	3	of	of	ADP
fuelectenerg-1427	1365	4	the	the	DET
fuelectenerg-1427	1365	5	presented	present	VERB
fuelectenerg-1427	1365	6	tifs	tif	NOUN
fuelectenerg-1427	1365	7	and	and	CCONJ
fuelectenerg-1427	1365	8	tgifs	tgif	NOUN
fuelectenerg-1427	1365	9	can	can	AUX
fuelectenerg-1427	1365	10	be	be	AUX
fuelectenerg-1427	1365	11	used	use	VERB
fuelectenerg-1427	1365	12	to	to	PART
fuelectenerg-1427	1365	13	find	find	VERB
fuelectenerg-1427	1365	14	minimum	minimum	ADJ
fuelectenerg-1427	1365	15	gfsop	gfsop	NOUN
fuelectenerg-1427	1365	16	for	for	ADP
fuelectenerg-1427	1365	17	multiple	multiple	ADV
fuelectenerg-1427	1365	18	-	-	PUNCT
fuelectenerg-1427	1365	19	valued	value	VERB
fuelectenerg-1427	1365	20	inputs	input	NOUN
fuelectenerg-1427	1365	21	-	-	PUNCT
fuelectenerg-1427	1365	22	outputs	output	NOUN
fuelectenerg-1427	1365	23	within	within	ADP
fuelectenerg-1427	1365	24	logic	logic	NOUN
fuelectenerg-1427	1365	25	synthesis	synthesis	NOUN
fuelectenerg-1427	1365	26	,	,	PUNCT
fuelectenerg-1427	1365	27	where	where	SCONJ
fuelectenerg-1427	1365	28	a	a	DET
fuelectenerg-1427	1365	29	gfsop	gfsop	NOUN
fuelectenerg-1427	1365	30	minimizer	minimizer	NOUN
fuelectenerg-1427	1365	31	based	base	VERB
fuelectenerg-1427	1365	32	on	on	ADP
fuelectenerg-1427	1365	33	if	if	SCONJ
fuelectenerg-1427	1365	34	polarity	polarity	NOUN
fuelectenerg-1427	1365	35	can	can	AUX
fuelectenerg-1427	1365	36	be	be	AUX
fuelectenerg-1427	1365	37	used	use	VERB
fuelectenerg-1427	1365	38	to	to	PART
fuelectenerg-1427	1365	39	minimize	minimize	VERB
fuelectenerg-1427	1365	40	the	the	DET
fuelectenerg-1427	1365	41	corresponding	correspond	VERB
fuelectenerg-1427	1365	42	multiple	multiple	ADV
fuelectenerg-1427	1365	43	-	-	PUNCT
fuelectenerg-1427	1365	44	valued	value	VERB
fuelectenerg-1427	1365	45	gfsop	gfsop	NOUN
fuelectenerg-1427	1365	46	expressions	expression	NOUN
fuelectenerg-1427	1365	47	.	.	PUNCT
fuelectenerg-1427	1366	1	115	115	NUM
fuelectenerg-1427	1366	2	62	62	NUM
fuelectenerg-1427	1366	3	a.	a.	NOUN
fuelectenerg-1427	1366	4	n.	n.	PROPN
fuelectenerg-1427	1366	5	al	al	PROPN
fuelectenerg-1427	1366	6	-	-	PUNCT
fuelectenerg-1427	1366	7	rabadi	rabadi	VERB
fuelectenerg-1427	1366	8	an	an	DET
fuelectenerg-1427	1366	9	extended	extended	ADJ
fuelectenerg-1427	1366	10	green	green	ADJ
fuelectenerg-1427	1366	11	sasao	sasao	PROPN
fuelectenerg-1427	1366	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1366	13	of	of	ADP
fuelectenerg-1427	1366	14	canonical	canonical	ADJ
fuelectenerg-1427	1366	15	ternary	ternary	ADJ
fuelectenerg-1427	1366	16	galois	galois	NOUN
fuelectenerg-1427	1366	17	forms	form	NOUN
fuelectenerg-1427	1366	18	and	and	CCONJ
fuelectenerg-1427	1366	19	universal	universal	ADJ
fuelectenerg-1427	1366	20	logic	logic	NOUN
fuelectenerg-1427	1366	21	modules	module	NOUN
fuelectenerg-1427	1366	22	63	63	NUM
fuelectenerg-1427	1366	23	an	an	DET
fuelectenerg-1427	1366	24	extended	extended	ADJ
fuelectenerg-1427	1366	25	green	green	ADJ
fuelectenerg-1427	1366	26	sasao	sasao	PROPN
fuelectenerg-1427	1366	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1366	28	of	of	ADP
fuelectenerg-1427	1366	29	canonical	canonical	ADJ
fuelectenerg-1427	1366	30	ternary	ternary	ADJ
fuelectenerg-1427	1366	31	galois	galois	NOUN
fuelectenerg-1427	1366	32	forms	form	NOUN
fuelectenerg-1427	1366	33	...	...	PUNCT
fuelectenerg-1427	1366	34	3	3	NUM
fuelectenerg-1427	1366	35	universal	universal	ADJ
fuelectenerg-1427	1366	36	logic	logic	NOUN
fuelectenerg-1427	1366	37	modules	module	NOUN
fuelectenerg-1427	1366	38	for	for	ADP
fuelectenerg-1427	1366	39	the	the	DET
fuelectenerg-1427	1366	40	circuit	circuit	NOUN
fuelectenerg-1427	1366	41	realization	realization	NOUN
fuelectenerg-1427	1366	42	of	of	ADP
fuelectenerg-1427	1366	43	s	s	PROPN
fuelectenerg-1427	1366	44	/	/	SYM
fuelectenerg-1427	1366	45	d	d	NOUN
fuelectenerg-1427	1366	46	trees	tree	NOUN
fuelectenerg-1427	1366	47	the	the	DET
fuelectenerg-1427	1366	48	nonsingular	nonsingular	ADJ
fuelectenerg-1427	1366	49	expansions	expansion	NOUN
fuelectenerg-1427	1366	50	of	of	ADP
fuelectenerg-1427	1366	51	ternary	ternary	ADJ
fuelectenerg-1427	1366	52	shannon	shannon	NOUN
fuelectenerg-1427	1366	53	(	(	PUNCT
fuelectenerg-1427	1366	54	s	s	NOUN
fuelectenerg-1427	1366	55	)	)	PUNCT
fuelectenerg-1427	1366	56	and	and	CCONJ
fuelectenerg-1427	1366	57	ternary	ternary	ADJ
fuelectenerg-1427	1366	58	davio	davio	NOUN
fuelectenerg-1427	1366	59	(	(	PUNCT
fuelectenerg-1427	1366	60	d0	d0	NOUN
fuelectenerg-1427	1366	61	,	,	PUNCT
fuelectenerg-1427	1366	62	d1	d1	PROPN
fuelectenerg-1427	1366	63	and	and	CCONJ
fuelectenerg-1427	1366	64	d2	d2	PROPN
fuelectenerg-1427	1366	65	)	)	PUNCT
fuelectenerg-1427	1366	66	,	,	PUNCT
fuelectenerg-1427	1366	67	can	can	AUX
fuelectenerg-1427	1366	68	be	be	AUX
fuelectenerg-1427	1366	69	realized	realize	VERB
fuelectenerg-1427	1366	70	using	use	VERB
fuelectenerg-1427	1366	71	a	a	DET
fuelectenerg-1427	1366	72	universal	universal	ADJ
fuelectenerg-1427	1366	73	logic	logic	NOUN
fuelectenerg-1427	1366	74	module	module	NOUN
fuelectenerg-1427	1366	75	(	(	PUNCT
fuelectenerg-1427	1366	76	ulm	ulm	PROPN
fuelectenerg-1427	1366	77	)	)	PUNCT
fuelectenerg-1427	1366	78	with	with	ADP
fuelectenerg-1427	1366	79	control	control	NOUN
fuelectenerg-1427	1366	80	variables	variable	NOUN
fuelectenerg-1427	1366	81	corresponding	correspond	VERB
fuelectenerg-1427	1366	82	to	to	ADP
fuelectenerg-1427	1366	83	the	the	DET
fuelectenerg-1427	1366	84	variables	variable	NOUN
fuelectenerg-1427	1366	85	of	of	ADP
fuelectenerg-1427	1366	86	the	the	DET
fuelectenerg-1427	1366	87	basis	basis	NOUN
fuelectenerg-1427	1366	88	functions	function	NOUN
fuelectenerg-1427	1366	89	which	which	PRON
fuelectenerg-1427	1366	90	are	be	AUX
fuelectenerg-1427	1366	91	the	the	DET
fuelectenerg-1427	1366	92	variables	variable	NOUN
fuelectenerg-1427	1366	93	we	we	PRON
fuelectenerg-1427	1366	94	are	be	AUX
fuelectenerg-1427	1366	95	expanding	expand	VERB
fuelectenerg-1427	1366	96	upon	upon	SCONJ
fuelectenerg-1427	1366	97	.	.	PUNCT
fuelectenerg-1427	1367	1	we	we	PRON
fuelectenerg-1427	1367	2	call	call	VERB
fuelectenerg-1427	1367	3	it	it	PRON
fuelectenerg-1427	1367	4	a	a	DET
fuelectenerg-1427	1367	5	universal	universal	ADJ
fuelectenerg-1427	1367	6	logic	logic	NOUN
fuelectenerg-1427	1367	7	module	module	NOUN
fuelectenerg-1427	1367	8	,	,	PUNCT
fuelectenerg-1427	1367	9	because	because	SCONJ
fuelectenerg-1427	1367	10	similarly	similarly	ADV
fuelectenerg-1427	1367	11	to	to	ADP
fuelectenerg-1427	1367	12	a	a	DET
fuelectenerg-1427	1367	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1367	14	,	,	PUNCT
fuelectenerg-1427	1367	15	all	all	DET
fuelectenerg-1427	1367	16	functions	function	NOUN
fuelectenerg-1427	1367	17	of	of	ADP
fuelectenerg-1427	1367	18	two	two	NUM
fuelectenerg-1427	1367	19	variables	variable	NOUN
fuelectenerg-1427	1367	20	can	can	AUX
fuelectenerg-1427	1367	21	be	be	AUX
fuelectenerg-1427	1367	22	realized	realize	VERB
fuelectenerg-1427	1367	23	with	with	ADP
fuelectenerg-1427	1367	24	two	two	NUM
fuelectenerg-1427	1367	25	-	-	PUNCT
fuelectenerg-1427	1367	26	level	level	NOUN
fuelectenerg-1427	1367	27	trees	tree	NOUN
fuelectenerg-1427	1367	28	of	of	ADP
fuelectenerg-1427	1367	29	such	such	ADJ
fuelectenerg-1427	1367	30	modules	module	NOUN
fuelectenerg-1427	1367	31	using	use	VERB
fuelectenerg-1427	1367	32	constants	constant	NOUN
fuelectenerg-1427	1367	33	on	on	ADP
fuelectenerg-1427	1367	34	the	the	DET
fuelectenerg-1427	1367	35	second	second	ADJ
fuelectenerg-1427	1367	36	-	-	PUNCT
fuelectenerg-1427	1367	37	level	level	NOUN
fuelectenerg-1427	1367	38	data	datum	NOUN
fuelectenerg-1427	1367	39	inputs	input	NOUN
fuelectenerg-1427	1367	40	.	.	PUNCT
fuelectenerg-1427	1368	1	the	the	DET
fuelectenerg-1427	1368	2	presented	present	VERB
fuelectenerg-1427	1368	3	ulms	ulm	NOUN
fuelectenerg-1427	1368	4	are	be	AUX
fuelectenerg-1427	1368	5	complete	complete	ADJ
fuelectenerg-1427	1368	6	systems	system	NOUN
fuelectenerg-1427	1368	7	because	because	SCONJ
fuelectenerg-1427	1368	8	they	they	PRON
fuelectenerg-1427	1368	9	can	can	AUX
fuelectenerg-1427	1368	10	implement	implement	VERB
fuelectenerg-1427	1368	11	all	all	DET
fuelectenerg-1427	1368	12	possible	possible	ADJ
fuelectenerg-1427	1368	13	functions	function	NOUN
fuelectenerg-1427	1368	14	with	with	ADP
fuelectenerg-1427	1368	15	certain	certain	ADJ
fuelectenerg-1427	1368	16	number	number	NOUN
fuelectenerg-1427	1368	17	of	of	ADP
fuelectenerg-1427	1368	18	variables	variable	NOUN
fuelectenerg-1427	1368	19	.	.	PUNCT
fuelectenerg-1427	1369	1	the	the	DET
fuelectenerg-1427	1369	2	concept	concept	NOUN
fuelectenerg-1427	1369	3	of	of	ADP
fuelectenerg-1427	1369	4	the	the	DET
fuelectenerg-1427	1369	5	universal	universal	ADJ
fuelectenerg-1427	1369	6	logic	logic	NOUN
fuelectenerg-1427	1369	7	module	module	NOUN
fuelectenerg-1427	1369	8	was	be	AUX
fuelectenerg-1427	1369	9	used	use	VERB
fuelectenerg-1427	1369	10	for	for	ADP
fuelectenerg-1427	1369	11	binary	binary	PROPN
fuelectenerg-1427	1369	12	rm	rm	PROPN
fuelectenerg-1427	1369	13	logic	logic	PROPN
fuelectenerg-1427	1369	14	over	over	ADP
fuelectenerg-1427	1369	15	gf(2	gf(2	PROPN
fuelectenerg-1427	1369	16	)	)	PUNCT
fuelectenerg-1427	1369	17	,	,	PUNCT
fuelectenerg-1427	1369	18	as	as	ADV
fuelectenerg-1427	1369	19	well	well	ADV
fuelectenerg-1427	1369	20	as	as	ADP
fuelectenerg-1427	1369	21	the	the	DET
fuelectenerg-1427	1369	22	general	general	ADJ
fuelectenerg-1427	1369	23	case	case	NOUN
fuelectenerg-1427	1369	24	of	of	ADP
fuelectenerg-1427	1369	25	linearly	linearly	ADV
fuelectenerg-1427	1369	26	independent	independent	ADJ
fuelectenerg-1427	1369	27	(	(	PUNCT
fuelectenerg-1427	1369	28	li	li	NOUN
fuelectenerg-1427	1369	29	)	)	PUNCT
fuelectenerg-1427	1369	30	logic	logic	NOUN
fuelectenerg-1427	1369	31	that	that	PRON
fuelectenerg-1427	1369	32	includes	include	VERB
fuelectenerg-1427	1369	33	rm	rm	NOUN
fuelectenerg-1427	1369	34	logic	logic	NOUN
fuelectenerg-1427	1369	35	as	as	ADP
fuelectenerg-1427	1369	36	a	a	DET
fuelectenerg-1427	1369	37	special	special	ADJ
fuelectenerg-1427	1369	38	case	case	NOUN
fuelectenerg-1427	1369	39	.	.	PUNCT
fuelectenerg-1427	1370	1	binary	binary	PROPN
fuelectenerg-1427	1370	2	li	li	PROPN
fuelectenerg-1427	1370	3	logic	logic	PROPN
fuelectenerg-1427	1370	4	extended	extend	VERB
fuelectenerg-1427	1370	5	the	the	DET
fuelectenerg-1427	1370	6	universal	universal	ADJ
fuelectenerg-1427	1370	7	logic	logic	NOUN
fuelectenerg-1427	1370	8	module	module	NOUN
fuelectenerg-1427	1370	9	from	from	ADP
fuelectenerg-1427	1370	10	just	just	ADV
fuelectenerg-1427	1370	11	being	be	AUX
fuelectenerg-1427	1370	12	a	a	DET
fuelectenerg-1427	1370	13	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1370	14	(	(	PUNCT
fuelectenerg-1427	1370	15	shannon	shannon	PROPN
fuelectenerg-1427	1370	16	expansion	expansion	PROPN
fuelectenerg-1427	1370	17	)	)	PUNCT
fuelectenerg-1427	1370	18	,	,	PUNCT
fuelectenerg-1427	1370	19	and	and	CCONJ
fuelectenerg-1427	1370	20	/	/	SYM
fuelectenerg-1427	1370	21	exor	exor	PROPN
fuelectenerg-1427	1370	22	gate	gate	PROPN
fuelectenerg-1427	1370	23	(	(	PUNCT
fuelectenerg-1427	1370	24	positive	positive	ADJ
fuelectenerg-1427	1370	25	davio	davio	NOUN
fuelectenerg-1427	1370	26	expansion	expansion	NOUN
fuelectenerg-1427	1370	27	)	)	PUNCT
fuelectenerg-1427	1370	28	and	and	CCONJ
fuelectenerg-1427	1370	29	and	and	CCONJ
fuelectenerg-1427	1370	30	/	/	SYM
fuelectenerg-1427	1370	31	exor	exor	PROPN
fuelectenerg-1427	1370	32	/	/	SYM
fuelectenerg-1427	1370	33	not	not	PART
fuelectenerg-1427	1370	34	gate	gate	VERB
fuelectenerg-1427	1370	35	with	with	ADP
fuelectenerg-1427	1370	36	inverted	inverted	ADJ
fuelectenerg-1427	1370	37	control	control	NOUN
fuelectenerg-1427	1370	38	variable	variable	NOUN
fuelectenerg-1427	1370	39	(	(	PUNCT
fuelectenerg-1427	1370	40	negative	negative	ADJ
fuelectenerg-1427	1370	41	davio	davio	NOUN
fuelectenerg-1427	1370	42	expansion	expansion	NOUN
fuelectenerg-1427	1370	43	)	)	PUNCT
fuelectenerg-1427	1370	44	,	,	PUNCT
fuelectenerg-1427	1370	45	to	to	ADP
fuelectenerg-1427	1370	46	the	the	DET
fuelectenerg-1427	1370	47	universal	universal	ADJ
fuelectenerg-1427	1370	48	logic	logic	NOUN
fuelectenerg-1427	1370	49	modules	module	NOUN
fuelectenerg-1427	1370	50	for	for	ADP
fuelectenerg-1427	1370	51	any	any	DET
fuelectenerg-1427	1370	52	expansion	expansion	NOUN
fuelectenerg-1427	1370	53	over	over	ADP
fuelectenerg-1427	1370	54	any	any	DET
fuelectenerg-1427	1370	55	linearly	linearly	ADV
fuelectenerg-1427	1370	56	independent	independent	ADJ
fuelectenerg-1427	1370	57	basis	basis	NOUN
fuelectenerg-1427	1370	58	functions	function	NOUN
fuelectenerg-1427	1370	59	.	.	PUNCT
fuelectenerg-1427	1371	1	analogously	analogously	ADV
fuelectenerg-1427	1371	2	to	to	ADP
fuelectenerg-1427	1371	3	the	the	DET
fuelectenerg-1427	1371	4	binary	binary	ADJ
fuelectenerg-1427	1371	5	case	case	NOUN
fuelectenerg-1427	1371	6	,	,	PUNCT
fuelectenerg-1427	1371	7	figure	figure	VERB
fuelectenerg-1427	1371	8	7	7	NUM
fuelectenerg-1427	1371	9	presents	present	VERB
fuelectenerg-1427	1371	10	universal	universal	ADJ
fuelectenerg-1427	1371	11	logic	logic	NOUN
fuelectenerg-1427	1371	12	modules	module	NOUN
fuelectenerg-1427	1371	13	for	for	ADP
fuelectenerg-1427	1371	14	ternary	ternary	ADJ
fuelectenerg-1427	1371	15	shannon	shannon	NOUN
fuelectenerg-1427	1371	16	and	and	CCONJ
fuelectenerg-1427	1371	17	ternary	ternary	ADJ
fuelectenerg-1427	1371	18	davio	davio	NOUN
fuelectenerg-1427	1371	19	,	,	PUNCT
fuelectenerg-1427	1371	20	respectively	respectively	ADV
fuelectenerg-1427	1371	21	.	.	PUNCT
fuelectenerg-1427	1372	1	one	one	PRON
fuelectenerg-1427	1372	2	can	can	AUX
fuelectenerg-1427	1372	3	note	note	VERB
fuelectenerg-1427	1372	4	,	,	PUNCT
fuelectenerg-1427	1372	5	that	that	SCONJ
fuelectenerg-1427	1372	6	any	any	DET
fuelectenerg-1427	1372	7	function	function	NOUN
fuelectenerg-1427	1372	8	f	f	PROPN
fuelectenerg-1427	1372	9	can	can	AUX
fuelectenerg-1427	1372	10	be	be	AUX
fuelectenerg-1427	1372	11	produced	produce	VERB
fuelectenerg-1427	1372	12	by	by	ADP
fuelectenerg-1427	1372	13	the	the	DET
fuelectenerg-1427	1372	14	application	application	NOUN
fuelectenerg-1427	1372	15	of	of	ADP
fuelectenerg-1427	1372	16	the	the	DET
fuelectenerg-1427	1372	17	independent	independent	ADJ
fuelectenerg-1427	1372	18	variable	variable	NOUN
fuelectenerg-1427	1372	19	x	x	PUNCT
fuelectenerg-1427	1372	20	and	and	CCONJ
fuelectenerg-1427	1372	21	the	the	DET
fuelectenerg-1427	1372	22	cofactors	cofactor	NOUN
fuelectenerg-1427	1372	23	{	{	PUNCT
fuelectenerg-1427	1372	24	fi	fi	NOUN
fuelectenerg-1427	1372	25	,	,	PUNCT
fuelectenerg-1427	1372	26	f	f	PROPN
fuelectenerg-1427	1372	27	j	j	PROPN
fuelectenerg-1427	1372	28	and	and	CCONJ
fuelectenerg-1427	1372	29	fk	fk	INTJ
fuelectenerg-1427	1372	30	}	}	PUNCT
fuelectenerg-1427	1372	31	as	as	ADP
fuelectenerg-1427	1372	32	inputs	input	NOUN
fuelectenerg-1427	1372	33	to	to	ADP
fuelectenerg-1427	1372	34	a	a	DET
fuelectenerg-1427	1372	35	ulm	ulm	NOUN
fuelectenerg-1427	1372	36	.	.	PUNCT
fuelectenerg-1427	1373	1	the	the	DET
fuelectenerg-1427	1373	2	form	form	NOUN
fuelectenerg-1427	1373	3	of	of	ADP
fuelectenerg-1427	1373	4	the	the	DET
fuelectenerg-1427	1373	5	resulting	result	VERB
fuelectenerg-1427	1373	6	function	function	NOUN
fuelectenerg-1427	1373	7	depends	depend	VERB
fuelectenerg-1427	1373	8	on	on	ADP
fuelectenerg-1427	1373	9	our	our	PRON
fuelectenerg-1427	1373	10	choice	choice	NOUN
fuelectenerg-1427	1373	11	of	of	ADP
fuelectenerg-1427	1373	12	the	the	DET
fuelectenerg-1427	1373	13	shift	shift	NOUN
fuelectenerg-1427	1373	14	and	and	CCONJ
fuelectenerg-1427	1373	15	power	power	NOUN
fuelectenerg-1427	1373	16	operations	operation	NOUN
fuelectenerg-1427	1373	17	that	that	PRON
fuelectenerg-1427	1373	18	we	we	PRON
fuelectenerg-1427	1373	19	choose	choose	VERB
fuelectenerg-1427	1373	20	inside	inside	ADP
fuelectenerg-1427	1373	21	the	the	DET
fuelectenerg-1427	1373	22	ulm	ulm	NOUN
fuelectenerg-1427	1373	23	for	for	ADP
fuelectenerg-1427	1373	24	the	the	DET
fuelectenerg-1427	1373	25	input	input	NOUN
fuelectenerg-1427	1373	26	independent	independent	ADJ
fuelectenerg-1427	1373	27	variable	variable	NOUN
fuelectenerg-1427	1373	28	,	,	PUNCT
fuelectenerg-1427	1373	29	and	and	CCONJ
fuelectenerg-1427	1373	30	on	on	ADP
fuelectenerg-1427	1373	31	our	our	PRON
fuelectenerg-1427	1373	32	choice	choice	NOUN
fuelectenerg-1427	1373	33	of	of	ADP
fuelectenerg-1427	1373	34	the	the	DET
fuelectenerg-1427	1373	35	weighted	weight	VERB
fuelectenerg-1427	1373	36	combinations	combination	NOUN
fuelectenerg-1427	1373	37	of	of	ADP
fuelectenerg-1427	1373	38	the	the	DET
fuelectenerg-1427	1373	39	input	input	NOUN
fuelectenerg-1427	1373	40	cofactors	cofactor	NOUN
fuelectenerg-1427	1373	41	.	.	PUNCT
fuelectenerg-1427	1374	1	utilizing	utilize	VERB
fuelectenerg-1427	1374	2	this	this	DET
fuelectenerg-1427	1374	3	note	note	NOUN
fuelectenerg-1427	1374	4	,	,	PUNCT
fuelectenerg-1427	1374	5	we	we	PRON
fuelectenerg-1427	1374	6	can	can	AUX
fuelectenerg-1427	1374	7	combine	combine	VERB
fuelectenerg-1427	1374	8	all	all	DET
fuelectenerg-1427	1374	9	davio	davio	NOUN
fuelectenerg-1427	1374	10	ulms	ulm	NOUN
fuelectenerg-1427	1374	11	to	to	PART
fuelectenerg-1427	1374	12	create	create	VERB
fuelectenerg-1427	1374	13	the	the	DET
fuelectenerg-1427	1374	14	single	single	ADJ
fuelectenerg-1427	1374	15	all	all	ADJ
fuelectenerg-1427	1374	16	-	-	PUNCT
fuelectenerg-1427	1374	17	davio	davio	NOUN
fuelectenerg-1427	1374	18	ulm	ulm	NOUN
fuelectenerg-1427	1374	19	,	,	PUNCT
fuelectenerg-1427	1374	20	where	where	SCONJ
fuelectenerg-1427	1374	21	figure	figure	NOUN
fuelectenerg-1427	1374	22	7(c	7(c	NOUN
fuelectenerg-1427	1374	23	)	)	PUNCT
fuelectenerg-1427	1374	24	illustrates	illustrate	VERB
fuelectenerg-1427	1374	25	this	this	DET
fuelectenerg-1427	1374	26	ulm	ulm	NOUN
fuelectenerg-1427	1374	27	.	.	PUNCT
fuelectenerg-1427	1375	1	also	also	ADV
fuelectenerg-1427	1375	2	,	,	PUNCT
fuelectenerg-1427	1375	3	the	the	DET
fuelectenerg-1427	1375	4	more	more	ADV
fuelectenerg-1427	1375	5	general	general	ADJ
fuelectenerg-1427	1375	6	ulm	ulm	NOUN
fuelectenerg-1427	1375	7	as	as	SCONJ
fuelectenerg-1427	1375	8	shown	show	VERB
fuelectenerg-1427	1375	9	in	in	ADP
fuelectenerg-1427	1375	10	figure	figure	NOUN
fuelectenerg-1427	1375	11	7(d	7(d	NUM
fuelectenerg-1427	1375	12	)	)	PUNCT
fuelectenerg-1427	1375	13	,	,	PUNCT
fuelectenerg-1427	1375	14	can	can	AUX
fuelectenerg-1427	1375	15	be	be	AUX
fuelectenerg-1427	1375	16	generated	generate	VERB
fuelectenerg-1427	1375	17	to	to	PART
fuelectenerg-1427	1375	18	implement	implement	VERB
fuelectenerg-1427	1375	19	all	all	DET
fuelectenerg-1427	1375	20	ternary	ternary	ADJ
fuelectenerg-1427	1375	21	gf(3	gf(3	PROPN
fuelectenerg-1427	1375	22	)	)	PUNCT
fuelectenerg-1427	1375	23	shannon	shannon	NOUN
fuelectenerg-1427	1375	24	and	and	CCONJ
fuelectenerg-1427	1375	25	davio	davio	NOUN
fuelectenerg-1427	1375	26	expansions	expansion	NOUN
fuelectenerg-1427	1375	27	.	.	PUNCT
fuelectenerg-1427	1376	1	in	in	ADP
fuelectenerg-1427	1376	2	general	general	ADJ
fuelectenerg-1427	1376	3	,	,	PUNCT
fuelectenerg-1427	1376	4	the	the	DET
fuelectenerg-1427	1376	5	gates	gate	NOUN
fuelectenerg-1427	1376	6	in	in	ADP
fuelectenerg-1427	1376	7	the	the	DET
fuelectenerg-1427	1376	8	ulms	ulm	NOUN
fuelectenerg-1427	1376	9	can	can	AUX
fuelectenerg-1427	1376	10	be	be	AUX
fuelectenerg-1427	1376	11	implemented	implement	VERB
fuelectenerg-1427	1376	12	,	,	PUNCT
fuelectenerg-1427	1376	13	among	among	ADP
fuelectenerg-1427	1376	14	other	other	ADJ
fuelectenerg-1427	1376	15	circuit	circuit	NOUN
fuelectenerg-1427	1376	16	technologies	technology	NOUN
fuelectenerg-1427	1376	17	,	,	PUNCT
fuelectenerg-1427	1376	18	by	by	ADP
fuelectenerg-1427	1376	19	using	use	VERB
fuelectenerg-1427	1376	20	binary	binary	ADJ
fuelectenerg-1427	1376	21	logic	logic	NOUN
fuelectenerg-1427	1376	22	over	over	ADP
fuelectenerg-1427	1376	23	gf(2	gf(2	PROPN
fuelectenerg-1427	1376	24	)	)	PUNCT
fuelectenerg-1427	1376	25	or	or	CCONJ
fuelectenerg-1427	1376	26	using	use	VERB
fuelectenerg-1427	1376	27	multiple	multiple	ADV
fuelectenerg-1427	1376	28	-	-	PUNCT
fuelectenerg-1427	1376	29	valued	value	VERB
fuelectenerg-1427	1376	30	circuit	circuit	NOUN
fuelectenerg-1427	1376	31	gates	gate	NOUN
fuelectenerg-1427	1376	32	.	.	PUNCT
fuelectenerg-1427	1377	1	each	each	DET
fuelectenerg-1427	1377	2	ternary	ternary	ADJ
fuelectenerg-1427	1377	3	ulm	ulm	PROPN
fuelectenerg-1427	1377	4	corresponds	correspond	VERB
fuelectenerg-1427	1377	5	to	to	ADP
fuelectenerg-1427	1377	6	a	a	DET
fuelectenerg-1427	1377	7	single	single	ADJ
fuelectenerg-1427	1377	8	node	node	NOUN
fuelectenerg-1427	1377	9	in	in	ADP
fuelectenerg-1427	1377	10	the	the	DET
fuelectenerg-1427	1377	11	nodes	node	NOUN
fuelectenerg-1427	1377	12	of	of	ADP
fuelectenerg-1427	1377	13	ternary	ternary	ADJ
fuelectenerg-1427	1377	14	dts	dts	NOUN
fuelectenerg-1427	1377	15	that	that	PRON
fuelectenerg-1427	1377	16	were	be	AUX
fuelectenerg-1427	1377	17	illustrated	illustrate	VERB
fuelectenerg-1427	1377	18	previously	previously	ADV
fuelectenerg-1427	1377	19	.	.	PUNCT
fuelectenerg-1427	1378	1	the	the	DET
fuelectenerg-1427	1378	2	main	main	ADJ
fuelectenerg-1427	1378	3	advantage	advantage	NOUN
fuelectenerg-1427	1378	4	of	of	ADP
fuelectenerg-1427	1378	5	such	such	ADJ
fuelectenerg-1427	1378	6	powerful	powerful	ADJ
fuelectenerg-1427	1378	7	ulms	ulm	NOUN
fuelectenerg-1427	1378	8	is	be	AUX
fuelectenerg-1427	1378	9	in	in	ADP
fuelectenerg-1427	1378	10	high	high	ADJ
fuelectenerg-1427	1378	11	layout	layout	NOUN
fuelectenerg-1427	1378	12	regularity	regularity	NOUN
fuelectenerg-1427	1378	13	that	that	PRON
fuelectenerg-1427	1378	14	is	be	AUX
fuelectenerg-1427	1378	15	required	require	VERB
fuelectenerg-1427	1378	16	by	by	ADP
fuelectenerg-1427	1378	17	future	future	ADJ
fuelectenerg-1427	1378	18	nanotechnologies	nanotechnology	NOUN
fuelectenerg-1427	1378	19	,	,	PUNCT
fuelectenerg-1427	1378	20	where	where	SCONJ
fuelectenerg-1427	1378	21	the	the	DET
fuelectenerg-1427	1378	22	trees	tree	NOUN
fuelectenerg-1427	1378	23	can	can	AUX
fuelectenerg-1427	1378	24	be	be	AUX
fuelectenerg-1427	1378	25	realized	realize	VERB
fuelectenerg-1427	1378	26	in	in	ADP
fuelectenerg-1427	1378	27	efficient	efficient	ADJ
fuelectenerg-1427	1378	28	layout	layout	NOUN
fuelectenerg-1427	1378	29	because	because	SCONJ
fuelectenerg-1427	1378	30	they	they	PRON
fuelectenerg-1427	1378	31	do	do	AUX
fuelectenerg-1427	1378	32	not	not	PART
fuelectenerg-1427	1378	33	grow	grow	VERB
fuelectenerg-1427	1378	34	exponentially	exponentially	ADV
fuelectenerg-1427	1378	35	for	for	ADP
fuelectenerg-1427	1378	36	practical	practical	ADJ
fuelectenerg-1427	1378	37	functions	function	NOUN
fuelectenerg-1427	1378	38	.	.	PUNCT
fuelectenerg-1427	1379	1	for	for	ADP
fuelectenerg-1427	1379	2	instance	instance	NOUN
fuelectenerg-1427	1379	3	,	,	PUNCT
fuelectenerg-1427	1379	4	assuming	assume	VERB
fuelectenerg-1427	1379	5	ulm	ulm	NOUN
fuelectenerg-1427	1379	6	from	from	ADP
fuelectenerg-1427	1379	7	figure	figure	NOUN
fuelectenerg-1427	1379	8	7	7	NUM
fuelectenerg-1427	1379	9	,	,	PUNCT
fuelectenerg-1427	1379	10	although	although	SCONJ
fuelectenerg-1427	1379	11	every	every	DET
fuelectenerg-1427	1379	12	two	two	NUM
fuelectenerg-1427	1379	13	-	-	PUNCT
fuelectenerg-1427	1379	14	variable	variable	NOUN
fuelectenerg-1427	1379	15	function	function	NOUN
fuelectenerg-1427	1379	16	can	can	AUX
fuelectenerg-1427	1379	17	be	be	AUX
fuelectenerg-1427	1379	18	realized	realize	VERB
fuelectenerg-1427	1379	19	with	with	ADP
fuelectenerg-1427	1379	20	four	four	NUM
fuelectenerg-1427	1379	21	such	such	ADJ
fuelectenerg-1427	1379	22	modules	module	NOUN
fuelectenerg-1427	1379	23	,	,	PUNCT
fuelectenerg-1427	1379	24	it	it	PRON
fuelectenerg-1427	1379	25	is	be	AUX
fuelectenerg-1427	1379	26	highly	highly	ADV
fuelectenerg-1427	1379	27	probable	probable	ADJ
fuelectenerg-1427	1379	28	that	that	SCONJ
fuelectenerg-1427	1379	29	most	most	ADJ
fuelectenerg-1427	1379	30	of	of	ADP
fuelectenerg-1427	1379	31	two	two	NUM
fuelectenerg-1427	1379	32	-	-	PUNCT
fuelectenerg-1427	1379	33	variable	variable	NOUN
fuelectenerg-1427	1379	34	functions	function	NOUN
fuelectenerg-1427	1379	35	will	will	AUX
fuelectenerg-1427	1379	36	require	require	VERB
fuelectenerg-1427	1379	37	less	less	ADJ
fuelectenerg-1427	1379	38	than	than	ADP
fuelectenerg-1427	1379	39	four	four	NUM
fuelectenerg-1427	1379	40	modules	module	NOUN
fuelectenerg-1427	1379	41	.	.	PUNCT
fuelectenerg-1427	1380	1	because	because	SCONJ
fuelectenerg-1427	1380	2	of	of	ADP
fuelectenerg-1427	1380	3	these	these	DET
fuelectenerg-1427	1380	4	properties	property	NOUN
fuelectenerg-1427	1380	5	,	,	PUNCT
fuelectenerg-1427	1380	6	this	this	DET
fuelectenerg-1427	1380	7	approach	approach	NOUN
fuelectenerg-1427	1380	8	is	be	AUX
fuelectenerg-1427	1380	9	further	far	ADV
fuelectenerg-1427	1380	10	expected	expect	VERB
fuelectenerg-1427	1380	11	to	to	PART
fuelectenerg-1427	1380	12	give	give	VERB
fuelectenerg-1427	1380	13	good	good	ADJ
fuelectenerg-1427	1380	14	results	result	NOUN
fuelectenerg-1427	1380	15	when	when	SCONJ
fuelectenerg-1427	1380	16	applied	apply	VERB
fuelectenerg-1427	1380	17	to	to	ADP
fuelectenerg-1427	1380	18	the	the	DET
fuelectenerg-1427	1380	19	corresponding	corresponding	ADJ
fuelectenerg-1427	1380	20	incompletely	incompletely	ADV
fuelectenerg-1427	1380	21	specified	specify	VERB
fuelectenerg-1427	1380	22	functions	function	NOUN
fuelectenerg-1427	1380	23	and	and	CCONJ
fuelectenerg-1427	1380	24	multiple	multiple	ADV
fuelectenerg-1427	1380	25	-	-	PUNCT
fuelectenerg-1427	1380	26	valued	value	VERB
fuelectenerg-1427	1380	27	relations	relation	NOUN
fuelectenerg-1427	1380	28	.	.	PUNCT
fuelectenerg-1427	1381	1	4	4	NUM
fuelectenerg-1427	1381	2	conclusions	conclusion	NOUN
fuelectenerg-1427	1381	3	and	and	CCONJ
fuelectenerg-1427	1381	4	future	future	ADJ
fuelectenerg-1427	1381	5	work	work	NOUN
fuelectenerg-1427	1381	6	in	in	ADP
fuelectenerg-1427	1381	7	this	this	DET
fuelectenerg-1427	1381	8	paper	paper	NOUN
fuelectenerg-1427	1381	9	,	,	PUNCT
fuelectenerg-1427	1381	10	an	an	DET
fuelectenerg-1427	1381	11	extended	extended	ADJ
fuelectenerg-1427	1381	12	green	green	ADJ
fuelectenerg-1427	1381	13	-	-	PUNCT
fuelectenerg-1427	1381	14	sasao	sasao	NOUN
fuelectenerg-1427	1381	15	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1381	16	of	of	ADP
fuelectenerg-1427	1381	17	families	family	NOUN
fuelectenerg-1427	1381	18	and	and	CCONJ
fuelectenerg-1427	1381	19	forms	form	NOUN
fuelectenerg-1427	1381	20	is	be	AUX
fuelectenerg-1427	1381	21	introduced	introduce	VERB
fuelectenerg-1427	1381	22	.	.	PUNCT
fuelectenerg-1427	1382	1	analogously	analogously	ADV
fuelectenerg-1427	1382	2	to	to	ADP
fuelectenerg-1427	1382	3	the	the	DET
fuelectenerg-1427	1382	4	binary	binary	ADJ
fuelectenerg-1427	1382	5	case	case	NOUN
fuelectenerg-1427	1382	6	,	,	PUNCT
fuelectenerg-1427	1382	7	two	two	NUM
fuelectenerg-1427	1382	8	general	general	ADJ
fuelectenerg-1427	1382	9	families	family	NOUN
fuelectenerg-1427	1382	10	of	of	ADP
fuelectenerg-1427	1382	11	canonical	canonical	ADJ
fuelectenerg-1427	1382	12	ternary	ternary	ADJ
fuelectenerg-1427	1382	13	reed	reed	NOUN
fuelectenerg-1427	1382	14	-	-	PUNCT
fuelectenerg-1427	1382	15	muller	muller	NOUN
fuelectenerg-1427	1382	16	forms	form	NOUN
fuelectenerg-1427	1382	17	,	,	PUNCT
fuelectenerg-1427	1382	18	called	call	VERB
fuelectenerg-1427	1382	19	ternary	ternary	ADJ
fuelectenerg-1427	1382	20	inclusive	inclusive	ADJ
fuelectenerg-1427	1382	21	forms	form	NOUN
fuelectenerg-1427	1382	22	(	(	PUNCT
fuelectenerg-1427	1382	23	tifs	tifs	PROPN
fuelectenerg-1427	1382	24	)	)	PUNCT
fuelectenerg-1427	1382	25	and	and	CCONJ
fuelectenerg-1427	1382	26	their	their	PRON
fuelectenerg-1427	1382	27	generalization	generalization	NOUN
fuelectenerg-1427	1382	28	of	of	ADP
fuelectenerg-1427	1382	29	ternary	ternary	ADJ
fuelectenerg-1427	1382	30	generalized	generalize	VERB
fuelectenerg-1427	1382	31	inclusive	inclusive	ADJ
fuelectenerg-1427	1382	32	forms	form	NOUN
fuelectenerg-1427	1382	33	(	(	PUNCT
fuelectenerg-1427	1382	34	tgifs	tgif	NOUN
fuelectenerg-1427	1382	35	)	)	PUNCT
fuelectenerg-1427	1382	36	,	,	PUNCT
fuelectenerg-1427	1382	37	are	be	AUX
fuelectenerg-1427	1382	38	presented	present	VERB
fuelectenerg-1427	1382	39	.	.	PUNCT
fuelectenerg-1427	1383	1	the	the	DET
fuelectenerg-1427	1383	2	second	second	ADJ
fuelectenerg-1427	1383	3	family	family	NOUN
fuelectenerg-1427	1383	4	includes	include	VERB
fuelectenerg-1427	1383	5	minimum	minimum	ADJ
fuelectenerg-1427	1383	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1383	7	)	)	PUNCT
fuelectenerg-1427	1383	8	galois	galois	PROPN
fuelectenerg-1427	1383	9	field	field	NOUN
fuelectenerg-1427	1383	10	sum	sum	NOUN
fuelectenerg-1427	1383	11	-	-	PUNCT
fuelectenerg-1427	1383	12	of	of	ADP
fuelectenerg-1427	1383	13	-	-	PUNCT
fuelectenerg-1427	1383	14	products	product	NOUN
fuelectenerg-1427	1383	15	(	(	PUNCT
fuelectenerg-1427	1383	16	gfsops	gfsop	NOUN
fuelectenerg-1427	1383	17	)	)	PUNCT
fuelectenerg-1427	1383	18	.	.	PUNCT
fuelectenerg-1427	1384	1	the	the	DET
fuelectenerg-1427	1384	2	multiple	multiple	ADV
fuelectenerg-1427	1384	3	-	-	PUNCT
fuelectenerg-1427	1384	4	valued	value	VERB
fuelectenerg-1427	1384	5	shannon	shannon	NOUN
fuelectenerg-1427	1384	6	-	-	PUNCT
fuelectenerg-1427	1384	7	davio	davio	NOUN
fuelectenerg-1427	1384	8	(	(	PUNCT
fuelectenerg-1427	1384	9	s	s	NOUN
fuelectenerg-1427	1384	10	/	/	SYM
fuelectenerg-1427	1384	11	d	d	NOUN
fuelectenerg-1427	1384	12	)	)	PUNCT
fuelectenerg-1427	1384	13	trees	tree	NOUN
fuelectenerg-1427	1384	14	developed	develop	VERB
fuelectenerg-1427	1384	15	in	in	ADP
fuelectenerg-1427	1384	16	this	this	DET
fuelectenerg-1427	1384	17	paper	paper	NOUN
fuelectenerg-1427	1384	18	provide	provide	VERB
fuelectenerg-1427	1384	19	more	more	ADJ
fuelectenerg-1427	1384	20	general	general	ADJ
fuelectenerg-1427	1384	21	polarity	polarity	NOUN
fuelectenerg-1427	1384	22	with	with	ADP
fuelectenerg-1427	1384	23	regards	regard	NOUN
fuelectenerg-1427	1384	24	to	to	ADP
fuelectenerg-1427	1384	25	the	the	DET
fuelectenerg-1427	1384	26	114	114	NUM
fuelectenerg-1427	1384	27	an	an	DET
fuelectenerg-1427	1384	28	extended	extended	ADJ
fuelectenerg-1427	1384	29	green	green	ADJ
fuelectenerg-1427	1384	30	sasao	sasao	PROPN
fuelectenerg-1427	1384	31	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1384	32	of	of	ADP
fuelectenerg-1427	1384	33	canonical	canonical	ADJ
fuelectenerg-1427	1384	34	ternary	ternary	ADJ
fuelectenerg-1427	1384	35	galois	galois	NOUN
fuelectenerg-1427	1384	36	forms	form	NOUN
fuelectenerg-1427	1384	37	...	...	PUNCT
fuelectenerg-1427	1385	1	•	•	NUM
fuelectenerg-1427	1385	2	•	•	NOUN
fuelectenerg-1427	1385	3	x	x	SYM
fuelectenerg-1427	1385	4	f0	f0	PROPN
fuelectenerg-1427	1385	5	f2	f2	PROPN
fuelectenerg-1427	1385	6	f1	f1	NOUN
fuelectenerg-1427	1385	7	0x	0x	NOUN
fuelectenerg-1427	1385	8	2	2	NUM
fuelectenerg-1427	1385	9	x	x	SYM
fuelectenerg-1427	1385	10	1	1	NUM
fuelectenerg-1427	1385	11	x	x	SYM
fuelectenerg-1427	1385	12	x	x	NOUN
fuelectenerg-1427	1385	13	f1	f1	NOUN
fuelectenerg-1427	1385	14	f0	f0	PROPN
fuelectenerg-1427	1386	1	+	+	PROPN
fuelectenerg-1427	1386	2	f	f	PROPN
fuelectenerg-1427	1386	3	1	1	NUM
fuelectenerg-1427	1386	4	+	+	NOUN
fuelectenerg-1427	1386	5	f	f	PROPN
fuelectenerg-1427	1386	6	2	2	NUM
fuelectenerg-1427	1386	7	2f2	2f2	NUM
fuelectenerg-1427	1387	1	+	+	NOUN
fuelectenerg-1427	1387	2	f	f	NOUN
fuelectenerg-1427	1387	3	0	0	NUM
fuelectenerg-1427	1387	4	1	1	NUM
fuelectenerg-1427	1387	5	2	2	NUM
fuelectenerg-1427	1387	6	(	(	PUNCT
fuelectenerg-1427	1387	7	”	"	PUNCT
fuelectenerg-1427	1387	8	)	)	PUNCT
fuelectenerg-1427	1387	9	x	x	SYM
fuelectenerg-1427	1387	10	2	2	NUM
fuelectenerg-1427	1387	11	x	x	NOUN
fuelectenerg-1427	1387	12	”	"	PUNCT
fuelectenerg-1427	1387	13	x	x	NUM
fuelectenerg-1427	1387	14	f0	f0	NOUN
fuelectenerg-1427	1387	15	f0	f0	PROPN
fuelectenerg-1427	1388	1	+	+	NOUN
fuelectenerg-1427	1388	2	f	f	PROPN
fuelectenerg-1427	1388	3	1	1	NUM
fuelectenerg-1427	1389	1	+	+	NOUN
fuelectenerg-1427	1389	2	f	f	PROPN
fuelectenerg-1427	1389	3	2	2	NUM
fuelectenerg-1427	1389	4	2f1	2f1	NUM
fuelectenerg-1427	1389	5	+	+	NOUN
fuelectenerg-1427	1389	6	f	f	PROPN
fuelectenerg-1427	1389	7	2	2	NUM
fuelectenerg-1427	1389	8	1	1	NUM
fuelectenerg-1427	1389	9	2	2	NUM
fuelectenerg-1427	1389	10	(	(	PUNCT
fuelectenerg-1427	1389	11	)	)	PUNCT
fuelectenerg-1427	1389	12	x	x	SYM
fuelectenerg-1427	1389	13	2	2	NUM
fuelectenerg-1427	1389	14	x	x	SYM
fuelectenerg-1427	1389	15	2	2	NUM
fuelectenerg-1427	1389	16	(	(	PUNCT
fuelectenerg-1427	1389	17	’	'	PUNCT
fuelectenerg-1427	1389	18	)	)	PUNCT
fuelectenerg-1427	1389	19	x	x	SYM
fuelectenerg-1427	1389	20	2	2	NUM
fuelectenerg-1427	1389	21	x	x	SYM
fuelectenerg-1427	1389	22	f2	f2	PROPN
fuelectenerg-1427	1389	23	f0	f0	PROPN
fuelectenerg-1427	1390	1	+	+	PROPN
fuelectenerg-1427	1390	2	f	f	PROPN
fuelectenerg-1427	1390	3	1	1	NUM
fuelectenerg-1427	1390	4	+	+	NOUN
fuelectenerg-1427	1390	5	f	f	PROPN
fuelectenerg-1427	1390	6	2	2	NUM
fuelectenerg-1427	1390	7	2f0	2f0	NUM
fuelectenerg-1427	1390	8	+	+	NOUN
fuelectenerg-1427	1390	9	f	f	NOUN
fuelectenerg-1427	1390	10	1	1	NUM
fuelectenerg-1427	1390	11	1	1	NUM
fuelectenerg-1427	1390	12	x	x	NOUN
fuelectenerg-1427	1390	13	’	'	PUNCT
fuelectenerg-1427	1391	1	+	+	PROPN
fuelectenerg-1427	1392	1	+	+	PUNCT
fuelectenerg-1427	1392	2	+	+	PUNCT
fuelectenerg-1427	1393	1	+	+	PUNCT
fuelectenerg-1427	1393	2	+	+	SYM
fuelectenerg-1427	1393	3	0	0	NUM
fuelectenerg-1427	1393	4	x	x	SYM
fuelectenerg-1427	1393	5	1	1	NUM
fuelectenerg-1427	1393	6	1	1	NUM
fuelectenerg-1427	1393	7	x	x	SYM
fuelectenerg-1427	1393	8	2	2	NUM
fuelectenerg-1427	1393	9	x	x	SYM
fuelectenerg-1427	1393	10	2	2	NUM
fuelectenerg-1427	1393	11	x	x	SYM
fuelectenerg-1427	1393	12	x	x	NOUN
fuelectenerg-1427	1393	13	’	'	PUNCT
fuelectenerg-1427	1393	14	x	x	ADJ
fuelectenerg-1427	1393	15	”	"	PUNCT
fuelectenerg-1427	1393	16	fi	fi	NOUN
fuelectenerg-1427	1393	17	fk	fk	INTJ
fuelectenerg-1427	1394	1	fj	fj	INTJ
fuelectenerg-1427	1394	2	f	f	NOUN
fuelectenerg-1427	1394	3	x	x	SYM
fuelectenerg-1427	1394	4	1	1	NUM
fuelectenerg-1427	1394	5	2	2	NUM
fuelectenerg-1427	1394	6	�	�	PROPN
fuelectenerg-1427	1394	7	�	�	PROPN
fuelectenerg-1427	1394	8	�	�	PROPN
fuelectenerg-1427	1394	9	�	�	PROPN
fuelectenerg-1427	1394	10	�	�	PROPN
fuelectenerg-1427	1394	11	�	�	PROPN
fuelectenerg-1427	1394	12	�	�	PROPN
fuelectenerg-1427	1394	13	+	+	CCONJ
fuelectenerg-1427	1394	14	+1	+1	PROPN
fuelectenerg-1427	1395	1	fi	fi	NOUN
fuelectenerg-1427	1395	2	fk	fk	INTJ
fuelectenerg-1427	1396	1	fj	fj	INTJ
fuelectenerg-1427	1396	2	f	f	PROPN
fuelectenerg-1427	1396	3	+1	+1	PROPN
fuelectenerg-1427	1396	4	(	(	PUNCT
fuelectenerg-1427	1396	5	a	a	NOUN
fuelectenerg-1427	1396	6	)	)	PUNCT
fuelectenerg-1427	1396	7	(	(	PUNCT
fuelectenerg-1427	1396	8	b	b	X
fuelectenerg-1427	1396	9	)	)	PUNCT
fuelectenerg-1427	1396	10	(	(	PUNCT
fuelectenerg-1427	1396	11	c	c	X
fuelectenerg-1427	1396	12	)	)	PUNCT
fuelectenerg-1427	1396	13	(	(	PUNCT
fuelectenerg-1427	1396	14	d	d	X
fuelectenerg-1427	1396	15	)	)	PUNCT
fuelectenerg-1427	1396	16	figure	figure	NOUN
fuelectenerg-1427	1396	17	7	7	NUM
fuelectenerg-1427	1396	18	:	:	PUNCT
fuelectenerg-1427	1396	19	various	various	ADJ
fuelectenerg-1427	1396	20	ternary	ternary	ADJ
fuelectenerg-1427	1396	21	ulms	ulm	NOUN
fuelectenerg-1427	1396	22	:	:	PUNCT
fuelectenerg-1427	1396	23	(	(	PUNCT
fuelectenerg-1427	1396	24	a	a	X
fuelectenerg-1427	1396	25	)	)	PUNCT
fuelectenerg-1427	1396	26	ulm	ulm	NOUN
fuelectenerg-1427	1396	27	of	of	ADP
fuelectenerg-1427	1396	28	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	29	)	)	PUNCT
fuelectenerg-1427	1396	30	shannon	shannon	NOUN
fuelectenerg-1427	1396	31	using	use	VERB
fuelectenerg-1427	1396	32	three	three	NUM
fuelectenerg-1427	1396	33	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	34	)	)	PUNCT
fuelectenerg-1427	1396	35	multiplication	multiplication	NOUN
fuelectenerg-1427	1396	36	gates	gate	NOUN
fuelectenerg-1427	1396	37	and	and	CCONJ
fuelectenerg-1427	1396	38	one	one	NUM
fuelectenerg-1427	1396	39	gf(3	gf(3	NOUN
fuelectenerg-1427	1396	40	)	)	PUNCT
fuelectenerg-1427	1396	41	addition	addition	NOUN
fuelectenerg-1427	1396	42	gate	gate	NOUN
fuelectenerg-1427	1396	43	,	,	PUNCT
fuelectenerg-1427	1396	44	(	(	PUNCT
fuelectenerg-1427	1396	45	b	b	X
fuelectenerg-1427	1396	46	)	)	PUNCT
fuelectenerg-1427	1396	47	ulms	ulm	NOUN
fuelectenerg-1427	1396	48	of	of	ADP
fuelectenerg-1427	1396	49	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	50	)	)	PUNCT
fuelectenerg-1427	1396	51	davio	davio	NOUN
fuelectenerg-1427	1396	52	{	{	PUNCT
fuelectenerg-1427	1396	53	d0,d1,d2	d0,d1,d2	PROPN
fuelectenerg-1427	1396	54	}	}	PUNCT
fuelectenerg-1427	1396	55	using	use	VERB
fuelectenerg-1427	1396	56	three	three	NUM
fuelectenerg-1427	1396	57	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	58	)	)	PUNCT
fuelectenerg-1427	1396	59	multiplication	multiplication	NOUN
fuelectenerg-1427	1396	60	gates	gate	NOUN
fuelectenerg-1427	1396	61	and	and	CCONJ
fuelectenerg-1427	1396	62	one	one	NUM
fuelectenerg-1427	1396	63	gf(3	gf(3	NOUN
fuelectenerg-1427	1396	64	)	)	PUNCT
fuelectenerg-1427	1396	65	addition	addition	NOUN
fuelectenerg-1427	1396	66	gate	gate	NOUN
fuelectenerg-1427	1396	67	,	,	PUNCT
fuelectenerg-1427	1396	68	(	(	PUNCT
fuelectenerg-1427	1396	69	c	c	X
fuelectenerg-1427	1396	70	)	)	PUNCT
fuelectenerg-1427	1396	71	ulm	ulm	NOUN
fuelectenerg-1427	1396	72	for	for	ADP
fuelectenerg-1427	1396	73	all	all	DET
fuelectenerg-1427	1396	74	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	75	)	)	PUNCT
fuelectenerg-1427	1396	76	davio	davio	NOUN
fuelectenerg-1427	1396	77	expansions	expansion	NOUN
fuelectenerg-1427	1396	78	using	use	VERB
fuelectenerg-1427	1396	79	four	four	NUM
fuelectenerg-1427	1396	80	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	81	)	)	PUNCT
fuelectenerg-1427	1396	82	multiplication	multiplication	NOUN
fuelectenerg-1427	1396	83	gates	gate	NOUN
fuelectenerg-1427	1396	84	,	,	PUNCT
fuelectenerg-1427	1396	85	one	one	NUM
fuelectenerg-1427	1396	86	gf(3	gf(3	NOUN
fuelectenerg-1427	1396	87	)	)	PUNCT
fuelectenerg-1427	1396	88	addition	addition	NOUN
fuelectenerg-1427	1396	89	gate	gate	NOUN
fuelectenerg-1427	1396	90	,	,	PUNCT
fuelectenerg-1427	1396	91	two	two	NUM
fuelectenerg-1427	1396	92	shift	shift	NOUN
fuelectenerg-1427	1396	93	operators	operator	NOUN
fuelectenerg-1427	1396	94	,	,	PUNCT
fuelectenerg-1427	1396	95	and	and	CCONJ
fuelectenerg-1427	1396	96	one	one	NUM
fuelectenerg-1427	1396	97	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1396	98	,	,	PUNCT
fuelectenerg-1427	1396	99	and	and	CCONJ
fuelectenerg-1427	1396	100	(	(	PUNCT
fuelectenerg-1427	1396	101	d	d	NOUN
fuelectenerg-1427	1396	102	)	)	PUNCT
fuelectenerg-1427	1396	103	general	general	ADJ
fuelectenerg-1427	1396	104	ulm	ulm	NOUN
fuelectenerg-1427	1396	105	of	of	ADP
fuelectenerg-1427	1396	106	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	107	)	)	PUNCT
fuelectenerg-1427	1396	108	s	s	PROPN
fuelectenerg-1427	1396	109	/	/	SYM
fuelectenerg-1427	1396	110	d	d	NOUN
fuelectenerg-1427	1396	111	node	node	NOUN
fuelectenerg-1427	1396	112	using	use	VERB
fuelectenerg-1427	1396	113	four	four	NUM
fuelectenerg-1427	1396	114	gf(3	gf(3	PROPN
fuelectenerg-1427	1396	115	)	)	PUNCT
fuelectenerg-1427	1396	116	multiplication	multiplication	NOUN
fuelectenerg-1427	1396	117	gates	gate	NOUN
fuelectenerg-1427	1396	118	,	,	PUNCT
fuelectenerg-1427	1396	119	one	one	NUM
fuelectenerg-1427	1396	120	gf(3	gf(3	NOUN
fuelectenerg-1427	1396	121	)	)	PUNCT
fuelectenerg-1427	1396	122	addition	addition	NOUN
fuelectenerg-1427	1396	123	gate	gate	NOUN
fuelectenerg-1427	1396	124	and	and	CCONJ
fuelectenerg-1427	1396	125	four	four	NUM
fuelectenerg-1427	1396	126	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1396	127	.	.	PUNCT
fuelectenerg-1427	1397	1	corresponding	correspond	VERB
fuelectenerg-1427	1397	2	if	if	SCONJ
fuelectenerg-1427	1397	3	polarity	polarity	NOUN
fuelectenerg-1427	1397	4	,	,	PUNCT
fuelectenerg-1427	1397	5	which	which	PRON
fuelectenerg-1427	1397	6	contains	contain	VERB
fuelectenerg-1427	1397	7	the	the	DET
fuelectenerg-1427	1397	8	grm	grm	NOUN
fuelectenerg-1427	1397	9	as	as	ADP
fuelectenerg-1427	1397	10	a	a	DET
fuelectenerg-1427	1397	11	special	special	ADJ
fuelectenerg-1427	1397	12	case	case	NOUN
fuelectenerg-1427	1397	13	.	.	PUNCT
fuelectenerg-1427	1398	1	since	since	SCONJ
fuelectenerg-1427	1398	2	universal	universal	ADJ
fuelectenerg-1427	1398	3	logic	logic	NOUN
fuelectenerg-1427	1398	4	modules	module	NOUN
fuelectenerg-1427	1398	5	(	(	PUNCT
fuelectenerg-1427	1398	6	ulms	ulm	NOUN
fuelectenerg-1427	1398	7	)	)	PUNCT
fuelectenerg-1427	1398	8	are	be	AUX
fuelectenerg-1427	1398	9	complete	complete	ADJ
fuelectenerg-1427	1398	10	systems	system	NOUN
fuelectenerg-1427	1398	11	that	that	PRON
fuelectenerg-1427	1398	12	can	can	AUX
fuelectenerg-1427	1398	13	implement	implement	VERB
fuelectenerg-1427	1398	14	all	all	DET
fuelectenerg-1427	1398	15	possible	possible	ADJ
fuelectenerg-1427	1398	16	logic	logic	NOUN
fuelectenerg-1427	1398	17	functions	function	NOUN
fuelectenerg-1427	1398	18	utilizing	utilize	VERB
fuelectenerg-1427	1398	19	s	s	PART
fuelectenerg-1427	1398	20	/	/	SYM
fuelectenerg-1427	1398	21	d	d	NOUN
fuelectenerg-1427	1398	22	expansions	expansion	NOUN
fuelectenerg-1427	1398	23	of	of	ADP
fuelectenerg-1427	1398	24	multiple	multiple	ADV
fuelectenerg-1427	1398	25	-	-	PUNCT
fuelectenerg-1427	1398	26	valued	value	VERB
fuelectenerg-1427	1398	27	shannon	shannon	NOUN
fuelectenerg-1427	1398	28	and	and	CCONJ
fuelectenerg-1427	1398	29	davio	davio	NOUN
fuelectenerg-1427	1398	30	decompositions	decomposition	NOUN
fuelectenerg-1427	1398	31	,	,	PUNCT
fuelectenerg-1427	1398	32	the	the	DET
fuelectenerg-1427	1398	33	realization	realization	NOUN
fuelectenerg-1427	1398	34	of	of	ADP
fuelectenerg-1427	1398	35	the	the	DET
fuelectenerg-1427	1398	36	presented	present	VERB
fuelectenerg-1427	1398	37	s	s	PROPN
fuelectenerg-1427	1398	38	/	/	SYM
fuelectenerg-1427	1398	39	d	d	NOUN
fuelectenerg-1427	1398	40	trees	tree	NOUN
fuelectenerg-1427	1398	41	utilizing	utilize	VERB
fuelectenerg-1427	1398	42	the	the	DET
fuelectenerg-1427	1398	43	corresponding	corresponding	ADJ
fuelectenerg-1427	1398	44	ulms	ulm	NOUN
fuelectenerg-1427	1398	45	is	be	AUX
fuelectenerg-1427	1398	46	also	also	ADV
fuelectenerg-1427	1398	47	introduced	introduce	VERB
fuelectenerg-1427	1398	48	.	.	PUNCT
fuelectenerg-1427	1399	1	the	the	DET
fuelectenerg-1427	1399	2	application	application	NOUN
fuelectenerg-1427	1399	3	of	of	ADP
fuelectenerg-1427	1399	4	the	the	DET
fuelectenerg-1427	1399	5	presented	present	VERB
fuelectenerg-1427	1399	6	tifs	tif	NOUN
fuelectenerg-1427	1399	7	and	and	CCONJ
fuelectenerg-1427	1399	8	tgifs	tgif	NOUN
fuelectenerg-1427	1399	9	can	can	AUX
fuelectenerg-1427	1399	10	be	be	AUX
fuelectenerg-1427	1399	11	used	use	VERB
fuelectenerg-1427	1399	12	to	to	PART
fuelectenerg-1427	1399	13	find	find	VERB
fuelectenerg-1427	1399	14	minimum	minimum	ADJ
fuelectenerg-1427	1399	15	gfsop	gfsop	NOUN
fuelectenerg-1427	1399	16	for	for	ADP
fuelectenerg-1427	1399	17	multiple	multiple	ADV
fuelectenerg-1427	1399	18	-	-	PUNCT
fuelectenerg-1427	1399	19	valued	value	VERB
fuelectenerg-1427	1399	20	inputs	input	NOUN
fuelectenerg-1427	1399	21	-	-	PUNCT
fuelectenerg-1427	1399	22	outputs	output	NOUN
fuelectenerg-1427	1399	23	within	within	ADP
fuelectenerg-1427	1399	24	logic	logic	NOUN
fuelectenerg-1427	1399	25	synthesis	synthesis	NOUN
fuelectenerg-1427	1399	26	,	,	PUNCT
fuelectenerg-1427	1399	27	where	where	SCONJ
fuelectenerg-1427	1399	28	a	a	DET
fuelectenerg-1427	1399	29	gfsop	gfsop	NOUN
fuelectenerg-1427	1399	30	minimizer	minimizer	NOUN
fuelectenerg-1427	1399	31	based	base	VERB
fuelectenerg-1427	1399	32	on	on	ADP
fuelectenerg-1427	1399	33	if	if	SCONJ
fuelectenerg-1427	1399	34	polarity	polarity	NOUN
fuelectenerg-1427	1399	35	can	can	AUX
fuelectenerg-1427	1399	36	be	be	AUX
fuelectenerg-1427	1399	37	used	use	VERB
fuelectenerg-1427	1399	38	to	to	PART
fuelectenerg-1427	1399	39	minimize	minimize	VERB
fuelectenerg-1427	1399	40	the	the	DET
fuelectenerg-1427	1399	41	corresponding	correspond	VERB
fuelectenerg-1427	1399	42	multiple	multiple	ADV
fuelectenerg-1427	1399	43	-	-	PUNCT
fuelectenerg-1427	1399	44	valued	value	VERB
fuelectenerg-1427	1399	45	gfsop	gfsop	NOUN
fuelectenerg-1427	1399	46	expressions	expression	NOUN
fuelectenerg-1427	1399	47	.	.	PUNCT
fuelectenerg-1427	1400	1	115	115	NUM
fuelectenerg-1427	1400	2	an	an	DET
fuelectenerg-1427	1400	3	extended	extend	VERB
fuelectenerg-1427	1400	4	green	green	ADJ
fuelectenerg-1427	1400	5	sasao	sasao	PROPN
fuelectenerg-1427	1400	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1400	7	of	of	ADP
fuelectenerg-1427	1400	8	canonical	canonical	ADJ
fuelectenerg-1427	1400	9	ternary	ternary	ADJ
fuelectenerg-1427	1400	10	galois	galois	NOUN
fuelectenerg-1427	1400	11	forms	form	NOUN
fuelectenerg-1427	1400	12	...	...	PUNCT
fuelectenerg-1427	1401	1	•	•	NUM
fuelectenerg-1427	1401	2	•	•	NOUN
fuelectenerg-1427	1401	3	x	x	SYM
fuelectenerg-1427	1401	4	f0	f0	PROPN
fuelectenerg-1427	1401	5	f2	f2	PROPN
fuelectenerg-1427	1401	6	f1	f1	NOUN
fuelectenerg-1427	1401	7	0x	0x	NOUN
fuelectenerg-1427	1401	8	2	2	NUM
fuelectenerg-1427	1401	9	x	x	SYM
fuelectenerg-1427	1401	10	1	1	NUM
fuelectenerg-1427	1401	11	x	x	SYM
fuelectenerg-1427	1401	12	x	x	NOUN
fuelectenerg-1427	1401	13	f1	f1	NOUN
fuelectenerg-1427	1401	14	f0	f0	PROPN
fuelectenerg-1427	1402	1	+	+	PROPN
fuelectenerg-1427	1402	2	f	f	PROPN
fuelectenerg-1427	1402	3	1	1	NUM
fuelectenerg-1427	1402	4	+	+	NOUN
fuelectenerg-1427	1402	5	f	f	PROPN
fuelectenerg-1427	1402	6	2	2	NUM
fuelectenerg-1427	1402	7	2f2	2f2	NUM
fuelectenerg-1427	1403	1	+	+	NOUN
fuelectenerg-1427	1403	2	f	f	NOUN
fuelectenerg-1427	1403	3	0	0	NUM
fuelectenerg-1427	1403	4	1	1	NUM
fuelectenerg-1427	1403	5	2	2	NUM
fuelectenerg-1427	1403	6	(	(	PUNCT
fuelectenerg-1427	1403	7	”	"	PUNCT
fuelectenerg-1427	1403	8	)	)	PUNCT
fuelectenerg-1427	1403	9	x	x	SYM
fuelectenerg-1427	1403	10	2	2	NUM
fuelectenerg-1427	1403	11	x	x	NOUN
fuelectenerg-1427	1403	12	”	"	PUNCT
fuelectenerg-1427	1403	13	x	x	NUM
fuelectenerg-1427	1403	14	f0	f0	NOUN
fuelectenerg-1427	1403	15	f0	f0	PROPN
fuelectenerg-1427	1404	1	+	+	NOUN
fuelectenerg-1427	1404	2	f	f	PROPN
fuelectenerg-1427	1404	3	1	1	NUM
fuelectenerg-1427	1405	1	+	+	NOUN
fuelectenerg-1427	1405	2	f	f	PROPN
fuelectenerg-1427	1405	3	2	2	NUM
fuelectenerg-1427	1405	4	2f1	2f1	NUM
fuelectenerg-1427	1405	5	+	+	NOUN
fuelectenerg-1427	1405	6	f	f	PROPN
fuelectenerg-1427	1405	7	2	2	NUM
fuelectenerg-1427	1405	8	1	1	NUM
fuelectenerg-1427	1405	9	2	2	NUM
fuelectenerg-1427	1405	10	(	(	PUNCT
fuelectenerg-1427	1405	11	)	)	PUNCT
fuelectenerg-1427	1405	12	x	x	SYM
fuelectenerg-1427	1405	13	2	2	NUM
fuelectenerg-1427	1405	14	x	x	SYM
fuelectenerg-1427	1405	15	2	2	NUM
fuelectenerg-1427	1405	16	(	(	PUNCT
fuelectenerg-1427	1405	17	’	'	PUNCT
fuelectenerg-1427	1405	18	)	)	PUNCT
fuelectenerg-1427	1405	19	x	x	SYM
fuelectenerg-1427	1405	20	2	2	NUM
fuelectenerg-1427	1405	21	x	x	SYM
fuelectenerg-1427	1405	22	f2	f2	PROPN
fuelectenerg-1427	1405	23	f0	f0	PROPN
fuelectenerg-1427	1406	1	+	+	PROPN
fuelectenerg-1427	1406	2	f	f	PROPN
fuelectenerg-1427	1406	3	1	1	NUM
fuelectenerg-1427	1406	4	+	+	NOUN
fuelectenerg-1427	1406	5	f	f	PROPN
fuelectenerg-1427	1406	6	2	2	NUM
fuelectenerg-1427	1406	7	2f0	2f0	NUM
fuelectenerg-1427	1406	8	+	+	NOUN
fuelectenerg-1427	1406	9	f	f	NOUN
fuelectenerg-1427	1406	10	1	1	NUM
fuelectenerg-1427	1406	11	1	1	NUM
fuelectenerg-1427	1406	12	x	x	NOUN
fuelectenerg-1427	1406	13	’	'	PUNCT
fuelectenerg-1427	1407	1	+	+	PROPN
fuelectenerg-1427	1408	1	+	+	PUNCT
fuelectenerg-1427	1408	2	+	+	PUNCT
fuelectenerg-1427	1409	1	+	+	PUNCT
fuelectenerg-1427	1409	2	+	+	SYM
fuelectenerg-1427	1409	3	0	0	NUM
fuelectenerg-1427	1409	4	x	x	SYM
fuelectenerg-1427	1409	5	1	1	NUM
fuelectenerg-1427	1409	6	1	1	NUM
fuelectenerg-1427	1409	7	x	x	SYM
fuelectenerg-1427	1409	8	2	2	NUM
fuelectenerg-1427	1409	9	x	x	SYM
fuelectenerg-1427	1409	10	2	2	NUM
fuelectenerg-1427	1409	11	x	x	SYM
fuelectenerg-1427	1409	12	x	x	NOUN
fuelectenerg-1427	1409	13	’	'	PUNCT
fuelectenerg-1427	1409	14	x	x	ADJ
fuelectenerg-1427	1409	15	”	"	PUNCT
fuelectenerg-1427	1409	16	fi	fi	NOUN
fuelectenerg-1427	1409	17	fk	fk	INTJ
fuelectenerg-1427	1410	1	fj	fj	INTJ
fuelectenerg-1427	1410	2	f	f	NOUN
fuelectenerg-1427	1410	3	x	x	SYM
fuelectenerg-1427	1410	4	1	1	NUM
fuelectenerg-1427	1410	5	2	2	NUM
fuelectenerg-1427	1410	6	�	�	PROPN
fuelectenerg-1427	1410	7	�	�	PROPN
fuelectenerg-1427	1410	8	�	�	PROPN
fuelectenerg-1427	1410	9	�	�	PROPN
fuelectenerg-1427	1410	10	�	�	PROPN
fuelectenerg-1427	1410	11	�	�	PROPN
fuelectenerg-1427	1410	12	�	�	PROPN
fuelectenerg-1427	1410	13	+	+	CCONJ
fuelectenerg-1427	1410	14	+1	+1	PROPN
fuelectenerg-1427	1411	1	fi	fi	NOUN
fuelectenerg-1427	1411	2	fk	fk	INTJ
fuelectenerg-1427	1412	1	fj	fj	INTJ
fuelectenerg-1427	1412	2	f	f	PROPN
fuelectenerg-1427	1412	3	+1	+1	PROPN
fuelectenerg-1427	1412	4	(	(	PUNCT
fuelectenerg-1427	1412	5	a	a	NOUN
fuelectenerg-1427	1412	6	)	)	PUNCT
fuelectenerg-1427	1412	7	(	(	PUNCT
fuelectenerg-1427	1412	8	b	b	X
fuelectenerg-1427	1412	9	)	)	PUNCT
fuelectenerg-1427	1412	10	(	(	PUNCT
fuelectenerg-1427	1412	11	c	c	X
fuelectenerg-1427	1412	12	)	)	PUNCT
fuelectenerg-1427	1412	13	(	(	PUNCT
fuelectenerg-1427	1412	14	d	d	X
fuelectenerg-1427	1412	15	)	)	PUNCT
fuelectenerg-1427	1412	16	figure	figure	NOUN
fuelectenerg-1427	1412	17	7	7	NUM
fuelectenerg-1427	1412	18	:	:	PUNCT
fuelectenerg-1427	1412	19	various	various	ADJ
fuelectenerg-1427	1412	20	ternary	ternary	ADJ
fuelectenerg-1427	1412	21	ulms	ulm	NOUN
fuelectenerg-1427	1412	22	:	:	PUNCT
fuelectenerg-1427	1412	23	(	(	PUNCT
fuelectenerg-1427	1412	24	a	a	X
fuelectenerg-1427	1412	25	)	)	PUNCT
fuelectenerg-1427	1412	26	ulm	ulm	NOUN
fuelectenerg-1427	1412	27	of	of	ADP
fuelectenerg-1427	1412	28	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	29	)	)	PUNCT
fuelectenerg-1427	1412	30	shannon	shannon	NOUN
fuelectenerg-1427	1412	31	using	use	VERB
fuelectenerg-1427	1412	32	three	three	NUM
fuelectenerg-1427	1412	33	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	34	)	)	PUNCT
fuelectenerg-1427	1412	35	multiplication	multiplication	NOUN
fuelectenerg-1427	1412	36	gates	gate	NOUN
fuelectenerg-1427	1412	37	and	and	CCONJ
fuelectenerg-1427	1412	38	one	one	NUM
fuelectenerg-1427	1412	39	gf(3	gf(3	NOUN
fuelectenerg-1427	1412	40	)	)	PUNCT
fuelectenerg-1427	1412	41	addition	addition	NOUN
fuelectenerg-1427	1412	42	gate	gate	NOUN
fuelectenerg-1427	1412	43	,	,	PUNCT
fuelectenerg-1427	1412	44	(	(	PUNCT
fuelectenerg-1427	1412	45	b	b	X
fuelectenerg-1427	1412	46	)	)	PUNCT
fuelectenerg-1427	1412	47	ulms	ulm	NOUN
fuelectenerg-1427	1412	48	of	of	ADP
fuelectenerg-1427	1412	49	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	50	)	)	PUNCT
fuelectenerg-1427	1412	51	davio	davio	NOUN
fuelectenerg-1427	1412	52	{	{	PUNCT
fuelectenerg-1427	1412	53	d0,d1,d2	d0,d1,d2	PROPN
fuelectenerg-1427	1412	54	}	}	PUNCT
fuelectenerg-1427	1412	55	using	use	VERB
fuelectenerg-1427	1412	56	three	three	NUM
fuelectenerg-1427	1412	57	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	58	)	)	PUNCT
fuelectenerg-1427	1412	59	multiplication	multiplication	NOUN
fuelectenerg-1427	1412	60	gates	gate	NOUN
fuelectenerg-1427	1412	61	and	and	CCONJ
fuelectenerg-1427	1412	62	one	one	NUM
fuelectenerg-1427	1412	63	gf(3	gf(3	NOUN
fuelectenerg-1427	1412	64	)	)	PUNCT
fuelectenerg-1427	1412	65	addition	addition	NOUN
fuelectenerg-1427	1412	66	gate	gate	NOUN
fuelectenerg-1427	1412	67	,	,	PUNCT
fuelectenerg-1427	1412	68	(	(	PUNCT
fuelectenerg-1427	1412	69	c	c	X
fuelectenerg-1427	1412	70	)	)	PUNCT
fuelectenerg-1427	1412	71	ulm	ulm	NOUN
fuelectenerg-1427	1412	72	for	for	ADP
fuelectenerg-1427	1412	73	all	all	DET
fuelectenerg-1427	1412	74	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	75	)	)	PUNCT
fuelectenerg-1427	1412	76	davio	davio	NOUN
fuelectenerg-1427	1412	77	expansions	expansion	NOUN
fuelectenerg-1427	1412	78	using	use	VERB
fuelectenerg-1427	1412	79	four	four	NUM
fuelectenerg-1427	1412	80	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	81	)	)	PUNCT
fuelectenerg-1427	1412	82	multiplication	multiplication	NOUN
fuelectenerg-1427	1412	83	gates	gate	NOUN
fuelectenerg-1427	1412	84	,	,	PUNCT
fuelectenerg-1427	1412	85	one	one	NUM
fuelectenerg-1427	1412	86	gf(3	gf(3	NOUN
fuelectenerg-1427	1412	87	)	)	PUNCT
fuelectenerg-1427	1412	88	addition	addition	NOUN
fuelectenerg-1427	1412	89	gate	gate	NOUN
fuelectenerg-1427	1412	90	,	,	PUNCT
fuelectenerg-1427	1412	91	two	two	NUM
fuelectenerg-1427	1412	92	shift	shift	NOUN
fuelectenerg-1427	1412	93	operators	operator	NOUN
fuelectenerg-1427	1412	94	,	,	PUNCT
fuelectenerg-1427	1412	95	and	and	CCONJ
fuelectenerg-1427	1412	96	one	one	NUM
fuelectenerg-1427	1412	97	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1412	98	,	,	PUNCT
fuelectenerg-1427	1412	99	and	and	CCONJ
fuelectenerg-1427	1412	100	(	(	PUNCT
fuelectenerg-1427	1412	101	d	d	NOUN
fuelectenerg-1427	1412	102	)	)	PUNCT
fuelectenerg-1427	1412	103	general	general	ADJ
fuelectenerg-1427	1412	104	ulm	ulm	NOUN
fuelectenerg-1427	1412	105	of	of	ADP
fuelectenerg-1427	1412	106	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	107	)	)	PUNCT
fuelectenerg-1427	1412	108	s	s	PROPN
fuelectenerg-1427	1412	109	/	/	SYM
fuelectenerg-1427	1412	110	d	d	NOUN
fuelectenerg-1427	1412	111	node	node	NOUN
fuelectenerg-1427	1412	112	using	use	VERB
fuelectenerg-1427	1412	113	four	four	NUM
fuelectenerg-1427	1412	114	gf(3	gf(3	PROPN
fuelectenerg-1427	1412	115	)	)	PUNCT
fuelectenerg-1427	1412	116	multiplication	multiplication	NOUN
fuelectenerg-1427	1412	117	gates	gate	NOUN
fuelectenerg-1427	1412	118	,	,	PUNCT
fuelectenerg-1427	1412	119	one	one	NUM
fuelectenerg-1427	1412	120	gf(3	gf(3	NOUN
fuelectenerg-1427	1412	121	)	)	PUNCT
fuelectenerg-1427	1412	122	addition	addition	NOUN
fuelectenerg-1427	1412	123	gate	gate	NOUN
fuelectenerg-1427	1412	124	and	and	CCONJ
fuelectenerg-1427	1412	125	four	four	NUM
fuelectenerg-1427	1412	126	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1412	127	.	.	PUNCT
fuelectenerg-1427	1413	1	corresponding	correspond	VERB
fuelectenerg-1427	1413	2	if	if	SCONJ
fuelectenerg-1427	1413	3	polarity	polarity	NOUN
fuelectenerg-1427	1413	4	,	,	PUNCT
fuelectenerg-1427	1413	5	which	which	PRON
fuelectenerg-1427	1413	6	contains	contain	VERB
fuelectenerg-1427	1413	7	the	the	DET
fuelectenerg-1427	1413	8	grm	grm	NOUN
fuelectenerg-1427	1413	9	as	as	ADP
fuelectenerg-1427	1413	10	a	a	DET
fuelectenerg-1427	1413	11	special	special	ADJ
fuelectenerg-1427	1413	12	case	case	NOUN
fuelectenerg-1427	1413	13	.	.	PUNCT
fuelectenerg-1427	1414	1	since	since	SCONJ
fuelectenerg-1427	1414	2	universal	universal	ADJ
fuelectenerg-1427	1414	3	logic	logic	NOUN
fuelectenerg-1427	1414	4	modules	module	NOUN
fuelectenerg-1427	1414	5	(	(	PUNCT
fuelectenerg-1427	1414	6	ulms	ulm	NOUN
fuelectenerg-1427	1414	7	)	)	PUNCT
fuelectenerg-1427	1414	8	are	be	AUX
fuelectenerg-1427	1414	9	complete	complete	ADJ
fuelectenerg-1427	1414	10	systems	system	NOUN
fuelectenerg-1427	1414	11	that	that	PRON
fuelectenerg-1427	1414	12	can	can	AUX
fuelectenerg-1427	1414	13	implement	implement	VERB
fuelectenerg-1427	1414	14	all	all	DET
fuelectenerg-1427	1414	15	possible	possible	ADJ
fuelectenerg-1427	1414	16	logic	logic	NOUN
fuelectenerg-1427	1414	17	functions	function	NOUN
fuelectenerg-1427	1414	18	utilizing	utilize	VERB
fuelectenerg-1427	1414	19	s	s	PART
fuelectenerg-1427	1414	20	/	/	SYM
fuelectenerg-1427	1414	21	d	d	NOUN
fuelectenerg-1427	1414	22	expansions	expansion	NOUN
fuelectenerg-1427	1414	23	of	of	ADP
fuelectenerg-1427	1414	24	multiple	multiple	ADV
fuelectenerg-1427	1414	25	-	-	PUNCT
fuelectenerg-1427	1414	26	valued	value	VERB
fuelectenerg-1427	1414	27	shannon	shannon	NOUN
fuelectenerg-1427	1414	28	and	and	CCONJ
fuelectenerg-1427	1414	29	davio	davio	NOUN
fuelectenerg-1427	1414	30	decompositions	decomposition	NOUN
fuelectenerg-1427	1414	31	,	,	PUNCT
fuelectenerg-1427	1414	32	the	the	DET
fuelectenerg-1427	1414	33	realization	realization	NOUN
fuelectenerg-1427	1414	34	of	of	ADP
fuelectenerg-1427	1414	35	the	the	DET
fuelectenerg-1427	1414	36	presented	present	VERB
fuelectenerg-1427	1414	37	s	s	PROPN
fuelectenerg-1427	1414	38	/	/	SYM
fuelectenerg-1427	1414	39	d	d	NOUN
fuelectenerg-1427	1414	40	trees	tree	NOUN
fuelectenerg-1427	1414	41	utilizing	utilize	VERB
fuelectenerg-1427	1414	42	the	the	DET
fuelectenerg-1427	1414	43	corresponding	corresponding	ADJ
fuelectenerg-1427	1414	44	ulms	ulm	NOUN
fuelectenerg-1427	1414	45	is	be	AUX
fuelectenerg-1427	1414	46	also	also	ADV
fuelectenerg-1427	1414	47	introduced	introduce	VERB
fuelectenerg-1427	1414	48	.	.	PUNCT
fuelectenerg-1427	1415	1	the	the	DET
fuelectenerg-1427	1415	2	application	application	NOUN
fuelectenerg-1427	1415	3	of	of	ADP
fuelectenerg-1427	1415	4	the	the	DET
fuelectenerg-1427	1415	5	presented	present	VERB
fuelectenerg-1427	1415	6	tifs	tif	NOUN
fuelectenerg-1427	1415	7	and	and	CCONJ
fuelectenerg-1427	1415	8	tgifs	tgif	NOUN
fuelectenerg-1427	1415	9	can	can	AUX
fuelectenerg-1427	1415	10	be	be	AUX
fuelectenerg-1427	1415	11	used	use	VERB
fuelectenerg-1427	1415	12	to	to	PART
fuelectenerg-1427	1415	13	find	find	VERB
fuelectenerg-1427	1415	14	minimum	minimum	ADJ
fuelectenerg-1427	1415	15	gfsop	gfsop	NOUN
fuelectenerg-1427	1415	16	for	for	ADP
fuelectenerg-1427	1415	17	multiple	multiple	ADV
fuelectenerg-1427	1415	18	-	-	PUNCT
fuelectenerg-1427	1415	19	valued	value	VERB
fuelectenerg-1427	1415	20	inputs	input	NOUN
fuelectenerg-1427	1415	21	-	-	PUNCT
fuelectenerg-1427	1415	22	outputs	output	NOUN
fuelectenerg-1427	1415	23	within	within	ADP
fuelectenerg-1427	1415	24	logic	logic	NOUN
fuelectenerg-1427	1415	25	synthesis	synthesis	NOUN
fuelectenerg-1427	1415	26	,	,	PUNCT
fuelectenerg-1427	1415	27	where	where	SCONJ
fuelectenerg-1427	1415	28	a	a	DET
fuelectenerg-1427	1415	29	gfsop	gfsop	NOUN
fuelectenerg-1427	1415	30	minimizer	minimizer	NOUN
fuelectenerg-1427	1415	31	based	base	VERB
fuelectenerg-1427	1415	32	on	on	ADP
fuelectenerg-1427	1415	33	if	if	SCONJ
fuelectenerg-1427	1415	34	polarity	polarity	NOUN
fuelectenerg-1427	1415	35	can	can	AUX
fuelectenerg-1427	1415	36	be	be	AUX
fuelectenerg-1427	1415	37	used	use	VERB
fuelectenerg-1427	1415	38	to	to	PART
fuelectenerg-1427	1415	39	minimize	minimize	VERB
fuelectenerg-1427	1415	40	the	the	DET
fuelectenerg-1427	1415	41	corresponding	correspond	VERB
fuelectenerg-1427	1415	42	multiple	multiple	ADV
fuelectenerg-1427	1415	43	-	-	PUNCT
fuelectenerg-1427	1415	44	valued	value	VERB
fuelectenerg-1427	1415	45	gfsop	gfsop	NOUN
fuelectenerg-1427	1415	46	expressions	expression	NOUN
fuelectenerg-1427	1415	47	.	.	PUNCT
fuelectenerg-1427	1416	1	115	115	NUM
fuelectenerg-1427	1416	2	an	an	DET
fuelectenerg-1427	1416	3	extended	extend	VERB
fuelectenerg-1427	1416	4	green	green	ADJ
fuelectenerg-1427	1416	5	sasao	sasao	PROPN
fuelectenerg-1427	1416	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1416	7	of	of	ADP
fuelectenerg-1427	1416	8	canonical	canonical	ADJ
fuelectenerg-1427	1416	9	ternary	ternary	ADJ
fuelectenerg-1427	1416	10	galois	galois	NOUN
fuelectenerg-1427	1416	11	forms	form	NOUN
fuelectenerg-1427	1416	12	...	...	PUNCT
fuelectenerg-1427	1417	1	•	•	NUM
fuelectenerg-1427	1417	2	•	•	NOUN
fuelectenerg-1427	1417	3	x	x	SYM
fuelectenerg-1427	1417	4	f0	f0	PROPN
fuelectenerg-1427	1417	5	f2	f2	PROPN
fuelectenerg-1427	1417	6	f1	f1	NOUN
fuelectenerg-1427	1417	7	0x	0x	NOUN
fuelectenerg-1427	1417	8	2	2	NUM
fuelectenerg-1427	1417	9	x	x	SYM
fuelectenerg-1427	1417	10	1	1	NUM
fuelectenerg-1427	1417	11	x	x	SYM
fuelectenerg-1427	1417	12	x	x	NOUN
fuelectenerg-1427	1417	13	f1	f1	NOUN
fuelectenerg-1427	1417	14	f0	f0	PROPN
fuelectenerg-1427	1418	1	+	+	PROPN
fuelectenerg-1427	1418	2	f	f	PROPN
fuelectenerg-1427	1418	3	1	1	NUM
fuelectenerg-1427	1418	4	+	+	NOUN
fuelectenerg-1427	1418	5	f	f	PROPN
fuelectenerg-1427	1418	6	2	2	NUM
fuelectenerg-1427	1418	7	2f2	2f2	NUM
fuelectenerg-1427	1419	1	+	+	NOUN
fuelectenerg-1427	1419	2	f	f	NOUN
fuelectenerg-1427	1419	3	0	0	NUM
fuelectenerg-1427	1419	4	1	1	NUM
fuelectenerg-1427	1419	5	2	2	NUM
fuelectenerg-1427	1419	6	(	(	PUNCT
fuelectenerg-1427	1419	7	”	"	PUNCT
fuelectenerg-1427	1419	8	)	)	PUNCT
fuelectenerg-1427	1419	9	x	x	SYM
fuelectenerg-1427	1419	10	2	2	NUM
fuelectenerg-1427	1419	11	x	x	NOUN
fuelectenerg-1427	1419	12	”	"	PUNCT
fuelectenerg-1427	1419	13	x	x	NUM
fuelectenerg-1427	1419	14	f0	f0	NOUN
fuelectenerg-1427	1419	15	f0	f0	PROPN
fuelectenerg-1427	1420	1	+	+	NOUN
fuelectenerg-1427	1420	2	f	f	PROPN
fuelectenerg-1427	1420	3	1	1	NUM
fuelectenerg-1427	1421	1	+	+	NOUN
fuelectenerg-1427	1421	2	f	f	PROPN
fuelectenerg-1427	1421	3	2	2	NUM
fuelectenerg-1427	1421	4	2f1	2f1	NUM
fuelectenerg-1427	1421	5	+	+	NOUN
fuelectenerg-1427	1421	6	f	f	PROPN
fuelectenerg-1427	1421	7	2	2	NUM
fuelectenerg-1427	1421	8	1	1	NUM
fuelectenerg-1427	1421	9	2	2	NUM
fuelectenerg-1427	1421	10	(	(	PUNCT
fuelectenerg-1427	1421	11	)	)	PUNCT
fuelectenerg-1427	1421	12	x	x	SYM
fuelectenerg-1427	1421	13	2	2	NUM
fuelectenerg-1427	1421	14	x	x	SYM
fuelectenerg-1427	1421	15	2	2	NUM
fuelectenerg-1427	1421	16	(	(	PUNCT
fuelectenerg-1427	1421	17	’	'	PUNCT
fuelectenerg-1427	1421	18	)	)	PUNCT
fuelectenerg-1427	1421	19	x	x	SYM
fuelectenerg-1427	1421	20	2	2	NUM
fuelectenerg-1427	1421	21	x	x	SYM
fuelectenerg-1427	1421	22	f2	f2	PROPN
fuelectenerg-1427	1421	23	f0	f0	PROPN
fuelectenerg-1427	1422	1	+	+	PROPN
fuelectenerg-1427	1422	2	f	f	PROPN
fuelectenerg-1427	1422	3	1	1	NUM
fuelectenerg-1427	1422	4	+	+	NOUN
fuelectenerg-1427	1422	5	f	f	PROPN
fuelectenerg-1427	1422	6	2	2	NUM
fuelectenerg-1427	1422	7	2f0	2f0	NUM
fuelectenerg-1427	1422	8	+	+	NOUN
fuelectenerg-1427	1422	9	f	f	NOUN
fuelectenerg-1427	1422	10	1	1	NUM
fuelectenerg-1427	1422	11	1	1	NUM
fuelectenerg-1427	1422	12	x	x	NOUN
fuelectenerg-1427	1422	13	’	'	PUNCT
fuelectenerg-1427	1423	1	+	+	PROPN
fuelectenerg-1427	1424	1	+	+	PUNCT
fuelectenerg-1427	1424	2	+	+	PUNCT
fuelectenerg-1427	1425	1	+	+	PUNCT
fuelectenerg-1427	1425	2	+	+	SYM
fuelectenerg-1427	1425	3	0	0	NUM
fuelectenerg-1427	1425	4	x	x	SYM
fuelectenerg-1427	1425	5	1	1	NUM
fuelectenerg-1427	1425	6	1	1	NUM
fuelectenerg-1427	1425	7	x	x	SYM
fuelectenerg-1427	1425	8	2	2	NUM
fuelectenerg-1427	1425	9	x	x	SYM
fuelectenerg-1427	1425	10	2	2	NUM
fuelectenerg-1427	1425	11	x	x	SYM
fuelectenerg-1427	1425	12	x	x	NOUN
fuelectenerg-1427	1425	13	’	'	PUNCT
fuelectenerg-1427	1425	14	x	x	ADJ
fuelectenerg-1427	1425	15	”	"	PUNCT
fuelectenerg-1427	1425	16	fi	fi	NOUN
fuelectenerg-1427	1425	17	fk	fk	INTJ
fuelectenerg-1427	1426	1	fj	fj	INTJ
fuelectenerg-1427	1426	2	f	f	NOUN
fuelectenerg-1427	1426	3	x	x	SYM
fuelectenerg-1427	1426	4	1	1	NUM
fuelectenerg-1427	1426	5	2	2	NUM
fuelectenerg-1427	1426	6	�	�	PROPN
fuelectenerg-1427	1426	7	�	�	PROPN
fuelectenerg-1427	1426	8	�	�	PROPN
fuelectenerg-1427	1426	9	�	�	PROPN
fuelectenerg-1427	1426	10	�	�	PROPN
fuelectenerg-1427	1426	11	�	�	PROPN
fuelectenerg-1427	1426	12	�	�	PROPN
fuelectenerg-1427	1426	13	+	+	CCONJ
fuelectenerg-1427	1426	14	+1	+1	PROPN
fuelectenerg-1427	1427	1	fi	fi	NOUN
fuelectenerg-1427	1427	2	fk	fk	INTJ
fuelectenerg-1427	1428	1	fj	fj	INTJ
fuelectenerg-1427	1428	2	f	f	PROPN
fuelectenerg-1427	1428	3	+1	+1	PROPN
fuelectenerg-1427	1428	4	(	(	PUNCT
fuelectenerg-1427	1428	5	a	a	NOUN
fuelectenerg-1427	1428	6	)	)	PUNCT
fuelectenerg-1427	1428	7	(	(	PUNCT
fuelectenerg-1427	1428	8	b	b	X
fuelectenerg-1427	1428	9	)	)	PUNCT
fuelectenerg-1427	1428	10	(	(	PUNCT
fuelectenerg-1427	1428	11	c	c	X
fuelectenerg-1427	1428	12	)	)	PUNCT
fuelectenerg-1427	1428	13	(	(	PUNCT
fuelectenerg-1427	1428	14	d	d	X
fuelectenerg-1427	1428	15	)	)	PUNCT
fuelectenerg-1427	1428	16	figure	figure	NOUN
fuelectenerg-1427	1428	17	7	7	NUM
fuelectenerg-1427	1428	18	:	:	PUNCT
fuelectenerg-1427	1428	19	various	various	ADJ
fuelectenerg-1427	1428	20	ternary	ternary	ADJ
fuelectenerg-1427	1428	21	ulms	ulm	NOUN
fuelectenerg-1427	1428	22	:	:	PUNCT
fuelectenerg-1427	1428	23	(	(	PUNCT
fuelectenerg-1427	1428	24	a	a	X
fuelectenerg-1427	1428	25	)	)	PUNCT
fuelectenerg-1427	1428	26	ulm	ulm	NOUN
fuelectenerg-1427	1428	27	of	of	ADP
fuelectenerg-1427	1428	28	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	29	)	)	PUNCT
fuelectenerg-1427	1428	30	shannon	shannon	NOUN
fuelectenerg-1427	1428	31	using	use	VERB
fuelectenerg-1427	1428	32	three	three	NUM
fuelectenerg-1427	1428	33	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	34	)	)	PUNCT
fuelectenerg-1427	1428	35	multiplication	multiplication	NOUN
fuelectenerg-1427	1428	36	gates	gate	NOUN
fuelectenerg-1427	1428	37	and	and	CCONJ
fuelectenerg-1427	1428	38	one	one	NUM
fuelectenerg-1427	1428	39	gf(3	gf(3	NOUN
fuelectenerg-1427	1428	40	)	)	PUNCT
fuelectenerg-1427	1428	41	addition	addition	NOUN
fuelectenerg-1427	1428	42	gate	gate	NOUN
fuelectenerg-1427	1428	43	,	,	PUNCT
fuelectenerg-1427	1428	44	(	(	PUNCT
fuelectenerg-1427	1428	45	b	b	X
fuelectenerg-1427	1428	46	)	)	PUNCT
fuelectenerg-1427	1428	47	ulms	ulm	NOUN
fuelectenerg-1427	1428	48	of	of	ADP
fuelectenerg-1427	1428	49	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	50	)	)	PUNCT
fuelectenerg-1427	1428	51	davio	davio	NOUN
fuelectenerg-1427	1428	52	{	{	PUNCT
fuelectenerg-1427	1428	53	d0,d1,d2	d0,d1,d2	PROPN
fuelectenerg-1427	1428	54	}	}	PUNCT
fuelectenerg-1427	1428	55	using	use	VERB
fuelectenerg-1427	1428	56	three	three	NUM
fuelectenerg-1427	1428	57	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	58	)	)	PUNCT
fuelectenerg-1427	1428	59	multiplication	multiplication	NOUN
fuelectenerg-1427	1428	60	gates	gate	NOUN
fuelectenerg-1427	1428	61	and	and	CCONJ
fuelectenerg-1427	1428	62	one	one	NUM
fuelectenerg-1427	1428	63	gf(3	gf(3	NOUN
fuelectenerg-1427	1428	64	)	)	PUNCT
fuelectenerg-1427	1428	65	addition	addition	NOUN
fuelectenerg-1427	1428	66	gate	gate	NOUN
fuelectenerg-1427	1428	67	,	,	PUNCT
fuelectenerg-1427	1428	68	(	(	PUNCT
fuelectenerg-1427	1428	69	c	c	X
fuelectenerg-1427	1428	70	)	)	PUNCT
fuelectenerg-1427	1428	71	ulm	ulm	NOUN
fuelectenerg-1427	1428	72	for	for	ADP
fuelectenerg-1427	1428	73	all	all	DET
fuelectenerg-1427	1428	74	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	75	)	)	PUNCT
fuelectenerg-1427	1428	76	davio	davio	NOUN
fuelectenerg-1427	1428	77	expansions	expansion	NOUN
fuelectenerg-1427	1428	78	using	use	VERB
fuelectenerg-1427	1428	79	four	four	NUM
fuelectenerg-1427	1428	80	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	81	)	)	PUNCT
fuelectenerg-1427	1428	82	multiplication	multiplication	NOUN
fuelectenerg-1427	1428	83	gates	gate	NOUN
fuelectenerg-1427	1428	84	,	,	PUNCT
fuelectenerg-1427	1428	85	one	one	NUM
fuelectenerg-1427	1428	86	gf(3	gf(3	NOUN
fuelectenerg-1427	1428	87	)	)	PUNCT
fuelectenerg-1427	1428	88	addition	addition	NOUN
fuelectenerg-1427	1428	89	gate	gate	NOUN
fuelectenerg-1427	1428	90	,	,	PUNCT
fuelectenerg-1427	1428	91	two	two	NUM
fuelectenerg-1427	1428	92	shift	shift	NOUN
fuelectenerg-1427	1428	93	operators	operator	NOUN
fuelectenerg-1427	1428	94	,	,	PUNCT
fuelectenerg-1427	1428	95	and	and	CCONJ
fuelectenerg-1427	1428	96	one	one	NUM
fuelectenerg-1427	1428	97	multiplexer	multiplexer	NOUN
fuelectenerg-1427	1428	98	,	,	PUNCT
fuelectenerg-1427	1428	99	and	and	CCONJ
fuelectenerg-1427	1428	100	(	(	PUNCT
fuelectenerg-1427	1428	101	d	d	NOUN
fuelectenerg-1427	1428	102	)	)	PUNCT
fuelectenerg-1427	1428	103	general	general	ADJ
fuelectenerg-1427	1428	104	ulm	ulm	NOUN
fuelectenerg-1427	1428	105	of	of	ADP
fuelectenerg-1427	1428	106	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	107	)	)	PUNCT
fuelectenerg-1427	1428	108	s	s	PROPN
fuelectenerg-1427	1428	109	/	/	SYM
fuelectenerg-1427	1428	110	d	d	NOUN
fuelectenerg-1427	1428	111	node	node	NOUN
fuelectenerg-1427	1428	112	using	use	VERB
fuelectenerg-1427	1428	113	four	four	NUM
fuelectenerg-1427	1428	114	gf(3	gf(3	PROPN
fuelectenerg-1427	1428	115	)	)	PUNCT
fuelectenerg-1427	1428	116	multiplication	multiplication	NOUN
fuelectenerg-1427	1428	117	gates	gate	NOUN
fuelectenerg-1427	1428	118	,	,	PUNCT
fuelectenerg-1427	1428	119	one	one	NUM
fuelectenerg-1427	1428	120	gf(3	gf(3	NOUN
fuelectenerg-1427	1428	121	)	)	PUNCT
fuelectenerg-1427	1428	122	addition	addition	NOUN
fuelectenerg-1427	1428	123	gate	gate	NOUN
fuelectenerg-1427	1428	124	and	and	CCONJ
fuelectenerg-1427	1428	125	four	four	NUM
fuelectenerg-1427	1428	126	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1428	127	.	.	PUNCT
fuelectenerg-1427	1429	1	corresponding	correspond	VERB
fuelectenerg-1427	1429	2	if	if	SCONJ
fuelectenerg-1427	1429	3	polarity	polarity	NOUN
fuelectenerg-1427	1429	4	,	,	PUNCT
fuelectenerg-1427	1429	5	which	which	PRON
fuelectenerg-1427	1429	6	contains	contain	VERB
fuelectenerg-1427	1429	7	the	the	DET
fuelectenerg-1427	1429	8	grm	grm	NOUN
fuelectenerg-1427	1429	9	as	as	ADP
fuelectenerg-1427	1429	10	a	a	DET
fuelectenerg-1427	1429	11	special	special	ADJ
fuelectenerg-1427	1429	12	case	case	NOUN
fuelectenerg-1427	1429	13	.	.	PUNCT
fuelectenerg-1427	1430	1	since	since	SCONJ
fuelectenerg-1427	1430	2	universal	universal	ADJ
fuelectenerg-1427	1430	3	logic	logic	NOUN
fuelectenerg-1427	1430	4	modules	module	NOUN
fuelectenerg-1427	1430	5	(	(	PUNCT
fuelectenerg-1427	1430	6	ulms	ulm	NOUN
fuelectenerg-1427	1430	7	)	)	PUNCT
fuelectenerg-1427	1430	8	are	be	AUX
fuelectenerg-1427	1430	9	complete	complete	ADJ
fuelectenerg-1427	1430	10	systems	system	NOUN
fuelectenerg-1427	1430	11	that	that	PRON
fuelectenerg-1427	1430	12	can	can	AUX
fuelectenerg-1427	1430	13	implement	implement	VERB
fuelectenerg-1427	1430	14	all	all	DET
fuelectenerg-1427	1430	15	possible	possible	ADJ
fuelectenerg-1427	1430	16	logic	logic	NOUN
fuelectenerg-1427	1430	17	functions	function	NOUN
fuelectenerg-1427	1430	18	utilizing	utilize	VERB
fuelectenerg-1427	1430	19	s	s	PART
fuelectenerg-1427	1430	20	/	/	SYM
fuelectenerg-1427	1430	21	d	d	NOUN
fuelectenerg-1427	1430	22	expansions	expansion	NOUN
fuelectenerg-1427	1430	23	of	of	ADP
fuelectenerg-1427	1430	24	multiple	multiple	ADV
fuelectenerg-1427	1430	25	-	-	PUNCT
fuelectenerg-1427	1430	26	valued	value	VERB
fuelectenerg-1427	1430	27	shannon	shannon	NOUN
fuelectenerg-1427	1430	28	and	and	CCONJ
fuelectenerg-1427	1430	29	davio	davio	NOUN
fuelectenerg-1427	1430	30	decompositions	decomposition	NOUN
fuelectenerg-1427	1430	31	,	,	PUNCT
fuelectenerg-1427	1430	32	the	the	DET
fuelectenerg-1427	1430	33	realization	realization	NOUN
fuelectenerg-1427	1430	34	of	of	ADP
fuelectenerg-1427	1430	35	the	the	DET
fuelectenerg-1427	1430	36	presented	present	VERB
fuelectenerg-1427	1430	37	s	s	PROPN
fuelectenerg-1427	1430	38	/	/	SYM
fuelectenerg-1427	1430	39	d	d	NOUN
fuelectenerg-1427	1430	40	trees	tree	NOUN
fuelectenerg-1427	1430	41	utilizing	utilize	VERB
fuelectenerg-1427	1430	42	the	the	DET
fuelectenerg-1427	1430	43	corresponding	corresponding	ADJ
fuelectenerg-1427	1430	44	ulms	ulm	NOUN
fuelectenerg-1427	1430	45	is	be	AUX
fuelectenerg-1427	1430	46	also	also	ADV
fuelectenerg-1427	1430	47	introduced	introduce	VERB
fuelectenerg-1427	1430	48	.	.	PUNCT
fuelectenerg-1427	1431	1	the	the	DET
fuelectenerg-1427	1431	2	application	application	NOUN
fuelectenerg-1427	1431	3	of	of	ADP
fuelectenerg-1427	1431	4	the	the	DET
fuelectenerg-1427	1431	5	presented	present	VERB
fuelectenerg-1427	1431	6	tifs	tif	NOUN
fuelectenerg-1427	1431	7	and	and	CCONJ
fuelectenerg-1427	1431	8	tgifs	tgif	NOUN
fuelectenerg-1427	1431	9	can	can	AUX
fuelectenerg-1427	1431	10	be	be	AUX
fuelectenerg-1427	1431	11	used	use	VERB
fuelectenerg-1427	1431	12	to	to	PART
fuelectenerg-1427	1431	13	find	find	VERB
fuelectenerg-1427	1431	14	minimum	minimum	ADJ
fuelectenerg-1427	1431	15	gfsop	gfsop	NOUN
fuelectenerg-1427	1431	16	for	for	ADP
fuelectenerg-1427	1431	17	multiple	multiple	ADV
fuelectenerg-1427	1431	18	-	-	PUNCT
fuelectenerg-1427	1431	19	valued	value	VERB
fuelectenerg-1427	1431	20	inputs	input	NOUN
fuelectenerg-1427	1431	21	-	-	PUNCT
fuelectenerg-1427	1431	22	outputs	output	NOUN
fuelectenerg-1427	1431	23	within	within	ADP
fuelectenerg-1427	1431	24	logic	logic	NOUN
fuelectenerg-1427	1431	25	synthesis	synthesis	NOUN
fuelectenerg-1427	1431	26	,	,	PUNCT
fuelectenerg-1427	1431	27	where	where	SCONJ
fuelectenerg-1427	1431	28	a	a	DET
fuelectenerg-1427	1431	29	gfsop	gfsop	NOUN
fuelectenerg-1427	1431	30	minimizer	minimizer	NOUN
fuelectenerg-1427	1431	31	based	base	VERB
fuelectenerg-1427	1431	32	on	on	ADP
fuelectenerg-1427	1431	33	if	if	SCONJ
fuelectenerg-1427	1431	34	polarity	polarity	NOUN
fuelectenerg-1427	1431	35	can	can	AUX
fuelectenerg-1427	1431	36	be	be	AUX
fuelectenerg-1427	1431	37	used	use	VERB
fuelectenerg-1427	1431	38	to	to	PART
fuelectenerg-1427	1431	39	minimize	minimize	VERB
fuelectenerg-1427	1431	40	the	the	DET
fuelectenerg-1427	1431	41	corresponding	correspond	VERB
fuelectenerg-1427	1431	42	multiple	multiple	ADV
fuelectenerg-1427	1431	43	-	-	PUNCT
fuelectenerg-1427	1431	44	valued	value	VERB
fuelectenerg-1427	1431	45	gfsop	gfsop	NOUN
fuelectenerg-1427	1431	46	expressions	expression	NOUN
fuelectenerg-1427	1431	47	.	.	PUNCT
fuelectenerg-1427	1432	1	115	115	NUM
fuelectenerg-1427	1432	2	64	64	NUM
fuelectenerg-1427	1432	3	a.	a.	NOUN
fuelectenerg-1427	1432	4	n.	n.	PROPN
fuelectenerg-1427	1432	5	al	al	PROPN
fuelectenerg-1427	1432	6	-	-	PUNCT
fuelectenerg-1427	1432	7	rabadi	rabadi	VERB
fuelectenerg-1427	1432	8	an	an	DET
fuelectenerg-1427	1432	9	extended	extended	ADJ
fuelectenerg-1427	1432	10	green	green	ADJ
fuelectenerg-1427	1432	11	sasao	sasao	PROPN
fuelectenerg-1427	1432	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1432	13	of	of	ADP
fuelectenerg-1427	1432	14	canonical	canonical	ADJ
fuelectenerg-1427	1432	15	ternary	ternary	ADJ
fuelectenerg-1427	1432	16	galois	galois	NOUN
fuelectenerg-1427	1432	17	forms	form	NOUN
fuelectenerg-1427	1432	18	and	and	CCONJ
fuelectenerg-1427	1432	19	universal	universal	ADJ
fuelectenerg-1427	1432	20	logic	logic	NOUN
fuelectenerg-1427	1432	21	modules	module	NOUN
fuelectenerg-1427	1432	22	65	65	NUM
fuelectenerg-1427	1432	23	an	an	DET
fuelectenerg-1427	1432	24	extended	extend	VERB
fuelectenerg-1427	1432	25	green	green	ADJ
fuelectenerg-1427	1432	26	sasao	sasao	PROPN
fuelectenerg-1427	1432	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1432	28	of	of	ADP
fuelectenerg-1427	1432	29	canonical	canonical	ADJ
fuelectenerg-1427	1432	30	ternary	ternary	ADJ
fuelectenerg-1427	1432	31	galois	galois	NOUN
fuelectenerg-1427	1432	32	forms	form	NOUN
fuelectenerg-1427	1432	33	...	...	PUNCT
fuelectenerg-1427	1433	1	future	future	ADJ
fuelectenerg-1427	1433	2	work	work	NOUN
fuelectenerg-1427	1433	3	will	will	AUX
fuelectenerg-1427	1433	4	include	include	VERB
fuelectenerg-1427	1433	5	the	the	DET
fuelectenerg-1427	1433	6	following	following	ADJ
fuelectenerg-1427	1433	7	items	item	NOUN
fuelectenerg-1427	1433	8	:	:	PUNCT
fuelectenerg-1427	1434	1	1	1	X
fuelectenerg-1427	1434	2	.	.	X
fuelectenerg-1427	1434	3	the	the	DET
fuelectenerg-1427	1434	4	investigation	investigation	NOUN
fuelectenerg-1427	1434	5	of	of	ADP
fuelectenerg-1427	1434	6	the	the	DET
fuelectenerg-1427	1434	7	various	various	ADJ
fuelectenerg-1427	1434	8	multiple	multiple	ADV
fuelectenerg-1427	1434	9	-	-	PUNCT
fuelectenerg-1427	1434	10	valued	value	VERB
fuelectenerg-1427	1434	11	and	and	CCONJ
fuelectenerg-1427	1434	12	two	two	NUM
fuelectenerg-1427	1434	13	-	-	PUNCT
fuelectenerg-1427	1434	14	valued	value	VERB
fuelectenerg-1427	1434	15	techniques	technique	NOUN
fuelectenerg-1427	1434	16	for	for	ADP
fuelectenerg-1427	1434	17	the	the	DET
fuelectenerg-1427	1434	18	ulm	ulm	NOUN
fuelectenerg-1427	1434	19	implementation	implementation	NOUN
fuelectenerg-1427	1434	20	for	for	ADP
fuelectenerg-1427	1434	21	the	the	DET
fuelectenerg-1427	1434	22	important	important	ADJ
fuelectenerg-1427	1434	23	case	case	NOUN
fuelectenerg-1427	1434	24	of	of	ADP
fuelectenerg-1427	1434	25	quaternary	quaternary	ADJ
fuelectenerg-1427	1434	26	logic	logic	NOUN
fuelectenerg-1427	1434	27	.	.	PUNCT
fuelectenerg-1427	1435	1	since	since	SCONJ
fuelectenerg-1427	1435	2	the	the	DET
fuelectenerg-1427	1435	3	ulm	ulm	PROPN
fuelectenerg-1427	1435	4	realization	realization	NOUN
fuelectenerg-1427	1435	5	over	over	ADP
fuelectenerg-1427	1435	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1435	7	)	)	PUNCT
fuelectenerg-1427	1435	8	extends	extend	VERB
fuelectenerg-1427	1435	9	and	and	CCONJ
fuelectenerg-1427	1435	10	generalizes	generalize	VERB
fuelectenerg-1427	1435	11	from	from	ADP
fuelectenerg-1427	1435	12	the	the	DET
fuelectenerg-1427	1435	13	binary	binary	ADJ
fuelectenerg-1427	1435	14	case	case	NOUN
fuelectenerg-1427	1435	15	of	of	ADP
fuelectenerg-1427	1435	16	the	the	DET
fuelectenerg-1427	1435	17	gf(2	gf(2	PROPN
fuelectenerg-1427	1435	18	)	)	PUNCT
fuelectenerg-1427	1435	19	ulm	ulm	PROPN
fuelectenerg-1427	1435	20	realization	realization	NOUN
fuelectenerg-1427	1435	21	where	where	SCONJ
fuelectenerg-1427	1435	22	most	most	ADJ
fuelectenerg-1427	1435	23	digital	digital	ADJ
fuelectenerg-1427	1435	24	system	system	NOUN
fuelectenerg-1427	1435	25	designs	design	NOUN
fuelectenerg-1427	1435	26	are	be	AUX
fuelectenerg-1427	1435	27	performed	perform	VERB
fuelectenerg-1427	1435	28	the	the	DET
fuelectenerg-1427	1435	29	special	special	ADJ
fuelectenerg-1427	1435	30	case	case	NOUN
fuelectenerg-1427	1435	31	of	of	ADP
fuelectenerg-1427	1435	32	the	the	DET
fuelectenerg-1427	1435	33	extension	extension	NOUN
fuelectenerg-1427	1435	34	into	into	ADP
fuelectenerg-1427	1435	35	gf(4	gf(4	NOUN
fuelectenerg-1427	1435	36	)	)	PUNCT
fuelectenerg-1427	1435	37	becomes	become	VERB
fuelectenerg-1427	1435	38	important	important	ADJ
fuelectenerg-1427	1435	39	as	as	SCONJ
fuelectenerg-1427	1435	40	this	this	DET
fuelectenerg-1427	1435	41	gf(4	gf(4	NOUN
fuelectenerg-1427	1435	42	)	)	PUNCT
fuelectenerg-1427	1435	43	ulm	ulm	NOUN
fuelectenerg-1427	1435	44	realization	realization	NOUN
fuelectenerg-1427	1435	45	can	can	AUX
fuelectenerg-1427	1435	46	be	be	AUX
fuelectenerg-1427	1435	47	achieved	achieve	VERB
fuelectenerg-1427	1435	48	by	by	ADP
fuelectenerg-1427	1435	49	utilizing	utilize	VERB
fuelectenerg-1427	1435	50	the	the	DET
fuelectenerg-1427	1435	51	currently	currently	ADV
fuelectenerg-1427	1435	52	existing	exist	VERB
fuelectenerg-1427	1435	53	and	and	CCONJ
fuelectenerg-1427	1435	54	widely	widely	ADV
fuelectenerg-1427	1435	55	-	-	PUNCT
fuelectenerg-1427	1435	56	used	use	VERB
fuelectenerg-1427	1435	57	implementations	implementation	NOUN
fuelectenerg-1427	1435	58	over	over	ADP
fuelectenerg-1427	1435	59	gf(2	gf(2	PROPN
fuelectenerg-1427	1435	60	)	)	PUNCT
fuelectenerg-1427	1435	61	.	.	PUNCT
fuelectenerg-1427	1436	1	this	this	DET
fuelectenerg-1427	1436	2	two	two	NUM
fuelectenerg-1427	1436	3	-	-	PUNCT
fuelectenerg-1427	1436	4	valued	value	VERB
fuelectenerg-1427	1436	5	realization	realization	NOUN
fuelectenerg-1427	1436	6	of	of	ADP
fuelectenerg-1427	1436	7	quaternary	quaternary	ADJ
fuelectenerg-1427	1436	8	ulm	ulm	NOUN
fuelectenerg-1427	1436	9	can	can	AUX
fuelectenerg-1427	1436	10	be	be	AUX
fuelectenerg-1427	1436	11	done	do	VERB
fuelectenerg-1427	1436	12	for	for	ADP
fuelectenerg-1427	1436	13	gf(4	gf(4	NOUN
fuelectenerg-1427	1436	14	)	)	PUNCT
fuelectenerg-1427	1436	15	addition	addition	NOUN
fuelectenerg-1427	1436	16	utilizing	utilize	VERB
fuelectenerg-1427	1436	17	gf(2	gf(2	NOUN
fuelectenerg-1427	1436	18	)	)	PUNCT
fuelectenerg-1427	1436	19	addition	addition	NOUN
fuelectenerg-1427	1436	20	using	use	VERB
fuelectenerg-1427	1436	21	vector	vector	NOUN
fuelectenerg-1427	1436	22	of	of	ADP
fuelectenerg-1427	1436	23	exors	exor	NOUN
fuelectenerg-1427	1436	24	,	,	PUNCT
fuelectenerg-1427	1436	25	(	(	PUNCT
fuelectenerg-1427	1436	26	4/2	4/2	NUM
fuelectenerg-1427	1436	27	)	)	PUNCT
fuelectenerg-1427	1436	28	and	and	CCONJ
fuelectenerg-1427	1436	29	(	(	PUNCT
fuelectenerg-1427	1436	30	2/4	2/4	NUM
fuelectenerg-1427	1436	31	)	)	PUNCT
fuelectenerg-1427	1436	32	decoders	decoder	NOUN
fuelectenerg-1427	1436	33	,	,	PUNCT
fuelectenerg-1427	1436	34	and	and	CCONJ
fuelectenerg-1427	1436	35	for	for	ADP
fuelectenerg-1427	1436	36	gf(4	gf(4	NOUN
fuelectenerg-1427	1436	37	)	)	PUNCT
fuelectenerg-1427	1436	38	multiplication	multiplication	NOUN
fuelectenerg-1427	1436	39	utilizing	utilize	VERB
fuelectenerg-1427	1436	40	gf(2	gf(2	PROPN
fuelectenerg-1427	1436	41	)	)	PUNCT
fuelectenerg-1427	1436	42	operations	operation	NOUN
fuelectenerg-1427	1436	43	using	use	VERB
fuelectenerg-1427	1436	44	vectors	vector	NOUN
fuelectenerg-1427	1436	45	of	of	ADP
fuelectenerg-1427	1436	46	xors	xor	NOUN
fuelectenerg-1427	1436	47	,	,	PUNCT
fuelectenerg-1427	1436	48	ands	and	NOUN
fuelectenerg-1427	1436	49	,	,	PUNCT
fuelectenerg-1427	1436	50	(	(	PUNCT
fuelectenerg-1427	1436	51	4/2	4/2	NUM
fuelectenerg-1427	1436	52	)	)	PUNCT
fuelectenerg-1427	1436	53	and	and	CCONJ
fuelectenerg-1427	1436	54	(	(	PUNCT
fuelectenerg-1427	1436	55	2/4	2/4	NUM
fuelectenerg-1427	1436	56	)	)	PUNCT
fuelectenerg-1427	1436	57	decoders	decoder	NOUN
fuelectenerg-1427	1436	58	,	,	PUNCT
fuelectenerg-1427	1436	59	and	and	CCONJ
fuelectenerg-1427	1436	60	therefore	therefore	ADV
fuelectenerg-1427	1436	61	the	the	DET
fuelectenerg-1427	1436	62	gf(4	gf(4	NOUN
fuelectenerg-1427	1436	63	)	)	PUNCT
fuelectenerg-1427	1436	64	ulm	ulm	NOUN
fuelectenerg-1427	1436	65	producing	produce	VERB
fuelectenerg-1427	1436	66	quaternary	quaternary	ADJ
fuelectenerg-1427	1436	67	shannon	shannon	NOUN
fuelectenerg-1427	1436	68	and	and	CCONJ
fuelectenerg-1427	1436	69	all	all	DET
fuelectenerg-1427	1436	70	davio	davio	NOUN
fuelectenerg-1427	1436	71	expansions	expansion	NOUN
fuelectenerg-1427	1436	72	can	can	AUX
fuelectenerg-1427	1436	73	be	be	AUX
fuelectenerg-1427	1436	74	achieved	achieve	VERB
fuelectenerg-1427	1436	75	using	use	VERB
fuelectenerg-1427	1436	76	the	the	DET
fuelectenerg-1427	1436	77	corresponding	correspond	VERB
fuelectenerg-1427	1436	78	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1436	79	and	and	CCONJ
fuelectenerg-1427	1436	80	gf(4	gf(4	NOUN
fuelectenerg-1427	1436	81	)	)	PUNCT
fuelectenerg-1427	1436	82	additions	addition	NOUN
fuelectenerg-1427	1436	83	and	and	CCONJ
fuelectenerg-1427	1436	84	multiplications	multiplication	NOUN
fuelectenerg-1427	1436	85	which	which	PRON
fuelectenerg-1427	1436	86	can	can	AUX
fuelectenerg-1427	1436	87	be	be	AUX
fuelectenerg-1427	1436	88	accordingly	accordingly	ADV
fuelectenerg-1427	1436	89	realized	realize	VERB
fuelectenerg-1427	1436	90	using	use	VERB
fuelectenerg-1427	1436	91	gf(2	gf(2	PROPN
fuelectenerg-1427	1436	92	)	)	PUNCT
fuelectenerg-1427	1436	93	methods	method	NOUN
fuelectenerg-1427	1436	94	.	.	PUNCT
fuelectenerg-1427	1437	1	2	2	X
fuelectenerg-1427	1437	2	.	.	X
fuelectenerg-1427	1437	3	the	the	DET
fuelectenerg-1427	1437	4	implementation	implementation	NOUN
fuelectenerg-1427	1437	5	of	of	ADP
fuelectenerg-1427	1437	6	the	the	DET
fuelectenerg-1427	1437	7	introduced	introduce	VERB
fuelectenerg-1427	1437	8	ulms	ulm	NOUN
fuelectenerg-1427	1437	9	using	use	VERB
fuelectenerg-1427	1437	10	nanotechnology	nanotechnology	NOUN
fuelectenerg-1427	1437	11	methods	method	NOUN
fuelectenerg-1427	1437	12	such	such	ADJ
fuelectenerg-1427	1437	13	as	as	ADP
fuelectenerg-1427	1437	14	quantum	quantum	NOUN
fuelectenerg-1427	1437	15	computing	computing	NOUN
fuelectenerg-1427	1437	16	,	,	PUNCT
fuelectenerg-1427	1437	17	quantum	quantum	ADJ
fuelectenerg-1427	1437	18	dots	dot	NOUN
fuelectenerg-1427	1437	19	and	and	CCONJ
fuelectenerg-1427	1437	20	carbon	carbon	NOUN
fuelectenerg-1427	1437	21	nanotubes	nanotube	NOUN
fuelectenerg-1427	1437	22	.	.	PUNCT
fuelectenerg-1427	1438	1	3	3	X
fuelectenerg-1427	1438	2	.	.	X
fuelectenerg-1427	1438	3	the	the	DET
fuelectenerg-1427	1438	4	utilization	utilization	NOUN
fuelectenerg-1427	1438	5	of	of	ADP
fuelectenerg-1427	1438	6	evolutionary	evolutionary	ADJ
fuelectenerg-1427	1438	7	algorithms	algorithm	NOUN
fuelectenerg-1427	1438	8	for	for	ADP
fuelectenerg-1427	1438	9	function	function	NOUN
fuelectenerg-1427	1438	10	minimization	minimization	NOUN
fuelectenerg-1427	1438	11	using	use	VERB
fuelectenerg-1427	1438	12	the	the	DET
fuelectenerg-1427	1438	13	introduced	introduce	VERB
fuelectenerg-1427	1438	14	s	s	PROPN
fuelectenerg-1427	1438	15	/	/	SYM
fuelectenerg-1427	1438	16	d	d	NOUN
fuelectenerg-1427	1438	17	trees	tree	NOUN
fuelectenerg-1427	1438	18	.	.	PUNCT
fuelectenerg-1427	1439	1	4	4	X
fuelectenerg-1427	1439	2	.	.	X
fuelectenerg-1427	1439	3	the	the	DET
fuelectenerg-1427	1439	4	investigation	investigation	NOUN
fuelectenerg-1427	1439	5	using	use	VERB
fuelectenerg-1427	1439	6	other	other	ADJ
fuelectenerg-1427	1439	7	more	more	ADV
fuelectenerg-1427	1439	8	complex	complex	ADJ
fuelectenerg-1427	1439	9	types	type	NOUN
fuelectenerg-1427	1439	10	of	of	ADP
fuelectenerg-1427	1439	11	literals	literal	NOUN
fuelectenerg-1427	1439	12	such	such	ADJ
fuelectenerg-1427	1439	13	as	as	ADP
fuelectenerg-1427	1439	14	the	the	DET
fuelectenerg-1427	1439	15	presented	present	VERB
fuelectenerg-1427	1439	16	generalized	generalized	ADJ
fuelectenerg-1427	1439	17	literal	literal	ADJ
fuelectenerg-1427	1439	18	(	(	PUNCT
fuelectenerg-1427	1439	19	gl	gl	NOUN
fuelectenerg-1427	1439	20	)	)	PUNCT
fuelectenerg-1427	1439	21	and	and	CCONJ
fuelectenerg-1427	1439	22	universal	universal	ADJ
fuelectenerg-1427	1439	23	literal	literal	ADJ
fuelectenerg-1427	1439	24	(	(	PUNCT
fuelectenerg-1427	1439	25	ul	ul	INTJ
fuelectenerg-1427	1439	26	)	)	PUNCT
fuelectenerg-1427	1439	27	to	to	PART
fuelectenerg-1427	1439	28	expand	expand	VERB
fuelectenerg-1427	1439	29	upon	upon	SCONJ
fuelectenerg-1427	1439	30	and	and	CCONJ
fuelectenerg-1427	1439	31	consequently	consequently	ADV
fuelectenerg-1427	1439	32	construct	construct	VERB
fuelectenerg-1427	1439	33	the	the	DET
fuelectenerg-1427	1439	34	corresponding	corresponding	ADJ
fuelectenerg-1427	1439	35	new	new	ADJ
fuelectenerg-1427	1439	36	ulms	ulm	NOUN
fuelectenerg-1427	1439	37	.	.	PUNCT
fuelectenerg-1427	1440	1	acknowledgment	acknowledgment	NOUN
fuelectenerg-1427	1440	2	this	this	DET
fuelectenerg-1427	1440	3	research	research	NOUN
fuelectenerg-1427	1440	4	was	be	AUX
fuelectenerg-1427	1440	5	performed	perform	VERB
fuelectenerg-1427	1440	6	during	during	ADP
fuelectenerg-1427	1440	7	sabbatical	sabbatical	ADJ
fuelectenerg-1427	1440	8	leave	leave	NOUN
fuelectenerg-1427	1440	9	in	in	ADP
fuelectenerg-1427	1440	10	2015	2015	NUM
fuelectenerg-1427	1440	11	-	-	SYM
fuelectenerg-1427	1440	12	2016	2016	NUM
fuelectenerg-1427	1440	13	granted	grant	VERB
fuelectenerg-1427	1440	14	from	from	ADP
fuelectenerg-1427	1440	15	the	the	DET
fuelectenerg-1427	1440	16	university	university	NOUN
fuelectenerg-1427	1440	17	jordan	jordan	PROPN
fuelectenerg-1427	1440	18	and	and	CCONJ
fuelectenerg-1427	1440	19	spent	spend	VERB
fuelectenerg-1427	1440	20	at	at	ADP
fuelectenerg-1427	1440	21	philadelphia	philadelphia	PROPN
fuelectenerg-1427	1440	22	university	university	NOUN
fuelectenerg-1427	1440	23	references	reference	NOUN
fuelectenerg-1427	1441	1	[	[	X
fuelectenerg-1427	1441	2	1	1	NUM
fuelectenerg-1427	1441	3	]	]	PUNCT
fuelectenerg-1427	1441	4	a.	a.	NOUN
fuelectenerg-1427	1441	5	n.	n.	PROPN
fuelectenerg-1427	1441	6	al	al	PROPN
fuelectenerg-1427	1441	7	-	-	PUNCT
fuelectenerg-1427	1441	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1441	9	,	,	PUNCT
fuelectenerg-1427	1441	10	reversible	reversible	ADJ
fuelectenerg-1427	1441	11	logic	logic	NOUN
fuelectenerg-1427	1441	12	synthesis	synthesis	NOUN
fuelectenerg-1427	1441	13	:	:	PUNCT
fuelectenerg-1427	1441	14	from	from	ADP
fuelectenerg-1427	1441	15	fundamentals	fundamental	NOUN
fuelectenerg-1427	1441	16	to	to	ADP
fuelectenerg-1427	1441	17	quantum	quantum	ADJ
fuelectenerg-1427	1441	18	computing	computing	NOUN
fuelectenerg-1427	1441	19	,	,	PUNCT
fuelectenerg-1427	1441	20	springer	springer	NOUN
fuelectenerg-1427	1441	21	-	-	PUNCT
fuelectenerg-1427	1441	22	verlag	verlag	PROPN
fuelectenerg-1427	1441	23	,	,	PUNCT
fuelectenerg-1427	1441	24	2004	2004	NUM
fuelectenerg-1427	1441	25	.	.	PUNCT
fuelectenerg-1427	1442	1	[	[	X
fuelectenerg-1427	1442	2	2	2	NUM
fuelectenerg-1427	1442	3	]	]	PUNCT
fuelectenerg-1427	1442	4	a.	a.	NOUN
fuelectenerg-1427	1442	5	n.	n.	PROPN
fuelectenerg-1427	1442	6	al	al	PROPN
fuelectenerg-1427	1442	7	-	-	PUNCT
fuelectenerg-1427	1442	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1442	9	,	,	PUNCT
fuelectenerg-1427	1442	10	"	"	PUNCT
fuelectenerg-1427	1442	11	three	three	NUM
fuelectenerg-1427	1442	12	-	-	PUNCT
fuelectenerg-1427	1442	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1442	14	lattice	lattice	ADJ
fuelectenerg-1427	1442	15	logic	logic	NOUN
fuelectenerg-1427	1442	16	circuits	circuit	NOUN
fuelectenerg-1427	1442	17	,	,	PUNCT
fuelectenerg-1427	1442	18	part	part	NOUN
fuelectenerg-1427	1442	19	iii	iii	NOUN
fuelectenerg-1427	1442	20	:	:	PUNCT
fuelectenerg-1427	1442	21	solving	solve	VERB
fuelectenerg-1427	1442	22	3d	3d	NUM
fuelectenerg-1427	1442	23	volume	volume	NOUN
fuelectenerg-1427	1442	24	congestion	congestion	NOUN
fuelectenerg-1427	1442	25	problem	problem	NOUN
fuelectenerg-1427	1442	26	,	,	PUNCT
fuelectenerg-1427	1442	27	"	"	PUNCT
fuelectenerg-1427	1442	28	facta	facta	PROPN
fuelectenerg-1427	1442	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1442	30	electronics	electronic	NOUN
fuelectenerg-1427	1442	31	and	and	CCONJ
fuelectenerg-1427	1442	32	energetics	energetic	NOUN
fuelectenerg-1427	1442	33	,	,	PUNCT
fuelectenerg-1427	1442	34	vol	vol	NOUN
fuelectenerg-1427	1442	35	.	.	PROPN
fuelectenerg-1427	1442	36	18	18	NUM
fuelectenerg-1427	1442	37	,	,	PUNCT
fuelectenerg-1427	1442	38	no	no	INTJ
fuelectenerg-1427	1442	39	.	.	NOUN
fuelectenerg-1427	1442	40	1	1	NUM
fuelectenerg-1427	1442	41	,	,	PUNCT
fuelectenerg-1427	1442	42	pp	pp	ADJ
fuelectenerg-1427	1442	43	.	.	PUNCT
fuelectenerg-1427	1443	1	29	29	NUM
fuelectenerg-1427	1443	2	43	43	NUM
fuelectenerg-1427	1443	3	,	,	PUNCT
fuelectenerg-1427	1443	4	2005	2005	NUM
fuelectenerg-1427	1443	5	.	.	PUNCT
fuelectenerg-1427	1444	1	[	[	X
fuelectenerg-1427	1444	2	3	3	NUM
fuelectenerg-1427	1444	3	]	]	PUNCT
fuelectenerg-1427	1444	4	a.	a.	NOUN
fuelectenerg-1427	1444	5	n.	n.	PROPN
fuelectenerg-1427	1444	6	al	al	PROPN
fuelectenerg-1427	1444	7	-	-	PUNCT
fuelectenerg-1427	1444	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1444	9	,	,	PUNCT
fuelectenerg-1427	1444	10	"	"	PUNCT
fuelectenerg-1427	1444	11	three	three	NUM
fuelectenerg-1427	1444	12	-	-	PUNCT
fuelectenerg-1427	1444	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1444	14	lattice	lattice	ADJ
fuelectenerg-1427	1444	15	logic	logic	NOUN
fuelectenerg-1427	1444	16	circuits	circuit	NOUN
fuelectenerg-1427	1444	17	,	,	PUNCT
fuelectenerg-1427	1444	18	part	part	PROPN
fuelectenerg-1427	1444	19	ii	ii	PROPN
fuelectenerg-1427	1444	20	:	:	PUNCT
fuelectenerg-1427	1444	21	formal	formal	ADJ
fuelectenerg-1427	1444	22	methods	method	NOUN
fuelectenerg-1427	1444	23	,	,	PUNCT
fuelectenerg-1427	1444	24	"	"	PUNCT
fuelectenerg-1427	1444	25	facta	facta	PROPN
fuelectenerg-1427	1444	26	universitatis	universitatis	PROPN
fuelectenerg-1427	1444	27	electronics	electronic	NOUN
fuelectenerg-1427	1444	28	and	and	CCONJ
fuelectenerg-1427	1444	29	energetics	energetic	NOUN
fuelectenerg-1427	1444	30	,	,	PUNCT
fuelectenerg-1427	1444	31	vol	vol	NOUN
fuelectenerg-1427	1444	32	.	.	PROPN
fuelectenerg-1427	1444	33	18	18	NUM
fuelectenerg-1427	1444	34	,	,	PUNCT
fuelectenerg-1427	1444	35	no	no	INTJ
fuelectenerg-1427	1444	36	.	.	NOUN
fuelectenerg-1427	1444	37	1	1	NUM
fuelectenerg-1427	1444	38	,	,	PUNCT
fuelectenerg-1427	1444	39	pp	pp	ADJ
fuelectenerg-1427	1444	40	.	.	PUNCT
fuelectenerg-1427	1445	1	15	15	NUM
fuelectenerg-1427	1445	2	28	28	NUM
fuelectenerg-1427	1445	3	,	,	PUNCT
fuelectenerg-1427	1445	4	2005	2005	NUM
fuelectenerg-1427	1445	5	.	.	PUNCT
fuelectenerg-1427	1446	1	[	[	X
fuelectenerg-1427	1446	2	4	4	NUM
fuelectenerg-1427	1446	3	]	]	PUNCT
fuelectenerg-1427	1446	4	a.	a.	NOUN
fuelectenerg-1427	1446	5	n.	n.	PROPN
fuelectenerg-1427	1446	6	al	al	PROPN
fuelectenerg-1427	1446	7	-	-	PUNCT
fuelectenerg-1427	1446	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1446	9	,	,	PUNCT
fuelectenerg-1427	1446	10	"	"	PUNCT
fuelectenerg-1427	1446	11	three	three	NUM
fuelectenerg-1427	1446	12	-	-	PUNCT
fuelectenerg-1427	1446	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1446	14	lattice	lattice	ADJ
fuelectenerg-1427	1446	15	logic	logic	NOUN
fuelectenerg-1427	1446	16	circuits	circuit	NOUN
fuelectenerg-1427	1446	17	,	,	PUNCT
fuelectenerg-1427	1446	18	part	part	NOUN
fuelectenerg-1427	1446	19	i	i	PRON
fuelectenerg-1427	1446	20	:	:	PUNCT
fuelectenerg-1427	1446	21	fundamentals	fundamental	NOUN
fuelectenerg-1427	1446	22	,	,	PUNCT
fuelectenerg-1427	1446	23	"	"	PUNCT
fuelectenerg-1427	1446	24	facta	facta	PROPN
fuelectenerg-1427	1446	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1446	26	electronics	electronic	NOUN
fuelectenerg-1427	1446	27	and	and	CCONJ
fuelectenerg-1427	1446	28	energetics	energetic	NOUN
fuelectenerg-1427	1446	29	,	,	PUNCT
fuelectenerg-1427	1446	30	vol	vol	NOUN
fuelectenerg-1427	1446	31	.	.	PROPN
fuelectenerg-1427	1446	32	18	18	NUM
fuelectenerg-1427	1446	33	,	,	PUNCT
fuelectenerg-1427	1446	34	no	no	INTJ
fuelectenerg-1427	1446	35	.	.	NOUN
fuelectenerg-1427	1446	36	1	1	NUM
fuelectenerg-1427	1446	37	,	,	PUNCT
fuelectenerg-1427	1446	38	pp	pp	ADJ
fuelectenerg-1427	1446	39	.	.	PUNCT
fuelectenerg-1427	1446	40	1	1	NUM
fuelectenerg-1427	1446	41	13	13	NUM
fuelectenerg-1427	1446	42	,	,	PUNCT
fuelectenerg-1427	1446	43	2005	2005	NUM
fuelectenerg-1427	1446	44	.	.	PUNCT
fuelectenerg-1427	1447	1	116	116	NUM
fuelectenerg-1427	1447	2	an	an	DET
fuelectenerg-1427	1447	3	extended	extend	VERB
fuelectenerg-1427	1447	4	green	green	ADJ
fuelectenerg-1427	1447	5	sasao	sasao	PROPN
fuelectenerg-1427	1447	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1447	7	of	of	ADP
fuelectenerg-1427	1447	8	canonical	canonical	ADJ
fuelectenerg-1427	1447	9	ternary	ternary	ADJ
fuelectenerg-1427	1447	10	galois	galois	NOUN
fuelectenerg-1427	1447	11	forms	form	NOUN
fuelectenerg-1427	1447	12	...	...	PUNCT
fuelectenerg-1427	1447	13	future	future	ADJ
fuelectenerg-1427	1447	14	work	work	NOUN
fuelectenerg-1427	1447	15	will	will	AUX
fuelectenerg-1427	1447	16	include	include	VERB
fuelectenerg-1427	1447	17	the	the	DET
fuelectenerg-1427	1447	18	following	following	ADJ
fuelectenerg-1427	1447	19	items	item	NOUN
fuelectenerg-1427	1447	20	:	:	PUNCT
fuelectenerg-1427	1448	1	1	1	X
fuelectenerg-1427	1448	2	.	.	X
fuelectenerg-1427	1448	3	the	the	DET
fuelectenerg-1427	1448	4	investigation	investigation	NOUN
fuelectenerg-1427	1448	5	of	of	ADP
fuelectenerg-1427	1448	6	the	the	DET
fuelectenerg-1427	1448	7	various	various	ADJ
fuelectenerg-1427	1448	8	multiple	multiple	ADV
fuelectenerg-1427	1448	9	-	-	PUNCT
fuelectenerg-1427	1448	10	valued	value	VERB
fuelectenerg-1427	1448	11	and	and	CCONJ
fuelectenerg-1427	1448	12	two	two	NUM
fuelectenerg-1427	1448	13	-	-	PUNCT
fuelectenerg-1427	1448	14	valued	value	VERB
fuelectenerg-1427	1448	15	techniques	technique	NOUN
fuelectenerg-1427	1448	16	for	for	ADP
fuelectenerg-1427	1448	17	the	the	DET
fuelectenerg-1427	1448	18	ulm	ulm	NOUN
fuelectenerg-1427	1448	19	implementation	implementation	NOUN
fuelectenerg-1427	1448	20	for	for	ADP
fuelectenerg-1427	1448	21	the	the	DET
fuelectenerg-1427	1448	22	important	important	ADJ
fuelectenerg-1427	1448	23	case	case	NOUN
fuelectenerg-1427	1448	24	of	of	ADP
fuelectenerg-1427	1448	25	quaternary	quaternary	ADJ
fuelectenerg-1427	1448	26	logic	logic	NOUN
fuelectenerg-1427	1448	27	.	.	PUNCT
fuelectenerg-1427	1449	1	since	since	SCONJ
fuelectenerg-1427	1449	2	the	the	DET
fuelectenerg-1427	1449	3	ulm	ulm	PROPN
fuelectenerg-1427	1449	4	realization	realization	NOUN
fuelectenerg-1427	1449	5	over	over	ADP
fuelectenerg-1427	1449	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1449	7	)	)	PUNCT
fuelectenerg-1427	1449	8	extends	extend	VERB
fuelectenerg-1427	1449	9	and	and	CCONJ
fuelectenerg-1427	1449	10	generalizes	generalize	VERB
fuelectenerg-1427	1449	11	from	from	ADP
fuelectenerg-1427	1449	12	the	the	DET
fuelectenerg-1427	1449	13	binary	binary	ADJ
fuelectenerg-1427	1449	14	case	case	NOUN
fuelectenerg-1427	1449	15	of	of	ADP
fuelectenerg-1427	1449	16	the	the	DET
fuelectenerg-1427	1449	17	gf(2	gf(2	PROPN
fuelectenerg-1427	1449	18	)	)	PUNCT
fuelectenerg-1427	1449	19	ulm	ulm	PROPN
fuelectenerg-1427	1449	20	realization	realization	NOUN
fuelectenerg-1427	1449	21	where	where	SCONJ
fuelectenerg-1427	1449	22	most	most	ADJ
fuelectenerg-1427	1449	23	digital	digital	ADJ
fuelectenerg-1427	1449	24	system	system	NOUN
fuelectenerg-1427	1449	25	designs	design	NOUN
fuelectenerg-1427	1449	26	are	be	AUX
fuelectenerg-1427	1449	27	performed	perform	VERB
fuelectenerg-1427	1449	28	the	the	DET
fuelectenerg-1427	1449	29	special	special	ADJ
fuelectenerg-1427	1449	30	case	case	NOUN
fuelectenerg-1427	1449	31	of	of	ADP
fuelectenerg-1427	1449	32	the	the	DET
fuelectenerg-1427	1449	33	extension	extension	NOUN
fuelectenerg-1427	1449	34	into	into	ADP
fuelectenerg-1427	1449	35	gf(4	gf(4	NOUN
fuelectenerg-1427	1449	36	)	)	PUNCT
fuelectenerg-1427	1449	37	becomes	become	VERB
fuelectenerg-1427	1449	38	important	important	ADJ
fuelectenerg-1427	1449	39	as	as	SCONJ
fuelectenerg-1427	1449	40	this	this	DET
fuelectenerg-1427	1449	41	gf(4	gf(4	NOUN
fuelectenerg-1427	1449	42	)	)	PUNCT
fuelectenerg-1427	1449	43	ulm	ulm	NOUN
fuelectenerg-1427	1449	44	realization	realization	NOUN
fuelectenerg-1427	1449	45	can	can	AUX
fuelectenerg-1427	1449	46	be	be	AUX
fuelectenerg-1427	1449	47	achieved	achieve	VERB
fuelectenerg-1427	1449	48	by	by	ADP
fuelectenerg-1427	1449	49	utilizing	utilize	VERB
fuelectenerg-1427	1449	50	the	the	DET
fuelectenerg-1427	1449	51	currently	currently	ADV
fuelectenerg-1427	1449	52	existing	exist	VERB
fuelectenerg-1427	1449	53	and	and	CCONJ
fuelectenerg-1427	1449	54	widely	widely	ADV
fuelectenerg-1427	1449	55	-	-	PUNCT
fuelectenerg-1427	1449	56	used	use	VERB
fuelectenerg-1427	1449	57	implementations	implementation	NOUN
fuelectenerg-1427	1449	58	over	over	ADP
fuelectenerg-1427	1449	59	gf(2	gf(2	PROPN
fuelectenerg-1427	1449	60	)	)	PUNCT
fuelectenerg-1427	1449	61	.	.	PUNCT
fuelectenerg-1427	1450	1	this	this	DET
fuelectenerg-1427	1450	2	two	two	NUM
fuelectenerg-1427	1450	3	-	-	PUNCT
fuelectenerg-1427	1450	4	valued	value	VERB
fuelectenerg-1427	1450	5	realization	realization	NOUN
fuelectenerg-1427	1450	6	of	of	ADP
fuelectenerg-1427	1450	7	quaternary	quaternary	ADJ
fuelectenerg-1427	1450	8	ulm	ulm	NOUN
fuelectenerg-1427	1450	9	can	can	AUX
fuelectenerg-1427	1450	10	be	be	AUX
fuelectenerg-1427	1450	11	done	do	VERB
fuelectenerg-1427	1450	12	for	for	ADP
fuelectenerg-1427	1450	13	gf(4	gf(4	NOUN
fuelectenerg-1427	1450	14	)	)	PUNCT
fuelectenerg-1427	1450	15	addition	addition	NOUN
fuelectenerg-1427	1450	16	utilizing	utilize	VERB
fuelectenerg-1427	1450	17	gf(2	gf(2	NOUN
fuelectenerg-1427	1450	18	)	)	PUNCT
fuelectenerg-1427	1450	19	addition	addition	NOUN
fuelectenerg-1427	1450	20	using	use	VERB
fuelectenerg-1427	1450	21	vector	vector	NOUN
fuelectenerg-1427	1450	22	of	of	ADP
fuelectenerg-1427	1450	23	exors	exor	NOUN
fuelectenerg-1427	1450	24	,	,	PUNCT
fuelectenerg-1427	1450	25	(	(	PUNCT
fuelectenerg-1427	1450	26	4/2	4/2	NUM
fuelectenerg-1427	1450	27	)	)	PUNCT
fuelectenerg-1427	1450	28	and	and	CCONJ
fuelectenerg-1427	1450	29	(	(	PUNCT
fuelectenerg-1427	1450	30	2/4	2/4	NUM
fuelectenerg-1427	1450	31	)	)	PUNCT
fuelectenerg-1427	1450	32	decoders	decoder	NOUN
fuelectenerg-1427	1450	33	,	,	PUNCT
fuelectenerg-1427	1450	34	and	and	CCONJ
fuelectenerg-1427	1450	35	for	for	ADP
fuelectenerg-1427	1450	36	gf(4	gf(4	NOUN
fuelectenerg-1427	1450	37	)	)	PUNCT
fuelectenerg-1427	1450	38	multiplication	multiplication	NOUN
fuelectenerg-1427	1450	39	utilizing	utilize	VERB
fuelectenerg-1427	1450	40	gf(2	gf(2	PROPN
fuelectenerg-1427	1450	41	)	)	PUNCT
fuelectenerg-1427	1450	42	operations	operation	NOUN
fuelectenerg-1427	1450	43	using	use	VERB
fuelectenerg-1427	1450	44	vectors	vector	NOUN
fuelectenerg-1427	1450	45	of	of	ADP
fuelectenerg-1427	1450	46	xors	xor	NOUN
fuelectenerg-1427	1450	47	,	,	PUNCT
fuelectenerg-1427	1450	48	ands	and	NOUN
fuelectenerg-1427	1450	49	,	,	PUNCT
fuelectenerg-1427	1450	50	(	(	PUNCT
fuelectenerg-1427	1450	51	4/2	4/2	NUM
fuelectenerg-1427	1450	52	)	)	PUNCT
fuelectenerg-1427	1450	53	and	and	CCONJ
fuelectenerg-1427	1450	54	(	(	PUNCT
fuelectenerg-1427	1450	55	2/4	2/4	NUM
fuelectenerg-1427	1450	56	)	)	PUNCT
fuelectenerg-1427	1450	57	decoders	decoder	NOUN
fuelectenerg-1427	1450	58	,	,	PUNCT
fuelectenerg-1427	1450	59	and	and	CCONJ
fuelectenerg-1427	1450	60	therefore	therefore	ADV
fuelectenerg-1427	1450	61	the	the	DET
fuelectenerg-1427	1450	62	gf(4	gf(4	NOUN
fuelectenerg-1427	1450	63	)	)	PUNCT
fuelectenerg-1427	1450	64	ulm	ulm	NOUN
fuelectenerg-1427	1450	65	producing	produce	VERB
fuelectenerg-1427	1450	66	quaternary	quaternary	ADJ
fuelectenerg-1427	1450	67	shannon	shannon	NOUN
fuelectenerg-1427	1450	68	and	and	CCONJ
fuelectenerg-1427	1450	69	all	all	DET
fuelectenerg-1427	1450	70	davio	davio	NOUN
fuelectenerg-1427	1450	71	expansions	expansion	NOUN
fuelectenerg-1427	1450	72	can	can	AUX
fuelectenerg-1427	1450	73	be	be	AUX
fuelectenerg-1427	1450	74	achieved	achieve	VERB
fuelectenerg-1427	1450	75	using	use	VERB
fuelectenerg-1427	1450	76	the	the	DET
fuelectenerg-1427	1450	77	corresponding	correspond	VERB
fuelectenerg-1427	1450	78	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1450	79	and	and	CCONJ
fuelectenerg-1427	1450	80	gf(4	gf(4	NOUN
fuelectenerg-1427	1450	81	)	)	PUNCT
fuelectenerg-1427	1450	82	additions	addition	NOUN
fuelectenerg-1427	1450	83	and	and	CCONJ
fuelectenerg-1427	1450	84	multiplications	multiplication	NOUN
fuelectenerg-1427	1450	85	which	which	PRON
fuelectenerg-1427	1450	86	can	can	AUX
fuelectenerg-1427	1450	87	be	be	AUX
fuelectenerg-1427	1450	88	accordingly	accordingly	ADV
fuelectenerg-1427	1450	89	realized	realize	VERB
fuelectenerg-1427	1450	90	using	use	VERB
fuelectenerg-1427	1450	91	gf(2	gf(2	PROPN
fuelectenerg-1427	1450	92	)	)	PUNCT
fuelectenerg-1427	1450	93	methods	method	NOUN
fuelectenerg-1427	1450	94	.	.	PUNCT
fuelectenerg-1427	1451	1	2	2	X
fuelectenerg-1427	1451	2	.	.	X
fuelectenerg-1427	1451	3	the	the	DET
fuelectenerg-1427	1451	4	implementation	implementation	NOUN
fuelectenerg-1427	1451	5	of	of	ADP
fuelectenerg-1427	1451	6	the	the	DET
fuelectenerg-1427	1451	7	introduced	introduce	VERB
fuelectenerg-1427	1451	8	ulms	ulm	NOUN
fuelectenerg-1427	1451	9	using	use	VERB
fuelectenerg-1427	1451	10	nanotechnology	nanotechnology	NOUN
fuelectenerg-1427	1451	11	methods	method	NOUN
fuelectenerg-1427	1451	12	such	such	ADJ
fuelectenerg-1427	1451	13	as	as	ADP
fuelectenerg-1427	1451	14	quantum	quantum	NOUN
fuelectenerg-1427	1451	15	computing	computing	NOUN
fuelectenerg-1427	1451	16	,	,	PUNCT
fuelectenerg-1427	1451	17	quantum	quantum	ADJ
fuelectenerg-1427	1451	18	dots	dot	NOUN
fuelectenerg-1427	1451	19	and	and	CCONJ
fuelectenerg-1427	1451	20	carbon	carbon	NOUN
fuelectenerg-1427	1451	21	nanotubes	nanotube	NOUN
fuelectenerg-1427	1451	22	.	.	PUNCT
fuelectenerg-1427	1452	1	3	3	X
fuelectenerg-1427	1452	2	.	.	X
fuelectenerg-1427	1452	3	the	the	DET
fuelectenerg-1427	1452	4	utilization	utilization	NOUN
fuelectenerg-1427	1452	5	of	of	ADP
fuelectenerg-1427	1452	6	evolutionary	evolutionary	ADJ
fuelectenerg-1427	1452	7	algorithms	algorithm	NOUN
fuelectenerg-1427	1452	8	for	for	ADP
fuelectenerg-1427	1452	9	function	function	NOUN
fuelectenerg-1427	1452	10	minimization	minimization	NOUN
fuelectenerg-1427	1452	11	using	use	VERB
fuelectenerg-1427	1452	12	the	the	DET
fuelectenerg-1427	1452	13	introduced	introduce	VERB
fuelectenerg-1427	1452	14	s	s	PROPN
fuelectenerg-1427	1452	15	/	/	SYM
fuelectenerg-1427	1452	16	d	d	NOUN
fuelectenerg-1427	1452	17	trees	tree	NOUN
fuelectenerg-1427	1452	18	.	.	PUNCT
fuelectenerg-1427	1453	1	4	4	X
fuelectenerg-1427	1453	2	.	.	X
fuelectenerg-1427	1453	3	the	the	DET
fuelectenerg-1427	1453	4	investigation	investigation	NOUN
fuelectenerg-1427	1453	5	using	use	VERB
fuelectenerg-1427	1453	6	other	other	ADJ
fuelectenerg-1427	1453	7	more	more	ADV
fuelectenerg-1427	1453	8	complex	complex	ADJ
fuelectenerg-1427	1453	9	types	type	NOUN
fuelectenerg-1427	1453	10	of	of	ADP
fuelectenerg-1427	1453	11	literals	literal	NOUN
fuelectenerg-1427	1453	12	such	such	ADJ
fuelectenerg-1427	1453	13	as	as	ADP
fuelectenerg-1427	1453	14	the	the	DET
fuelectenerg-1427	1453	15	presented	present	VERB
fuelectenerg-1427	1453	16	generalized	generalized	ADJ
fuelectenerg-1427	1453	17	literal	literal	ADJ
fuelectenerg-1427	1453	18	(	(	PUNCT
fuelectenerg-1427	1453	19	gl	gl	NOUN
fuelectenerg-1427	1453	20	)	)	PUNCT
fuelectenerg-1427	1453	21	and	and	CCONJ
fuelectenerg-1427	1453	22	universal	universal	ADJ
fuelectenerg-1427	1453	23	literal	literal	ADJ
fuelectenerg-1427	1453	24	(	(	PUNCT
fuelectenerg-1427	1453	25	ul	ul	INTJ
fuelectenerg-1427	1453	26	)	)	PUNCT
fuelectenerg-1427	1453	27	to	to	PART
fuelectenerg-1427	1453	28	expand	expand	VERB
fuelectenerg-1427	1453	29	upon	upon	SCONJ
fuelectenerg-1427	1453	30	and	and	CCONJ
fuelectenerg-1427	1453	31	consequently	consequently	ADV
fuelectenerg-1427	1453	32	construct	construct	VERB
fuelectenerg-1427	1453	33	the	the	DET
fuelectenerg-1427	1453	34	corresponding	corresponding	ADJ
fuelectenerg-1427	1453	35	new	new	ADJ
fuelectenerg-1427	1453	36	ulms	ulm	NOUN
fuelectenerg-1427	1453	37	.	.	PUNCT
fuelectenerg-1427	1454	1	acknowledgment	acknowledgment	NOUN
fuelectenerg-1427	1454	2	this	this	DET
fuelectenerg-1427	1454	3	research	research	NOUN
fuelectenerg-1427	1454	4	was	be	AUX
fuelectenerg-1427	1454	5	performed	perform	VERB
fuelectenerg-1427	1454	6	during	during	ADP
fuelectenerg-1427	1454	7	sabbatical	sabbatical	ADJ
fuelectenerg-1427	1454	8	leave	leave	NOUN
fuelectenerg-1427	1454	9	in	in	ADP
fuelectenerg-1427	1454	10	2015	2015	NUM
fuelectenerg-1427	1454	11	-	-	SYM
fuelectenerg-1427	1454	12	2016	2016	NUM
fuelectenerg-1427	1454	13	granted	grant	VERB
fuelectenerg-1427	1454	14	from	from	ADP
fuelectenerg-1427	1454	15	the	the	DET
fuelectenerg-1427	1454	16	university	university	NOUN
fuelectenerg-1427	1454	17	jordan	jordan	PROPN
fuelectenerg-1427	1454	18	and	and	CCONJ
fuelectenerg-1427	1454	19	spent	spend	VERB
fuelectenerg-1427	1454	20	at	at	ADP
fuelectenerg-1427	1454	21	philadelphia	philadelphia	PROPN
fuelectenerg-1427	1454	22	university	university	NOUN
fuelectenerg-1427	1454	23	references	reference	NOUN
fuelectenerg-1427	1455	1	[	[	X
fuelectenerg-1427	1455	2	1	1	NUM
fuelectenerg-1427	1455	3	]	]	PUNCT
fuelectenerg-1427	1455	4	a.	a.	NOUN
fuelectenerg-1427	1455	5	n.	n.	PROPN
fuelectenerg-1427	1455	6	al	al	PROPN
fuelectenerg-1427	1455	7	-	-	PUNCT
fuelectenerg-1427	1455	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1455	9	,	,	PUNCT
fuelectenerg-1427	1455	10	reversible	reversible	ADJ
fuelectenerg-1427	1455	11	logic	logic	NOUN
fuelectenerg-1427	1455	12	synthesis	synthesis	NOUN
fuelectenerg-1427	1455	13	:	:	PUNCT
fuelectenerg-1427	1455	14	from	from	ADP
fuelectenerg-1427	1455	15	fundamentals	fundamental	NOUN
fuelectenerg-1427	1455	16	to	to	ADP
fuelectenerg-1427	1455	17	quantum	quantum	ADJ
fuelectenerg-1427	1455	18	computing	computing	NOUN
fuelectenerg-1427	1455	19	,	,	PUNCT
fuelectenerg-1427	1455	20	springer	springer	NOUN
fuelectenerg-1427	1455	21	-	-	PUNCT
fuelectenerg-1427	1455	22	verlag	verlag	PROPN
fuelectenerg-1427	1455	23	,	,	PUNCT
fuelectenerg-1427	1455	24	2004	2004	NUM
fuelectenerg-1427	1455	25	.	.	PUNCT
fuelectenerg-1427	1456	1	[	[	X
fuelectenerg-1427	1456	2	2	2	NUM
fuelectenerg-1427	1456	3	]	]	PUNCT
fuelectenerg-1427	1456	4	a.	a.	NOUN
fuelectenerg-1427	1456	5	n.	n.	PROPN
fuelectenerg-1427	1456	6	al	al	PROPN
fuelectenerg-1427	1456	7	-	-	PUNCT
fuelectenerg-1427	1456	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1456	9	,	,	PUNCT
fuelectenerg-1427	1456	10	"	"	PUNCT
fuelectenerg-1427	1456	11	three	three	NUM
fuelectenerg-1427	1456	12	-	-	PUNCT
fuelectenerg-1427	1456	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1456	14	lattice	lattice	ADJ
fuelectenerg-1427	1456	15	logic	logic	NOUN
fuelectenerg-1427	1456	16	circuits	circuit	NOUN
fuelectenerg-1427	1456	17	,	,	PUNCT
fuelectenerg-1427	1456	18	part	part	NOUN
fuelectenerg-1427	1456	19	iii	iii	NOUN
fuelectenerg-1427	1456	20	:	:	PUNCT
fuelectenerg-1427	1456	21	solving	solve	VERB
fuelectenerg-1427	1456	22	3d	3d	NUM
fuelectenerg-1427	1456	23	volume	volume	NOUN
fuelectenerg-1427	1456	24	congestion	congestion	NOUN
fuelectenerg-1427	1456	25	problem	problem	NOUN
fuelectenerg-1427	1456	26	,	,	PUNCT
fuelectenerg-1427	1456	27	"	"	PUNCT
fuelectenerg-1427	1456	28	facta	facta	PROPN
fuelectenerg-1427	1456	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1456	30	electronics	electronic	NOUN
fuelectenerg-1427	1456	31	and	and	CCONJ
fuelectenerg-1427	1456	32	energetics	energetic	NOUN
fuelectenerg-1427	1456	33	,	,	PUNCT
fuelectenerg-1427	1456	34	vol	vol	NOUN
fuelectenerg-1427	1456	35	.	.	PROPN
fuelectenerg-1427	1456	36	18	18	NUM
fuelectenerg-1427	1456	37	,	,	PUNCT
fuelectenerg-1427	1456	38	no	no	INTJ
fuelectenerg-1427	1456	39	.	.	NOUN
fuelectenerg-1427	1456	40	1	1	NUM
fuelectenerg-1427	1456	41	,	,	PUNCT
fuelectenerg-1427	1456	42	pp	pp	ADJ
fuelectenerg-1427	1456	43	.	.	PUNCT
fuelectenerg-1427	1457	1	29	29	NUM
fuelectenerg-1427	1457	2	43	43	NUM
fuelectenerg-1427	1457	3	,	,	PUNCT
fuelectenerg-1427	1457	4	2005	2005	NUM
fuelectenerg-1427	1457	5	.	.	PUNCT
fuelectenerg-1427	1458	1	[	[	X
fuelectenerg-1427	1458	2	3	3	NUM
fuelectenerg-1427	1458	3	]	]	PUNCT
fuelectenerg-1427	1458	4	a.	a.	NOUN
fuelectenerg-1427	1458	5	n.	n.	PROPN
fuelectenerg-1427	1458	6	al	al	PROPN
fuelectenerg-1427	1458	7	-	-	PUNCT
fuelectenerg-1427	1458	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1458	9	,	,	PUNCT
fuelectenerg-1427	1458	10	"	"	PUNCT
fuelectenerg-1427	1458	11	three	three	NUM
fuelectenerg-1427	1458	12	-	-	PUNCT
fuelectenerg-1427	1458	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1458	14	lattice	lattice	ADJ
fuelectenerg-1427	1458	15	logic	logic	NOUN
fuelectenerg-1427	1458	16	circuits	circuit	NOUN
fuelectenerg-1427	1458	17	,	,	PUNCT
fuelectenerg-1427	1458	18	part	part	PROPN
fuelectenerg-1427	1458	19	ii	ii	PROPN
fuelectenerg-1427	1458	20	:	:	PUNCT
fuelectenerg-1427	1458	21	formal	formal	ADJ
fuelectenerg-1427	1458	22	methods	method	NOUN
fuelectenerg-1427	1458	23	,	,	PUNCT
fuelectenerg-1427	1458	24	"	"	PUNCT
fuelectenerg-1427	1458	25	facta	facta	PROPN
fuelectenerg-1427	1458	26	universitatis	universitatis	PROPN
fuelectenerg-1427	1458	27	electronics	electronic	NOUN
fuelectenerg-1427	1458	28	and	and	CCONJ
fuelectenerg-1427	1458	29	energetics	energetic	NOUN
fuelectenerg-1427	1458	30	,	,	PUNCT
fuelectenerg-1427	1458	31	vol	vol	NOUN
fuelectenerg-1427	1458	32	.	.	PROPN
fuelectenerg-1427	1458	33	18	18	NUM
fuelectenerg-1427	1458	34	,	,	PUNCT
fuelectenerg-1427	1458	35	no	no	INTJ
fuelectenerg-1427	1458	36	.	.	NOUN
fuelectenerg-1427	1458	37	1	1	NUM
fuelectenerg-1427	1458	38	,	,	PUNCT
fuelectenerg-1427	1458	39	pp	pp	ADJ
fuelectenerg-1427	1458	40	.	.	PUNCT
fuelectenerg-1427	1459	1	15	15	NUM
fuelectenerg-1427	1459	2	28	28	NUM
fuelectenerg-1427	1459	3	,	,	PUNCT
fuelectenerg-1427	1459	4	2005	2005	NUM
fuelectenerg-1427	1459	5	.	.	PUNCT
fuelectenerg-1427	1460	1	[	[	X
fuelectenerg-1427	1460	2	4	4	NUM
fuelectenerg-1427	1460	3	]	]	PUNCT
fuelectenerg-1427	1460	4	a.	a.	NOUN
fuelectenerg-1427	1460	5	n.	n.	PROPN
fuelectenerg-1427	1460	6	al	al	PROPN
fuelectenerg-1427	1460	7	-	-	PUNCT
fuelectenerg-1427	1460	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1460	9	,	,	PUNCT
fuelectenerg-1427	1460	10	"	"	PUNCT
fuelectenerg-1427	1460	11	three	three	NUM
fuelectenerg-1427	1460	12	-	-	PUNCT
fuelectenerg-1427	1460	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1460	14	lattice	lattice	ADJ
fuelectenerg-1427	1460	15	logic	logic	NOUN
fuelectenerg-1427	1460	16	circuits	circuit	NOUN
fuelectenerg-1427	1460	17	,	,	PUNCT
fuelectenerg-1427	1460	18	part	part	NOUN
fuelectenerg-1427	1460	19	i	i	PRON
fuelectenerg-1427	1460	20	:	:	PUNCT
fuelectenerg-1427	1460	21	fundamentals	fundamental	NOUN
fuelectenerg-1427	1460	22	,	,	PUNCT
fuelectenerg-1427	1460	23	"	"	PUNCT
fuelectenerg-1427	1460	24	facta	facta	PROPN
fuelectenerg-1427	1460	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1460	26	electronics	electronic	NOUN
fuelectenerg-1427	1460	27	and	and	CCONJ
fuelectenerg-1427	1460	28	energetics	energetic	NOUN
fuelectenerg-1427	1460	29	,	,	PUNCT
fuelectenerg-1427	1460	30	vol	vol	NOUN
fuelectenerg-1427	1460	31	.	.	PROPN
fuelectenerg-1427	1460	32	18	18	NUM
fuelectenerg-1427	1460	33	,	,	PUNCT
fuelectenerg-1427	1460	34	no	no	INTJ
fuelectenerg-1427	1460	35	.	.	NOUN
fuelectenerg-1427	1460	36	1	1	NUM
fuelectenerg-1427	1460	37	,	,	PUNCT
fuelectenerg-1427	1460	38	pp	pp	ADJ
fuelectenerg-1427	1460	39	.	.	PUNCT
fuelectenerg-1427	1460	40	1	1	NUM
fuelectenerg-1427	1460	41	13	13	NUM
fuelectenerg-1427	1460	42	,	,	PUNCT
fuelectenerg-1427	1460	43	2005	2005	NUM
fuelectenerg-1427	1460	44	.	.	PUNCT
fuelectenerg-1427	1461	1	116	116	NUM
fuelectenerg-1427	1461	2	an	an	DET
fuelectenerg-1427	1461	3	extended	extend	VERB
fuelectenerg-1427	1461	4	green	green	ADJ
fuelectenerg-1427	1461	5	sasao	sasao	PROPN
fuelectenerg-1427	1461	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1461	7	of	of	ADP
fuelectenerg-1427	1461	8	canonical	canonical	ADJ
fuelectenerg-1427	1461	9	ternary	ternary	ADJ
fuelectenerg-1427	1461	10	galois	galois	NOUN
fuelectenerg-1427	1461	11	forms	form	NOUN
fuelectenerg-1427	1461	12	...	...	PUNCT
fuelectenerg-1427	1461	13	future	future	ADJ
fuelectenerg-1427	1461	14	work	work	NOUN
fuelectenerg-1427	1461	15	will	will	AUX
fuelectenerg-1427	1461	16	include	include	VERB
fuelectenerg-1427	1461	17	the	the	DET
fuelectenerg-1427	1461	18	following	following	ADJ
fuelectenerg-1427	1461	19	items	item	NOUN
fuelectenerg-1427	1461	20	:	:	PUNCT
fuelectenerg-1427	1462	1	1	1	X
fuelectenerg-1427	1462	2	.	.	X
fuelectenerg-1427	1462	3	the	the	DET
fuelectenerg-1427	1462	4	investigation	investigation	NOUN
fuelectenerg-1427	1462	5	of	of	ADP
fuelectenerg-1427	1462	6	the	the	DET
fuelectenerg-1427	1462	7	various	various	ADJ
fuelectenerg-1427	1462	8	multiple	multiple	ADV
fuelectenerg-1427	1462	9	-	-	PUNCT
fuelectenerg-1427	1462	10	valued	value	VERB
fuelectenerg-1427	1462	11	and	and	CCONJ
fuelectenerg-1427	1462	12	two	two	NUM
fuelectenerg-1427	1462	13	-	-	PUNCT
fuelectenerg-1427	1462	14	valued	value	VERB
fuelectenerg-1427	1462	15	techniques	technique	NOUN
fuelectenerg-1427	1462	16	for	for	ADP
fuelectenerg-1427	1462	17	the	the	DET
fuelectenerg-1427	1462	18	ulm	ulm	NOUN
fuelectenerg-1427	1462	19	implementation	implementation	NOUN
fuelectenerg-1427	1462	20	for	for	ADP
fuelectenerg-1427	1462	21	the	the	DET
fuelectenerg-1427	1462	22	important	important	ADJ
fuelectenerg-1427	1462	23	case	case	NOUN
fuelectenerg-1427	1462	24	of	of	ADP
fuelectenerg-1427	1462	25	quaternary	quaternary	ADJ
fuelectenerg-1427	1462	26	logic	logic	NOUN
fuelectenerg-1427	1462	27	.	.	PUNCT
fuelectenerg-1427	1463	1	since	since	SCONJ
fuelectenerg-1427	1463	2	the	the	DET
fuelectenerg-1427	1463	3	ulm	ulm	PROPN
fuelectenerg-1427	1463	4	realization	realization	NOUN
fuelectenerg-1427	1463	5	over	over	ADP
fuelectenerg-1427	1463	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1463	7	)	)	PUNCT
fuelectenerg-1427	1463	8	extends	extend	VERB
fuelectenerg-1427	1463	9	and	and	CCONJ
fuelectenerg-1427	1463	10	generalizes	generalize	VERB
fuelectenerg-1427	1463	11	from	from	ADP
fuelectenerg-1427	1463	12	the	the	DET
fuelectenerg-1427	1463	13	binary	binary	ADJ
fuelectenerg-1427	1463	14	case	case	NOUN
fuelectenerg-1427	1463	15	of	of	ADP
fuelectenerg-1427	1463	16	the	the	DET
fuelectenerg-1427	1463	17	gf(2	gf(2	PROPN
fuelectenerg-1427	1463	18	)	)	PUNCT
fuelectenerg-1427	1463	19	ulm	ulm	PROPN
fuelectenerg-1427	1463	20	realization	realization	NOUN
fuelectenerg-1427	1463	21	where	where	SCONJ
fuelectenerg-1427	1463	22	most	most	ADJ
fuelectenerg-1427	1463	23	digital	digital	ADJ
fuelectenerg-1427	1463	24	system	system	NOUN
fuelectenerg-1427	1463	25	designs	design	NOUN
fuelectenerg-1427	1463	26	are	be	AUX
fuelectenerg-1427	1463	27	performed	perform	VERB
fuelectenerg-1427	1463	28	the	the	DET
fuelectenerg-1427	1463	29	special	special	ADJ
fuelectenerg-1427	1463	30	case	case	NOUN
fuelectenerg-1427	1463	31	of	of	ADP
fuelectenerg-1427	1463	32	the	the	DET
fuelectenerg-1427	1463	33	extension	extension	NOUN
fuelectenerg-1427	1463	34	into	into	ADP
fuelectenerg-1427	1463	35	gf(4	gf(4	NOUN
fuelectenerg-1427	1463	36	)	)	PUNCT
fuelectenerg-1427	1463	37	becomes	become	VERB
fuelectenerg-1427	1463	38	important	important	ADJ
fuelectenerg-1427	1463	39	as	as	SCONJ
fuelectenerg-1427	1463	40	this	this	DET
fuelectenerg-1427	1463	41	gf(4	gf(4	NOUN
fuelectenerg-1427	1463	42	)	)	PUNCT
fuelectenerg-1427	1463	43	ulm	ulm	NOUN
fuelectenerg-1427	1463	44	realization	realization	NOUN
fuelectenerg-1427	1463	45	can	can	AUX
fuelectenerg-1427	1463	46	be	be	AUX
fuelectenerg-1427	1463	47	achieved	achieve	VERB
fuelectenerg-1427	1463	48	by	by	ADP
fuelectenerg-1427	1463	49	utilizing	utilize	VERB
fuelectenerg-1427	1463	50	the	the	DET
fuelectenerg-1427	1463	51	currently	currently	ADV
fuelectenerg-1427	1463	52	existing	exist	VERB
fuelectenerg-1427	1463	53	and	and	CCONJ
fuelectenerg-1427	1463	54	widely	widely	ADV
fuelectenerg-1427	1463	55	-	-	PUNCT
fuelectenerg-1427	1463	56	used	use	VERB
fuelectenerg-1427	1463	57	implementations	implementation	NOUN
fuelectenerg-1427	1463	58	over	over	ADP
fuelectenerg-1427	1463	59	gf(2	gf(2	PROPN
fuelectenerg-1427	1463	60	)	)	PUNCT
fuelectenerg-1427	1463	61	.	.	PUNCT
fuelectenerg-1427	1464	1	this	this	DET
fuelectenerg-1427	1464	2	two	two	NUM
fuelectenerg-1427	1464	3	-	-	PUNCT
fuelectenerg-1427	1464	4	valued	value	VERB
fuelectenerg-1427	1464	5	realization	realization	NOUN
fuelectenerg-1427	1464	6	of	of	ADP
fuelectenerg-1427	1464	7	quaternary	quaternary	ADJ
fuelectenerg-1427	1464	8	ulm	ulm	NOUN
fuelectenerg-1427	1464	9	can	can	AUX
fuelectenerg-1427	1464	10	be	be	AUX
fuelectenerg-1427	1464	11	done	do	VERB
fuelectenerg-1427	1464	12	for	for	ADP
fuelectenerg-1427	1464	13	gf(4	gf(4	NOUN
fuelectenerg-1427	1464	14	)	)	PUNCT
fuelectenerg-1427	1464	15	addition	addition	NOUN
fuelectenerg-1427	1464	16	utilizing	utilize	VERB
fuelectenerg-1427	1464	17	gf(2	gf(2	NOUN
fuelectenerg-1427	1464	18	)	)	PUNCT
fuelectenerg-1427	1464	19	addition	addition	NOUN
fuelectenerg-1427	1464	20	using	use	VERB
fuelectenerg-1427	1464	21	vector	vector	NOUN
fuelectenerg-1427	1464	22	of	of	ADP
fuelectenerg-1427	1464	23	exors	exor	NOUN
fuelectenerg-1427	1464	24	,	,	PUNCT
fuelectenerg-1427	1464	25	(	(	PUNCT
fuelectenerg-1427	1464	26	4/2	4/2	NUM
fuelectenerg-1427	1464	27	)	)	PUNCT
fuelectenerg-1427	1464	28	and	and	CCONJ
fuelectenerg-1427	1464	29	(	(	PUNCT
fuelectenerg-1427	1464	30	2/4	2/4	NUM
fuelectenerg-1427	1464	31	)	)	PUNCT
fuelectenerg-1427	1464	32	decoders	decoder	NOUN
fuelectenerg-1427	1464	33	,	,	PUNCT
fuelectenerg-1427	1464	34	and	and	CCONJ
fuelectenerg-1427	1464	35	for	for	ADP
fuelectenerg-1427	1464	36	gf(4	gf(4	NOUN
fuelectenerg-1427	1464	37	)	)	PUNCT
fuelectenerg-1427	1464	38	multiplication	multiplication	NOUN
fuelectenerg-1427	1464	39	utilizing	utilize	VERB
fuelectenerg-1427	1464	40	gf(2	gf(2	PROPN
fuelectenerg-1427	1464	41	)	)	PUNCT
fuelectenerg-1427	1464	42	operations	operation	NOUN
fuelectenerg-1427	1464	43	using	use	VERB
fuelectenerg-1427	1464	44	vectors	vector	NOUN
fuelectenerg-1427	1464	45	of	of	ADP
fuelectenerg-1427	1464	46	xors	xor	NOUN
fuelectenerg-1427	1464	47	,	,	PUNCT
fuelectenerg-1427	1464	48	ands	and	NOUN
fuelectenerg-1427	1464	49	,	,	PUNCT
fuelectenerg-1427	1464	50	(	(	PUNCT
fuelectenerg-1427	1464	51	4/2	4/2	NUM
fuelectenerg-1427	1464	52	)	)	PUNCT
fuelectenerg-1427	1464	53	and	and	CCONJ
fuelectenerg-1427	1464	54	(	(	PUNCT
fuelectenerg-1427	1464	55	2/4	2/4	NUM
fuelectenerg-1427	1464	56	)	)	PUNCT
fuelectenerg-1427	1464	57	decoders	decoder	NOUN
fuelectenerg-1427	1464	58	,	,	PUNCT
fuelectenerg-1427	1464	59	and	and	CCONJ
fuelectenerg-1427	1464	60	therefore	therefore	ADV
fuelectenerg-1427	1464	61	the	the	DET
fuelectenerg-1427	1464	62	gf(4	gf(4	NOUN
fuelectenerg-1427	1464	63	)	)	PUNCT
fuelectenerg-1427	1464	64	ulm	ulm	NOUN
fuelectenerg-1427	1464	65	producing	produce	VERB
fuelectenerg-1427	1464	66	quaternary	quaternary	ADJ
fuelectenerg-1427	1464	67	shannon	shannon	NOUN
fuelectenerg-1427	1464	68	and	and	CCONJ
fuelectenerg-1427	1464	69	all	all	DET
fuelectenerg-1427	1464	70	davio	davio	NOUN
fuelectenerg-1427	1464	71	expansions	expansion	NOUN
fuelectenerg-1427	1464	72	can	can	AUX
fuelectenerg-1427	1464	73	be	be	AUX
fuelectenerg-1427	1464	74	achieved	achieve	VERB
fuelectenerg-1427	1464	75	using	use	VERB
fuelectenerg-1427	1464	76	the	the	DET
fuelectenerg-1427	1464	77	corresponding	correspond	VERB
fuelectenerg-1427	1464	78	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1464	79	and	and	CCONJ
fuelectenerg-1427	1464	80	gf(4	gf(4	NOUN
fuelectenerg-1427	1464	81	)	)	PUNCT
fuelectenerg-1427	1464	82	additions	addition	NOUN
fuelectenerg-1427	1464	83	and	and	CCONJ
fuelectenerg-1427	1464	84	multiplications	multiplication	NOUN
fuelectenerg-1427	1464	85	which	which	PRON
fuelectenerg-1427	1464	86	can	can	AUX
fuelectenerg-1427	1464	87	be	be	AUX
fuelectenerg-1427	1464	88	accordingly	accordingly	ADV
fuelectenerg-1427	1464	89	realized	realize	VERB
fuelectenerg-1427	1464	90	using	use	VERB
fuelectenerg-1427	1464	91	gf(2	gf(2	PROPN
fuelectenerg-1427	1464	92	)	)	PUNCT
fuelectenerg-1427	1464	93	methods	method	NOUN
fuelectenerg-1427	1464	94	.	.	PUNCT
fuelectenerg-1427	1465	1	2	2	X
fuelectenerg-1427	1465	2	.	.	X
fuelectenerg-1427	1465	3	the	the	DET
fuelectenerg-1427	1465	4	implementation	implementation	NOUN
fuelectenerg-1427	1465	5	of	of	ADP
fuelectenerg-1427	1465	6	the	the	DET
fuelectenerg-1427	1465	7	introduced	introduce	VERB
fuelectenerg-1427	1465	8	ulms	ulm	NOUN
fuelectenerg-1427	1465	9	using	use	VERB
fuelectenerg-1427	1465	10	nanotechnology	nanotechnology	NOUN
fuelectenerg-1427	1465	11	methods	method	NOUN
fuelectenerg-1427	1465	12	such	such	ADJ
fuelectenerg-1427	1465	13	as	as	ADP
fuelectenerg-1427	1465	14	quantum	quantum	NOUN
fuelectenerg-1427	1465	15	computing	computing	NOUN
fuelectenerg-1427	1465	16	,	,	PUNCT
fuelectenerg-1427	1465	17	quantum	quantum	ADJ
fuelectenerg-1427	1465	18	dots	dot	NOUN
fuelectenerg-1427	1465	19	and	and	CCONJ
fuelectenerg-1427	1465	20	carbon	carbon	NOUN
fuelectenerg-1427	1465	21	nanotubes	nanotube	NOUN
fuelectenerg-1427	1465	22	.	.	PUNCT
fuelectenerg-1427	1466	1	3	3	X
fuelectenerg-1427	1466	2	.	.	X
fuelectenerg-1427	1466	3	the	the	DET
fuelectenerg-1427	1466	4	utilization	utilization	NOUN
fuelectenerg-1427	1466	5	of	of	ADP
fuelectenerg-1427	1466	6	evolutionary	evolutionary	ADJ
fuelectenerg-1427	1466	7	algorithms	algorithm	NOUN
fuelectenerg-1427	1466	8	for	for	ADP
fuelectenerg-1427	1466	9	function	function	NOUN
fuelectenerg-1427	1466	10	minimization	minimization	NOUN
fuelectenerg-1427	1466	11	using	use	VERB
fuelectenerg-1427	1466	12	the	the	DET
fuelectenerg-1427	1466	13	introduced	introduce	VERB
fuelectenerg-1427	1466	14	s	s	PROPN
fuelectenerg-1427	1466	15	/	/	SYM
fuelectenerg-1427	1466	16	d	d	NOUN
fuelectenerg-1427	1466	17	trees	tree	NOUN
fuelectenerg-1427	1466	18	.	.	PUNCT
fuelectenerg-1427	1467	1	4	4	X
fuelectenerg-1427	1467	2	.	.	X
fuelectenerg-1427	1467	3	the	the	DET
fuelectenerg-1427	1467	4	investigation	investigation	NOUN
fuelectenerg-1427	1467	5	using	use	VERB
fuelectenerg-1427	1467	6	other	other	ADJ
fuelectenerg-1427	1467	7	more	more	ADV
fuelectenerg-1427	1467	8	complex	complex	ADJ
fuelectenerg-1427	1467	9	types	type	NOUN
fuelectenerg-1427	1467	10	of	of	ADP
fuelectenerg-1427	1467	11	literals	literal	NOUN
fuelectenerg-1427	1467	12	such	such	ADJ
fuelectenerg-1427	1467	13	as	as	ADP
fuelectenerg-1427	1467	14	the	the	DET
fuelectenerg-1427	1467	15	presented	present	VERB
fuelectenerg-1427	1467	16	generalized	generalized	ADJ
fuelectenerg-1427	1467	17	literal	literal	ADJ
fuelectenerg-1427	1467	18	(	(	PUNCT
fuelectenerg-1427	1467	19	gl	gl	NOUN
fuelectenerg-1427	1467	20	)	)	PUNCT
fuelectenerg-1427	1467	21	and	and	CCONJ
fuelectenerg-1427	1467	22	universal	universal	ADJ
fuelectenerg-1427	1467	23	literal	literal	ADJ
fuelectenerg-1427	1467	24	(	(	PUNCT
fuelectenerg-1427	1467	25	ul	ul	INTJ
fuelectenerg-1427	1467	26	)	)	PUNCT
fuelectenerg-1427	1467	27	to	to	PART
fuelectenerg-1427	1467	28	expand	expand	VERB
fuelectenerg-1427	1467	29	upon	upon	SCONJ
fuelectenerg-1427	1467	30	and	and	CCONJ
fuelectenerg-1427	1467	31	consequently	consequently	ADV
fuelectenerg-1427	1467	32	construct	construct	VERB
fuelectenerg-1427	1467	33	the	the	DET
fuelectenerg-1427	1467	34	corresponding	corresponding	ADJ
fuelectenerg-1427	1467	35	new	new	ADJ
fuelectenerg-1427	1467	36	ulms	ulm	NOUN
fuelectenerg-1427	1467	37	.	.	PUNCT
fuelectenerg-1427	1468	1	acknowledgment	acknowledgment	NOUN
fuelectenerg-1427	1468	2	this	this	DET
fuelectenerg-1427	1468	3	research	research	NOUN
fuelectenerg-1427	1468	4	was	be	AUX
fuelectenerg-1427	1468	5	performed	perform	VERB
fuelectenerg-1427	1468	6	during	during	ADP
fuelectenerg-1427	1468	7	sabbatical	sabbatical	ADJ
fuelectenerg-1427	1468	8	leave	leave	NOUN
fuelectenerg-1427	1468	9	in	in	ADP
fuelectenerg-1427	1468	10	2015	2015	NUM
fuelectenerg-1427	1468	11	-	-	SYM
fuelectenerg-1427	1468	12	2016	2016	NUM
fuelectenerg-1427	1468	13	granted	grant	VERB
fuelectenerg-1427	1468	14	from	from	ADP
fuelectenerg-1427	1468	15	the	the	DET
fuelectenerg-1427	1468	16	university	university	NOUN
fuelectenerg-1427	1468	17	jordan	jordan	PROPN
fuelectenerg-1427	1468	18	and	and	CCONJ
fuelectenerg-1427	1468	19	spent	spend	VERB
fuelectenerg-1427	1468	20	at	at	ADP
fuelectenerg-1427	1468	21	philadelphia	philadelphia	PROPN
fuelectenerg-1427	1468	22	university	university	NOUN
fuelectenerg-1427	1468	23	references	reference	NOUN
fuelectenerg-1427	1469	1	[	[	X
fuelectenerg-1427	1469	2	1	1	NUM
fuelectenerg-1427	1469	3	]	]	PUNCT
fuelectenerg-1427	1469	4	a.	a.	NOUN
fuelectenerg-1427	1469	5	n.	n.	PROPN
fuelectenerg-1427	1469	6	al	al	PROPN
fuelectenerg-1427	1469	7	-	-	PUNCT
fuelectenerg-1427	1469	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1469	9	,	,	PUNCT
fuelectenerg-1427	1469	10	reversible	reversible	ADJ
fuelectenerg-1427	1469	11	logic	logic	NOUN
fuelectenerg-1427	1469	12	synthesis	synthesis	NOUN
fuelectenerg-1427	1469	13	:	:	PUNCT
fuelectenerg-1427	1469	14	from	from	ADP
fuelectenerg-1427	1469	15	fundamentals	fundamental	NOUN
fuelectenerg-1427	1469	16	to	to	ADP
fuelectenerg-1427	1469	17	quantum	quantum	ADJ
fuelectenerg-1427	1469	18	computing	computing	NOUN
fuelectenerg-1427	1469	19	,	,	PUNCT
fuelectenerg-1427	1469	20	springer	springer	NOUN
fuelectenerg-1427	1469	21	-	-	PUNCT
fuelectenerg-1427	1469	22	verlag	verlag	PROPN
fuelectenerg-1427	1469	23	,	,	PUNCT
fuelectenerg-1427	1469	24	2004	2004	NUM
fuelectenerg-1427	1469	25	.	.	PUNCT
fuelectenerg-1427	1470	1	[	[	X
fuelectenerg-1427	1470	2	2	2	NUM
fuelectenerg-1427	1470	3	]	]	PUNCT
fuelectenerg-1427	1470	4	a.	a.	NOUN
fuelectenerg-1427	1470	5	n.	n.	PROPN
fuelectenerg-1427	1470	6	al	al	PROPN
fuelectenerg-1427	1470	7	-	-	PUNCT
fuelectenerg-1427	1470	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1470	9	,	,	PUNCT
fuelectenerg-1427	1470	10	"	"	PUNCT
fuelectenerg-1427	1470	11	three	three	NUM
fuelectenerg-1427	1470	12	-	-	PUNCT
fuelectenerg-1427	1470	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1470	14	lattice	lattice	ADJ
fuelectenerg-1427	1470	15	logic	logic	NOUN
fuelectenerg-1427	1470	16	circuits	circuit	NOUN
fuelectenerg-1427	1470	17	,	,	PUNCT
fuelectenerg-1427	1470	18	part	part	NOUN
fuelectenerg-1427	1470	19	iii	iii	NOUN
fuelectenerg-1427	1470	20	:	:	PUNCT
fuelectenerg-1427	1470	21	solving	solve	VERB
fuelectenerg-1427	1470	22	3d	3d	NUM
fuelectenerg-1427	1470	23	volume	volume	NOUN
fuelectenerg-1427	1470	24	congestion	congestion	NOUN
fuelectenerg-1427	1470	25	problem	problem	NOUN
fuelectenerg-1427	1470	26	,	,	PUNCT
fuelectenerg-1427	1470	27	"	"	PUNCT
fuelectenerg-1427	1470	28	facta	facta	PROPN
fuelectenerg-1427	1470	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1470	30	electronics	electronic	NOUN
fuelectenerg-1427	1470	31	and	and	CCONJ
fuelectenerg-1427	1470	32	energetics	energetic	NOUN
fuelectenerg-1427	1470	33	,	,	PUNCT
fuelectenerg-1427	1470	34	vol	vol	NOUN
fuelectenerg-1427	1470	35	.	.	PROPN
fuelectenerg-1427	1470	36	18	18	NUM
fuelectenerg-1427	1470	37	,	,	PUNCT
fuelectenerg-1427	1470	38	no	no	INTJ
fuelectenerg-1427	1470	39	.	.	NOUN
fuelectenerg-1427	1470	40	1	1	NUM
fuelectenerg-1427	1470	41	,	,	PUNCT
fuelectenerg-1427	1470	42	pp	pp	ADJ
fuelectenerg-1427	1470	43	.	.	PUNCT
fuelectenerg-1427	1471	1	29	29	NUM
fuelectenerg-1427	1471	2	43	43	NUM
fuelectenerg-1427	1471	3	,	,	PUNCT
fuelectenerg-1427	1471	4	2005	2005	NUM
fuelectenerg-1427	1471	5	.	.	PUNCT
fuelectenerg-1427	1472	1	[	[	X
fuelectenerg-1427	1472	2	3	3	NUM
fuelectenerg-1427	1472	3	]	]	PUNCT
fuelectenerg-1427	1472	4	a.	a.	NOUN
fuelectenerg-1427	1472	5	n.	n.	PROPN
fuelectenerg-1427	1472	6	al	al	PROPN
fuelectenerg-1427	1472	7	-	-	PUNCT
fuelectenerg-1427	1472	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1472	9	,	,	PUNCT
fuelectenerg-1427	1472	10	"	"	PUNCT
fuelectenerg-1427	1472	11	three	three	NUM
fuelectenerg-1427	1472	12	-	-	PUNCT
fuelectenerg-1427	1472	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1472	14	lattice	lattice	ADJ
fuelectenerg-1427	1472	15	logic	logic	NOUN
fuelectenerg-1427	1472	16	circuits	circuit	NOUN
fuelectenerg-1427	1472	17	,	,	PUNCT
fuelectenerg-1427	1472	18	part	part	PROPN
fuelectenerg-1427	1472	19	ii	ii	PROPN
fuelectenerg-1427	1472	20	:	:	PUNCT
fuelectenerg-1427	1472	21	formal	formal	ADJ
fuelectenerg-1427	1472	22	methods	method	NOUN
fuelectenerg-1427	1472	23	,	,	PUNCT
fuelectenerg-1427	1472	24	"	"	PUNCT
fuelectenerg-1427	1472	25	facta	facta	PROPN
fuelectenerg-1427	1472	26	universitatis	universitatis	PROPN
fuelectenerg-1427	1472	27	electronics	electronic	NOUN
fuelectenerg-1427	1472	28	and	and	CCONJ
fuelectenerg-1427	1472	29	energetics	energetic	NOUN
fuelectenerg-1427	1472	30	,	,	PUNCT
fuelectenerg-1427	1472	31	vol	vol	NOUN
fuelectenerg-1427	1472	32	.	.	PROPN
fuelectenerg-1427	1472	33	18	18	NUM
fuelectenerg-1427	1472	34	,	,	PUNCT
fuelectenerg-1427	1472	35	no	no	INTJ
fuelectenerg-1427	1472	36	.	.	NOUN
fuelectenerg-1427	1472	37	1	1	NUM
fuelectenerg-1427	1472	38	,	,	PUNCT
fuelectenerg-1427	1472	39	pp	pp	ADJ
fuelectenerg-1427	1472	40	.	.	PUNCT
fuelectenerg-1427	1473	1	15	15	NUM
fuelectenerg-1427	1473	2	28	28	NUM
fuelectenerg-1427	1473	3	,	,	PUNCT
fuelectenerg-1427	1473	4	2005	2005	NUM
fuelectenerg-1427	1473	5	.	.	PUNCT
fuelectenerg-1427	1474	1	[	[	X
fuelectenerg-1427	1474	2	4	4	NUM
fuelectenerg-1427	1474	3	]	]	PUNCT
fuelectenerg-1427	1474	4	a.	a.	NOUN
fuelectenerg-1427	1474	5	n.	n.	PROPN
fuelectenerg-1427	1474	6	al	al	PROPN
fuelectenerg-1427	1474	7	-	-	PUNCT
fuelectenerg-1427	1474	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1474	9	,	,	PUNCT
fuelectenerg-1427	1474	10	"	"	PUNCT
fuelectenerg-1427	1474	11	three	three	NUM
fuelectenerg-1427	1474	12	-	-	PUNCT
fuelectenerg-1427	1474	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1474	14	lattice	lattice	ADJ
fuelectenerg-1427	1474	15	logic	logic	NOUN
fuelectenerg-1427	1474	16	circuits	circuit	NOUN
fuelectenerg-1427	1474	17	,	,	PUNCT
fuelectenerg-1427	1474	18	part	part	NOUN
fuelectenerg-1427	1474	19	i	i	PRON
fuelectenerg-1427	1474	20	:	:	PUNCT
fuelectenerg-1427	1474	21	fundamentals	fundamental	NOUN
fuelectenerg-1427	1474	22	,	,	PUNCT
fuelectenerg-1427	1474	23	"	"	PUNCT
fuelectenerg-1427	1474	24	facta	facta	PROPN
fuelectenerg-1427	1474	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1474	26	electronics	electronic	NOUN
fuelectenerg-1427	1474	27	and	and	CCONJ
fuelectenerg-1427	1474	28	energetics	energetic	NOUN
fuelectenerg-1427	1474	29	,	,	PUNCT
fuelectenerg-1427	1474	30	vol	vol	NOUN
fuelectenerg-1427	1474	31	.	.	PROPN
fuelectenerg-1427	1474	32	18	18	NUM
fuelectenerg-1427	1474	33	,	,	PUNCT
fuelectenerg-1427	1474	34	no	no	INTJ
fuelectenerg-1427	1474	35	.	.	NOUN
fuelectenerg-1427	1474	36	1	1	NUM
fuelectenerg-1427	1474	37	,	,	PUNCT
fuelectenerg-1427	1474	38	pp	pp	ADJ
fuelectenerg-1427	1474	39	.	.	PUNCT
fuelectenerg-1427	1474	40	1	1	NUM
fuelectenerg-1427	1474	41	13	13	NUM
fuelectenerg-1427	1474	42	,	,	PUNCT
fuelectenerg-1427	1474	43	2005	2005	NUM
fuelectenerg-1427	1474	44	.	.	PUNCT
fuelectenerg-1427	1475	1	116	116	NUM
fuelectenerg-1427	1475	2	an	an	DET
fuelectenerg-1427	1475	3	extended	extend	VERB
fuelectenerg-1427	1475	4	green	green	ADJ
fuelectenerg-1427	1475	5	sasao	sasao	PROPN
fuelectenerg-1427	1475	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1475	7	of	of	ADP
fuelectenerg-1427	1475	8	canonical	canonical	ADJ
fuelectenerg-1427	1475	9	ternary	ternary	ADJ
fuelectenerg-1427	1475	10	galois	galois	NOUN
fuelectenerg-1427	1475	11	forms	form	NOUN
fuelectenerg-1427	1475	12	...	...	PUNCT
fuelectenerg-1427	1475	13	future	future	ADJ
fuelectenerg-1427	1475	14	work	work	NOUN
fuelectenerg-1427	1475	15	will	will	AUX
fuelectenerg-1427	1475	16	include	include	VERB
fuelectenerg-1427	1475	17	the	the	DET
fuelectenerg-1427	1475	18	following	following	ADJ
fuelectenerg-1427	1475	19	items	item	NOUN
fuelectenerg-1427	1475	20	:	:	PUNCT
fuelectenerg-1427	1476	1	1	1	X
fuelectenerg-1427	1476	2	.	.	X
fuelectenerg-1427	1476	3	the	the	DET
fuelectenerg-1427	1476	4	investigation	investigation	NOUN
fuelectenerg-1427	1476	5	of	of	ADP
fuelectenerg-1427	1476	6	the	the	DET
fuelectenerg-1427	1476	7	various	various	ADJ
fuelectenerg-1427	1476	8	multiple	multiple	ADV
fuelectenerg-1427	1476	9	-	-	PUNCT
fuelectenerg-1427	1476	10	valued	value	VERB
fuelectenerg-1427	1476	11	and	and	CCONJ
fuelectenerg-1427	1476	12	two	two	NUM
fuelectenerg-1427	1476	13	-	-	PUNCT
fuelectenerg-1427	1476	14	valued	value	VERB
fuelectenerg-1427	1476	15	techniques	technique	NOUN
fuelectenerg-1427	1476	16	for	for	ADP
fuelectenerg-1427	1476	17	the	the	DET
fuelectenerg-1427	1476	18	ulm	ulm	NOUN
fuelectenerg-1427	1476	19	implementation	implementation	NOUN
fuelectenerg-1427	1476	20	for	for	ADP
fuelectenerg-1427	1476	21	the	the	DET
fuelectenerg-1427	1476	22	important	important	ADJ
fuelectenerg-1427	1476	23	case	case	NOUN
fuelectenerg-1427	1476	24	of	of	ADP
fuelectenerg-1427	1476	25	quaternary	quaternary	ADJ
fuelectenerg-1427	1476	26	logic	logic	NOUN
fuelectenerg-1427	1476	27	.	.	PUNCT
fuelectenerg-1427	1477	1	since	since	SCONJ
fuelectenerg-1427	1477	2	the	the	DET
fuelectenerg-1427	1477	3	ulm	ulm	PROPN
fuelectenerg-1427	1477	4	realization	realization	NOUN
fuelectenerg-1427	1477	5	over	over	ADP
fuelectenerg-1427	1477	6	gf(3	gf(3	PROPN
fuelectenerg-1427	1477	7	)	)	PUNCT
fuelectenerg-1427	1477	8	extends	extend	VERB
fuelectenerg-1427	1477	9	and	and	CCONJ
fuelectenerg-1427	1477	10	generalizes	generalize	VERB
fuelectenerg-1427	1477	11	from	from	ADP
fuelectenerg-1427	1477	12	the	the	DET
fuelectenerg-1427	1477	13	binary	binary	ADJ
fuelectenerg-1427	1477	14	case	case	NOUN
fuelectenerg-1427	1477	15	of	of	ADP
fuelectenerg-1427	1477	16	the	the	DET
fuelectenerg-1427	1477	17	gf(2	gf(2	PROPN
fuelectenerg-1427	1477	18	)	)	PUNCT
fuelectenerg-1427	1477	19	ulm	ulm	PROPN
fuelectenerg-1427	1477	20	realization	realization	NOUN
fuelectenerg-1427	1477	21	where	where	SCONJ
fuelectenerg-1427	1477	22	most	most	ADJ
fuelectenerg-1427	1477	23	digital	digital	ADJ
fuelectenerg-1427	1477	24	system	system	NOUN
fuelectenerg-1427	1477	25	designs	design	NOUN
fuelectenerg-1427	1477	26	are	be	AUX
fuelectenerg-1427	1477	27	performed	perform	VERB
fuelectenerg-1427	1477	28	the	the	DET
fuelectenerg-1427	1477	29	special	special	ADJ
fuelectenerg-1427	1477	30	case	case	NOUN
fuelectenerg-1427	1477	31	of	of	ADP
fuelectenerg-1427	1477	32	the	the	DET
fuelectenerg-1427	1477	33	extension	extension	NOUN
fuelectenerg-1427	1477	34	into	into	ADP
fuelectenerg-1427	1477	35	gf(4	gf(4	NOUN
fuelectenerg-1427	1477	36	)	)	PUNCT
fuelectenerg-1427	1477	37	becomes	become	VERB
fuelectenerg-1427	1477	38	important	important	ADJ
fuelectenerg-1427	1477	39	as	as	SCONJ
fuelectenerg-1427	1477	40	this	this	DET
fuelectenerg-1427	1477	41	gf(4	gf(4	NOUN
fuelectenerg-1427	1477	42	)	)	PUNCT
fuelectenerg-1427	1477	43	ulm	ulm	NOUN
fuelectenerg-1427	1477	44	realization	realization	NOUN
fuelectenerg-1427	1477	45	can	can	AUX
fuelectenerg-1427	1477	46	be	be	AUX
fuelectenerg-1427	1477	47	achieved	achieve	VERB
fuelectenerg-1427	1477	48	by	by	ADP
fuelectenerg-1427	1477	49	utilizing	utilize	VERB
fuelectenerg-1427	1477	50	the	the	DET
fuelectenerg-1427	1477	51	currently	currently	ADV
fuelectenerg-1427	1477	52	existing	exist	VERB
fuelectenerg-1427	1477	53	and	and	CCONJ
fuelectenerg-1427	1477	54	widely	widely	ADV
fuelectenerg-1427	1477	55	-	-	PUNCT
fuelectenerg-1427	1477	56	used	use	VERB
fuelectenerg-1427	1477	57	implementations	implementation	NOUN
fuelectenerg-1427	1477	58	over	over	ADP
fuelectenerg-1427	1477	59	gf(2	gf(2	PROPN
fuelectenerg-1427	1477	60	)	)	PUNCT
fuelectenerg-1427	1477	61	.	.	PUNCT
fuelectenerg-1427	1478	1	this	this	DET
fuelectenerg-1427	1478	2	two	two	NUM
fuelectenerg-1427	1478	3	-	-	PUNCT
fuelectenerg-1427	1478	4	valued	value	VERB
fuelectenerg-1427	1478	5	realization	realization	NOUN
fuelectenerg-1427	1478	6	of	of	ADP
fuelectenerg-1427	1478	7	quaternary	quaternary	ADJ
fuelectenerg-1427	1478	8	ulm	ulm	NOUN
fuelectenerg-1427	1478	9	can	can	AUX
fuelectenerg-1427	1478	10	be	be	AUX
fuelectenerg-1427	1478	11	done	do	VERB
fuelectenerg-1427	1478	12	for	for	ADP
fuelectenerg-1427	1478	13	gf(4	gf(4	NOUN
fuelectenerg-1427	1478	14	)	)	PUNCT
fuelectenerg-1427	1478	15	addition	addition	NOUN
fuelectenerg-1427	1478	16	utilizing	utilize	VERB
fuelectenerg-1427	1478	17	gf(2	gf(2	NOUN
fuelectenerg-1427	1478	18	)	)	PUNCT
fuelectenerg-1427	1478	19	addition	addition	NOUN
fuelectenerg-1427	1478	20	using	use	VERB
fuelectenerg-1427	1478	21	vector	vector	NOUN
fuelectenerg-1427	1478	22	of	of	ADP
fuelectenerg-1427	1478	23	exors	exor	NOUN
fuelectenerg-1427	1478	24	,	,	PUNCT
fuelectenerg-1427	1478	25	(	(	PUNCT
fuelectenerg-1427	1478	26	4/2	4/2	NUM
fuelectenerg-1427	1478	27	)	)	PUNCT
fuelectenerg-1427	1478	28	and	and	CCONJ
fuelectenerg-1427	1478	29	(	(	PUNCT
fuelectenerg-1427	1478	30	2/4	2/4	NUM
fuelectenerg-1427	1478	31	)	)	PUNCT
fuelectenerg-1427	1478	32	decoders	decoder	NOUN
fuelectenerg-1427	1478	33	,	,	PUNCT
fuelectenerg-1427	1478	34	and	and	CCONJ
fuelectenerg-1427	1478	35	for	for	ADP
fuelectenerg-1427	1478	36	gf(4	gf(4	NOUN
fuelectenerg-1427	1478	37	)	)	PUNCT
fuelectenerg-1427	1478	38	multiplication	multiplication	NOUN
fuelectenerg-1427	1478	39	utilizing	utilize	VERB
fuelectenerg-1427	1478	40	gf(2	gf(2	PROPN
fuelectenerg-1427	1478	41	)	)	PUNCT
fuelectenerg-1427	1478	42	operations	operation	NOUN
fuelectenerg-1427	1478	43	using	use	VERB
fuelectenerg-1427	1478	44	vectors	vector	NOUN
fuelectenerg-1427	1478	45	of	of	ADP
fuelectenerg-1427	1478	46	xors	xor	NOUN
fuelectenerg-1427	1478	47	,	,	PUNCT
fuelectenerg-1427	1478	48	ands	and	NOUN
fuelectenerg-1427	1478	49	,	,	PUNCT
fuelectenerg-1427	1478	50	(	(	PUNCT
fuelectenerg-1427	1478	51	4/2	4/2	NUM
fuelectenerg-1427	1478	52	)	)	PUNCT
fuelectenerg-1427	1478	53	and	and	CCONJ
fuelectenerg-1427	1478	54	(	(	PUNCT
fuelectenerg-1427	1478	55	2/4	2/4	NUM
fuelectenerg-1427	1478	56	)	)	PUNCT
fuelectenerg-1427	1478	57	decoders	decoder	NOUN
fuelectenerg-1427	1478	58	,	,	PUNCT
fuelectenerg-1427	1478	59	and	and	CCONJ
fuelectenerg-1427	1478	60	therefore	therefore	ADV
fuelectenerg-1427	1478	61	the	the	DET
fuelectenerg-1427	1478	62	gf(4	gf(4	NOUN
fuelectenerg-1427	1478	63	)	)	PUNCT
fuelectenerg-1427	1478	64	ulm	ulm	NOUN
fuelectenerg-1427	1478	65	producing	produce	VERB
fuelectenerg-1427	1478	66	quaternary	quaternary	ADJ
fuelectenerg-1427	1478	67	shannon	shannon	NOUN
fuelectenerg-1427	1478	68	and	and	CCONJ
fuelectenerg-1427	1478	69	all	all	DET
fuelectenerg-1427	1478	70	davio	davio	NOUN
fuelectenerg-1427	1478	71	expansions	expansion	NOUN
fuelectenerg-1427	1478	72	can	can	AUX
fuelectenerg-1427	1478	73	be	be	AUX
fuelectenerg-1427	1478	74	achieved	achieve	VERB
fuelectenerg-1427	1478	75	using	use	VERB
fuelectenerg-1427	1478	76	the	the	DET
fuelectenerg-1427	1478	77	corresponding	correspond	VERB
fuelectenerg-1427	1478	78	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1478	79	and	and	CCONJ
fuelectenerg-1427	1478	80	gf(4	gf(4	NOUN
fuelectenerg-1427	1478	81	)	)	PUNCT
fuelectenerg-1427	1478	82	additions	addition	NOUN
fuelectenerg-1427	1478	83	and	and	CCONJ
fuelectenerg-1427	1478	84	multiplications	multiplication	NOUN
fuelectenerg-1427	1478	85	which	which	PRON
fuelectenerg-1427	1478	86	can	can	AUX
fuelectenerg-1427	1478	87	be	be	AUX
fuelectenerg-1427	1478	88	accordingly	accordingly	ADV
fuelectenerg-1427	1478	89	realized	realize	VERB
fuelectenerg-1427	1478	90	using	use	VERB
fuelectenerg-1427	1478	91	gf(2	gf(2	PROPN
fuelectenerg-1427	1478	92	)	)	PUNCT
fuelectenerg-1427	1478	93	methods	method	NOUN
fuelectenerg-1427	1478	94	.	.	PUNCT
fuelectenerg-1427	1479	1	2	2	X
fuelectenerg-1427	1479	2	.	.	X
fuelectenerg-1427	1479	3	the	the	DET
fuelectenerg-1427	1479	4	implementation	implementation	NOUN
fuelectenerg-1427	1479	5	of	of	ADP
fuelectenerg-1427	1479	6	the	the	DET
fuelectenerg-1427	1479	7	introduced	introduce	VERB
fuelectenerg-1427	1479	8	ulms	ulm	NOUN
fuelectenerg-1427	1479	9	using	use	VERB
fuelectenerg-1427	1479	10	nanotechnology	nanotechnology	NOUN
fuelectenerg-1427	1479	11	methods	method	NOUN
fuelectenerg-1427	1479	12	such	such	ADJ
fuelectenerg-1427	1479	13	as	as	ADP
fuelectenerg-1427	1479	14	quantum	quantum	NOUN
fuelectenerg-1427	1479	15	computing	computing	NOUN
fuelectenerg-1427	1479	16	,	,	PUNCT
fuelectenerg-1427	1479	17	quantum	quantum	ADJ
fuelectenerg-1427	1479	18	dots	dot	NOUN
fuelectenerg-1427	1479	19	and	and	CCONJ
fuelectenerg-1427	1479	20	carbon	carbon	NOUN
fuelectenerg-1427	1479	21	nanotubes	nanotube	NOUN
fuelectenerg-1427	1479	22	.	.	PUNCT
fuelectenerg-1427	1480	1	3	3	X
fuelectenerg-1427	1480	2	.	.	X
fuelectenerg-1427	1480	3	the	the	DET
fuelectenerg-1427	1480	4	utilization	utilization	NOUN
fuelectenerg-1427	1480	5	of	of	ADP
fuelectenerg-1427	1480	6	evolutionary	evolutionary	ADJ
fuelectenerg-1427	1480	7	algorithms	algorithm	NOUN
fuelectenerg-1427	1480	8	for	for	ADP
fuelectenerg-1427	1480	9	function	function	NOUN
fuelectenerg-1427	1480	10	minimization	minimization	NOUN
fuelectenerg-1427	1480	11	using	use	VERB
fuelectenerg-1427	1480	12	the	the	DET
fuelectenerg-1427	1480	13	introduced	introduce	VERB
fuelectenerg-1427	1480	14	s	s	PROPN
fuelectenerg-1427	1480	15	/	/	SYM
fuelectenerg-1427	1480	16	d	d	NOUN
fuelectenerg-1427	1480	17	trees	tree	NOUN
fuelectenerg-1427	1480	18	.	.	PUNCT
fuelectenerg-1427	1481	1	4	4	X
fuelectenerg-1427	1481	2	.	.	X
fuelectenerg-1427	1481	3	the	the	DET
fuelectenerg-1427	1481	4	investigation	investigation	NOUN
fuelectenerg-1427	1481	5	using	use	VERB
fuelectenerg-1427	1481	6	other	other	ADJ
fuelectenerg-1427	1481	7	more	more	ADV
fuelectenerg-1427	1481	8	complex	complex	ADJ
fuelectenerg-1427	1481	9	types	type	NOUN
fuelectenerg-1427	1481	10	of	of	ADP
fuelectenerg-1427	1481	11	literals	literal	NOUN
fuelectenerg-1427	1481	12	such	such	ADJ
fuelectenerg-1427	1481	13	as	as	ADP
fuelectenerg-1427	1481	14	the	the	DET
fuelectenerg-1427	1481	15	presented	present	VERB
fuelectenerg-1427	1481	16	generalized	generalized	ADJ
fuelectenerg-1427	1481	17	literal	literal	ADJ
fuelectenerg-1427	1481	18	(	(	PUNCT
fuelectenerg-1427	1481	19	gl	gl	NOUN
fuelectenerg-1427	1481	20	)	)	PUNCT
fuelectenerg-1427	1481	21	and	and	CCONJ
fuelectenerg-1427	1481	22	universal	universal	ADJ
fuelectenerg-1427	1481	23	literal	literal	ADJ
fuelectenerg-1427	1481	24	(	(	PUNCT
fuelectenerg-1427	1481	25	ul	ul	INTJ
fuelectenerg-1427	1481	26	)	)	PUNCT
fuelectenerg-1427	1481	27	to	to	PART
fuelectenerg-1427	1481	28	expand	expand	VERB
fuelectenerg-1427	1481	29	upon	upon	SCONJ
fuelectenerg-1427	1481	30	and	and	CCONJ
fuelectenerg-1427	1481	31	consequently	consequently	ADV
fuelectenerg-1427	1481	32	construct	construct	VERB
fuelectenerg-1427	1481	33	the	the	DET
fuelectenerg-1427	1481	34	corresponding	corresponding	ADJ
fuelectenerg-1427	1481	35	new	new	ADJ
fuelectenerg-1427	1481	36	ulms	ulm	NOUN
fuelectenerg-1427	1481	37	.	.	PUNCT
fuelectenerg-1427	1482	1	acknowledgment	acknowledgment	NOUN
fuelectenerg-1427	1482	2	this	this	DET
fuelectenerg-1427	1482	3	research	research	NOUN
fuelectenerg-1427	1482	4	was	be	AUX
fuelectenerg-1427	1482	5	performed	perform	VERB
fuelectenerg-1427	1482	6	during	during	ADP
fuelectenerg-1427	1482	7	sabbatical	sabbatical	ADJ
fuelectenerg-1427	1482	8	leave	leave	NOUN
fuelectenerg-1427	1482	9	in	in	ADP
fuelectenerg-1427	1482	10	2015	2015	NUM
fuelectenerg-1427	1482	11	-	-	SYM
fuelectenerg-1427	1482	12	2016	2016	NUM
fuelectenerg-1427	1482	13	granted	grant	VERB
fuelectenerg-1427	1482	14	from	from	ADP
fuelectenerg-1427	1482	15	the	the	DET
fuelectenerg-1427	1482	16	university	university	NOUN
fuelectenerg-1427	1482	17	jordan	jordan	PROPN
fuelectenerg-1427	1482	18	and	and	CCONJ
fuelectenerg-1427	1482	19	spent	spend	VERB
fuelectenerg-1427	1482	20	at	at	ADP
fuelectenerg-1427	1482	21	philadelphia	philadelphia	PROPN
fuelectenerg-1427	1482	22	university	university	NOUN
fuelectenerg-1427	1482	23	references	reference	NOUN
fuelectenerg-1427	1483	1	[	[	X
fuelectenerg-1427	1483	2	1	1	NUM
fuelectenerg-1427	1483	3	]	]	PUNCT
fuelectenerg-1427	1483	4	a.	a.	NOUN
fuelectenerg-1427	1483	5	n.	n.	PROPN
fuelectenerg-1427	1483	6	al	al	PROPN
fuelectenerg-1427	1483	7	-	-	PUNCT
fuelectenerg-1427	1483	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1483	9	,	,	PUNCT
fuelectenerg-1427	1483	10	reversible	reversible	ADJ
fuelectenerg-1427	1483	11	logic	logic	NOUN
fuelectenerg-1427	1483	12	synthesis	synthesis	NOUN
fuelectenerg-1427	1483	13	:	:	PUNCT
fuelectenerg-1427	1483	14	from	from	ADP
fuelectenerg-1427	1483	15	fundamentals	fundamental	NOUN
fuelectenerg-1427	1483	16	to	to	ADP
fuelectenerg-1427	1483	17	quantum	quantum	ADJ
fuelectenerg-1427	1483	18	computing	computing	NOUN
fuelectenerg-1427	1483	19	,	,	PUNCT
fuelectenerg-1427	1483	20	springer	springer	NOUN
fuelectenerg-1427	1483	21	-	-	PUNCT
fuelectenerg-1427	1483	22	verlag	verlag	PROPN
fuelectenerg-1427	1483	23	,	,	PUNCT
fuelectenerg-1427	1483	24	2004	2004	NUM
fuelectenerg-1427	1483	25	.	.	PUNCT
fuelectenerg-1427	1484	1	[	[	X
fuelectenerg-1427	1484	2	2	2	NUM
fuelectenerg-1427	1484	3	]	]	PUNCT
fuelectenerg-1427	1484	4	a.	a.	NOUN
fuelectenerg-1427	1484	5	n.	n.	PROPN
fuelectenerg-1427	1484	6	al	al	PROPN
fuelectenerg-1427	1484	7	-	-	PUNCT
fuelectenerg-1427	1484	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1484	9	,	,	PUNCT
fuelectenerg-1427	1484	10	"	"	PUNCT
fuelectenerg-1427	1484	11	three	three	NUM
fuelectenerg-1427	1484	12	-	-	PUNCT
fuelectenerg-1427	1484	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1484	14	lattice	lattice	ADJ
fuelectenerg-1427	1484	15	logic	logic	NOUN
fuelectenerg-1427	1484	16	circuits	circuit	NOUN
fuelectenerg-1427	1484	17	,	,	PUNCT
fuelectenerg-1427	1484	18	part	part	NOUN
fuelectenerg-1427	1484	19	iii	iii	NOUN
fuelectenerg-1427	1484	20	:	:	PUNCT
fuelectenerg-1427	1484	21	solving	solve	VERB
fuelectenerg-1427	1484	22	3d	3d	NUM
fuelectenerg-1427	1484	23	volume	volume	NOUN
fuelectenerg-1427	1484	24	congestion	congestion	NOUN
fuelectenerg-1427	1484	25	problem	problem	NOUN
fuelectenerg-1427	1484	26	,	,	PUNCT
fuelectenerg-1427	1484	27	"	"	PUNCT
fuelectenerg-1427	1484	28	facta	facta	PROPN
fuelectenerg-1427	1484	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1484	30	electronics	electronic	NOUN
fuelectenerg-1427	1484	31	and	and	CCONJ
fuelectenerg-1427	1484	32	energetics	energetic	NOUN
fuelectenerg-1427	1484	33	,	,	PUNCT
fuelectenerg-1427	1484	34	vol	vol	NOUN
fuelectenerg-1427	1484	35	.	.	PROPN
fuelectenerg-1427	1484	36	18	18	NUM
fuelectenerg-1427	1484	37	,	,	PUNCT
fuelectenerg-1427	1484	38	no	no	INTJ
fuelectenerg-1427	1484	39	.	.	NOUN
fuelectenerg-1427	1484	40	1	1	NUM
fuelectenerg-1427	1484	41	,	,	PUNCT
fuelectenerg-1427	1484	42	pp	pp	ADJ
fuelectenerg-1427	1484	43	.	.	PUNCT
fuelectenerg-1427	1485	1	29	29	NUM
fuelectenerg-1427	1485	2	43	43	NUM
fuelectenerg-1427	1485	3	,	,	PUNCT
fuelectenerg-1427	1485	4	2005	2005	NUM
fuelectenerg-1427	1485	5	.	.	PUNCT
fuelectenerg-1427	1486	1	[	[	X
fuelectenerg-1427	1486	2	3	3	NUM
fuelectenerg-1427	1486	3	]	]	PUNCT
fuelectenerg-1427	1486	4	a.	a.	NOUN
fuelectenerg-1427	1486	5	n.	n.	PROPN
fuelectenerg-1427	1486	6	al	al	PROPN
fuelectenerg-1427	1486	7	-	-	PUNCT
fuelectenerg-1427	1486	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1486	9	,	,	PUNCT
fuelectenerg-1427	1486	10	"	"	PUNCT
fuelectenerg-1427	1486	11	three	three	NUM
fuelectenerg-1427	1486	12	-	-	PUNCT
fuelectenerg-1427	1486	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1486	14	lattice	lattice	ADJ
fuelectenerg-1427	1486	15	logic	logic	NOUN
fuelectenerg-1427	1486	16	circuits	circuit	NOUN
fuelectenerg-1427	1486	17	,	,	PUNCT
fuelectenerg-1427	1486	18	part	part	PROPN
fuelectenerg-1427	1486	19	ii	ii	PROPN
fuelectenerg-1427	1486	20	:	:	PUNCT
fuelectenerg-1427	1486	21	formal	formal	ADJ
fuelectenerg-1427	1486	22	methods	method	NOUN
fuelectenerg-1427	1486	23	,	,	PUNCT
fuelectenerg-1427	1486	24	"	"	PUNCT
fuelectenerg-1427	1486	25	facta	facta	PROPN
fuelectenerg-1427	1486	26	universitatis	universitatis	PROPN
fuelectenerg-1427	1486	27	electronics	electronic	NOUN
fuelectenerg-1427	1486	28	and	and	CCONJ
fuelectenerg-1427	1486	29	energetics	energetic	NOUN
fuelectenerg-1427	1486	30	,	,	PUNCT
fuelectenerg-1427	1486	31	vol	vol	NOUN
fuelectenerg-1427	1486	32	.	.	PROPN
fuelectenerg-1427	1486	33	18	18	NUM
fuelectenerg-1427	1486	34	,	,	PUNCT
fuelectenerg-1427	1486	35	no	no	INTJ
fuelectenerg-1427	1486	36	.	.	NOUN
fuelectenerg-1427	1486	37	1	1	NUM
fuelectenerg-1427	1486	38	,	,	PUNCT
fuelectenerg-1427	1486	39	pp	pp	ADJ
fuelectenerg-1427	1486	40	.	.	PUNCT
fuelectenerg-1427	1487	1	15	15	NUM
fuelectenerg-1427	1487	2	28	28	NUM
fuelectenerg-1427	1487	3	,	,	PUNCT
fuelectenerg-1427	1487	4	2005	2005	NUM
fuelectenerg-1427	1487	5	.	.	PUNCT
fuelectenerg-1427	1488	1	[	[	X
fuelectenerg-1427	1488	2	4	4	NUM
fuelectenerg-1427	1488	3	]	]	PUNCT
fuelectenerg-1427	1488	4	a.	a.	NOUN
fuelectenerg-1427	1488	5	n.	n.	PROPN
fuelectenerg-1427	1488	6	al	al	PROPN
fuelectenerg-1427	1488	7	-	-	PUNCT
fuelectenerg-1427	1488	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1488	9	,	,	PUNCT
fuelectenerg-1427	1488	10	"	"	PUNCT
fuelectenerg-1427	1488	11	three	three	NUM
fuelectenerg-1427	1488	12	-	-	PUNCT
fuelectenerg-1427	1488	13	dimensional	dimensional	ADJ
fuelectenerg-1427	1488	14	lattice	lattice	ADJ
fuelectenerg-1427	1488	15	logic	logic	NOUN
fuelectenerg-1427	1488	16	circuits	circuit	NOUN
fuelectenerg-1427	1488	17	,	,	PUNCT
fuelectenerg-1427	1488	18	part	part	NOUN
fuelectenerg-1427	1488	19	i	i	PRON
fuelectenerg-1427	1488	20	:	:	PUNCT
fuelectenerg-1427	1488	21	fundamentals	fundamental	NOUN
fuelectenerg-1427	1488	22	,	,	PUNCT
fuelectenerg-1427	1488	23	"	"	PUNCT
fuelectenerg-1427	1488	24	facta	facta	PROPN
fuelectenerg-1427	1488	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1488	26	electronics	electronic	NOUN
fuelectenerg-1427	1488	27	and	and	CCONJ
fuelectenerg-1427	1488	28	energetics	energetic	NOUN
fuelectenerg-1427	1488	29	,	,	PUNCT
fuelectenerg-1427	1488	30	vol	vol	NOUN
fuelectenerg-1427	1488	31	.	.	PROPN
fuelectenerg-1427	1488	32	18	18	NUM
fuelectenerg-1427	1488	33	,	,	PUNCT
fuelectenerg-1427	1488	34	no	no	INTJ
fuelectenerg-1427	1488	35	.	.	NOUN
fuelectenerg-1427	1488	36	1	1	NUM
fuelectenerg-1427	1488	37	,	,	PUNCT
fuelectenerg-1427	1488	38	pp	pp	ADJ
fuelectenerg-1427	1488	39	.	.	PUNCT
fuelectenerg-1427	1488	40	1	1	NUM
fuelectenerg-1427	1488	41	13	13	NUM
fuelectenerg-1427	1488	42	,	,	PUNCT
fuelectenerg-1427	1488	43	2005	2005	NUM
fuelectenerg-1427	1488	44	.	.	PUNCT
fuelectenerg-1427	1489	1	116	116	NUM
fuelectenerg-1427	1489	2	an	an	DET
fuelectenerg-1427	1489	3	extended	extend	VERB
fuelectenerg-1427	1489	4	green	green	ADJ
fuelectenerg-1427	1489	5	sasao	sasao	PROPN
fuelectenerg-1427	1489	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1489	7	of	of	ADP
fuelectenerg-1427	1489	8	canonical	canonical	ADJ
fuelectenerg-1427	1489	9	ternary	ternary	ADJ
fuelectenerg-1427	1489	10	galois	galois	NOUN
fuelectenerg-1427	1489	11	forms	form	NOUN
fuelectenerg-1427	1489	12	...	...	PUNCT
fuelectenerg-1427	1490	1	[	[	X
fuelectenerg-1427	1490	2	5	5	NUM
fuelectenerg-1427	1490	3	]	]	PUNCT
fuelectenerg-1427	1490	4	a.	a.	NOUN
fuelectenerg-1427	1490	5	n.	n.	PROPN
fuelectenerg-1427	1490	6	al	al	PROPN
fuelectenerg-1427	1490	7	-	-	PUNCT
fuelectenerg-1427	1490	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1490	9	,	,	PUNCT
fuelectenerg-1427	1490	10	"	"	PUNCT
fuelectenerg-1427	1490	11	quantum	quantum	ADJ
fuelectenerg-1427	1490	12	logic	logic	NOUN
fuelectenerg-1427	1490	13	circuit	circuit	NOUN
fuelectenerg-1427	1490	14	design	design	NOUN
fuelectenerg-1427	1490	15	of	of	ADP
fuelectenerg-1427	1490	16	many	many	ADV
fuelectenerg-1427	1490	17	-	-	PUNCT
fuelectenerg-1427	1490	18	valued	value	VERB
fuelectenerg-1427	1490	19	galois	galois	PROPN
fuelectenerg-1427	1490	20	reversible	reversible	ADJ
fuelectenerg-1427	1490	21	expansions	expansion	NOUN
fuelectenerg-1427	1490	22	and	and	CCONJ
fuelectenerg-1427	1490	23	fast	fast	ADJ
fuelectenerg-1427	1490	24	transforms	transform	NOUN
fuelectenerg-1427	1490	25	,	,	PUNCT
fuelectenerg-1427	1490	26	"	"	PUNCT
fuelectenerg-1427	1490	27	journal	journal	NOUN
fuelectenerg-1427	1490	28	of	of	ADP
fuelectenerg-1427	1490	29	circuits	circuit	NOUN
fuelectenerg-1427	1490	30	,	,	PUNCT
fuelectenerg-1427	1490	31	systems	system	NOUN
fuelectenerg-1427	1490	32	,	,	PUNCT
fuelectenerg-1427	1490	33	and	and	CCONJ
fuelectenerg-1427	1490	34	computers	computer	NOUN
fuelectenerg-1427	1490	35	,	,	PUNCT
fuelectenerg-1427	1490	36	world	world	NOUN
fuelectenerg-1427	1490	37	scientific	scientific	ADJ
fuelectenerg-1427	1490	38	,	,	PUNCT
fuelectenerg-1427	1490	39	vol	vol	NOUN
fuelectenerg-1427	1490	40	.	.	PROPN
fuelectenerg-1427	1490	41	16	16	NUM
fuelectenerg-1427	1490	42	,	,	PUNCT
fuelectenerg-1427	1490	43	no	no	INTJ
fuelectenerg-1427	1490	44	.	.	NOUN
fuelectenerg-1427	1490	45	5	5	NUM
fuelectenerg-1427	1490	46	,	,	PUNCT
fuelectenerg-1427	1490	47	pp	pp	ADJ
fuelectenerg-1427	1490	48	.	.	PUNCT
fuelectenerg-1427	1491	1	641	641	NUM
fuelectenerg-1427	1491	2	671	671	NUM
fuelectenerg-1427	1491	3	,	,	PUNCT
fuelectenerg-1427	1491	4	2007	2007	NUM
fuelectenerg-1427	1491	5	.	.	PUNCT
fuelectenerg-1427	1492	1	[	[	X
fuelectenerg-1427	1492	2	6	6	NUM
fuelectenerg-1427	1492	3	]	]	PUNCT
fuelectenerg-1427	1492	4	a.	a.	NOUN
fuelectenerg-1427	1492	5	n.	n.	PROPN
fuelectenerg-1427	1492	6	al	al	PROPN
fuelectenerg-1427	1492	7	-	-	PUNCT
fuelectenerg-1427	1492	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1492	9	,	,	PUNCT
fuelectenerg-1427	1492	10	"	"	PUNCT
fuelectenerg-1427	1492	11	representations	representation	NOUN
fuelectenerg-1427	1492	12	,	,	PUNCT
fuelectenerg-1427	1492	13	operations	operation	NOUN
fuelectenerg-1427	1492	14	,	,	PUNCT
fuelectenerg-1427	1492	15	and	and	CCONJ
fuelectenerg-1427	1492	16	applications	application	NOUN
fuelectenerg-1427	1492	17	of	of	ADP
fuelectenerg-1427	1492	18	switching	switch	VERB
fuelectenerg-1427	1492	19	circuits	circuit	NOUN
fuelectenerg-1427	1492	20	in	in	ADP
fuelectenerg-1427	1492	21	the	the	DET
fuelectenerg-1427	1492	22	reversible	reversible	ADJ
fuelectenerg-1427	1492	23	and	and	CCONJ
fuelectenerg-1427	1492	24	quantum	quantum	ADJ
fuelectenerg-1427	1492	25	spaces	space	NOUN
fuelectenerg-1427	1492	26	,	,	PUNCT
fuelectenerg-1427	1492	27	"	"	PUNCT
fuelectenerg-1427	1492	28	facta	facta	PROPN
fuelectenerg-1427	1492	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1492	30	electronics	electronic	NOUN
fuelectenerg-1427	1492	31	and	and	CCONJ
fuelectenerg-1427	1492	32	energetics	energetic	NOUN
fuelectenerg-1427	1492	33	,	,	PUNCT
fuelectenerg-1427	1492	34	vol	vol	NOUN
fuelectenerg-1427	1492	35	.	.	PROPN
fuelectenerg-1427	1492	36	20	20	NUM
fuelectenerg-1427	1492	37	,	,	PUNCT
fuelectenerg-1427	1492	38	no	no	INTJ
fuelectenerg-1427	1492	39	.	.	NOUN
fuelectenerg-1427	1492	40	3	3	NUM
fuelectenerg-1427	1492	41	,	,	PUNCT
fuelectenerg-1427	1492	42	pp	pp	ADJ
fuelectenerg-1427	1492	43	.	.	PUNCT
fuelectenerg-1427	1493	1	507	507	NUM
fuelectenerg-1427	1493	2	539	539	NUM
fuelectenerg-1427	1493	3	,	,	PUNCT
fuelectenerg-1427	1493	4	2007	2007	NUM
fuelectenerg-1427	1493	5	.	.	PUNCT
fuelectenerg-1427	1494	1	[	[	X
fuelectenerg-1427	1494	2	7	7	NUM
fuelectenerg-1427	1494	3	]	]	PUNCT
fuelectenerg-1427	1494	4	a.	a.	NOUN
fuelectenerg-1427	1494	5	n.	n.	PROPN
fuelectenerg-1427	1494	6	al	al	PROPN
fuelectenerg-1427	1494	7	-	-	PUNCT
fuelectenerg-1427	1494	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1494	9	,	,	PUNCT
fuelectenerg-1427	1494	10	"	"	PUNCT
fuelectenerg-1427	1494	11	multi	multi	ADJ
fuelectenerg-1427	1494	12	-	-	ADJ
fuelectenerg-1427	1494	13	valued	value	VERB
fuelectenerg-1427	1494	14	galois	galois	PROPN
fuelectenerg-1427	1494	15	shannon	shannon	PROPN
fuelectenerg-1427	1494	16	-	-	PUNCT
fuelectenerg-1427	1494	17	davio	davio	NOUN
fuelectenerg-1427	1494	18	trees	tree	NOUN
fuelectenerg-1427	1494	19	and	and	CCONJ
fuelectenerg-1427	1494	20	their	their	PRON
fuelectenerg-1427	1494	21	complexity	complexity	NOUN
fuelectenerg-1427	1494	22	,	,	PUNCT
fuelectenerg-1427	1494	23	"	"	PUNCT
fuelectenerg-1427	1494	24	facta	facta	PROPN
fuelectenerg-1427	1494	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1494	26	electronics	electronic	NOUN
fuelectenerg-1427	1494	27	and	and	CCONJ
fuelectenerg-1427	1494	28	energetics	energetic	NOUN
fuelectenerg-1427	1494	29	,	,	PUNCT
fuelectenerg-1427	1494	30	vol	vol	NOUN
fuelectenerg-1427	1494	31	.	.	PROPN
fuelectenerg-1427	1494	32	29	29	NUM
fuelectenerg-1427	1494	33	,	,	PUNCT
fuelectenerg-1427	1494	34	no	no	INTJ
fuelectenerg-1427	1494	35	.	.	NOUN
fuelectenerg-1427	1494	36	4	4	NUM
fuelectenerg-1427	1494	37	,	,	PUNCT
fuelectenerg-1427	1494	38	pp	pp	ADJ
fuelectenerg-1427	1494	39	.	.	PUNCT
fuelectenerg-1427	1495	1	701	701	NUM
fuelectenerg-1427	1495	2	-	-	SYM
fuelectenerg-1427	1495	3	720	720	NUM
fuelectenerg-1427	1495	4	,	,	PUNCT
fuelectenerg-1427	1495	5	2016	2016	NUM
fuelectenerg-1427	1495	6	.	.	PUNCT
fuelectenerg-1427	1496	1	[	[	X
fuelectenerg-1427	1496	2	8	8	NUM
fuelectenerg-1427	1496	3	]	]	X
fuelectenerg-1427	1496	4	b.	b.	PROPN
fuelectenerg-1427	1496	5	falkowski	falkowski	NOUN
fuelectenerg-1427	1496	6	and	and	CCONJ
fuelectenerg-1427	1496	7	l.-s	l.-s	PROPN
fuelectenerg-1427	1496	8	.	.	PUNCT
fuelectenerg-1427	1497	1	lim	lim	PROPN
fuelectenerg-1427	1497	2	,	,	PUNCT
fuelectenerg-1427	1497	3	"	"	PUNCT
fuelectenerg-1427	1497	4	gray	gray	ADJ
fuelectenerg-1427	1497	5	scale	scale	NOUN
fuelectenerg-1427	1497	6	image	image	NOUN
fuelectenerg-1427	1497	7	compression	compression	NOUN
fuelectenerg-1427	1497	8	based	base	VERB
fuelectenerg-1427	1497	9	on	on	ADP
fuelectenerg-1427	1497	10	multiple	multiple	ADV
fuelectenerg-1427	1497	11	-	-	PUNCT
fuelectenerg-1427	1497	12	valued	value	VERB
fuelectenerg-1427	1497	13	input	input	NOUN
fuelectenerg-1427	1497	14	binary	binary	NOUN
fuelectenerg-1427	1497	15	functions	function	NOUN
fuelectenerg-1427	1497	16	,	,	PUNCT
fuelectenerg-1427	1497	17	walsh	walsh	NOUN
fuelectenerg-1427	1497	18	and	and	CCONJ
fuelectenerg-1427	1497	19	reed	reed	PROPN
fuelectenerg-1427	1497	20	-	-	PUNCT
fuelectenerg-1427	1497	21	muller	muller	PROPN
fuelectenerg-1427	1497	22	spectra	spectra	PROPN
fuelectenerg-1427	1497	23	,	,	PUNCT
fuelectenerg-1427	1497	24	"	"	PUNCT
fuelectenerg-1427	1497	25	proc	proc	NOUN
fuelectenerg-1427	1497	26	.	.	PUNCT
fuelectenerg-1427	1498	1	ismvl	ismvl	PROPN
fuelectenerg-1427	1498	2	,	,	PUNCT
fuelectenerg-1427	1498	3	2000	2000	NUM
fuelectenerg-1427	1498	4	,	,	PUNCT
fuelectenerg-1427	1498	5	pp	pp	ADJ
fuelectenerg-1427	1498	6	.	.	PUNCT
fuelectenerg-1427	1499	1	279	279	NUM
fuelectenerg-1427	1499	2	-	-	SYM
fuelectenerg-1427	1499	3	284	284	NUM
fuelectenerg-1427	1499	4	.	.	PUNCT
fuelectenerg-1427	1500	1	[	[	X
fuelectenerg-1427	1500	2	9	9	NUM
fuelectenerg-1427	1500	3	]	]	PUNCT
fuelectenerg-1427	1500	4	h.	h.	PROPN
fuelectenerg-1427	1500	5	fujiwara	fujiwara	PROPN
fuelectenerg-1427	1500	6	,	,	PUNCT
fuelectenerg-1427	1500	7	logic	logic	NOUN
fuelectenerg-1427	1500	8	testing	testing	NOUN
fuelectenerg-1427	1500	9	and	and	CCONJ
fuelectenerg-1427	1500	10	design	design	NOUN
fuelectenerg-1427	1500	11	for	for	ADP
fuelectenerg-1427	1500	12	testability	testability	NOUN
fuelectenerg-1427	1500	13	,	,	PUNCT
fuelectenerg-1427	1500	14	mit	mit	NOUN
fuelectenerg-1427	1500	15	press	press	NOUN
fuelectenerg-1427	1500	16	,	,	PUNCT
fuelectenerg-1427	1500	17	1985	1985	NUM
fuelectenerg-1427	1500	18	.	.	PUNCT
fuelectenerg-1427	1501	1	[	[	X
fuelectenerg-1427	1501	2	10	10	NUM
fuelectenerg-1427	1501	3	]	]	X
fuelectenerg-1427	1501	4	d.	d.	PROPN
fuelectenerg-1427	1501	5	h.	h.	PROPN
fuelectenerg-1427	1501	6	green	green	PROPN
fuelectenerg-1427	1501	7	,	,	PUNCT
fuelectenerg-1427	1501	8	"	"	PUNCT
fuelectenerg-1427	1501	9	families	family	NOUN
fuelectenerg-1427	1501	10	of	of	ADP
fuelectenerg-1427	1501	11	reed	reed	NOUN
fuelectenerg-1427	1501	12	-	-	PUNCT
fuelectenerg-1427	1501	13	muller	muller	NOUN
fuelectenerg-1427	1501	14	canonical	canonical	ADJ
fuelectenerg-1427	1501	15	forms	form	NOUN
fuelectenerg-1427	1501	16	,	,	PUNCT
fuelectenerg-1427	1501	17	"	"	PUNCT
fuelectenerg-1427	1501	18	int	int	NOUN
fuelectenerg-1427	1501	19	.	.	PUNCT
fuelectenerg-1427	1502	1	j.	j.	PROPN
fuelectenerg-1427	1502	2	electronics	electronics	PROPN
fuelectenerg-1427	1502	3	,	,	PUNCT
fuelectenerg-1427	1502	4	no	no	INTJ
fuelectenerg-1427	1502	5	.	.	NOUN
fuelectenerg-1427	1502	6	2	2	NUM
fuelectenerg-1427	1502	7	,	,	PUNCT
fuelectenerg-1427	1502	8	pp	pp	ADJ
fuelectenerg-1427	1502	9	.	.	PUNCT
fuelectenerg-1427	1503	1	259	259	NUM
fuelectenerg-1427	1503	2	-	-	SYM
fuelectenerg-1427	1503	3	280	280	NUM
fuelectenerg-1427	1503	4	,	,	PUNCT
fuelectenerg-1427	1503	5	1991	1991	NUM
fuelectenerg-1427	1503	6	.	.	PUNCT
fuelectenerg-1427	1504	1	[	[	X
fuelectenerg-1427	1504	2	11	11	NUM
fuelectenerg-1427	1504	3	]	]	PUNCT
fuelectenerg-1427	1504	4	m.	m.	NOUN
fuelectenerg-1427	1504	5	helliwell	helliwell	NOUN
fuelectenerg-1427	1504	6	and	and	CCONJ
fuelectenerg-1427	1504	7	m.	m.	PROPN
fuelectenerg-1427	1504	8	a.	a.	PROPN
fuelectenerg-1427	1504	9	perkowski	perkowski	PROPN
fuelectenerg-1427	1504	10	,	,	PUNCT
fuelectenerg-1427	1504	11	"	"	PUNCT
fuelectenerg-1427	1504	12	a	a	DET
fuelectenerg-1427	1504	13	fast	fast	ADJ
fuelectenerg-1427	1504	14	algorithm	algorithm	NOUN
fuelectenerg-1427	1504	15	to	to	PART
fuelectenerg-1427	1504	16	minimize	minimize	VERB
fuelectenerg-1427	1504	17	multi	multi	ADJ
fuelectenerg-1427	1504	18	-	-	ADJ
fuelectenerg-1427	1504	19	output	output	ADJ
fuelectenerg-1427	1504	20	mixed	mix	VERB
fuelectenerg-1427	1504	21	-	-	PUNCT
fuelectenerg-1427	1504	22	polarity	polarity	NOUN
fuelectenerg-1427	1504	23	generalized	generalize	VERB
fuelectenerg-1427	1504	24	reed	reed	NOUN
fuelectenerg-1427	1504	25	-	-	PUNCT
fuelectenerg-1427	1504	26	muller	muller	NOUN
fuelectenerg-1427	1504	27	forms	form	NOUN
fuelectenerg-1427	1504	28	,	,	PUNCT
fuelectenerg-1427	1504	29	"	"	PUNCT
fuelectenerg-1427	1504	30	proc	proc	NOUN
fuelectenerg-1427	1504	31	.	.	PUNCT
fuelectenerg-1427	1505	1	design	design	NOUN
fuelectenerg-1427	1505	2	automation	automation	NOUN
fuelectenerg-1427	1505	3	conference	conference	NOUN
fuelectenerg-1427	1505	4	,	,	PUNCT
fuelectenerg-1427	1505	5	1988	1988	NUM
fuelectenerg-1427	1505	6	,	,	PUNCT
fuelectenerg-1427	1505	7	pp	pp	ADV
fuelectenerg-1427	1505	8	.	.	PUNCT
fuelectenerg-1427	1506	1	427	427	NUM
fuelectenerg-1427	1506	2	-	-	SYM
fuelectenerg-1427	1506	3	432	432	NUM
fuelectenerg-1427	1506	4	.	.	PUNCT
fuelectenerg-1427	1507	1	[	[	X
fuelectenerg-1427	1507	2	12	12	NUM
fuelectenerg-1427	1507	3	]	]	PUNCT
fuelectenerg-1427	1507	4	s.	s.	PROPN
fuelectenerg-1427	1507	5	l.	l.	PROPN
fuelectenerg-1427	1507	6	hurst	hurst	PROPN
fuelectenerg-1427	1507	7	,	,	PUNCT
fuelectenerg-1427	1507	8	d.	d.	PROPN
fuelectenerg-1427	1507	9	m.	m.	PROPN
fuelectenerg-1427	1507	10	miller	miller	PROPN
fuelectenerg-1427	1507	11	,	,	PUNCT
fuelectenerg-1427	1507	12	and	and	CCONJ
fuelectenerg-1427	1507	13	j.	j.	PROPN
fuelectenerg-1427	1507	14	c.	c.	PROPN
fuelectenerg-1427	1507	15	muzio	muzio	PROPN
fuelectenerg-1427	1507	16	,	,	PUNCT
fuelectenerg-1427	1507	17	spectral	spectral	ADJ
fuelectenerg-1427	1507	18	techniques	technique	NOUN
fuelectenerg-1427	1507	19	in	in	ADP
fuelectenerg-1427	1507	20	digital	digital	ADJ
fuelectenerg-1427	1507	21	logic	logic	NOUN
fuelectenerg-1427	1507	22	,	,	PUNCT
fuelectenerg-1427	1507	23	academic	academic	PROPN
fuelectenerg-1427	1507	24	press	press	PROPN
fuelectenerg-1427	1507	25	inc	inc	PROPN
fuelectenerg-1427	1507	26	.	.	PROPN
fuelectenerg-1427	1507	27	,	,	PUNCT
fuelectenerg-1427	1507	28	1985	1985	NUM
fuelectenerg-1427	1507	29	.	.	PUNCT
fuelectenerg-1427	1508	1	[	[	X
fuelectenerg-1427	1508	2	13	13	NUM
fuelectenerg-1427	1508	3	]	]	PUNCT
fuelectenerg-1427	1508	4	m.	m.	NOUN
fuelectenerg-1427	1508	5	g.	g.	PROPN
fuelectenerg-1427	1508	6	karpovsky	karpovsky	PROPN
fuelectenerg-1427	1508	7	,	,	PUNCT
fuelectenerg-1427	1508	8	finite	finite	PROPN
fuelectenerg-1427	1508	9	orthogonal	orthogonal	ADJ
fuelectenerg-1427	1508	10	series	series	NOUN
fuelectenerg-1427	1508	11	in	in	ADP
fuelectenerg-1427	1508	12	the	the	DET
fuelectenerg-1427	1508	13	design	design	NOUN
fuelectenerg-1427	1508	14	of	of	ADP
fuelectenerg-1427	1508	15	digital	digital	ADJ
fuelectenerg-1427	1508	16	devices	device	NOUN
fuelectenerg-1427	1508	17	,	,	PUNCT
fuelectenerg-1427	1508	18	wiley	wiley	NOUN
fuelectenerg-1427	1508	19	,	,	PUNCT
fuelectenerg-1427	1508	20	1976	1976	NUM
fuelectenerg-1427	1508	21	.	.	PUNCT
fuelectenerg-1427	1509	1	[	[	X
fuelectenerg-1427	1509	2	14	14	NUM
fuelectenerg-1427	1509	3	]	]	X
fuelectenerg-1427	1509	4	s.	s.	PROPN
fuelectenerg-1427	1509	5	m.	m.	PROPN
fuelectenerg-1427	1509	6	reddy	reddy	PROPN
fuelectenerg-1427	1509	7	,	,	PUNCT
fuelectenerg-1427	1509	8	"	"	PUNCT
fuelectenerg-1427	1509	9	easily	easily	ADV
fuelectenerg-1427	1509	10	testable	testable	ADJ
fuelectenerg-1427	1509	11	realizations	realization	NOUN
fuelectenerg-1427	1509	12	of	of	ADP
fuelectenerg-1427	1509	13	logic	logic	NOUN
fuelectenerg-1427	1509	14	functions	function	NOUN
fuelectenerg-1427	1509	15	,	,	PUNCT
fuelectenerg-1427	1509	16	"	"	PUNCT
fuelectenerg-1427	1509	17	ieee	ieee	NOUN
fuelectenerg-1427	1509	18	trans	tran	NOUN
fuelectenerg-1427	1509	19	.	.	PUNCT
fuelectenerg-1427	1510	1	comp	comp	PROPN
fuelectenerg-1427	1510	2	.	.	PUNCT
fuelectenerg-1427	1510	3	,	,	PUNCT
fuelectenerg-1427	1510	4	c-21	c-21	PROPN
fuelectenerg-1427	1510	5	,	,	PUNCT
fuelectenerg-1427	1510	6	pp	pp	ADV
fuelectenerg-1427	1510	7	.	.	PUNCT
fuelectenerg-1427	1511	1	1183	1183	NUM
fuelectenerg-1427	1511	2	-	-	SYM
fuelectenerg-1427	1511	3	1188	1188	NUM
fuelectenerg-1427	1511	4	,	,	PUNCT
fuelectenerg-1427	1511	5	1972	1972	NUM
fuelectenerg-1427	1511	6	.	.	PUNCT
fuelectenerg-1427	1512	1	[	[	X
fuelectenerg-1427	1512	2	15	15	X
fuelectenerg-1427	1512	3	]	]	X
fuelectenerg-1427	1512	4	t.	t.	PROPN
fuelectenerg-1427	1512	5	sasao	sasao	PROPN
fuelectenerg-1427	1512	6	and	and	CCONJ
fuelectenerg-1427	1512	7	m.	m.	PROPN
fuelectenerg-1427	1512	8	fujita	fujita	PROPN
fuelectenerg-1427	1512	9	(	(	PUNCT
fuelectenerg-1427	1512	10	editors	editor	NOUN
fuelectenerg-1427	1512	11	)	)	PUNCT
fuelectenerg-1427	1512	12	,	,	PUNCT
fuelectenerg-1427	1512	13	representations	representation	NOUN
fuelectenerg-1427	1512	14	of	of	ADP
fuelectenerg-1427	1512	15	discrete	discrete	ADJ
fuelectenerg-1427	1512	16	functions	function	NOUN
fuelectenerg-1427	1512	17	,	,	PUNCT
fuelectenerg-1427	1512	18	kluwer	kluwer	NOUN
fuelectenerg-1427	1512	19	academic	academic	ADJ
fuelectenerg-1427	1512	20	publishers	publisher	NOUN
fuelectenerg-1427	1512	21	,	,	PUNCT
fuelectenerg-1427	1512	22	1996	1996	NUM
fuelectenerg-1427	1512	23	.	.	PUNCT
fuelectenerg-1427	1513	1	[	[	X
fuelectenerg-1427	1513	2	16	16	NUM
fuelectenerg-1427	1513	3	]	]	PUNCT
fuelectenerg-1427	1513	4	t.	t.	PROPN
fuelectenerg-1427	1513	5	sasao	sasao	PROPN
fuelectenerg-1427	1513	6	,	,	PUNCT
fuelectenerg-1427	1513	7	"	"	PUNCT
fuelectenerg-1427	1513	8	easily	easily	ADV
fuelectenerg-1427	1513	9	testable	testable	ADJ
fuelectenerg-1427	1513	10	realizations	realization	NOUN
fuelectenerg-1427	1513	11	for	for	ADP
fuelectenerg-1427	1513	12	generalized	generalized	ADJ
fuelectenerg-1427	1513	13	reed	reed	NOUN
fuelectenerg-1427	1513	14	-	-	PUNCT
fuelectenerg-1427	1513	15	muller	muller	NOUN
fuelectenerg-1427	1513	16	expressions	expression	NOUN
fuelectenerg-1427	1513	17	,	,	PUNCT
fuelectenerg-1427	1513	18	"	"	PUNCT
fuelectenerg-1427	1513	19	ieee	ieee	NOUN
fuelectenerg-1427	1513	20	trans	tran	NOUN
fuelectenerg-1427	1513	21	.	.	PUNCT
fuelectenerg-1427	1514	1	comp	comp	PROPN
fuelectenerg-1427	1514	2	.	.	PUNCT
fuelectenerg-1427	1514	3	,	,	PUNCT
fuelectenerg-1427	1514	4	vol	vol	NOUN
fuelectenerg-1427	1514	5	.	.	PROPN
fuelectenerg-1427	1515	1	46	46	NUM
fuelectenerg-1427	1515	2	,	,	PUNCT
fuelectenerg-1427	1515	3	pp	pp	ADJ
fuelectenerg-1427	1515	4	.	.	PUNCT
fuelectenerg-1427	1516	1	709	709	NUM
fuelectenerg-1427	1516	2	-	-	PUNCT
fuelectenerg-1427	1516	3	716	716	NUM
fuelectenerg-1427	1516	4	,	,	PUNCT
fuelectenerg-1427	1516	5	1997	1997	NUM
fuelectenerg-1427	1516	6	.	.	PUNCT
fuelectenerg-1427	1517	1	[	[	X
fuelectenerg-1427	1517	2	17	17	NUM
fuelectenerg-1427	1517	3	]	]	X
fuelectenerg-1427	1517	4	r.	r.	PROPN
fuelectenerg-1427	1517	5	s.	s.	PROPN
fuelectenerg-1427	1517	6	stanković	stanković	PROPN
fuelectenerg-1427	1517	7	,	,	PUNCT
fuelectenerg-1427	1517	8	spectral	spectral	ADJ
fuelectenerg-1427	1517	9	transform	transform	VERB
fuelectenerg-1427	1517	10	decision	decision	NOUN
fuelectenerg-1427	1517	11	diagrams	diagram	NOUN
fuelectenerg-1427	1517	12	in	in	ADP
fuelectenerg-1427	1517	13	simple	simple	ADJ
fuelectenerg-1427	1517	14	questions	question	NOUN
fuelectenerg-1427	1517	15	and	and	CCONJ
fuelectenerg-1427	1517	16	simple	simple	ADJ
fuelectenerg-1427	1517	17	answers	answer	NOUN
fuelectenerg-1427	1517	18	,	,	PUNCT
fuelectenerg-1427	1517	19	nauka	nauka	PROPN
fuelectenerg-1427	1517	20	,	,	PUNCT
fuelectenerg-1427	1517	21	1998	1998	NUM
fuelectenerg-1427	1517	22	.	.	PUNCT
fuelectenerg-1427	1518	1	[	[	X
fuelectenerg-1427	1518	2	18	18	NUM
fuelectenerg-1427	1518	3	]	]	X
fuelectenerg-1427	1518	4	r.	r.	PROPN
fuelectenerg-1427	1518	5	s.	s.	PROPN
fuelectenerg-1427	1518	6	stanković	stanković	PROPN
fuelectenerg-1427	1518	7	,	,	PUNCT
fuelectenerg-1427	1518	8	c.	c.	PROPN
fuelectenerg-1427	1518	9	moraga	moraga	PROPN
fuelectenerg-1427	1518	10	,	,	PUNCT
fuelectenerg-1427	1518	11	and	and	CCONJ
fuelectenerg-1427	1518	12	j.	j.	PROPN
fuelectenerg-1427	1518	13	t.	t.	PROPN
fuelectenerg-1427	1518	14	astola	astola	PROPN
fuelectenerg-1427	1518	15	,	,	PUNCT
fuelectenerg-1427	1518	16	"	"	PUNCT
fuelectenerg-1427	1518	17	reed	reed	NOUN
fuelectenerg-1427	1518	18	-	-	PUNCT
fuelectenerg-1427	1518	19	muller	muller	NOUN
fuelectenerg-1427	1518	20	expressions	expression	NOUN
fuelectenerg-1427	1518	21	in	in	ADP
fuelectenerg-1427	1518	22	the	the	DET
fuelectenerg-1427	1518	23	previous	previous	ADJ
fuelectenerg-1427	1518	24	decade	decade	NOUN
fuelectenerg-1427	1518	25	,	,	PUNCT
fuelectenerg-1427	1518	26	"	"	PUNCT
fuelectenerg-1427	1518	27	proc	proc	NOUN
fuelectenerg-1427	1518	28	.	.	PUNCT
fuelectenerg-1427	1519	1	reed	reed	NOUN
fuelectenerg-1427	1519	2	-	-	PUNCT
fuelectenerg-1427	1519	3	muller	muller	NOUN
fuelectenerg-1427	1519	4	,	,	PUNCT
fuelectenerg-1427	1519	5	starkville	starkville	PROPN
fuelectenerg-1427	1519	6	,	,	PUNCT
fuelectenerg-1427	1519	7	2001	2001	NUM
fuelectenerg-1427	1519	8	,	,	PUNCT
fuelectenerg-1427	1519	9	pp	pp	ADJ
fuelectenerg-1427	1519	10	.	.	PUNCT
fuelectenerg-1427	1520	1	7	7	NUM
fuelectenerg-1427	1520	2	-	-	SYM
fuelectenerg-1427	1520	3	26	26	NUM
fuelectenerg-1427	1520	4	.	.	PUNCT
fuelectenerg-1427	1521	1	[	[	X
fuelectenerg-1427	1521	2	19	19	NUM
fuelectenerg-1427	1521	3	]	]	PUNCT
fuelectenerg-1427	1521	4	s.	s.	PROPN
fuelectenerg-1427	1521	5	b.	b.	PROPN
fuelectenerg-1427	1521	6	akers	akers	PROPN
fuelectenerg-1427	1521	7	,	,	PUNCT
fuelectenerg-1427	1521	8	"	"	PUNCT
fuelectenerg-1427	1521	9	binary	binary	ADJ
fuelectenerg-1427	1521	10	decision	decision	NOUN
fuelectenerg-1427	1521	11	diagrams	diagram	NOUN
fuelectenerg-1427	1521	12	,	,	PUNCT
fuelectenerg-1427	1521	13	"	"	PUNCT
fuelectenerg-1427	1521	14	ieee	ieee	NOUN
fuelectenerg-1427	1521	15	trans	tran	NOUN
fuelectenerg-1427	1521	16	.	.	PUNCT
fuelectenerg-1427	1522	1	comp	comp	PROPN
fuelectenerg-1427	1522	2	.	.	PUNCT
fuelectenerg-1427	1522	3	,	,	PUNCT
fuelectenerg-1427	1522	4	vol	vol	NOUN
fuelectenerg-1427	1522	5	.	.	PUNCT
fuelectenerg-1427	1523	1	c-27	c-27	PROPN
fuelectenerg-1427	1523	2	,	,	PUNCT
fuelectenerg-1427	1523	3	no	no	INTJ
fuelectenerg-1427	1523	4	.	.	NOUN
fuelectenerg-1427	1523	5	6	6	NUM
fuelectenerg-1427	1523	6	,	,	PUNCT
fuelectenerg-1427	1523	7	pp	pp	ADJ
fuelectenerg-1427	1523	8	.	.	PUNCT
fuelectenerg-1427	1524	1	509	509	NUM
fuelectenerg-1427	1524	2	-	-	SYM
fuelectenerg-1427	1524	3	516	516	NUM
fuelectenerg-1427	1524	4	,	,	PUNCT
fuelectenerg-1427	1524	5	june	june	PROPN
fuelectenerg-1427	1524	6	1978	1978	NUM
fuelectenerg-1427	1524	7	.	.	PUNCT
fuelectenerg-1427	1525	1	[	[	X
fuelectenerg-1427	1525	2	20	20	NUM
fuelectenerg-1427	1525	3	]	]	PUNCT
fuelectenerg-1427	1525	4	r.	r.	PROPN
fuelectenerg-1427	1525	5	e.	e.	PROPN
fuelectenerg-1427	1525	6	bryant	bryant	PROPN
fuelectenerg-1427	1525	7	,	,	PUNCT
fuelectenerg-1427	1525	8	"	"	PUNCT
fuelectenerg-1427	1525	9	graph	graph	NOUN
fuelectenerg-1427	1525	10	-	-	PUNCT
fuelectenerg-1427	1525	11	based	base	VERB
fuelectenerg-1427	1525	12	algorithms	algorithm	NOUN
fuelectenerg-1427	1525	13	for	for	ADP
fuelectenerg-1427	1525	14	boolean	boolean	ADJ
fuelectenerg-1427	1525	15	functions	function	NOUN
fuelectenerg-1427	1525	16	manipulation	manipulation	NOUN
fuelectenerg-1427	1525	17	,	,	PUNCT
fuelectenerg-1427	1525	18	"	"	PUNCT
fuelectenerg-1427	1525	19	ieee	ieee	NOUN
fuelectenerg-1427	1525	20	trans	tran	NOUN
fuelectenerg-1427	1525	21	.	.	PUNCT
fuelectenerg-1427	1526	1	on	on	ADP
fuelectenerg-1427	1526	2	comp	comp	PROPN
fuelectenerg-1427	1526	3	.	.	PUNCT
fuelectenerg-1427	1526	4	,	,	PUNCT
fuelectenerg-1427	1526	5	vol	vol	NOUN
fuelectenerg-1427	1526	6	.	.	PUNCT
fuelectenerg-1427	1527	1	c-35	c-35	PROPN
fuelectenerg-1427	1527	2	,	,	PUNCT
fuelectenerg-1427	1527	3	no.8	no.8	PROPN
fuelectenerg-1427	1527	4	,	,	PUNCT
fuelectenerg-1427	1527	5	pp	pp	ADV
fuelectenerg-1427	1527	6	.	.	PUNCT
fuelectenerg-1427	1528	1	667	667	NUM
fuelectenerg-1427	1528	2	-	-	SYM
fuelectenerg-1427	1528	3	691	691	NUM
fuelectenerg-1427	1528	4	,	,	PUNCT
fuelectenerg-1427	1528	5	1986	1986	NUM
fuelectenerg-1427	1528	6	.	.	PUNCT
fuelectenerg-1427	1529	1	[	[	X
fuelectenerg-1427	1529	2	21	21	NUM
fuelectenerg-1427	1529	3	]	]	X
fuelectenerg-1427	1529	4	d.	d.	PROPN
fuelectenerg-1427	1529	5	k.	k.	PROPN
fuelectenerg-1427	1529	6	pradhan	pradhan	PROPN
fuelectenerg-1427	1529	7	,	,	PUNCT
fuelectenerg-1427	1529	8	"	"	PUNCT
fuelectenerg-1427	1529	9	universal	universal	ADJ
fuelectenerg-1427	1529	10	test	test	NOUN
fuelectenerg-1427	1529	11	sets	set	NOUN
fuelectenerg-1427	1529	12	for	for	ADP
fuelectenerg-1427	1529	13	multiple	multiple	ADJ
fuelectenerg-1427	1529	14	fault	fault	NOUN
fuelectenerg-1427	1529	15	detection	detection	NOUN
fuelectenerg-1427	1529	16	in	in	ADP
fuelectenerg-1427	1529	17	and	and	CCONJ
fuelectenerg-1427	1529	18	-	-	PUNCT
fuelectenerg-1427	1529	19	exor	exor	PROPN
fuelectenerg-1427	1529	20	arrays	array	VERB
fuelectenerg-1427	1529	21	,	,	PUNCT
fuelectenerg-1427	1529	22	"	"	PUNCT
fuelectenerg-1427	1529	23	ieee	ieee	NOUN
fuelectenerg-1427	1529	24	trans	tran	NOUN
fuelectenerg-1427	1529	25	.	.	PUNCT
fuelectenerg-1427	1530	1	comp	comp	PROPN
fuelectenerg-1427	1530	2	.	.	PUNCT
fuelectenerg-1427	1530	3	,	,	PUNCT
fuelectenerg-1427	1530	4	vol	vol	NOUN
fuelectenerg-1427	1530	5	.	.	PROPN
fuelectenerg-1427	1531	1	27	27	NUM
fuelectenerg-1427	1531	2	,	,	PUNCT
fuelectenerg-1427	1531	3	pp	pp	ADJ
fuelectenerg-1427	1531	4	.	.	PUNCT
fuelectenerg-1427	1532	1	181	181	NUM
fuelectenerg-1427	1532	2	-	-	SYM
fuelectenerg-1427	1532	3	187	187	NUM
fuelectenerg-1427	1532	4	,	,	PUNCT
fuelectenerg-1427	1532	5	1978	1978	NUM
fuelectenerg-1427	1532	6	.	.	PUNCT
fuelectenerg-1427	1533	1	117	117	NUM
fuelectenerg-1427	1533	2	this	this	DET
fuelectenerg-1427	1533	3	research	research	NOUN
fuelectenerg-1427	1533	4	was	be	AUX
fuelectenerg-1427	1533	5	performed	perform	VERB
fuelectenerg-1427	1533	6	during	during	ADP
fuelectenerg-1427	1533	7	sabbatical	sabbatical	ADJ
fuelectenerg-1427	1533	8	leave	leave	NOUN
fuelectenerg-1427	1533	9	in	in	ADP
fuelectenerg-1427	1533	10	2015	2015	NUM
fuelectenerg-1427	1533	11	-	-	SYM
fuelectenerg-1427	1533	12	2016	2016	NUM
fuelectenerg-1427	1533	13	granted	grant	VERB
fuelectenerg-1427	1533	14	from	from	ADP
fuelectenerg-1427	1533	15	the	the	DET
fuelectenerg-1427	1533	16	university	university	PROPN
fuelectenerg-1427	1533	17	of	of	ADP
fuelectenerg-1427	1533	18	jordan	jordan	PROPN
fuelectenerg-1427	1533	19	and	and	CCONJ
fuelectenerg-1427	1533	20	spent	spend	VERB
fuelectenerg-1427	1533	21	at	at	ADP
fuelectenerg-1427	1533	22	philadelphia	philadelphia	PROPN
fuelectenerg-1427	1533	23	university	university	NOUN
fuelectenerg-1427	1533	24	.	.	PUNCT
fuelectenerg-1427	1534	1	64	64	NUM
fuelectenerg-1427	1534	2	a.	a.	NOUN
fuelectenerg-1427	1534	3	n.	n.	PROPN
fuelectenerg-1427	1534	4	al	al	PROPN
fuelectenerg-1427	1534	5	-	-	PUNCT
fuelectenerg-1427	1534	6	rabadi	rabadi	VERB
fuelectenerg-1427	1534	7	an	an	DET
fuelectenerg-1427	1534	8	extended	extended	ADJ
fuelectenerg-1427	1534	9	green	green	ADJ
fuelectenerg-1427	1534	10	sasao	sasao	PROPN
fuelectenerg-1427	1534	11	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1534	12	of	of	ADP
fuelectenerg-1427	1534	13	canonical	canonical	ADJ
fuelectenerg-1427	1534	14	ternary	ternary	ADJ
fuelectenerg-1427	1534	15	galois	galois	NOUN
fuelectenerg-1427	1534	16	forms	form	NOUN
fuelectenerg-1427	1534	17	and	and	CCONJ
fuelectenerg-1427	1534	18	universal	universal	ADJ
fuelectenerg-1427	1534	19	logic	logic	NOUN
fuelectenerg-1427	1534	20	modules	module	NOUN
fuelectenerg-1427	1534	21	65	65	NUM
fuelectenerg-1427	1534	22	an	an	DET
fuelectenerg-1427	1534	23	extended	extend	VERB
fuelectenerg-1427	1534	24	green	green	ADJ
fuelectenerg-1427	1534	25	sasao	sasao	PROPN
fuelectenerg-1427	1534	26	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1534	27	of	of	ADP
fuelectenerg-1427	1534	28	canonical	canonical	ADJ
fuelectenerg-1427	1534	29	ternary	ternary	ADJ
fuelectenerg-1427	1534	30	galois	galois	NOUN
fuelectenerg-1427	1534	31	forms	form	NOUN
fuelectenerg-1427	1534	32	...	...	PUNCT
fuelectenerg-1427	1535	1	[	[	X
fuelectenerg-1427	1535	2	5	5	NUM
fuelectenerg-1427	1535	3	]	]	PUNCT
fuelectenerg-1427	1535	4	a.	a.	NOUN
fuelectenerg-1427	1535	5	n.	n.	PROPN
fuelectenerg-1427	1535	6	al	al	PROPN
fuelectenerg-1427	1535	7	-	-	PUNCT
fuelectenerg-1427	1535	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1535	9	,	,	PUNCT
fuelectenerg-1427	1535	10	"	"	PUNCT
fuelectenerg-1427	1535	11	quantum	quantum	ADJ
fuelectenerg-1427	1535	12	logic	logic	NOUN
fuelectenerg-1427	1535	13	circuit	circuit	NOUN
fuelectenerg-1427	1535	14	design	design	NOUN
fuelectenerg-1427	1535	15	of	of	ADP
fuelectenerg-1427	1535	16	many	many	ADV
fuelectenerg-1427	1535	17	-	-	PUNCT
fuelectenerg-1427	1535	18	valued	value	VERB
fuelectenerg-1427	1535	19	galois	galois	PROPN
fuelectenerg-1427	1535	20	reversible	reversible	ADJ
fuelectenerg-1427	1535	21	expansions	expansion	NOUN
fuelectenerg-1427	1535	22	and	and	CCONJ
fuelectenerg-1427	1535	23	fast	fast	ADJ
fuelectenerg-1427	1535	24	transforms	transform	NOUN
fuelectenerg-1427	1535	25	,	,	PUNCT
fuelectenerg-1427	1535	26	"	"	PUNCT
fuelectenerg-1427	1535	27	journal	journal	NOUN
fuelectenerg-1427	1535	28	of	of	ADP
fuelectenerg-1427	1535	29	circuits	circuit	NOUN
fuelectenerg-1427	1535	30	,	,	PUNCT
fuelectenerg-1427	1535	31	systems	system	NOUN
fuelectenerg-1427	1535	32	,	,	PUNCT
fuelectenerg-1427	1535	33	and	and	CCONJ
fuelectenerg-1427	1535	34	computers	computer	NOUN
fuelectenerg-1427	1535	35	,	,	PUNCT
fuelectenerg-1427	1535	36	world	world	NOUN
fuelectenerg-1427	1535	37	scientific	scientific	ADJ
fuelectenerg-1427	1535	38	,	,	PUNCT
fuelectenerg-1427	1535	39	vol	vol	NOUN
fuelectenerg-1427	1535	40	.	.	PROPN
fuelectenerg-1427	1535	41	16	16	NUM
fuelectenerg-1427	1535	42	,	,	PUNCT
fuelectenerg-1427	1535	43	no	no	INTJ
fuelectenerg-1427	1535	44	.	.	NOUN
fuelectenerg-1427	1535	45	5	5	NUM
fuelectenerg-1427	1535	46	,	,	PUNCT
fuelectenerg-1427	1535	47	pp	pp	ADJ
fuelectenerg-1427	1535	48	.	.	PUNCT
fuelectenerg-1427	1536	1	641	641	NUM
fuelectenerg-1427	1536	2	671	671	NUM
fuelectenerg-1427	1536	3	,	,	PUNCT
fuelectenerg-1427	1536	4	2007	2007	NUM
fuelectenerg-1427	1536	5	.	.	PUNCT
fuelectenerg-1427	1537	1	[	[	X
fuelectenerg-1427	1537	2	6	6	NUM
fuelectenerg-1427	1537	3	]	]	PUNCT
fuelectenerg-1427	1537	4	a.	a.	NOUN
fuelectenerg-1427	1537	5	n.	n.	PROPN
fuelectenerg-1427	1537	6	al	al	PROPN
fuelectenerg-1427	1537	7	-	-	PUNCT
fuelectenerg-1427	1537	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1537	9	,	,	PUNCT
fuelectenerg-1427	1537	10	"	"	PUNCT
fuelectenerg-1427	1537	11	representations	representation	NOUN
fuelectenerg-1427	1537	12	,	,	PUNCT
fuelectenerg-1427	1537	13	operations	operation	NOUN
fuelectenerg-1427	1537	14	,	,	PUNCT
fuelectenerg-1427	1537	15	and	and	CCONJ
fuelectenerg-1427	1537	16	applications	application	NOUN
fuelectenerg-1427	1537	17	of	of	ADP
fuelectenerg-1427	1537	18	switching	switch	VERB
fuelectenerg-1427	1537	19	circuits	circuit	NOUN
fuelectenerg-1427	1537	20	in	in	ADP
fuelectenerg-1427	1537	21	the	the	DET
fuelectenerg-1427	1537	22	reversible	reversible	ADJ
fuelectenerg-1427	1537	23	and	and	CCONJ
fuelectenerg-1427	1537	24	quantum	quantum	ADJ
fuelectenerg-1427	1537	25	spaces	space	NOUN
fuelectenerg-1427	1537	26	,	,	PUNCT
fuelectenerg-1427	1537	27	"	"	PUNCT
fuelectenerg-1427	1537	28	facta	facta	PROPN
fuelectenerg-1427	1537	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1537	30	electronics	electronic	NOUN
fuelectenerg-1427	1537	31	and	and	CCONJ
fuelectenerg-1427	1537	32	energetics	energetic	NOUN
fuelectenerg-1427	1537	33	,	,	PUNCT
fuelectenerg-1427	1537	34	vol	vol	NOUN
fuelectenerg-1427	1537	35	.	.	PROPN
fuelectenerg-1427	1537	36	20	20	NUM
fuelectenerg-1427	1537	37	,	,	PUNCT
fuelectenerg-1427	1537	38	no	no	INTJ
fuelectenerg-1427	1537	39	.	.	NOUN
fuelectenerg-1427	1537	40	3	3	NUM
fuelectenerg-1427	1537	41	,	,	PUNCT
fuelectenerg-1427	1537	42	pp	pp	ADJ
fuelectenerg-1427	1537	43	.	.	PUNCT
fuelectenerg-1427	1538	1	507	507	NUM
fuelectenerg-1427	1538	2	539	539	NUM
fuelectenerg-1427	1538	3	,	,	PUNCT
fuelectenerg-1427	1538	4	2007	2007	NUM
fuelectenerg-1427	1538	5	.	.	PUNCT
fuelectenerg-1427	1539	1	[	[	X
fuelectenerg-1427	1539	2	7	7	NUM
fuelectenerg-1427	1539	3	]	]	PUNCT
fuelectenerg-1427	1539	4	a.	a.	NOUN
fuelectenerg-1427	1539	5	n.	n.	PROPN
fuelectenerg-1427	1539	6	al	al	PROPN
fuelectenerg-1427	1539	7	-	-	PUNCT
fuelectenerg-1427	1539	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1539	9	,	,	PUNCT
fuelectenerg-1427	1539	10	"	"	PUNCT
fuelectenerg-1427	1539	11	multi	multi	ADJ
fuelectenerg-1427	1539	12	-	-	ADJ
fuelectenerg-1427	1539	13	valued	value	VERB
fuelectenerg-1427	1539	14	galois	galois	PROPN
fuelectenerg-1427	1539	15	shannon	shannon	PROPN
fuelectenerg-1427	1539	16	-	-	PUNCT
fuelectenerg-1427	1539	17	davio	davio	NOUN
fuelectenerg-1427	1539	18	trees	tree	NOUN
fuelectenerg-1427	1539	19	and	and	CCONJ
fuelectenerg-1427	1539	20	their	their	PRON
fuelectenerg-1427	1539	21	complexity	complexity	NOUN
fuelectenerg-1427	1539	22	,	,	PUNCT
fuelectenerg-1427	1539	23	"	"	PUNCT
fuelectenerg-1427	1539	24	facta	facta	PROPN
fuelectenerg-1427	1539	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1539	26	electronics	electronic	NOUN
fuelectenerg-1427	1539	27	and	and	CCONJ
fuelectenerg-1427	1539	28	energetics	energetic	NOUN
fuelectenerg-1427	1539	29	,	,	PUNCT
fuelectenerg-1427	1539	30	vol	vol	NOUN
fuelectenerg-1427	1539	31	.	.	PROPN
fuelectenerg-1427	1539	32	29	29	NUM
fuelectenerg-1427	1539	33	,	,	PUNCT
fuelectenerg-1427	1539	34	no	no	INTJ
fuelectenerg-1427	1539	35	.	.	NOUN
fuelectenerg-1427	1539	36	4	4	NUM
fuelectenerg-1427	1539	37	,	,	PUNCT
fuelectenerg-1427	1539	38	pp	pp	ADJ
fuelectenerg-1427	1539	39	.	.	PUNCT
fuelectenerg-1427	1540	1	701	701	NUM
fuelectenerg-1427	1540	2	-	-	SYM
fuelectenerg-1427	1540	3	720	720	NUM
fuelectenerg-1427	1540	4	,	,	PUNCT
fuelectenerg-1427	1540	5	2016	2016	NUM
fuelectenerg-1427	1540	6	.	.	PUNCT
fuelectenerg-1427	1541	1	[	[	X
fuelectenerg-1427	1541	2	8	8	NUM
fuelectenerg-1427	1541	3	]	]	X
fuelectenerg-1427	1541	4	b.	b.	PROPN
fuelectenerg-1427	1541	5	falkowski	falkowski	NOUN
fuelectenerg-1427	1541	6	and	and	CCONJ
fuelectenerg-1427	1541	7	l.-s	l.-s	PROPN
fuelectenerg-1427	1541	8	.	.	PUNCT
fuelectenerg-1427	1542	1	lim	lim	PROPN
fuelectenerg-1427	1542	2	,	,	PUNCT
fuelectenerg-1427	1542	3	"	"	PUNCT
fuelectenerg-1427	1542	4	gray	gray	ADJ
fuelectenerg-1427	1542	5	scale	scale	NOUN
fuelectenerg-1427	1542	6	image	image	NOUN
fuelectenerg-1427	1542	7	compression	compression	NOUN
fuelectenerg-1427	1542	8	based	base	VERB
fuelectenerg-1427	1542	9	on	on	ADP
fuelectenerg-1427	1542	10	multiple	multiple	ADV
fuelectenerg-1427	1542	11	-	-	PUNCT
fuelectenerg-1427	1542	12	valued	value	VERB
fuelectenerg-1427	1542	13	input	input	NOUN
fuelectenerg-1427	1542	14	binary	binary	NOUN
fuelectenerg-1427	1542	15	functions	function	NOUN
fuelectenerg-1427	1542	16	,	,	PUNCT
fuelectenerg-1427	1542	17	walsh	walsh	NOUN
fuelectenerg-1427	1542	18	and	and	CCONJ
fuelectenerg-1427	1542	19	reed	reed	PROPN
fuelectenerg-1427	1542	20	-	-	PUNCT
fuelectenerg-1427	1542	21	muller	muller	PROPN
fuelectenerg-1427	1542	22	spectra	spectra	PROPN
fuelectenerg-1427	1542	23	,	,	PUNCT
fuelectenerg-1427	1542	24	"	"	PUNCT
fuelectenerg-1427	1542	25	proc	proc	NOUN
fuelectenerg-1427	1542	26	.	.	PUNCT
fuelectenerg-1427	1543	1	ismvl	ismvl	PROPN
fuelectenerg-1427	1543	2	,	,	PUNCT
fuelectenerg-1427	1543	3	2000	2000	NUM
fuelectenerg-1427	1543	4	,	,	PUNCT
fuelectenerg-1427	1543	5	pp	pp	ADJ
fuelectenerg-1427	1543	6	.	.	PUNCT
fuelectenerg-1427	1544	1	279	279	NUM
fuelectenerg-1427	1544	2	-	-	SYM
fuelectenerg-1427	1544	3	284	284	NUM
fuelectenerg-1427	1544	4	.	.	PUNCT
fuelectenerg-1427	1545	1	[	[	X
fuelectenerg-1427	1545	2	9	9	NUM
fuelectenerg-1427	1545	3	]	]	PUNCT
fuelectenerg-1427	1545	4	h.	h.	PROPN
fuelectenerg-1427	1545	5	fujiwara	fujiwara	PROPN
fuelectenerg-1427	1545	6	,	,	PUNCT
fuelectenerg-1427	1545	7	logic	logic	NOUN
fuelectenerg-1427	1545	8	testing	testing	NOUN
fuelectenerg-1427	1545	9	and	and	CCONJ
fuelectenerg-1427	1545	10	design	design	NOUN
fuelectenerg-1427	1545	11	for	for	ADP
fuelectenerg-1427	1545	12	testability	testability	NOUN
fuelectenerg-1427	1545	13	,	,	PUNCT
fuelectenerg-1427	1545	14	mit	mit	NOUN
fuelectenerg-1427	1545	15	press	press	NOUN
fuelectenerg-1427	1545	16	,	,	PUNCT
fuelectenerg-1427	1545	17	1985	1985	NUM
fuelectenerg-1427	1545	18	.	.	PUNCT
fuelectenerg-1427	1546	1	[	[	X
fuelectenerg-1427	1546	2	10	10	NUM
fuelectenerg-1427	1546	3	]	]	X
fuelectenerg-1427	1546	4	d.	d.	PROPN
fuelectenerg-1427	1546	5	h.	h.	PROPN
fuelectenerg-1427	1546	6	green	green	PROPN
fuelectenerg-1427	1546	7	,	,	PUNCT
fuelectenerg-1427	1546	8	"	"	PUNCT
fuelectenerg-1427	1546	9	families	family	NOUN
fuelectenerg-1427	1546	10	of	of	ADP
fuelectenerg-1427	1546	11	reed	reed	NOUN
fuelectenerg-1427	1546	12	-	-	PUNCT
fuelectenerg-1427	1546	13	muller	muller	NOUN
fuelectenerg-1427	1546	14	canonical	canonical	ADJ
fuelectenerg-1427	1546	15	forms	form	NOUN
fuelectenerg-1427	1546	16	,	,	PUNCT
fuelectenerg-1427	1546	17	"	"	PUNCT
fuelectenerg-1427	1546	18	int	int	NOUN
fuelectenerg-1427	1546	19	.	.	PUNCT
fuelectenerg-1427	1547	1	j.	j.	PROPN
fuelectenerg-1427	1547	2	electronics	electronics	PROPN
fuelectenerg-1427	1547	3	,	,	PUNCT
fuelectenerg-1427	1547	4	no	no	INTJ
fuelectenerg-1427	1547	5	.	.	NOUN
fuelectenerg-1427	1547	6	2	2	NUM
fuelectenerg-1427	1547	7	,	,	PUNCT
fuelectenerg-1427	1547	8	pp	pp	ADJ
fuelectenerg-1427	1547	9	.	.	PUNCT
fuelectenerg-1427	1548	1	259	259	NUM
fuelectenerg-1427	1548	2	-	-	SYM
fuelectenerg-1427	1548	3	280	280	NUM
fuelectenerg-1427	1548	4	,	,	PUNCT
fuelectenerg-1427	1548	5	1991	1991	NUM
fuelectenerg-1427	1548	6	.	.	PUNCT
fuelectenerg-1427	1549	1	[	[	X
fuelectenerg-1427	1549	2	11	11	NUM
fuelectenerg-1427	1549	3	]	]	PUNCT
fuelectenerg-1427	1549	4	m.	m.	NOUN
fuelectenerg-1427	1549	5	helliwell	helliwell	NOUN
fuelectenerg-1427	1549	6	and	and	CCONJ
fuelectenerg-1427	1549	7	m.	m.	PROPN
fuelectenerg-1427	1549	8	a.	a.	PROPN
fuelectenerg-1427	1549	9	perkowski	perkowski	PROPN
fuelectenerg-1427	1549	10	,	,	PUNCT
fuelectenerg-1427	1549	11	"	"	PUNCT
fuelectenerg-1427	1549	12	a	a	DET
fuelectenerg-1427	1549	13	fast	fast	ADJ
fuelectenerg-1427	1549	14	algorithm	algorithm	NOUN
fuelectenerg-1427	1549	15	to	to	PART
fuelectenerg-1427	1549	16	minimize	minimize	VERB
fuelectenerg-1427	1549	17	multi	multi	ADJ
fuelectenerg-1427	1549	18	-	-	ADJ
fuelectenerg-1427	1549	19	output	output	ADJ
fuelectenerg-1427	1549	20	mixed	mix	VERB
fuelectenerg-1427	1549	21	-	-	PUNCT
fuelectenerg-1427	1549	22	polarity	polarity	NOUN
fuelectenerg-1427	1549	23	generalized	generalize	VERB
fuelectenerg-1427	1549	24	reed	reed	NOUN
fuelectenerg-1427	1549	25	-	-	PUNCT
fuelectenerg-1427	1549	26	muller	muller	NOUN
fuelectenerg-1427	1549	27	forms	form	NOUN
fuelectenerg-1427	1549	28	,	,	PUNCT
fuelectenerg-1427	1549	29	"	"	PUNCT
fuelectenerg-1427	1549	30	proc	proc	NOUN
fuelectenerg-1427	1549	31	.	.	PUNCT
fuelectenerg-1427	1550	1	design	design	NOUN
fuelectenerg-1427	1550	2	automation	automation	NOUN
fuelectenerg-1427	1550	3	conference	conference	NOUN
fuelectenerg-1427	1550	4	,	,	PUNCT
fuelectenerg-1427	1550	5	1988	1988	NUM
fuelectenerg-1427	1550	6	,	,	PUNCT
fuelectenerg-1427	1550	7	pp	pp	ADV
fuelectenerg-1427	1550	8	.	.	PUNCT
fuelectenerg-1427	1551	1	427	427	NUM
fuelectenerg-1427	1551	2	-	-	SYM
fuelectenerg-1427	1551	3	432	432	NUM
fuelectenerg-1427	1551	4	.	.	PUNCT
fuelectenerg-1427	1552	1	[	[	X
fuelectenerg-1427	1552	2	12	12	NUM
fuelectenerg-1427	1552	3	]	]	PUNCT
fuelectenerg-1427	1552	4	s.	s.	PROPN
fuelectenerg-1427	1552	5	l.	l.	PROPN
fuelectenerg-1427	1552	6	hurst	hurst	PROPN
fuelectenerg-1427	1552	7	,	,	PUNCT
fuelectenerg-1427	1552	8	d.	d.	PROPN
fuelectenerg-1427	1552	9	m.	m.	PROPN
fuelectenerg-1427	1552	10	miller	miller	PROPN
fuelectenerg-1427	1552	11	,	,	PUNCT
fuelectenerg-1427	1552	12	and	and	CCONJ
fuelectenerg-1427	1552	13	j.	j.	PROPN
fuelectenerg-1427	1552	14	c.	c.	PROPN
fuelectenerg-1427	1552	15	muzio	muzio	PROPN
fuelectenerg-1427	1552	16	,	,	PUNCT
fuelectenerg-1427	1552	17	spectral	spectral	ADJ
fuelectenerg-1427	1552	18	techniques	technique	NOUN
fuelectenerg-1427	1552	19	in	in	ADP
fuelectenerg-1427	1552	20	digital	digital	ADJ
fuelectenerg-1427	1552	21	logic	logic	NOUN
fuelectenerg-1427	1552	22	,	,	PUNCT
fuelectenerg-1427	1552	23	academic	academic	PROPN
fuelectenerg-1427	1552	24	press	press	PROPN
fuelectenerg-1427	1552	25	inc	inc	PROPN
fuelectenerg-1427	1552	26	.	.	PROPN
fuelectenerg-1427	1552	27	,	,	PUNCT
fuelectenerg-1427	1552	28	1985	1985	NUM
fuelectenerg-1427	1552	29	.	.	PUNCT
fuelectenerg-1427	1553	1	[	[	X
fuelectenerg-1427	1553	2	13	13	NUM
fuelectenerg-1427	1553	3	]	]	PUNCT
fuelectenerg-1427	1553	4	m.	m.	NOUN
fuelectenerg-1427	1553	5	g.	g.	PROPN
fuelectenerg-1427	1553	6	karpovsky	karpovsky	PROPN
fuelectenerg-1427	1553	7	,	,	PUNCT
fuelectenerg-1427	1553	8	finite	finite	PROPN
fuelectenerg-1427	1553	9	orthogonal	orthogonal	ADJ
fuelectenerg-1427	1553	10	series	series	NOUN
fuelectenerg-1427	1553	11	in	in	ADP
fuelectenerg-1427	1553	12	the	the	DET
fuelectenerg-1427	1553	13	design	design	NOUN
fuelectenerg-1427	1553	14	of	of	ADP
fuelectenerg-1427	1553	15	digital	digital	ADJ
fuelectenerg-1427	1553	16	devices	device	NOUN
fuelectenerg-1427	1553	17	,	,	PUNCT
fuelectenerg-1427	1553	18	wiley	wiley	NOUN
fuelectenerg-1427	1553	19	,	,	PUNCT
fuelectenerg-1427	1553	20	1976	1976	NUM
fuelectenerg-1427	1553	21	.	.	PUNCT
fuelectenerg-1427	1554	1	[	[	X
fuelectenerg-1427	1554	2	14	14	NUM
fuelectenerg-1427	1554	3	]	]	X
fuelectenerg-1427	1554	4	s.	s.	PROPN
fuelectenerg-1427	1554	5	m.	m.	PROPN
fuelectenerg-1427	1554	6	reddy	reddy	PROPN
fuelectenerg-1427	1554	7	,	,	PUNCT
fuelectenerg-1427	1554	8	"	"	PUNCT
fuelectenerg-1427	1554	9	easily	easily	ADV
fuelectenerg-1427	1554	10	testable	testable	ADJ
fuelectenerg-1427	1554	11	realizations	realization	NOUN
fuelectenerg-1427	1554	12	of	of	ADP
fuelectenerg-1427	1554	13	logic	logic	NOUN
fuelectenerg-1427	1554	14	functions	function	NOUN
fuelectenerg-1427	1554	15	,	,	PUNCT
fuelectenerg-1427	1554	16	"	"	PUNCT
fuelectenerg-1427	1554	17	ieee	ieee	NOUN
fuelectenerg-1427	1554	18	trans	tran	NOUN
fuelectenerg-1427	1554	19	.	.	PUNCT
fuelectenerg-1427	1555	1	comp	comp	PROPN
fuelectenerg-1427	1555	2	.	.	PUNCT
fuelectenerg-1427	1555	3	,	,	PUNCT
fuelectenerg-1427	1555	4	c-21	c-21	PROPN
fuelectenerg-1427	1555	5	,	,	PUNCT
fuelectenerg-1427	1555	6	pp	pp	ADV
fuelectenerg-1427	1555	7	.	.	PUNCT
fuelectenerg-1427	1556	1	1183	1183	NUM
fuelectenerg-1427	1556	2	-	-	SYM
fuelectenerg-1427	1556	3	1188	1188	NUM
fuelectenerg-1427	1556	4	,	,	PUNCT
fuelectenerg-1427	1556	5	1972	1972	NUM
fuelectenerg-1427	1556	6	.	.	PUNCT
fuelectenerg-1427	1557	1	[	[	X
fuelectenerg-1427	1557	2	15	15	X
fuelectenerg-1427	1557	3	]	]	X
fuelectenerg-1427	1557	4	t.	t.	PROPN
fuelectenerg-1427	1557	5	sasao	sasao	PROPN
fuelectenerg-1427	1557	6	and	and	CCONJ
fuelectenerg-1427	1557	7	m.	m.	PROPN
fuelectenerg-1427	1557	8	fujita	fujita	PROPN
fuelectenerg-1427	1557	9	(	(	PUNCT
fuelectenerg-1427	1557	10	editors	editor	NOUN
fuelectenerg-1427	1557	11	)	)	PUNCT
fuelectenerg-1427	1557	12	,	,	PUNCT
fuelectenerg-1427	1557	13	representations	representation	NOUN
fuelectenerg-1427	1557	14	of	of	ADP
fuelectenerg-1427	1557	15	discrete	discrete	ADJ
fuelectenerg-1427	1557	16	functions	function	NOUN
fuelectenerg-1427	1557	17	,	,	PUNCT
fuelectenerg-1427	1557	18	kluwer	kluwer	NOUN
fuelectenerg-1427	1557	19	academic	academic	ADJ
fuelectenerg-1427	1557	20	publishers	publisher	NOUN
fuelectenerg-1427	1557	21	,	,	PUNCT
fuelectenerg-1427	1557	22	1996	1996	NUM
fuelectenerg-1427	1557	23	.	.	PUNCT
fuelectenerg-1427	1558	1	[	[	X
fuelectenerg-1427	1558	2	16	16	NUM
fuelectenerg-1427	1558	3	]	]	PUNCT
fuelectenerg-1427	1558	4	t.	t.	PROPN
fuelectenerg-1427	1558	5	sasao	sasao	PROPN
fuelectenerg-1427	1558	6	,	,	PUNCT
fuelectenerg-1427	1558	7	"	"	PUNCT
fuelectenerg-1427	1558	8	easily	easily	ADV
fuelectenerg-1427	1558	9	testable	testable	ADJ
fuelectenerg-1427	1558	10	realizations	realization	NOUN
fuelectenerg-1427	1558	11	for	for	ADP
fuelectenerg-1427	1558	12	generalized	generalized	ADJ
fuelectenerg-1427	1558	13	reed	reed	NOUN
fuelectenerg-1427	1558	14	-	-	PUNCT
fuelectenerg-1427	1558	15	muller	muller	NOUN
fuelectenerg-1427	1558	16	expressions	expression	NOUN
fuelectenerg-1427	1558	17	,	,	PUNCT
fuelectenerg-1427	1558	18	"	"	PUNCT
fuelectenerg-1427	1558	19	ieee	ieee	NOUN
fuelectenerg-1427	1558	20	trans	tran	NOUN
fuelectenerg-1427	1558	21	.	.	PUNCT
fuelectenerg-1427	1559	1	comp	comp	PROPN
fuelectenerg-1427	1559	2	.	.	PUNCT
fuelectenerg-1427	1559	3	,	,	PUNCT
fuelectenerg-1427	1559	4	vol	vol	NOUN
fuelectenerg-1427	1559	5	.	.	PROPN
fuelectenerg-1427	1560	1	46	46	NUM
fuelectenerg-1427	1560	2	,	,	PUNCT
fuelectenerg-1427	1560	3	pp	pp	ADJ
fuelectenerg-1427	1560	4	.	.	PUNCT
fuelectenerg-1427	1561	1	709	709	NUM
fuelectenerg-1427	1561	2	-	-	PUNCT
fuelectenerg-1427	1561	3	716	716	NUM
fuelectenerg-1427	1561	4	,	,	PUNCT
fuelectenerg-1427	1561	5	1997	1997	NUM
fuelectenerg-1427	1561	6	.	.	PUNCT
fuelectenerg-1427	1562	1	[	[	X
fuelectenerg-1427	1562	2	17	17	NUM
fuelectenerg-1427	1562	3	]	]	X
fuelectenerg-1427	1562	4	r.	r.	PROPN
fuelectenerg-1427	1562	5	s.	s.	PROPN
fuelectenerg-1427	1562	6	stanković	stanković	PROPN
fuelectenerg-1427	1562	7	,	,	PUNCT
fuelectenerg-1427	1562	8	spectral	spectral	ADJ
fuelectenerg-1427	1562	9	transform	transform	VERB
fuelectenerg-1427	1562	10	decision	decision	NOUN
fuelectenerg-1427	1562	11	diagrams	diagram	NOUN
fuelectenerg-1427	1562	12	in	in	ADP
fuelectenerg-1427	1562	13	simple	simple	ADJ
fuelectenerg-1427	1562	14	questions	question	NOUN
fuelectenerg-1427	1562	15	and	and	CCONJ
fuelectenerg-1427	1562	16	simple	simple	ADJ
fuelectenerg-1427	1562	17	answers	answer	NOUN
fuelectenerg-1427	1562	18	,	,	PUNCT
fuelectenerg-1427	1562	19	nauka	nauka	PROPN
fuelectenerg-1427	1562	20	,	,	PUNCT
fuelectenerg-1427	1562	21	1998	1998	NUM
fuelectenerg-1427	1562	22	.	.	PUNCT
fuelectenerg-1427	1563	1	[	[	X
fuelectenerg-1427	1563	2	18	18	NUM
fuelectenerg-1427	1563	3	]	]	X
fuelectenerg-1427	1563	4	r.	r.	PROPN
fuelectenerg-1427	1563	5	s.	s.	PROPN
fuelectenerg-1427	1563	6	stanković	stanković	PROPN
fuelectenerg-1427	1563	7	,	,	PUNCT
fuelectenerg-1427	1563	8	c.	c.	PROPN
fuelectenerg-1427	1563	9	moraga	moraga	PROPN
fuelectenerg-1427	1563	10	,	,	PUNCT
fuelectenerg-1427	1563	11	and	and	CCONJ
fuelectenerg-1427	1563	12	j.	j.	PROPN
fuelectenerg-1427	1563	13	t.	t.	PROPN
fuelectenerg-1427	1563	14	astola	astola	PROPN
fuelectenerg-1427	1563	15	,	,	PUNCT
fuelectenerg-1427	1563	16	"	"	PUNCT
fuelectenerg-1427	1563	17	reed	reed	NOUN
fuelectenerg-1427	1563	18	-	-	PUNCT
fuelectenerg-1427	1563	19	muller	muller	NOUN
fuelectenerg-1427	1563	20	expressions	expression	NOUN
fuelectenerg-1427	1563	21	in	in	ADP
fuelectenerg-1427	1563	22	the	the	DET
fuelectenerg-1427	1563	23	previous	previous	ADJ
fuelectenerg-1427	1563	24	decade	decade	NOUN
fuelectenerg-1427	1563	25	,	,	PUNCT
fuelectenerg-1427	1563	26	"	"	PUNCT
fuelectenerg-1427	1563	27	proc	proc	NOUN
fuelectenerg-1427	1563	28	.	.	PUNCT
fuelectenerg-1427	1564	1	reed	reed	NOUN
fuelectenerg-1427	1564	2	-	-	PUNCT
fuelectenerg-1427	1564	3	muller	muller	NOUN
fuelectenerg-1427	1564	4	,	,	PUNCT
fuelectenerg-1427	1564	5	starkville	starkville	PROPN
fuelectenerg-1427	1564	6	,	,	PUNCT
fuelectenerg-1427	1564	7	2001	2001	NUM
fuelectenerg-1427	1564	8	,	,	PUNCT
fuelectenerg-1427	1564	9	pp	pp	ADJ
fuelectenerg-1427	1564	10	.	.	PUNCT
fuelectenerg-1427	1565	1	7	7	NUM
fuelectenerg-1427	1565	2	-	-	SYM
fuelectenerg-1427	1565	3	26	26	NUM
fuelectenerg-1427	1565	4	.	.	PUNCT
fuelectenerg-1427	1566	1	[	[	X
fuelectenerg-1427	1566	2	19	19	NUM
fuelectenerg-1427	1566	3	]	]	PUNCT
fuelectenerg-1427	1566	4	s.	s.	PROPN
fuelectenerg-1427	1566	5	b.	b.	PROPN
fuelectenerg-1427	1566	6	akers	akers	PROPN
fuelectenerg-1427	1566	7	,	,	PUNCT
fuelectenerg-1427	1566	8	"	"	PUNCT
fuelectenerg-1427	1566	9	binary	binary	ADJ
fuelectenerg-1427	1566	10	decision	decision	NOUN
fuelectenerg-1427	1566	11	diagrams	diagram	NOUN
fuelectenerg-1427	1566	12	,	,	PUNCT
fuelectenerg-1427	1566	13	"	"	PUNCT
fuelectenerg-1427	1566	14	ieee	ieee	NOUN
fuelectenerg-1427	1566	15	trans	tran	NOUN
fuelectenerg-1427	1566	16	.	.	PUNCT
fuelectenerg-1427	1567	1	comp	comp	PROPN
fuelectenerg-1427	1567	2	.	.	PUNCT
fuelectenerg-1427	1567	3	,	,	PUNCT
fuelectenerg-1427	1567	4	vol	vol	NOUN
fuelectenerg-1427	1567	5	.	.	PUNCT
fuelectenerg-1427	1568	1	c-27	c-27	PROPN
fuelectenerg-1427	1568	2	,	,	PUNCT
fuelectenerg-1427	1568	3	no	no	INTJ
fuelectenerg-1427	1568	4	.	.	NOUN
fuelectenerg-1427	1568	5	6	6	NUM
fuelectenerg-1427	1568	6	,	,	PUNCT
fuelectenerg-1427	1568	7	pp	pp	ADJ
fuelectenerg-1427	1568	8	.	.	PUNCT
fuelectenerg-1427	1569	1	509	509	NUM
fuelectenerg-1427	1569	2	-	-	SYM
fuelectenerg-1427	1569	3	516	516	NUM
fuelectenerg-1427	1569	4	,	,	PUNCT
fuelectenerg-1427	1569	5	june	june	PROPN
fuelectenerg-1427	1569	6	1978	1978	NUM
fuelectenerg-1427	1569	7	.	.	PUNCT
fuelectenerg-1427	1570	1	[	[	X
fuelectenerg-1427	1570	2	20	20	NUM
fuelectenerg-1427	1570	3	]	]	PUNCT
fuelectenerg-1427	1570	4	r.	r.	PROPN
fuelectenerg-1427	1570	5	e.	e.	PROPN
fuelectenerg-1427	1570	6	bryant	bryant	PROPN
fuelectenerg-1427	1570	7	,	,	PUNCT
fuelectenerg-1427	1570	8	"	"	PUNCT
fuelectenerg-1427	1570	9	graph	graph	NOUN
fuelectenerg-1427	1570	10	-	-	PUNCT
fuelectenerg-1427	1570	11	based	base	VERB
fuelectenerg-1427	1570	12	algorithms	algorithm	NOUN
fuelectenerg-1427	1570	13	for	for	ADP
fuelectenerg-1427	1570	14	boolean	boolean	ADJ
fuelectenerg-1427	1570	15	functions	function	NOUN
fuelectenerg-1427	1570	16	manipulation	manipulation	NOUN
fuelectenerg-1427	1570	17	,	,	PUNCT
fuelectenerg-1427	1570	18	"	"	PUNCT
fuelectenerg-1427	1570	19	ieee	ieee	NOUN
fuelectenerg-1427	1570	20	trans	tran	NOUN
fuelectenerg-1427	1570	21	.	.	PUNCT
fuelectenerg-1427	1571	1	on	on	ADP
fuelectenerg-1427	1571	2	comp	comp	PROPN
fuelectenerg-1427	1571	3	.	.	PUNCT
fuelectenerg-1427	1571	4	,	,	PUNCT
fuelectenerg-1427	1571	5	vol	vol	NOUN
fuelectenerg-1427	1571	6	.	.	PUNCT
fuelectenerg-1427	1572	1	c-35	c-35	PROPN
fuelectenerg-1427	1572	2	,	,	PUNCT
fuelectenerg-1427	1572	3	no.8	no.8	PROPN
fuelectenerg-1427	1572	4	,	,	PUNCT
fuelectenerg-1427	1572	5	pp	pp	ADV
fuelectenerg-1427	1572	6	.	.	PUNCT
fuelectenerg-1427	1573	1	667	667	NUM
fuelectenerg-1427	1573	2	-	-	SYM
fuelectenerg-1427	1573	3	691	691	NUM
fuelectenerg-1427	1573	4	,	,	PUNCT
fuelectenerg-1427	1573	5	1986	1986	NUM
fuelectenerg-1427	1573	6	.	.	PUNCT
fuelectenerg-1427	1574	1	[	[	X
fuelectenerg-1427	1574	2	21	21	NUM
fuelectenerg-1427	1574	3	]	]	X
fuelectenerg-1427	1574	4	d.	d.	PROPN
fuelectenerg-1427	1574	5	k.	k.	PROPN
fuelectenerg-1427	1574	6	pradhan	pradhan	PROPN
fuelectenerg-1427	1574	7	,	,	PUNCT
fuelectenerg-1427	1574	8	"	"	PUNCT
fuelectenerg-1427	1574	9	universal	universal	ADJ
fuelectenerg-1427	1574	10	test	test	NOUN
fuelectenerg-1427	1574	11	sets	set	NOUN
fuelectenerg-1427	1574	12	for	for	ADP
fuelectenerg-1427	1574	13	multiple	multiple	ADJ
fuelectenerg-1427	1574	14	fault	fault	NOUN
fuelectenerg-1427	1574	15	detection	detection	NOUN
fuelectenerg-1427	1574	16	in	in	ADP
fuelectenerg-1427	1574	17	and	and	CCONJ
fuelectenerg-1427	1574	18	-	-	PUNCT
fuelectenerg-1427	1574	19	exor	exor	PROPN
fuelectenerg-1427	1574	20	arrays	array	VERB
fuelectenerg-1427	1574	21	,	,	PUNCT
fuelectenerg-1427	1574	22	"	"	PUNCT
fuelectenerg-1427	1574	23	ieee	ieee	NOUN
fuelectenerg-1427	1574	24	trans	tran	NOUN
fuelectenerg-1427	1574	25	.	.	PUNCT
fuelectenerg-1427	1575	1	comp	comp	PROPN
fuelectenerg-1427	1575	2	.	.	PUNCT
fuelectenerg-1427	1575	3	,	,	PUNCT
fuelectenerg-1427	1575	4	vol	vol	NOUN
fuelectenerg-1427	1575	5	.	.	PROPN
fuelectenerg-1427	1576	1	27	27	NUM
fuelectenerg-1427	1576	2	,	,	PUNCT
fuelectenerg-1427	1576	3	pp	pp	ADJ
fuelectenerg-1427	1576	4	.	.	PUNCT
fuelectenerg-1427	1577	1	181	181	NUM
fuelectenerg-1427	1577	2	-	-	SYM
fuelectenerg-1427	1577	3	187	187	NUM
fuelectenerg-1427	1577	4	,	,	PUNCT
fuelectenerg-1427	1577	5	1978	1978	NUM
fuelectenerg-1427	1577	6	.	.	PUNCT
fuelectenerg-1427	1578	1	117	117	NUM
fuelectenerg-1427	1578	2	66	66	NUM
fuelectenerg-1427	1578	3	a.	a.	NOUN
fuelectenerg-1427	1578	4	n.	n.	PROPN
fuelectenerg-1427	1578	5	al	al	PROPN
fuelectenerg-1427	1578	6	-	-	PUNCT
fuelectenerg-1427	1578	7	rabadi	rabadi	VERB
fuelectenerg-1427	1578	8	an	an	DET
fuelectenerg-1427	1578	9	extended	extended	ADJ
fuelectenerg-1427	1578	10	green	green	ADJ
fuelectenerg-1427	1578	11	sasao	sasao	PROPN
fuelectenerg-1427	1578	12	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1578	13	of	of	ADP
fuelectenerg-1427	1578	14	canonical	canonical	ADJ
fuelectenerg-1427	1578	15	ternary	ternary	ADJ
fuelectenerg-1427	1578	16	galois	galois	NOUN
fuelectenerg-1427	1578	17	forms	form	NOUN
fuelectenerg-1427	1578	18	and	and	CCONJ
fuelectenerg-1427	1578	19	universal	universal	ADJ
fuelectenerg-1427	1578	20	logic	logic	NOUN
fuelectenerg-1427	1578	21	modules	module	NOUN
fuelectenerg-1427	1578	22	pb	pb	ADP
fuelectenerg-1427	1578	23	an	an	DET
fuelectenerg-1427	1578	24	extended	extend	VERB
fuelectenerg-1427	1578	25	green	green	PROPN
fuelectenerg-1427	1578	26	sasao	sasao	PROPN
fuelectenerg-1427	1578	27	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1578	28	of	of	ADP
fuelectenerg-1427	1578	29	canonical	canonical	ADJ
fuelectenerg-1427	1578	30	ternary	ternary	ADJ
fuelectenerg-1427	1578	31	galois	galois	NOUN
fuelectenerg-1427	1578	32	forms	form	NOUN
fuelectenerg-1427	1578	33	...	...	PUNCT
fuelectenerg-1427	1579	1	[	[	X
fuelectenerg-1427	1579	2	5	5	NUM
fuelectenerg-1427	1579	3	]	]	PUNCT
fuelectenerg-1427	1579	4	a.	a.	NOUN
fuelectenerg-1427	1579	5	n.	n.	PROPN
fuelectenerg-1427	1579	6	al	al	PROPN
fuelectenerg-1427	1579	7	-	-	PUNCT
fuelectenerg-1427	1579	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1579	9	,	,	PUNCT
fuelectenerg-1427	1579	10	"	"	PUNCT
fuelectenerg-1427	1579	11	quantum	quantum	ADJ
fuelectenerg-1427	1579	12	logic	logic	NOUN
fuelectenerg-1427	1579	13	circuit	circuit	NOUN
fuelectenerg-1427	1579	14	design	design	NOUN
fuelectenerg-1427	1579	15	of	of	ADP
fuelectenerg-1427	1579	16	many	many	ADV
fuelectenerg-1427	1579	17	-	-	PUNCT
fuelectenerg-1427	1579	18	valued	value	VERB
fuelectenerg-1427	1579	19	galois	galois	PROPN
fuelectenerg-1427	1579	20	reversible	reversible	ADJ
fuelectenerg-1427	1579	21	expansions	expansion	NOUN
fuelectenerg-1427	1579	22	and	and	CCONJ
fuelectenerg-1427	1579	23	fast	fast	ADJ
fuelectenerg-1427	1579	24	transforms	transform	NOUN
fuelectenerg-1427	1579	25	,	,	PUNCT
fuelectenerg-1427	1579	26	"	"	PUNCT
fuelectenerg-1427	1579	27	journal	journal	NOUN
fuelectenerg-1427	1579	28	of	of	ADP
fuelectenerg-1427	1579	29	circuits	circuit	NOUN
fuelectenerg-1427	1579	30	,	,	PUNCT
fuelectenerg-1427	1579	31	systems	system	NOUN
fuelectenerg-1427	1579	32	,	,	PUNCT
fuelectenerg-1427	1579	33	and	and	CCONJ
fuelectenerg-1427	1579	34	computers	computer	NOUN
fuelectenerg-1427	1579	35	,	,	PUNCT
fuelectenerg-1427	1579	36	world	world	NOUN
fuelectenerg-1427	1579	37	scientific	scientific	ADJ
fuelectenerg-1427	1579	38	,	,	PUNCT
fuelectenerg-1427	1579	39	vol	vol	NOUN
fuelectenerg-1427	1579	40	.	.	PROPN
fuelectenerg-1427	1579	41	16	16	NUM
fuelectenerg-1427	1579	42	,	,	PUNCT
fuelectenerg-1427	1579	43	no	no	INTJ
fuelectenerg-1427	1579	44	.	.	NOUN
fuelectenerg-1427	1579	45	5	5	NUM
fuelectenerg-1427	1579	46	,	,	PUNCT
fuelectenerg-1427	1579	47	pp	pp	ADJ
fuelectenerg-1427	1579	48	.	.	PUNCT
fuelectenerg-1427	1580	1	641	641	NUM
fuelectenerg-1427	1580	2	671	671	NUM
fuelectenerg-1427	1580	3	,	,	PUNCT
fuelectenerg-1427	1580	4	2007	2007	NUM
fuelectenerg-1427	1580	5	.	.	PUNCT
fuelectenerg-1427	1581	1	[	[	X
fuelectenerg-1427	1581	2	6	6	NUM
fuelectenerg-1427	1581	3	]	]	PUNCT
fuelectenerg-1427	1581	4	a.	a.	NOUN
fuelectenerg-1427	1581	5	n.	n.	PROPN
fuelectenerg-1427	1581	6	al	al	PROPN
fuelectenerg-1427	1581	7	-	-	PUNCT
fuelectenerg-1427	1581	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1581	9	,	,	PUNCT
fuelectenerg-1427	1581	10	"	"	PUNCT
fuelectenerg-1427	1581	11	representations	representation	NOUN
fuelectenerg-1427	1581	12	,	,	PUNCT
fuelectenerg-1427	1581	13	operations	operation	NOUN
fuelectenerg-1427	1581	14	,	,	PUNCT
fuelectenerg-1427	1581	15	and	and	CCONJ
fuelectenerg-1427	1581	16	applications	application	NOUN
fuelectenerg-1427	1581	17	of	of	ADP
fuelectenerg-1427	1581	18	switching	switch	VERB
fuelectenerg-1427	1581	19	circuits	circuit	NOUN
fuelectenerg-1427	1581	20	in	in	ADP
fuelectenerg-1427	1581	21	the	the	DET
fuelectenerg-1427	1581	22	reversible	reversible	ADJ
fuelectenerg-1427	1581	23	and	and	CCONJ
fuelectenerg-1427	1581	24	quantum	quantum	ADJ
fuelectenerg-1427	1581	25	spaces	space	NOUN
fuelectenerg-1427	1581	26	,	,	PUNCT
fuelectenerg-1427	1581	27	"	"	PUNCT
fuelectenerg-1427	1581	28	facta	facta	PROPN
fuelectenerg-1427	1581	29	universitatis	universitatis	PROPN
fuelectenerg-1427	1581	30	electronics	electronic	NOUN
fuelectenerg-1427	1581	31	and	and	CCONJ
fuelectenerg-1427	1581	32	energetics	energetic	NOUN
fuelectenerg-1427	1581	33	,	,	PUNCT
fuelectenerg-1427	1581	34	vol	vol	NOUN
fuelectenerg-1427	1581	35	.	.	PROPN
fuelectenerg-1427	1581	36	20	20	NUM
fuelectenerg-1427	1581	37	,	,	PUNCT
fuelectenerg-1427	1581	38	no	no	INTJ
fuelectenerg-1427	1581	39	.	.	NOUN
fuelectenerg-1427	1581	40	3	3	NUM
fuelectenerg-1427	1581	41	,	,	PUNCT
fuelectenerg-1427	1581	42	pp	pp	ADJ
fuelectenerg-1427	1581	43	.	.	PUNCT
fuelectenerg-1427	1582	1	507	507	NUM
fuelectenerg-1427	1582	2	539	539	NUM
fuelectenerg-1427	1582	3	,	,	PUNCT
fuelectenerg-1427	1582	4	2007	2007	NUM
fuelectenerg-1427	1582	5	.	.	PUNCT
fuelectenerg-1427	1583	1	[	[	X
fuelectenerg-1427	1583	2	7	7	NUM
fuelectenerg-1427	1583	3	]	]	PUNCT
fuelectenerg-1427	1583	4	a.	a.	NOUN
fuelectenerg-1427	1583	5	n.	n.	PROPN
fuelectenerg-1427	1583	6	al	al	PROPN
fuelectenerg-1427	1583	7	-	-	PUNCT
fuelectenerg-1427	1583	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1583	9	,	,	PUNCT
fuelectenerg-1427	1583	10	"	"	PUNCT
fuelectenerg-1427	1583	11	multi	multi	ADJ
fuelectenerg-1427	1583	12	-	-	ADJ
fuelectenerg-1427	1583	13	valued	value	VERB
fuelectenerg-1427	1583	14	galois	galois	PROPN
fuelectenerg-1427	1583	15	shannon	shannon	PROPN
fuelectenerg-1427	1583	16	-	-	PUNCT
fuelectenerg-1427	1583	17	davio	davio	NOUN
fuelectenerg-1427	1583	18	trees	tree	NOUN
fuelectenerg-1427	1583	19	and	and	CCONJ
fuelectenerg-1427	1583	20	their	their	PRON
fuelectenerg-1427	1583	21	complexity	complexity	NOUN
fuelectenerg-1427	1583	22	,	,	PUNCT
fuelectenerg-1427	1583	23	"	"	PUNCT
fuelectenerg-1427	1583	24	facta	facta	PROPN
fuelectenerg-1427	1583	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1583	26	electronics	electronic	NOUN
fuelectenerg-1427	1583	27	and	and	CCONJ
fuelectenerg-1427	1583	28	energetics	energetic	NOUN
fuelectenerg-1427	1583	29	,	,	PUNCT
fuelectenerg-1427	1583	30	vol	vol	NOUN
fuelectenerg-1427	1583	31	.	.	PROPN
fuelectenerg-1427	1583	32	29	29	NUM
fuelectenerg-1427	1583	33	,	,	PUNCT
fuelectenerg-1427	1583	34	no	no	INTJ
fuelectenerg-1427	1583	35	.	.	NOUN
fuelectenerg-1427	1583	36	4	4	NUM
fuelectenerg-1427	1583	37	,	,	PUNCT
fuelectenerg-1427	1583	38	pp	pp	ADJ
fuelectenerg-1427	1583	39	.	.	PUNCT
fuelectenerg-1427	1584	1	701	701	NUM
fuelectenerg-1427	1584	2	-	-	SYM
fuelectenerg-1427	1584	3	720	720	NUM
fuelectenerg-1427	1584	4	,	,	PUNCT
fuelectenerg-1427	1584	5	2016	2016	NUM
fuelectenerg-1427	1584	6	.	.	PUNCT
fuelectenerg-1427	1585	1	[	[	X
fuelectenerg-1427	1585	2	8	8	NUM
fuelectenerg-1427	1585	3	]	]	X
fuelectenerg-1427	1585	4	b.	b.	PROPN
fuelectenerg-1427	1585	5	falkowski	falkowski	NOUN
fuelectenerg-1427	1585	6	and	and	CCONJ
fuelectenerg-1427	1585	7	l.-s	l.-s	PROPN
fuelectenerg-1427	1585	8	.	.	PUNCT
fuelectenerg-1427	1586	1	lim	lim	PROPN
fuelectenerg-1427	1586	2	,	,	PUNCT
fuelectenerg-1427	1586	3	"	"	PUNCT
fuelectenerg-1427	1586	4	gray	gray	ADJ
fuelectenerg-1427	1586	5	scale	scale	NOUN
fuelectenerg-1427	1586	6	image	image	NOUN
fuelectenerg-1427	1586	7	compression	compression	NOUN
fuelectenerg-1427	1586	8	based	base	VERB
fuelectenerg-1427	1586	9	on	on	ADP
fuelectenerg-1427	1586	10	multiple	multiple	ADV
fuelectenerg-1427	1586	11	-	-	PUNCT
fuelectenerg-1427	1586	12	valued	value	VERB
fuelectenerg-1427	1586	13	input	input	NOUN
fuelectenerg-1427	1586	14	binary	binary	NOUN
fuelectenerg-1427	1586	15	functions	function	NOUN
fuelectenerg-1427	1586	16	,	,	PUNCT
fuelectenerg-1427	1586	17	walsh	walsh	NOUN
fuelectenerg-1427	1586	18	and	and	CCONJ
fuelectenerg-1427	1586	19	reed	reed	PROPN
fuelectenerg-1427	1586	20	-	-	PUNCT
fuelectenerg-1427	1586	21	muller	muller	PROPN
fuelectenerg-1427	1586	22	spectra	spectra	PROPN
fuelectenerg-1427	1586	23	,	,	PUNCT
fuelectenerg-1427	1586	24	"	"	PUNCT
fuelectenerg-1427	1586	25	proc	proc	NOUN
fuelectenerg-1427	1586	26	.	.	PUNCT
fuelectenerg-1427	1587	1	ismvl	ismvl	PROPN
fuelectenerg-1427	1587	2	,	,	PUNCT
fuelectenerg-1427	1587	3	2000	2000	NUM
fuelectenerg-1427	1587	4	,	,	PUNCT
fuelectenerg-1427	1587	5	pp	pp	ADJ
fuelectenerg-1427	1587	6	.	.	PUNCT
fuelectenerg-1427	1588	1	279	279	NUM
fuelectenerg-1427	1588	2	-	-	SYM
fuelectenerg-1427	1588	3	284	284	NUM
fuelectenerg-1427	1588	4	.	.	PUNCT
fuelectenerg-1427	1589	1	[	[	X
fuelectenerg-1427	1589	2	9	9	NUM
fuelectenerg-1427	1589	3	]	]	PUNCT
fuelectenerg-1427	1589	4	h.	h.	PROPN
fuelectenerg-1427	1589	5	fujiwara	fujiwara	PROPN
fuelectenerg-1427	1589	6	,	,	PUNCT
fuelectenerg-1427	1589	7	logic	logic	NOUN
fuelectenerg-1427	1589	8	testing	testing	NOUN
fuelectenerg-1427	1589	9	and	and	CCONJ
fuelectenerg-1427	1589	10	design	design	NOUN
fuelectenerg-1427	1589	11	for	for	ADP
fuelectenerg-1427	1589	12	testability	testability	NOUN
fuelectenerg-1427	1589	13	,	,	PUNCT
fuelectenerg-1427	1589	14	mit	mit	NOUN
fuelectenerg-1427	1589	15	press	press	NOUN
fuelectenerg-1427	1589	16	,	,	PUNCT
fuelectenerg-1427	1589	17	1985	1985	NUM
fuelectenerg-1427	1589	18	.	.	PUNCT
fuelectenerg-1427	1590	1	[	[	X
fuelectenerg-1427	1590	2	10	10	NUM
fuelectenerg-1427	1590	3	]	]	X
fuelectenerg-1427	1590	4	d.	d.	PROPN
fuelectenerg-1427	1590	5	h.	h.	PROPN
fuelectenerg-1427	1590	6	green	green	PROPN
fuelectenerg-1427	1590	7	,	,	PUNCT
fuelectenerg-1427	1590	8	"	"	PUNCT
fuelectenerg-1427	1590	9	families	family	NOUN
fuelectenerg-1427	1590	10	of	of	ADP
fuelectenerg-1427	1590	11	reed	reed	NOUN
fuelectenerg-1427	1590	12	-	-	PUNCT
fuelectenerg-1427	1590	13	muller	muller	NOUN
fuelectenerg-1427	1590	14	canonical	canonical	ADJ
fuelectenerg-1427	1590	15	forms	form	NOUN
fuelectenerg-1427	1590	16	,	,	PUNCT
fuelectenerg-1427	1590	17	"	"	PUNCT
fuelectenerg-1427	1590	18	int	int	NOUN
fuelectenerg-1427	1590	19	.	.	PUNCT
fuelectenerg-1427	1591	1	j.	j.	PROPN
fuelectenerg-1427	1591	2	electronics	electronics	PROPN
fuelectenerg-1427	1591	3	,	,	PUNCT
fuelectenerg-1427	1591	4	no	no	INTJ
fuelectenerg-1427	1591	5	.	.	NOUN
fuelectenerg-1427	1591	6	2	2	NUM
fuelectenerg-1427	1591	7	,	,	PUNCT
fuelectenerg-1427	1591	8	pp	pp	ADJ
fuelectenerg-1427	1591	9	.	.	PUNCT
fuelectenerg-1427	1592	1	259	259	NUM
fuelectenerg-1427	1592	2	-	-	SYM
fuelectenerg-1427	1592	3	280	280	NUM
fuelectenerg-1427	1592	4	,	,	PUNCT
fuelectenerg-1427	1592	5	1991	1991	NUM
fuelectenerg-1427	1592	6	.	.	PUNCT
fuelectenerg-1427	1593	1	[	[	X
fuelectenerg-1427	1593	2	11	11	NUM
fuelectenerg-1427	1593	3	]	]	PUNCT
fuelectenerg-1427	1593	4	m.	m.	NOUN
fuelectenerg-1427	1593	5	helliwell	helliwell	NOUN
fuelectenerg-1427	1593	6	and	and	CCONJ
fuelectenerg-1427	1593	7	m.	m.	PROPN
fuelectenerg-1427	1593	8	a.	a.	PROPN
fuelectenerg-1427	1593	9	perkowski	perkowski	PROPN
fuelectenerg-1427	1593	10	,	,	PUNCT
fuelectenerg-1427	1593	11	"	"	PUNCT
fuelectenerg-1427	1593	12	a	a	DET
fuelectenerg-1427	1593	13	fast	fast	ADJ
fuelectenerg-1427	1593	14	algorithm	algorithm	NOUN
fuelectenerg-1427	1593	15	to	to	PART
fuelectenerg-1427	1593	16	minimize	minimize	VERB
fuelectenerg-1427	1593	17	multi	multi	ADJ
fuelectenerg-1427	1593	18	-	-	ADJ
fuelectenerg-1427	1593	19	output	output	ADJ
fuelectenerg-1427	1593	20	mixed	mix	VERB
fuelectenerg-1427	1593	21	-	-	PUNCT
fuelectenerg-1427	1593	22	polarity	polarity	NOUN
fuelectenerg-1427	1593	23	generalized	generalize	VERB
fuelectenerg-1427	1593	24	reed	reed	NOUN
fuelectenerg-1427	1593	25	-	-	PUNCT
fuelectenerg-1427	1593	26	muller	muller	NOUN
fuelectenerg-1427	1593	27	forms	form	NOUN
fuelectenerg-1427	1593	28	,	,	PUNCT
fuelectenerg-1427	1593	29	"	"	PUNCT
fuelectenerg-1427	1593	30	proc	proc	NOUN
fuelectenerg-1427	1593	31	.	.	PUNCT
fuelectenerg-1427	1594	1	design	design	NOUN
fuelectenerg-1427	1594	2	automation	automation	NOUN
fuelectenerg-1427	1594	3	conference	conference	NOUN
fuelectenerg-1427	1594	4	,	,	PUNCT
fuelectenerg-1427	1594	5	1988	1988	NUM
fuelectenerg-1427	1594	6	,	,	PUNCT
fuelectenerg-1427	1594	7	pp	pp	ADV
fuelectenerg-1427	1594	8	.	.	PUNCT
fuelectenerg-1427	1595	1	427	427	NUM
fuelectenerg-1427	1595	2	-	-	SYM
fuelectenerg-1427	1595	3	432	432	NUM
fuelectenerg-1427	1595	4	.	.	PUNCT
fuelectenerg-1427	1596	1	[	[	X
fuelectenerg-1427	1596	2	12	12	NUM
fuelectenerg-1427	1596	3	]	]	PUNCT
fuelectenerg-1427	1596	4	s.	s.	PROPN
fuelectenerg-1427	1596	5	l.	l.	PROPN
fuelectenerg-1427	1596	6	hurst	hurst	PROPN
fuelectenerg-1427	1596	7	,	,	PUNCT
fuelectenerg-1427	1596	8	d.	d.	PROPN
fuelectenerg-1427	1596	9	m.	m.	PROPN
fuelectenerg-1427	1596	10	miller	miller	PROPN
fuelectenerg-1427	1596	11	,	,	PUNCT
fuelectenerg-1427	1596	12	and	and	CCONJ
fuelectenerg-1427	1596	13	j.	j.	PROPN
fuelectenerg-1427	1596	14	c.	c.	PROPN
fuelectenerg-1427	1596	15	muzio	muzio	PROPN
fuelectenerg-1427	1596	16	,	,	PUNCT
fuelectenerg-1427	1596	17	spectral	spectral	ADJ
fuelectenerg-1427	1596	18	techniques	technique	NOUN
fuelectenerg-1427	1596	19	in	in	ADP
fuelectenerg-1427	1596	20	digital	digital	ADJ
fuelectenerg-1427	1596	21	logic	logic	NOUN
fuelectenerg-1427	1596	22	,	,	PUNCT
fuelectenerg-1427	1596	23	academic	academic	PROPN
fuelectenerg-1427	1596	24	press	press	PROPN
fuelectenerg-1427	1596	25	inc	inc	PROPN
fuelectenerg-1427	1596	26	.	.	PROPN
fuelectenerg-1427	1596	27	,	,	PUNCT
fuelectenerg-1427	1596	28	1985	1985	NUM
fuelectenerg-1427	1596	29	.	.	PUNCT
fuelectenerg-1427	1597	1	[	[	X
fuelectenerg-1427	1597	2	13	13	NUM
fuelectenerg-1427	1597	3	]	]	PUNCT
fuelectenerg-1427	1597	4	m.	m.	NOUN
fuelectenerg-1427	1597	5	g.	g.	PROPN
fuelectenerg-1427	1597	6	karpovsky	karpovsky	PROPN
fuelectenerg-1427	1597	7	,	,	PUNCT
fuelectenerg-1427	1597	8	finite	finite	PROPN
fuelectenerg-1427	1597	9	orthogonal	orthogonal	ADJ
fuelectenerg-1427	1597	10	series	series	NOUN
fuelectenerg-1427	1597	11	in	in	ADP
fuelectenerg-1427	1597	12	the	the	DET
fuelectenerg-1427	1597	13	design	design	NOUN
fuelectenerg-1427	1597	14	of	of	ADP
fuelectenerg-1427	1597	15	digital	digital	ADJ
fuelectenerg-1427	1597	16	devices	device	NOUN
fuelectenerg-1427	1597	17	,	,	PUNCT
fuelectenerg-1427	1597	18	wiley	wiley	NOUN
fuelectenerg-1427	1597	19	,	,	PUNCT
fuelectenerg-1427	1597	20	1976	1976	NUM
fuelectenerg-1427	1597	21	.	.	PUNCT
fuelectenerg-1427	1598	1	[	[	X
fuelectenerg-1427	1598	2	14	14	NUM
fuelectenerg-1427	1598	3	]	]	X
fuelectenerg-1427	1598	4	s.	s.	PROPN
fuelectenerg-1427	1598	5	m.	m.	PROPN
fuelectenerg-1427	1598	6	reddy	reddy	PROPN
fuelectenerg-1427	1598	7	,	,	PUNCT
fuelectenerg-1427	1598	8	"	"	PUNCT
fuelectenerg-1427	1598	9	easily	easily	ADV
fuelectenerg-1427	1598	10	testable	testable	ADJ
fuelectenerg-1427	1598	11	realizations	realization	NOUN
fuelectenerg-1427	1598	12	of	of	ADP
fuelectenerg-1427	1598	13	logic	logic	NOUN
fuelectenerg-1427	1598	14	functions	function	NOUN
fuelectenerg-1427	1598	15	,	,	PUNCT
fuelectenerg-1427	1598	16	"	"	PUNCT
fuelectenerg-1427	1598	17	ieee	ieee	NOUN
fuelectenerg-1427	1598	18	trans	tran	NOUN
fuelectenerg-1427	1598	19	.	.	PUNCT
fuelectenerg-1427	1599	1	comp	comp	PROPN
fuelectenerg-1427	1599	2	.	.	PUNCT
fuelectenerg-1427	1599	3	,	,	PUNCT
fuelectenerg-1427	1599	4	c-21	c-21	PROPN
fuelectenerg-1427	1599	5	,	,	PUNCT
fuelectenerg-1427	1599	6	pp	pp	ADV
fuelectenerg-1427	1599	7	.	.	PUNCT
fuelectenerg-1427	1600	1	1183	1183	NUM
fuelectenerg-1427	1600	2	-	-	SYM
fuelectenerg-1427	1600	3	1188	1188	NUM
fuelectenerg-1427	1600	4	,	,	PUNCT
fuelectenerg-1427	1600	5	1972	1972	NUM
fuelectenerg-1427	1600	6	.	.	PUNCT
fuelectenerg-1427	1601	1	[	[	X
fuelectenerg-1427	1601	2	15	15	X
fuelectenerg-1427	1601	3	]	]	X
fuelectenerg-1427	1601	4	t.	t.	PROPN
fuelectenerg-1427	1601	5	sasao	sasao	PROPN
fuelectenerg-1427	1601	6	and	and	CCONJ
fuelectenerg-1427	1601	7	m.	m.	PROPN
fuelectenerg-1427	1601	8	fujita	fujita	PROPN
fuelectenerg-1427	1601	9	(	(	PUNCT
fuelectenerg-1427	1601	10	editors	editor	NOUN
fuelectenerg-1427	1601	11	)	)	PUNCT
fuelectenerg-1427	1601	12	,	,	PUNCT
fuelectenerg-1427	1601	13	representations	representation	NOUN
fuelectenerg-1427	1601	14	of	of	ADP
fuelectenerg-1427	1601	15	discrete	discrete	ADJ
fuelectenerg-1427	1601	16	functions	function	NOUN
fuelectenerg-1427	1601	17	,	,	PUNCT
fuelectenerg-1427	1601	18	kluwer	kluwer	NOUN
fuelectenerg-1427	1601	19	academic	academic	ADJ
fuelectenerg-1427	1601	20	publishers	publisher	NOUN
fuelectenerg-1427	1601	21	,	,	PUNCT
fuelectenerg-1427	1601	22	1996	1996	NUM
fuelectenerg-1427	1601	23	.	.	PUNCT
fuelectenerg-1427	1602	1	[	[	X
fuelectenerg-1427	1602	2	16	16	NUM
fuelectenerg-1427	1602	3	]	]	PUNCT
fuelectenerg-1427	1602	4	t.	t.	PROPN
fuelectenerg-1427	1602	5	sasao	sasao	PROPN
fuelectenerg-1427	1602	6	,	,	PUNCT
fuelectenerg-1427	1602	7	"	"	PUNCT
fuelectenerg-1427	1602	8	easily	easily	ADV
fuelectenerg-1427	1602	9	testable	testable	ADJ
fuelectenerg-1427	1602	10	realizations	realization	NOUN
fuelectenerg-1427	1602	11	for	for	ADP
fuelectenerg-1427	1602	12	generalized	generalized	ADJ
fuelectenerg-1427	1602	13	reed	reed	NOUN
fuelectenerg-1427	1602	14	-	-	PUNCT
fuelectenerg-1427	1602	15	muller	muller	NOUN
fuelectenerg-1427	1602	16	expressions	expression	NOUN
fuelectenerg-1427	1602	17	,	,	PUNCT
fuelectenerg-1427	1602	18	"	"	PUNCT
fuelectenerg-1427	1602	19	ieee	ieee	NOUN
fuelectenerg-1427	1602	20	trans	tran	NOUN
fuelectenerg-1427	1602	21	.	.	PUNCT
fuelectenerg-1427	1603	1	comp	comp	PROPN
fuelectenerg-1427	1603	2	.	.	PUNCT
fuelectenerg-1427	1603	3	,	,	PUNCT
fuelectenerg-1427	1603	4	vol	vol	NOUN
fuelectenerg-1427	1603	5	.	.	PROPN
fuelectenerg-1427	1604	1	46	46	NUM
fuelectenerg-1427	1604	2	,	,	PUNCT
fuelectenerg-1427	1604	3	pp	pp	ADJ
fuelectenerg-1427	1604	4	.	.	PUNCT
fuelectenerg-1427	1605	1	709	709	NUM
fuelectenerg-1427	1605	2	-	-	PUNCT
fuelectenerg-1427	1605	3	716	716	NUM
fuelectenerg-1427	1605	4	,	,	PUNCT
fuelectenerg-1427	1605	5	1997	1997	NUM
fuelectenerg-1427	1605	6	.	.	PUNCT
fuelectenerg-1427	1606	1	[	[	X
fuelectenerg-1427	1606	2	17	17	NUM
fuelectenerg-1427	1606	3	]	]	X
fuelectenerg-1427	1606	4	r.	r.	PROPN
fuelectenerg-1427	1606	5	s.	s.	PROPN
fuelectenerg-1427	1606	6	stanković	stanković	PROPN
fuelectenerg-1427	1606	7	,	,	PUNCT
fuelectenerg-1427	1606	8	spectral	spectral	ADJ
fuelectenerg-1427	1606	9	transform	transform	VERB
fuelectenerg-1427	1606	10	decision	decision	NOUN
fuelectenerg-1427	1606	11	diagrams	diagram	NOUN
fuelectenerg-1427	1606	12	in	in	ADP
fuelectenerg-1427	1606	13	simple	simple	ADJ
fuelectenerg-1427	1606	14	questions	question	NOUN
fuelectenerg-1427	1606	15	and	and	CCONJ
fuelectenerg-1427	1606	16	simple	simple	ADJ
fuelectenerg-1427	1606	17	answers	answer	NOUN
fuelectenerg-1427	1606	18	,	,	PUNCT
fuelectenerg-1427	1606	19	nauka	nauka	PROPN
fuelectenerg-1427	1606	20	,	,	PUNCT
fuelectenerg-1427	1606	21	1998	1998	NUM
fuelectenerg-1427	1606	22	.	.	PUNCT
fuelectenerg-1427	1607	1	[	[	X
fuelectenerg-1427	1607	2	18	18	NUM
fuelectenerg-1427	1607	3	]	]	X
fuelectenerg-1427	1607	4	r.	r.	PROPN
fuelectenerg-1427	1607	5	s.	s.	PROPN
fuelectenerg-1427	1607	6	stanković	stanković	PROPN
fuelectenerg-1427	1607	7	,	,	PUNCT
fuelectenerg-1427	1607	8	c.	c.	PROPN
fuelectenerg-1427	1607	9	moraga	moraga	PROPN
fuelectenerg-1427	1607	10	,	,	PUNCT
fuelectenerg-1427	1607	11	and	and	CCONJ
fuelectenerg-1427	1607	12	j.	j.	PROPN
fuelectenerg-1427	1607	13	t.	t.	PROPN
fuelectenerg-1427	1607	14	astola	astola	PROPN
fuelectenerg-1427	1607	15	,	,	PUNCT
fuelectenerg-1427	1607	16	"	"	PUNCT
fuelectenerg-1427	1607	17	reed	reed	NOUN
fuelectenerg-1427	1607	18	-	-	PUNCT
fuelectenerg-1427	1607	19	muller	muller	NOUN
fuelectenerg-1427	1607	20	expressions	expression	NOUN
fuelectenerg-1427	1607	21	in	in	ADP
fuelectenerg-1427	1607	22	the	the	DET
fuelectenerg-1427	1607	23	previous	previous	ADJ
fuelectenerg-1427	1607	24	decade	decade	NOUN
fuelectenerg-1427	1607	25	,	,	PUNCT
fuelectenerg-1427	1607	26	"	"	PUNCT
fuelectenerg-1427	1607	27	proc	proc	NOUN
fuelectenerg-1427	1607	28	.	.	PUNCT
fuelectenerg-1427	1608	1	reed	reed	NOUN
fuelectenerg-1427	1608	2	-	-	PUNCT
fuelectenerg-1427	1608	3	muller	muller	NOUN
fuelectenerg-1427	1608	4	,	,	PUNCT
fuelectenerg-1427	1608	5	starkville	starkville	PROPN
fuelectenerg-1427	1608	6	,	,	PUNCT
fuelectenerg-1427	1608	7	2001	2001	NUM
fuelectenerg-1427	1608	8	,	,	PUNCT
fuelectenerg-1427	1608	9	pp	pp	ADJ
fuelectenerg-1427	1608	10	.	.	PUNCT
fuelectenerg-1427	1609	1	7	7	NUM
fuelectenerg-1427	1609	2	-	-	SYM
fuelectenerg-1427	1609	3	26	26	NUM
fuelectenerg-1427	1609	4	.	.	PUNCT
fuelectenerg-1427	1610	1	[	[	X
fuelectenerg-1427	1610	2	19	19	NUM
fuelectenerg-1427	1610	3	]	]	PUNCT
fuelectenerg-1427	1610	4	s.	s.	PROPN
fuelectenerg-1427	1610	5	b.	b.	PROPN
fuelectenerg-1427	1610	6	akers	akers	PROPN
fuelectenerg-1427	1610	7	,	,	PUNCT
fuelectenerg-1427	1610	8	"	"	PUNCT
fuelectenerg-1427	1610	9	binary	binary	ADJ
fuelectenerg-1427	1610	10	decision	decision	NOUN
fuelectenerg-1427	1610	11	diagrams	diagram	NOUN
fuelectenerg-1427	1610	12	,	,	PUNCT
fuelectenerg-1427	1610	13	"	"	PUNCT
fuelectenerg-1427	1610	14	ieee	ieee	NOUN
fuelectenerg-1427	1610	15	trans	tran	NOUN
fuelectenerg-1427	1610	16	.	.	PUNCT
fuelectenerg-1427	1611	1	comp	comp	PROPN
fuelectenerg-1427	1611	2	.	.	PUNCT
fuelectenerg-1427	1611	3	,	,	PUNCT
fuelectenerg-1427	1611	4	vol	vol	NOUN
fuelectenerg-1427	1611	5	.	.	PUNCT
fuelectenerg-1427	1612	1	c-27	c-27	PROPN
fuelectenerg-1427	1612	2	,	,	PUNCT
fuelectenerg-1427	1612	3	no	no	INTJ
fuelectenerg-1427	1612	4	.	.	NOUN
fuelectenerg-1427	1612	5	6	6	NUM
fuelectenerg-1427	1612	6	,	,	PUNCT
fuelectenerg-1427	1612	7	pp	pp	ADJ
fuelectenerg-1427	1612	8	.	.	PUNCT
fuelectenerg-1427	1613	1	509	509	NUM
fuelectenerg-1427	1613	2	-	-	SYM
fuelectenerg-1427	1613	3	516	516	NUM
fuelectenerg-1427	1613	4	,	,	PUNCT
fuelectenerg-1427	1613	5	june	june	PROPN
fuelectenerg-1427	1613	6	1978	1978	NUM
fuelectenerg-1427	1613	7	.	.	PUNCT
fuelectenerg-1427	1614	1	[	[	X
fuelectenerg-1427	1614	2	20	20	NUM
fuelectenerg-1427	1614	3	]	]	PUNCT
fuelectenerg-1427	1614	4	r.	r.	PROPN
fuelectenerg-1427	1614	5	e.	e.	PROPN
fuelectenerg-1427	1614	6	bryant	bryant	PROPN
fuelectenerg-1427	1614	7	,	,	PUNCT
fuelectenerg-1427	1614	8	"	"	PUNCT
fuelectenerg-1427	1614	9	graph	graph	NOUN
fuelectenerg-1427	1614	10	-	-	PUNCT
fuelectenerg-1427	1614	11	based	base	VERB
fuelectenerg-1427	1614	12	algorithms	algorithm	NOUN
fuelectenerg-1427	1614	13	for	for	ADP
fuelectenerg-1427	1614	14	boolean	boolean	ADJ
fuelectenerg-1427	1614	15	functions	function	NOUN
fuelectenerg-1427	1614	16	manipulation	manipulation	NOUN
fuelectenerg-1427	1614	17	,	,	PUNCT
fuelectenerg-1427	1614	18	"	"	PUNCT
fuelectenerg-1427	1614	19	ieee	ieee	NOUN
fuelectenerg-1427	1614	20	trans	tran	NOUN
fuelectenerg-1427	1614	21	.	.	PUNCT
fuelectenerg-1427	1615	1	on	on	ADP
fuelectenerg-1427	1615	2	comp	comp	PROPN
fuelectenerg-1427	1615	3	.	.	PUNCT
fuelectenerg-1427	1615	4	,	,	PUNCT
fuelectenerg-1427	1615	5	vol	vol	NOUN
fuelectenerg-1427	1615	6	.	.	PUNCT
fuelectenerg-1427	1616	1	c-35	c-35	PROPN
fuelectenerg-1427	1616	2	,	,	PUNCT
fuelectenerg-1427	1616	3	no.8	no.8	PROPN
fuelectenerg-1427	1616	4	,	,	PUNCT
fuelectenerg-1427	1616	5	pp	pp	ADV
fuelectenerg-1427	1616	6	.	.	PUNCT
fuelectenerg-1427	1617	1	667	667	NUM
fuelectenerg-1427	1617	2	-	-	SYM
fuelectenerg-1427	1617	3	691	691	NUM
fuelectenerg-1427	1617	4	,	,	PUNCT
fuelectenerg-1427	1617	5	1986	1986	NUM
fuelectenerg-1427	1617	6	.	.	PUNCT
fuelectenerg-1427	1618	1	[	[	X
fuelectenerg-1427	1618	2	21	21	NUM
fuelectenerg-1427	1618	3	]	]	X
fuelectenerg-1427	1618	4	d.	d.	PROPN
fuelectenerg-1427	1618	5	k.	k.	PROPN
fuelectenerg-1427	1618	6	pradhan	pradhan	PROPN
fuelectenerg-1427	1618	7	,	,	PUNCT
fuelectenerg-1427	1618	8	"	"	PUNCT
fuelectenerg-1427	1618	9	universal	universal	ADJ
fuelectenerg-1427	1618	10	test	test	NOUN
fuelectenerg-1427	1618	11	sets	set	NOUN
fuelectenerg-1427	1618	12	for	for	ADP
fuelectenerg-1427	1618	13	multiple	multiple	ADJ
fuelectenerg-1427	1618	14	fault	fault	NOUN
fuelectenerg-1427	1618	15	detection	detection	NOUN
fuelectenerg-1427	1618	16	in	in	ADP
fuelectenerg-1427	1618	17	and	and	CCONJ
fuelectenerg-1427	1618	18	-	-	PUNCT
fuelectenerg-1427	1618	19	exor	exor	PROPN
fuelectenerg-1427	1618	20	arrays	array	VERB
fuelectenerg-1427	1618	21	,	,	PUNCT
fuelectenerg-1427	1618	22	"	"	PUNCT
fuelectenerg-1427	1618	23	ieee	ieee	NOUN
fuelectenerg-1427	1618	24	trans	tran	NOUN
fuelectenerg-1427	1618	25	.	.	PUNCT
fuelectenerg-1427	1619	1	comp	comp	PROPN
fuelectenerg-1427	1619	2	.	.	PUNCT
fuelectenerg-1427	1619	3	,	,	PUNCT
fuelectenerg-1427	1619	4	vol	vol	NOUN
fuelectenerg-1427	1619	5	.	.	PROPN
fuelectenerg-1427	1620	1	27	27	NUM
fuelectenerg-1427	1620	2	,	,	PUNCT
fuelectenerg-1427	1620	3	pp	pp	ADJ
fuelectenerg-1427	1620	4	.	.	PUNCT
fuelectenerg-1427	1621	1	181	181	NUM
fuelectenerg-1427	1621	2	-	-	SYM
fuelectenerg-1427	1621	3	187	187	NUM
fuelectenerg-1427	1621	4	,	,	PUNCT
fuelectenerg-1427	1621	5	1978	1978	NUM
fuelectenerg-1427	1621	6	.	.	PUNCT
fuelectenerg-1427	1622	1	117	117	NUM
fuelectenerg-1427	1622	2	an	an	DET
fuelectenerg-1427	1622	3	extended	extend	VERB
fuelectenerg-1427	1622	4	green	green	ADJ
fuelectenerg-1427	1622	5	sasao	sasao	PROPN
fuelectenerg-1427	1622	6	hierarchy	hierarchy	NOUN
fuelectenerg-1427	1622	7	of	of	ADP
fuelectenerg-1427	1622	8	canonical	canonical	ADJ
fuelectenerg-1427	1622	9	ternary	ternary	ADJ
fuelectenerg-1427	1622	10	galois	galois	NOUN
fuelectenerg-1427	1622	11	forms	form	NOUN
fuelectenerg-1427	1622	12	...	...	PUNCT
fuelectenerg-1427	1623	1	[	[	X
fuelectenerg-1427	1623	2	22	22	NUM
fuelectenerg-1427	1623	3	]	]	PUNCT
fuelectenerg-1427	1623	4	m.	m.	NOUN
fuelectenerg-1427	1623	5	cohn	cohn	PROPN
fuelectenerg-1427	1623	6	,	,	PUNCT
fuelectenerg-1427	1623	7	switching	switch	VERB
fuelectenerg-1427	1623	8	function	function	NOUN
fuelectenerg-1427	1623	9	canonical	canonical	ADJ
fuelectenerg-1427	1623	10	form	form	NOUN
fuelectenerg-1427	1623	11	over	over	ADP
fuelectenerg-1427	1623	12	integer	integer	NOUN
fuelectenerg-1427	1623	13	fields	field	NOUN
fuelectenerg-1427	1623	14	,	,	PUNCT
fuelectenerg-1427	1623	15	ph.d	ph.d	PROPN
fuelectenerg-1427	1623	16	.	.	PUNCT
fuelectenerg-1427	1623	17	dissertation	dissertation	PROPN
fuelectenerg-1427	1623	18	,	,	PUNCT
fuelectenerg-1427	1623	19	harvard	harvard	PROPN
fuelectenerg-1427	1623	20	university	university	PROPN
fuelectenerg-1427	1623	21	,	,	PUNCT
fuelectenerg-1427	1623	22	1960	1960	NUM
fuelectenerg-1427	1623	23	.	.	PUNCT
fuelectenerg-1427	1624	1	[	[	X
fuelectenerg-1427	1624	2	23	23	NUM
fuelectenerg-1427	1624	3	]	]	X
fuelectenerg-1427	1624	4	r.	r.	PROPN
fuelectenerg-1427	1624	5	drechsler	drechsler	PROPN
fuelectenerg-1427	1624	6	,	,	PUNCT
fuelectenerg-1427	1624	7	a.	a.	NOUN
fuelectenerg-1427	1624	8	sarabi	sarabi	PROPN
fuelectenerg-1427	1624	9	,	,	PUNCT
fuelectenerg-1427	1624	10	m.	m.	NOUN
fuelectenerg-1427	1624	11	theobald	theobald	PROPN
fuelectenerg-1427	1624	12	,	,	PUNCT
fuelectenerg-1427	1624	13	b.	b.	PROPN
fuelectenerg-1427	1624	14	becker	becker	PROPN
fuelectenerg-1427	1624	15	,	,	PUNCT
fuelectenerg-1427	1624	16	and	and	CCONJ
fuelectenerg-1427	1624	17	m.	m.	PROPN
fuelectenerg-1427	1624	18	a.	a.	PROPN
fuelectenerg-1427	1624	19	perkowski	perkowski	PROPN
fuelectenerg-1427	1624	20	,	,	PUNCT
fuelectenerg-1427	1624	21	"	"	PUNCT
fuelectenerg-1427	1624	22	efficient	efficient	ADJ
fuelectenerg-1427	1624	23	representation	representation	NOUN
fuelectenerg-1427	1624	24	and	and	CCONJ
fuelectenerg-1427	1624	25	manipulation	manipulation	NOUN
fuelectenerg-1427	1624	26	of	of	ADP
fuelectenerg-1427	1624	27	switching	switch	VERB
fuelectenerg-1427	1624	28	functions	function	NOUN
fuelectenerg-1427	1624	29	based	base	VERB
fuelectenerg-1427	1624	30	on	on	ADP
fuelectenerg-1427	1624	31	ordered	order	VERB
fuelectenerg-1427	1624	32	kronecker	kronecker	NOUN
fuelectenerg-1427	1624	33	functional	functional	ADJ
fuelectenerg-1427	1624	34	decision	decision	NOUN
fuelectenerg-1427	1624	35	diagrams	diagram	NOUN
fuelectenerg-1427	1624	36	,	,	PUNCT
fuelectenerg-1427	1624	37	"	"	PUNCT
fuelectenerg-1427	1624	38	proc	proc	NOUN
fuelectenerg-1427	1624	39	.	.	PUNCT
fuelectenerg-1427	1625	1	dac	dac	PROPN
fuelectenerg-1427	1625	2	,	,	PUNCT
fuelectenerg-1427	1625	3	1994	1994	NUM
fuelectenerg-1427	1625	4	,	,	PUNCT
fuelectenerg-1427	1625	5	pp	pp	ADJ
fuelectenerg-1427	1625	6	.	.	PUNCT
fuelectenerg-1427	1625	7	415419	415419	NUM
fuelectenerg-1427	1625	8	.	.	PUNCT
fuelectenerg-1427	1626	1	[	[	X
fuelectenerg-1427	1626	2	24	24	NUM
fuelectenerg-1427	1626	3	]	]	PUNCT
fuelectenerg-1427	1626	4	b.	b.	PROPN
fuelectenerg-1427	1626	5	j.	j.	PROPN
fuelectenerg-1427	1626	6	falkowski	falkowski	PROPN
fuelectenerg-1427	1626	7	and	and	CCONJ
fuelectenerg-1427	1626	8	s.	s.	PROPN
fuelectenerg-1427	1626	9	rahardja	rahardja	PROPN
fuelectenerg-1427	1626	10	,	,	PUNCT
fuelectenerg-1427	1626	11	"	"	PUNCT
fuelectenerg-1427	1626	12	classification	classification	NOUN
fuelectenerg-1427	1626	13	and	and	CCONJ
fuelectenerg-1427	1626	14	properties	property	NOUN
fuelectenerg-1427	1626	15	of	of	ADP
fuelectenerg-1427	1626	16	fast	fast	ADJ
fuelectenerg-1427	1626	17	linearly	linearly	ADV
fuelectenerg-1427	1626	18	independent	independent	ADJ
fuelectenerg-1427	1626	19	logic	logic	NOUN
fuelectenerg-1427	1626	20	transformations	transformation	NOUN
fuelectenerg-1427	1626	21	,	,	PUNCT
fuelectenerg-1427	1626	22	"	"	PUNCT
fuelectenerg-1427	1626	23	ieee	ieee	NOUN
fuelectenerg-1427	1626	24	trans	tran	NOUN
fuelectenerg-1427	1626	25	.	.	PUNCT
fuelectenerg-1427	1627	1	on	on	ADP
fuelectenerg-1427	1627	2	circuits	circuit	NOUN
fuelectenerg-1427	1627	3	and	and	CCONJ
fuelectenerg-1427	1627	4	systems	system	NOUN
fuelectenerg-1427	1627	5	-	-	PUNCT
fuelectenerg-1427	1627	6	ii	ii	NOUN
fuelectenerg-1427	1627	7	,	,	PUNCT
fuelectenerg-1427	1627	8	vol	vol	NOUN
fuelectenerg-1427	1627	9	.	.	PROPN
fuelectenerg-1427	1627	10	44	44	NUM
fuelectenerg-1427	1627	11	,	,	PUNCT
fuelectenerg-1427	1627	12	no	no	INTJ
fuelectenerg-1427	1627	13	.	.	NOUN
fuelectenerg-1427	1627	14	8	8	NUM
fuelectenerg-1427	1627	15	,	,	PUNCT
fuelectenerg-1427	1627	16	pp	pp	ADJ
fuelectenerg-1427	1627	17	.	.	PUNCT
fuelectenerg-1427	1627	18	646	646	NUM
fuelectenerg-1427	1627	19	-	-	SYM
fuelectenerg-1427	1627	20	655	655	NUM
fuelectenerg-1427	1627	21	,	,	PUNCT
fuelectenerg-1427	1627	22	august	august	PROPN
fuelectenerg-1427	1627	23	1997	1997	NUM
fuelectenerg-1427	1627	24	.	.	PUNCT
fuelectenerg-1427	1628	1	[	[	X
fuelectenerg-1427	1628	2	25	25	NUM
fuelectenerg-1427	1628	3	]	]	PUNCT
fuelectenerg-1427	1628	4	a.	a.	NOUN
fuelectenerg-1427	1628	5	gaidukov	gaidukov	NOUN
fuelectenerg-1427	1628	6	,	,	PUNCT
fuelectenerg-1427	1628	7	"	"	PUNCT
fuelectenerg-1427	1628	8	algorithm	algorithm	NOUN
fuelectenerg-1427	1628	9	to	to	PART
fuelectenerg-1427	1628	10	derive	derive	VERB
fuelectenerg-1427	1628	11	minimum	minimum	ADJ
fuelectenerg-1427	1628	12	esop	esop	NOUN
fuelectenerg-1427	1628	13	for	for	ADP
fuelectenerg-1427	1628	14	6	6	NUM
fuelectenerg-1427	1628	15	-	-	PUNCT
fuelectenerg-1427	1628	16	variable	variable	ADJ
fuelectenerg-1427	1628	17	function	function	NOUN
fuelectenerg-1427	1628	18	,	,	PUNCT
fuelectenerg-1427	1628	19	"	"	PUNCT
fuelectenerg-1427	1628	20	proc	proc	NOUN
fuelectenerg-1427	1628	21	.	.	PUNCT
fuelectenerg-1427	1629	1	int	int	NOUN
fuelectenerg-1427	1629	2	.	.	PUNCT
fuelectenerg-1427	1630	1	workshop	workshop	NOUN
fuelectenerg-1427	1630	2	on	on	ADP
fuelectenerg-1427	1630	3	boolean	boolean	ADJ
fuelectenerg-1427	1630	4	problems	problem	NOUN
fuelectenerg-1427	1630	5	,	,	PUNCT
fuelectenerg-1427	1630	6	freiberg	freiberg	PROPN
fuelectenerg-1427	1630	7	,	,	PUNCT
fuelectenerg-1427	1630	8	2002	2002	NUM
fuelectenerg-1427	1630	9	,	,	PUNCT
fuelectenerg-1427	1630	10	pp	pp	ADJ
fuelectenerg-1427	1630	11	.	.	PUNCT
fuelectenerg-1427	1631	1	141	141	NUM
fuelectenerg-1427	1631	2	-	-	SYM
fuelectenerg-1427	1631	3	148	148	NUM
fuelectenerg-1427	1631	4	.	.	PUNCT
fuelectenerg-1427	1632	1	[	[	X
fuelectenerg-1427	1632	2	26	26	NUM
fuelectenerg-1427	1632	3	]	]	X
fuelectenerg-1427	1632	4	s.	s.	PROPN
fuelectenerg-1427	1632	5	hassoun	hassoun	PROPN
fuelectenerg-1427	1632	6	,	,	PUNCT
fuelectenerg-1427	1632	7	t.	t.	PROPN
fuelectenerg-1427	1632	8	sasao	sasao	PROPN
fuelectenerg-1427	1632	9	,	,	PUNCT
fuelectenerg-1427	1632	10	and	and	CCONJ
fuelectenerg-1427	1632	11	r.	r.	PROPN
fuelectenerg-1427	1632	12	brayton	brayton	PROPN
fuelectenerg-1427	1632	13	(	(	PUNCT
fuelectenerg-1427	1632	14	editors	editor	NOUN
fuelectenerg-1427	1632	15	)	)	PUNCT
fuelectenerg-1427	1632	16	,	,	PUNCT
fuelectenerg-1427	1632	17	logic	logic	NOUN
fuelectenerg-1427	1632	18	synthesis	synthesis	NOUN
fuelectenerg-1427	1632	19	and	and	CCONJ
fuelectenerg-1427	1632	20	verification	verification	NOUN
fuelectenerg-1427	1632	21	,	,	PUNCT
fuelectenerg-1427	1632	22	kluwer	kluwer	NOUN
fuelectenerg-1427	1632	23	acad	acad	PROPN
fuelectenerg-1427	1632	24	.	.	PUNCT
fuelectenerg-1427	1633	1	publishers	publisher	NOUN
fuelectenerg-1427	1633	2	,	,	PUNCT
fuelectenerg-1427	1633	3	2001	2001	NUM
fuelectenerg-1427	1633	4	.	.	PUNCT
fuelectenerg-1427	1634	1	[	[	X
fuelectenerg-1427	1634	2	27	27	NUM
fuelectenerg-1427	1634	3	]	]	X
fuelectenerg-1427	1634	4	c.	c.	PROPN
fuelectenerg-1427	1634	5	y.	y.	PROPN
fuelectenerg-1427	1634	6	lee	lee	PROPN
fuelectenerg-1427	1634	7	,	,	PUNCT
fuelectenerg-1427	1634	8	"	"	PUNCT
fuelectenerg-1427	1634	9	representation	representation	NOUN
fuelectenerg-1427	1634	10	of	of	ADP
fuelectenerg-1427	1634	11	switching	switch	VERB
fuelectenerg-1427	1634	12	circuits	circuit	NOUN
fuelectenerg-1427	1634	13	by	by	ADP
fuelectenerg-1427	1634	14	binary	binary	ADJ
fuelectenerg-1427	1634	15	decision	decision	NOUN
fuelectenerg-1427	1634	16	diagrams	diagram	NOUN
fuelectenerg-1427	1634	17	,	,	PUNCT
fuelectenerg-1427	1634	18	"	"	PUNCT
fuelectenerg-1427	1634	19	bell	bell	NOUN
fuelectenerg-1427	1634	20	syst	syst	NOUN
fuelectenerg-1427	1634	21	.	.	PUNCT
fuelectenerg-1427	1635	1	tech	tech	PROPN
fuelectenerg-1427	1635	2	.	.	PUNCT
fuelectenerg-1427	1636	1	j.	j.	PROPN
fuelectenerg-1427	1636	2	,	,	PUNCT
fuelectenerg-1427	1636	3	vol	vol	NOUN
fuelectenerg-1427	1636	4	.	.	PROPN
fuelectenerg-1427	1636	5	38	38	NUM
fuelectenerg-1427	1636	6	,	,	PUNCT
fuelectenerg-1427	1636	7	pp	pp	ADJ
fuelectenerg-1427	1636	8	.	.	PUNCT
fuelectenerg-1427	1637	1	985	985	NUM
fuelectenerg-1427	1637	2	-	-	SYM
fuelectenerg-1427	1637	3	999	999	NUM
fuelectenerg-1427	1637	4	,	,	PUNCT
fuelectenerg-1427	1637	5	1959	1959	NUM
fuelectenerg-1427	1637	6	.	.	PUNCT
fuelectenerg-1427	1638	1	[	[	X
fuelectenerg-1427	1638	2	28	28	NUM
fuelectenerg-1427	1638	3	]	]	X
fuelectenerg-1427	1638	4	c.	c.	PROPN
fuelectenerg-1427	1638	5	moraga	moraga	PROPN
fuelectenerg-1427	1638	6	,	,	PUNCT
fuelectenerg-1427	1638	7	"	"	PUNCT
fuelectenerg-1427	1638	8	ternary	ternary	ADJ
fuelectenerg-1427	1638	9	spectral	spectral	ADJ
fuelectenerg-1427	1638	10	logic	logic	NOUN
fuelectenerg-1427	1638	11	,	,	PUNCT
fuelectenerg-1427	1638	12	"	"	PUNCT
fuelectenerg-1427	1638	13	proc	proc	NOUN
fuelectenerg-1427	1638	14	.	.	PUNCT
fuelectenerg-1427	1639	1	ismvl	ismvl	PROPN
fuelectenerg-1427	1639	2	,	,	PUNCT
fuelectenerg-1427	1639	3	pp	pp	ADJ
fuelectenerg-1427	1639	4	.	.	PUNCT
fuelectenerg-1427	1640	1	7	7	NUM
fuelectenerg-1427	1640	2	-	-	SYM
fuelectenerg-1427	1640	3	12	12	NUM
fuelectenerg-1427	1640	4	,	,	PUNCT
fuelectenerg-1427	1640	5	1977	1977	NUM
fuelectenerg-1427	1640	6	.	.	PUNCT
fuelectenerg-1427	1641	1	[	[	X
fuelectenerg-1427	1641	2	29	29	NUM
fuelectenerg-1427	1641	3	]	]	X
fuelectenerg-1427	1641	4	j.	j.	PROPN
fuelectenerg-1427	1641	5	c.	c.	PROPN
fuelectenerg-1427	1641	6	muzio	muzio	PROPN
fuelectenerg-1427	1641	7	and	and	CCONJ
fuelectenerg-1427	1641	8	t.	t.	PROPN
fuelectenerg-1427	1641	9	wesselkamper	wesselkamper	NOUN
fuelectenerg-1427	1641	10	,	,	PUNCT
fuelectenerg-1427	1641	11	multiple	multiple	ADV
fuelectenerg-1427	1641	12	-	-	PUNCT
fuelectenerg-1427	1641	13	valued	value	VERB
fuelectenerg-1427	1641	14	switching	switching	NOUN
fuelectenerg-1427	1641	15	theory	theory	NOUN
fuelectenerg-1427	1641	16	,	,	PUNCT
fuelectenerg-1427	1641	17	adamhilger	adamhilger	NOUN
fuelectenerg-1427	1641	18	,	,	PUNCT
fuelectenerg-1427	1641	19	1985	1985	NUM
fuelectenerg-1427	1641	20	.	.	PUNCT
fuelectenerg-1427	1642	1	[	[	X
fuelectenerg-1427	1642	2	30	30	NUM
fuelectenerg-1427	1642	3	]	]	X
fuelectenerg-1427	1642	4	r.	r.	PROPN
fuelectenerg-1427	1642	5	s.	s.	PROPN
fuelectenerg-1427	1642	6	stanković	stanković	PROPN
fuelectenerg-1427	1642	7	,	,	PUNCT
fuelectenerg-1427	1642	8	"	"	PUNCT
fuelectenerg-1427	1642	9	functional	functional	ADJ
fuelectenerg-1427	1642	10	decision	decision	NOUN
fuelectenerg-1427	1642	11	diagrams	diagram	NOUN
fuelectenerg-1427	1642	12	for	for	ADP
fuelectenerg-1427	1642	13	multiple	multiple	ADV
fuelectenerg-1427	1642	14	-	-	PUNCT
fuelectenerg-1427	1642	15	valued	value	VERB
fuelectenerg-1427	1642	16	functions	function	NOUN
fuelectenerg-1427	1642	17	,	,	PUNCT
fuelectenerg-1427	1642	18	"	"	PUNCT
fuelectenerg-1427	1642	19	proc	proc	NOUN
fuelectenerg-1427	1642	20	.	.	PUNCT
fuelectenerg-1427	1643	1	ismvl	ismvl	PROPN
fuelectenerg-1427	1643	2	,	,	PUNCT
fuelectenerg-1427	1643	3	1995	1995	NUM
fuelectenerg-1427	1643	4	,	,	PUNCT
fuelectenerg-1427	1643	5	pp	pp	ADJ
fuelectenerg-1427	1643	6	.	.	PUNCT
fuelectenerg-1427	1644	1	284	284	NUM
fuelectenerg-1427	1644	2	-	-	SYM
fuelectenerg-1427	1644	3	289	289	NUM
fuelectenerg-1427	1644	4	.	.	PUNCT
fuelectenerg-1427	1645	1	[	[	X
fuelectenerg-1427	1645	2	31	31	NUM
fuelectenerg-1427	1645	3	]	]	PUNCT
fuelectenerg-1427	1645	4	b.	b.	PROPN
fuelectenerg-1427	1645	5	steinbach	steinbach	PROPN
fuelectenerg-1427	1645	6	and	and	CCONJ
fuelectenerg-1427	1645	7	a.	a.	NOUN
fuelectenerg-1427	1645	8	mishchenko	mishchenko	PROPN
fuelectenerg-1427	1645	9	,	,	PUNCT
fuelectenerg-1427	1645	10	"	"	PUNCT
fuelectenerg-1427	1645	11	a	a	DET
fuelectenerg-1427	1645	12	new	new	ADJ
fuelectenerg-1427	1645	13	approach	approach	NOUN
fuelectenerg-1427	1645	14	to	to	PART
fuelectenerg-1427	1645	15	exact	exact	VERB
fuelectenerg-1427	1645	16	esop	esop	PROPN
fuelectenerg-1427	1645	17	minimization	minimization	NOUN
fuelectenerg-1427	1645	18	,	,	PUNCT
fuelectenerg-1427	1645	19	"	"	PUNCT
fuelectenerg-1427	1645	20	proc	proc	NOUN
fuelectenerg-1427	1645	21	.	.	PUNCT
fuelectenerg-1427	1646	1	reed	reed	NOUN
fuelectenerg-1427	1646	2	-	-	PUNCT
fuelectenerg-1427	1646	3	muller	muller	NOUN
fuelectenerg-1427	1646	4	,	,	PUNCT
fuelectenerg-1427	1646	5	starkville	starkville	PROPN
fuelectenerg-1427	1646	6	,	,	PUNCT
fuelectenerg-1427	1646	7	2001	2001	NUM
fuelectenerg-1427	1646	8	,	,	PUNCT
fuelectenerg-1427	1646	9	pp	pp	ADJ
fuelectenerg-1427	1646	10	.	.	PUNCT
fuelectenerg-1427	1647	1	66	66	NUM
fuelectenerg-1427	1647	2	-	-	SYM
fuelectenerg-1427	1647	3	81	81	NUM
fuelectenerg-1427	1647	4	.	.	PUNCT
fuelectenerg-1427	1648	1	[	[	X
fuelectenerg-1427	1648	2	32	32	NUM
fuelectenerg-1427	1648	3	]	]	PUNCT
fuelectenerg-1427	1648	4	i.	i.	NOUN
fuelectenerg-1427	1648	5	zhegalkin	zhegalkin	PROPN
fuelectenerg-1427	1648	6	,	,	PUNCT
fuelectenerg-1427	1648	7	"	"	PUNCT
fuelectenerg-1427	1648	8	arithmetic	arithmetic	ADJ
fuelectenerg-1427	1648	9	representations	representation	NOUN
fuelectenerg-1427	1648	10	for	for	ADP
fuelectenerg-1427	1648	11	symbolic	symbolic	ADJ
fuelectenerg-1427	1648	12	logic	logic	NOUN
fuelectenerg-1427	1648	13	,	,	PUNCT
fuelectenerg-1427	1648	14	"	"	PUNCT
fuelectenerg-1427	1648	15	math	math	NOUN
fuelectenerg-1427	1648	16	.	.	PUNCT
fuelectenerg-1427	1649	1	sb	sb	PROPN
fuelectenerg-1427	1649	2	.	.	PROPN
fuelectenerg-1427	1649	3	,	,	PUNCT
fuelectenerg-1427	1649	4	vol	vol	NOUN
fuelectenerg-1427	1649	5	.	.	PROPN
fuelectenerg-1427	1649	6	35	35	NUM
fuelectenerg-1427	1649	7	,	,	PUNCT
fuelectenerg-1427	1650	1	pp	pp	ADJ
fuelectenerg-1427	1650	2	.	.	PUNCT
fuelectenerg-1427	1651	1	311	311	NUM
fuelectenerg-1427	1651	2	-	-	SYM
fuelectenerg-1427	1651	3	377	377	NUM
fuelectenerg-1427	1651	4	,	,	PUNCT
fuelectenerg-1427	1651	5	1928	1928	NUM
fuelectenerg-1427	1651	6	.	.	PUNCT
fuelectenerg-1427	1652	1	[	[	X
fuelectenerg-1427	1652	2	33	33	NUM
fuelectenerg-1427	1652	3	]	]	PUNCT
fuelectenerg-1427	1652	4	a.	a.	NOUN
fuelectenerg-1427	1652	5	n.	n.	PROPN
fuelectenerg-1427	1652	6	al	al	PROPN
fuelectenerg-1427	1652	7	-	-	PUNCT
fuelectenerg-1427	1652	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1652	9	,	,	PUNCT
fuelectenerg-1427	1652	10	"	"	PUNCT
fuelectenerg-1427	1652	11	carbon	carbon	NOUN
fuelectenerg-1427	1652	12	nano	nano	NOUN
fuelectenerg-1427	1652	13	tube	tube	NOUN
fuelectenerg-1427	1652	14	(	(	PUNCT
fuelectenerg-1427	1652	15	cnt	cnt	PROPN
fuelectenerg-1427	1652	16	)	)	PUNCT
fuelectenerg-1427	1652	17	multiplexers	multiplexer	NOUN
fuelectenerg-1427	1652	18	for	for	ADP
fuelectenerg-1427	1652	19	multiple	multiple	ADV
fuelectenerg-1427	1652	20	-	-	PUNCT
fuelectenerg-1427	1652	21	valued	value	VERB
fuelectenerg-1427	1652	22	computing	computing	NOUN
fuelectenerg-1427	1652	23	,	,	PUNCT
fuelectenerg-1427	1652	24	"	"	PUNCT
fuelectenerg-1427	1652	25	facta	facta	PROPN
fuelectenerg-1427	1652	26	universitatis	universitatis	PROPN
fuelectenerg-1427	1652	27	electronics	electronic	NOUN
fuelectenerg-1427	1652	28	and	and	CCONJ
fuelectenerg-1427	1652	29	energetics	energetic	NOUN
fuelectenerg-1427	1652	30	,	,	PUNCT
fuelectenerg-1427	1652	31	vol	vol	NOUN
fuelectenerg-1427	1652	32	.	.	PROPN
fuelectenerg-1427	1652	33	20	20	NUM
fuelectenerg-1427	1652	34	,	,	PUNCT
fuelectenerg-1427	1652	35	no	no	INTJ
fuelectenerg-1427	1652	36	.	.	NOUN
fuelectenerg-1427	1652	37	2	2	NUM
fuelectenerg-1427	1652	38	,	,	PUNCT
fuelectenerg-1427	1652	39	pp	pp	ADJ
fuelectenerg-1427	1652	40	.	.	PUNCT
fuelectenerg-1427	1653	1	175	175	NUM
fuelectenerg-1427	1653	2	186	186	NUM
fuelectenerg-1427	1653	3	,	,	PUNCT
fuelectenerg-1427	1653	4	2007	2007	NUM
fuelectenerg-1427	1653	5	.	.	PUNCT
fuelectenerg-1427	1654	1	[	[	X
fuelectenerg-1427	1654	2	34	34	NUM
fuelectenerg-1427	1654	3	]	]	PUNCT
fuelectenerg-1427	1654	4	a.	a.	PROPN
fuelectenerg-1427	1654	5	n.	n.	PROPN
fuelectenerg-1427	1654	6	al	al	PROPN
fuelectenerg-1427	1654	7	-	-	PUNCT
fuelectenerg-1427	1654	8	rabadi	rabadi	PROPN
fuelectenerg-1427	1654	9	,	,	PUNCT
fuelectenerg-1427	1654	10	"	"	PUNCT
fuelectenerg-1427	1654	11	closed	closed	ADJ
fuelectenerg-1427	1654	12	-	-	PUNCT
fuelectenerg-1427	1654	13	system	system	NOUN
fuelectenerg-1427	1654	14	quantum	quantum	ADJ
fuelectenerg-1427	1654	15	logic	logic	NOUN
fuelectenerg-1427	1654	16	network	network	NOUN
fuelectenerg-1427	1654	17	implementation	implementation	NOUN
fuelectenerg-1427	1654	18	of	of	ADP
fuelectenerg-1427	1654	19	the	the	DET
fuelectenerg-1427	1654	20	viterbi	viterbi	ADJ
fuelectenerg-1427	1654	21	algorithm	algorithm	NOUN
fuelectenerg-1427	1654	22	,	,	PUNCT
fuelectenerg-1427	1654	23	"	"	PUNCT
fuelectenerg-1427	1654	24	facta	facta	PROPN
fuelectenerg-1427	1654	25	universitatis	universitatis	PROPN
fuelectenerg-1427	1654	26	electronics	electronic	NOUN
fuelectenerg-1427	1654	27	and	and	CCONJ
fuelectenerg-1427	1654	28	energetics	energetic	NOUN
fuelectenerg-1427	1654	29	,	,	PUNCT
fuelectenerg-1427	1654	30	vol	vol	NOUN
fuelectenerg-1427	1654	31	.	.	PROPN
fuelectenerg-1427	1655	1	22	22	NUM
fuelectenerg-1427	1655	2	,	,	PUNCT
fuelectenerg-1427	1655	3	no	no	INTJ
fuelectenerg-1427	1655	4	.	.	NOUN
fuelectenerg-1427	1655	5	1	1	NUM
fuelectenerg-1427	1655	6	,	,	PUNCT
fuelectenerg-1427	1655	7	pp	pp	ADJ
fuelectenerg-1427	1655	8	.	.	PUNCT
fuelectenerg-1427	1656	1	1	1	NUM
fuelectenerg-1427	1656	2	33	33	NUM
fuelectenerg-1427	1656	3	,	,	PUNCT
fuelectenerg-1427	1656	4	2009	2009	NUM
fuelectenerg-1427	1656	5	.	.	PUNCT
fuelectenerg-1427	1657	1	118	118	NUM