id	sid	tid	token	lemma	pos
fuelectenerg-1426	1	1	facta	facta	PROPN
fuelectenerg-1426	1	2	universitatis	universitatis	PROPN
fuelectenerg-1426	1	3	series	series	NOUN
fuelectenerg-1426	1	4	:	:	PUNCT
fuelectenerg-1426	1	5	electronics	electronic	NOUN
fuelectenerg-1426	1	6	and	and	CCONJ
fuelectenerg-1426	1	7	energetics	energetics	NOUN
fuelectenerg-1426	1	8	vol	vol	NOUN
fuelectenerg-1426	1	9	.	.	PROPN
fuelectenerg-1426	1	10	29	29	NUM
fuelectenerg-1426	1	11	,	,	PUNCT
fuelectenerg-1426	1	12	no	no	DET
fuelectenerg-1426	1	13	4	4	NUM
fuelectenerg-1426	1	14	,	,	PUNCT
fuelectenerg-1426	1	15	december	december	PROPN
fuelectenerg-1426	1	16	2016	2016	NUM
fuelectenerg-1426	1	17	,	,	PUNCT
fuelectenerg-1426	1	18	pp	pp	ADJ
fuelectenerg-1426	1	19	.	.	PUNCT
fuelectenerg-1426	2	1	701	701	NUM
fuelectenerg-1426	2	2	720	720	NUM
fuelectenerg-1426	2	3	doi	doi	NOUN
fuelectenerg-1426	2	4	:	:	PUNCT
fuelectenerg-1426	2	5	10.2298	10.2298	NUM
fuelectenerg-1426	2	6	/	/	SYM
fuelectenerg-1426	2	7	fuee1604701a	fuee1604701a	PROPN
fuelectenerg-1426	2	8	anas	anas	PROPN
fuelectenerg-1426	2	9	n.	n.	PROPN
fuelectenerg-1426	2	10	al	al	PROPN
fuelectenerg-1426	2	11	-	-	PROPN
fuelectenerg-1426	2	12	rabadi1,2	rabadi1,2	PROPN
fuelectenerg-1426	2	13	received	receive	VERB
fuelectenerg-1426	2	14	november	november	PROPN
fuelectenerg-1426	2	15	28	28	NUM
fuelectenerg-1426	2	16	,	,	PUNCT
fuelectenerg-1426	2	17	2015	2015	NUM
fuelectenerg-1426	2	18	;	;	PUNCT
fuelectenerg-1426	2	19	received	receive	VERB
fuelectenerg-1426	2	20	in	in	ADP
fuelectenerg-1426	2	21	revised	revise	VERB
fuelectenerg-1426	2	22	form	form	NOUN
fuelectenerg-1426	2	23	april	april	PROPN
fuelectenerg-1426	2	24	13	13	NUM
fuelectenerg-1426	2	25	,	,	PUNCT
fuelectenerg-1426	2	26	2016	2016	NUM
fuelectenerg-1426	2	27	corresponding	correspond	VERB
fuelectenerg-1426	2	28	author	author	NOUN
fuelectenerg-1426	2	29	:	:	PUNCT
fuelectenerg-1426	2	30	anas	anas	PROPN
fuelectenerg-1426	2	31	n.	n.	PROPN
fuelectenerg-1426	2	32	al	al	PROPN
fuelectenerg-1426	2	33	-	-	PUNCT
fuelectenerg-1426	2	34	rabadi	rabadi	PROPN
fuelectenerg-1426	2	35	electrical	electrical	ADJ
fuelectenerg-1426	2	36	engineering	engineering	NOUN
fuelectenerg-1426	2	37	department	department	PROPN
fuelectenerg-1426	2	38	,	,	PUNCT
fuelectenerg-1426	2	39	philadelphia	philadelphia	PROPN
fuelectenerg-1426	2	40	university	university	PROPN
fuelectenerg-1426	2	41	,	,	PUNCT
fuelectenerg-1426	2	42	jordan	jordan	PROPN
fuelectenerg-1426	2	43	&	&	CCONJ
fuelectenerg-1426	2	44	computer	computer	PROPN
fuelectenerg-1426	2	45	engineering	engineering	PROPN
fuelectenerg-1426	2	46	department	department	PROPN
fuelectenerg-1426	2	47	,	,	PUNCT
fuelectenerg-1426	2	48	the	the	DET
fuelectenerg-1426	2	49	university	university	PROPN
fuelectenerg-1426	2	50	of	of	ADP
fuelectenerg-1426	2	51	jordan	jordan	PROPN
fuelectenerg-1426	2	52	,	,	PUNCT
fuelectenerg-1426	2	53	amman	amman	PROPN
fuelectenerg-1426	2	54	-	-	PUNCT
fuelectenerg-1426	2	55	jordan	jordan	PROPN
fuelectenerg-1426	2	56	(	(	PUNCT
fuelectenerg-1426	2	57	email	email	NOUN
fuelectenerg-1426	2	58	:	:	PUNCT
fuelectenerg-1426	2	59	alrabadi@yahoo.com	alrabadi@yahoo.com	X
fuelectenerg-1426	2	60	)	)	PUNCT
fuelectenerg-1426	2	61	facta	facta	PROPN
fuelectenerg-1426	2	62	universitatis	universitatis	PROPN
fuelectenerg-1426	2	63	series	series	NOUN
fuelectenerg-1426	2	64	:	:	PUNCT
fuelectenerg-1426	2	65	electronics	electronic	NOUN
fuelectenerg-1426	2	66	and	and	CCONJ
fuelectenerg-1426	2	67	energetics	energetics	NOUN
fuelectenerg-1426	2	68	vol	vol	NOUN
fuelectenerg-1426	2	69	.	.	PUNCT
fuelectenerg-1426	3	1	28	28	NUM
fuelectenerg-1426	3	2	,	,	PUNCT
fuelectenerg-1426	3	3	no	no	DET
fuelectenerg-1426	3	4	4	4	NUM
fuelectenerg-1426	3	5	,	,	PUNCT
fuelectenerg-1426	3	6	december	december	PROPN
fuelectenerg-1426	3	7	2015	2015	NUM
fuelectenerg-1426	3	8	,	,	PUNCT
fuelectenerg-1426	3	9	pp	pp	ADJ
fuelectenerg-1426	3	10	.	.	PUNCT
fuelectenerg-1426	4	1	507	507	NUM
fuelectenerg-1426	4	2	525	525	NUM
fuelectenerg-1426	4	3	doi	doi	NOUN
fuelectenerg-1426	4	4	:	:	PUNCT
fuelectenerg-1426	4	5	10.2298	10.2298	NUM
fuelectenerg-1426	4	6	/	/	SYM
fuelectenerg-1426	4	7	fuee1504507s	fuee1504507	VERB
fuelectenerg-1426	4	8	horizontal	horizontal	ADJ
fuelectenerg-1426	4	9	current	current	ADJ
fuelectenerg-1426	4	10	bipolar	bipolar	ADJ
fuelectenerg-1426	4	11	transistor	transistor	NOUN
fuelectenerg-1426	4	12	(	(	PUNCT
fuelectenerg-1426	4	13	hcbt	hcbt	NOUN
fuelectenerg-1426	4	14	)	)	PUNCT
fuelectenerg-1426	4	15	–	–	PUNCT
fuelectenerg-1426	4	16	a	a	DET
fuelectenerg-1426	4	17	low	low	ADJ
fuelectenerg-1426	4	18	-	-	PUNCT
fuelectenerg-1426	4	19	cost	cost	NOUN
fuelectenerg-1426	4	20	,	,	PUNCT
fuelectenerg-1426	4	21	high	high	ADJ
fuelectenerg-1426	4	22	-	-	PUNCT
fuelectenerg-1426	4	23	performance	performance	NOUN
fuelectenerg-1426	4	24	flexible	flexible	ADJ
fuelectenerg-1426	4	25	bicmos	bicmos	PROPN
fuelectenerg-1426	4	26	technology	technology	PROPN
fuelectenerg-1426	4	27	for	for	ADP
fuelectenerg-1426	4	28	rf	rf	NOUN
fuelectenerg-1426	4	29	communication	communication	NOUN
fuelectenerg-1426	4	30	applications	applications	X
fuelectenerg-1426	4	31	tomislav	tomislav	PROPN
fuelectenerg-1426	4	32	suligoj1	suligoj1	PROPN
fuelectenerg-1426	4	33	,	,	PUNCT
fuelectenerg-1426	4	34	marko	marko	PROPN
fuelectenerg-1426	4	35	koričić1	koričić1	PROPN
fuelectenerg-1426	4	36	,	,	PUNCT
fuelectenerg-1426	4	37	josip	josip	PROPN
fuelectenerg-1426	4	38	žilak1	žilak1	PROPN
fuelectenerg-1426	4	39	,	,	PUNCT
fuelectenerg-1426	4	40	hidenori	hidenori	PROPN
fuelectenerg-1426	4	41	mochizuki2	mochizuki2	PROPN
fuelectenerg-1426	4	42	,	,	PUNCT
fuelectenerg-1426	4	43	so	so	ADV
fuelectenerg-1426	4	44	-	-	PUNCT
fuelectenerg-1426	4	45	ichi	ichi	ADJ
fuelectenerg-1426	4	46	morita2	morita2	NOUN
fuelectenerg-1426	4	47	,	,	PUNCT
fuelectenerg-1426	4	48	katsumi	katsumi	PROPN
fuelectenerg-1426	4	49	shinomura2	shinomura2	PROPN
fuelectenerg-1426	4	50	,	,	PUNCT
fuelectenerg-1426	4	51	hisaya	hisaya	NOUN
fuelectenerg-1426	4	52	imai2	imai2	PROPN
fuelectenerg-1426	4	53	1university	1university	NUM
fuelectenerg-1426	4	54	of	of	ADP
fuelectenerg-1426	4	55	zagreb	zagreb	PROPN
fuelectenerg-1426	4	56	,	,	PUNCT
fuelectenerg-1426	4	57	faculty	faculty	NOUN
fuelectenerg-1426	4	58	of	of	ADP
fuelectenerg-1426	4	59	electrical	electrical	ADJ
fuelectenerg-1426	4	60	engineering	engineering	NOUN
fuelectenerg-1426	4	61	and	and	CCONJ
fuelectenerg-1426	4	62	computing	computing	NOUN
fuelectenerg-1426	4	63	,	,	PUNCT
fuelectenerg-1426	4	64	department	department	NOUN
fuelectenerg-1426	4	65	of	of	ADP
fuelectenerg-1426	4	66	electronics	electronic	NOUN
fuelectenerg-1426	4	67	,	,	PUNCT
fuelectenerg-1426	4	68	microand	microand	NOUN
fuelectenerg-1426	4	69	nano	nano	NOUN
fuelectenerg-1426	4	70	-	-	PUNCT
fuelectenerg-1426	4	71	electronics	electronic	NOUN
fuelectenerg-1426	4	72	laboratory	laboratory	NOUN
fuelectenerg-1426	4	73	,	,	PUNCT
fuelectenerg-1426	4	74	croatia	croatia	PROPN
fuelectenerg-1426	4	75	2asahi	2asahi	PROPN
fuelectenerg-1426	4	76	kasei	kasei	PROPN
fuelectenerg-1426	4	77	microdevices	microdevices	PROPN
fuelectenerg-1426	4	78	co.	co.	PROPN
fuelectenerg-1426	4	79	5	5	NUM
fuelectenerg-1426	4	80	-	-	SYM
fuelectenerg-1426	4	81	4960	4960	NUM
fuelectenerg-1426	4	82	,	,	PUNCT
fuelectenerg-1426	4	83	nobeoka	nobeoka	NOUN
fuelectenerg-1426	4	84	,	,	PUNCT
fuelectenerg-1426	4	85	miyazaki	miyazaki	PROPN
fuelectenerg-1426	4	86	,	,	PUNCT
fuelectenerg-1426	4	87	882	882	NUM
fuelectenerg-1426	4	88	-	-	SYM
fuelectenerg-1426	4	89	0031	0031	NUM
fuelectenerg-1426	4	90	,	,	PUNCT
fuelectenerg-1426	4	91	japan	japan	PROPN
fuelectenerg-1426	4	92	abstract	abstract	PROPN
fuelectenerg-1426	4	93	.	.	PUNCT
fuelectenerg-1426	5	1	in	in	ADP
fuelectenerg-1426	5	2	an	an	DET
fuelectenerg-1426	5	3	overview	overview	NOUN
fuelectenerg-1426	5	4	of	of	ADP
fuelectenerg-1426	5	5	horizontal	horizontal	ADJ
fuelectenerg-1426	5	6	current	current	ADJ
fuelectenerg-1426	5	7	bipolar	bipolar	ADJ
fuelectenerg-1426	5	8	transistor	transistor	NOUN
fuelectenerg-1426	5	9	(	(	PUNCT
fuelectenerg-1426	5	10	hcbt	hcbt	NOUN
fuelectenerg-1426	5	11	)	)	PUNCT
fuelectenerg-1426	5	12	technology	technology	NOUN
fuelectenerg-1426	5	13	,	,	PUNCT
fuelectenerg-1426	5	14	the	the	DET
fuelectenerg-1426	5	15	state	state	NOUN
fuelectenerg-1426	5	16	-	-	PUNCT
fuelectenerg-1426	5	17	of	of	ADP
fuelectenerg-1426	5	18	-	-	PUNCT
fuelectenerg-1426	5	19	the	the	DET
fuelectenerg-1426	5	20	-	-	PUNCT
fuelectenerg-1426	5	21	art	art	NOUN
fuelectenerg-1426	5	22	integrated	integrate	VERB
fuelectenerg-1426	5	23	silicon	silicon	NOUN
fuelectenerg-1426	5	24	bipolar	bipolar	ADJ
fuelectenerg-1426	5	25	transistors	transistor	NOUN
fuelectenerg-1426	5	26	are	be	AUX
fuelectenerg-1426	5	27	described	describe	VERB
fuelectenerg-1426	5	28	which	which	PRON
fuelectenerg-1426	5	29	exhibit	exhibit	VERB
fuelectenerg-1426	5	30	ft	ft	PROPN
fuelectenerg-1426	5	31	and	and	CCONJ
fuelectenerg-1426	5	32	fmax	fmax	PROPN
fuelectenerg-1426	5	33	of	of	ADP
fuelectenerg-1426	5	34	51	51	NUM
fuelectenerg-1426	5	35	ghz	ghz	NOUN
fuelectenerg-1426	5	36	and	and	CCONJ
fuelectenerg-1426	5	37	61	61	NUM
fuelectenerg-1426	5	38	ghz	ghz	NOUN
fuelectenerg-1426	5	39	and	and	CCONJ
fuelectenerg-1426	5	40	ftbvceo	ftbvceo	ADJ
fuelectenerg-1426	5	41	product	product	NOUN
fuelectenerg-1426	5	42	of	of	ADP
fuelectenerg-1426	5	43	173	173	NUM
fuelectenerg-1426	5	44	ghzv	ghzv	NOUN
fuelectenerg-1426	5	45	that	that	PRON
fuelectenerg-1426	5	46	are	be	AUX
fuelectenerg-1426	5	47	among	among	ADP
fuelectenerg-1426	5	48	the	the	DET
fuelectenerg-1426	5	49	highest	high	ADJ
fuelectenerg-1426	5	50	-	-	PUNCT
fuelectenerg-1426	5	51	performance	performance	NOUN
fuelectenerg-1426	5	52	implanted	implant	VERB
fuelectenerg-1426	5	53	-	-	PUNCT
fuelectenerg-1426	5	54	base	base	NOUN
fuelectenerg-1426	5	55	,	,	PUNCT
fuelectenerg-1426	5	56	silicon	silicon	NOUN
fuelectenerg-1426	5	57	bipolar	bipolar	ADJ
fuelectenerg-1426	5	58	transistors	transistor	NOUN
fuelectenerg-1426	5	59	.	.	PUNCT
fuelectenerg-1426	6	1	hbct	hbct	ADV
fuelectenerg-1426	6	2	is	be	AUX
fuelectenerg-1426	6	3	integrated	integrate	VERB
fuelectenerg-1426	6	4	with	with	ADP
fuelectenerg-1426	6	5	cmos	cmos	PROPN
fuelectenerg-1426	6	6	in	in	ADP
fuelectenerg-1426	6	7	a	a	DET
fuelectenerg-1426	6	8	considerably	considerably	ADV
fuelectenerg-1426	6	9	lower	low	ADJ
fuelectenerg-1426	6	10	-	-	PUNCT
fuelectenerg-1426	6	11	cost	cost	NOUN
fuelectenerg-1426	6	12	fabrication	fabrication	NOUN
fuelectenerg-1426	6	13	sequence	sequence	NOUN
fuelectenerg-1426	6	14	as	as	ADP
fuelectenerg-1426	6	15	compared	compare	VERB
fuelectenerg-1426	6	16	to	to	ADP
fuelectenerg-1426	6	17	standard	standard	ADJ
fuelectenerg-1426	6	18	vertical	vertical	ADJ
fuelectenerg-1426	6	19	-	-	PUNCT
fuelectenerg-1426	6	20	current	current	ADJ
fuelectenerg-1426	6	21	bipolar	bipolar	ADJ
fuelectenerg-1426	6	22	transistors	transistor	NOUN
fuelectenerg-1426	6	23	with	with	ADP
fuelectenerg-1426	6	24	only	only	ADV
fuelectenerg-1426	6	25	2	2	NUM
fuelectenerg-1426	6	26	or	or	CCONJ
fuelectenerg-1426	6	27	3	3	NUM
fuelectenerg-1426	6	28	additional	additional	ADJ
fuelectenerg-1426	6	29	masks	mask	NOUN
fuelectenerg-1426	6	30	and	and	CCONJ
fuelectenerg-1426	6	31	fewer	few	ADJ
fuelectenerg-1426	6	32	process	process	NOUN
fuelectenerg-1426	6	33	steps	step	NOUN
fuelectenerg-1426	6	34	.	.	PUNCT
fuelectenerg-1426	7	1	due	due	ADP
fuelectenerg-1426	7	2	to	to	ADP
fuelectenerg-1426	7	3	its	its	PRON
fuelectenerg-1426	7	4	specific	specific	ADJ
fuelectenerg-1426	7	5	structure	structure	NOUN
fuelectenerg-1426	7	6	,	,	PUNCT
fuelectenerg-1426	7	7	the	the	DET
fuelectenerg-1426	7	8	charge	charge	NOUN
fuelectenerg-1426	7	9	sharing	sharing	NOUN
fuelectenerg-1426	7	10	effect	effect	NOUN
fuelectenerg-1426	7	11	can	can	AUX
fuelectenerg-1426	7	12	be	be	AUX
fuelectenerg-1426	7	13	employed	employ	VERB
fuelectenerg-1426	7	14	to	to	PART
fuelectenerg-1426	7	15	increase	increase	VERB
fuelectenerg-1426	7	16	bvceo	bvceo	ADV
fuelectenerg-1426	7	17	without	without	ADP
fuelectenerg-1426	7	18	sacrificing	sacrifice	VERB
fuelectenerg-1426	7	19	ft	ft	X
fuelectenerg-1426	7	20	and	and	CCONJ
fuelectenerg-1426	7	21	fmax	fmax	PROPN
fuelectenerg-1426	7	22	.	.	PUNCT
fuelectenerg-1426	8	1	moreover	moreover	ADV
fuelectenerg-1426	8	2	,	,	PUNCT
fuelectenerg-1426	8	3	the	the	DET
fuelectenerg-1426	8	4	electric	electric	ADJ
fuelectenerg-1426	8	5	field	field	NOUN
fuelectenerg-1426	8	6	can	can	AUX
fuelectenerg-1426	8	7	be	be	AUX
fuelectenerg-1426	8	8	engineered	engineer	VERB
fuelectenerg-1426	8	9	just	just	ADV
fuelectenerg-1426	8	10	by	by	ADP
fuelectenerg-1426	8	11	manipulating	manipulate	VERB
fuelectenerg-1426	8	12	the	the	DET
fuelectenerg-1426	8	13	lithography	lithography	NOUN
fuelectenerg-1426	8	14	masks	mask	NOUN
fuelectenerg-1426	8	15	achieving	achieve	VERB
fuelectenerg-1426	8	16	the	the	DET
fuelectenerg-1426	8	17	high	high	ADJ
fuelectenerg-1426	8	18	-	-	PUNCT
fuelectenerg-1426	8	19	voltage	voltage	NOUN
fuelectenerg-1426	8	20	hcbts	hcbt	NOUN
fuelectenerg-1426	8	21	with	with	ADP
fuelectenerg-1426	8	22	breakdowns	breakdown	NOUN
fuelectenerg-1426	8	23	up	up	ADP
fuelectenerg-1426	8	24	to	to	PART
fuelectenerg-1426	8	25	36	36	NUM
fuelectenerg-1426	8	26	v	v	NOUN
fuelectenerg-1426	8	27	integrated	integrate	VERB
fuelectenerg-1426	8	28	in	in	ADP
fuelectenerg-1426	8	29	the	the	DET
fuelectenerg-1426	8	30	same	same	ADJ
fuelectenerg-1426	8	31	process	process	NOUN
fuelectenerg-1426	8	32	flow	flow	NOUN
fuelectenerg-1426	8	33	with	with	ADP
fuelectenerg-1426	8	34	high	high	ADJ
fuelectenerg-1426	8	35	-	-	PUNCT
fuelectenerg-1426	8	36	speed	speed	NOUN
fuelectenerg-1426	8	37	devices	device	NOUN
fuelectenerg-1426	8	38	,	,	PUNCT
fuelectenerg-1426	8	39	i.e.	i.e.	X
fuelectenerg-1426	8	40	at	at	ADP
fuelectenerg-1426	8	41	zero	zero	NUM
fuelectenerg-1426	8	42	additional	additional	ADJ
fuelectenerg-1426	8	43	costs	cost	NOUN
fuelectenerg-1426	8	44	.	.	PUNCT
fuelectenerg-1426	9	1	double	double	ADJ
fuelectenerg-1426	9	2	-	-	PUNCT
fuelectenerg-1426	9	3	balanced	balanced	ADJ
fuelectenerg-1426	9	4	active	active	ADJ
fuelectenerg-1426	9	5	mixer	mixer	NOUN
fuelectenerg-1426	9	6	circuit	circuit	NOUN
fuelectenerg-1426	9	7	is	be	AUX
fuelectenerg-1426	9	8	designed	design	VERB
fuelectenerg-1426	9	9	and	and	CCONJ
fuelectenerg-1426	9	10	fabricated	fabricate	VERB
fuelectenerg-1426	9	11	in	in	ADP
fuelectenerg-1426	9	12	hcbt	hcbt	NOUN
fuelectenerg-1426	9	13	technology	technology	NOUN
fuelectenerg-1426	9	14	.	.	PUNCT
fuelectenerg-1426	10	1	the	the	DET
fuelectenerg-1426	10	2	maximum	maximum	ADJ
fuelectenerg-1426	10	3	iip3	iip3	NOUN
fuelectenerg-1426	10	4	of	of	ADP
fuelectenerg-1426	10	5	17.7	17.7	NUM
fuelectenerg-1426	10	6	dbm	dbm	NOUN
fuelectenerg-1426	10	7	at	at	ADP
fuelectenerg-1426	10	8	mixer	mixer	PROPN
fuelectenerg-1426	10	9	current	current	ADJ
fuelectenerg-1426	10	10	of	of	ADP
fuelectenerg-1426	10	11	9.2	9.2	NUM
fuelectenerg-1426	10	12	ma	ma	PROPN
fuelectenerg-1426	10	13	and	and	CCONJ
fuelectenerg-1426	10	14	conversion	conversion	NOUN
fuelectenerg-1426	10	15	gain	gain	NOUN
fuelectenerg-1426	10	16	of	of	ADP
fuelectenerg-1426	10	17	-5	-5	INTJ
fuelectenerg-1426	10	18	db	db	PROPN
fuelectenerg-1426	10	19	are	be	AUX
fuelectenerg-1426	10	20	achieved	achieve	VERB
fuelectenerg-1426	10	21	.	.	PUNCT
fuelectenerg-1426	11	1	key	key	ADJ
fuelectenerg-1426	11	2	words	word	NOUN
fuelectenerg-1426	11	3	:	:	PUNCT
fuelectenerg-1426	11	4	bicmos	bicmos	ADJ
fuelectenerg-1426	11	5	technology	technology	NOUN
fuelectenerg-1426	11	6	,	,	PUNCT
fuelectenerg-1426	11	7	bipolar	bipolar	ADJ
fuelectenerg-1426	11	8	transistors	transistor	NOUN
fuelectenerg-1426	11	9	,	,	PUNCT
fuelectenerg-1426	11	10	horizontal	horizontal	ADJ
fuelectenerg-1426	11	11	current	current	ADJ
fuelectenerg-1426	11	12	bipolar	bipolar	ADJ
fuelectenerg-1426	11	13	transistor	transistor	NOUN
fuelectenerg-1426	11	14	,	,	PUNCT
fuelectenerg-1426	11	15	radio	radio	NOUN
fuelectenerg-1426	11	16	frequency	frequency	NOUN
fuelectenerg-1426	11	17	integrated	integrate	VERB
fuelectenerg-1426	11	18	circuits	circuit	NOUN
fuelectenerg-1426	11	19	,	,	PUNCT
fuelectenerg-1426	11	20	mixer	mixer	NOUN
fuelectenerg-1426	11	21	,	,	PUNCT
fuelectenerg-1426	11	22	high	high	ADJ
fuelectenerg-1426	11	23	-	-	PUNCT
fuelectenerg-1426	11	24	voltage	voltage	NOUN
fuelectenerg-1426	11	25	bipolar	bipolar	ADJ
fuelectenerg-1426	11	26	transistors	transistor	NOUN
fuelectenerg-1426	11	27	.	.	PUNCT
fuelectenerg-1426	12	1	1	1	X
fuelectenerg-1426	12	2	.	.	X
fuelectenerg-1426	12	3	introduction	introduction	NOUN
fuelectenerg-1426	12	4	in	in	ADP
fuelectenerg-1426	12	5	the	the	DET
fuelectenerg-1426	12	6	highly	highly	ADV
fuelectenerg-1426	12	7	competitive	competitive	ADJ
fuelectenerg-1426	12	8	wireless	wireless	ADJ
fuelectenerg-1426	12	9	communication	communication	NOUN
fuelectenerg-1426	12	10	markets	market	NOUN
fuelectenerg-1426	12	11	,	,	PUNCT
fuelectenerg-1426	12	12	the	the	DET
fuelectenerg-1426	12	13	rf	rf	ADJ
fuelectenerg-1426	12	14	circuits	circuit	NOUN
fuelectenerg-1426	12	15	and	and	CCONJ
fuelectenerg-1426	12	16	systems	system	NOUN
fuelectenerg-1426	12	17	are	be	AUX
fuelectenerg-1426	12	18	fabricated	fabricate	VERB
fuelectenerg-1426	12	19	in	in	ADP
fuelectenerg-1426	12	20	the	the	DET
fuelectenerg-1426	12	21	technologies	technology	NOUN
fuelectenerg-1426	12	22	that	that	PRON
fuelectenerg-1426	12	23	are	be	AUX
fuelectenerg-1426	12	24	very	very	ADV
fuelectenerg-1426	12	25	cost	cost	NOUN
fuelectenerg-1426	12	26	-	-	PUNCT
fuelectenerg-1426	12	27	sensitive	sensitive	ADJ
fuelectenerg-1426	12	28	.	.	PUNCT
fuelectenerg-1426	13	1	in	in	ADP
fuelectenerg-1426	13	2	order	order	NOUN
fuelectenerg-1426	13	3	to	to	PART
fuelectenerg-1426	13	4	minimize	minimize	VERB
fuelectenerg-1426	13	5	the	the	DET
fuelectenerg-1426	13	6	fabrication	fabrication	NOUN
fuelectenerg-1426	13	7	costs	cost	NOUN
fuelectenerg-1426	13	8	,	,	PUNCT
fuelectenerg-1426	13	9	the	the	DET
fuelectenerg-1426	13	10	sub-10	sub-10	NUM
fuelectenerg-1426	13	11	ghz	ghz	NOUN
fuelectenerg-1426	13	12	applications	application	NOUN
fuelectenerg-1426	13	13	can	can	AUX
fuelectenerg-1426	13	14	be	be	AUX
fuelectenerg-1426	13	15	processed	process	VERB
fuelectenerg-1426	13	16	by	by	ADP
fuelectenerg-1426	13	17	using	use	VERB
fuelectenerg-1426	13	18	the	the	DET
fuelectenerg-1426	13	19	high	high	ADJ
fuelectenerg-1426	13	20	-	-	PUNCT
fuelectenerg-1426	13	21	volume	volume	NOUN
fuelectenerg-1426	13	22	silicon	silicon	NOUN
fuelectenerg-1426	13	23	technologies	technology	NOUN
fuelectenerg-1426	13	24	.	.	PUNCT
fuelectenerg-1426	14	1	it	it	PRON
fuelectenerg-1426	14	2	has	have	AUX
fuelectenerg-1426	14	3	been	be	AUX
fuelectenerg-1426	14	4	identified	identify	VERB
fuelectenerg-1426	14	5	that	that	SCONJ
fuelectenerg-1426	14	6	the	the	DET
fuelectenerg-1426	14	7	optimum	optimum	ADJ
fuelectenerg-1426	14	8	solution	solution	NOUN
fuelectenerg-1426	14	9	might	might	AUX
fuelectenerg-1426	14	10	received	receive	VERB
fuelectenerg-1426	14	11	march	march	PROPN
fuelectenerg-1426	14	12	9	9	NUM
fuelectenerg-1426	14	13	,	,	PUNCT
fuelectenerg-1426	14	14	2015	2015	NUM
fuelectenerg-1426	14	15	corresponding	correspond	VERB
fuelectenerg-1426	14	16	author	author	NOUN
fuelectenerg-1426	14	17	:	:	PUNCT
fuelectenerg-1426	14	18	tomislav	tomislav	PROPN
fuelectenerg-1426	14	19	suligoj	suligoj	PROPN
fuelectenerg-1426	14	20	university	university	PROPN
fuelectenerg-1426	14	21	of	of	ADP
fuelectenerg-1426	14	22	zagreb	zagreb	PROPN
fuelectenerg-1426	14	23	,	,	PUNCT
fuelectenerg-1426	14	24	faculty	faculty	NOUN
fuelectenerg-1426	14	25	of	of	ADP
fuelectenerg-1426	14	26	electrical	electrical	ADJ
fuelectenerg-1426	14	27	engineering	engineering	NOUN
fuelectenerg-1426	14	28	and	and	CCONJ
fuelectenerg-1426	14	29	computing	computing	NOUN
fuelectenerg-1426	14	30	,	,	PUNCT
fuelectenerg-1426	14	31	department	department	NOUN
fuelectenerg-1426	14	32	of	of	ADP
fuelectenerg-1426	14	33	electronics	electronic	NOUN
fuelectenerg-1426	14	34	,	,	PUNCT
fuelectenerg-1426	14	35	microand	microand	NOUN
fuelectenerg-1426	14	36	nano	nano	NOUN
fuelectenerg-1426	14	37	-	-	PUNCT
fuelectenerg-1426	14	38	electronics	electronic	NOUN
fuelectenerg-1426	14	39	laboratory	laboratory	NOUN
fuelectenerg-1426	14	40	,	,	PUNCT
fuelectenerg-1426	14	41	croatia	croatia	PROPN
fuelectenerg-1426	14	42	(	(	PUNCT
fuelectenerg-1426	14	43	e	e	NOUN
fuelectenerg-1426	14	44	-	-	NOUN
fuelectenerg-1426	14	45	mail	mail	NOUN
fuelectenerg-1426	14	46	:	:	PUNCT
fuelectenerg-1426	14	47	tom@zemris.fer.hr	tom@zemris.fer.hr	X
fuelectenerg-1426	14	48	)	)	PUNCT
fuelectenerg-1426	14	49	facta	facta	NOUN
fuelectenerg-1426	14	50	universitatis	universitatis	PROPN
fuelectenerg-1426	14	51	,	,	PUNCT
fuelectenerg-1426	14	52	series	series	NOUN
fuelectenerg-1426	14	53	:	:	PUNCT
fuelectenerg-1426	14	54	electronics	electronic	NOUN
fuelectenerg-1426	14	55	and	and	CCONJ
fuelectenerg-1426	14	56	energetics	energetics	NOUN
fuelectenerg-1426	14	57	vol	vol	NOUN
fuelectenerg-1426	14	58	.	.	PUNCT
fuelectenerg-1426	15	1	22	22	NUM
fuelectenerg-1426	15	2	,	,	PUNCT
fuelectenerg-1426	15	3	no	no	INTJ
fuelectenerg-1426	15	4	.	.	NOUN
fuelectenerg-1426	15	5	4	4	NUM
fuelectenerg-1426	15	6	,	,	PUNCT
fuelectenerg-1426	15	7	december	december	PROPN
fuelectenerg-1426	15	8	2016	2016	NUM
fuelectenerg-1426	15	9	,	,	PUNCT
fuelectenerg-1426	15	10	100	100	NUM
fuelectenerg-1426	15	11	-	-	SYM
fuelectenerg-1426	15	12	118	118	NUM
fuelectenerg-1426	15	13	udk	udk	ADJ
fuelectenerg-1426	15	14	:	:	PUNCT
fuelectenerg-1426	15	15	doi	doi	NOUN
fuelectenerg-1426	15	16	:	:	PUNCT
fuelectenerg-1426	15	17	multi	multi	ADJ
fuelectenerg-1426	15	18	-	-	ADJ
fuelectenerg-1426	15	19	valued	value	VERB
fuelectenerg-1426	15	20	galois	galois	PROPN
fuelectenerg-1426	15	21	shannon	shannon	PROPN
fuelectenerg-1426	15	22	davio	davio	PROPN
fuelectenerg-1426	15	23	trees	tree	NOUN
fuelectenerg-1426	15	24	and	and	CCONJ
fuelectenerg-1426	15	25	their	their	PRON
fuelectenerg-1426	15	26	complexity	complexity	NOUN
fuelectenerg-1426	15	27	anas	anas	PROPN
fuelectenerg-1426	15	28	n.	n.	PROPN
fuelectenerg-1426	15	29	al	al	PROPN
fuelectenerg-1426	15	30	-	-	PUNCT
fuelectenerg-1426	15	31	rabadi	rabadi	PROPN
fuelectenerg-1426	15	32	abstract	abstract	NOUN
fuelectenerg-1426	15	33	:	:	PUNCT
fuelectenerg-1426	15	34	the	the	DET
fuelectenerg-1426	15	35	idea	idea	NOUN
fuelectenerg-1426	15	36	of	of	ADP
fuelectenerg-1426	15	37	shannon	shannon	NOUN
fuelectenerg-1426	15	38	-	-	PUNCT
fuelectenerg-1426	15	39	davio	davio	NOUN
fuelectenerg-1426	15	40	(	(	PUNCT
fuelectenerg-1426	15	41	s	s	NOUN
fuelectenerg-1426	15	42	/	/	SYM
fuelectenerg-1426	15	43	d	d	NOUN
fuelectenerg-1426	15	44	)	)	PUNCT
fuelectenerg-1426	15	45	trees	tree	NOUN
fuelectenerg-1426	15	46	for	for	ADP
fuelectenerg-1426	15	47	binary	binary	ADJ
fuelectenerg-1426	15	48	logic	logic	NOUN
fuelectenerg-1426	15	49	is	be	AUX
fuelectenerg-1426	15	50	a	a	DET
fuelectenerg-1426	15	51	general	general	ADJ
fuelectenerg-1426	15	52	concept	concept	NOUN
fuelectenerg-1426	15	53	that	that	PRON
fuelectenerg-1426	15	54	found	find	VERB
fuelectenerg-1426	15	55	applications	application	NOUN
fuelectenerg-1426	15	56	in	in	ADP
fuelectenerg-1426	15	57	the	the	DET
fuelectenerg-1426	15	58	sum	sum	NOUN
fuelectenerg-1426	15	59	-	-	PUNCT
fuelectenerg-1426	15	60	of	of	ADP
fuelectenerg-1426	15	61	-	-	PUNCT
fuelectenerg-1426	15	62	product	product	NOUN
fuelectenerg-1426	15	63	(	(	PUNCT
fuelectenerg-1426	15	64	sop	sop	PROPN
fuelectenerg-1426	15	65	)	)	PUNCT
fuelectenerg-1426	15	66	minimization	minimization	NOUN
fuelectenerg-1426	15	67	and	and	CCONJ
fuelectenerg-1426	15	68	the	the	DET
fuelectenerg-1426	15	69	generation	generation	NOUN
fuelectenerg-1426	15	70	of	of	ADP
fuelectenerg-1426	15	71	new	new	ADJ
fuelectenerg-1426	15	72	diagrams	diagram	NOUN
fuelectenerg-1426	15	73	and	and	CCONJ
fuelectenerg-1426	15	74	canonical	canonical	ADJ
fuelectenerg-1426	15	75	forms	form	NOUN
fuelectenerg-1426	15	76	.	.	PUNCT
fuelectenerg-1426	16	1	extended	extend	VERB
fuelectenerg-1426	16	2	s	s	PROPN
fuelectenerg-1426	16	3	/	/	SYM
fuelectenerg-1426	16	4	d	d	NOUN
fuelectenerg-1426	16	5	trees	tree	NOUN
fuelectenerg-1426	16	6	are	be	AUX
fuelectenerg-1426	16	7	used	use	VERB
fuelectenerg-1426	16	8	to	to	PART
fuelectenerg-1426	16	9	generate	generate	VERB
fuelectenerg-1426	16	10	forms	form	NOUN
fuelectenerg-1426	16	11	that	that	PRON
fuelectenerg-1426	16	12	include	include	VERB
fuelectenerg-1426	16	13	a	a	DET
fuelectenerg-1426	16	14	minimum	minimum	ADJ
fuelectenerg-1426	16	15	galois	galois	NOUN
fuelectenerg-1426	16	16	field	field	NOUN
fuelectenerg-1426	16	17	sum	sum	NOUN
fuelectenerg-1426	16	18	-	-	PUNCT
fuelectenerg-1426	16	19	of	of	ADP
fuelectenerg-1426	16	20	-	-	PUNCT
fuelectenerg-1426	16	21	products	product	NOUN
fuelectenerg-1426	16	22	(	(	PUNCT
fuelectenerg-1426	16	23	gfsop	gfsop	NOUN
fuelectenerg-1426	16	24	)	)	PUNCT
fuelectenerg-1426	16	25	forms	form	NOUN
fuelectenerg-1426	16	26	.	.	PUNCT
fuelectenerg-1426	17	1	since	since	SCONJ
fuelectenerg-1426	17	2	there	there	PRON
fuelectenerg-1426	17	3	exist	exist	VERB
fuelectenerg-1426	17	4	many	many	ADJ
fuelectenerg-1426	17	5	applications	application	NOUN
fuelectenerg-1426	17	6	of	of	ADP
fuelectenerg-1426	17	7	galois	galois	PROPN
fuelectenerg-1426	17	8	field	field	NOUN
fuelectenerg-1426	17	9	of	of	ADP
fuelectenerg-1426	17	10	quaternary	quaternary	ADJ
fuelectenerg-1426	17	11	radix	radix	NOUN
fuelectenerg-1426	17	12	especially	especially	ADV
fuelectenerg-1426	17	13	that	that	DET
fuelectenerg-1426	17	14	gf(4	gf(4	NOUN
fuelectenerg-1426	17	15	)	)	PUNCT
fuelectenerg-1426	17	16	is	be	AUX
fuelectenerg-1426	17	17	considered	consider	VERB
fuelectenerg-1426	17	18	as	as	ADP
fuelectenerg-1426	17	19	an	an	DET
fuelectenerg-1426	17	20	important	important	ADJ
fuelectenerg-1426	17	21	extension	extension	NOUN
fuelectenerg-1426	17	22	of	of	ADP
fuelectenerg-1426	17	23	gf(2	gf(2	PROPN
fuelectenerg-1426	17	24	)	)	PUNCT
fuelectenerg-1426	17	25	,	,	PUNCT
fuelectenerg-1426	17	26	the	the	DET
fuelectenerg-1426	17	27	extension	extension	NOUN
fuelectenerg-1426	17	28	of	of	ADP
fuelectenerg-1426	17	29	the	the	DET
fuelectenerg-1426	17	30	s	s	PROPN
fuelectenerg-1426	17	31	/	/	SYM
fuelectenerg-1426	17	32	d	d	NOUN
fuelectenerg-1426	17	33	trees	tree	NOUN
fuelectenerg-1426	17	34	to	to	ADP
fuelectenerg-1426	17	35	gf(4	gf(4	NOUN
fuelectenerg-1426	17	36	)	)	PUNCT
fuelectenerg-1426	17	37	is	be	AUX
fuelectenerg-1426	17	38	presented	present	VERB
fuelectenerg-1426	17	39	here	here	ADV
fuelectenerg-1426	17	40	.	.	PUNCT
fuelectenerg-1426	18	1	a	a	DET
fuelectenerg-1426	18	2	general	general	ADJ
fuelectenerg-1426	18	3	formula	formula	NOUN
fuelectenerg-1426	18	4	to	to	PART
fuelectenerg-1426	18	5	calculate	calculate	VERB
fuelectenerg-1426	18	6	the	the	DET
fuelectenerg-1426	18	7	number	number	NOUN
fuelectenerg-1426	18	8	of	of	ADP
fuelectenerg-1426	18	9	inclusive	inclusive	ADJ
fuelectenerg-1426	18	10	forms	form	NOUN
fuelectenerg-1426	18	11	(	(	PUNCT
fuelectenerg-1426	18	12	ifs	ifs	PROPN
fuelectenerg-1426	18	13	)	)	PUNCT
fuelectenerg-1426	18	14	per	per	ADP
fuelectenerg-1426	18	15	variable	variable	ADJ
fuelectenerg-1426	18	16	order	order	NOUN
fuelectenerg-1426	18	17	for	for	ADP
fuelectenerg-1426	18	18	an	an	DET
fuelectenerg-1426	18	19	arbitrary	arbitrary	ADJ
fuelectenerg-1426	18	20	galois	galois	NOUN
fuelectenerg-1426	18	21	field	field	NOUN
fuelectenerg-1426	18	22	radix	radix	NOUN
fuelectenerg-1426	18	23	and	and	CCONJ
fuelectenerg-1426	18	24	arbitrary	arbitrary	ADJ
fuelectenerg-1426	18	25	number	number	NOUN
fuelectenerg-1426	18	26	of	of	ADP
fuelectenerg-1426	18	27	variables	variable	NOUN
fuelectenerg-1426	18	28	is	be	AUX
fuelectenerg-1426	18	29	derived	derive	VERB
fuelectenerg-1426	18	30	and	and	CCONJ
fuelectenerg-1426	18	31	introduced	introduce	VERB
fuelectenerg-1426	18	32	.	.	PUNCT
fuelectenerg-1426	19	1	a	a	DET
fuelectenerg-1426	19	2	new	new	ADJ
fuelectenerg-1426	19	3	fast	fast	ADJ
fuelectenerg-1426	19	4	method	method	NOUN
fuelectenerg-1426	19	5	to	to	PART
fuelectenerg-1426	19	6	count	count	VERB
fuelectenerg-1426	19	7	the	the	DET
fuelectenerg-1426	19	8	number	number	NOUN
fuelectenerg-1426	19	9	of	of	ADP
fuelectenerg-1426	19	10	ifs	ifs	PROPN
fuelectenerg-1426	19	11	for	for	ADP
fuelectenerg-1426	19	12	an	an	DET
fuelectenerg-1426	19	13	arbitrary	arbitrary	ADJ
fuelectenerg-1426	19	14	galois	galois	PROPN
fuelectenerg-1426	19	15	radix	radix	NOUN
fuelectenerg-1426	19	16	and	and	CCONJ
fuelectenerg-1426	19	17	functions	function	NOUN
fuelectenerg-1426	19	18	of	of	ADP
fuelectenerg-1426	19	19	two	two	NUM
fuelectenerg-1426	19	20	variables	variable	NOUN
fuelectenerg-1426	19	21	is	be	AUX
fuelectenerg-1426	19	22	also	also	ADV
fuelectenerg-1426	19	23	introduced	introduce	VERB
fuelectenerg-1426	19	24	;	;	PUNCT
fuelectenerg-1426	19	25	the	the	DET
fuelectenerg-1426	19	26	ifn,2	ifn,2	ADJ
fuelectenerg-1426	19	27	triangles	triangle	NOUN
fuelectenerg-1426	19	28	.	.	PUNCT
fuelectenerg-1426	20	1	the	the	DET
fuelectenerg-1426	20	2	results	result	NOUN
fuelectenerg-1426	20	3	introduced	introduce	VERB
fuelectenerg-1426	20	4	in	in	ADP
fuelectenerg-1426	20	5	this	this	DET
fuelectenerg-1426	20	6	work	work	NOUN
fuelectenerg-1426	20	7	can	can	AUX
fuelectenerg-1426	20	8	be	be	AUX
fuelectenerg-1426	20	9	useful	useful	ADJ
fuelectenerg-1426	20	10	for	for	ADP
fuelectenerg-1426	20	11	the	the	DET
fuelectenerg-1426	20	12	creation	creation	NOUN
fuelectenerg-1426	20	13	of	of	ADP
fuelectenerg-1426	20	14	an	an	DET
fuelectenerg-1426	20	15	efficient	efficient	ADJ
fuelectenerg-1426	20	16	gfsop	gfsop	NOUN
fuelectenerg-1426	20	17	minimizer	minimizer	NOUN
fuelectenerg-1426	20	18	for	for	ADP
fuelectenerg-1426	20	19	galois	galois	PROPN
fuelectenerg-1426	20	20	logic	logic	NOUN
fuelectenerg-1426	20	21	and	and	CCONJ
fuelectenerg-1426	20	22	in	in	ADP
fuelectenerg-1426	20	23	other	other	ADJ
fuelectenerg-1426	20	24	applications	application	NOUN
fuelectenerg-1426	20	25	such	such	ADJ
fuelectenerg-1426	20	26	as	as	ADP
fuelectenerg-1426	20	27	in	in	ADP
fuelectenerg-1426	20	28	reversible	reversible	ADJ
fuelectenerg-1426	20	29	logic	logic	NOUN
fuelectenerg-1426	20	30	synthesis	synthesis	NOUN
fuelectenerg-1426	20	31	.	.	PUNCT
fuelectenerg-1426	21	1	keywords	keyword	NOUN
fuelectenerg-1426	21	2	:	:	PUNCT
fuelectenerg-1426	21	3	complexity	complexity	NOUN
fuelectenerg-1426	21	4	,	,	PUNCT
fuelectenerg-1426	21	5	galois	galois	PROPN
fuelectenerg-1426	21	6	field	field	NOUN
fuelectenerg-1426	21	7	sum	sum	NOUN
fuelectenerg-1426	21	8	-	-	PUNCT
fuelectenerg-1426	21	9	of	of	ADP
fuelectenerg-1426	21	10	-	-	PUNCT
fuelectenerg-1426	21	11	product	product	NOUN
fuelectenerg-1426	21	12	(	(	PUNCT
fuelectenerg-1426	21	13	gfsop	gfsop	PROPN
fuelectenerg-1426	21	14	)	)	PUNCT
fuelectenerg-1426	21	15	,	,	PUNCT
fuelectenerg-1426	21	16	galois	galois	PROPN
fuelectenerg-1426	21	17	forms	form	NOUN
fuelectenerg-1426	21	18	,	,	PUNCT
fuelectenerg-1426	21	19	inclusive	inclusive	ADJ
fuelectenerg-1426	21	20	forms	form	NOUN
fuelectenerg-1426	21	21	,	,	PUNCT
fuelectenerg-1426	21	22	multi	multi	ADJ
fuelectenerg-1426	21	23	-	-	ADJ
fuelectenerg-1426	21	24	valued	value	VERB
fuelectenerg-1426	21	25	logic	logic	NOUN
fuelectenerg-1426	21	26	,	,	PUNCT
fuelectenerg-1426	21	27	quaternary	quaternary	ADJ
fuelectenerg-1426	21	28	logic	logic	NOUN
fuelectenerg-1426	21	29	,	,	PUNCT
fuelectenerg-1426	21	30	shannon	shannon	PROPN
fuelectenerg-1426	21	31	-	-	PUNCT
fuelectenerg-1426	21	32	davio	davio	NOUN
fuelectenerg-1426	21	33	(	(	PUNCT
fuelectenerg-1426	21	34	s	s	NOUN
fuelectenerg-1426	21	35	/	/	SYM
fuelectenerg-1426	21	36	d	d	NOUN
fuelectenerg-1426	21	37	)	)	PUNCT
fuelectenerg-1426	21	38	trees	tree	NOUN
fuelectenerg-1426	21	39	.	.	PUNCT
fuelectenerg-1426	22	1	1	1	NUM
fuelectenerg-1426	22	2	introduction	introduction	NOUN
fuelectenerg-1426	22	3	spectral	spectral	ADJ
fuelectenerg-1426	22	4	transforms	transform	VERB
fuelectenerg-1426	22	5	play	play	VERB
fuelectenerg-1426	22	6	an	an	DET
fuelectenerg-1426	22	7	important	important	ADJ
fuelectenerg-1426	22	8	role	role	NOUN
fuelectenerg-1426	22	9	in	in	ADP
fuelectenerg-1426	22	10	the	the	DET
fuelectenerg-1426	22	11	synthesis	synthesis	NOUN
fuelectenerg-1426	22	12	,	,	PUNCT
fuelectenerg-1426	22	13	analysis	analysis	NOUN
fuelectenerg-1426	22	14	,	,	PUNCT
fuelectenerg-1426	22	15	testing	testing	NOUN
fuelectenerg-1426	22	16	,	,	PUNCT
fuelectenerg-1426	22	17	classification	classification	NOUN
fuelectenerg-1426	22	18	,	,	PUNCT
fuelectenerg-1426	22	19	formal	formal	ADJ
fuelectenerg-1426	22	20	verification	verification	NOUN
fuelectenerg-1426	22	21	and	and	CCONJ
fuelectenerg-1426	22	22	simulation	simulation	NOUN
fuelectenerg-1426	22	23	of	of	ADP
fuelectenerg-1426	22	24	logic	logic	NOUN
fuelectenerg-1426	22	25	circuits	circuit	NOUN
fuelectenerg-1426	22	26	and	and	CCONJ
fuelectenerg-1426	22	27	systems	system	NOUN
fuelectenerg-1426	22	28	.	.	PUNCT
fuelectenerg-1426	23	1	dyadic	dyadic	ADJ
fuelectenerg-1426	23	2	families	family	NOUN
fuelectenerg-1426	23	3	of	of	ADP
fuelectenerg-1426	23	4	discrete	discrete	ADJ
fuelectenerg-1426	23	5	transforms	transform	NOUN
fuelectenerg-1426	23	6	;	;	PUNCT
fuelectenerg-1426	23	7	reed	reed	NOUN
fuelectenerg-1426	23	8	-	-	PUNCT
fuelectenerg-1426	23	9	muller	muller	NOUN
fuelectenerg-1426	23	10	and	and	CCONJ
fuelectenerg-1426	23	11	green	green	ADJ
fuelectenerg-1426	23	12	-	-	PUNCT
fuelectenerg-1426	23	13	sasao	sasao	PROPN
fuelectenerg-1426	23	14	hierarchy	hierarchy	NOUN
fuelectenerg-1426	23	15	,	,	PUNCT
fuelectenerg-1426	23	16	walsh	walsh	NOUN
fuelectenerg-1426	23	17	,	,	PUNCT
fuelectenerg-1426	23	18	arithmetic	arithmetic	ADJ
fuelectenerg-1426	23	19	,	,	PUNCT
fuelectenerg-1426	23	20	adding	add	VERB
fuelectenerg-1426	23	21	and	and	CCONJ
fuelectenerg-1426	23	22	haar	haar	PROPN
fuelectenerg-1426	23	23	transforms	transform	VERB
fuelectenerg-1426	23	24	and	and	CCONJ
fuelectenerg-1426	23	25	their	their	PRON
fuelectenerg-1426	23	26	generalizations	generalization	NOUN
fuelectenerg-1426	23	27	to	to	ADP
fuelectenerg-1426	23	28	p	p	NOUN
fuelectenerg-1426	23	29	-	-	PUNCT
fuelectenerg-1426	23	30	adic	adic	ADJ
fuelectenerg-1426	23	31	(	(	PUNCT
fuelectenerg-1426	23	32	multi	multi	ADJ
fuelectenerg-1426	23	33	-	-	ADJ
fuelectenerg-1426	23	34	valued	value	VERB
fuelectenerg-1426	23	35	)	)	PUNCT
fuelectenerg-1426	23	36	transforms	transform	VERB
fuelectenerg-1426	23	37	,	,	PUNCT
fuelectenerg-1426	23	38	have	have	AUX
fuelectenerg-1426	23	39	found	find	VERB
fuelectenerg-1426	23	40	a	a	DET
fuelectenerg-1426	23	41	fruitful	fruitful	ADJ
fuelectenerg-1426	23	42	use	use	NOUN
fuelectenerg-1426	23	43	in	in	ADP
fuelectenerg-1426	23	44	digital	digital	ADJ
fuelectenerg-1426	23	45	system	system	NOUN
fuelectenerg-1426	23	46	design	design	NOUN
fuelectenerg-1426	23	47	[	[	X
fuelectenerg-1426	23	48	1	1	NUM
fuelectenerg-1426	23	49	,	,	PUNCT
fuelectenerg-1426	23	50	2	2	NUM
fuelectenerg-1426	23	51	,	,	PUNCT
fuelectenerg-1426	23	52	6	6	NUM
fuelectenerg-1426	23	53	-	-	SYM
fuelectenerg-1426	23	54	35	35	NUM
fuelectenerg-1426	23	55	]	]	PUNCT
fuelectenerg-1426	23	56	.	.	PUNCT
fuelectenerg-1426	24	1	reed	reed	NOUN
fuelectenerg-1426	24	2	-	-	PUNCT
fuelectenerg-1426	24	3	muller	muller	NOUN
fuelectenerg-1426	24	4	-	-	PUNCT
fuelectenerg-1426	24	5	like	like	ADJ
fuelectenerg-1426	24	6	spectral	spectral	ADJ
fuelectenerg-1426	24	7	transforms	transform	VERB
fuelectenerg-1426	24	8	[	[	X
fuelectenerg-1426	24	9	2	2	NUM
fuelectenerg-1426	24	10	-	-	SYM
fuelectenerg-1426	24	11	6	6	NUM
fuelectenerg-1426	24	12	,	,	PUNCT
fuelectenerg-1426	24	13	12	12	NUM
fuelectenerg-1426	24	14	-	-	SYM
fuelectenerg-1426	24	15	14	14	NUM
fuelectenerg-1426	24	16	,	,	PUNCT
fuelectenerg-1426	24	17	16	16	NUM
fuelectenerg-1426	24	18	-	-	SYM
fuelectenerg-1426	24	19	18	18	NUM
fuelectenerg-1426	24	20	,	,	PUNCT
fuelectenerg-1426	24	21	21	21	NUM
fuelectenerg-1426	24	22	,	,	PUNCT
fuelectenerg-1426	24	23	25	25	NUM
fuelectenerg-1426	24	24	,	,	PUNCT
fuelectenerg-1426	24	25	27	27	NUM
fuelectenerg-1426	24	26	,	,	PUNCT
fuelectenerg-1426	24	27	29	29	NUM
fuelectenerg-1426	24	28	,	,	PUNCT
fuelectenerg-1426	24	29	33	33	NUM
fuelectenerg-1426	24	30	,	,	PUNCT
fuelectenerg-1426	24	31	35	35	NUM
fuelectenerg-1426	24	32	]	]	PUNCT
fuelectenerg-1426	24	33	have	have	AUX
fuelectenerg-1426	24	34	found	find	VERB
fuelectenerg-1426	24	35	a	a	DET
fuelectenerg-1426	24	36	variety	variety	NOUN
fuelectenerg-1426	24	37	of	of	ADP
fuelectenerg-1426	24	38	useful	useful	ADJ
fuelectenerg-1426	24	39	applications	application	NOUN
fuelectenerg-1426	24	40	in	in	ADP
fuelectenerg-1426	24	41	minimizing	minimize	VERB
fuelectenerg-1426	24	42	exclusive	exclusive	ADJ
fuelectenerg-1426	24	43	sum	sum	NOUN
fuelectenerg-1426	24	44	-	-	PUNCT
fuelectenerg-1426	24	45	of	of	ADP
fuelectenerg-1426	24	46	-	-	PUNCT
fuelectenerg-1426	24	47	products	product	NOUN
fuelectenerg-1426	24	48	(	(	PUNCT
fuelectenerg-1426	24	49	esop	esop	PROPN
fuelectenerg-1426	24	50	)	)	PUNCT
fuelectenerg-1426	24	51	and	and	CCONJ
fuelectenerg-1426	24	52	galois	galois	PROPN
fuelectenerg-1426	24	53	field	field	NOUN
fuelectenerg-1426	24	54	sop	sop	PROPN
fuelectenerg-1426	24	55	(	(	PUNCT
fuelectenerg-1426	24	56	gfsop	gfsop	NOUN
fuelectenerg-1426	24	57	)	)	PUNCT
fuelectenerg-1426	24	58	expressions	expression	NOUN
fuelectenerg-1426	24	59	,	,	PUNCT
fuelectenerg-1426	24	60	creation	creation	NOUN
fuelectenerg-1426	24	61	of	of	ADP
fuelectenerg-1426	24	62	new	new	ADJ
fuelectenerg-1426	24	63	forms	form	NOUN
fuelectenerg-1426	24	64	,	,	PUNCT
fuelectenerg-1426	24	65	binary	binary	ADJ
fuelectenerg-1426	24	66	decision	decision	NOUN
fuelectenerg-1426	24	67	diagrams	diagram	NOUN
fuelectenerg-1426	24	68	,	,	PUNCT
fuelectenerg-1426	24	69	spectral	spectral	ADJ
fuelectenerg-1426	24	70	decision	decision	NOUN
fuelectenerg-1426	24	71	diagrams	diagram	NOUN
fuelectenerg-1426	24	72	,	,	PUNCT
fuelectenerg-1426	24	73	regular	regular	ADJ
fuelectenerg-1426	24	74	manuscript	manuscript	NOUN
fuelectenerg-1426	24	75	received	receive	VERB
fuelectenerg-1426	24	76	july	july	PROPN
fuelectenerg-1426	24	77	15	15	NUM
fuelectenerg-1426	24	78	,	,	PUNCT
fuelectenerg-1426	24	79	2015	2015	NUM
fuelectenerg-1426	24	80	;	;	PUNCT
fuelectenerg-1426	24	81	revised	revise	VERB
fuelectenerg-1426	24	82	electrical	electrical	ADJ
fuelectenerg-1426	24	83	engineering	engineering	NOUN
fuelectenerg-1426	24	84	department	department	PROPN
fuelectenerg-1426	24	85	,	,	PUNCT
fuelectenerg-1426	24	86	philadelphia	philadelphia	PROPN
fuelectenerg-1426	24	87	university	university	PROPN
fuelectenerg-1426	24	88	,	,	PUNCT
fuelectenerg-1426	24	89	jordan	jordan	PROPN
fuelectenerg-1426	24	90	&	&	CCONJ
fuelectenerg-1426	24	91	computer	computer	PROPN
fuelectenerg-1426	24	92	engineering	engineering	PROPN
fuelectenerg-1426	24	93	department	department	PROPN
fuelectenerg-1426	24	94	,	,	PUNCT
fuelectenerg-1426	24	95	the	the	DET
fuelectenerg-1426	24	96	university	university	PROPN
fuelectenerg-1426	24	97	of	of	ADP
fuelectenerg-1426	24	98	jordan	jordan	PROPN
fuelectenerg-1426	24	99	,	,	PUNCT
fuelectenerg-1426	24	100	amman	amman	PROPN
fuelectenerg-1426	24	101	-	-	PUNCT
fuelectenerg-1426	24	102	jordan	jordan	PROPN
fuelectenerg-1426	24	103	e	e	PROPN
fuelectenerg-1426	24	104	-	-	NOUN
fuelectenerg-1426	24	105	mail	mail	NOUN
fuelectenerg-1426	24	106	:	:	PUNCT
fuelectenerg-1426	24	107	alrabadi@yahoo.com	alrabadi@yahoo.com	X
fuelectenerg-1426	25	1	this	this	DET
fuelectenerg-1426	25	2	research	research	NOUN
fuelectenerg-1426	25	3	was	be	AUX
fuelectenerg-1426	25	4	performed	perform	VERB
fuelectenerg-1426	25	5	during	during	ADP
fuelectenerg-1426	25	6	sabbatical	sabbatical	ADJ
fuelectenerg-1426	25	7	leave	leave	NOUN
fuelectenerg-1426	25	8	in	in	ADP
fuelectenerg-1426	25	9	2015	2015	NUM
fuelectenerg-1426	25	10	-	-	SYM
fuelectenerg-1426	25	11	2016	2016	NUM
fuelectenerg-1426	25	12	granted	grant	VERB
fuelectenerg-1426	25	13	from	from	ADP
fuelectenerg-1426	25	14	the	the	DET
fuelectenerg-1426	25	15	university	university	NOUN
fuelectenerg-1426	25	16	jordan	jordan	PROPN
fuelectenerg-1426	25	17	and	and	CCONJ
fuelectenerg-1426	25	18	spent	spend	VERB
fuelectenerg-1426	25	19	at	at	ADP
fuelectenerg-1426	25	20	philadelphia	philadelphia	PROPN
fuelectenerg-1426	25	21	university	university	PROPN
fuelectenerg-1426	25	22	101	101	NUM
fuelectenerg-1426	25	23	multi	multi	ADJ
fuelectenerg-1426	25	24	-	-	ADJ
fuelectenerg-1426	25	25	valued	value	VERB
fuelectenerg-1426	25	26	galois	galois	PROPN
fuelectenerg-1426	25	27	shannon	shannon	PROPN
fuelectenerg-1426	25	28	davio	davio	PROPN
fuelectenerg-1426	25	29	trees	tree	NOUN
fuelectenerg-1426	25	30	and	and	CCONJ
fuelectenerg-1426	25	31	their	their	PRON
fuelectenerg-1426	25	32	complexity	complexity	NOUN
fuelectenerg-1426	25	33	1electrical	1electrical	NUM
fuelectenerg-1426	25	34	engineering	engineering	NOUN
fuelectenerg-1426	25	35	department	department	PROPN
fuelectenerg-1426	25	36	,	,	PUNCT
fuelectenerg-1426	25	37	philadelphia	philadelphia	PROPN
fuelectenerg-1426	25	38	university	university	PROPN
fuelectenerg-1426	25	39	,	,	PUNCT
fuelectenerg-1426	25	40	2jordan	2jordan	NUM
fuelectenerg-1426	25	41	&	&	CCONJ
fuelectenerg-1426	25	42	computer	computer	PROPN
fuelectenerg-1426	25	43	engineering	engineering	PROPN
fuelectenerg-1426	25	44	department	department	PROPN
fuelectenerg-1426	25	45	,	,	PUNCT
fuelectenerg-1426	25	46	the	the	DET
fuelectenerg-1426	25	47	university	university	PROPN
fuelectenerg-1426	25	48	of	of	ADP
fuelectenerg-1426	25	49	jordan	jordan	PROPN
fuelectenerg-1426	25	50	,	,	PUNCT
fuelectenerg-1426	25	51	amman	amman	PROPN
fuelectenerg-1426	25	52	-	-	PUNCT
fuelectenerg-1426	25	53	jordan	jordan	PROPN
fuelectenerg-1426	25	54	abstract	abstract	PROPN
fuelectenerg-1426	25	55	.	.	PUNCT
fuelectenerg-1426	26	1	the	the	DET
fuelectenerg-1426	26	2	idea	idea	NOUN
fuelectenerg-1426	26	3	of	of	ADP
fuelectenerg-1426	26	4	shannon	shannon	NOUN
fuelectenerg-1426	26	5	-	-	PUNCT
fuelectenerg-1426	26	6	davio	davio	NOUN
fuelectenerg-1426	26	7	(	(	PUNCT
fuelectenerg-1426	26	8	s	s	NOUN
fuelectenerg-1426	26	9	/	/	SYM
fuelectenerg-1426	26	10	d	d	NOUN
fuelectenerg-1426	26	11	)	)	PUNCT
fuelectenerg-1426	26	12	trees	tree	NOUN
fuelectenerg-1426	26	13	for	for	ADP
fuelectenerg-1426	26	14	binary	binary	ADJ
fuelectenerg-1426	26	15	logic	logic	NOUN
fuelectenerg-1426	26	16	is	be	AUX
fuelectenerg-1426	26	17	a	a	DET
fuelectenerg-1426	26	18	general	general	ADJ
fuelectenerg-1426	26	19	concept	concept	NOUN
fuelectenerg-1426	26	20	that	that	PRON
fuelectenerg-1426	26	21	found	find	VERB
fuelectenerg-1426	26	22	applications	application	NOUN
fuelectenerg-1426	26	23	in	in	ADP
fuelectenerg-1426	26	24	the	the	DET
fuelectenerg-1426	26	25	sum	sum	NOUN
fuelectenerg-1426	26	26	-	-	PUNCT
fuelectenerg-1426	26	27	of	of	ADP
fuelectenerg-1426	26	28	-	-	PUNCT
fuelectenerg-1426	26	29	product	product	NOUN
fuelectenerg-1426	26	30	(	(	PUNCT
fuelectenerg-1426	26	31	sop	sop	PROPN
fuelectenerg-1426	26	32	)	)	PUNCT
fuelectenerg-1426	26	33	minimization	minimization	NOUN
fuelectenerg-1426	26	34	and	and	CCONJ
fuelectenerg-1426	26	35	the	the	DET
fuelectenerg-1426	26	36	generation	generation	NOUN
fuelectenerg-1426	26	37	of	of	ADP
fuelectenerg-1426	26	38	new	new	ADJ
fuelectenerg-1426	26	39	diagrams	diagram	NOUN
fuelectenerg-1426	26	40	and	and	CCONJ
fuelectenerg-1426	26	41	canonical	canonical	ADJ
fuelectenerg-1426	26	42	forms	form	NOUN
fuelectenerg-1426	26	43	.	.	PUNCT
fuelectenerg-1426	27	1	extended	extend	VERB
fuelectenerg-1426	27	2	s	s	PROPN
fuelectenerg-1426	27	3	/	/	SYM
fuelectenerg-1426	27	4	d	d	NOUN
fuelectenerg-1426	27	5	trees	tree	NOUN
fuelectenerg-1426	27	6	are	be	AUX
fuelectenerg-1426	27	7	used	use	VERB
fuelectenerg-1426	27	8	to	to	PART
fuelectenerg-1426	27	9	generate	generate	VERB
fuelectenerg-1426	27	10	forms	form	NOUN
fuelectenerg-1426	27	11	that	that	PRON
fuelectenerg-1426	27	12	include	include	VERB
fuelectenerg-1426	27	13	a	a	DET
fuelectenerg-1426	27	14	minimum	minimum	ADJ
fuelectenerg-1426	27	15	galois	galois	NOUN
fuelectenerg-1426	27	16	field	field	NOUN
fuelectenerg-1426	27	17	sum	sum	NOUN
fuelectenerg-1426	27	18	-	-	PUNCT
fuelectenerg-1426	27	19	of	of	ADP
fuelectenerg-1426	27	20	-	-	PUNCT
fuelectenerg-1426	27	21	products	product	NOUN
fuelectenerg-1426	27	22	(	(	PUNCT
fuelectenerg-1426	27	23	gfsop	gfsop	NOUN
fuelectenerg-1426	27	24	)	)	PUNCT
fuelectenerg-1426	27	25	forms	form	NOUN
fuelectenerg-1426	27	26	.	.	PUNCT
fuelectenerg-1426	28	1	since	since	SCONJ
fuelectenerg-1426	28	2	there	there	PRON
fuelectenerg-1426	28	3	exist	exist	VERB
fuelectenerg-1426	28	4	many	many	ADJ
fuelectenerg-1426	28	5	applications	application	NOUN
fuelectenerg-1426	28	6	of	of	ADP
fuelectenerg-1426	28	7	galois	galois	PROPN
fuelectenerg-1426	28	8	field	field	NOUN
fuelectenerg-1426	28	9	of	of	ADP
fuelectenerg-1426	28	10	quaternary	quaternary	ADJ
fuelectenerg-1426	28	11	radix	radix	NOUN
fuelectenerg-1426	28	12	especially	especially	ADV
fuelectenerg-1426	28	13	that	that	DET
fuelectenerg-1426	28	14	gf(4	gf(4	NOUN
fuelectenerg-1426	28	15	)	)	PUNCT
fuelectenerg-1426	28	16	is	be	AUX
fuelectenerg-1426	28	17	considered	consider	VERB
fuelectenerg-1426	28	18	as	as	ADP
fuelectenerg-1426	28	19	an	an	DET
fuelectenerg-1426	28	20	important	important	ADJ
fuelectenerg-1426	28	21	extension	extension	NOUN
fuelectenerg-1426	28	22	of	of	ADP
fuelectenerg-1426	28	23	gf(2	gf(2	PROPN
fuelectenerg-1426	28	24	)	)	PUNCT
fuelectenerg-1426	28	25	,	,	PUNCT
fuelectenerg-1426	28	26	the	the	DET
fuelectenerg-1426	28	27	extension	extension	NOUN
fuelectenerg-1426	28	28	of	of	ADP
fuelectenerg-1426	28	29	the	the	DET
fuelectenerg-1426	28	30	s	s	PROPN
fuelectenerg-1426	28	31	/	/	SYM
fuelectenerg-1426	28	32	d	d	NOUN
fuelectenerg-1426	28	33	trees	tree	NOUN
fuelectenerg-1426	28	34	to	to	ADP
fuelectenerg-1426	28	35	gf(4	gf(4	NOUN
fuelectenerg-1426	28	36	)	)	PUNCT
fuelectenerg-1426	28	37	is	be	AUX
fuelectenerg-1426	28	38	presented	present	VERB
fuelectenerg-1426	28	39	here	here	ADV
fuelectenerg-1426	28	40	.	.	PUNCT
fuelectenerg-1426	29	1	a	a	DET
fuelectenerg-1426	29	2	general	general	ADJ
fuelectenerg-1426	29	3	formula	formula	NOUN
fuelectenerg-1426	29	4	to	to	PART
fuelectenerg-1426	29	5	calculate	calculate	VERB
fuelectenerg-1426	29	6	the	the	DET
fuelectenerg-1426	29	7	number	number	NOUN
fuelectenerg-1426	29	8	of	of	ADP
fuelectenerg-1426	29	9	inclusive	inclusive	ADJ
fuelectenerg-1426	29	10	forms	form	NOUN
fuelectenerg-1426	29	11	(	(	PUNCT
fuelectenerg-1426	29	12	ifs	ifs	PROPN
fuelectenerg-1426	29	13	)	)	PUNCT
fuelectenerg-1426	29	14	per	per	ADP
fuelectenerg-1426	29	15	variable	variable	ADJ
fuelectenerg-1426	29	16	order	order	NOUN
fuelectenerg-1426	29	17	for	for	ADP
fuelectenerg-1426	29	18	an	an	DET
fuelectenerg-1426	29	19	arbitrary	arbitrary	ADJ
fuelectenerg-1426	29	20	galois	galois	NOUN
fuelectenerg-1426	29	21	field	field	NOUN
fuelectenerg-1426	29	22	radix	radix	NOUN
fuelectenerg-1426	29	23	and	and	CCONJ
fuelectenerg-1426	29	24	arbitrary	arbitrary	ADJ
fuelectenerg-1426	29	25	number	number	NOUN
fuelectenerg-1426	29	26	of	of	ADP
fuelectenerg-1426	29	27	variables	variable	NOUN
fuelectenerg-1426	29	28	is	be	AUX
fuelectenerg-1426	29	29	derived	derive	VERB
fuelectenerg-1426	29	30	and	and	CCONJ
fuelectenerg-1426	29	31	introduced	introduce	VERB
fuelectenerg-1426	29	32	.	.	PUNCT
fuelectenerg-1426	30	1	a	a	DET
fuelectenerg-1426	30	2	new	new	ADJ
fuelectenerg-1426	30	3	fast	fast	ADJ
fuelectenerg-1426	30	4	method	method	NOUN
fuelectenerg-1426	30	5	to	to	PART
fuelectenerg-1426	30	6	count	count	VERB
fuelectenerg-1426	30	7	the	the	DET
fuelectenerg-1426	30	8	number	number	NOUN
fuelectenerg-1426	30	9	of	of	ADP
fuelectenerg-1426	30	10	ifs	ifs	PROPN
fuelectenerg-1426	30	11	for	for	ADP
fuelectenerg-1426	30	12	an	an	DET
fuelectenerg-1426	30	13	arbitrary	arbitrary	ADJ
fuelectenerg-1426	30	14	galois	galois	PROPN
fuelectenerg-1426	30	15	radix	radix	NOUN
fuelectenerg-1426	30	16	and	and	CCONJ
fuelectenerg-1426	30	17	functions	function	NOUN
fuelectenerg-1426	30	18	of	of	ADP
fuelectenerg-1426	30	19	two	two	NUM
fuelectenerg-1426	30	20	variables	variable	NOUN
fuelectenerg-1426	30	21	is	be	AUX
fuelectenerg-1426	30	22	also	also	ADV
fuelectenerg-1426	30	23	introduced	introduce	VERB
fuelectenerg-1426	30	24	;	;	PUNCT
fuelectenerg-1426	30	25	the	the	DET
fuelectenerg-1426	30	26	ifn,2	ifn,2	ADJ
fuelectenerg-1426	30	27	triangles	triangle	NOUN
fuelectenerg-1426	30	28	.	.	PUNCT
fuelectenerg-1426	31	1	the	the	DET
fuelectenerg-1426	31	2	results	result	NOUN
fuelectenerg-1426	31	3	introduced	introduce	VERB
fuelectenerg-1426	31	4	in	in	ADP
fuelectenerg-1426	31	5	this	this	DET
fuelectenerg-1426	31	6	work	work	NOUN
fuelectenerg-1426	31	7	can	can	AUX
fuelectenerg-1426	31	8	be	be	AUX
fuelectenerg-1426	31	9	useful	useful	ADJ
fuelectenerg-1426	31	10	for	for	ADP
fuelectenerg-1426	31	11	the	the	DET
fuelectenerg-1426	31	12	creation	creation	NOUN
fuelectenerg-1426	31	13	of	of	ADP
fuelectenerg-1426	31	14	an	an	DET
fuelectenerg-1426	31	15	efficient	efficient	ADJ
fuelectenerg-1426	31	16	gfsop	gfsop	NOUN
fuelectenerg-1426	31	17	minimizer	minimizer	NOUN
fuelectenerg-1426	31	18	for	for	ADP
fuelectenerg-1426	31	19	galois	galois	PROPN
fuelectenerg-1426	31	20	logic	logic	NOUN
fuelectenerg-1426	31	21	and	and	CCONJ
fuelectenerg-1426	31	22	in	in	ADP
fuelectenerg-1426	31	23	other	other	ADJ
fuelectenerg-1426	31	24	applications	application	NOUN
fuelectenerg-1426	31	25	such	such	ADJ
fuelectenerg-1426	31	26	as	as	ADP
fuelectenerg-1426	31	27	in	in	ADP
fuelectenerg-1426	31	28	reversible	reversible	ADJ
fuelectenerg-1426	31	29	logic	logic	NOUN
fuelectenerg-1426	31	30	synthesis	synthesis	NOUN
fuelectenerg-1426	31	31	.	.	PUNCT
fuelectenerg-1426	32	1	key	key	ADJ
fuelectenerg-1426	32	2	words	word	NOUN
fuelectenerg-1426	32	3	:	:	PUNCT
fuelectenerg-1426	32	4	complexity	complexity	NOUN
fuelectenerg-1426	32	5	,	,	PUNCT
fuelectenerg-1426	32	6	galois	galois	PROPN
fuelectenerg-1426	32	7	field	field	NOUN
fuelectenerg-1426	32	8	sum	sum	NOUN
fuelectenerg-1426	32	9	-	-	PUNCT
fuelectenerg-1426	32	10	of	of	ADP
fuelectenerg-1426	32	11	-	-	PUNCT
fuelectenerg-1426	32	12	product	product	NOUN
fuelectenerg-1426	32	13	(	(	PUNCT
fuelectenerg-1426	32	14	gfsop	gfsop	PROPN
fuelectenerg-1426	32	15	)	)	PUNCT
fuelectenerg-1426	32	16	,	,	PUNCT
fuelectenerg-1426	32	17	galois	galois	PROPN
fuelectenerg-1426	32	18	forms	form	NOUN
fuelectenerg-1426	32	19	,	,	PUNCT
fuelectenerg-1426	32	20	inclusive	inclusive	ADJ
fuelectenerg-1426	32	21	forms	form	NOUN
fuelectenerg-1426	32	22	,	,	PUNCT
fuelectenerg-1426	32	23	multi	multi	ADJ
fuelectenerg-1426	32	24	-	-	ADJ
fuelectenerg-1426	32	25	valued	value	VERB
fuelectenerg-1426	32	26	logic	logic	NOUN
fuelectenerg-1426	32	27	,	,	PUNCT
fuelectenerg-1426	32	28	quaternary	quaternary	ADJ
fuelectenerg-1426	32	29	logic	logic	NOUN
fuelectenerg-1426	32	30	,	,	PUNCT
fuelectenerg-1426	32	31	shannon	shannon	PROPN
fuelectenerg-1426	32	32	-	-	PUNCT
fuelectenerg-1426	32	33	davio	davio	NOUN
fuelectenerg-1426	32	34	(	(	PUNCT
fuelectenerg-1426	32	35	s	s	NOUN
fuelectenerg-1426	32	36	/	/	SYM
fuelectenerg-1426	32	37	d	d	NOUN
fuelectenerg-1426	32	38	)	)	PUNCT
fuelectenerg-1426	32	39	trees	tree	NOUN
fuelectenerg-1426	32	40	.	.	PUNCT
fuelectenerg-1426	33	1	702	702	NUM
fuelectenerg-1426	33	2	a.	a.	NOUN
fuelectenerg-1426	33	3	n.	n.	PROPN
fuelectenerg-1426	33	4	al	al	PROPN
fuelectenerg-1426	33	5	-	-	PUNCT
fuelectenerg-1426	33	6	rabadi	rabadi	PROPN
fuelectenerg-1426	33	7	multi	multi	ADJ
fuelectenerg-1426	33	8	-	-	ADJ
fuelectenerg-1426	33	9	valued	value	VERB
fuelectenerg-1426	33	10	galois	galois	PROPN
fuelectenerg-1426	33	11	shannon	shannon	PROPN
fuelectenerg-1426	33	12	davio	davio	PROPN
fuelectenerg-1426	33	13	trees	tree	NOUN
fuelectenerg-1426	33	14	and	and	CCONJ
fuelectenerg-1426	33	15	their	their	PRON
fuelectenerg-1426	33	16	complexity	complexity	NOUN
fuelectenerg-1426	33	17	703	703	NUM
fuelectenerg-1426	33	18	multi	multi	ADV
fuelectenerg-1426	33	19	-	-	ADJ
fuelectenerg-1426	33	20	valued	value	VERB
fuelectenerg-1426	33	21	galois	galois	PROPN
fuelectenerg-1426	33	22	shannon	shannon	PROPN
fuelectenerg-1426	33	23	davio	davio	PROPN
fuelectenerg-1426	33	24	trees	tree	NOUN
fuelectenerg-1426	33	25	and	and	CCONJ
fuelectenerg-1426	33	26	their	their	PRON
fuelectenerg-1426	33	27	complexity	complexity	NOUN
fuelectenerg-1426	33	28	structures	structure	NOUN
fuelectenerg-1426	33	29	,	,	PUNCT
fuelectenerg-1426	33	30	besides	besides	SCONJ
fuelectenerg-1426	33	31	their	their	PRON
fuelectenerg-1426	33	32	well	well	ADV
fuelectenerg-1426	33	33	-	-	PUNCT
fuelectenerg-1426	33	34	known	know	VERB
fuelectenerg-1426	33	35	uses	use	NOUN
fuelectenerg-1426	33	36	in	in	ADP
fuelectenerg-1426	33	37	digital	digital	ADJ
fuelectenerg-1426	33	38	communications	communication	NOUN
fuelectenerg-1426	33	39	,	,	PUNCT
fuelectenerg-1426	33	40	digital	digital	ADJ
fuelectenerg-1426	33	41	signal	signal	NOUN
fuelectenerg-1426	33	42	processing	processing	NOUN
fuelectenerg-1426	33	43	,	,	PUNCT
fuelectenerg-1426	33	44	digital	digital	ADJ
fuelectenerg-1426	33	45	image	image	NOUN
fuelectenerg-1426	33	46	processing	processing	NOUN
fuelectenerg-1426	33	47	and	and	CCONJ
fuelectenerg-1426	33	48	fault	fault	VERB
fuelectenerg-1426	33	49	detection	detection	NOUN
fuelectenerg-1426	33	50	and	and	CCONJ
fuelectenerg-1426	33	51	testing	testing	NOUN
fuelectenerg-1426	33	52	[	[	X
fuelectenerg-1426	33	53	1	1	NUM
fuelectenerg-1426	33	54	-	-	SYM
fuelectenerg-1426	33	55	7	7	NUM
fuelectenerg-1426	33	56	,	,	PUNCT
fuelectenerg-1426	33	57	12	12	NUM
fuelectenerg-1426	33	58	,	,	PUNCT
fuelectenerg-1426	33	59	13	13	NUM
fuelectenerg-1426	33	60	,	,	PUNCT
fuelectenerg-1426	33	61	15	15	NUM
fuelectenerg-1426	33	62	-	-	SYM
fuelectenerg-1426	33	63	19	19	NUM
fuelectenerg-1426	33	64	,	,	PUNCT
fuelectenerg-1426	33	65	21	21	NUM
fuelectenerg-1426	33	66	-	-	SYM
fuelectenerg-1426	33	67	25	25	NUM
fuelectenerg-1426	33	68	,	,	PUNCT
fuelectenerg-1426	33	69	27	27	NUM
fuelectenerg-1426	33	70	,	,	PUNCT
fuelectenerg-1426	33	71	29	29	NUM
fuelectenerg-1426	33	72	,	,	PUNCT
fuelectenerg-1426	33	73	32	32	NUM
fuelectenerg-1426	33	74	,	,	PUNCT
fuelectenerg-1426	33	75	35	35	NUM
fuelectenerg-1426	33	76	]	]	PUNCT
fuelectenerg-1426	33	77	.	.	PUNCT
fuelectenerg-1426	34	1	the	the	DET
fuelectenerg-1426	34	2	method	method	NOUN
fuelectenerg-1426	34	3	of	of	ADP
fuelectenerg-1426	34	4	generating	generate	VERB
fuelectenerg-1426	34	5	the	the	DET
fuelectenerg-1426	34	6	new	new	ADJ
fuelectenerg-1426	34	7	families	family	NOUN
fuelectenerg-1426	34	8	of	of	ADP
fuelectenerg-1426	34	9	multi	multi	ADJ
fuelectenerg-1426	34	10	-	-	ADJ
fuelectenerg-1426	34	11	valued	value	VERB
fuelectenerg-1426	34	12	shannon	shannon	NOUN
fuelectenerg-1426	34	13	and	and	CCONJ
fuelectenerg-1426	34	14	davio	davio	PROPN
fuelectenerg-1426	34	15	spectral	spectral	ADJ
fuelectenerg-1426	34	16	transforms	transform	NOUN
fuelectenerg-1426	34	17	is	be	AUX
fuelectenerg-1426	34	18	based	base	VERB
fuelectenerg-1426	34	19	on	on	ADP
fuelectenerg-1426	34	20	the	the	DET
fuelectenerg-1426	34	21	fundamental	fundamental	ADJ
fuelectenerg-1426	34	22	multi	multi	ADJ
fuelectenerg-1426	34	23	-	-	ADJ
fuelectenerg-1426	34	24	valued	value	VERB
fuelectenerg-1426	34	25	shannon	shannon	NOUN
fuelectenerg-1426	34	26	and	and	CCONJ
fuelectenerg-1426	34	27	davio	davio	NOUN
fuelectenerg-1426	34	28	expansions	expansion	NOUN
fuelectenerg-1426	34	29	,	,	PUNCT
fuelectenerg-1426	34	30	respectively	respectively	ADV
fuelectenerg-1426	34	31	.	.	PUNCT
fuelectenerg-1426	35	1	the	the	DET
fuelectenerg-1426	35	2	remainder	remainder	NOUN
fuelectenerg-1426	35	3	of	of	ADP
fuelectenerg-1426	35	4	this	this	DET
fuelectenerg-1426	35	5	paper	paper	NOUN
fuelectenerg-1426	35	6	is	be	AUX
fuelectenerg-1426	35	7	organized	organize	VERB
fuelectenerg-1426	35	8	as	as	SCONJ
fuelectenerg-1426	35	9	follows	follow	VERB
fuelectenerg-1426	35	10	:	:	PUNCT
fuelectenerg-1426	35	11	basic	basic	ADJ
fuelectenerg-1426	35	12	definitions	definition	NOUN
fuelectenerg-1426	35	13	of	of	ADP
fuelectenerg-1426	35	14	the	the	DET
fuelectenerg-1426	35	15	fundamental	fundamental	ADJ
fuelectenerg-1426	35	16	binary	binary	ADJ
fuelectenerg-1426	35	17	expansions	expansion	NOUN
fuelectenerg-1426	35	18	and	and	CCONJ
fuelectenerg-1426	35	19	their	their	PRON
fuelectenerg-1426	35	20	multi	multi	ADJ
fuelectenerg-1426	35	21	-	-	ADJ
fuelectenerg-1426	35	22	valued	value	VERB
fuelectenerg-1426	35	23	extensions	extension	NOUN
fuelectenerg-1426	35	24	are	be	AUX
fuelectenerg-1426	35	25	given	give	VERB
fuelectenerg-1426	35	26	in	in	ADP
fuelectenerg-1426	35	27	section	section	NOUN
fuelectenerg-1426	35	28	2	2	NUM
fuelectenerg-1426	35	29	.	.	PUNCT
fuelectenerg-1426	35	30	section	section	NOUN
fuelectenerg-1426	35	31	3	3	NUM
fuelectenerg-1426	35	32	presents	present	VERB
fuelectenerg-1426	35	33	the	the	DET
fuelectenerg-1426	35	34	quaternary	quaternary	ADJ
fuelectenerg-1426	35	35	galois	galois	PROPN
fuelectenerg-1426	35	36	shannon	shannon	PROPN
fuelectenerg-1426	35	37	-	-	PUNCT
fuelectenerg-1426	35	38	davio	davio	NOUN
fuelectenerg-1426	35	39	(	(	PUNCT
fuelectenerg-1426	35	40	s	s	NOUN
fuelectenerg-1426	35	41	/	/	SYM
fuelectenerg-1426	35	42	d	d	NOUN
fuelectenerg-1426	35	43	)	)	PUNCT
fuelectenerg-1426	35	44	trees	tree	NOUN
fuelectenerg-1426	35	45	.	.	PUNCT
fuelectenerg-1426	36	1	the	the	DET
fuelectenerg-1426	36	2	number	number	NOUN
fuelectenerg-1426	36	3	of	of	ADP
fuelectenerg-1426	36	4	s	s	PROPN
fuelectenerg-1426	36	5	/	/	SYM
fuelectenerg-1426	36	6	d	d	NOUN
fuelectenerg-1426	36	7	inclusive	inclusive	ADJ
fuelectenerg-1426	36	8	forms	form	NOUN
fuelectenerg-1426	36	9	and	and	CCONJ
fuelectenerg-1426	36	10	the	the	DET
fuelectenerg-1426	36	11	new	new	ADJ
fuelectenerg-1426	36	12	ifn,2	ifn,2	ADJ
fuelectenerg-1426	36	13	triangles	triangle	NOUN
fuelectenerg-1426	36	14	are	be	AUX
fuelectenerg-1426	36	15	introduced	introduce	VERB
fuelectenerg-1426	36	16	in	in	ADP
fuelectenerg-1426	36	17	section	section	NOUN
fuelectenerg-1426	36	18	4	4	NUM
fuelectenerg-1426	36	19	.	.	PUNCT
fuelectenerg-1426	36	20	conclusions	conclusion	NOUN
fuelectenerg-1426	36	21	and	and	CCONJ
fuelectenerg-1426	36	22	future	future	ADJ
fuelectenerg-1426	36	23	work	work	NOUN
fuelectenerg-1426	36	24	are	be	AUX
fuelectenerg-1426	36	25	presented	present	VERB
fuelectenerg-1426	36	26	in	in	ADP
fuelectenerg-1426	36	27	section	section	NOUN
fuelectenerg-1426	36	28	5	5	NUM
fuelectenerg-1426	36	29	.	.	SYM
fuelectenerg-1426	36	30	2	2	NUM
fuelectenerg-1426	36	31	basic	basic	ADJ
fuelectenerg-1426	36	32	shannon	shannon	NOUN
fuelectenerg-1426	36	33	and	and	CCONJ
fuelectenerg-1426	36	34	davio	davio	NOUN
fuelectenerg-1426	36	35	decompositions	decomposition	NOUN
fuelectenerg-1426	36	36	this	this	DET
fuelectenerg-1426	36	37	section	section	NOUN
fuelectenerg-1426	36	38	presents	present	VERB
fuelectenerg-1426	36	39	necessary	necessary	ADJ
fuelectenerg-1426	36	40	mathematical	mathematical	ADJ
fuelectenerg-1426	36	41	background	background	NOUN
fuelectenerg-1426	36	42	and	and	CCONJ
fuelectenerg-1426	36	43	the	the	DET
fuelectenerg-1426	36	44	fundamental	fundamental	ADJ
fuelectenerg-1426	36	45	formalisms	formalism	NOUN
fuelectenerg-1426	36	46	of	of	ADP
fuelectenerg-1426	36	47	the	the	DET
fuelectenerg-1426	36	48	work	work	NOUN
fuelectenerg-1426	36	49	that	that	PRON
fuelectenerg-1426	36	50	will	will	AUX
fuelectenerg-1426	36	51	be	be	AUX
fuelectenerg-1426	36	52	introduced	introduce	VERB
fuelectenerg-1426	36	53	and	and	CCONJ
fuelectenerg-1426	36	54	further	far	ADV
fuelectenerg-1426	36	55	developed	develop	VERB
fuelectenerg-1426	36	56	in	in	ADP
fuelectenerg-1426	36	57	the	the	DET
fuelectenerg-1426	36	58	following	follow	VERB
fuelectenerg-1426	36	59	sections	section	NOUN
fuelectenerg-1426	36	60	.	.	PUNCT
fuelectenerg-1426	37	1	normal	normal	ADJ
fuelectenerg-1426	37	2	canonical	canonical	ADJ
fuelectenerg-1426	37	3	forms	form	NOUN
fuelectenerg-1426	37	4	play	play	VERB
fuelectenerg-1426	37	5	an	an	DET
fuelectenerg-1426	37	6	important	important	ADJ
fuelectenerg-1426	37	7	role	role	NOUN
fuelectenerg-1426	37	8	in	in	ADP
fuelectenerg-1426	37	9	the	the	DET
fuelectenerg-1426	37	10	synthesis	synthesis	NOUN
fuelectenerg-1426	37	11	of	of	ADP
fuelectenerg-1426	37	12	logic	logic	NOUN
fuelectenerg-1426	37	13	circuits	circuit	NOUN
fuelectenerg-1426	37	14	which	which	PRON
fuelectenerg-1426	37	15	includes	include	VERB
fuelectenerg-1426	37	16	synthesis	synthesis	NOUN
fuelectenerg-1426	37	17	,	,	PUNCT
fuelectenerg-1426	37	18	testing	testing	NOUN
fuelectenerg-1426	37	19	and	and	CCONJ
fuelectenerg-1426	37	20	optimization	optimization	NOUN
fuelectenerg-1426	37	21	[	[	X
fuelectenerg-1426	37	22	2	2	NUM
fuelectenerg-1426	37	23	,	,	PUNCT
fuelectenerg-1426	37	24	8	8	NUM
fuelectenerg-1426	37	25	,	,	PUNCT
fuelectenerg-1426	37	26	13	13	NUM
fuelectenerg-1426	37	27	,	,	PUNCT
fuelectenerg-1426	37	28	15	15	NUM
fuelectenerg-1426	37	29	,	,	PUNCT
fuelectenerg-1426	37	30	17	17	NUM
fuelectenerg-1426	37	31	,	,	PUNCT
fuelectenerg-1426	37	32	18	18	NUM
fuelectenerg-1426	37	33	,	,	PUNCT
fuelectenerg-1426	37	34	21	21	NUM
fuelectenerg-1426	37	35	,	,	PUNCT
fuelectenerg-1426	37	36	23	23	NUM
fuelectenerg-1426	37	37	,	,	PUNCT
fuelectenerg-1426	37	38	25	25	NUM
fuelectenerg-1426	37	39	,	,	PUNCT
fuelectenerg-1426	37	40	27	27	NUM
fuelectenerg-1426	37	41	,	,	PUNCT
fuelectenerg-1426	37	42	29	29	NUM
fuelectenerg-1426	37	43	,	,	PUNCT
fuelectenerg-1426	37	44	32	32	NUM
fuelectenerg-1426	37	45	,	,	PUNCT
fuelectenerg-1426	37	46	35	35	NUM
fuelectenerg-1426	37	47	-	-	SYM
fuelectenerg-1426	37	48	37	37	NUM
fuelectenerg-1426	37	49	]	]	PUNCT
fuelectenerg-1426	37	50	.	.	PUNCT
fuelectenerg-1426	38	1	the	the	DET
fuelectenerg-1426	38	2	main	main	ADJ
fuelectenerg-1426	38	3	algebraic	algebraic	ADJ
fuelectenerg-1426	38	4	structure	structure	NOUN
fuelectenerg-1426	38	5	which	which	PRON
fuelectenerg-1426	38	6	is	be	AUX
fuelectenerg-1426	38	7	used	use	VERB
fuelectenerg-1426	38	8	in	in	ADP
fuelectenerg-1426	38	9	this	this	DET
fuelectenerg-1426	38	10	work	work	NOUN
fuelectenerg-1426	38	11	for	for	ADP
fuelectenerg-1426	38	12	developing	develop	VERB
fuelectenerg-1426	38	13	the	the	DET
fuelectenerg-1426	38	14	canonical	canonical	ADJ
fuelectenerg-1426	38	15	normal	normal	ADJ
fuelectenerg-1426	38	16	forms	form	NOUN
fuelectenerg-1426	38	17	is	be	AUX
fuelectenerg-1426	38	18	the	the	DET
fuelectenerg-1426	38	19	galois	galois	PROPN
fuelectenerg-1426	38	20	field	field	NOUN
fuelectenerg-1426	38	21	(	(	PUNCT
fuelectenerg-1426	38	22	gf	gf	NOUN
fuelectenerg-1426	38	23	)	)	PUNCT
fuelectenerg-1426	38	24	algebraic	algebraic	ADJ
fuelectenerg-1426	38	25	structure	structure	NOUN
fuelectenerg-1426	38	26	,	,	PUNCT
fuelectenerg-1426	38	27	which	which	PRON
fuelectenerg-1426	38	28	is	be	AUX
fuelectenerg-1426	38	29	a	a	DET
fuelectenerg-1426	38	30	fundamental	fundamental	ADJ
fuelectenerg-1426	38	31	algebraic	algebraic	ADJ
fuelectenerg-1426	38	32	structure	structure	NOUN
fuelectenerg-1426	38	33	in	in	ADP
fuelectenerg-1426	38	34	the	the	DET
fuelectenerg-1426	38	35	theory	theory	NOUN
fuelectenerg-1426	38	36	of	of	ADP
fuelectenerg-1426	38	37	algebras	algebras	PROPN
fuelectenerg-1426	38	38	[	[	X
fuelectenerg-1426	38	39	2	2	NUM
fuelectenerg-1426	38	40	,	,	PUNCT
fuelectenerg-1426	38	41	8	8	NUM
fuelectenerg-1426	38	42	,	,	PUNCT
fuelectenerg-1426	38	43	17	17	NUM
fuelectenerg-1426	38	44	,	,	PUNCT
fuelectenerg-1426	38	45	18	18	NUM
fuelectenerg-1426	38	46	,	,	PUNCT
fuelectenerg-1426	38	47	21	21	NUM
fuelectenerg-1426	38	48	,	,	PUNCT
fuelectenerg-1426	38	49	32	32	NUM
fuelectenerg-1426	38	50	]	]	PUNCT
fuelectenerg-1426	38	51	.	.	PUNCT
fuelectenerg-1426	39	1	galois	galois	PROPN
fuelectenerg-1426	39	2	field	field	NOUN
fuelectenerg-1426	39	3	has	have	AUX
fuelectenerg-1426	39	4	proven	prove	VERB
fuelectenerg-1426	39	5	high	high	ADJ
fuelectenerg-1426	39	6	efficiency	efficiency	NOUN
fuelectenerg-1426	39	7	in	in	ADP
fuelectenerg-1426	39	8	various	various	ADJ
fuelectenerg-1426	39	9	applications	application	NOUN
fuelectenerg-1426	39	10	of	of	ADP
fuelectenerg-1426	39	11	logic	logic	NOUN
fuelectenerg-1426	39	12	synthesis	synthesis	NOUN
fuelectenerg-1426	39	13	,	,	PUNCT
fuelectenerg-1426	39	14	such	such	ADJ
fuelectenerg-1426	39	15	as	as	ADP
fuelectenerg-1426	39	16	in	in	ADP
fuelectenerg-1426	39	17	the	the	DET
fuelectenerg-1426	39	18	design	design	NOUN
fuelectenerg-1426	39	19	for	for	ADP
fuelectenerg-1426	39	20	test	test	NOUN
fuelectenerg-1426	39	21	,	,	PUNCT
fuelectenerg-1426	39	22	error	error	NOUN
fuelectenerg-1426	39	23	correction	correction	NOUN
fuelectenerg-1426	39	24	codes	code	NOUN
fuelectenerg-1426	39	25	,	,	PUNCT
fuelectenerg-1426	39	26	and	and	CCONJ
fuelectenerg-1426	39	27	even	even	ADV
fuelectenerg-1426	39	28	in	in	ADP
fuelectenerg-1426	39	29	the	the	DET
fuelectenerg-1426	39	30	proof	proof	NOUN
fuelectenerg-1426	39	31	of	of	ADP
fuelectenerg-1426	39	32	the	the	DET
fuelectenerg-1426	39	33	well	well	ADV
fuelectenerg-1426	39	34	-	-	PUNCT
fuelectenerg-1426	39	35	known	know	VERB
fuelectenerg-1426	39	36	fermat	fermat	PROPN
fuelectenerg-1426	39	37	’s	’s	PART
fuelectenerg-1426	39	38	last	last	ADJ
fuelectenerg-1426	39	39	theorem	theorem	NOUN
fuelectenerg-1426	39	40	.	.	PUNCT
fuelectenerg-1426	40	1	the	the	DET
fuelectenerg-1426	40	2	importance	importance	NOUN
fuelectenerg-1426	40	3	of	of	ADP
fuelectenerg-1426	40	4	gf	gf	PROPN
fuelectenerg-1426	40	5	for	for	ADP
fuelectenerg-1426	40	6	logic	logic	ADJ
fuelectenerg-1426	40	7	synthesis	synthesis	NOUN
fuelectenerg-1426	40	8	results	result	NOUN
fuelectenerg-1426	40	9	from	from	ADP
fuelectenerg-1426	40	10	the	the	DET
fuelectenerg-1426	40	11	fact	fact	NOUN
fuelectenerg-1426	40	12	that	that	SCONJ
fuelectenerg-1426	40	13	every	every	DET
fuelectenerg-1426	40	14	finite	finite	ADJ
fuelectenerg-1426	40	15	field	field	NOUN
fuelectenerg-1426	40	16	is	be	AUX
fuelectenerg-1426	40	17	isomorphic	isomorphic	ADJ
fuelectenerg-1426	40	18	to	to	ADP
fuelectenerg-1426	40	19	a	a	DET
fuelectenerg-1426	40	20	galois	galois	PROPN
fuelectenerg-1426	40	21	field	field	NOUN
fuelectenerg-1426	40	22	.	.	PUNCT
fuelectenerg-1426	41	1	in	in	ADP
fuelectenerg-1426	41	2	general	general	ADJ
fuelectenerg-1426	41	3	,	,	PUNCT
fuelectenerg-1426	41	4	the	the	DET
fuelectenerg-1426	41	5	attractive	attractive	ADJ
fuelectenerg-1426	41	6	properties	property	NOUN
fuelectenerg-1426	41	7	of	of	ADP
fuelectenerg-1426	41	8	gf	gf	NOUN
fuelectenerg-1426	41	9	-	-	PUNCT
fuelectenerg-1426	41	10	based	base	VERB
fuelectenerg-1426	41	11	circuits	circuit	NOUN
fuelectenerg-1426	41	12	,	,	PUNCT
fuelectenerg-1426	41	13	such	such	ADJ
fuelectenerg-1426	41	14	as	as	ADP
fuelectenerg-1426	41	15	high	high	ADJ
fuelectenerg-1426	41	16	testability	testability	NOUN
fuelectenerg-1426	41	17	of	of	ADP
fuelectenerg-1426	41	18	such	such	ADJ
fuelectenerg-1426	41	19	circuits	circuit	NOUN
fuelectenerg-1426	41	20	,	,	PUNCT
fuelectenerg-1426	41	21	are	be	AUX
fuelectenerg-1426	41	22	due	due	ADJ
fuelectenerg-1426	41	23	to	to	ADP
fuelectenerg-1426	41	24	the	the	DET
fuelectenerg-1426	41	25	fact	fact	NOUN
fuelectenerg-1426	41	26	that	that	SCONJ
fuelectenerg-1426	41	27	the	the	DET
fuelectenerg-1426	41	28	gf	gf	PROPN
fuelectenerg-1426	41	29	operators	operator	NOUN
fuelectenerg-1426	41	30	exhibit	exhibit	VERB
fuelectenerg-1426	41	31	the	the	DET
fuelectenerg-1426	41	32	cyclic	cyclic	ADJ
fuelectenerg-1426	41	33	group	group	NOUN
fuelectenerg-1426	41	34	also	also	ADV
fuelectenerg-1426	41	35	called	call	VERB
fuelectenerg-1426	41	36	latin	latin	PROPN
fuelectenerg-1426	41	37	square	square	ADJ
fuelectenerg-1426	41	38	property	property	NOUN
fuelectenerg-1426	41	39	which	which	PRON
fuelectenerg-1426	41	40	can	can	AUX
fuelectenerg-1426	41	41	be	be	AUX
fuelectenerg-1426	41	42	explained	explain	VERB
fuelectenerg-1426	41	43	,	,	PUNCT
fuelectenerg-1426	41	44	for	for	ADP
fuelectenerg-1426	41	45	example	example	NOUN
fuelectenerg-1426	41	46	,	,	PUNCT
fuelectenerg-1426	41	47	using	use	VERB
fuelectenerg-1426	41	48	gf(4	gf(4	NOUN
fuelectenerg-1426	41	49	)	)	PUNCT
fuelectenerg-1426	41	50	(	(	PUNCT
fuelectenerg-1426	41	51	quaternary	quaternary	ADJ
fuelectenerg-1426	41	52	)	)	PUNCT
fuelectenerg-1426	41	53	operators	operator	NOUN
fuelectenerg-1426	41	54	as	as	SCONJ
fuelectenerg-1426	41	55	shown	show	VERB
fuelectenerg-1426	41	56	in	in	ADP
fuelectenerg-1426	41	57	figures	figure	NOUN
fuelectenerg-1426	41	58	1(a	1(a	NUM
fuelectenerg-1426	41	59	)	)	PUNCT
fuelectenerg-1426	41	60	and	and	CCONJ
fuelectenerg-1426	41	61	1(b	1(b	NUM
fuelectenerg-1426	41	62	)	)	PUNCT
fuelectenerg-1426	41	63	,	,	PUNCT
fuelectenerg-1426	41	64	respectively	respectively	ADV
fuelectenerg-1426	41	65	;	;	PUNCT
fuelectenerg-1426	41	66	note	note	VERB
fuelectenerg-1426	41	67	that	that	SCONJ
fuelectenerg-1426	41	68	in	in	ADP
fuelectenerg-1426	41	69	any	any	DET
fuelectenerg-1426	41	70	row	row	NOUN
fuelectenerg-1426	41	71	and	and	CCONJ
fuelectenerg-1426	41	72	column	column	NOUN
fuelectenerg-1426	41	73	of	of	ADP
fuelectenerg-1426	41	74	the	the	DET
fuelectenerg-1426	41	75	addition	addition	NOUN
fuelectenerg-1426	41	76	table	table	NOUN
fuelectenerg-1426	41	77	in	in	ADP
fuelectenerg-1426	41	78	figure	figure	NOUN
fuelectenerg-1426	41	79	1(a	1(a	NUM
fuelectenerg-1426	41	80	)	)	PUNCT
fuelectenerg-1426	41	81	,	,	PUNCT
fuelectenerg-1426	41	82	the	the	DET
fuelectenerg-1426	41	83	elements	element	NOUN
fuelectenerg-1426	41	84	are	be	AUX
fuelectenerg-1426	41	85	all	all	ADV
fuelectenerg-1426	41	86	different	different	ADJ
fuelectenerg-1426	41	87	which	which	PRON
fuelectenerg-1426	41	88	is	be	AUX
fuelectenerg-1426	41	89	cyclic	cyclic	ADJ
fuelectenerg-1426	41	90	,	,	PUNCT
fuelectenerg-1426	41	91	and	and	CCONJ
fuelectenerg-1426	41	92	that	that	SCONJ
fuelectenerg-1426	41	93	the	the	DET
fuelectenerg-1426	41	94	elements	element	NOUN
fuelectenerg-1426	41	95	have	have	VERB
fuelectenerg-1426	41	96	a	a	DET
fuelectenerg-1426	41	97	different	different	ADJ
fuelectenerg-1426	41	98	order	order	NOUN
fuelectenerg-1426	41	99	in	in	ADP
fuelectenerg-1426	41	100	each	each	DET
fuelectenerg-1426	41	101	row	row	NOUN
fuelectenerg-1426	41	102	and	and	CCONJ
fuelectenerg-1426	41	103	column	column	NOUN
fuelectenerg-1426	41	104	.	.	PUNCT
fuelectenerg-1426	42	1	another	another	DET
fuelectenerg-1426	42	2	cyclic	cyclic	ADJ
fuelectenerg-1426	42	3	group	group	NOUN
fuelectenerg-1426	42	4	can	can	AUX
fuelectenerg-1426	42	5	be	be	AUX
fuelectenerg-1426	42	6	observed	observe	VERB
fuelectenerg-1426	42	7	in	in	ADP
fuelectenerg-1426	42	8	the	the	DET
fuelectenerg-1426	42	9	multiplication	multiplication	NOUN
fuelectenerg-1426	42	10	table	table	NOUN
fuelectenerg-1426	42	11	;	;	PUNCT
fuelectenerg-1426	42	12	if	if	SCONJ
fuelectenerg-1426	42	13	the	the	DET
fuelectenerg-1426	42	14	zero	zero	NUM
fuelectenerg-1426	42	15	elements	element	NOUN
fuelectenerg-1426	42	16	are	be	AUX
fuelectenerg-1426	42	17	removed	remove	VERB
fuelectenerg-1426	42	18	from	from	ADP
fuelectenerg-1426	42	19	the	the	DET
fuelectenerg-1426	42	20	multiplication	multiplication	NOUN
fuelectenerg-1426	42	21	table	table	NOUN
fuelectenerg-1426	42	22	in	in	ADP
fuelectenerg-1426	42	23	figure	figure	NOUN
fuelectenerg-1426	42	24	1(b	1(b	NUM
fuelectenerg-1426	42	25	)	)	PUNCT
fuelectenerg-1426	42	26	,	,	PUNCT
fuelectenerg-1426	42	27	then	then	ADV
fuelectenerg-1426	42	28	the	the	DET
fuelectenerg-1426	42	29	remaining	remain	VERB
fuelectenerg-1426	42	30	elements	element	NOUN
fuelectenerg-1426	42	31	form	form	VERB
fuelectenerg-1426	42	32	a	a	DET
fuelectenerg-1426	42	33	cyclic	cyclic	ADJ
fuelectenerg-1426	42	34	group	group	NOUN
fuelectenerg-1426	42	35	.	.	PUNCT
fuelectenerg-1426	43	1	in	in	ADP
fuelectenerg-1426	43	2	binary	binary	NOUN
fuelectenerg-1426	43	3	,	,	PUNCT
fuelectenerg-1426	43	4	for	for	ADP
fuelectenerg-1426	43	5	example	example	NOUN
fuelectenerg-1426	43	6	,	,	PUNCT
fuelectenerg-1426	43	7	gf(2	gf(2	PROPN
fuelectenerg-1426	43	8	)	)	PUNCT
fuelectenerg-1426	43	9	addition	addition	NOUN
fuelectenerg-1426	43	10	operator	operator	NOUN
fuelectenerg-1426	43	11	exor	exor	X
fuelectenerg-1426	43	12	has	have	VERB
fuelectenerg-1426	43	13	the	the	DET
fuelectenerg-1426	43	14	cyclic	cyclic	ADJ
fuelectenerg-1426	43	15	group	group	NOUN
fuelectenerg-1426	43	16	property	property	NOUN
fuelectenerg-1426	43	17	.	.	PUNCT
fuelectenerg-1426	44	1	+	+	CCONJ
fuelectenerg-1426	44	2	0	0	NUM
fuelectenerg-1426	44	3	1	1	NUM
fuelectenerg-1426	44	4	2	2	NUM
fuelectenerg-1426	44	5	3	3	NUM
fuelectenerg-1426	44	6	0	0	NUM
fuelectenerg-1426	44	7	0	0	NUM
fuelectenerg-1426	44	8	1	1	NUM
fuelectenerg-1426	44	9	2	2	NUM
fuelectenerg-1426	44	10	3	3	NUM
fuelectenerg-1426	44	11	1	1	NUM
fuelectenerg-1426	44	12	1	1	NUM
fuelectenerg-1426	44	13	0	0	NUM
fuelectenerg-1426	44	14	3	3	NUM
fuelectenerg-1426	44	15	2	2	NUM
fuelectenerg-1426	44	16	2	2	NUM
fuelectenerg-1426	44	17	2	2	NUM
fuelectenerg-1426	44	18	3	3	NUM
fuelectenerg-1426	44	19	0	0	NUM
fuelectenerg-1426	44	20	1	1	NUM
fuelectenerg-1426	44	21	3	3	NUM
fuelectenerg-1426	44	22	3	3	NUM
fuelectenerg-1426	44	23	2	2	NUM
fuelectenerg-1426	44	24	1	1	NUM
fuelectenerg-1426	44	25	0	0	NUM
fuelectenerg-1426	44	26	∗	∗	NOUN
fuelectenerg-1426	44	27	0	0	NUM
fuelectenerg-1426	44	28	1	1	NUM
fuelectenerg-1426	44	29	2	2	NUM
fuelectenerg-1426	44	30	3	3	NUM
fuelectenerg-1426	44	31	0	0	NUM
fuelectenerg-1426	44	32	0	0	NUM
fuelectenerg-1426	44	33	0	0	NUM
fuelectenerg-1426	44	34	0	0	NUM
fuelectenerg-1426	44	35	0	0	NUM
fuelectenerg-1426	44	36	1	1	NUM
fuelectenerg-1426	44	37	0	0	NUM
fuelectenerg-1426	44	38	1	1	NUM
fuelectenerg-1426	44	39	2	2	NUM
fuelectenerg-1426	44	40	3	3	NUM
fuelectenerg-1426	44	41	2	2	NUM
fuelectenerg-1426	44	42	0	0	NUM
fuelectenerg-1426	44	43	2	2	NUM
fuelectenerg-1426	44	44	3	3	NUM
fuelectenerg-1426	44	45	1	1	NUM
fuelectenerg-1426	44	46	3	3	NUM
fuelectenerg-1426	44	47	0	0	NUM
fuelectenerg-1426	44	48	3	3	NUM
fuelectenerg-1426	44	49	1	1	NUM
fuelectenerg-1426	44	50	2	2	NUM
fuelectenerg-1426	44	51	(	(	PUNCT
fuelectenerg-1426	44	52	a	a	NOUN
fuelectenerg-1426	44	53	)	)	PUNCT
fuelectenerg-1426	44	54	(	(	PUNCT
fuelectenerg-1426	44	55	b	b	X
fuelectenerg-1426	44	56	)	)	PUNCT
fuelectenerg-1426	44	57	fig	fig	NOUN
fuelectenerg-1426	44	58	.	.	PUNCT
fuelectenerg-1426	45	1	1	1	NUM
fuelectenerg-1426	45	2	:	:	PUNCT
fuelectenerg-1426	45	3	gf(4	gf(4	NOUN
fuelectenerg-1426	45	4	)	)	PUNCT
fuelectenerg-1426	45	5	addition	addition	NOUN
fuelectenerg-1426	45	6	and	and	CCONJ
fuelectenerg-1426	45	7	multiplication	multiplication	NOUN
fuelectenerg-1426	45	8	tables	table	NOUN
fuelectenerg-1426	45	9	.	.	PUNCT
fuelectenerg-1426	46	1	reed	reed	NOUN
fuelectenerg-1426	46	2	-	-	PUNCT
fuelectenerg-1426	46	3	muller	muller	NOUN
fuelectenerg-1426	46	4	based	base	VERB
fuelectenerg-1426	46	5	normal	normal	ADJ
fuelectenerg-1426	46	6	forms	form	NOUN
fuelectenerg-1426	46	7	have	have	AUX
fuelectenerg-1426	46	8	been	be	AUX
fuelectenerg-1426	46	9	classified	classify	VERB
fuelectenerg-1426	46	10	using	use	VERB
fuelectenerg-1426	46	11	the	the	DET
fuelectenerg-1426	46	12	green	green	ADJ
fuelectenerg-1426	46	13	-	-	PUNCT
fuelectenerg-1426	46	14	sasao	sasao	NOUN
fuelectenerg-1426	46	15	hierarchy	hierarchy	NOUN
fuelectenerg-1426	46	16	.	.	PUNCT
fuelectenerg-1426	47	1	the	the	DET
fuelectenerg-1426	47	2	green	green	PROPN
fuelectenerg-1426	47	3	-	-	PUNCT
fuelectenerg-1426	47	4	sasao	sasao	PROPN
fuelectenerg-1426	47	5	hierarchy	hierarchy	NOUN
fuelectenerg-1426	47	6	of	of	ADP
fuelectenerg-1426	47	7	families	family	NOUN
fuelectenerg-1426	47	8	of	of	ADP
fuelectenerg-1426	47	9	canonical	canonical	ADJ
fuelectenerg-1426	47	10	forms	form	NOUN
fuelectenerg-1426	47	11	and	and	CCONJ
fuelectenerg-1426	47	12	corresponding	correspond	VERB
fuelectenerg-1426	47	13	decision	decision	NOUN
fuelectenerg-1426	47	14	di102	di102	PROPN
fuelectenerg-1426	47	15	702	702	NUM
fuelectenerg-1426	47	16	a.	a.	NOUN
fuelectenerg-1426	47	17	n.	n.	PROPN
fuelectenerg-1426	47	18	al	al	PROPN
fuelectenerg-1426	47	19	-	-	PUNCT
fuelectenerg-1426	47	20	rabadi	rabadi	PROPN
fuelectenerg-1426	47	21	multi	multi	ADJ
fuelectenerg-1426	47	22	-	-	ADJ
fuelectenerg-1426	47	23	valued	value	VERB
fuelectenerg-1426	47	24	galois	galois	PROPN
fuelectenerg-1426	47	25	shannon	shannon	PROPN
fuelectenerg-1426	47	26	davio	davio	PROPN
fuelectenerg-1426	47	27	trees	tree	NOUN
fuelectenerg-1426	47	28	and	and	CCONJ
fuelectenerg-1426	47	29	their	their	PRON
fuelectenerg-1426	47	30	complexity	complexity	NOUN
fuelectenerg-1426	47	31	703	703	NUM
fuelectenerg-1426	47	32	multi	multi	ADV
fuelectenerg-1426	47	33	-	-	ADJ
fuelectenerg-1426	47	34	valued	value	VERB
fuelectenerg-1426	47	35	galois	galois	PROPN
fuelectenerg-1426	47	36	shannon	shannon	PROPN
fuelectenerg-1426	47	37	davio	davio	PROPN
fuelectenerg-1426	47	38	trees	tree	NOUN
fuelectenerg-1426	47	39	and	and	CCONJ
fuelectenerg-1426	47	40	their	their	PRON
fuelectenerg-1426	47	41	complexity	complexity	NOUN
fuelectenerg-1426	47	42	agrams	agram	NOUN
fuelectenerg-1426	47	43	is	be	AUX
fuelectenerg-1426	47	44	based	base	VERB
fuelectenerg-1426	47	45	on	on	ADP
fuelectenerg-1426	47	46	three	three	NUM
fuelectenerg-1426	47	47	generic	generic	ADJ
fuelectenerg-1426	47	48	expansions	expansion	NOUN
fuelectenerg-1426	47	49	;	;	PUNCT
fuelectenerg-1426	47	50	shannon	shannon	PROPN
fuelectenerg-1426	47	51	,	,	PUNCT
fuelectenerg-1426	47	52	positive	positive	ADJ
fuelectenerg-1426	47	53	davio	davio	NOUN
fuelectenerg-1426	47	54	and	and	CCONJ
fuelectenerg-1426	47	55	negative	negative	ADJ
fuelectenerg-1426	47	56	davio	davio	NOUN
fuelectenerg-1426	47	57	expansions	expansion	NOUN
fuelectenerg-1426	47	58	.	.	PUNCT
fuelectenerg-1426	48	1	the	the	DET
fuelectenerg-1426	48	2	corresponding	corresponding	ADJ
fuelectenerg-1426	48	3	shannon	shannon	PROPN
fuelectenerg-1426	48	4	,	,	PUNCT
fuelectenerg-1426	48	5	positive	positive	ADJ
fuelectenerg-1426	48	6	davio	davio	NOUN
fuelectenerg-1426	48	7	and	and	CCONJ
fuelectenerg-1426	48	8	negative	negative	ADJ
fuelectenerg-1426	48	9	davio	davio	NOUN
fuelectenerg-1426	48	10	expansions	expansion	NOUN
fuelectenerg-1426	48	11	are	be	AUX
fuelectenerg-1426	48	12	given	give	VERB
fuelectenerg-1426	48	13	as	as	SCONJ
fuelectenerg-1426	48	14	follows	follow	VERB
fuelectenerg-1426	48	15	[	[	X
fuelectenerg-1426	48	16	2	2	NUM
fuelectenerg-1426	48	17	,	,	PUNCT
fuelectenerg-1426	48	18	32	32	NUM
fuelectenerg-1426	48	19	]	]	PUNCT
fuelectenerg-1426	48	20	:	:	PUNCT
fuelectenerg-1426	48	21	f	f	X
fuelectenerg-1426	48	22	(	(	PUNCT
fuelectenerg-1426	48	23	x1,x2	x1,x2	PROPN
fuelectenerg-1426	48	24	,	,	PUNCT
fuelectenerg-1426	48	25	.	.	PUNCT
fuelectenerg-1426	48	26	.	.	PUNCT
fuelectenerg-1426	48	27	.	.	PUNCT
fuelectenerg-1426	49	1	,	,	PUNCT
fuelectenerg-1426	49	2	xn	xn	X
fuelectenerg-1426	49	3	)	)	PUNCT
fuelectenerg-1426	49	4	=	=	SYM
fuelectenerg-1426	49	5	x̄1	x̄1	NOUN
fuelectenerg-1426	49	6	·	·	PUNCT
fuelectenerg-1426	49	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1426	49	8	,	,	PUNCT
fuelectenerg-1426	49	9	.	.	PUNCT
fuelectenerg-1426	49	10	.	.	PUNCT
fuelectenerg-1426	49	11	.	.	PUNCT
fuelectenerg-1426	50	1	,	,	PUNCT
fuelectenerg-1426	50	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1426	50	3	x1	x1	PRON
fuelectenerg-1426	50	4	·	·	PUNCT
fuelectenerg-1426	50	5	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1426	50	6	,	,	PUNCT
fuelectenerg-1426	50	7	.	.	PUNCT
fuelectenerg-1426	50	8	.	.	PUNCT
fuelectenerg-1426	50	9	.	.	PUNCT
fuelectenerg-1426	51	1	,	,	PUNCT
fuelectenerg-1426	51	2	xn	xn	PROPN
fuelectenerg-1426	51	3	)	)	PUNCT
fuelectenerg-1426	51	4	,	,	PUNCT
fuelectenerg-1426	51	5	=	=	PUNCT
fuelectenerg-1426	51	6	[	[	PUNCT
fuelectenerg-1426	51	7	x̄1	x̄1	X
fuelectenerg-1426	51	8	x1	x1	X
fuelectenerg-1426	51	9	]	]	PUNCT
fuelectenerg-1426	52	1	[	[	PUNCT
fuelectenerg-1426	52	2	1	1	NUM
fuelectenerg-1426	52	3	0	0	NUM
fuelectenerg-1426	52	4	0	0	NUM
fuelectenerg-1426	52	5	1	1	NUM
fuelectenerg-1426	52	6	]	]	PUNCT
fuelectenerg-1426	52	7	[	[	PUNCT
fuelectenerg-1426	52	8	f0	f0	PROPN
fuelectenerg-1426	52	9	f1	f1	NOUN
fuelectenerg-1426	52	10	]	]	PUNCT
fuelectenerg-1426	52	11	,	,	PUNCT
fuelectenerg-1426	52	12	(	(	PUNCT
fuelectenerg-1426	52	13	1	1	X
fuelectenerg-1426	52	14	)	)	PUNCT
fuelectenerg-1426	52	15	f	f	NOUN
fuelectenerg-1426	52	16	(	(	PUNCT
fuelectenerg-1426	52	17	x1,x2	x1,x2	PROPN
fuelectenerg-1426	52	18	,	,	PUNCT
fuelectenerg-1426	52	19	.	.	PUNCT
fuelectenerg-1426	52	20	.	.	PUNCT
fuelectenerg-1426	52	21	.	.	PUNCT
fuelectenerg-1426	53	1	,	,	PUNCT
fuelectenerg-1426	53	2	xn	xn	X
fuelectenerg-1426	53	3	)	)	PUNCT
fuelectenerg-1426	53	4	=	=	SYM
fuelectenerg-1426	53	5	1	1	NUM
fuelectenerg-1426	53	6	·	·	PUNCT
fuelectenerg-1426	53	7	f0(x1,x2	f0(x1,x2	VERB
fuelectenerg-1426	53	8	,	,	PUNCT
fuelectenerg-1426	53	9	.	.	PUNCT
fuelectenerg-1426	53	10	.	.	PUNCT
fuelectenerg-1426	53	11	.	.	PUNCT
fuelectenerg-1426	54	1	,	,	PUNCT
fuelectenerg-1426	54	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1426	54	3	x1	x1	PRON
fuelectenerg-1426	54	4	·	·	PUNCT
fuelectenerg-1426	54	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1426	54	6	,	,	PUNCT
fuelectenerg-1426	54	7	.	.	PUNCT
fuelectenerg-1426	54	8	.	.	PUNCT
fuelectenerg-1426	54	9	.	.	PUNCT
fuelectenerg-1426	55	1	,	,	PUNCT
fuelectenerg-1426	55	2	xn	xn	PROPN
fuelectenerg-1426	55	3	)	)	PUNCT
fuelectenerg-1426	55	4	,	,	PUNCT
fuelectenerg-1426	56	1	=	=	PUNCT
fuelectenerg-1426	56	2	[	[	PUNCT
fuelectenerg-1426	56	3	1	1	NUM
fuelectenerg-1426	56	4	x1	x1	NOUN
fuelectenerg-1426	56	5	]	]	PUNCT
fuelectenerg-1426	56	6	[	[	PUNCT
fuelectenerg-1426	56	7	1	1	NUM
fuelectenerg-1426	56	8	0	0	NUM
fuelectenerg-1426	56	9	1	1	NUM
fuelectenerg-1426	56	10	1	1	NUM
fuelectenerg-1426	56	11	]	]	PUNCT
fuelectenerg-1426	56	12	[	[	PUNCT
fuelectenerg-1426	56	13	f0	f0	PROPN
fuelectenerg-1426	56	14	f1	f1	NOUN
fuelectenerg-1426	56	15	]	]	PUNCT
fuelectenerg-1426	56	16	,	,	PUNCT
fuelectenerg-1426	56	17	(	(	PUNCT
fuelectenerg-1426	56	18	2	2	X
fuelectenerg-1426	56	19	)	)	PUNCT
fuelectenerg-1426	56	20	f	f	NOUN
fuelectenerg-1426	56	21	(	(	PUNCT
fuelectenerg-1426	56	22	x1,x2	x1,x2	PROPN
fuelectenerg-1426	56	23	,	,	PUNCT
fuelectenerg-1426	56	24	.	.	PUNCT
fuelectenerg-1426	56	25	.	.	PUNCT
fuelectenerg-1426	56	26	.	.	PUNCT
fuelectenerg-1426	57	1	,	,	PUNCT
fuelectenerg-1426	57	2	xn	xn	X
fuelectenerg-1426	57	3	)	)	PUNCT
fuelectenerg-1426	57	4	=	=	SYM
fuelectenerg-1426	57	5	1	1	X
fuelectenerg-1426	57	6	·	·	PUNCT
fuelectenerg-1426	57	7	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1426	57	8	,	,	PUNCT
fuelectenerg-1426	57	9	.	.	PUNCT
fuelectenerg-1426	57	10	.	.	PUNCT
fuelectenerg-1426	57	11	.	.	PUNCT
fuelectenerg-1426	58	1	,	,	PUNCT
fuelectenerg-1426	58	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1426	58	3	x̄1	x̄1	PROPN
fuelectenerg-1426	58	4	·	·	PUNCT
fuelectenerg-1426	58	5	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1426	58	6	,	,	PUNCT
fuelectenerg-1426	58	7	.	.	PUNCT
fuelectenerg-1426	58	8	.	.	PUNCT
fuelectenerg-1426	58	9	.	.	PUNCT
fuelectenerg-1426	59	1	,	,	PUNCT
fuelectenerg-1426	59	2	xn	xn	X
fuelectenerg-1426	59	3	)	)	PUNCT
fuelectenerg-1426	60	1	=	=	PUNCT
fuelectenerg-1426	60	2	[	[	PUNCT
fuelectenerg-1426	60	3	1	1	NUM
fuelectenerg-1426	60	4	x̄1	x̄1	NOUN
fuelectenerg-1426	60	5	]	]	PUNCT
fuelectenerg-1426	61	1	[	[	PUNCT
fuelectenerg-1426	61	2	0	0	NUM
fuelectenerg-1426	61	3	1	1	NUM
fuelectenerg-1426	61	4	1	1	NUM
fuelectenerg-1426	61	5	1	1	NUM
fuelectenerg-1426	61	6	]	]	PUNCT
fuelectenerg-1426	61	7	[	[	PUNCT
fuelectenerg-1426	61	8	f0	f0	PROPN
fuelectenerg-1426	61	9	f1	f1	NOUN
fuelectenerg-1426	61	10	]	]	PUNCT
fuelectenerg-1426	61	11	,	,	PUNCT
fuelectenerg-1426	61	12	(	(	PUNCT
fuelectenerg-1426	61	13	3	3	X
fuelectenerg-1426	61	14	)	)	PUNCT
fuelectenerg-1426	61	15	where	where	SCONJ
fuelectenerg-1426	61	16	f0(x1,x2	f0(x1,x2	NOUN
fuelectenerg-1426	61	17	,	,	PUNCT
fuelectenerg-1426	61	18	.	.	PUNCT
fuelectenerg-1426	61	19	.	.	PUNCT
fuelectenerg-1426	61	20	.	.	PUNCT
fuelectenerg-1426	62	1	,	,	PUNCT
fuelectenerg-1426	62	2	xn	xn	X
fuelectenerg-1426	62	3	)	)	PUNCT
fuelectenerg-1426	62	4	=	=	SYM
fuelectenerg-1426	62	5	f	f	PROPN
fuelectenerg-1426	62	6	(	(	PUNCT
fuelectenerg-1426	62	7	0,x2	0,x2	NOUN
fuelectenerg-1426	62	8	,	,	PUNCT
fuelectenerg-1426	62	9	.	.	PUNCT
fuelectenerg-1426	62	10	.	.	PUNCT
fuelectenerg-1426	62	11	.	.	PUNCT
fuelectenerg-1426	63	1	,	,	PUNCT
fuelectenerg-1426	63	2	xn	xn	X
fuelectenerg-1426	63	3	)	)	PUNCT
fuelectenerg-1426	63	4	=	=	SYM
fuelectenerg-1426	63	5	f0	f0	PROPN
fuelectenerg-1426	63	6	is	be	AUX
fuelectenerg-1426	63	7	the	the	DET
fuelectenerg-1426	63	8	negative	negative	ADJ
fuelectenerg-1426	63	9	cofactor	cofactor	NOUN
fuelectenerg-1426	63	10	of	of	ADP
fuelectenerg-1426	63	11	variable	variable	ADJ
fuelectenerg-1426	63	12	x1	x1	PROPN
fuelectenerg-1426	63	13	,	,	PUNCT
fuelectenerg-1426	63	14	f1(x1,x2	f1(x1,x2	PROPN
fuelectenerg-1426	63	15	,	,	PUNCT
fuelectenerg-1426	63	16	.	.	PUNCT
fuelectenerg-1426	63	17	.	.	PUNCT
fuelectenerg-1426	64	1	.	.	PUNCT
fuelectenerg-1426	65	1	,	,	PUNCT
fuelectenerg-1426	65	2	xn	xn	X
fuelectenerg-1426	65	3	)	)	PUNCT
fuelectenerg-1426	65	4	=	=	SYM
fuelectenerg-1426	65	5	f	f	PROPN
fuelectenerg-1426	65	6	(	(	PUNCT
fuelectenerg-1426	65	7	1,x2	1,x2	NUM
fuelectenerg-1426	65	8	,	,	PUNCT
fuelectenerg-1426	65	9	.	.	PUNCT
fuelectenerg-1426	65	10	.	.	PUNCT
fuelectenerg-1426	65	11	.	.	PUNCT
fuelectenerg-1426	66	1	,	,	PUNCT
fuelectenerg-1426	66	2	xn	xn	X
fuelectenerg-1426	66	3	)	)	PUNCT
fuelectenerg-1426	66	4	=	=	SYM
fuelectenerg-1426	66	5	f1	f1	NOUN
fuelectenerg-1426	66	6	is	be	AUX
fuelectenerg-1426	66	7	the	the	DET
fuelectenerg-1426	66	8	positive	positive	ADJ
fuelectenerg-1426	66	9	cofactor	cofactor	NOUN
fuelectenerg-1426	66	10	of	of	ADP
fuelectenerg-1426	66	11	variable	variable	NOUN
fuelectenerg-1426	66	12	x1	x1	PROPN
fuelectenerg-1426	66	13	,	,	PUNCT
fuelectenerg-1426	66	14	and	and	CCONJ
fuelectenerg-1426	66	15	f2(x1,x2	f2(x1,x2	NOUN
fuelectenerg-1426	66	16	,	,	PUNCT
fuelectenerg-1426	66	17	.	.	PUNCT
fuelectenerg-1426	66	18	.	.	PUNCT
fuelectenerg-1426	67	1	.	.	PUNCT
fuelectenerg-1426	68	1	,	,	PUNCT
fuelectenerg-1426	68	2	xn	xn	X
fuelectenerg-1426	68	3	)	)	PUNCT
fuelectenerg-1426	68	4	=	=	SYM
fuelectenerg-1426	68	5	f	f	PROPN
fuelectenerg-1426	68	6	(	(	PUNCT
fuelectenerg-1426	68	7	0,x2	0,x2	NOUN
fuelectenerg-1426	68	8	,	,	PUNCT
fuelectenerg-1426	68	9	.	.	PUNCT
fuelectenerg-1426	68	10	.	.	PUNCT
fuelectenerg-1426	68	11	.	.	PUNCT
fuelectenerg-1426	69	1	,	,	PUNCT
fuelectenerg-1426	69	2	xn)⊕	xn)⊕	PROPN
fuelectenerg-1426	69	3	f	f	PROPN
fuelectenerg-1426	69	4	(	(	PUNCT
fuelectenerg-1426	69	5	1,x2	1,x2	NUM
fuelectenerg-1426	69	6	,	,	PUNCT
fuelectenerg-1426	69	7	.	.	PUNCT
fuelectenerg-1426	69	8	.	.	PUNCT
fuelectenerg-1426	69	9	.	.	PUNCT
fuelectenerg-1426	70	1	,	,	PUNCT
fuelectenerg-1426	70	2	xn	xn	X
fuelectenerg-1426	70	3	)	)	PUNCT
fuelectenerg-1426	70	4	=	=	SYM
fuelectenerg-1426	70	5	f0	f0	PROPN
fuelectenerg-1426	70	6	⊕	⊕	PROPN
fuelectenerg-1426	70	7	f1	f1	NOUN
fuelectenerg-1426	70	8	.	.	PUNCT
fuelectenerg-1426	71	1	an	an	DET
fuelectenerg-1426	71	2	arbitrary	arbitrary	ADJ
fuelectenerg-1426	71	3	n	n	CCONJ
fuelectenerg-1426	71	4	-	-	PUNCT
fuelectenerg-1426	71	5	variable	variable	ADJ
fuelectenerg-1426	71	6	function	function	NOUN
fuelectenerg-1426	71	7	f	f	PROPN
fuelectenerg-1426	71	8	(	(	PUNCT
fuelectenerg-1426	71	9	x1,x2	x1,x2	PROPN
fuelectenerg-1426	71	10	,	,	PUNCT
fuelectenerg-1426	71	11	.	.	PUNCT
fuelectenerg-1426	71	12	.	.	PUNCT
fuelectenerg-1426	71	13	.	.	PUNCT
fuelectenerg-1426	72	1	,	,	PUNCT
fuelectenerg-1426	72	2	xn	xn	X
fuelectenerg-1426	72	3	)	)	PUNCT
fuelectenerg-1426	72	4	can	can	AUX
fuelectenerg-1426	72	5	be	be	AUX
fuelectenerg-1426	72	6	represented	represent	VERB
fuelectenerg-1426	72	7	using	use	VERB
fuelectenerg-1426	72	8	the	the	DET
fuelectenerg-1426	72	9	positive	positive	ADJ
fuelectenerg-1426	72	10	polarity	polarity	NOUN
fuelectenerg-1426	72	11	reed	reed	NOUN
fuelectenerg-1426	72	12	-	-	PUNCT
fuelectenerg-1426	72	13	muller	muller	NOUN
fuelectenerg-1426	72	14	(	(	PUNCT
fuelectenerg-1426	72	15	pprm	pprm	ADJ
fuelectenerg-1426	72	16	)	)	PUNCT
fuelectenerg-1426	72	17	expansion	expansion	NOUN
fuelectenerg-1426	72	18	as	as	SCONJ
fuelectenerg-1426	72	19	follows	follow	VERB
fuelectenerg-1426	72	20	:	:	PUNCT
fuelectenerg-1426	72	21	f	f	PROPN
fuelectenerg-1426	72	22	(	(	PUNCT
fuelectenerg-1426	72	23	x1,x2	x1,x2	PROPN
fuelectenerg-1426	72	24	,	,	PUNCT
fuelectenerg-1426	72	25	.	.	PUNCT
fuelectenerg-1426	72	26	.	.	PUNCT
fuelectenerg-1426	73	1	.	.	PUNCT
fuelectenerg-1426	74	1	,	,	PUNCT
fuelectenerg-1426	74	2	xn	xn	X
fuelectenerg-1426	74	3	)	)	PUNCT
fuelectenerg-1426	75	1	=	=	PROPN
fuelectenerg-1426	75	2	a0	a0	PROPN
fuelectenerg-1426	75	3	⊕	⊕	PROPN
fuelectenerg-1426	75	4	a1x1	a1x1	PROPN
fuelectenerg-1426	75	5	⊕	⊕	PROPN
fuelectenerg-1426	75	6	a2x2	a2x2	PROPN
fuelectenerg-1426	75	7	⊕	⊕	PROPN
fuelectenerg-1426	75	8	.	.	PUNCT
fuelectenerg-1426	75	9	.	.	PUNCT
fuelectenerg-1426	76	1	.⊕anxn	.⊕anxn	NOUN
fuelectenerg-1426	76	2	⊕a12x1x2	⊕a12x1x2	PROPN
fuelectenerg-1426	76	3	⊕a13x1x3	⊕a13x1x3	PROPN
fuelectenerg-1426	76	4	⊕an−1,nxn−1xn	⊕an−1,nxn−1xn	VERB
fuelectenerg-1426	76	5	⊕	⊕	PROPN
fuelectenerg-1426	76	6	.	.	PUNCT
fuelectenerg-1426	76	7	.	.	PUNCT
fuelectenerg-1426	77	1	.⊕	.⊕	PROPN
fuelectenerg-1426	77	2	a12	a12	PROPN
fuelectenerg-1426	77	3	...	...	PUNCT
fuelectenerg-1426	77	4	nx1x2	nx1x2	X
fuelectenerg-1426	77	5	.	.	PUNCT
fuelectenerg-1426	77	6	.	.	PUNCT
fuelectenerg-1426	78	1	.xn	.xn	PROPN
fuelectenerg-1426	78	2	.	.	PUNCT
fuelectenerg-1426	79	1	(	(	PUNCT
fuelectenerg-1426	79	2	4	4	X
fuelectenerg-1426	79	3	)	)	PUNCT
fuelectenerg-1426	79	4	for	for	ADP
fuelectenerg-1426	79	5	each	each	DET
fuelectenerg-1426	79	6	function	function	NOUN
fuelectenerg-1426	79	7	f	f	PROPN
fuelectenerg-1426	79	8	,	,	PUNCT
fuelectenerg-1426	79	9	the	the	DET
fuelectenerg-1426	79	10	coefficients	coefficient	NOUN
fuelectenerg-1426	79	11	ai	ai	VERB
fuelectenerg-1426	79	12	in	in	ADP
fuelectenerg-1426	79	13	equation	equation	NOUN
fuelectenerg-1426	79	14	(	(	PUNCT
fuelectenerg-1426	79	15	4	4	X
fuelectenerg-1426	79	16	)	)	PUNCT
fuelectenerg-1426	79	17	are	be	AUX
fuelectenerg-1426	79	18	determined	determine	VERB
fuelectenerg-1426	79	19	uniquely	uniquely	ADV
fuelectenerg-1426	79	20	,	,	PUNCT
fuelectenerg-1426	79	21	so	so	ADV
fuelectenerg-1426	79	22	pprm	pprm	ADJ
fuelectenerg-1426	79	23	is	be	AUX
fuelectenerg-1426	79	24	a	a	DET
fuelectenerg-1426	79	25	canonical	canonical	ADJ
fuelectenerg-1426	79	26	form	form	NOUN
fuelectenerg-1426	79	27	.	.	PUNCT
fuelectenerg-1426	80	1	if	if	SCONJ
fuelectenerg-1426	80	2	we	we	PRON
fuelectenerg-1426	80	3	use	use	VERB
fuelectenerg-1426	80	4	either	either	CCONJ
fuelectenerg-1426	80	5	only	only	ADV
fuelectenerg-1426	80	6	the	the	DET
fuelectenerg-1426	80	7	positive	positive	ADJ
fuelectenerg-1426	80	8	literal	literal	NOUN
fuelectenerg-1426	80	9	or	or	CCONJ
fuelectenerg-1426	80	10	only	only	ADV
fuelectenerg-1426	80	11	the	the	DET
fuelectenerg-1426	80	12	negative	negative	ADJ
fuelectenerg-1426	80	13	literal	literal	NOUN
fuelectenerg-1426	80	14	for	for	ADP
fuelectenerg-1426	80	15	each	each	DET
fuelectenerg-1426	80	16	variable	variable	NOUN
fuelectenerg-1426	80	17	in	in	ADP
fuelectenerg-1426	80	18	equation	equation	NOUN
fuelectenerg-1426	80	19	(	(	PUNCT
fuelectenerg-1426	80	20	4	4	X
fuelectenerg-1426	80	21	)	)	PUNCT
fuelectenerg-1426	80	22	we	we	PRON
fuelectenerg-1426	80	23	obtain	obtain	VERB
fuelectenerg-1426	80	24	the	the	DET
fuelectenerg-1426	80	25	fixed	fix	VERB
fuelectenerg-1426	80	26	polarity	polarity	NOUN
fuelectenerg-1426	80	27	reed	reed	NOUN
fuelectenerg-1426	80	28	-	-	PUNCT
fuelectenerg-1426	80	29	muller	muller	NOUN
fuelectenerg-1426	80	30	(	(	PUNCT
fuelectenerg-1426	80	31	fprm	fprm	PROPN
fuelectenerg-1426	80	32	)	)	PUNCT
fuelectenerg-1426	80	33	form	form	NOUN
fuelectenerg-1426	80	34	.	.	PUNCT
fuelectenerg-1426	81	1	there	there	PRON
fuelectenerg-1426	81	2	are	be	VERB
fuelectenerg-1426	81	3	2n	2n	NUM
fuelectenerg-1426	81	4	possible	possible	ADJ
fuelectenerg-1426	81	5	combinations	combination	NOUN
fuelectenerg-1426	81	6	of	of	ADP
fuelectenerg-1426	81	7	polarities	polarity	NOUN
fuelectenerg-1426	81	8	and	and	CCONJ
fuelectenerg-1426	81	9	as	as	ADV
fuelectenerg-1426	81	10	many	many	ADJ
fuelectenerg-1426	81	11	fprms	fprm	NOUN
fuelectenerg-1426	81	12	for	for	ADP
fuelectenerg-1426	81	13	any	any	DET
fuelectenerg-1426	81	14	given	give	VERB
fuelectenerg-1426	81	15	logic	logic	NOUN
fuelectenerg-1426	81	16	function	function	NOUN
fuelectenerg-1426	81	17	[	[	X
fuelectenerg-1426	81	18	2	2	NUM
fuelectenerg-1426	81	19	,	,	PUNCT
fuelectenerg-1426	81	20	32	32	NUM
fuelectenerg-1426	81	21	]	]	PUNCT
fuelectenerg-1426	81	22	.	.	PUNCT
fuelectenerg-1426	82	1	if	if	SCONJ
fuelectenerg-1426	82	2	we	we	PRON
fuelectenerg-1426	82	3	freely	freely	ADV
fuelectenerg-1426	82	4	choose	choose	VERB
fuelectenerg-1426	82	5	the	the	DET
fuelectenerg-1426	82	6	polarity	polarity	NOUN
fuelectenerg-1426	82	7	of	of	ADP
fuelectenerg-1426	82	8	each	each	DET
fuelectenerg-1426	82	9	literal	literal	ADJ
fuelectenerg-1426	82	10	in	in	ADP
fuelectenerg-1426	82	11	equation	equation	NOUN
fuelectenerg-1426	82	12	(	(	PUNCT
fuelectenerg-1426	82	13	4	4	NUM
fuelectenerg-1426	82	14	)	)	PUNCT
fuelectenerg-1426	82	15	,	,	PUNCT
fuelectenerg-1426	82	16	we	we	PRON
fuelectenerg-1426	82	17	obtain	obtain	VERB
fuelectenerg-1426	82	18	the	the	DET
fuelectenerg-1426	82	19	generalized	generalize	VERB
fuelectenerg-1426	82	20	reed	reed	NOUN
fuelectenerg-1426	82	21	-	-	PUNCT
fuelectenerg-1426	82	22	muller	muller	NOUN
fuelectenerg-1426	82	23	(	(	PUNCT
fuelectenerg-1426	82	24	grm	grm	NOUN
fuelectenerg-1426	82	25	)	)	PUNCT
fuelectenerg-1426	82	26	form	form	NOUN
fuelectenerg-1426	82	27	.	.	PUNCT
fuelectenerg-1426	83	1	in	in	ADP
fuelectenerg-1426	83	2	grms	grm	NOUN
fuelectenerg-1426	83	3	,	,	PUNCT
fuelectenerg-1426	83	4	contrary	contrary	ADV
fuelectenerg-1426	83	5	to	to	ADP
fuelectenerg-1426	83	6	fprms	fprm	NOUN
fuelectenerg-1426	83	7	,	,	PUNCT
fuelectenerg-1426	83	8	the	the	DET
fuelectenerg-1426	83	9	same	same	ADJ
fuelectenerg-1426	83	10	variable	variable	NOUN
fuelectenerg-1426	83	11	can	can	AUX
fuelectenerg-1426	83	12	appear	appear	VERB
fuelectenerg-1426	83	13	in	in	ADP
fuelectenerg-1426	83	14	both	both	CCONJ
fuelectenerg-1426	83	15	positive	positive	ADJ
fuelectenerg-1426	83	16	and	and	CCONJ
fuelectenerg-1426	83	17	negative	negative	ADJ
fuelectenerg-1426	83	18	polarities	polarity	NOUN
fuelectenerg-1426	83	19	.	.	PUNCT
fuelectenerg-1426	84	1	there	there	PRON
fuelectenerg-1426	84	2	are	be	VERB
fuelectenerg-1426	84	3	n2(n−1	n2(n−1	NOUN
fuelectenerg-1426	84	4	)	)	PUNCT
fuelectenerg-1426	84	5	literals	literal	NOUN
fuelectenerg-1426	84	6	in	in	ADP
fuelectenerg-1426	84	7	equation	equation	NOUN
fuelectenerg-1426	84	8	(	(	PUNCT
fuelectenerg-1426	84	9	4	4	NUM
fuelectenerg-1426	84	10	)	)	PUNCT
fuelectenerg-1426	84	11	so	so	SCONJ
fuelectenerg-1426	84	12	there	there	PRON
fuelectenerg-1426	84	13	are	be	VERB
fuelectenerg-1426	84	14	2n2(n−1	2n2(n−1	ADJ
fuelectenerg-1426	84	15	)	)	PUNCT
fuelectenerg-1426	84	16	polarities	polarity	NOUN
fuelectenerg-1426	84	17	for	for	ADP
fuelectenerg-1426	84	18	an	an	DET
fuelectenerg-1426	84	19	n	n	CCONJ
fuelectenerg-1426	84	20	-	-	PUNCT
fuelectenerg-1426	84	21	variable	variable	ADJ
fuelectenerg-1426	84	22	function	function	NOUN
fuelectenerg-1426	84	23	and	and	CCONJ
fuelectenerg-1426	84	24	as	as	ADV
fuelectenerg-1426	84	25	many	many	ADJ
fuelectenerg-1426	84	26	grms	grm	NOUN
fuelectenerg-1426	84	27	[	[	X
fuelectenerg-1426	84	28	32	32	NUM
fuelectenerg-1426	84	29	]	]	PUNCT
fuelectenerg-1426	84	30	.	.	PUNCT
fuelectenerg-1426	85	1	each	each	PRON
fuelectenerg-1426	85	2	of	of	ADP
fuelectenerg-1426	85	3	the	the	DET
fuelectenerg-1426	85	4	polarities	polarity	NOUN
fuelectenerg-1426	85	5	determines	determine	VERB
fuelectenerg-1426	85	6	a	a	DET
fuelectenerg-1426	85	7	unique	unique	ADJ
fuelectenerg-1426	85	8	set	set	NOUN
fuelectenerg-1426	85	9	of	of	ADP
fuelectenerg-1426	85	10	coefficients	coefficient	NOUN
fuelectenerg-1426	85	11	,	,	PUNCT
fuelectenerg-1426	85	12	and	and	CCONJ
fuelectenerg-1426	85	13	thus	thus	ADV
fuelectenerg-1426	85	14	each	each	DET
fuelectenerg-1426	85	15	grm	grm	NOUN
fuelectenerg-1426	85	16	is	be	AUX
fuelectenerg-1426	85	17	a	a	DET
fuelectenerg-1426	85	18	canonical	canonical	ADJ
fuelectenerg-1426	85	19	representation	representation	NOUN
fuelectenerg-1426	85	20	of	of	ADP
fuelectenerg-1426	85	21	a	a	DET
fuelectenerg-1426	85	22	function	function	NOUN
fuelectenerg-1426	85	23	.	.	PUNCT
fuelectenerg-1426	86	1	two	two	NUM
fuelectenerg-1426	86	2	other	other	ADJ
fuelectenerg-1426	86	3	types	type	NOUN
fuelectenerg-1426	86	4	of	of	ADP
fuelectenerg-1426	86	5	expansions	expansion	NOUN
fuelectenerg-1426	86	6	result	result	VERB
fuelectenerg-1426	86	7	from	from	ADP
fuelectenerg-1426	86	8	the	the	DET
fuelectenerg-1426	86	9	flattening	flattening	NOUN
fuelectenerg-1426	86	10	of	of	ADP
fuelectenerg-1426	86	11	certain	certain	ADJ
fuelectenerg-1426	86	12	binary	binary	ADJ
fuelectenerg-1426	86	13	trees	tree	NOUN
fuelectenerg-1426	86	14	that	that	PRON
fuelectenerg-1426	86	15	will	will	AUX
fuelectenerg-1426	86	16	produce	produce	VERB
fuelectenerg-1426	86	17	kronecker	kronecker	NOUN
fuelectenerg-1426	86	18	(	(	PUNCT
fuelectenerg-1426	86	19	kro	kro	PROPN
fuelectenerg-1426	86	20	)	)	PUNCT
fuelectenerg-1426	86	21	forms	form	NOUN
fuelectenerg-1426	86	22	and	and	CCONJ
fuelectenerg-1426	86	23	pseudo	pseudo	NOUN
fuelectenerg-1426	86	24	kronecker	kronecker	NOUN
fuelectenerg-1426	86	25	(	(	PUNCT
fuelectenerg-1426	86	26	pkro	pkro	ADJ
fuelectenerg-1426	86	27	)	)	PUNCT
fuelectenerg-1426	86	28	forms	form	NOUN
fuelectenerg-1426	86	29	for	for	ADP
fuelectenerg-1426	86	30	shannon	shannon	NOUN
fuelectenerg-1426	86	31	,	,	PUNCT
fuelectenerg-1426	86	32	positive	positive	ADJ
fuelectenerg-1426	86	33	davio	davio	NOUN
fuelectenerg-1426	86	34	and	and	CCONJ
fuelectenerg-1426	86	35	negative	negative	ADJ
fuelectenerg-1426	86	36	davio	davio	NOUN
fuelectenerg-1426	86	37	expansions	expansion	NOUN
fuelectenerg-1426	86	38	.	.	PUNCT
fuelectenerg-1426	87	1	there	there	PRON
fuelectenerg-1426	87	2	are	be	VERB
fuelectenerg-1426	87	3	3n	3n	NUM
fuelectenerg-1426	87	4	and	and	CCONJ
fuelectenerg-1426	87	5	at	at	ADP
fuelectenerg-1426	87	6	most	most	ADJ
fuelectenerg-1426	87	7	32n−1	32n−1	NUM
fuelectenerg-1426	87	8	different	different	ADJ
fuelectenerg-1426	87	9	kros	kro	NOUN
fuelectenerg-1426	87	10	and	and	CCONJ
fuelectenerg-1426	87	11	pkros	pkro	NOUN
fuelectenerg-1426	87	12	,	,	PUNCT
fuelectenerg-1426	87	13	respectively	respectively	ADV
fuelectenerg-1426	87	14	[	[	X
fuelectenerg-1426	87	15	32	32	NUM
fuelectenerg-1426	87	16	]	]	PUNCT
fuelectenerg-1426	87	17	.	.	PUNCT
fuelectenerg-1426	88	1	the	the	DET
fuelectenerg-1426	88	2	good	good	ADJ
fuelectenerg-1426	88	3	selection	selection	NOUN
fuelectenerg-1426	88	4	of	of	ADP
fuelectenerg-1426	88	5	the	the	DET
fuelectenerg-1426	88	6	various	various	ADJ
fuelectenerg-1426	88	7	permutations	permutation	NOUN
fuelectenerg-1426	88	8	using	use	VERB
fuelectenerg-1426	88	9	the	the	DET
fuelectenerg-1426	88	10	shannon	shannon	NOUN
fuelectenerg-1426	88	11	and	and	CCONJ
fuelectenerg-1426	88	12	davio	davio	NOUN
fuelectenerg-1426	88	13	expansions	expansion	NOUN
fuelectenerg-1426	88	14	as	as	SCONJ
fuelectenerg-1426	88	15	internal	internal	ADJ
fuelectenerg-1426	88	16	nodes	node	NOUN
fuelectenerg-1426	88	17	in	in	ADP
fuelectenerg-1426	88	18	decision	decision	NOUN
fuelectenerg-1426	88	19	trees	tree	NOUN
fuelectenerg-1426	88	20	(	(	PUNCT
fuelectenerg-1426	88	21	dts	dts	NOUN
fuelectenerg-1426	88	22	)	)	PUNCT
fuelectenerg-1426	88	23	and	and	CCONJ
fuelectenerg-1426	88	24	diagrams	diagram	NOUN
fuelectenerg-1426	88	25	(	(	PUNCT
fuelectenerg-1426	88	26	dds	dds	PROPN
fuelectenerg-1426	88	27	)	)	PUNCT
fuelectenerg-1426	88	28	will	will	AUX
fuelectenerg-1426	88	29	result	result	VERB
fuelectenerg-1426	88	30	in	in	ADP
fuelectenerg-1426	88	31	dts	dts	PROPN
fuelectenerg-1426	88	32	and	and	CCONJ
fuelectenerg-1426	88	33	dds	dds	PROPN
fuelectenerg-1426	88	34	,	,	PUNCT
fuelectenerg-1426	88	35	that	that	PRON
fuelectenerg-1426	88	36	represent	represent	VERB
fuelectenerg-1426	88	37	the	the	DET
fuelectenerg-1426	88	38	corresponding	corresponding	ADJ
fuelectenerg-1426	88	39	logic	logic	NOUN
fuelectenerg-1426	88	40	functions	function	NOUN
fuelectenerg-1426	88	41	,	,	PUNCT
fuelectenerg-1426	88	42	with	with	ADP
fuelectenerg-1426	88	43	smaller	small	ADJ
fuelectenerg-1426	88	44	sizes	size	NOUN
fuelectenerg-1426	88	45	in	in	ADP
fuelectenerg-1426	88	46	terms	term	NOUN
fuelectenerg-1426	88	47	of	of	ADP
fuelectenerg-1426	88	48	the	the	DET
fuelectenerg-1426	88	49	total	total	ADJ
fuelectenerg-1426	88	50	number	number	NOUN
fuelectenerg-1426	88	51	of	of	ADP
fuelectenerg-1426	88	52	hierarchical	hierarchical	ADJ
fuelectenerg-1426	88	53	levels	level	NOUN
fuelectenerg-1426	88	54	used	use	VERB
fuelectenerg-1426	88	55	,	,	PUNCT
fuelectenerg-1426	88	56	and	and	CCONJ
fuelectenerg-1426	88	57	the	the	DET
fuelectenerg-1426	88	58	total	total	ADJ
fuelectenerg-1426	88	59	number	number	NOUN
fuelectenerg-1426	88	60	of	of	ADP
fuelectenerg-1426	88	61	internal	internal	ADJ
fuelectenerg-1426	88	62	nodes	node	NOUN
fuelectenerg-1426	88	63	needed	need	VERB
fuelectenerg-1426	88	64	.	.	PUNCT
fuelectenerg-1426	89	1	the	the	DET
fuelectenerg-1426	89	2	minimization	minimization	NOUN
fuelectenerg-1426	89	3	of	of	ADP
fuelectenerg-1426	89	4	the	the	DET
fuelectenerg-1426	89	5	size	size	NOUN
fuelectenerg-1426	89	6	of	of	ADP
fuelectenerg-1426	89	7	dd	dd	NOUN
fuelectenerg-1426	89	8	,	,	PUNCT
fuelectenerg-1426	89	9	to	to	PART
fuelectenerg-1426	89	10	represent	represent	VERB
fuelectenerg-1426	89	11	a	a	DET
fuelectenerg-1426	89	12	logic	logic	NOUN
fuelectenerg-1426	89	13	function	function	NOUN
fuelectenerg-1426	89	14	,	,	PUNCT
fuelectenerg-1426	89	15	will	will	AUX
fuelectenerg-1426	89	16	result	result	VERB
fuelectenerg-1426	89	17	in	in	ADP
fuelectenerg-1426	89	18	speeding	speed	VERB
fuelectenerg-1426	89	19	up	up	ADP
fuelectenerg-1426	89	20	the	the	DET
fuelectenerg-1426	89	21	manipulations	manipulation	NOUN
fuelectenerg-1426	89	22	of	of	ADP
fuelectenerg-1426	89	23	logic	logic	NOUN
fuelectenerg-1426	89	24	functions	function	NOUN
fuelectenerg-1426	89	25	using	use	VERB
fuelectenerg-1426	89	26	dd	dd	NOUN
fuelectenerg-1426	89	27	as	as	ADP
fuelectenerg-1426	89	28	data	data	NOUN
fuelectenerg-1426	89	29	structure	structure	NOUN
fuelectenerg-1426	89	30	,	,	PUNCT
fuelectenerg-1426	89	31	and	and	CCONJ
fuelectenerg-1426	89	32	the	the	DET
fuelectenerg-1426	89	33	minimization	minimization	NOUN
fuelectenerg-1426	89	34	of	of	ADP
fuelectenerg-1426	89	35	the	the	DET
fuelectenerg-1426	89	36	use	use	NOUN
fuelectenerg-1426	89	37	of	of	ADP
fuelectenerg-1426	89	38	memory	memory	NOUN
fuelectenerg-1426	89	39	space	space	NOUN
fuelectenerg-1426	89	40	during	during	ADP
fuelectenerg-1426	89	41	the	the	DET
fuelectenerg-1426	89	42	execution	execution	NOUN
fuelectenerg-1426	89	43	of	of	ADP
fuelectenerg-1426	89	44	such	such	ADJ
fuelectenerg-1426	89	45	manipulations	manipulation	NOUN
fuelectenerg-1426	89	46	.	.	PUNCT
fuelectenerg-1426	90	1	one	one	PRON
fuelectenerg-1426	90	2	can	can	AUX
fuelectenerg-1426	90	3	observe	observe	VERB
fuelectenerg-1426	90	4	that	that	SCONJ
fuelectenerg-1426	90	5	103	103	NUM
fuelectenerg-1426	90	6	704	704	NUM
fuelectenerg-1426	90	7	a.	a.	NOUN
fuelectenerg-1426	90	8	n.	n.	PROPN
fuelectenerg-1426	90	9	al	al	PROPN
fuelectenerg-1426	90	10	-	-	PUNCT
fuelectenerg-1426	90	11	rabadi	rabadi	PROPN
fuelectenerg-1426	90	12	multi	multi	ADJ
fuelectenerg-1426	90	13	-	-	ADJ
fuelectenerg-1426	90	14	valued	value	VERB
fuelectenerg-1426	90	15	galois	galois	PROPN
fuelectenerg-1426	90	16	shannon	shannon	PROPN
fuelectenerg-1426	90	17	davio	davio	PROPN
fuelectenerg-1426	90	18	trees	tree	NOUN
fuelectenerg-1426	90	19	and	and	CCONJ
fuelectenerg-1426	90	20	their	their	PRON
fuelectenerg-1426	90	21	complexity	complexity	NOUN
fuelectenerg-1426	90	22	705	705	NUM
fuelectenerg-1426	90	23	multi	multi	ADJ
fuelectenerg-1426	90	24	-	-	ADJ
fuelectenerg-1426	90	25	valued	value	VERB
fuelectenerg-1426	90	26	galois	galois	PROPN
fuelectenerg-1426	90	27	shannon	shannon	PROPN
fuelectenerg-1426	90	28	davio	davio	PROPN
fuelectenerg-1426	90	29	trees	tree	NOUN
fuelectenerg-1426	90	30	and	and	CCONJ
fuelectenerg-1426	90	31	their	their	PRON
fuelectenerg-1426	90	32	complexity	complexity	NOUN
fuelectenerg-1426	90	33	by	by	ADP
fuelectenerg-1426	90	34	going	go	VERB
fuelectenerg-1426	90	35	from	from	ADP
fuelectenerg-1426	90	36	pprm	pprm	ADJ
fuelectenerg-1426	90	37	to	to	ADP
fuelectenerg-1426	90	38	grm	grm	NOUN
fuelectenerg-1426	90	39	forms	form	NOUN
fuelectenerg-1426	90	40	,	,	PUNCT
fuelectenerg-1426	90	41	less	less	ADJ
fuelectenerg-1426	90	42	constraints	constraint	NOUN
fuelectenerg-1426	90	43	are	be	AUX
fuelectenerg-1426	90	44	imposed	impose	VERB
fuelectenerg-1426	90	45	on	on	ADP
fuelectenerg-1426	90	46	the	the	DET
fuelectenerg-1426	90	47	canonical	canonical	ADJ
fuelectenerg-1426	90	48	forms	form	NOUN
fuelectenerg-1426	90	49	due	due	ADJ
fuelectenerg-1426	90	50	to	to	ADP
fuelectenerg-1426	90	51	the	the	DET
fuelectenerg-1426	90	52	enlarged	enlarged	ADJ
fuelectenerg-1426	90	53	set	set	NOUN
fuelectenerg-1426	90	54	of	of	ADP
fuelectenerg-1426	90	55	polarities	polarity	NOUN
fuelectenerg-1426	90	56	that	that	PRON
fuelectenerg-1426	90	57	one	one	PRON
fuelectenerg-1426	90	58	can	can	AUX
fuelectenerg-1426	90	59	choose	choose	VERB
fuelectenerg-1426	90	60	from	from	ADP
fuelectenerg-1426	90	61	.	.	PUNCT
fuelectenerg-1426	91	1	the	the	DET
fuelectenerg-1426	91	2	gain	gain	NOUN
fuelectenerg-1426	91	3	of	of	ADP
fuelectenerg-1426	91	4	more	more	ADJ
fuelectenerg-1426	91	5	freedom	freedom	NOUN
fuelectenerg-1426	91	6	(	(	PUNCT
fuelectenerg-1426	91	7	less	less	ADJ
fuelectenerg-1426	91	8	constraints	constraint	NOUN
fuelectenerg-1426	91	9	)	)	PUNCT
fuelectenerg-1426	91	10	on	on	ADP
fuelectenerg-1426	91	11	the	the	DET
fuelectenerg-1426	91	12	polarity	polarity	NOUN
fuelectenerg-1426	91	13	of	of	ADP
fuelectenerg-1426	91	14	the	the	DET
fuelectenerg-1426	91	15	canonical	canonical	ADJ
fuelectenerg-1426	91	16	expansions	expansion	NOUN
fuelectenerg-1426	91	17	will	will	AUX
fuelectenerg-1426	91	18	provide	provide	VERB
fuelectenerg-1426	91	19	an	an	DET
fuelectenerg-1426	91	20	advantage	advantage	NOUN
fuelectenerg-1426	91	21	of	of	ADP
fuelectenerg-1426	91	22	obtaining	obtain	VERB
fuelectenerg-1426	91	23	exclusive	exclusive	ADJ
fuelectenerg-1426	91	24	-	-	PUNCT
fuelectenerg-1426	91	25	sum	sum	NOUN
fuelectenerg-1426	91	26	-	-	PUNCT
fuelectenerg-1426	91	27	of	of	ADP
fuelectenerg-1426	91	28	-	-	PUNCT
fuelectenerg-1426	91	29	product	product	NOUN
fuelectenerg-1426	91	30	(	(	PUNCT
fuelectenerg-1426	91	31	esop	esop	PROPN
fuelectenerg-1426	91	32	)	)	PUNCT
fuelectenerg-1426	91	33	expressions	expression	NOUN
fuelectenerg-1426	91	34	with	with	ADP
fuelectenerg-1426	91	35	less	less	ADJ
fuelectenerg-1426	91	36	number	number	NOUN
fuelectenerg-1426	91	37	of	of	ADP
fuelectenerg-1426	91	38	terms	term	NOUN
fuelectenerg-1426	91	39	and	and	CCONJ
fuelectenerg-1426	91	40	literals	literal	NOUN
fuelectenerg-1426	91	41	,	,	PUNCT
fuelectenerg-1426	91	42	and	and	CCONJ
fuelectenerg-1426	91	43	consequently	consequently	ADV
fuelectenerg-1426	91	44	expressing	express	VERB
fuelectenerg-1426	91	45	boolean	boolean	ADJ
fuelectenerg-1426	91	46	functions	function	NOUN
fuelectenerg-1426	91	47	using	use	VERB
fuelectenerg-1426	91	48	esop	esop	NOUN
fuelectenerg-1426	91	49	forms	form	NOUN
fuelectenerg-1426	91	50	will	will	AUX
fuelectenerg-1426	91	51	produce	produce	VERB
fuelectenerg-1426	91	52	on	on	ADP
fuelectenerg-1426	91	53	average	average	ADJ
fuelectenerg-1426	91	54	expressions	expression	NOUN
fuelectenerg-1426	91	55	with	with	ADP
fuelectenerg-1426	91	56	less	less	ADJ
fuelectenerg-1426	91	57	size	size	NOUN
fuelectenerg-1426	91	58	as	as	SCONJ
fuelectenerg-1426	91	59	if	if	SCONJ
fuelectenerg-1426	91	60	compared	compare	VERB
fuelectenerg-1426	91	61	to	to	ADP
fuelectenerg-1426	91	62	sum	sum	NOUN
fuelectenerg-1426	91	63	-	-	PUNCT
fuelectenerg-1426	91	64	of	of	ADP
fuelectenerg-1426	91	65	-	-	PUNCT
fuelectenerg-1426	91	66	product	product	NOUN
fuelectenerg-1426	91	67	(	(	PUNCT
fuelectenerg-1426	91	68	sop	sop	NOUN
fuelectenerg-1426	91	69	)	)	PUNCT
fuelectenerg-1426	91	70	expressions	expression	NOUN
fuelectenerg-1426	91	71	.	.	PUNCT
fuelectenerg-1426	92	1	in	in	ADP
fuelectenerg-1426	92	2	general	general	ADJ
fuelectenerg-1426	92	3	,	,	PUNCT
fuelectenerg-1426	92	4	a	a	DET
fuelectenerg-1426	92	5	literal	literal	NOUN
fuelectenerg-1426	92	6	can	can	AUX
fuelectenerg-1426	92	7	be	be	AUX
fuelectenerg-1426	92	8	defined	define	VERB
fuelectenerg-1426	92	9	as	as	ADP
fuelectenerg-1426	92	10	any	any	DET
fuelectenerg-1426	92	11	function	function	NOUN
fuelectenerg-1426	92	12	of	of	ADP
fuelectenerg-1426	92	13	a	a	DET
fuelectenerg-1426	92	14	single	single	ADJ
fuelectenerg-1426	92	15	variable	variable	NOUN
fuelectenerg-1426	92	16	[	[	X
fuelectenerg-1426	92	17	2	2	NUM
fuelectenerg-1426	92	18	,	,	PUNCT
fuelectenerg-1426	92	19	18	18	NUM
fuelectenerg-1426	92	20	,	,	PUNCT
fuelectenerg-1426	92	21	32	32	NUM
fuelectenerg-1426	92	22	]	]	PUNCT
fuelectenerg-1426	92	23	.	.	PUNCT
fuelectenerg-1426	93	1	basis	basis	NOUN
fuelectenerg-1426	93	2	functions	function	NOUN
fuelectenerg-1426	93	3	in	in	ADP
fuelectenerg-1426	93	4	the	the	DET
fuelectenerg-1426	93	5	general	general	ADJ
fuelectenerg-1426	93	6	case	case	NOUN
fuelectenerg-1426	93	7	of	of	ADP
fuelectenerg-1426	93	8	multi	multi	ADJ
fuelectenerg-1426	93	9	-	-	ADJ
fuelectenerg-1426	93	10	valued	value	VERB
fuelectenerg-1426	93	11	expansions	expansion	NOUN
fuelectenerg-1426	93	12	are	be	AUX
fuelectenerg-1426	93	13	constructed	construct	VERB
fuelectenerg-1426	93	14	using	use	VERB
fuelectenerg-1426	93	15	literals	literal	NOUN
fuelectenerg-1426	93	16	.	.	PUNCT
fuelectenerg-1426	94	1	galois	galois	PROPN
fuelectenerg-1426	94	2	field	field	PROPN
fuelectenerg-1426	94	3	sop	sop	PROPN
fuelectenerg-1426	94	4	expansions	expansion	NOUN
fuelectenerg-1426	94	5	can	can	AUX
fuelectenerg-1426	94	6	be	be	AUX
fuelectenerg-1426	94	7	performed	perform	VERB
fuelectenerg-1426	94	8	on	on	ADP
fuelectenerg-1426	94	9	variety	variety	NOUN
fuelectenerg-1426	94	10	of	of	ADP
fuelectenerg-1426	94	11	literals	literal	NOUN
fuelectenerg-1426	94	12	.	.	PUNCT
fuelectenerg-1426	95	1	for	for	ADP
fuelectenerg-1426	95	2	example	example	NOUN
fuelectenerg-1426	95	3	,	,	PUNCT
fuelectenerg-1426	95	4	one	one	PRON
fuelectenerg-1426	95	5	can	can	AUX
fuelectenerg-1426	95	6	use	use	VERB
fuelectenerg-1426	95	7	among	among	ADP
fuelectenerg-1426	95	8	others	other	NOUN
fuelectenerg-1426	95	9	:	:	PUNCT
fuelectenerg-1426	95	10	k	k	ADJ
fuelectenerg-1426	95	11	-	-	PUNCT
fuelectenerg-1426	95	12	reduced	reduce	VERB
fuelectenerg-1426	95	13	post	post	NOUN
fuelectenerg-1426	95	14	literal	literal	ADJ
fuelectenerg-1426	95	15	(	(	PUNCT
fuelectenerg-1426	95	16	k	k	X
fuelectenerg-1426	95	17	-	-	NOUN
fuelectenerg-1426	95	18	rpl	rpl	NOUN
fuelectenerg-1426	95	19	)	)	PUNCT
fuelectenerg-1426	95	20	to	to	PART
fuelectenerg-1426	95	21	produce	produce	VERB
fuelectenerg-1426	95	22	k	k	ADJ
fuelectenerg-1426	95	23	-	-	ADJ
fuelectenerg-1426	95	24	rpl	rpl	PROPN
fuelectenerg-1426	95	25	gfsop	gfsop	NOUN
fuelectenerg-1426	95	26	,	,	PUNCT
fuelectenerg-1426	95	27	post	post	VERB
fuelectenerg-1426	95	28	literal	literal	ADJ
fuelectenerg-1426	95	29	to	to	PART
fuelectenerg-1426	95	30	produce	produce	VERB
fuelectenerg-1426	95	31	pl	pl	PROPN
fuelectenerg-1426	95	32	gfsop	gfsop	NOUN
fuelectenerg-1426	95	33	,	,	PUNCT
fuelectenerg-1426	95	34	window	window	NOUN
fuelectenerg-1426	95	35	literal	literal	NOUN
fuelectenerg-1426	95	36	to	to	PART
fuelectenerg-1426	95	37	produce	produce	VERB
fuelectenerg-1426	95	38	wl	wl	NOUN
fuelectenerg-1426	95	39	gfsop	gfsop	PROPN
fuelectenerg-1426	95	40	,	,	PUNCT
fuelectenerg-1426	95	41	generalized	generalize	VERB
fuelectenerg-1426	95	42	(	(	PUNCT
fuelectenerg-1426	95	43	post	post	NOUN
fuelectenerg-1426	95	44	)	)	PUNCT
fuelectenerg-1426	95	45	literal	literal	ADJ
fuelectenerg-1426	95	46	to	to	PART
fuelectenerg-1426	95	47	produce	produce	VERB
fuelectenerg-1426	95	48	gl	gl	NOUN
fuelectenerg-1426	95	49	gfsop	gfsop	PROPN
fuelectenerg-1426	95	50	,	,	PUNCT
fuelectenerg-1426	95	51	or	or	CCONJ
fuelectenerg-1426	95	52	universal	universal	ADJ
fuelectenerg-1426	95	53	literal	literal	ADJ
fuelectenerg-1426	95	54	to	to	PART
fuelectenerg-1426	95	55	produce	produce	VERB
fuelectenerg-1426	95	56	ul	ul	INTJ
fuelectenerg-1426	95	57	gfsop	gfsop	PROPN
fuelectenerg-1426	95	58	.	.	PUNCT
fuelectenerg-1426	96	1	figure	figure	NOUN
fuelectenerg-1426	96	2	2	2	NUM
fuelectenerg-1426	96	3	demonstrates	demonstrate	VERB
fuelectenerg-1426	96	4	set	set	VERB
fuelectenerg-1426	96	5	-	-	PUNCT
fuelectenerg-1426	96	6	theoretic	theoretic	NOUN
fuelectenerg-1426	96	7	relationships	relationship	NOUN
fuelectenerg-1426	96	8	between	between	ADP
fuelectenerg-1426	96	9	the	the	DET
fuelectenerg-1426	96	10	various	various	ADJ
fuelectenerg-1426	96	11	literals	literal	NOUN
fuelectenerg-1426	96	12	,	,	PUNCT
fuelectenerg-1426	96	13	where	where	SCONJ
fuelectenerg-1426	96	14	the	the	DET
fuelectenerg-1426	96	15	shaded	shaded	ADJ
fuelectenerg-1426	96	16	reduced	reduced	ADJ
fuelectenerg-1426	96	17	post	post	NOUN
fuelectenerg-1426	96	18	literal	literal	ADJ
fuelectenerg-1426	96	19	is	be	AUX
fuelectenerg-1426	96	20	the	the	DET
fuelectenerg-1426	96	21	type	type	NOUN
fuelectenerg-1426	96	22	of	of	ADP
fuelectenerg-1426	96	23	literal	literal	NOUN
fuelectenerg-1426	96	24	that	that	PRON
fuelectenerg-1426	96	25	will	will	AUX
fuelectenerg-1426	96	26	be	be	AUX
fuelectenerg-1426	96	27	used	use	VERB
fuelectenerg-1426	96	28	through	through	ADP
fuelectenerg-1426	96	29	this	this	DET
fuelectenerg-1426	96	30	paper	paper	NOUN
fuelectenerg-1426	96	31	.	.	PUNCT
fuelectenerg-1426	97	1	one	one	PRON
fuelectenerg-1426	97	2	may	may	AUX
fuelectenerg-1426	97	3	note	note	VERB
fuelectenerg-1426	97	4	that	that	SCONJ
fuelectenerg-1426	97	5	the	the	DET
fuelectenerg-1426	97	6	rpl	rpl	NOUN
fuelectenerg-1426	97	7	in	in	ADP
fuelectenerg-1426	97	8	the	the	DET
fuelectenerg-1426	97	9	discrete	discrete	ADJ
fuelectenerg-1426	97	10	domain	domain	NOUN
fuelectenerg-1426	97	11	is	be	AUX
fuelectenerg-1426	97	12	analogous	analogous	ADJ
fuelectenerg-1426	97	13	to	to	ADP
fuelectenerg-1426	97	14	the	the	DET
fuelectenerg-1426	97	15	delta	delta	NOUN
fuelectenerg-1426	97	16	function	function	NOUN
fuelectenerg-1426	97	17	in	in	ADP
fuelectenerg-1426	97	18	the	the	DET
fuelectenerg-1426	97	19	continuous	continuous	ADJ
fuelectenerg-1426	97	20	domain	domain	NOUN
fuelectenerg-1426	97	21	.	.	PUNCT
fuelectenerg-1426	98	1	reduced	reduce	VERB
fuelectenerg-1426	98	2	post	post	NOUN
fuelectenerg-1426	98	3	literal	literal	ADJ
fuelectenerg-1426	98	4	post	post	NOUN
fuelectenerg-1426	98	5	literal	literal	ADJ
fuelectenerg-1426	98	6	window	window	NOUN
fuelectenerg-1426	98	7	literal	literal	NOUN
fuelectenerg-1426	98	8	generalized	generalize	VERB
fuelectenerg-1426	98	9	(	(	PUNCT
fuelectenerg-1426	98	10	post	post	ADJ
fuelectenerg-1426	98	11	)	)	PUNCT
fuelectenerg-1426	98	12	literal	literal	ADJ
fuelectenerg-1426	98	13	universal	universal	ADJ
fuelectenerg-1426	98	14	literal	literal	ADJ
fuelectenerg-1426	98	15	fig	fig	NOUN
fuelectenerg-1426	98	16	.	.	PUNCT
fuelectenerg-1426	99	1	2	2	NUM
fuelectenerg-1426	99	2	:	:	PUNCT
fuelectenerg-1426	99	3	inclusion	inclusion	NOUN
fuelectenerg-1426	99	4	relationship	relationship	NOUN
fuelectenerg-1426	99	5	of	of	ADP
fuelectenerg-1426	99	6	various	various	ADJ
fuelectenerg-1426	99	7	types	type	NOUN
fuelectenerg-1426	99	8	of	of	ADP
fuelectenerg-1426	99	9	literals	literal	NOUN
fuelectenerg-1426	99	10	.	.	PUNCT
fuelectenerg-1426	100	1	example	example	NOUN
fuelectenerg-1426	101	1	1	1	NUM
fuelectenerg-1426	101	2	.	.	X
fuelectenerg-1426	102	1	figure	figure	NOUN
fuelectenerg-1426	102	2	3	3	NUM
fuelectenerg-1426	102	3	demonstrates	demonstrate	VERB
fuelectenerg-1426	102	4	several	several	ADJ
fuelectenerg-1426	102	5	literal	literal	ADJ
fuelectenerg-1426	102	6	types	type	NOUN
fuelectenerg-1426	102	7	,	,	PUNCT
fuelectenerg-1426	102	8	where	where	SCONJ
fuelectenerg-1426	102	9	one	one	NUM
fuelectenerg-1426	102	10	proceeds	proceed	VERB
fuelectenerg-1426	102	11	from	from	ADP
fuelectenerg-1426	102	12	the	the	DET
fuelectenerg-1426	102	13	simplest	simple	ADJ
fuelectenerg-1426	102	14	rpl	rpl	NOUN
fuelectenerg-1426	102	15	literal	literal	NOUN
fuelectenerg-1426	102	16	in	in	ADP
fuelectenerg-1426	102	17	figure	figure	NOUN
fuelectenerg-1426	102	18	3(a	3(a	NUM
fuelectenerg-1426	102	19	)	)	PUNCT
fuelectenerg-1426	102	20	to	to	ADP
fuelectenerg-1426	102	21	the	the	DET
fuelectenerg-1426	102	22	more	more	ADV
fuelectenerg-1426	102	23	complex	complex	ADJ
fuelectenerg-1426	102	24	wl	wl	X
fuelectenerg-1426	102	25	literal	literal	NOUN
fuelectenerg-1426	102	26	in	in	ADP
fuelectenerg-1426	102	27	figure	figure	NOUN
fuelectenerg-1426	102	28	3(c	3(c	NUM
fuelectenerg-1426	102	29	)	)	PUNCT
fuelectenerg-1426	102	30	.	.	PUNCT
fuelectenerg-1426	103	1	for	for	ADP
fuelectenerg-1426	103	2	rpl	rpl	NOUN
fuelectenerg-1426	103	3	in	in	ADP
fuelectenerg-1426	103	4	figure	figure	NOUN
fuelectenerg-1426	103	5	3(a	3(a	NUM
fuelectenerg-1426	103	6	)	)	PUNCT
fuelectenerg-1426	103	7	,	,	PUNCT
fuelectenerg-1426	103	8	a	a	DET
fuelectenerg-1426	103	9	value	value	NOUN
fuelectenerg-1426	103	10	k	k	NOUN
fuelectenerg-1426	103	11	is	be	AUX
fuelectenerg-1426	103	12	produced	produce	VERB
fuelectenerg-1426	103	13	by	by	ADP
fuelectenerg-1426	103	14	the	the	DET
fuelectenerg-1426	103	15	literal	literal	NOUN
fuelectenerg-1426	103	16	when	when	SCONJ
fuelectenerg-1426	103	17	the	the	DET
fuelectenerg-1426	103	18	value	value	NOUN
fuelectenerg-1426	103	19	of	of	ADP
fuelectenerg-1426	103	20	the	the	DET
fuelectenerg-1426	103	21	variable	variable	NOUN
fuelectenerg-1426	103	22	is	be	AUX
fuelectenerg-1426	103	23	equal	equal	ADJ
fuelectenerg-1426	103	24	to	to	ADP
fuelectenerg-1426	103	25	a	a	DET
fuelectenerg-1426	103	26	specific	specific	ADJ
fuelectenerg-1426	103	27	state	state	NOUN
fuelectenerg-1426	103	28	,	,	PUNCT
fuelectenerg-1426	103	29	and	and	CCONJ
fuelectenerg-1426	103	30	in	in	ADP
fuelectenerg-1426	103	31	this	this	DET
fuelectenerg-1426	103	32	particular	particular	ADJ
fuelectenerg-1426	103	33	example	example	NOUN
fuelectenerg-1426	103	34	a	a	DET
fuelectenerg-1426	103	35	value	value	NOUN
fuelectenerg-1426	103	36	k	k	NOUN
fuelectenerg-1426	103	37	=	=	SYM
fuelectenerg-1426	103	38	1	1	NUM
fuelectenerg-1426	103	39	is	be	AUX
fuelectenerg-1426	103	40	generated	generate	VERB
fuelectenerg-1426	103	41	by	by	ADP
fuelectenerg-1426	103	42	the	the	DET
fuelectenerg-1426	103	43	1	1	NUM
fuelectenerg-1426	103	44	-	-	PUNCT
fuelectenerg-1426	103	45	rpl	rpl	NOUN
fuelectenerg-1426	103	46	when	when	SCONJ
fuelectenerg-1426	103	47	the	the	DET
fuelectenerg-1426	103	48	value	value	NOUN
fuelectenerg-1426	103	49	of	of	ADP
fuelectenerg-1426	103	50	variable	variable	NOUN
fuelectenerg-1426	103	51	x	x	PUNCT
fuelectenerg-1426	103	52	is	be	AUX
fuelectenerg-1426	103	53	equal	equal	ADJ
fuelectenerg-1426	103	54	to	to	ADP
fuelectenerg-1426	103	55	certain	certain	ADJ
fuelectenerg-1426	103	56	state	state	NOUN
fuelectenerg-1426	103	57	(	(	PUNCT
fuelectenerg-1426	103	58	here	here	ADV
fuelectenerg-1426	103	59	this	this	DET
fuelectenerg-1426	103	60	state	state	NOUN
fuelectenerg-1426	103	61	is	be	AUX
fuelectenerg-1426	103	62	equal	equal	ADJ
fuelectenerg-1426	103	63	to	to	ADP
fuelectenerg-1426	103	64	one	one	NUM
fuelectenerg-1426	103	65	)	)	PUNCT
fuelectenerg-1426	103	66	.	.	PUNCT
fuelectenerg-1426	104	1	figure	figure	NOUN
fuelectenerg-1426	104	2	3(b	3(b	NUM
fuelectenerg-1426	104	3	)	)	PUNCT
fuelectenerg-1426	104	4	shows	show	VERB
fuelectenerg-1426	104	5	pl	pl	X
fuelectenerg-1426	104	6	where	where	SCONJ
fuelectenerg-1426	104	7	the	the	DET
fuelectenerg-1426	104	8	value	value	NOUN
fuelectenerg-1426	104	9	generated	generate	VERB
fuelectenerg-1426	104	10	by	by	ADP
fuelectenerg-1426	104	11	the	the	DET
fuelectenerg-1426	104	12	literal	literal	NOUN
fuelectenerg-1426	104	13	at	at	ADP
fuelectenerg-1426	104	14	a	a	DET
fuelectenerg-1426	104	15	specific	specific	ADJ
fuelectenerg-1426	104	16	state	state	NOUN
fuelectenerg-1426	104	17	is	be	AUX
fuelectenerg-1426	104	18	equal	equal	ADJ
fuelectenerg-1426	104	19	to	to	ADP
fuelectenerg-1426	104	20	the	the	DET
fuelectenerg-1426	104	21	maximum	maximum	ADJ
fuelectenerg-1426	104	22	value	value	NOUN
fuelectenerg-1426	104	23	(	(	PUNCT
fuelectenerg-1426	104	24	i.e.	i.e.	X
fuelectenerg-1426	104	25	,	,	PUNCT
fuelectenerg-1426	104	26	radix	radix	NOUN
fuelectenerg-1426	104	27	)	)	PUNCT
fuelectenerg-1426	104	28	of	of	ADP
fuelectenerg-1426	104	29	that	that	DET
fuelectenerg-1426	104	30	logic	logic	NOUN
fuelectenerg-1426	104	31	,	,	PUNCT
fuelectenerg-1426	104	32	and	and	CCONJ
fuelectenerg-1426	104	33	wl	wl	X
fuelectenerg-1426	104	34	in	in	ADP
fuelectenerg-1426	104	35	figure	figure	NOUN
fuelectenerg-1426	104	36	3(c	3(c	NUM
fuelectenerg-1426	104	37	)	)	PUNCT
fuelectenerg-1426	104	38	generates	generate	VERB
fuelectenerg-1426	104	39	a	a	DET
fuelectenerg-1426	104	40	value	value	NOUN
fuelectenerg-1426	104	41	equal	equal	ADJ
fuelectenerg-1426	104	42	to	to	ADP
fuelectenerg-1426	104	43	the	the	DET
fuelectenerg-1426	104	44	radix	radix	NOUN
fuelectenerg-1426	104	45	for	for	ADP
fuelectenerg-1426	104	46	a	a	DET
fuelectenerg-1426	104	47	"	"	PUNCT
fuelectenerg-1426	104	48	window	window	NOUN
fuelectenerg-1426	104	49	"	"	PUNCT
fuelectenerg-1426	104	50	of	of	ADP
fuelectenerg-1426	104	51	specific	specific	ADJ
fuelectenerg-1426	104	52	states	state	NOUN
fuelectenerg-1426	104	53	.	.	PUNCT
fuelectenerg-1426	105	1	since	since	SCONJ
fuelectenerg-1426	105	2	k	k	PROPN
fuelectenerg-1426	105	3	-	-	PROPN
fuelectenerg-1426	105	4	rpl	rpl	PROPN
fuelectenerg-1426	105	5	gfsop	gfsop	NOUN
fuelectenerg-1426	105	6	is	be	AUX
fuelectenerg-1426	105	7	as	as	ADV
fuelectenerg-1426	105	8	simple	simple	ADJ
fuelectenerg-1426	105	9	as	as	ADP
fuelectenerg-1426	105	10	pl	pl	PROPN
fuelectenerg-1426	105	11	and	and	CCONJ
fuelectenerg-1426	105	12	it	it	PRON
fuelectenerg-1426	105	13	is	be	AUX
fuelectenerg-1426	105	14	simpler	simple	ADJ
fuelectenerg-1426	105	15	from	from	ADP
fuelectenerg-1426	105	16	implementation	implementation	NOUN
fuelectenerg-1426	105	17	point	point	NOUN
fuelectenerg-1426	105	18	of	of	ADP
fuelectenerg-1426	105	19	view	view	NOUN
fuelectenerg-1426	105	20	than	than	ADP
fuelectenerg-1426	105	21	other	other	ADJ
fuelectenerg-1426	105	22	kind	kind	NOUN
fuelectenerg-1426	105	23	of	of	ADP
fuelectenerg-1426	105	24	literals	literal	NOUN
fuelectenerg-1426	105	25	,	,	PUNCT
fuelectenerg-1426	105	26	we	we	PRON
fuelectenerg-1426	105	27	will	will	AUX
fuelectenerg-1426	105	28	perform	perform	VERB
fuelectenerg-1426	105	29	all	all	PRON
fuelectenerg-1426	105	30	of	of	ADP
fuelectenerg-1426	105	31	the	the	DET
fuelectenerg-1426	105	32	gfsop	gfsop	NOUN
fuelectenerg-1426	105	33	expansions	expansion	NOUN
fuelectenerg-1426	105	34	utilizing	utilize	VERB
fuelectenerg-1426	105	35	the	the	DET
fuelectenerg-1426	105	36	corresponding	correspond	VERB
fuelectenerg-1426	105	37	1	1	NUM
fuelectenerg-1426	105	38	-	-	PUNCT
fuelectenerg-1426	105	39	reduced	reduce	VERB
fuelectenerg-1426	105	40	post	post	NOUN
fuelectenerg-1426	105	41	literal	literal	ADJ
fuelectenerg-1426	105	42	gfsop	gfsop	NOUN
fuelectenerg-1426	105	43	.	.	PUNCT
fuelectenerg-1426	106	1	consequently	consequently	ADV
fuelectenerg-1426	106	2	,	,	PUNCT
fuelectenerg-1426	106	3	let	let	VERB
fuelectenerg-1426	106	4	us	we	PRON
fuelectenerg-1426	106	5	define	define	VERB
fuelectenerg-1426	106	6	the	the	DET
fuelectenerg-1426	106	7	1	1	NUM
fuelectenerg-1426	106	8	-	-	PUNCT
fuelectenerg-1426	106	9	rpl	rpl	NOUN
fuelectenerg-1426	106	10	as	as	ADP
fuelectenerg-1426	106	11	[	[	X
fuelectenerg-1426	106	12	2	2	NUM
fuelectenerg-1426	106	13	,	,	PUNCT
fuelectenerg-1426	106	14	32	32	NUM
fuelectenerg-1426	106	15	]	]	PUNCT
fuelectenerg-1426	106	16	:	:	PUNCT
fuelectenerg-1426	106	17	ix	ix	ADP
fuelectenerg-1426	106	18	=	=	SYM
fuelectenerg-1426	106	19	1	1	NUM
fuelectenerg-1426	106	20	iff	iff	NOUN
fuelectenerg-1426	106	21	x	x	PROPN
fuelectenerg-1426	107	1	=	=	PUNCT
fuelectenerg-1426	107	2	i	i	PRON
fuelectenerg-1426	107	3	else	else	ADV
fuelectenerg-1426	107	4	ix	ix	ADP
fuelectenerg-1426	107	5	=	=	NOUN
fuelectenerg-1426	107	6	0	0	PROPN
fuelectenerg-1426	107	7	.	.	PUNCT
fuelectenerg-1426	108	1	(	(	PUNCT
fuelectenerg-1426	108	2	5	5	NUM
fuelectenerg-1426	108	3	)	)	PUNCT
fuelectenerg-1426	108	4	for	for	ADP
fuelectenerg-1426	108	5	example	example	NOUN
fuelectenerg-1426	108	6	{	{	PUNCT
fuelectenerg-1426	108	7	0x	0x	NOUN
fuelectenerg-1426	108	8	,	,	PUNCT
fuelectenerg-1426	108	9	1x	1x	NUM
fuelectenerg-1426	108	10	,	,	PUNCT
fuelectenerg-1426	108	11	2x	2x	NUM
fuelectenerg-1426	108	12	}	}	PUNCT
fuelectenerg-1426	108	13	are	be	AUX
fuelectenerg-1426	108	14	the	the	DET
fuelectenerg-1426	108	15	zero	zero	NUM
fuelectenerg-1426	108	16	,	,	PUNCT
fuelectenerg-1426	108	17	first	first	ADJ
fuelectenerg-1426	108	18	and	and	CCONJ
fuelectenerg-1426	108	19	second	second	ADJ
fuelectenerg-1426	108	20	polarities	polarity	NOUN
fuelectenerg-1426	108	21	of	of	ADP
fuelectenerg-1426	108	22	the	the	DET
fuelectenerg-1426	108	23	1	1	NUM
fuelectenerg-1426	108	24	-	-	PUNCT
fuelectenerg-1426	108	25	reduced	reduce	VERB
fuelectenerg-1426	108	26	post	post	NOUN
fuelectenerg-1426	108	27	literal	literal	ADJ
fuelectenerg-1426	108	28	,	,	PUNCT
fuelectenerg-1426	108	29	respectively	respectively	ADV
fuelectenerg-1426	108	30	.	.	PUNCT
fuelectenerg-1426	109	1	also	also	ADV
fuelectenerg-1426	109	2	,	,	PUNCT
fuelectenerg-1426	109	3	let	let	VERB
fuelectenerg-1426	109	4	us	we	PRON
fuelectenerg-1426	109	5	define	define	VERB
fuelectenerg-1426	109	6	the	the	DET
fuelectenerg-1426	109	7	ternary	ternary	ADJ
fuelectenerg-1426	109	8	shifts	shift	NOUN
fuelectenerg-1426	109	9	over	over	ADP
fuelectenerg-1426	109	10	x	x	ADJ
fuelectenerg-1426	109	11	variable	variable	ADJ
fuelectenerg-1426	109	12	{	{	PUNCT
fuelectenerg-1426	109	13	x	x	NOUN
fuelectenerg-1426	109	14	,	,	PUNCT
fuelectenerg-1426	109	15	x′,x′′	x′,x′′	PROPN
fuelectenerg-1426	109	16	}	}	PUNCT
fuelectenerg-1426	109	17	as	as	ADP
fuelectenerg-1426	109	18	104	104	NUM
fuelectenerg-1426	109	19	704	704	NUM
fuelectenerg-1426	109	20	a.	a.	NOUN
fuelectenerg-1426	109	21	n.	n.	PROPN
fuelectenerg-1426	109	22	al	al	PROPN
fuelectenerg-1426	109	23	-	-	PUNCT
fuelectenerg-1426	109	24	rabadi	rabadi	PROPN
fuelectenerg-1426	109	25	multi	multi	ADJ
fuelectenerg-1426	109	26	-	-	ADJ
fuelectenerg-1426	109	27	valued	value	VERB
fuelectenerg-1426	109	28	galois	galois	PROPN
fuelectenerg-1426	109	29	shannon	shannon	PROPN
fuelectenerg-1426	109	30	davio	davio	PROPN
fuelectenerg-1426	109	31	trees	tree	NOUN
fuelectenerg-1426	109	32	and	and	CCONJ
fuelectenerg-1426	109	33	their	their	PRON
fuelectenerg-1426	109	34	complexity	complexity	NOUN
fuelectenerg-1426	109	35	705	705	NUM
fuelectenerg-1426	109	36	multi	multi	ADJ
fuelectenerg-1426	109	37	-	-	ADJ
fuelectenerg-1426	109	38	valued	value	VERB
fuelectenerg-1426	109	39	galois	galois	PROPN
fuelectenerg-1426	109	40	shannon	shannon	PROPN
fuelectenerg-1426	109	41	davio	davio	PROPN
fuelectenerg-1426	109	42	trees	tree	NOUN
fuelectenerg-1426	109	43	and	and	CCONJ
fuelectenerg-1426	109	44	their	their	PRON
fuelectenerg-1426	109	45	complexity	complexity	NOUN
fuelectenerg-1426	109	46	1	1	NUM
fuelectenerg-1426	109	47	0	0	NUM
fuelectenerg-1426	109	48	1	1	NUM
fuelectenerg-1426	109	49	2	2	NUM
fuelectenerg-1426	109	50	3	3	NUM
fuelectenerg-1426	109	51	4	4	NUM
fuelectenerg-1426	109	52	x	x	SYM
fuelectenerg-1426	109	53	2	2	NUM
fuelectenerg-1426	109	54	3	3	NUM
fuelectenerg-1426	109	55	4	4	NUM
fuelectenerg-1426	109	56	1	1	NUM
fuelectenerg-1426	109	57	x	x	SYM
fuelectenerg-1426	109	58	0	0	NUM
fuelectenerg-1426	109	59	1	1	NUM
fuelectenerg-1426	109	60	2	2	NUM
fuelectenerg-1426	109	61	3	3	NUM
fuelectenerg-1426	109	62	4	4	NUM
fuelectenerg-1426	109	63	x	x	SYM
fuelectenerg-1426	109	64	1	1	NUM
fuelectenerg-1426	109	65	2	2	NUM
fuelectenerg-1426	109	66	3	3	NUM
fuelectenerg-1426	109	67	4	4	NUM
fuelectenerg-1426	109	68	l	l	NOUN
fuelectenerg-1426	109	69	1	1	NUM
fuelectenerg-1426	109	70	(	(	PUNCT
fuelectenerg-1426	109	71	x	x	NOUN
fuelectenerg-1426	109	72	)	)	PUNCT
fuelectenerg-1426	109	73	0	0	NUM
fuelectenerg-1426	109	74	1	1	NUM
fuelectenerg-1426	109	75	2	2	NUM
fuelectenerg-1426	109	76	3	3	NUM
fuelectenerg-1426	109	77	4	4	NUM
fuelectenerg-1426	109	78	x	x	SYM
fuelectenerg-1426	109	79	1	1	NUM
fuelectenerg-1426	109	80	2	2	NUM
fuelectenerg-1426	109	81	3	3	NUM
fuelectenerg-1426	109	82	4	4	NUM
fuelectenerg-1426	109	83	l	l	NOUN
fuelectenerg-1426	110	1	[	[	X
fuelectenerg-1426	110	2	1:2	1:2	NUM
fuelectenerg-1426	110	3	]	]	X
fuelectenerg-1426	110	4	(	(	PUNCT
fuelectenerg-1426	110	5	x	x	X
fuelectenerg-1426	110	6	)	)	PUNCT
fuelectenerg-1426	110	7	(	(	PUNCT
fuelectenerg-1426	110	8	a	a	X
fuelectenerg-1426	110	9	)	)	PUNCT
fuelectenerg-1426	110	10	(	(	PUNCT
fuelectenerg-1426	110	11	b	b	X
fuelectenerg-1426	110	12	)	)	PUNCT
fuelectenerg-1426	110	13	(	(	PUNCT
fuelectenerg-1426	110	14	c	c	X
fuelectenerg-1426	110	15	)	)	PUNCT
fuelectenerg-1426	110	16	fig	fig	NOUN
fuelectenerg-1426	110	17	.	.	PUNCT
fuelectenerg-1426	111	1	3	3	NUM
fuelectenerg-1426	111	2	:	:	PUNCT
fuelectenerg-1426	111	3	an	an	DET
fuelectenerg-1426	111	4	example	example	NOUN
fuelectenerg-1426	111	5	of	of	ADP
fuelectenerg-1426	111	6	different	different	ADJ
fuelectenerg-1426	111	7	types	type	NOUN
fuelectenerg-1426	111	8	of	of	ADP
fuelectenerg-1426	111	9	literals	literal	NOUN
fuelectenerg-1426	111	10	over	over	ADP
fuelectenerg-1426	111	11	an	an	DET
fuelectenerg-1426	111	12	arbitrary	arbitrary	ADJ
fuelectenerg-1426	111	13	five	five	NUM
fuelectenerg-1426	111	14	-	-	PUNCT
fuelectenerg-1426	111	15	radix	radix	NOUN
fuelectenerg-1426	111	16	logic	logic	NOUN
fuelectenerg-1426	111	17	:	:	PUNCT
fuelectenerg-1426	111	18	(	(	PUNCT
fuelectenerg-1426	111	19	a	a	X
fuelectenerg-1426	111	20	)	)	PUNCT
fuelectenerg-1426	111	21	1	1	NUM
fuelectenerg-1426	111	22	-	-	PUNCT
fuelectenerg-1426	111	23	reduced	reduce	VERB
fuelectenerg-1426	111	24	post	post	NOUN
fuelectenerg-1426	111	25	literal	literal	ADJ
fuelectenerg-1426	111	26	(	(	PUNCT
fuelectenerg-1426	111	27	1	1	NUM
fuelectenerg-1426	111	28	-	-	PUNCT
fuelectenerg-1426	111	29	rpl	rpl	NOUN
fuelectenerg-1426	111	30	)	)	PUNCT
fuelectenerg-1426	111	31	,	,	PUNCT
fuelectenerg-1426	111	32	(	(	PUNCT
fuelectenerg-1426	111	33	b	b	X
fuelectenerg-1426	111	34	)	)	PUNCT
fuelectenerg-1426	111	35	post	post	NOUN
fuelectenerg-1426	111	36	literal	literal	ADJ
fuelectenerg-1426	111	37	(	(	PUNCT
fuelectenerg-1426	111	38	pl	pl	NOUN
fuelectenerg-1426	111	39	)	)	PUNCT
fuelectenerg-1426	111	40	,	,	PUNCT
fuelectenerg-1426	111	41	and	and	CCONJ
fuelectenerg-1426	111	42	(	(	PUNCT
fuelectenerg-1426	111	43	c	c	NOUN
fuelectenerg-1426	111	44	)	)	PUNCT
fuelectenerg-1426	111	45	window	window	NOUN
fuelectenerg-1426	111	46	literal	literal	NOUN
fuelectenerg-1426	111	47	(	(	PUNCT
fuelectenerg-1426	111	48	wl	wl	PROPN
fuelectenerg-1426	111	49	)	)	PUNCT
fuelectenerg-1426	111	50	.	.	PUNCT
fuelectenerg-1426	112	1	the	the	DET
fuelectenerg-1426	112	2	zero	zero	NUM
fuelectenerg-1426	112	3	,	,	PUNCT
fuelectenerg-1426	112	4	first	first	ADJ
fuelectenerg-1426	112	5	and	and	CCONJ
fuelectenerg-1426	112	6	second	second	ADJ
fuelectenerg-1426	112	7	shifts	shift	NOUN
fuelectenerg-1426	112	8	of	of	ADP
fuelectenerg-1426	112	9	the	the	DET
fuelectenerg-1426	112	10	variable	variable	NOUN
fuelectenerg-1426	112	11	x	x	PUNCT
fuelectenerg-1426	112	12	respectively	respectively	ADV
fuelectenerg-1426	112	13	(	(	PUNCT
fuelectenerg-1426	112	14	i.e.	i.e.	X
fuelectenerg-1426	112	15	,	,	PUNCT
fuelectenerg-1426	112	16	x	x	SYM
fuelectenerg-1426	112	17	=	=	SYM
fuelectenerg-1426	112	18	x+0	x+0	PROPN
fuelectenerg-1426	112	19	,	,	PUNCT
fuelectenerg-1426	112	20	x′	x′	PROPN
fuelectenerg-1426	112	21	=	=	SYM
fuelectenerg-1426	112	22	x+1	x+1	PROPN
fuelectenerg-1426	112	23	and	and	CCONJ
fuelectenerg-1426	112	24	x′′	x′′	PROPN
fuelectenerg-1426	112	25	=	=	PUNCT
fuelectenerg-1426	112	26	x+2	x+2	PROPN
fuelectenerg-1426	112	27	,	,	PUNCT
fuelectenerg-1426	112	28	respectively	respectively	ADV
fuelectenerg-1426	112	29	)	)	PUNCT
fuelectenerg-1426	112	30	,	,	PUNCT
fuelectenerg-1426	112	31	and	and	CCONJ
fuelectenerg-1426	112	32	x	x	PRON
fuelectenerg-1426	112	33	can	can	AUX
fuelectenerg-1426	112	34	take	take	VERB
fuelectenerg-1426	112	35	any	any	DET
fuelectenerg-1426	112	36	value	value	NOUN
fuelectenerg-1426	112	37	in	in	ADP
fuelectenerg-1426	112	38	the	the	DET
fuelectenerg-1426	112	39	set	set	NOUN
fuelectenerg-1426	112	40	{	{	PUNCT
fuelectenerg-1426	112	41	0,1,2	0,1,2	NUM
fuelectenerg-1426	112	42	}	}	PUNCT
fuelectenerg-1426	112	43	.	.	PUNCT
fuelectenerg-1426	113	1	we	we	PRON
fuelectenerg-1426	113	2	chose	choose	VERB
fuelectenerg-1426	113	3	to	to	PART
fuelectenerg-1426	113	4	represent	represent	VERB
fuelectenerg-1426	113	5	the	the	DET
fuelectenerg-1426	113	6	1	1	NUM
fuelectenerg-1426	113	7	-	-	PUNCT
fuelectenerg-1426	113	8	reduced	reduce	VERB
fuelectenerg-1426	113	9	post	post	NOUN
fuelectenerg-1426	113	10	literals	literal	NOUN
fuelectenerg-1426	113	11	in	in	ADP
fuelectenerg-1426	113	12	terms	term	NOUN
fuelectenerg-1426	113	13	of	of	ADP
fuelectenerg-1426	113	14	shifts	shift	NOUN
fuelectenerg-1426	113	15	and	and	CCONJ
fuelectenerg-1426	113	16	powers	power	NOUN
fuelectenerg-1426	113	17	,	,	PUNCT
fuelectenerg-1426	113	18	among	among	ADP
fuelectenerg-1426	113	19	others	other	NOUN
fuelectenerg-1426	113	20	,	,	PUNCT
fuelectenerg-1426	113	21	because	because	SCONJ
fuelectenerg-1426	113	22	of	of	ADP
fuelectenerg-1426	113	23	the	the	DET
fuelectenerg-1426	113	24	ease	ease	NOUN
fuelectenerg-1426	113	25	of	of	ADP
fuelectenerg-1426	113	26	the	the	DET
fuelectenerg-1426	113	27	implementation	implementation	NOUN
fuelectenerg-1426	113	28	of	of	ADP
fuelectenerg-1426	113	29	powers	power	NOUN
fuelectenerg-1426	113	30	of	of	ADP
fuelectenerg-1426	113	31	shifted	shift	VERB
fuelectenerg-1426	113	32	variables	variable	NOUN
fuelectenerg-1426	113	33	in	in	ADP
fuelectenerg-1426	113	34	hardware	hardware	NOUN
fuelectenerg-1426	113	35	such	such	ADJ
fuelectenerg-1426	113	36	as	as	ADP
fuelectenerg-1426	113	37	in	in	ADP
fuelectenerg-1426	113	38	universal	universal	ADJ
fuelectenerg-1426	113	39	logic	logic	NOUN
fuelectenerg-1426	113	40	modules	module	NOUN
fuelectenerg-1426	113	41	(	(	PUNCT
fuelectenerg-1426	113	42	ulms	ulm	NOUN
fuelectenerg-1426	113	43	)	)	PUNCT
fuelectenerg-1426	114	1	[	[	X
fuelectenerg-1426	114	2	2	2	NUM
fuelectenerg-1426	114	3	]	]	PUNCT
fuelectenerg-1426	114	4	.	.	PUNCT
fuelectenerg-1426	115	1	analogously	analogously	ADV
fuelectenerg-1426	115	2	to	to	ADP
fuelectenerg-1426	115	3	the	the	DET
fuelectenerg-1426	115	4	binary	binary	ADJ
fuelectenerg-1426	115	5	and	and	CCONJ
fuelectenerg-1426	115	6	ternary	ternary	ADJ
fuelectenerg-1426	115	7	cases	case	NOUN
fuelectenerg-1426	115	8	,	,	PUNCT
fuelectenerg-1426	115	9	quaternary	quaternary	ADJ
fuelectenerg-1426	115	10	shannon	shannon	NOUN
fuelectenerg-1426	115	11	expansion	expansion	NOUN
fuelectenerg-1426	115	12	over	over	ADP
fuelectenerg-1426	115	13	gf(4	gf(4	NOUN
fuelectenerg-1426	115	14	)	)	PUNCT
fuelectenerg-1426	115	15	for	for	ADP
fuelectenerg-1426	115	16	a	a	DET
fuelectenerg-1426	115	17	function	function	NOUN
fuelectenerg-1426	115	18	with	with	ADP
fuelectenerg-1426	115	19	single	single	ADJ
fuelectenerg-1426	115	20	variable	variable	NOUN
fuelectenerg-1426	115	21	is	be	AUX
fuelectenerg-1426	115	22	:	:	PUNCT
fuelectenerg-1426	115	23	f	f	X
fuelectenerg-1426	116	1	=	=	SYM
fuelectenerg-1426	116	2	0x	0x	NUM
fuelectenerg-1426	116	3	f0	f0	PROPN
fuelectenerg-1426	116	4	+	+	CCONJ
fuelectenerg-1426	116	5	1x	1x	NUM
fuelectenerg-1426	116	6	f1	f1	NOUN
fuelectenerg-1426	116	7	+	+	CCONJ
fuelectenerg-1426	116	8	2x	2x	NUM
fuelectenerg-1426	116	9	f2	f2	PROPN
fuelectenerg-1426	116	10	+	+	CCONJ
fuelectenerg-1426	116	11	3x	3x	NUM
fuelectenerg-1426	116	12	f3	f3	NOUN
fuelectenerg-1426	116	13	,	,	PUNCT
fuelectenerg-1426	116	14	(	(	PUNCT
fuelectenerg-1426	116	15	6	6	NUM
fuelectenerg-1426	116	16	)	)	PUNCT
fuelectenerg-1426	116	17	where	where	SCONJ
fuelectenerg-1426	116	18	f0	f0	PROPN
fuelectenerg-1426	116	19	is	be	AUX
fuelectenerg-1426	116	20	the	the	DET
fuelectenerg-1426	116	21	cofactor	cofactor	NOUN
fuelectenerg-1426	116	22	of	of	ADP
fuelectenerg-1426	116	23	f	f	PROPN
fuelectenerg-1426	116	24	with	with	ADP
fuelectenerg-1426	116	25	respect	respect	NOUN
fuelectenerg-1426	116	26	to	to	ADP
fuelectenerg-1426	116	27	variable	variable	NOUN
fuelectenerg-1426	116	28	x	x	PUNCT
fuelectenerg-1426	116	29	of	of	ADP
fuelectenerg-1426	116	30	value	value	NOUN
fuelectenerg-1426	116	31	0	0	NUM
fuelectenerg-1426	116	32	,	,	PUNCT
fuelectenerg-1426	116	33	f1	f1	NOUN
fuelectenerg-1426	116	34	is	be	AUX
fuelectenerg-1426	116	35	the	the	DET
fuelectenerg-1426	116	36	cofactor	cofactor	NOUN
fuelectenerg-1426	116	37	of	of	ADP
fuelectenerg-1426	116	38	f	f	PROPN
fuelectenerg-1426	116	39	with	with	ADP
fuelectenerg-1426	116	40	respect	respect	NOUN
fuelectenerg-1426	116	41	to	to	ADP
fuelectenerg-1426	116	42	variable	variable	NOUN
fuelectenerg-1426	116	43	x	x	PUNCT
fuelectenerg-1426	116	44	of	of	ADP
fuelectenerg-1426	116	45	value	value	NOUN
fuelectenerg-1426	116	46	1	1	NUM
fuelectenerg-1426	116	47	,	,	PUNCT
fuelectenerg-1426	116	48	f2	f2	PROPN
fuelectenerg-1426	116	49	is	be	AUX
fuelectenerg-1426	116	50	the	the	DET
fuelectenerg-1426	116	51	cofactor	cofactor	NOUN
fuelectenerg-1426	116	52	of	of	ADP
fuelectenerg-1426	116	53	f	f	PROPN
fuelectenerg-1426	116	54	with	with	ADP
fuelectenerg-1426	116	55	respect	respect	NOUN
fuelectenerg-1426	116	56	to	to	ADP
fuelectenerg-1426	116	57	variable	variable	NOUN
fuelectenerg-1426	116	58	x	x	PUNCT
fuelectenerg-1426	116	59	of	of	ADP
fuelectenerg-1426	116	60	value	value	NOUN
fuelectenerg-1426	116	61	2	2	NUM
fuelectenerg-1426	116	62	,	,	PUNCT
fuelectenerg-1426	116	63	and	and	CCONJ
fuelectenerg-1426	116	64	f3	f3	PROPN
fuelectenerg-1426	116	65	is	be	AUX
fuelectenerg-1426	116	66	the	the	DET
fuelectenerg-1426	116	67	cofactor	cofactor	NOUN
fuelectenerg-1426	116	68	of	of	ADP
fuelectenerg-1426	116	69	f	f	PROPN
fuelectenerg-1426	116	70	with	with	ADP
fuelectenerg-1426	116	71	respect	respect	NOUN
fuelectenerg-1426	116	72	to	to	ADP
fuelectenerg-1426	116	73	variable	variable	NOUN
fuelectenerg-1426	116	74	x	x	PUNCT
fuelectenerg-1426	116	75	of	of	ADP
fuelectenerg-1426	116	76	value	value	NOUN
fuelectenerg-1426	116	77	3	3	NUM
fuelectenerg-1426	116	78	.	.	NOUN
fuelectenerg-1426	116	79	example	example	NOUN
fuelectenerg-1426	117	1	2	2	NUM
fuelectenerg-1426	117	2	.	.	PUNCT
fuelectenerg-1426	117	3	let	let	VERB
fuelectenerg-1426	117	4	f	f	PROPN
fuelectenerg-1426	117	5	(	(	PUNCT
fuelectenerg-1426	117	6	x1,x2	x1,x2	PROPN
fuelectenerg-1426	117	7	)	)	PUNCT
fuelectenerg-1426	118	1	=	=	PUNCT
fuelectenerg-1426	119	1	x′′1x2+x′′′2	x′′1x2+x′′′2	PROPN
fuelectenerg-1426	119	2	x1	x1	PROPN
fuelectenerg-1426	119	3	.	.	PUNCT
fuelectenerg-1426	120	1	by	by	ADP
fuelectenerg-1426	120	2	using	use	VERB
fuelectenerg-1426	120	3	figure	figure	NOUN
fuelectenerg-1426	120	4	(	(	PUNCT
fuelectenerg-1426	120	5	1	1	NUM
fuelectenerg-1426	120	6	)	)	PUNCT
fuelectenerg-1426	120	7	,	,	PUNCT
fuelectenerg-1426	120	8	the	the	DET
fuelectenerg-1426	120	9	quaternary	quaternary	ADJ
fuelectenerg-1426	120	10	truth	truth	NOUN
fuelectenerg-1426	120	11	vector	vector	NOUN
fuelectenerg-1426	120	12	in	in	ADP
fuelectenerg-1426	120	13	the	the	DET
fuelectenerg-1426	120	14	variable	variable	ADJ
fuelectenerg-1426	120	15	order	order	NOUN
fuelectenerg-1426	120	16	{	{	PUNCT
fuelectenerg-1426	120	17	x1,x2	x1,x2	PROPN
fuelectenerg-1426	120	18	}	}	PUNCT
fuelectenerg-1426	120	19	is	be	AUX
fuelectenerg-1426	120	20	f	f	X
fuelectenerg-1426	120	21	=	=	PUNCT
fuelectenerg-1426	121	1	[	[	AUX
fuelectenerg-1426	121	2	0,3,1,2,2,1,3,0,3,0,2,1,1,2,0,3]t	0,3,1,2,2,1,3,0,3,0,2,1,1,2,0,3]t	X
fuelectenerg-1426	121	3	.	.	PUNCT
fuelectenerg-1426	121	4	utilizing	utilize	VERB
fuelectenerg-1426	121	5	equation	equation	NOUN
fuelectenerg-1426	121	6	(	(	PUNCT
fuelectenerg-1426	121	7	6	6	NUM
fuelectenerg-1426	121	8	)	)	PUNCT
fuelectenerg-1426	121	9	,	,	PUNCT
fuelectenerg-1426	121	10	one	one	PRON
fuelectenerg-1426	121	11	obtains	obtain	VERB
fuelectenerg-1426	121	12	the	the	DET
fuelectenerg-1426	121	13	following	following	ADJ
fuelectenerg-1426	121	14	gf(4	gf(4	NOUN
fuelectenerg-1426	121	15	)	)	PUNCT
fuelectenerg-1426	121	16	shannon	shannon	NOUN
fuelectenerg-1426	121	17	expansion	expansion	NOUN
fuelectenerg-1426	121	18	for	for	ADP
fuelectenerg-1426	121	19	f	f	PROPN
fuelectenerg-1426	121	20	:	:	PUNCT
fuelectenerg-1426	121	21	f	f	PROPN
fuelectenerg-1426	121	22	=	=	SYM
fuelectenerg-1426	121	23	2	2	NUM
fuelectenerg-1426	121	24	·	·	PUNCT
fuelectenerg-1426	121	25	0x1	0x1	NOUN
fuelectenerg-1426	121	26	1x2	1x2	NUM
fuelectenerg-1426	122	1	+	+	CCONJ
fuelectenerg-1426	122	2	3	3	NUM
fuelectenerg-1426	122	3	·	·	PUNCT
fuelectenerg-1426	122	4	0x1	0x1	NOUN
fuelectenerg-1426	122	5	2x2	2x2	NUM
fuelectenerg-1426	122	6	+	+	CCONJ
fuelectenerg-1426	122	7	0x1	0x1	NOUN
fuelectenerg-1426	122	8	3x2	3x2	NUM
fuelectenerg-1426	122	9	+3	+3	PROPN
fuelectenerg-1426	122	10	·	·	PUNCT
fuelectenerg-1426	123	1	1x1	1x1	NUM
fuelectenerg-1426	123	2	0x2	0x2	NOUN
fuelectenerg-1426	123	3	+	+	CCONJ
fuelectenerg-1426	123	4	1x1	1x1	NUM
fuelectenerg-1426	123	5	1x2	1x2	NUM
fuelectenerg-1426	123	6	+2	+2	PRON
fuelectenerg-1426	123	7	·	·	PUNCT
fuelectenerg-1426	123	8	1x1	1x1	NUM
fuelectenerg-1426	123	9	3x2	3x2	NUM
fuelectenerg-1426	123	10	+	+	SYM
fuelectenerg-1426	123	11	2x1	2x1	NUM
fuelectenerg-1426	123	12	0x2	0x2	NOUN
fuelectenerg-1426	123	13	+	+	CCONJ
fuelectenerg-1426	123	14	3	3	NUM
fuelectenerg-1426	123	15	·	·	SYM
fuelectenerg-1426	123	16	2x1	2x1	NUM
fuelectenerg-1426	123	17	1x2	1x2	NUM
fuelectenerg-1426	123	18	+2	+2	PRON
fuelectenerg-1426	123	19	·	·	PUNCT
fuelectenerg-1426	124	1	2x1	2x1	NUM
fuelectenerg-1426	124	2	2x2	2x2	NUM
fuelectenerg-1426	124	3	+2	+2	PROPN
fuelectenerg-1426	124	4	·	·	PUNCT
fuelectenerg-1426	124	5	3x1	3x1	NUM
fuelectenerg-1426	124	6	0x2	0x2	NOUN
fuelectenerg-1426	124	7	+	+	CCONJ
fuelectenerg-1426	124	8	3x1	3x1	NUM
fuelectenerg-1426	124	9	2x2	2x2	NUM
fuelectenerg-1426	124	10	+3	+3	PROPN
fuelectenerg-1426	124	11	·	·	PUNCT
fuelectenerg-1426	124	12	3x1	3x1	NUM
fuelectenerg-1426	124	13	3x2	3x2	NUM
fuelectenerg-1426	124	14	.	.	PUNCT
fuelectenerg-1426	125	1	using	use	VERB
fuelectenerg-1426	125	2	the	the	DET
fuelectenerg-1426	125	3	axioms	axiom	NOUN
fuelectenerg-1426	125	4	of	of	ADP
fuelectenerg-1426	125	5	gf(4	gf(4	NOUN
fuelectenerg-1426	125	6	)	)	PUNCT
fuelectenerg-1426	125	7	that	that	PRON
fuelectenerg-1426	125	8	are	be	AUX
fuelectenerg-1426	125	9	manifested	manifest	VERB
fuelectenerg-1426	125	10	in	in	ADP
fuelectenerg-1426	125	11	the	the	DET
fuelectenerg-1426	125	12	operators	operator	NOUN
fuelectenerg-1426	125	13	shown	show	VERB
fuelectenerg-1426	125	14	in	in	ADP
fuelectenerg-1426	125	15	figure	figure	NOUN
fuelectenerg-1426	125	16	1	1	NUM
fuelectenerg-1426	125	17	,	,	PUNCT
fuelectenerg-1426	125	18	the	the	DET
fuelectenerg-1426	125	19	1	1	NUM
fuelectenerg-1426	125	20	-	-	PUNCT
fuelectenerg-1426	125	21	rpl	rpl	NOUN
fuelectenerg-1426	125	22	defined	define	VERB
fuelectenerg-1426	125	23	in	in	ADP
fuelectenerg-1426	125	24	equation	equation	NOUN
fuelectenerg-1426	125	25	(	(	PUNCT
fuelectenerg-1426	125	26	5	5	NUM
fuelectenerg-1426	125	27	)	)	PUNCT
fuelectenerg-1426	125	28	is	be	AUX
fuelectenerg-1426	125	29	related	relate	VERB
fuelectenerg-1426	125	30	to	to	ADP
fuelectenerg-1426	125	31	the	the	DET
fuelectenerg-1426	125	32	shifts	shift	NOUN
fuelectenerg-1426	125	33	of	of	ADP
fuelectenerg-1426	125	34	variables	variable	NOUN
fuelectenerg-1426	125	35	over	over	ADP
fuelectenerg-1426	125	36	gf(4	gf(4	NOUN
fuelectenerg-1426	125	37	)	)	PUNCT
fuelectenerg-1426	125	38	in	in	ADP
fuelectenerg-1426	125	39	terms	term	NOUN
fuelectenerg-1426	125	40	of	of	ADP
fuelectenerg-1426	125	41	powers	power	NOUN
fuelectenerg-1426	125	42	[	[	X
fuelectenerg-1426	125	43	2	2	NUM
fuelectenerg-1426	125	44	-	-	SYM
fuelectenerg-1426	125	45	5	5	NUM
fuelectenerg-1426	125	46	]	]	PUNCT
fuelectenerg-1426	125	47	as	as	SCONJ
fuelectenerg-1426	125	48	follows	follow	VERB
fuelectenerg-1426	125	49	:	:	PUNCT
fuelectenerg-1426	125	50	105	105	NUM
fuelectenerg-1426	125	51	706	706	NUM
fuelectenerg-1426	125	52	a.	a.	NOUN
fuelectenerg-1426	125	53	n.	n.	PROPN
fuelectenerg-1426	125	54	al	al	PROPN
fuelectenerg-1426	125	55	-	-	PUNCT
fuelectenerg-1426	125	56	rabadi	rabadi	PROPN
fuelectenerg-1426	125	57	multi	multi	ADJ
fuelectenerg-1426	125	58	-	-	ADJ
fuelectenerg-1426	125	59	valued	value	VERB
fuelectenerg-1426	125	60	galois	galois	PROPN
fuelectenerg-1426	125	61	shannon	shannon	PROPN
fuelectenerg-1426	125	62	davio	davio	PROPN
fuelectenerg-1426	125	63	trees	tree	NOUN
fuelectenerg-1426	125	64	and	and	CCONJ
fuelectenerg-1426	125	65	their	their	PRON
fuelectenerg-1426	125	66	complexity	complexity	NOUN
fuelectenerg-1426	125	67	707	707	NUM
fuelectenerg-1426	125	68	multi	multi	ADJ
fuelectenerg-1426	125	69	-	-	ADJ
fuelectenerg-1426	125	70	valued	value	VERB
fuelectenerg-1426	125	71	galois	galois	PROPN
fuelectenerg-1426	125	72	shannon	shannon	PROPN
fuelectenerg-1426	125	73	davio	davio	PROPN
fuelectenerg-1426	125	74	trees	tree	NOUN
fuelectenerg-1426	125	75	and	and	CCONJ
fuelectenerg-1426	125	76	their	their	PRON
fuelectenerg-1426	125	77	complexity	complexity	NOUN
fuelectenerg-1426	125	78	0x	0x	NOUN
fuelectenerg-1426	125	79	=	=	SYM
fuelectenerg-1426	125	80	x3	x3	PROPN
fuelectenerg-1426	125	81	+1	+1	PROPN
fuelectenerg-1426	125	82	,	,	PUNCT
fuelectenerg-1426	125	83	(	(	PUNCT
fuelectenerg-1426	125	84	7	7	X
fuelectenerg-1426	125	85	)	)	PUNCT
fuelectenerg-1426	125	86	0x	0x	NOUN
fuelectenerg-1426	125	87	=	=	SYM
fuelectenerg-1426	126	1	x′+(x′)2	x′+(x′)2	PROPN
fuelectenerg-1426	127	1	+	+	PROPN
fuelectenerg-1426	127	2	(	(	PUNCT
fuelectenerg-1426	127	3	x′)3	x′)3	PROPN
fuelectenerg-1426	127	4	,	,	PUNCT
fuelectenerg-1426	127	5	(	(	PUNCT
fuelectenerg-1426	127	6	8)	8)	NUM
fuelectenerg-1426	127	7	0x	0x	NOUN
fuelectenerg-1426	127	8	=	=	SYM
fuelectenerg-1426	127	9	3(x′′)+2(x′′)2	3(x′′)+2(x′′)2	NUM
fuelectenerg-1426	127	10	+	+	ADJ
fuelectenerg-1426	127	11	(	(	PUNCT
fuelectenerg-1426	127	12	x′′)3	x′′)3	PROPN
fuelectenerg-1426	127	13	,	,	PUNCT
fuelectenerg-1426	127	14	(	(	PUNCT
fuelectenerg-1426	127	15	9	9	X
fuelectenerg-1426	127	16	)	)	PUNCT
fuelectenerg-1426	127	17	0x	0x	NOUN
fuelectenerg-1426	127	18	=	=	SYM
fuelectenerg-1426	127	19	2(x′′′)+3(x′′′)2	2(x′′′)+3(x′′′)2	NUM
fuelectenerg-1426	127	20	+	+	ADJ
fuelectenerg-1426	127	21	(	(	PUNCT
fuelectenerg-1426	127	22	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	127	23	,	,	PUNCT
fuelectenerg-1426	127	24	(	(	PUNCT
fuelectenerg-1426	127	25	10	10	NUM
fuelectenerg-1426	127	26	)	)	PUNCT
fuelectenerg-1426	127	27	1x	1x	NOUN
fuelectenerg-1426	127	28	=	=	PUNCT
fuelectenerg-1426	128	1	x+(x)2	x+(x)2	PUNCT
fuelectenerg-1426	129	1	+	+	ADJ
fuelectenerg-1426	129	2	(	(	PUNCT
fuelectenerg-1426	129	3	x)3	x)3	X
fuelectenerg-1426	129	4	,	,	PUNCT
fuelectenerg-1426	129	5	(	(	PUNCT
fuelectenerg-1426	129	6	11	11	NUM
fuelectenerg-1426	129	7	)	)	PUNCT
fuelectenerg-1426	129	8	1x	1x	NOUN
fuelectenerg-1426	130	1	=	=	SYM
fuelectenerg-1426	130	2	(	(	PUNCT
fuelectenerg-1426	130	3	x′)3	x′)3	PROPN
fuelectenerg-1426	130	4	+1	+1	PROPN
fuelectenerg-1426	130	5	,	,	PUNCT
fuelectenerg-1426	130	6	(	(	PUNCT
fuelectenerg-1426	130	7	12	12	NUM
fuelectenerg-1426	130	8	)	)	PUNCT
fuelectenerg-1426	130	9	1x	1x	NOUN
fuelectenerg-1426	130	10	=	=	PUNCT
fuelectenerg-1426	131	1	2(x′′)+3(x′′)2	2(x′′)+3(x′′)2	NUM
fuelectenerg-1426	131	2	+	+	ADJ
fuelectenerg-1426	131	3	(	(	PUNCT
fuelectenerg-1426	131	4	x′′)3	x′′)3	PROPN
fuelectenerg-1426	131	5	,	,	PUNCT
fuelectenerg-1426	131	6	(	(	PUNCT
fuelectenerg-1426	131	7	13	13	NUM
fuelectenerg-1426	131	8	)	)	PUNCT
fuelectenerg-1426	131	9	1x	1x	NOUN
fuelectenerg-1426	132	1	=	=	PUNCT
fuelectenerg-1426	133	1	3(x′′′)+2(x′′′)2	3(x′′′)+2(x′′′)2	NUM
fuelectenerg-1426	133	2	+	+	ADJ
fuelectenerg-1426	133	3	(	(	PUNCT
fuelectenerg-1426	133	4	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	133	5	,	,	PUNCT
fuelectenerg-1426	133	6	(	(	PUNCT
fuelectenerg-1426	133	7	14	14	NUM
fuelectenerg-1426	133	8	)	)	PUNCT
fuelectenerg-1426	133	9	2x	2x	NOUN
fuelectenerg-1426	134	1	=	=	NOUN
fuelectenerg-1426	134	2	3(x)+2(x)2	3(x)+2(x)2	NOUN
fuelectenerg-1426	134	3	+	+	ADJ
fuelectenerg-1426	134	4	(	(	PUNCT
fuelectenerg-1426	134	5	x)3	x)3	X
fuelectenerg-1426	134	6	,	,	PUNCT
fuelectenerg-1426	134	7	(	(	PUNCT
fuelectenerg-1426	134	8	15	15	NUM
fuelectenerg-1426	134	9	)	)	PUNCT
fuelectenerg-1426	134	10	2x	2x	NOUN
fuelectenerg-1426	135	1	=	=	NOUN
fuelectenerg-1426	135	2	2(x′)+3(x′)2	2(x′)+3(x′)2	NUM
fuelectenerg-1426	135	3	+	+	ADJ
fuelectenerg-1426	135	4	(	(	PUNCT
fuelectenerg-1426	135	5	x′)3	x′)3	PROPN
fuelectenerg-1426	135	6	,	,	PUNCT
fuelectenerg-1426	135	7	(	(	PUNCT
fuelectenerg-1426	135	8	16	16	NUM
fuelectenerg-1426	135	9	)	)	PUNCT
fuelectenerg-1426	135	10	2x	2x	NOUN
fuelectenerg-1426	135	11	=	=	SYM
fuelectenerg-1426	135	12	(	(	PUNCT
fuelectenerg-1426	135	13	x′′)3	x′′)3	PROPN
fuelectenerg-1426	135	14	+1	+1	PROPN
fuelectenerg-1426	135	15	,	,	PUNCT
fuelectenerg-1426	135	16	(	(	PUNCT
fuelectenerg-1426	135	17	17	17	NUM
fuelectenerg-1426	135	18	)	)	PUNCT
fuelectenerg-1426	135	19	2x	2x	NOUN
fuelectenerg-1426	135	20	=	=	PUNCT
fuelectenerg-1426	135	21	x′′′+(x′′′)2	x′′′+(x′′′)2	PROPN
fuelectenerg-1426	136	1	+	+	ADJ
fuelectenerg-1426	136	2	(	(	PUNCT
fuelectenerg-1426	136	3	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	136	4	,	,	PUNCT
fuelectenerg-1426	136	5	(	(	PUNCT
fuelectenerg-1426	136	6	18	18	NUM
fuelectenerg-1426	136	7	)	)	PUNCT
fuelectenerg-1426	136	8	3x	3x	NOUN
fuelectenerg-1426	137	1	=	=	PUNCT
fuelectenerg-1426	137	2	2(x)+3(x)2	2(x)+3(x)2	NOUN
fuelectenerg-1426	138	1	+	+	ADJ
fuelectenerg-1426	138	2	(	(	PUNCT
fuelectenerg-1426	138	3	x)3	x)3	NOUN
fuelectenerg-1426	138	4	,	,	PUNCT
fuelectenerg-1426	138	5	(	(	PUNCT
fuelectenerg-1426	138	6	19	19	NUM
fuelectenerg-1426	138	7	)	)	PUNCT
fuelectenerg-1426	138	8	3x	3x	NOUN
fuelectenerg-1426	139	1	=	=	SYM
fuelectenerg-1426	139	2	3(x′)+2(x′)2	3(x′)+2(x′)2	NUM
fuelectenerg-1426	140	1	+	+	ADJ
fuelectenerg-1426	140	2	(	(	PUNCT
fuelectenerg-1426	140	3	x′)3	x′)3	PROPN
fuelectenerg-1426	140	4	,	,	PUNCT
fuelectenerg-1426	140	5	(	(	PUNCT
fuelectenerg-1426	140	6	20	20	NUM
fuelectenerg-1426	140	7	)	)	PUNCT
fuelectenerg-1426	140	8	3x	3x	NOUN
fuelectenerg-1426	140	9	=	=	SYM
fuelectenerg-1426	140	10	x′′+(x′′)2	x′′+(x′′)2	PUNCT
fuelectenerg-1426	141	1	+	+	ADJ
fuelectenerg-1426	141	2	(	(	PUNCT
fuelectenerg-1426	141	3	x′′)3	x′′)3	PROPN
fuelectenerg-1426	141	4	,	,	PUNCT
fuelectenerg-1426	141	5	(	(	PUNCT
fuelectenerg-1426	141	6	21	21	NUM
fuelectenerg-1426	141	7	)	)	PUNCT
fuelectenerg-1426	141	8	3x	3x	NOUN
fuelectenerg-1426	142	1	=	=	SYM
fuelectenerg-1426	143	1	(	(	PUNCT
fuelectenerg-1426	143	2	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	143	3	+1	+1	PROPN
fuelectenerg-1426	143	4	,	,	PUNCT
fuelectenerg-1426	143	5	(	(	PUNCT
fuelectenerg-1426	143	6	22	22	NUM
fuelectenerg-1426	143	7	)	)	PUNCT
fuelectenerg-1426	143	8	where	where	SCONJ
fuelectenerg-1426	143	9	{	{	PUNCT
fuelectenerg-1426	143	10	0x	0x	NOUN
fuelectenerg-1426	143	11	,	,	PUNCT
fuelectenerg-1426	143	12	1x	1x	NUM
fuelectenerg-1426	143	13	,	,	PUNCT
fuelectenerg-1426	143	14	2x	2x	NUM
fuelectenerg-1426	143	15	,	,	PUNCT
fuelectenerg-1426	143	16	3x	3x	NUM
fuelectenerg-1426	143	17	}	}	PUNCT
fuelectenerg-1426	143	18	are	be	AUX
fuelectenerg-1426	143	19	the	the	DET
fuelectenerg-1426	143	20	zero	zero	NUM
fuelectenerg-1426	143	21	,	,	PUNCT
fuelectenerg-1426	143	22	first	first	ADJ
fuelectenerg-1426	143	23	,	,	PUNCT
fuelectenerg-1426	143	24	second	second	ADJ
fuelectenerg-1426	143	25	and	and	CCONJ
fuelectenerg-1426	143	26	third	third	ADJ
fuelectenerg-1426	143	27	polarities	polarity	NOUN
fuelectenerg-1426	143	28	of	of	ADP
fuelectenerg-1426	143	29	the	the	DET
fuelectenerg-1426	143	30	1	1	NUM
fuelectenerg-1426	143	31	-	-	PUNCT
fuelectenerg-1426	143	32	rpl	rpl	NOUN
fuelectenerg-1426	143	33	,	,	PUNCT
fuelectenerg-1426	143	34	respectively	respectively	ADV
fuelectenerg-1426	143	35	.	.	PUNCT
fuelectenerg-1426	144	1	also	also	ADV
fuelectenerg-1426	144	2	,	,	PUNCT
fuelectenerg-1426	144	3	{	{	PUNCT
fuelectenerg-1426	144	4	x	x	NOUN
fuelectenerg-1426	144	5	,	,	PUNCT
fuelectenerg-1426	144	6	x′,x′′,x′′′	x′,x′′,x′′′	PROPN
fuelectenerg-1426	144	7	}	}	PUNCT
fuelectenerg-1426	144	8	are	be	AUX
fuelectenerg-1426	144	9	the	the	DET
fuelectenerg-1426	144	10	zero	zero	NUM
fuelectenerg-1426	144	11	,	,	PUNCT
fuelectenerg-1426	144	12	first	first	ADJ
fuelectenerg-1426	144	13	,	,	PUNCT
fuelectenerg-1426	144	14	second	second	ADJ
fuelectenerg-1426	144	15	and	and	CCONJ
fuelectenerg-1426	144	16	third	third	ADJ
fuelectenerg-1426	144	17	shifts	shift	NOUN
fuelectenerg-1426	144	18	(	(	PUNCT
fuelectenerg-1426	144	19	inversions	inversion	NOUN
fuelectenerg-1426	144	20	)	)	PUNCT
fuelectenerg-1426	144	21	of	of	ADP
fuelectenerg-1426	144	22	the	the	DET
fuelectenerg-1426	144	23	variable	variable	NOUN
fuelectenerg-1426	144	24	x	x	PUNCT
fuelectenerg-1426	144	25	respectively	respectively	ADV
fuelectenerg-1426	144	26	,	,	PUNCT
fuelectenerg-1426	144	27	and	and	CCONJ
fuelectenerg-1426	144	28	variable	variable	NOUN
fuelectenerg-1426	144	29	x	x	PUNCT
fuelectenerg-1426	144	30	can	can	AUX
fuelectenerg-1426	144	31	take	take	VERB
fuelectenerg-1426	144	32	any	any	DET
fuelectenerg-1426	144	33	value	value	NOUN
fuelectenerg-1426	144	34	of	of	ADP
fuelectenerg-1426	144	35	the	the	DET
fuelectenerg-1426	144	36	set	set	NOUN
fuelectenerg-1426	144	37	{	{	PUNCT
fuelectenerg-1426	144	38	0,1,2,3	0,1,2,3	NUM
fuelectenerg-1426	144	39	}	}	PUNCT
fuelectenerg-1426	144	40	.	.	PUNCT
fuelectenerg-1426	145	1	analogous	analogous	ADJ
fuelectenerg-1426	145	2	to	to	ADP
fuelectenerg-1426	145	3	the	the	DET
fuelectenerg-1426	145	4	ternary	ternary	ADJ
fuelectenerg-1426	145	5	case	case	NOUN
fuelectenerg-1426	145	6	,	,	PUNCT
fuelectenerg-1426	145	7	we	we	PRON
fuelectenerg-1426	145	8	chose	choose	VERB
fuelectenerg-1426	145	9	to	to	PART
fuelectenerg-1426	145	10	represent	represent	VERB
fuelectenerg-1426	145	11	the	the	DET
fuelectenerg-1426	145	12	1	1	NUM
fuelectenerg-1426	145	13	-	-	PUNCT
fuelectenerg-1426	145	14	rpl	rpl	NOUN
fuelectenerg-1426	145	15	in	in	ADP
fuelectenerg-1426	145	16	terms	term	NOUN
fuelectenerg-1426	145	17	of	of	ADP
fuelectenerg-1426	145	18	shifts	shift	NOUN
fuelectenerg-1426	145	19	and	and	CCONJ
fuelectenerg-1426	145	20	powers	power	NOUN
fuelectenerg-1426	145	21	,	,	PUNCT
fuelectenerg-1426	145	22	among	among	ADP
fuelectenerg-1426	145	23	others	other	NOUN
fuelectenerg-1426	145	24	,	,	PUNCT
fuelectenerg-1426	145	25	because	because	SCONJ
fuelectenerg-1426	145	26	of	of	ADP
fuelectenerg-1426	145	27	the	the	DET
fuelectenerg-1426	145	28	ease	ease	NOUN
fuelectenerg-1426	145	29	of	of	ADP
fuelectenerg-1426	145	30	the	the	DET
fuelectenerg-1426	145	31	implementation	implementation	NOUN
fuelectenerg-1426	145	32	of	of	ADP
fuelectenerg-1426	145	33	powers	power	NOUN
fuelectenerg-1426	145	34	of	of	ADP
fuelectenerg-1426	145	35	shifted	shift	VERB
fuelectenerg-1426	145	36	variables	variable	NOUN
fuelectenerg-1426	145	37	in	in	ADP
fuelectenerg-1426	145	38	hardware	hardware	NOUN
fuelectenerg-1426	145	39	.	.	PUNCT
fuelectenerg-1426	146	1	after	after	ADP
fuelectenerg-1426	146	2	the	the	DET
fuelectenerg-1426	146	3	substitution	substitution	NOUN
fuelectenerg-1426	146	4	of	of	ADP
fuelectenerg-1426	146	5	equations	equation	NOUN
fuelectenerg-1426	146	6	(	(	PUNCT
fuelectenerg-1426	146	7	7	7	NUM
fuelectenerg-1426	146	8	)	)	PUNCT
fuelectenerg-1426	146	9	(	(	PUNCT
fuelectenerg-1426	146	10	22	22	NUM
fuelectenerg-1426	146	11	)	)	PUNCT
fuelectenerg-1426	146	12	in	in	ADP
fuelectenerg-1426	146	13	equation	equation	NOUN
fuelectenerg-1426	146	14	(	(	PUNCT
fuelectenerg-1426	146	15	6	6	NUM
fuelectenerg-1426	146	16	)	)	PUNCT
fuelectenerg-1426	146	17	,	,	PUNCT
fuelectenerg-1426	146	18	and	and	CCONJ
fuelectenerg-1426	146	19	after	after	ADP
fuelectenerg-1426	146	20	the	the	DET
fuelectenerg-1426	146	21	rearrangement	rearrangement	NOUN
fuelectenerg-1426	146	22	and	and	CCONJ
fuelectenerg-1426	146	23	reduction	reduction	NOUN
fuelectenerg-1426	146	24	of	of	ADP
fuelectenerg-1426	146	25	terms	term	NOUN
fuelectenerg-1426	146	26	according	accord	VERB
fuelectenerg-1426	146	27	to	to	ADP
fuelectenerg-1426	146	28	the	the	DET
fuelectenerg-1426	146	29	gf(4	gf(4	NOUN
fuelectenerg-1426	146	30	)	)	PUNCT
fuelectenerg-1426	146	31	operations	operation	NOUN
fuelectenerg-1426	146	32	in	in	ADP
fuelectenerg-1426	146	33	figure	figure	NOUN
fuelectenerg-1426	146	34	1	1	NUM
fuelectenerg-1426	146	35	,	,	PUNCT
fuelectenerg-1426	146	36	one	one	PRON
fuelectenerg-1426	146	37	obtains	obtain	VERB
fuelectenerg-1426	146	38	:	:	PUNCT
fuelectenerg-1426	147	1	f	f	NOUN
fuelectenerg-1426	147	2	=	=	SYM
fuelectenerg-1426	147	3	1	1	X
fuelectenerg-1426	147	4	·	·	PUNCT
fuelectenerg-1426	147	5	f0	f0	PROPN
fuelectenerg-1426	147	6	+	+	CCONJ
fuelectenerg-1426	147	7	x	x	X
fuelectenerg-1426	147	8	(	(	PUNCT
fuelectenerg-1426	147	9	f1	f1	NOUN
fuelectenerg-1426	147	10	+	+	CCONJ
fuelectenerg-1426	147	11	3	3	NUM
fuelectenerg-1426	147	12	f2	f2	ADJ
fuelectenerg-1426	147	13	+	+	NOUN
fuelectenerg-1426	147	14	2	2	NUM
fuelectenerg-1426	147	15	f3)+	f3)+	NOUN
fuelectenerg-1426	147	16	(	(	PUNCT
fuelectenerg-1426	147	17	x)2	x)2	PROPN
fuelectenerg-1426	147	18	(	(	PUNCT
fuelectenerg-1426	147	19	f1	f1	NOUN
fuelectenerg-1426	147	20	+2	+2	PROPN
fuelectenerg-1426	147	21	f2	f2	PROPN
fuelectenerg-1426	147	22	+3	+3	PROPN
fuelectenerg-1426	147	23	f3)+	f3)+	NOUN
fuelectenerg-1426	147	24	(	(	PUNCT
fuelectenerg-1426	147	25	x)3	x)3	PROPN
fuelectenerg-1426	147	26	(	(	PUNCT
fuelectenerg-1426	147	27	f0	f0	PROPN
fuelectenerg-1426	147	28	+	+	CCONJ
fuelectenerg-1426	147	29	f1	f1	NOUN
fuelectenerg-1426	147	30	+	+	CCONJ
fuelectenerg-1426	147	31	f2	f2	PROPN
fuelectenerg-1426	147	32	+	+	CCONJ
fuelectenerg-1426	147	33	f3	f3	ADJ
fuelectenerg-1426	147	34	)	)	PUNCT
fuelectenerg-1426	147	35	,	,	PUNCT
fuelectenerg-1426	147	36	(	(	PUNCT
fuelectenerg-1426	147	37	23	23	NUM
fuelectenerg-1426	147	38	)	)	PUNCT
fuelectenerg-1426	147	39	f	f	NOUN
fuelectenerg-1426	148	1	=	=	SYM
fuelectenerg-1426	148	2	1	1	NUM
fuelectenerg-1426	148	3	·	·	PUNCT
fuelectenerg-1426	148	4	f1	f1	NOUN
fuelectenerg-1426	148	5	+	+	PROPN
fuelectenerg-1426	148	6	(	(	PUNCT
fuelectenerg-1426	148	7	x′	x′	NUM
fuelectenerg-1426	148	8	)	)	PUNCT
fuelectenerg-1426	148	9	(	(	PUNCT
fuelectenerg-1426	148	10	f0	f0	PROPN
fuelectenerg-1426	148	11	+	+	CCONJ
fuelectenerg-1426	148	12	2	2	NUM
fuelectenerg-1426	148	13	f2	f2	ADJ
fuelectenerg-1426	148	14	+	+	NOUN
fuelectenerg-1426	148	15	3	3	NUM
fuelectenerg-1426	148	16	f3)+	f3)+	NOUN
fuelectenerg-1426	148	17	(	(	PUNCT
fuelectenerg-1426	148	18	x′)2	x′)2	PROPN
fuelectenerg-1426	148	19	(	(	PUNCT
fuelectenerg-1426	148	20	f0	f0	PROPN
fuelectenerg-1426	148	21	+3	+3	PROPN
fuelectenerg-1426	148	22	f2	f2	PROPN
fuelectenerg-1426	148	23	+2	+2	PROPN
fuelectenerg-1426	148	24	f3)+	f3)+	NOUN
fuelectenerg-1426	148	25	(	(	PUNCT
fuelectenerg-1426	148	26	x′)3	x′)3	PROPN
fuelectenerg-1426	148	27	(	(	PUNCT
fuelectenerg-1426	148	28	f0	f0	PROPN
fuelectenerg-1426	148	29	+	+	CCONJ
fuelectenerg-1426	148	30	f1	f1	NOUN
fuelectenerg-1426	148	31	+	+	CCONJ
fuelectenerg-1426	148	32	f2	f2	PROPN
fuelectenerg-1426	148	33	+	+	CCONJ
fuelectenerg-1426	148	34	f3	f3	ADJ
fuelectenerg-1426	148	35	)	)	PUNCT
fuelectenerg-1426	148	36	,	,	PUNCT
fuelectenerg-1426	148	37	(	(	PUNCT
fuelectenerg-1426	148	38	24	24	NUM
fuelectenerg-1426	148	39	)	)	PUNCT
fuelectenerg-1426	148	40	f	f	NOUN
fuelectenerg-1426	149	1	=	=	SYM
fuelectenerg-1426	149	2	1	1	X
fuelectenerg-1426	149	3	·	·	PUNCT
fuelectenerg-1426	149	4	f2	f2	PROPN
fuelectenerg-1426	149	5	+	+	PROPN
fuelectenerg-1426	149	6	(	(	PUNCT
fuelectenerg-1426	149	7	x′′)(3	x′′)(3	PROPN
fuelectenerg-1426	149	8	f0	f0	PROPN
fuelectenerg-1426	149	9	+	+	CCONJ
fuelectenerg-1426	149	10	2	2	NUM
fuelectenerg-1426	149	11	f1	f1	NOUN
fuelectenerg-1426	149	12	+	+	CCONJ
fuelectenerg-1426	149	13	f3)+	f3)+	NOUN
fuelectenerg-1426	149	14	(	(	PUNCT
fuelectenerg-1426	149	15	x′′)2(2	x′′)2(2	PROPN
fuelectenerg-1426	149	16	f0	f0	PROPN
fuelectenerg-1426	149	17	+3	+3	PROPN
fuelectenerg-1426	149	18	f1	f1	NOUN
fuelectenerg-1426	149	19	+	+	CCONJ
fuelectenerg-1426	149	20	f3)+	f3)+	NOUN
fuelectenerg-1426	149	21	(	(	PUNCT
fuelectenerg-1426	149	22	x′′)3	x′′)3	PROPN
fuelectenerg-1426	149	23	(	(	PUNCT
fuelectenerg-1426	149	24	f0	f0	PROPN
fuelectenerg-1426	149	25	+	+	CCONJ
fuelectenerg-1426	149	26	f1	f1	NOUN
fuelectenerg-1426	149	27	+	+	CCONJ
fuelectenerg-1426	149	28	f2	f2	PROPN
fuelectenerg-1426	149	29	+	+	CCONJ
fuelectenerg-1426	149	30	f3	f3	ADJ
fuelectenerg-1426	149	31	)	)	PUNCT
fuelectenerg-1426	149	32	,	,	PUNCT
fuelectenerg-1426	149	33	(	(	PUNCT
fuelectenerg-1426	149	34	25	25	NUM
fuelectenerg-1426	149	35	)	)	PUNCT
fuelectenerg-1426	149	36	f	f	NOUN
fuelectenerg-1426	149	37	=	=	SYM
fuelectenerg-1426	149	38	1	1	NUM
fuelectenerg-1426	149	39	·	·	PUNCT
fuelectenerg-1426	149	40	f3	f3	PROPN
fuelectenerg-1426	149	41	+	+	PROPN
fuelectenerg-1426	149	42	(	(	PUNCT
fuelectenerg-1426	149	43	x′′′	x′′′	PROPN
fuelectenerg-1426	149	44	)	)	PUNCT
fuelectenerg-1426	149	45	(	(	PUNCT
fuelectenerg-1426	149	46	f2	f2	PROPN
fuelectenerg-1426	149	47	+	+	NOUN
fuelectenerg-1426	149	48	3	3	NUM
fuelectenerg-1426	149	49	f1	f1	NOUN
fuelectenerg-1426	149	50	+	+	CCONJ
fuelectenerg-1426	149	51	2	2	NUM
fuelectenerg-1426	149	52	f0)+	f0)+	NOUN
fuelectenerg-1426	149	53	(	(	PUNCT
fuelectenerg-1426	149	54	x′′′)2	x′′′)2	PROPN
fuelectenerg-1426	149	55	(	(	PUNCT
fuelectenerg-1426	149	56	f2	f2	PROPN
fuelectenerg-1426	149	57	+2	+2	PROPN
fuelectenerg-1426	149	58	f1	f1	NOUN
fuelectenerg-1426	149	59	+3	+3	PROPN
fuelectenerg-1426	149	60	f0)+	f0)+	NOUN
fuelectenerg-1426	149	61	(	(	PUNCT
fuelectenerg-1426	149	62	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	149	63	(	(	PUNCT
fuelectenerg-1426	149	64	f0	f0	PROPN
fuelectenerg-1426	149	65	+	+	CCONJ
fuelectenerg-1426	149	66	f1	f1	NOUN
fuelectenerg-1426	149	67	+	+	CCONJ
fuelectenerg-1426	149	68	f2	f2	PROPN
fuelectenerg-1426	149	69	+	+	CCONJ
fuelectenerg-1426	149	70	f3	f3	ADJ
fuelectenerg-1426	149	71	)	)	PUNCT
fuelectenerg-1426	149	72	.	.	PUNCT
fuelectenerg-1426	150	1	(	(	PUNCT
fuelectenerg-1426	150	2	26	26	NUM
fuelectenerg-1426	150	3	)	)	PUNCT
fuelectenerg-1426	150	4	equations	equation	NOUN
fuelectenerg-1426	150	5	(	(	PUNCT
fuelectenerg-1426	150	6	6	6	NUM
fuelectenerg-1426	150	7	)	)	PUNCT
fuelectenerg-1426	150	8	and	and	CCONJ
fuelectenerg-1426	150	9	(	(	PUNCT
fuelectenerg-1426	150	10	23	23	NUM
fuelectenerg-1426	150	11	)	)	PUNCT
fuelectenerg-1426	150	12	(	(	PUNCT
fuelectenerg-1426	150	13	26	26	NUM
fuelectenerg-1426	150	14	)	)	PUNCT
fuelectenerg-1426	150	15	are	be	AUX
fuelectenerg-1426	150	16	the	the	DET
fuelectenerg-1426	150	17	1	1	NUM
fuelectenerg-1426	150	18	-	-	PUNCT
fuelectenerg-1426	150	19	rpl	rpl	NOUN
fuelectenerg-1426	150	20	quaternary	quaternary	ADJ
fuelectenerg-1426	150	21	shannon	shannon	NOUN
fuelectenerg-1426	150	22	(	(	PUNCT
fuelectenerg-1426	150	23	s	s	NOUN
fuelectenerg-1426	150	24	)	)	PUNCT
fuelectenerg-1426	150	25	and	and	CCONJ
fuelectenerg-1426	150	26	davio	davio	NOUN
fuelectenerg-1426	150	27	(	(	PUNCT
fuelectenerg-1426	150	28	d0,d1,d2,d3	d0,d1,d2,d3	NOUN
fuelectenerg-1426	150	29	}	}	PUNCT
fuelectenerg-1426	150	30	expansions	expansion	NOUN
fuelectenerg-1426	150	31	for	for	ADP
fuelectenerg-1426	150	32	a	a	DET
fuelectenerg-1426	150	33	single	single	ADJ
fuelectenerg-1426	150	34	variable	variable	NOUN
fuelectenerg-1426	150	35	,	,	PUNCT
fuelectenerg-1426	150	36	respectively	respectively	ADV
fuelectenerg-1426	150	37	.	.	PUNCT
fuelectenerg-1426	151	1	these	these	DET
fuelectenerg-1426	151	2	equations	equation	NOUN
fuelectenerg-1426	151	3	can	can	AUX
fuelectenerg-1426	151	4	be	be	AUX
fuelectenerg-1426	151	5	re	re	VERB
fuelectenerg-1426	151	6	-	-	VERB
fuelectenerg-1426	151	7	written	write	VERB
fuelectenerg-1426	151	8	in	in	ADP
fuelectenerg-1426	151	9	the	the	DET
fuelectenerg-1426	151	10	following	follow	VERB
fuelectenerg-1426	151	11	matrix	matrix	NOUN
fuelectenerg-1426	151	12	-	-	PUNCT
fuelectenerg-1426	151	13	based	base	VERB
fuelectenerg-1426	151	14	convolution	convolution	NOUN
fuelectenerg-1426	151	15	-	-	PUNCT
fuelectenerg-1426	151	16	like	like	ADJ
fuelectenerg-1426	151	17	forms	form	NOUN
fuelectenerg-1426	151	18	,	,	PUNCT
fuelectenerg-1426	151	19	respectively	respectively	ADV
fuelectenerg-1426	151	20	:	:	PUNCT
fuelectenerg-1426	151	21	106	106	NUM
fuelectenerg-1426	151	22	706	706	NUM
fuelectenerg-1426	151	23	a.	a.	NOUN
fuelectenerg-1426	151	24	n.	n.	PROPN
fuelectenerg-1426	151	25	al	al	PROPN
fuelectenerg-1426	151	26	-	-	PUNCT
fuelectenerg-1426	151	27	rabadi	rabadi	PROPN
fuelectenerg-1426	151	28	multi	multi	ADJ
fuelectenerg-1426	151	29	-	-	ADJ
fuelectenerg-1426	151	30	valued	value	VERB
fuelectenerg-1426	151	31	galois	galois	PROPN
fuelectenerg-1426	151	32	shannon	shannon	PROPN
fuelectenerg-1426	151	33	davio	davio	PROPN
fuelectenerg-1426	151	34	trees	tree	NOUN
fuelectenerg-1426	151	35	and	and	CCONJ
fuelectenerg-1426	151	36	their	their	PRON
fuelectenerg-1426	151	37	complexity	complexity	NOUN
fuelectenerg-1426	151	38	707	707	NUM
fuelectenerg-1426	151	39	multi	multi	ADJ
fuelectenerg-1426	151	40	-	-	ADJ
fuelectenerg-1426	151	41	valued	value	VERB
fuelectenerg-1426	151	42	galois	galois	PROPN
fuelectenerg-1426	151	43	shannon	shannon	PROPN
fuelectenerg-1426	151	44	davio	davio	PROPN
fuelectenerg-1426	151	45	trees	tree	NOUN
fuelectenerg-1426	151	46	and	and	CCONJ
fuelectenerg-1426	151	47	their	their	PRON
fuelectenerg-1426	151	48	complexity	complexity	NOUN
fuelectenerg-1426	151	49	f	f	X
fuelectenerg-1426	151	50	=	=	SYM
fuelectenerg-1426	151	51	�	�	PROPN
fuelectenerg-1426	151	52	0x	0x	NOUN
fuelectenerg-1426	151	53	1x	1x	NUM
fuelectenerg-1426	152	1	2x	2x	NUM
fuelectenerg-1426	152	2	3x	3x	PROPN
fuelectenerg-1426	152	3	�	�	PROPN
fuelectenerg-1426	152	4			PROPN
fuelectenerg-1426	152	5			ADJ
fuelectenerg-1426	152	6			ADJ
fuelectenerg-1426	152	7			NUM
fuelectenerg-1426	152	8	1	1	NUM
fuelectenerg-1426	152	9	0	0	NUM
fuelectenerg-1426	152	10	0	0	NUM
fuelectenerg-1426	152	11	0	0	NUM
fuelectenerg-1426	152	12	0	0	NUM
fuelectenerg-1426	152	13	1	1	NUM
fuelectenerg-1426	152	14	0	0	NUM
fuelectenerg-1426	152	15	0	0	NUM
fuelectenerg-1426	152	16	0	0	NUM
fuelectenerg-1426	152	17	0	0	NUM
fuelectenerg-1426	152	18	1	1	NUM
fuelectenerg-1426	152	19	0	0	NUM
fuelectenerg-1426	152	20	0	0	NUM
fuelectenerg-1426	152	21	0	0	NUM
fuelectenerg-1426	152	22	0	0	NUM
fuelectenerg-1426	152	23	1	1	NUM
fuelectenerg-1426	152	24			PROPN
fuelectenerg-1426	152	25			PROPN
fuelectenerg-1426	152	26			PROPN
fuelectenerg-1426	152	27			PROPN
fuelectenerg-1426	152	28			NOUN
fuelectenerg-1426	152	29			ADJ
fuelectenerg-1426	152	30			ADJ
fuelectenerg-1426	152	31			NUM
fuelectenerg-1426	152	32	f0	f0	PROPN
fuelectenerg-1426	152	33	f1	f1	PROPN
fuelectenerg-1426	152	34	f2	f2	PROPN
fuelectenerg-1426	152	35	f3	f3	PROPN
fuelectenerg-1426	152	36			PROPN
fuelectenerg-1426	152	37			PROPN
fuelectenerg-1426	152	38			PROPN
fuelectenerg-1426	152	39			PROPN
fuelectenerg-1426	152	40	,	,	PUNCT
fuelectenerg-1426	152	41	(	(	PUNCT
fuelectenerg-1426	152	42	27	27	NUM
fuelectenerg-1426	152	43	)	)	PUNCT
fuelectenerg-1426	152	44	f	f	NOUN
fuelectenerg-1426	152	45	=	=	SYM
fuelectenerg-1426	152	46	�	�	PROPN
fuelectenerg-1426	152	47	1	1	NUM
fuelectenerg-1426	152	48	x	x	SYM
fuelectenerg-1426	152	49	x2	x2	PROPN
fuelectenerg-1426	152	50	x3	x3	PROPN
fuelectenerg-1426	152	51	�	�	PROPN
fuelectenerg-1426	152	52			NOUN
fuelectenerg-1426	152	53			ADJ
fuelectenerg-1426	152	54			ADJ
fuelectenerg-1426	152	55			NUM
fuelectenerg-1426	152	56	1	1	NUM
fuelectenerg-1426	152	57	0	0	NUM
fuelectenerg-1426	152	58	0	0	NUM
fuelectenerg-1426	152	59	0	0	NUM
fuelectenerg-1426	152	60	0	0	NUM
fuelectenerg-1426	152	61	1	1	NUM
fuelectenerg-1426	152	62	3	3	NUM
fuelectenerg-1426	152	63	2	2	NUM
fuelectenerg-1426	152	64	0	0	NUM
fuelectenerg-1426	152	65	1	1	NUM
fuelectenerg-1426	152	66	2	2	NUM
fuelectenerg-1426	152	67	3	3	NUM
fuelectenerg-1426	152	68	1	1	NUM
fuelectenerg-1426	152	69	1	1	NUM
fuelectenerg-1426	152	70	1	1	NUM
fuelectenerg-1426	152	71	1	1	NUM
fuelectenerg-1426	152	72			PROPN
fuelectenerg-1426	152	73			PROPN
fuelectenerg-1426	152	74			PROPN
fuelectenerg-1426	152	75			PROPN
fuelectenerg-1426	152	76			NOUN
fuelectenerg-1426	152	77			ADJ
fuelectenerg-1426	152	78			ADJ
fuelectenerg-1426	152	79			NUM
fuelectenerg-1426	152	80	f0	f0	PROPN
fuelectenerg-1426	152	81	f1	f1	PROPN
fuelectenerg-1426	152	82	f2	f2	PROPN
fuelectenerg-1426	152	83	f3	f3	PROPN
fuelectenerg-1426	152	84			PROPN
fuelectenerg-1426	152	85			PROPN
fuelectenerg-1426	152	86			PROPN
fuelectenerg-1426	152	87			PROPN
fuelectenerg-1426	152	88	,	,	PUNCT
fuelectenerg-1426	152	89	(	(	PUNCT
fuelectenerg-1426	152	90	28	28	NUM
fuelectenerg-1426	152	91	)	)	PUNCT
fuelectenerg-1426	152	92	f	f	NOUN
fuelectenerg-1426	152	93	=	=	SYM
fuelectenerg-1426	152	94	�	�	PROPN
fuelectenerg-1426	152	95	1	1	NUM
fuelectenerg-1426	152	96	x′	x′	PROPN
fuelectenerg-1426	152	97	(	(	PUNCT
fuelectenerg-1426	152	98	x′)2	x′)2	PROPN
fuelectenerg-1426	152	99	(	(	PUNCT
fuelectenerg-1426	152	100	x′)3	x′)3	PROPN
fuelectenerg-1426	152	101	�	�	PROPN
fuelectenerg-1426	152	102			VERB
fuelectenerg-1426	152	103			ADJ
fuelectenerg-1426	152	104			ADJ
fuelectenerg-1426	152	105			NOUN
fuelectenerg-1426	152	106	0	0	NUM
fuelectenerg-1426	152	107	1	1	NUM
fuelectenerg-1426	152	108	0	0	NUM
fuelectenerg-1426	152	109	0	0	NUM
fuelectenerg-1426	152	110	1	1	NUM
fuelectenerg-1426	152	111	0	0	NUM
fuelectenerg-1426	152	112	2	2	NUM
fuelectenerg-1426	152	113	3	3	NUM
fuelectenerg-1426	152	114	1	1	NUM
fuelectenerg-1426	152	115	0	0	NUM
fuelectenerg-1426	152	116	3	3	NUM
fuelectenerg-1426	152	117	2	2	NUM
fuelectenerg-1426	152	118	1	1	NUM
fuelectenerg-1426	152	119	1	1	NUM
fuelectenerg-1426	152	120	1	1	NUM
fuelectenerg-1426	152	121	1	1	NUM
fuelectenerg-1426	152	122			PROPN
fuelectenerg-1426	152	123			PROPN
fuelectenerg-1426	152	124			PROPN
fuelectenerg-1426	152	125			PROPN
fuelectenerg-1426	152	126			NOUN
fuelectenerg-1426	152	127			ADJ
fuelectenerg-1426	152	128			ADJ
fuelectenerg-1426	152	129			NUM
fuelectenerg-1426	152	130	f0	f0	PROPN
fuelectenerg-1426	152	131	f1	f1	PROPN
fuelectenerg-1426	152	132	f2	f2	PROPN
fuelectenerg-1426	152	133	f3	f3	PROPN
fuelectenerg-1426	152	134			PROPN
fuelectenerg-1426	152	135			PROPN
fuelectenerg-1426	152	136			PROPN
fuelectenerg-1426	152	137			PROPN
fuelectenerg-1426	152	138	,	,	PUNCT
fuelectenerg-1426	152	139	(	(	PUNCT
fuelectenerg-1426	152	140	29	29	NUM
fuelectenerg-1426	152	141	)	)	PUNCT
fuelectenerg-1426	152	142	f	f	NOUN
fuelectenerg-1426	152	143	=	=	SYM
fuelectenerg-1426	152	144	�	�	PROPN
fuelectenerg-1426	152	145	1	1	NUM
fuelectenerg-1426	152	146	x′′	x′′	PROPN
fuelectenerg-1426	152	147	(	(	PUNCT
fuelectenerg-1426	152	148	x′′)2	x′′)2	PROPN
fuelectenerg-1426	152	149	(	(	PUNCT
fuelectenerg-1426	152	150	x′′)3	x′′)3	PROPN
fuelectenerg-1426	152	151	�	�	PROPN
fuelectenerg-1426	152	152			VERB
fuelectenerg-1426	152	153			ADJ
fuelectenerg-1426	152	154			ADJ
fuelectenerg-1426	152	155			NOUN
fuelectenerg-1426	152	156	0	0	NUM
fuelectenerg-1426	152	157	0	0	NUM
fuelectenerg-1426	152	158	1	1	NUM
fuelectenerg-1426	152	159	0	0	NUM
fuelectenerg-1426	152	160	3	3	NUM
fuelectenerg-1426	152	161	2	2	NUM
fuelectenerg-1426	152	162	0	0	NUM
fuelectenerg-1426	152	163	1	1	NUM
fuelectenerg-1426	152	164	2	2	NUM
fuelectenerg-1426	152	165	3	3	NUM
fuelectenerg-1426	152	166	0	0	NUM
fuelectenerg-1426	152	167	1	1	NUM
fuelectenerg-1426	152	168	1	1	NUM
fuelectenerg-1426	152	169	1	1	NUM
fuelectenerg-1426	152	170	1	1	NUM
fuelectenerg-1426	152	171	1	1	NUM
fuelectenerg-1426	152	172			PROPN
fuelectenerg-1426	152	173			PROPN
fuelectenerg-1426	152	174			PROPN
fuelectenerg-1426	152	175			PROPN
fuelectenerg-1426	152	176			NOUN
fuelectenerg-1426	152	177			ADJ
fuelectenerg-1426	152	178			ADJ
fuelectenerg-1426	152	179			NUM
fuelectenerg-1426	152	180	f0	f0	PROPN
fuelectenerg-1426	152	181	f1	f1	PROPN
fuelectenerg-1426	152	182	f2	f2	PROPN
fuelectenerg-1426	152	183	f3	f3	PROPN
fuelectenerg-1426	152	184			PROPN
fuelectenerg-1426	152	185			PROPN
fuelectenerg-1426	152	186			PROPN
fuelectenerg-1426	152	187			PROPN
fuelectenerg-1426	152	188	,	,	PUNCT
fuelectenerg-1426	152	189	(	(	PUNCT
fuelectenerg-1426	152	190	30	30	NUM
fuelectenerg-1426	152	191	)	)	PUNCT
fuelectenerg-1426	152	192	f	f	NOUN
fuelectenerg-1426	152	193	=	=	SYM
fuelectenerg-1426	152	194	�	�	PROPN
fuelectenerg-1426	152	195	1	1	NUM
fuelectenerg-1426	152	196	x′′′	x′′′	PROPN
fuelectenerg-1426	152	197	(	(	PUNCT
fuelectenerg-1426	152	198	x′′′)2	x′′′)2	PROPN
fuelectenerg-1426	152	199	(	(	PUNCT
fuelectenerg-1426	152	200	x′′′)3	x′′′)3	PROPN
fuelectenerg-1426	152	201	�	�	PROPN
fuelectenerg-1426	152	202			PROPN
fuelectenerg-1426	152	203			ADJ
fuelectenerg-1426	152	204			ADJ
fuelectenerg-1426	152	205			NOUN
fuelectenerg-1426	152	206	0	0	NUM
fuelectenerg-1426	152	207	0	0	NUM
fuelectenerg-1426	152	208	0	0	NUM
fuelectenerg-1426	152	209	1	1	NUM
fuelectenerg-1426	152	210	2	2	NUM
fuelectenerg-1426	152	211	3	3	NUM
fuelectenerg-1426	152	212	1	1	NUM
fuelectenerg-1426	152	213	0	0	NUM
fuelectenerg-1426	152	214	3	3	NUM
fuelectenerg-1426	152	215	2	2	NUM
fuelectenerg-1426	152	216	1	1	NUM
fuelectenerg-1426	152	217	0	0	NUM
fuelectenerg-1426	152	218	1	1	NUM
fuelectenerg-1426	152	219	1	1	NUM
fuelectenerg-1426	152	220	1	1	NUM
fuelectenerg-1426	152	221	1	1	NUM
fuelectenerg-1426	152	222			PROPN
fuelectenerg-1426	152	223			PROPN
fuelectenerg-1426	152	224			PROPN
fuelectenerg-1426	152	225			PROPN
fuelectenerg-1426	152	226			NOUN
fuelectenerg-1426	152	227			ADJ
fuelectenerg-1426	152	228			ADJ
fuelectenerg-1426	152	229			NUM
fuelectenerg-1426	152	230	f0	f0	PROPN
fuelectenerg-1426	152	231	f1	f1	PROPN
fuelectenerg-1426	152	232	f2	f2	PROPN
fuelectenerg-1426	152	233	f3	f3	PROPN
fuelectenerg-1426	152	234			PROPN
fuelectenerg-1426	152	235			PROPN
fuelectenerg-1426	152	236			PROPN
fuelectenerg-1426	152	237			PROPN
fuelectenerg-1426	152	238	.	.	PUNCT
fuelectenerg-1426	153	1	(	(	PUNCT
fuelectenerg-1426	153	2	31	31	NUM
fuelectenerg-1426	153	3	)	)	PUNCT
fuelectenerg-1426	153	4	one	one	PRON
fuelectenerg-1426	153	5	can	can	AUX
fuelectenerg-1426	153	6	observe	observe	VERB
fuelectenerg-1426	153	7	that	that	SCONJ
fuelectenerg-1426	153	8	equations	equation	NOUN
fuelectenerg-1426	153	9	(	(	PUNCT
fuelectenerg-1426	153	10	27	27	NUM
fuelectenerg-1426	153	11	)	)	PUNCT
fuelectenerg-1426	153	12	(	(	PUNCT
fuelectenerg-1426	153	13	31	31	NUM
fuelectenerg-1426	153	14	)	)	PUNCT
fuelectenerg-1426	153	15	are	be	AUX
fuelectenerg-1426	153	16	expansions	expansion	NOUN
fuelectenerg-1426	153	17	for	for	ADP
fuelectenerg-1426	153	18	a	a	DET
fuelectenerg-1426	153	19	single	single	ADJ
fuelectenerg-1426	153	20	variable	variable	NOUN
fuelectenerg-1426	153	21	.	.	PUNCT
fuelectenerg-1426	154	1	yet	yet	ADV
fuelectenerg-1426	154	2	,	,	PUNCT
fuelectenerg-1426	154	3	these	these	DET
fuelectenerg-1426	154	4	canonical	canonical	ADJ
fuelectenerg-1426	154	5	expressions	expression	NOUN
fuelectenerg-1426	154	6	can	can	AUX
fuelectenerg-1426	154	7	be	be	AUX
fuelectenerg-1426	154	8	generated	generate	VERB
fuelectenerg-1426	154	9	for	for	ADP
fuelectenerg-1426	154	10	arbitrary	arbitrary	ADJ
fuelectenerg-1426	154	11	number	number	NOUN
fuelectenerg-1426	154	12	of	of	ADP
fuelectenerg-1426	154	13	variables	variable	NOUN
fuelectenerg-1426	154	14	n	n	CCONJ
fuelectenerg-1426	154	15	using	use	VERB
fuelectenerg-1426	154	16	the	the	DET
fuelectenerg-1426	154	17	kronecker	kronecker	NOUN
fuelectenerg-1426	154	18	(	(	PUNCT
fuelectenerg-1426	154	19	tensor	tensor	NOUN
fuelectenerg-1426	154	20	)	)	PUNCT
fuelectenerg-1426	154	21	product	product	NOUN
fuelectenerg-1426	154	22	.	.	PUNCT
fuelectenerg-1426	155	1	this	this	PRON
fuelectenerg-1426	155	2	can	can	AUX
fuelectenerg-1426	155	3	be	be	AUX
fuelectenerg-1426	155	4	expressed	express	VERB
fuelectenerg-1426	155	5	formally	formally	ADV
fuelectenerg-1426	155	6	as	as	ADP
fuelectenerg-1426	155	7	in	in	ADP
fuelectenerg-1426	155	8	the	the	DET
fuelectenerg-1426	155	9	following	follow	VERB
fuelectenerg-1426	155	10	discrete	discrete	ADJ
fuelectenerg-1426	155	11	convolution	convolution	NOUN
fuelectenerg-1426	155	12	-	-	PUNCT
fuelectenerg-1426	155	13	like	like	ADJ
fuelectenerg-1426	155	14	forms	form	NOUN
fuelectenerg-1426	155	15	for	for	ADP
fuelectenerg-1426	155	16	shannon	shannon	PROPN
fuelectenerg-1426	155	17	(	(	PUNCT
fuelectenerg-1426	155	18	s	s	NOUN
fuelectenerg-1426	155	19	)	)	PUNCT
fuelectenerg-1426	155	20	,	,	PUNCT
fuelectenerg-1426	155	21	and	and	CCONJ
fuelectenerg-1426	155	22	davio	davio	NOUN
fuelectenerg-1426	155	23	(	(	PUNCT
fuelectenerg-1426	155	24	d0	d0	NOUN
fuelectenerg-1426	155	25	,	,	PUNCT
fuelectenerg-1426	155	26	d1	d1	NOUN
fuelectenerg-1426	155	27	,	,	PUNCT
fuelectenerg-1426	155	28	d2	d2	PROPN
fuelectenerg-1426	155	29	and	and	CCONJ
fuelectenerg-1426	155	30	d3	d3	PROPN
fuelectenerg-1426	155	31	)	)	PUNCT
fuelectenerg-1426	155	32	expressions	expression	NOUN
fuelectenerg-1426	155	33	,	,	PUNCT
fuelectenerg-1426	155	34	respectively	respectively	ADV
fuelectenerg-1426	155	35	[	[	X
fuelectenerg-1426	155	36	2	2	NUM
fuelectenerg-1426	155	37	,	,	PUNCT
fuelectenerg-1426	155	38	32	32	NUM
fuelectenerg-1426	155	39	]	]	PUNCT
fuelectenerg-1426	155	40	:	:	PUNCT
fuelectenerg-1426	156	1	f	f	X
fuelectenerg-1426	156	2	=	=	SYM
fuelectenerg-1426	156	3	n	n	PRON
fuelectenerg-1426	156	4	�	�	PROPN
fuelectenerg-1426	156	5	i=1	i=1	PROPN
fuelectenerg-1426	156	6	�	�	PROPN
fuelectenerg-1426	156	7	0xi	0xi	NOUN
fuelectenerg-1426	156	8	1xi	1xi	PROPN
fuelectenerg-1426	156	9	2xi	2xi	ADJ
fuelectenerg-1426	156	10	3xi	3xi	ADJ
fuelectenerg-1426	156	11	�	�	PROPN
fuelectenerg-1426	156	12	n	n	CCONJ
fuelectenerg-1426	156	13	�	�	PROPN
fuelectenerg-1426	156	14	i=1	i=1	PROPN
fuelectenerg-1426	157	1	[	[	X
fuelectenerg-1426	157	2	s][	s][	PROPN
fuelectenerg-1426	157	3	�	�	PROPN
fuelectenerg-1426	157	4	f	f	X
fuelectenerg-1426	157	5	]	]	X
fuelectenerg-1426	157	6	,	,	PUNCT
fuelectenerg-1426	157	7	(	(	PUNCT
fuelectenerg-1426	157	8	32	32	NUM
fuelectenerg-1426	157	9	)	)	PUNCT
fuelectenerg-1426	157	10	f	f	NOUN
fuelectenerg-1426	158	1	=	=	SYM
fuelectenerg-1426	158	2	n	n	PRON
fuelectenerg-1426	158	3	�	�	PROPN
fuelectenerg-1426	158	4	i=1	i=1	PROPN
fuelectenerg-1426	158	5	�	�	PROPN
fuelectenerg-1426	158	6	1	1	NUM
fuelectenerg-1426	158	7	xi	xi	X
fuelectenerg-1426	158	8	x2	x2	INTJ
fuelectenerg-1426	159	1	i	i	PRON
fuelectenerg-1426	159	2	x3	x3	VERB
fuelectenerg-1426	160	1	i	i	PRON
fuelectenerg-1426	160	2	�	�	PROPN
fuelectenerg-1426	160	3	n	n	CCONJ
fuelectenerg-1426	160	4	�	�	PROPN
fuelectenerg-1426	160	5	i=1	i=1	X
fuelectenerg-1426	161	1	[	[	X
fuelectenerg-1426	161	2	d0][	d0][	NOUN
fuelectenerg-1426	161	3	�	�	X
fuelectenerg-1426	161	4	f	f	X
fuelectenerg-1426	161	5	]	]	X
fuelectenerg-1426	161	6	,	,	PUNCT
fuelectenerg-1426	161	7	(	(	PUNCT
fuelectenerg-1426	161	8	33	33	NUM
fuelectenerg-1426	161	9	)	)	PUNCT
fuelectenerg-1426	161	10	f	f	NOUN
fuelectenerg-1426	162	1	=	=	SYM
fuelectenerg-1426	162	2	n	n	PRON
fuelectenerg-1426	162	3	�	�	PROPN
fuelectenerg-1426	162	4	i=1	i=1	PROPN
fuelectenerg-1426	162	5	�	�	PROPN
fuelectenerg-1426	162	6	1	1	NUM
fuelectenerg-1426	162	7	x′i	x′i	PROPN
fuelectenerg-1426	162	8	(	(	PUNCT
fuelectenerg-1426	162	9	x′i)2	x′i)2	PROPN
fuelectenerg-1426	162	10	(	(	PUNCT
fuelectenerg-1426	162	11	x′i)3	x′i)3	PROPN
fuelectenerg-1426	162	12	�	�	PROPN
fuelectenerg-1426	162	13	n	n	CCONJ
fuelectenerg-1426	162	14	�	�	PROPN
fuelectenerg-1426	162	15	i=1	i=1	PART
fuelectenerg-1426	163	1	[	[	X
fuelectenerg-1426	163	2	d1][	d1][	X
fuelectenerg-1426	163	3	�	�	NOUN
fuelectenerg-1426	163	4	f	f	X
fuelectenerg-1426	163	5	]	]	X
fuelectenerg-1426	163	6	,	,	PUNCT
fuelectenerg-1426	163	7	(	(	PUNCT
fuelectenerg-1426	163	8	34	34	NUM
fuelectenerg-1426	163	9	)	)	PUNCT
fuelectenerg-1426	163	10	f	f	NOUN
fuelectenerg-1426	164	1	=	=	SYM
fuelectenerg-1426	164	2	n	n	PRON
fuelectenerg-1426	164	3	�	�	PROPN
fuelectenerg-1426	164	4	i=1	i=1	PROPN
fuelectenerg-1426	164	5	�	�	PROPN
fuelectenerg-1426	164	6	1	1	NUM
fuelectenerg-1426	164	7	x′′i	x′′i	PROPN
fuelectenerg-1426	164	8	(	(	PUNCT
fuelectenerg-1426	164	9	x′′i	x′′i	PROPN
fuelectenerg-1426	164	10	)	)	PUNCT
fuelectenerg-1426	164	11	2	2	PROPN
fuelectenerg-1426	164	12	(	(	PUNCT
fuelectenerg-1426	164	13	x′′i	x′′i	PROPN
fuelectenerg-1426	164	14	)	)	PUNCT
fuelectenerg-1426	164	15	3	3	NUM
fuelectenerg-1426	164	16	�	�	PROPN
fuelectenerg-1426	164	17	n	n	CCONJ
fuelectenerg-1426	164	18	�	�	PROPN
fuelectenerg-1426	164	19	i=1	i=1	PROPN
fuelectenerg-1426	165	1	[	[	AUX
fuelectenerg-1426	165	2	d2][	d2][	PROPN
fuelectenerg-1426	165	3	�	�	PROPN
fuelectenerg-1426	165	4	f	f	PROPN
fuelectenerg-1426	165	5	]	]	X
fuelectenerg-1426	165	6	,	,	PUNCT
fuelectenerg-1426	165	7	(	(	PUNCT
fuelectenerg-1426	165	8	35	35	NUM
fuelectenerg-1426	165	9	)	)	PUNCT
fuelectenerg-1426	165	10	f	f	NOUN
fuelectenerg-1426	166	1	=	=	SYM
fuelectenerg-1426	166	2	n	n	PRON
fuelectenerg-1426	166	3	�	�	PROPN
fuelectenerg-1426	166	4	i=1	i=1	PROPN
fuelectenerg-1426	166	5	�	�	PROPN
fuelectenerg-1426	166	6	1	1	NUM
fuelectenerg-1426	166	7	x′′′i	x′′′i	PUNCT
fuelectenerg-1426	166	8	(	(	PUNCT
fuelectenerg-1426	166	9	x′′′i	x′′′i	X
fuelectenerg-1426	166	10	)	)	PUNCT
fuelectenerg-1426	166	11	2	2	NUM
fuelectenerg-1426	166	12	(	(	PUNCT
fuelectenerg-1426	166	13	x′′′i	x′′′i	X
fuelectenerg-1426	166	14	)	)	PUNCT
fuelectenerg-1426	166	15	3	3	NUM
fuelectenerg-1426	166	16	�	�	PROPN
fuelectenerg-1426	166	17	n	n	CCONJ
fuelectenerg-1426	166	18	�	�	PROPN
fuelectenerg-1426	166	19	i=1	i=1	X
fuelectenerg-1426	167	1	[	[	X
fuelectenerg-1426	167	2	d3][	d3][	PROPN
fuelectenerg-1426	167	3	�	�	PROPN
fuelectenerg-1426	167	4	f	f	NOUN
fuelectenerg-1426	167	5	]	]	X
fuelectenerg-1426	167	6	.	.	PUNCT
fuelectenerg-1426	168	1	(	(	PUNCT
fuelectenerg-1426	168	2	36	36	NUM
fuelectenerg-1426	168	3	)	)	PUNCT
fuelectenerg-1426	168	4	the	the	DET
fuelectenerg-1426	168	5	following	follow	VERB
fuelectenerg-1426	168	6	section	section	NOUN
fuelectenerg-1426	168	7	utilizes	utilize	VERB
fuelectenerg-1426	168	8	the	the	DET
fuelectenerg-1426	168	9	presented	present	VERB
fuelectenerg-1426	168	10	gf(4	gf(4	NOUN
fuelectenerg-1426	168	11	)	)	PUNCT
fuelectenerg-1426	168	12	spectral	spectral	NOUN
fuelectenerg-1426	168	13	-	-	PUNCT
fuelectenerg-1426	168	14	based	base	VERB
fuelectenerg-1426	168	15	functional	functional	ADJ
fuelectenerg-1426	168	16	decompositions	decomposition	NOUN
fuelectenerg-1426	168	17	for	for	ADP
fuelectenerg-1426	168	18	the	the	DET
fuelectenerg-1426	168	19	synthesis	synthesis	NOUN
fuelectenerg-1426	168	20	of	of	ADP
fuelectenerg-1426	168	21	decision	decision	NOUN
fuelectenerg-1426	168	22	trees	tree	NOUN
fuelectenerg-1426	168	23	.	.	PUNCT
fuelectenerg-1426	169	1	in	in	ADP
fuelectenerg-1426	169	2	this	this	DET
fuelectenerg-1426	169	3	spectral	spectral	ADJ
fuelectenerg-1426	169	4	interpretation	interpretation	NOUN
fuelectenerg-1426	169	5	of	of	ADP
fuelectenerg-1426	169	6	decision	decision	NOUN
fuelectenerg-1426	169	7	trees	tree	NOUN
fuelectenerg-1426	169	8	,	,	PUNCT
fuelectenerg-1426	169	9	107	107	NUM
fuelectenerg-1426	169	10	708	708	NUM
fuelectenerg-1426	169	11	a.	a.	NOUN
fuelectenerg-1426	169	12	n.	n.	PROPN
fuelectenerg-1426	169	13	al	al	PROPN
fuelectenerg-1426	169	14	-	-	PUNCT
fuelectenerg-1426	169	15	rabadi	rabadi	PROPN
fuelectenerg-1426	169	16	multi	multi	ADJ
fuelectenerg-1426	169	17	-	-	ADJ
fuelectenerg-1426	169	18	valued	value	VERB
fuelectenerg-1426	169	19	galois	galois	PROPN
fuelectenerg-1426	169	20	shannon	shannon	PROPN
fuelectenerg-1426	169	21	davio	davio	PROPN
fuelectenerg-1426	169	22	trees	tree	NOUN
fuelectenerg-1426	169	23	and	and	CCONJ
fuelectenerg-1426	169	24	their	their	PRON
fuelectenerg-1426	169	25	complexity	complexity	NOUN
fuelectenerg-1426	169	26	709	709	NUM
fuelectenerg-1426	169	27	multi	multi	ADJ
fuelectenerg-1426	169	28	-	-	ADJ
fuelectenerg-1426	169	29	valued	value	VERB
fuelectenerg-1426	169	30	galois	galois	PROPN
fuelectenerg-1426	169	31	shannon	shannon	PROPN
fuelectenerg-1426	169	32	davio	davio	PROPN
fuelectenerg-1426	169	33	trees	tree	NOUN
fuelectenerg-1426	169	34	and	and	CCONJ
fuelectenerg-1426	169	35	their	their	PRON
fuelectenerg-1426	169	36	complexity	complexity	NOUN
fuelectenerg-1426	169	37	different	different	ADJ
fuelectenerg-1426	169	38	decision	decision	NOUN
fuelectenerg-1426	169	39	trees	tree	NOUN
fuelectenerg-1426	169	40	can	can	AUX
fuelectenerg-1426	169	41	be	be	AUX
fuelectenerg-1426	169	42	defined	define	VERB
fuelectenerg-1426	169	43	by	by	ADP
fuelectenerg-1426	169	44	using	use	VERB
fuelectenerg-1426	169	45	different	different	ADJ
fuelectenerg-1426	169	46	decomposition	decomposition	NOUN
fuelectenerg-1426	169	47	forms	form	NOUN
fuelectenerg-1426	169	48	which	which	PRON
fuelectenerg-1426	169	49	are	be	AUX
fuelectenerg-1426	169	50	specified	specify	VERB
fuelectenerg-1426	169	51	by	by	ADP
fuelectenerg-1426	169	52	the	the	DET
fuelectenerg-1426	169	53	corresponding	correspond	VERB
fuelectenerg-1426	169	54	transform	transform	NOUN
fuelectenerg-1426	169	55	matrices	matrix	NOUN
fuelectenerg-1426	169	56	and	and	CCONJ
fuelectenerg-1426	169	57	multi	multi	ADJ
fuelectenerg-1426	169	58	-	-	ADJ
fuelectenerg-1426	169	59	valued	value	VERB
fuelectenerg-1426	169	60	literals	literal	NOUN
fuelectenerg-1426	169	61	.	.	PUNCT
fuelectenerg-1426	170	1	the	the	DET
fuelectenerg-1426	170	2	utilized	utilize	VERB
fuelectenerg-1426	170	3	decision	decision	NOUN
fuelectenerg-1426	170	4	trees	tree	NOUN
fuelectenerg-1426	170	5	can	can	AUX
fuelectenerg-1426	170	6	therefore	therefore	ADV
fuelectenerg-1426	170	7	be	be	AUX
fuelectenerg-1426	170	8	viewed	view	VERB
fuelectenerg-1426	170	9	as	as	ADP
fuelectenerg-1426	170	10	graphical	graphical	ADJ
fuelectenerg-1426	170	11	representations	representation	NOUN
fuelectenerg-1426	170	12	of	of	ADP
fuelectenerg-1426	170	13	functional	functional	ADJ
fuelectenerg-1426	170	14	expressions	expression	NOUN
fuelectenerg-1426	170	15	where	where	SCONJ
fuelectenerg-1426	170	16	different	different	ADJ
fuelectenerg-1426	170	17	trees	tree	NOUN
fuelectenerg-1426	170	18	produce	produce	VERB
fuelectenerg-1426	170	19	different	different	ADJ
fuelectenerg-1426	170	20	functional	functional	ADJ
fuelectenerg-1426	170	21	expressions	expression	NOUN
fuelectenerg-1426	170	22	,	,	PUNCT
fuelectenerg-1426	170	23	and	and	CCONJ
fuelectenerg-1426	170	24	by	by	ADP
fuelectenerg-1426	170	25	counting	count	VERB
fuelectenerg-1426	170	26	the	the	DET
fuelectenerg-1426	170	27	number	number	NOUN
fuelectenerg-1426	170	28	of	of	ADP
fuelectenerg-1426	170	29	possible	possible	ADJ
fuelectenerg-1426	170	30	different	different	ADJ
fuelectenerg-1426	170	31	trees	tree	NOUN
fuelectenerg-1426	170	32	,	,	PUNCT
fuelectenerg-1426	170	33	that	that	PRON
fuelectenerg-1426	170	34	are	be	AUX
fuelectenerg-1426	170	35	derived	derive	VERB
fuelectenerg-1426	170	36	by	by	ADP
fuelectenerg-1426	170	37	assigning	assign	VERB
fuelectenerg-1426	170	38	different	different	ADJ
fuelectenerg-1426	170	39	decomposition	decomposition	NOUN
fuelectenerg-1426	170	40	rules	rule	NOUN
fuelectenerg-1426	170	41	to	to	ADP
fuelectenerg-1426	170	42	their	their	PRON
fuelectenerg-1426	170	43	nodes	node	NOUN
fuelectenerg-1426	170	44	,	,	PUNCT
fuelectenerg-1426	170	45	we	we	PRON
fuelectenerg-1426	170	46	can	can	AUX
fuelectenerg-1426	170	47	count	count	VERB
fuelectenerg-1426	170	48	the	the	DET
fuelectenerg-1426	170	49	number	number	NOUN
fuelectenerg-1426	170	50	of	of	ADP
fuelectenerg-1426	170	51	possible	possible	ADJ
fuelectenerg-1426	170	52	functional	functional	ADJ
fuelectenerg-1426	170	53	expressions	expression	NOUN
fuelectenerg-1426	170	54	.	.	PUNCT
fuelectenerg-1426	171	1	3	3	NUM
fuelectenerg-1426	171	2	quaternary	quaternary	ADJ
fuelectenerg-1426	171	3	shannon	shannon	NOUN
fuelectenerg-1426	171	4	-	-	PUNCT
fuelectenerg-1426	171	5	dvaio	dvaio	PROPN
fuelectenerg-1426	171	6	(	(	PUNCT
fuelectenerg-1426	171	7	s	s	NOUN
fuelectenerg-1426	171	8	/	/	SYM
fuelectenerg-1426	171	9	d	d	NOUN
fuelectenerg-1426	171	10	)	)	PUNCT
fuelectenerg-1426	171	11	trees	tree	NOUN
fuelectenerg-1426	171	12	the	the	DET
fuelectenerg-1426	171	13	basic	basic	ADJ
fuelectenerg-1426	171	14	s	s	PROPN
fuelectenerg-1426	171	15	,	,	PUNCT
fuelectenerg-1426	171	16	d0	d0	NOUN
fuelectenerg-1426	171	17	,	,	PUNCT
fuelectenerg-1426	171	18	d1	d1	NOUN
fuelectenerg-1426	171	19	,	,	PUNCT
fuelectenerg-1426	171	20	d2	d2	PROPN
fuelectenerg-1426	171	21	and	and	CCONJ
fuelectenerg-1426	171	22	d3	d3	VERB
fuelectenerg-1426	171	23	quaternary	quaternary	ADJ
fuelectenerg-1426	171	24	expansions	expansion	NOUN
fuelectenerg-1426	171	25	(	(	PUNCT
fuelectenerg-1426	171	26	i.e.	i.e.	X
fuelectenerg-1426	171	27	,	,	PUNCT
fuelectenerg-1426	171	28	flattened	flatten	VERB
fuelectenerg-1426	171	29	forms	form	NOUN
fuelectenerg-1426	171	30	)	)	PUNCT
fuelectenerg-1426	171	31	introduced	introduce	VERB
fuelectenerg-1426	171	32	previously	previously	ADV
fuelectenerg-1426	171	33	in	in	ADP
fuelectenerg-1426	171	34	equations	equation	NOUN
fuelectenerg-1426	171	35	(	(	PUNCT
fuelectenerg-1426	171	36	32	32	NUM
fuelectenerg-1426	171	37	)	)	PUNCT
fuelectenerg-1426	171	38	(	(	PUNCT
fuelectenerg-1426	171	39	36	36	NUM
fuelectenerg-1426	171	40	)	)	PUNCT
fuelectenerg-1426	171	41	can	can	AUX
fuelectenerg-1426	171	42	be	be	AUX
fuelectenerg-1426	171	43	represented	represent	VERB
fuelectenerg-1426	171	44	in	in	ADP
fuelectenerg-1426	171	45	quaternary	quaternary	ADJ
fuelectenerg-1426	171	46	dts	dts	NOUN
fuelectenerg-1426	171	47	(	(	PUNCT
fuelectenerg-1426	171	48	qudts	qudts	ADJ
fuelectenerg-1426	171	49	)	)	PUNCT
fuelectenerg-1426	171	50	and	and	CCONJ
fuelectenerg-1426	171	51	the	the	DET
fuelectenerg-1426	171	52	corresponding	corresponding	ADJ
fuelectenerg-1426	171	53	varieties	variety	NOUN
fuelectenerg-1426	171	54	of	of	ADP
fuelectenerg-1426	171	55	reduced	reduce	VERB
fuelectenerg-1426	171	56	quaternary	quaternary	ADJ
fuelectenerg-1426	171	57	dds	dds	PROPN
fuelectenerg-1426	171	58	(	(	PUNCT
fuelectenerg-1426	171	59	rqudds	rqudds	PROPN
fuelectenerg-1426	171	60	)	)	PUNCT
fuelectenerg-1426	171	61	according	accord	VERB
fuelectenerg-1426	171	62	to	to	ADP
fuelectenerg-1426	171	63	the	the	DET
fuelectenerg-1426	171	64	corresponding	corresponding	ADJ
fuelectenerg-1426	171	65	reduction	reduction	NOUN
fuelectenerg-1426	171	66	rules	rule	NOUN
fuelectenerg-1426	171	67	.	.	PUNCT
fuelectenerg-1426	172	1	for	for	ADP
fuelectenerg-1426	172	2	one	one	NUM
fuelectenerg-1426	172	3	variable	variable	NOUN
fuelectenerg-1426	172	4	(	(	PUNCT
fuelectenerg-1426	172	5	i.e.	i.e.	X
fuelectenerg-1426	172	6	,	,	PUNCT
fuelectenerg-1426	172	7	one	one	NUM
fuelectenerg-1426	172	8	level	level	NOUN
fuelectenerg-1426	172	9	of	of	ADP
fuelectenerg-1426	172	10	the	the	DET
fuelectenerg-1426	172	11	dt	dt	PROPN
fuelectenerg-1426	172	12	)	)	PUNCT
fuelectenerg-1426	172	13	,	,	PUNCT
fuelectenerg-1426	172	14	figures	figure	VERB
fuelectenerg-1426	172	15	4(a	4(a	NUM
fuelectenerg-1426	172	16	)	)	PUNCT
fuelectenerg-1426	172	17	4(e	4(e	NUM
fuelectenerg-1426	172	18	)	)	PUNCT
fuelectenerg-1426	172	19	represent	represent	VERB
fuelectenerg-1426	172	20	the	the	DET
fuelectenerg-1426	172	21	expansion	expansion	NOUN
fuelectenerg-1426	172	22	nodes	node	NOUN
fuelectenerg-1426	172	23	for	for	ADP
fuelectenerg-1426	172	24	{	{	PUNCT
fuelectenerg-1426	172	25	s	s	PROPN
fuelectenerg-1426	172	26	,	,	PUNCT
fuelectenerg-1426	172	27	d0,d1,d2,d3	d0,d1,d2,d3	PROPN
fuelectenerg-1426	172	28	}	}	PUNCT
fuelectenerg-1426	172	29	,	,	PUNCT
fuelectenerg-1426	172	30	respectively	respectively	ADV
fuelectenerg-1426	172	31	,	,	PUNCT
fuelectenerg-1426	172	32	and	and	CCONJ
fuelectenerg-1426	172	33	the	the	DET
fuelectenerg-1426	172	34	notation	notation	NOUN
fuelectenerg-1426	172	35	in	in	ADP
fuelectenerg-1426	172	36	figure	figure	NOUN
fuelectenerg-1426	172	37	4(f	4(f	NUM
fuelectenerg-1426	172	38	)	)	PUNCT
fuelectenerg-1426	172	39	means	mean	VERB
fuelectenerg-1426	172	40	that	that	SCONJ
fuelectenerg-1426	172	41	x	x	PRON
fuelectenerg-1426	172	42	corresponds	correspond	VERB
fuelectenerg-1426	172	43	to	to	ADP
fuelectenerg-1426	172	44	the	the	DET
fuelectenerg-1426	172	45	four	four	NUM
fuelectenerg-1426	172	46	possible	possible	ADJ
fuelectenerg-1426	172	47	shifts	shift	NOUN
fuelectenerg-1426	172	48	of	of	ADP
fuelectenerg-1426	172	49	the	the	DET
fuelectenerg-1426	172	50	variable	variable	NOUN
fuelectenerg-1426	172	51	x	x	PUNCT
fuelectenerg-1426	172	52	as	as	ADP
fuelectenerg-1426	172	53	:	:	PUNCT
fuelectenerg-1426	172	54	x	x	SYM
fuelectenerg-1426	172	55	∈	∈	NOUN
fuelectenerg-1426	172	56	{	{	PUNCT
fuelectenerg-1426	172	57	x	x	NOUN
fuelectenerg-1426	172	58	,	,	PUNCT
fuelectenerg-1426	172	59	x′,x′′,x′′′	x′,x′′,x′′′	PROPN
fuelectenerg-1426	172	60	}	}	PUNCT
fuelectenerg-1426	172	61	,	,	PUNCT
fuelectenerg-1426	172	62	over	over	ADP
fuelectenerg-1426	172	63	gf(4	gf(4	NOUN
fuelectenerg-1426	172	64	)	)	PUNCT
fuelectenerg-1426	172	65	.	.	PUNCT
fuelectenerg-1426	173	1	(	(	PUNCT
fuelectenerg-1426	173	2	37	37	NUM
fuelectenerg-1426	173	3	)	)	SYM
fuelectenerg-1426	173	4	1	1	NUM
fuelectenerg-1426	173	5	1	1	NUM
fuelectenerg-1426	173	6	1	1	NUM
fuelectenerg-1426	173	7	1	1	NUM
fuelectenerg-1426	173	8	1	1	NUM
fuelectenerg-1426	173	9	x	x	SYM
fuelectenerg-1426	173	10	(	(	PUNCT
fuelectenerg-1426	173	11	’	'	PUNCT
fuelectenerg-1426	173	12	)	)	PUNCT
fuelectenerg-1426	173	13	x	x	PROPN
fuelectenerg-1426	173	14	(	(	PUNCT
fuelectenerg-1426	173	15	’’	’'	PUNCT
fuelectenerg-1426	173	16	)	)	PUNCT
fuelectenerg-1426	173	17	x	x	PROPN
fuelectenerg-1426	173	18	(	(	PUNCT
fuelectenerg-1426	173	19	’’	’'	PUNCT
fuelectenerg-1426	173	20	’	'	PUNCT
fuelectenerg-1426	173	21	)	)	PUNCT
fuelectenerg-1426	173	22	x	x	SYM
fuelectenerg-1426	174	1	x	x	PUNCT
fuelectenerg-1426	174	2	x	x	X
fuelectenerg-1426	174	3	(	(	PUNCT
fuelectenerg-1426	174	4	’	'	PUNCT
fuelectenerg-1426	174	5	)	)	PUNCT
fuelectenerg-1426	174	6	x	x	PROPN
fuelectenerg-1426	174	7	(	(	PUNCT
fuelectenerg-1426	174	8	’’	’'	PUNCT
fuelectenerg-1426	174	9	)	)	PUNCT
fuelectenerg-1426	174	10	x	x	PROPN
fuelectenerg-1426	174	11	(	(	PUNCT
fuelectenerg-1426	174	12	’’	’'	PUNCT
fuelectenerg-1426	174	13	’	'	PUNCT
fuelectenerg-1426	174	14	)	)	PUNCT
fuelectenerg-1426	174	15	x	x	SYM
fuelectenerg-1426	174	16	(	(	PUNCT
fuelectenerg-1426	174	17	)	)	PUNCT
fuelectenerg-1426	174	18	x	x	SYM
fuelectenerg-1426	174	19	2	2	NUM
fuelectenerg-1426	174	20	2	2	NUM
fuelectenerg-1426	174	21	2	2	NUM
fuelectenerg-1426	174	22	2	2	NUM
fuelectenerg-1426	174	23	2	2	NUM
fuelectenerg-1426	174	24	x	x	SYM
fuelectenerg-1426	174	25	(	(	PUNCT
fuelectenerg-1426	174	26	’	'	PUNCT
fuelectenerg-1426	174	27	)	)	PUNCT
fuelectenerg-1426	174	28	x	x	PROPN
fuelectenerg-1426	174	29	(	(	PUNCT
fuelectenerg-1426	174	30	’’	’'	PUNCT
fuelectenerg-1426	174	31	)	)	PUNCT
fuelectenerg-1426	174	32	x	x	PROPN
fuelectenerg-1426	174	33	(	(	PUNCT
fuelectenerg-1426	174	34	’’	’'	PUNCT
fuelectenerg-1426	174	35	’	'	PUNCT
fuelectenerg-1426	174	36	)	)	PUNCT
fuelectenerg-1426	174	37	x	x	SYM
fuelectenerg-1426	174	38	(	(	PUNCT
fuelectenerg-1426	174	39	)	)	PUNCT
fuelectenerg-1426	174	40	x	x	SYM
fuelectenerg-1426	174	41	3	3	NUM
fuelectenerg-1426	174	42	3	3	NUM
fuelectenerg-1426	174	43	3	3	NUM
fuelectenerg-1426	174	44	3	3	NUM
fuelectenerg-1426	174	45	3	3	NUM
fuelectenerg-1426	174	46	0	0	NUM
fuelectenerg-1426	174	47	x	x	SYM
fuelectenerg-1426	174	48	1	1	NUM
fuelectenerg-1426	174	49	x	x	SYM
fuelectenerg-1426	174	50	2	2	NUM
fuelectenerg-1426	174	51	x	x	SYM
fuelectenerg-1426	174	52	3	3	NUM
fuelectenerg-1426	174	53	x	x	SYM
fuelectenerg-1426	174	54	s	s	PART
fuelectenerg-1426	174	55	d0	d0	NOUN
fuelectenerg-1426	174	56	d1	d1	PROPN
fuelectenerg-1426	174	57	d2	d2	PROPN
fuelectenerg-1426	174	58	d3	d3	PROPN
fuelectenerg-1426	174	59	d	d	PROPN
fuelectenerg-1426	174	60	(	(	PUNCT
fuelectenerg-1426	174	61	)	)	PUNCT
fuelectenerg-1426	174	62	a	a	DET
fuelectenerg-1426	174	63	(	(	PUNCT
fuelectenerg-1426	174	64	d	d	NOUN
fuelectenerg-1426	174	65	)	)	PUNCT
fuelectenerg-1426	174	66	(	(	PUNCT
fuelectenerg-1426	174	67	)	)	PUNCT
fuelectenerg-1426	174	68	b	b	X
fuelectenerg-1426	174	69	(	(	PUNCT
fuelectenerg-1426	174	70	e	e	NOUN
fuelectenerg-1426	174	71	)	)	PUNCT
fuelectenerg-1426	174	72	(	(	PUNCT
fuelectenerg-1426	174	73	)	)	PUNCT
fuelectenerg-1426	174	74	c	c	NOUN
fuelectenerg-1426	174	75	(	(	PUNCT
fuelectenerg-1426	174	76	f	f	PROPN
fuelectenerg-1426	174	77	)	)	PUNCT
fuelectenerg-1426	174	78	fig	fig	NOUN
fuelectenerg-1426	174	79	.	.	PUNCT
fuelectenerg-1426	175	1	4	4	NUM
fuelectenerg-1426	175	2	:	:	PUNCT
fuelectenerg-1426	175	3	quaternary	quaternary	ADJ
fuelectenerg-1426	175	4	decision	decision	NOUN
fuelectenerg-1426	175	5	nodes	node	NOUN
fuelectenerg-1426	175	6	:	:	PUNCT
fuelectenerg-1426	175	7	(	(	PUNCT
fuelectenerg-1426	175	8	a	a	X
fuelectenerg-1426	175	9	)	)	PUNCT
fuelectenerg-1426	175	10	shannon	shannon	NOUN
fuelectenerg-1426	175	11	in	in	ADP
fuelectenerg-1426	175	12	eq	eq	PROPN
fuelectenerg-1426	175	13	.	.	PUNCT
fuelectenerg-1426	176	1	(	(	PUNCT
fuelectenerg-1426	176	2	32	32	NUM
fuelectenerg-1426	176	3	)	)	PUNCT
fuelectenerg-1426	176	4	,	,	PUNCT
fuelectenerg-1426	176	5	(	(	PUNCT
fuelectenerg-1426	176	6	b	b	X
fuelectenerg-1426	176	7	)	)	PUNCT
fuelectenerg-1426	176	8	davio0	davio0	NOUN
fuelectenerg-1426	176	9	in	in	ADP
fuelectenerg-1426	176	10	eq	eq	PROPN
fuelectenerg-1426	176	11	.	.	PUNCT
fuelectenerg-1426	177	1	(	(	PUNCT
fuelectenerg-1426	177	2	33	33	NUM
fuelectenerg-1426	177	3	)	)	PUNCT
fuelectenerg-1426	177	4	,	,	PUNCT
fuelectenerg-1426	177	5	(	(	PUNCT
fuelectenerg-1426	177	6	c	c	X
fuelectenerg-1426	177	7	)	)	PUNCT
fuelectenerg-1426	177	8	davio1	davio1	NOUN
fuelectenerg-1426	177	9	in	in	ADP
fuelectenerg-1426	177	10	eq	eq	PROPN
fuelectenerg-1426	177	11	.	.	PUNCT
fuelectenerg-1426	178	1	(	(	PUNCT
fuelectenerg-1426	178	2	34	34	NUM
fuelectenerg-1426	178	3	)	)	PUNCT
fuelectenerg-1426	178	4	,	,	PUNCT
fuelectenerg-1426	178	5	(	(	PUNCT
fuelectenerg-1426	178	6	d	d	X
fuelectenerg-1426	178	7	)	)	PUNCT
fuelectenerg-1426	178	8	davio2	davio2	NOUN
fuelectenerg-1426	178	9	in	in	ADP
fuelectenerg-1426	178	10	eq	eq	PROPN
fuelectenerg-1426	178	11	.	.	PUNCT
fuelectenerg-1426	179	1	(	(	PUNCT
fuelectenerg-1426	179	2	35	35	NUM
fuelectenerg-1426	179	3	)	)	PUNCT
fuelectenerg-1426	179	4	,	,	PUNCT
fuelectenerg-1426	179	5	(	(	PUNCT
fuelectenerg-1426	179	6	e	e	NOUN
fuelectenerg-1426	179	7	)	)	PUNCT
fuelectenerg-1426	179	8	davio3	davio3	NOUN
fuelectenerg-1426	179	9	in	in	ADP
fuelectenerg-1426	179	10	eq	eq	ADP
fuelectenerg-1426	179	11	.	.	PUNCT
fuelectenerg-1426	180	1	(	(	PUNCT
fuelectenerg-1426	180	2	36	36	NUM
fuelectenerg-1426	180	3	)	)	PUNCT
fuelectenerg-1426	180	4	,	,	PUNCT
fuelectenerg-1426	180	5	and	and	CCONJ
fuelectenerg-1426	180	6	(	(	PUNCT
fuelectenerg-1426	180	7	f	f	X
fuelectenerg-1426	180	8	)	)	PUNCT
fuelectenerg-1426	180	9	generalized	generalized	ADJ
fuelectenerg-1426	180	10	quaternary	quaternary	ADJ
fuelectenerg-1426	180	11	davio	davio	NOUN
fuelectenerg-1426	180	12	defined	define	VERB
fuelectenerg-1426	180	13	in	in	ADP
fuelectenerg-1426	180	14	eq	eq	ADP
fuelectenerg-1426	180	15	.	.	PUNCT
fuelectenerg-1426	181	1	(	(	PUNCT
fuelectenerg-1426	181	2	37	37	NUM
fuelectenerg-1426	181	3	)	)	PUNCT
fuelectenerg-1426	181	4	.	.	PUNCT
fuelectenerg-1426	182	1	utilizing	utilize	VERB
fuelectenerg-1426	182	2	the	the	DET
fuelectenerg-1426	182	3	two	two	NUM
fuelectenerg-1426	182	4	nodes	node	NOUN
fuelectenerg-1426	182	5	defined	define	VERB
fuelectenerg-1426	182	6	for	for	ADP
fuelectenerg-1426	182	7	quaternary	quaternary	ADJ
fuelectenerg-1426	182	8	shannon	shannon	NOUN
fuelectenerg-1426	182	9	in	in	ADP
fuelectenerg-1426	182	10	figure	figure	NOUN
fuelectenerg-1426	182	11	4(a	4(a	NUM
fuelectenerg-1426	182	12	)	)	PUNCT
fuelectenerg-1426	182	13	and	and	CCONJ
fuelectenerg-1426	182	14	quaternary	quaternary	ADJ
fuelectenerg-1426	182	15	generalized	generalized	ADJ
fuelectenerg-1426	182	16	davio	davio	NOUN
fuelectenerg-1426	182	17	in	in	ADP
fuelectenerg-1426	182	18	figure	figure	NOUN
fuelectenerg-1426	182	19	4(f	4(f	NUM
fuelectenerg-1426	182	20	)	)	PUNCT
fuelectenerg-1426	182	21	,	,	PUNCT
fuelectenerg-1426	182	22	and	and	CCONJ
fuelectenerg-1426	182	23	analogously	analogously	ADV
fuelectenerg-1426	182	24	to	to	ADP
fuelectenerg-1426	182	25	the	the	DET
fuelectenerg-1426	182	26	binary	binary	ADJ
fuelectenerg-1426	182	27	and	and	CCONJ
fuelectenerg-1426	182	28	ternary	ternary	ADJ
fuelectenerg-1426	182	29	cases	case	NOUN
fuelectenerg-1426	182	30	,	,	PUNCT
fuelectenerg-1426	182	31	one	one	PRON
fuelectenerg-1426	182	32	can	can	AUX
fuelectenerg-1426	182	33	obtain	obtain	VERB
fuelectenerg-1426	182	34	the	the	DET
fuelectenerg-1426	182	35	quaternary	quaternary	ADJ
fuelectenerg-1426	182	36	shannon	shannon	NOUN
fuelectenerg-1426	182	37	-	-	PUNCT
fuelectenerg-1426	182	38	davio	davio	NOUN
fuelectenerg-1426	182	39	(	(	PUNCT
fuelectenerg-1426	182	40	s	s	NOUN
fuelectenerg-1426	182	41	/	/	SYM
fuelectenerg-1426	182	42	d	d	NOUN
fuelectenerg-1426	182	43	)	)	PUNCT
fuelectenerg-1426	182	44	trees	tree	NOUN
fuelectenerg-1426	182	45	for	for	ADP
fuelectenerg-1426	182	46	two	two	NUM
fuelectenerg-1426	182	47	variables	variable	NOUN
fuelectenerg-1426	182	48	(	(	PUNCT
fuelectenerg-1426	182	49	cf	cf	NOUN
fuelectenerg-1426	182	50	.	.	PUNCT
fuelectenerg-1426	182	51	figure	figure	NOUN
fuelectenerg-1426	182	52	5	5	NUM
fuelectenerg-1426	182	53	)	)	PUNCT
fuelectenerg-1426	182	54	,	,	PUNCT
fuelectenerg-1426	182	55	where	where	SCONJ
fuelectenerg-1426	182	56	general	general	ADJ
fuelectenerg-1426	182	57	family	family	NOUN
fuelectenerg-1426	182	58	called	call	VERB
fuelectenerg-1426	182	59	inclusive	inclusive	ADJ
fuelectenerg-1426	182	60	forms	form	NOUN
fuelectenerg-1426	182	61	(	(	PUNCT
fuelectenerg-1426	182	62	ifs	ifs	PROPN
fuelectenerg-1426	182	63	)	)	PUNCT
fuelectenerg-1426	182	64	is	be	AUX
fuelectenerg-1426	182	65	obtained	obtain	VERB
fuelectenerg-1426	182	66	as	as	ADP
fuelectenerg-1426	182	67	flattened	flatten	VERB
fuelectenerg-1426	182	68	expressions	expression	NOUN
fuelectenerg-1426	182	69	generated	generate	VERB
fuelectenerg-1426	182	70	by	by	ADP
fuelectenerg-1426	182	71	these	these	DET
fuelectenerg-1426	182	72	s	s	PROPN
fuelectenerg-1426	182	73	/	/	SYM
fuelectenerg-1426	182	74	d	d	NOUN
fuelectenerg-1426	182	75	trees	tree	NOUN
fuelectenerg-1426	182	76	.	.	PUNCT
fuelectenerg-1426	183	1	for	for	ADP
fuelectenerg-1426	183	2	example	example	NOUN
fuelectenerg-1426	183	3	,	,	PUNCT
fuelectenerg-1426	183	4	the	the	DET
fuelectenerg-1426	183	5	corresponding	correspond	VERB
fuelectenerg-1426	183	6	s	s	PROPN
fuelectenerg-1426	183	7	/	/	SYM
fuelectenerg-1426	183	8	d	d	NOUN
fuelectenerg-1426	183	9	trees	tree	NOUN
fuelectenerg-1426	183	10	for	for	ADP
fuelectenerg-1426	183	11	ifs	ifs	PROPN
fuelectenerg-1426	183	12	of	of	ADP
fuelectenerg-1426	183	13	two	two	NUM
fuelectenerg-1426	183	14	variables	variable	NOUN
fuelectenerg-1426	183	15	can	can	AUX
fuelectenerg-1426	183	16	be	be	AUX
fuelectenerg-1426	183	17	generated	generate	VERB
fuelectenerg-1426	183	18	for	for	ADP
fuelectenerg-1426	183	19	variable	variable	ADJ
fuelectenerg-1426	183	20	order	order	NOUN
fuelectenerg-1426	183	21	{	{	PUNCT
fuelectenerg-1426	183	22	a	a	DET
fuelectenerg-1426	183	23	,	,	PUNCT
fuelectenerg-1426	183	24	b	b	NOUN
fuelectenerg-1426	183	25	}	}	PUNCT
fuelectenerg-1426	183	26	and	and	CCONJ
fuelectenerg-1426	183	27	for	for	ADP
fuelectenerg-1426	183	28	variable	variable	ADJ
fuelectenerg-1426	183	29	order	order	NOUN
fuelectenerg-1426	183	30	{	{	PUNCT
fuelectenerg-1426	183	31	b	b	NOUN
fuelectenerg-1426	183	32	,	,	PUNCT
fuelectenerg-1426	183	33	a	a	PRON
fuelectenerg-1426	183	34	}	}	PUNCT
fuelectenerg-1426	183	35	as	as	ADV
fuelectenerg-1426	183	36	well	well	ADV
fuelectenerg-1426	183	37	.	.	PUNCT
fuelectenerg-1426	184	1	the	the	DET
fuelectenerg-1426	184	2	number	number	NOUN
fuelectenerg-1426	184	3	of	of	ADP
fuelectenerg-1426	184	4	these	these	DET
fuelectenerg-1426	184	5	s	s	NOUN
fuelectenerg-1426	184	6	/	/	SYM
fuelectenerg-1426	184	7	d	d	NOUN
fuelectenerg-1426	184	8	trees	tree	NOUN
fuelectenerg-1426	184	9	per	per	ADP
fuelectenerg-1426	184	10	variable	variable	ADJ
fuelectenerg-1426	184	11	order	order	NOUN
fuelectenerg-1426	184	12	is	be	AUX
fuelectenerg-1426	184	13	2(4	2(4	NUM
fuelectenerg-1426	184	14	+	+	NOUN
fuelectenerg-1426	184	15	1	1	NUM
fuelectenerg-1426	184	16	)	)	PUNCT
fuelectenerg-1426	184	17	=	=	SYM
fuelectenerg-1426	184	18	32	32	NUM
fuelectenerg-1426	184	19	,	,	PUNCT
fuelectenerg-1426	184	20	where	where	SCONJ
fuelectenerg-1426	184	21	the	the	DET
fuelectenerg-1426	184	22	number	number	NOUN
fuelectenerg-1426	184	23	of	of	ADP
fuelectenerg-1426	184	24	qifs	qif	NOUN
fuelectenerg-1426	184	25	per	per	ADP
fuelectenerg-1426	184	26	s	s	PROPN
fuelectenerg-1426	184	27	/	/	SYM
fuelectenerg-1426	184	28	d	d	NOUN
fuelectenerg-1426	184	29	tree	tree	NOUN
fuelectenerg-1426	184	30	will	will	AUX
fuelectenerg-1426	184	31	be	be	AUX
fuelectenerg-1426	184	32	later	later	ADV
fuelectenerg-1426	184	33	derived	derive	VERB
fuelectenerg-1426	184	34	in	in	ADP
fuelectenerg-1426	184	35	section	section	NOUN
fuelectenerg-1426	184	36	4	4	NUM
fuelectenerg-1426	184	37	in	in	ADP
fuelectenerg-1426	184	38	two	two	NUM
fuelectenerg-1426	184	39	different	different	ADJ
fuelectenerg-1426	184	40	ways	way	NOUN
fuelectenerg-1426	184	41	;	;	PUNCT
fuelectenerg-1426	184	42	the	the	DET
fuelectenerg-1426	184	43	first	first	ADJ
fuelectenerg-1426	184	44	method	method	NOUN
fuelectenerg-1426	184	45	108	108	NUM
fuelectenerg-1426	184	46	708	708	NUM
fuelectenerg-1426	184	47	a.	a.	NOUN
fuelectenerg-1426	184	48	n.	n.	PROPN
fuelectenerg-1426	184	49	al	al	PROPN
fuelectenerg-1426	184	50	-	-	PUNCT
fuelectenerg-1426	184	51	rabadi	rabadi	PROPN
fuelectenerg-1426	184	52	multi	multi	ADJ
fuelectenerg-1426	184	53	-	-	ADJ
fuelectenerg-1426	184	54	valued	value	VERB
fuelectenerg-1426	184	55	galois	galois	PROPN
fuelectenerg-1426	184	56	shannon	shannon	PROPN
fuelectenerg-1426	184	57	davio	davio	PROPN
fuelectenerg-1426	184	58	trees	tree	NOUN
fuelectenerg-1426	184	59	and	and	CCONJ
fuelectenerg-1426	184	60	their	their	PRON
fuelectenerg-1426	184	61	complexity	complexity	NOUN
fuelectenerg-1426	184	62	709	709	NUM
fuelectenerg-1426	184	63	multi	multi	ADJ
fuelectenerg-1426	184	64	-	-	ADJ
fuelectenerg-1426	184	65	valued	value	VERB
fuelectenerg-1426	184	66	galois	galois	PROPN
fuelectenerg-1426	184	67	shannon	shannon	PROPN
fuelectenerg-1426	184	68	davio	davio	PROPN
fuelectenerg-1426	184	69	trees	tree	NOUN
fuelectenerg-1426	184	70	and	and	CCONJ
fuelectenerg-1426	184	71	their	their	PRON
fuelectenerg-1426	184	72	complexity	complexity	NOUN
fuelectenerg-1426	184	73	is	be	AUX
fuelectenerg-1426	184	74	by	by	ADP
fuelectenerg-1426	184	75	using	use	VERB
fuelectenerg-1426	184	76	the	the	DET
fuelectenerg-1426	184	77	general	general	ADJ
fuelectenerg-1426	184	78	formula	formula	NOUN
fuelectenerg-1426	184	79	for	for	ADP
fuelectenerg-1426	184	80	an	an	DET
fuelectenerg-1426	184	81	arbitrary	arbitrary	ADJ
fuelectenerg-1426	184	82	number	number	NOUN
fuelectenerg-1426	184	83	of	of	ADP
fuelectenerg-1426	184	84	variables	variable	NOUN
fuelectenerg-1426	184	85	over	over	ADP
fuelectenerg-1426	184	86	gf(4	gf(4	NOUN
fuelectenerg-1426	184	87	)	)	PUNCT
fuelectenerg-1426	184	88	and	and	CCONJ
fuelectenerg-1426	184	89	the	the	DET
fuelectenerg-1426	184	90	second	second	ADJ
fuelectenerg-1426	184	91	method	method	NOUN
fuelectenerg-1426	184	92	is	be	AUX
fuelectenerg-1426	184	93	performed	perform	VERB
fuelectenerg-1426	184	94	by	by	ADP
fuelectenerg-1426	184	95	using	use	VERB
fuelectenerg-1426	184	96	the	the	DET
fuelectenerg-1426	184	97	general	general	ADJ
fuelectenerg-1426	184	98	formula	formula	NOUN
fuelectenerg-1426	184	99	for	for	ADP
fuelectenerg-1426	184	100	any	any	DET
fuelectenerg-1426	184	101	radix	radix	NOUN
fuelectenerg-1426	184	102	.	.	PUNCT
fuelectenerg-1426	185	1	the	the	DET
fuelectenerg-1426	185	2	number	number	NOUN
fuelectenerg-1426	185	3	of	of	ADP
fuelectenerg-1426	185	4	all	all	DET
fuelectenerg-1426	185	5	possible	possible	ADJ
fuelectenerg-1426	185	6	forms	form	NOUN
fuelectenerg-1426	185	7	is	be	AUX
fuelectenerg-1426	185	8	important	important	ADJ
fuelectenerg-1426	185	9	because	because	SCONJ
fuelectenerg-1426	185	10	it	it	PRON
fuelectenerg-1426	185	11	can	can	AUX
fuelectenerg-1426	185	12	be	be	AUX
fuelectenerg-1426	185	13	used	use	VERB
fuelectenerg-1426	185	14	as	as	ADP
fuelectenerg-1426	185	15	an	an	DET
fuelectenerg-1426	185	16	upper	upper	ADV
fuelectenerg-1426	185	17	-	-	PUNCT
fuelectenerg-1426	185	18	bound	bind	VERB
fuelectenerg-1426	185	19	parameter	parameter	NOUN
fuelectenerg-1426	185	20	in	in	ADP
fuelectenerg-1426	185	21	a	a	DET
fuelectenerg-1426	185	22	search	search	NOUN
fuelectenerg-1426	185	23	heuristic	heuristic	NOUN
fuelectenerg-1426	185	24	that	that	SCONJ
fuelectenerg-1426	185	25	searches	search	VERB
fuelectenerg-1426	185	26	for	for	ADP
fuelectenerg-1426	185	27	a	a	DET
fuelectenerg-1426	185	28	minimum	minimum	ADJ
fuelectenerg-1426	185	29	gfsop	gfsop	NOUN
fuelectenerg-1426	185	30	expression	expression	NOUN
fuelectenerg-1426	185	31	using	use	VERB
fuelectenerg-1426	185	32	the	the	DET
fuelectenerg-1426	185	33	corresponding	correspond	VERB
fuelectenerg-1426	185	34	s	s	PROPN
fuelectenerg-1426	185	35	/	/	SYM
fuelectenerg-1426	185	36	d	d	NOUN
fuelectenerg-1426	185	37	trees	tree	NOUN
fuelectenerg-1426	185	38	.	.	PUNCT
fuelectenerg-1426	186	1	example	example	NOUN
fuelectenerg-1426	186	2	3	3	NUM
fuelectenerg-1426	186	3	illustrates	illustrate	VERB
fuelectenerg-1426	186	4	some	some	PRON
fuelectenerg-1426	186	5	of	of	ADP
fuelectenerg-1426	186	6	the	the	DET
fuelectenerg-1426	186	7	quaternary	quaternary	ADJ
fuelectenerg-1426	186	8	s	s	PROPN
fuelectenerg-1426	186	9	/	/	SYM
fuelectenerg-1426	186	10	d	d	NOUN
fuelectenerg-1426	186	11	trees	tree	NOUN
fuelectenerg-1426	186	12	and	and	CCONJ
fuelectenerg-1426	186	13	some	some	PRON
fuelectenerg-1426	186	14	of	of	ADP
fuelectenerg-1426	186	15	the	the	DET
fuelectenerg-1426	186	16	quaternary	quaternary	ADJ
fuelectenerg-1426	186	17	trees	tree	NOUN
fuelectenerg-1426	186	18	they	they	PRON
fuelectenerg-1426	186	19	produce	produce	VERB
fuelectenerg-1426	186	20	.	.	PUNCT
fuelectenerg-1426	187	1	the	the	DET
fuelectenerg-1426	187	2	numbers	number	NOUN
fuelectenerg-1426	187	3	on	on	ADP
fuelectenerg-1426	187	4	top	top	NOUN
fuelectenerg-1426	187	5	of	of	ADP
fuelectenerg-1426	187	6	s	s	PROPN
fuelectenerg-1426	187	7	/	/	SYM
fuelectenerg-1426	187	8	d	d	NOUN
fuelectenerg-1426	187	9	trees	tree	NOUN
fuelectenerg-1426	187	10	in	in	ADP
fuelectenerg-1426	187	11	figures	figure	NOUN
fuelectenerg-1426	187	12	5(a	5(a	NUM
fuelectenerg-1426	187	13	)	)	PUNCT
fuelectenerg-1426	187	14	and	and	CCONJ
fuelectenerg-1426	187	15	6(a	6(a	NUM
fuelectenerg-1426	187	16	)	)	PUNCT
fuelectenerg-1426	187	17	are	be	AUX
fuelectenerg-1426	187	18	the	the	DET
fuelectenerg-1426	187	19	numbers	number	NOUN
fuelectenerg-1426	187	20	of	of	ADP
fuelectenerg-1426	187	21	total	total	ADJ
fuelectenerg-1426	187	22	qifs	qif	NOUN
fuelectenerg-1426	187	23	(	(	PUNCT
fuelectenerg-1426	187	24	i.e.	i.e.	X
fuelectenerg-1426	187	25	,	,	PUNCT
fuelectenerg-1426	187	26	total	total	ADJ
fuelectenerg-1426	187	27	number	number	NOUN
fuelectenerg-1426	187	28	of	of	ADP
fuelectenerg-1426	187	29	quaternary	quaternary	ADJ
fuelectenerg-1426	187	30	trees	tree	NOUN
fuelectenerg-1426	187	31	)	)	PUNCT
fuelectenerg-1426	187	32	that	that	PRON
fuelectenerg-1426	187	33	are	be	AUX
fuelectenerg-1426	187	34	generated	generate	VERB
fuelectenerg-1426	187	35	.	.	PUNCT
fuelectenerg-1426	188	1	example	example	NOUN
fuelectenerg-1426	189	1	3	3	NUM
fuelectenerg-1426	189	2	.	.	PUNCT
fuelectenerg-1426	189	3	utilizing	utilize	VERB
fuelectenerg-1426	189	4	the	the	DET
fuelectenerg-1426	189	5	notation	notation	NOUN
fuelectenerg-1426	189	6	in	in	ADP
fuelectenerg-1426	189	7	equation	equation	NOUN
fuelectenerg-1426	189	8	(	(	PUNCT
fuelectenerg-1426	189	9	37	37	NUM
fuelectenerg-1426	189	10	)	)	PUNCT
fuelectenerg-1426	189	11	,	,	PUNCT
fuelectenerg-1426	189	12	we	we	PRON
fuelectenerg-1426	189	13	obtain	obtain	VERB
fuelectenerg-1426	189	14	,	,	PUNCT
fuelectenerg-1426	189	15	for	for	ADP
fuelectenerg-1426	189	16	the	the	DET
fuelectenerg-1426	189	17	s	s	PROPN
fuelectenerg-1426	189	18	/	/	SYM
fuelectenerg-1426	189	19	d	d	NOUN
fuelectenerg-1426	189	20	trees	tree	NOUN
fuelectenerg-1426	189	21	in	in	ADP
fuelectenerg-1426	189	22	figures	figure	NOUN
fuelectenerg-1426	189	23	5(a	5(a	NUM
fuelectenerg-1426	189	24	)	)	PUNCT
fuelectenerg-1426	189	25	and	and	CCONJ
fuelectenerg-1426	189	26	6(a	6(a	NUM
fuelectenerg-1426	189	27	)	)	PUNCT
fuelectenerg-1426	189	28	,	,	PUNCT
fuelectenerg-1426	189	29	the	the	DET
fuelectenerg-1426	189	30	corresponding	correspond	VERB
fuelectenerg-1426	189	31	s	s	PROPN
fuelectenerg-1426	189	32	/	/	SYM
fuelectenerg-1426	189	33	d	d	NOUN
fuelectenerg-1426	189	34	trees	tree	NOUN
fuelectenerg-1426	189	35	in	in	ADP
fuelectenerg-1426	189	36	figures	figure	NOUN
fuelectenerg-1426	189	37	5(b	5(b	NUM
fuelectenerg-1426	189	38	)	)	PUNCT
fuelectenerg-1426	189	39	5(c	5(c	NUM
fuelectenerg-1426	189	40	)	)	PUNCT
fuelectenerg-1426	189	41	and	and	CCONJ
fuelectenerg-1426	189	42	figures	figure	NOUN
fuelectenerg-1426	189	43	6(b	6(b	NUM
fuelectenerg-1426	189	44	)	)	PUNCT
fuelectenerg-1426	189	45	6(c	6(c	NUM
fuelectenerg-1426	189	46	)	)	PUNCT
fuelectenerg-1426	189	47	,	,	PUNCT
fuelectenerg-1426	189	48	respectively	respectively	ADV
fuelectenerg-1426	189	49	.	.	PUNCT
fuelectenerg-1426	190	1	from	from	ADP
fuelectenerg-1426	190	2	the	the	DET
fuelectenerg-1426	190	3	quaternary	quaternary	ADJ
fuelectenerg-1426	190	4	s	s	PROPN
fuelectenerg-1426	190	5	/	/	SYM
fuelectenerg-1426	190	6	d	d	NOUN
fuelectenerg-1426	190	7	trees	tree	NOUN
fuelectenerg-1426	190	8	shown	show	VERB
fuelectenerg-1426	190	9	in	in	ADP
fuelectenerg-1426	190	10	figures	figure	NOUN
fuelectenerg-1426	190	11	5	5	NUM
fuelectenerg-1426	190	12	and	and	CCONJ
fuelectenerg-1426	190	13	6	6	NUM
fuelectenerg-1426	190	14	,	,	PUNCT
fuelectenerg-1426	190	15	by	by	ADP
fuelectenerg-1426	190	16	taking	take	VERB
fuelectenerg-1426	190	17	any	any	DET
fuelectenerg-1426	190	18	s	s	PROPN
fuelectenerg-1426	190	19	/	/	SYM
fuelectenerg-1426	190	20	d	d	NOUN
fuelectenerg-1426	190	21	tree	tree	NOUN
fuelectenerg-1426	190	22	,	,	PUNCT
fuelectenerg-1426	190	23	multiplying	multiply	VERB
fuelectenerg-1426	190	24	the	the	DET
fuelectenerg-1426	190	25	two	two	NUM
fuelectenerg-1426	190	26	-	-	PUNCT
fuelectenerg-1426	190	27	level	level	NOUN
fuelectenerg-1426	190	28	cofactors	cofactor	NOUN
fuelectenerg-1426	190	29	(	(	PUNCT
fuelectenerg-1426	190	30	which	which	PRON
fuelectenerg-1426	190	31	are	be	AUX
fuelectenerg-1426	190	32	in	in	ADP
fuelectenerg-1426	190	33	the	the	DET
fuelectenerg-1426	190	34	qudt	qudt	NOUN
fuelectenerg-1426	190	35	leafs	leafs	ADJ
fuelectenerg-1426	190	36	)	)	PUNCT
fuelectenerg-1426	190	37	each	each	PRON
fuelectenerg-1426	190	38	by	by	ADP
fuelectenerg-1426	190	39	the	the	DET
fuelectenerg-1426	190	40	corresponding	corresponding	ADJ
fuelectenerg-1426	190	41	path	path	NOUN
fuelectenerg-1426	190	42	in	in	ADP
fuelectenerg-1426	190	43	that	that	DET
fuelectenerg-1426	190	44	qudt	qudt	ADV
fuelectenerg-1426	190	45	,	,	PUNCT
fuelectenerg-1426	190	46	and	and	CCONJ
fuelectenerg-1426	190	47	next	next	ADV
fuelectenerg-1426	190	48	summing	sum	VERB
fuelectenerg-1426	190	49	all	all	DET
fuelectenerg-1426	190	50	the	the	DET
fuelectenerg-1426	190	51	resulting	result	VERB
fuelectenerg-1426	190	52	cubes	cube	NOUN
fuelectenerg-1426	190	53	(	(	PUNCT
fuelectenerg-1426	190	54	terms	term	NOUN
fuelectenerg-1426	190	55	or	or	CCONJ
fuelectenerg-1426	190	56	products	product	NOUN
fuelectenerg-1426	190	57	)	)	PUNCT
fuelectenerg-1426	190	58	over	over	ADP
fuelectenerg-1426	190	59	gf(4	gf(4	NOUN
fuelectenerg-1426	190	60	)	)	PUNCT
fuelectenerg-1426	190	61	,	,	PUNCT
fuelectenerg-1426	190	62	one	one	PRON
fuelectenerg-1426	190	63	obtains	obtain	VERB
fuelectenerg-1426	190	64	the	the	DET
fuelectenerg-1426	190	65	flattened	flatten	VERB
fuelectenerg-1426	190	66	if	if	SCONJ
fuelectenerg-1426	190	67	form	form	NOUN
fuelectenerg-1426	190	68	for	for	ADP
fuelectenerg-1426	190	69	the	the	DET
fuelectenerg-1426	190	70	function	function	NOUN
fuelectenerg-1426	190	71	f	f	PROPN
fuelectenerg-1426	190	72	as	as	ADP
fuelectenerg-1426	190	73	a	a	DET
fuelectenerg-1426	190	74	certain	certain	ADJ
fuelectenerg-1426	190	75	gfsop	gfsop	NOUN
fuelectenerg-1426	190	76	expression	expression	NOUN
fuelectenerg-1426	190	77	(	(	PUNCT
fuelectenerg-1426	190	78	expansion	expansion	NOUN
fuelectenerg-1426	190	79	)	)	PUNCT
fuelectenerg-1426	190	80	.	.	PUNCT
fuelectenerg-1426	191	1	for	for	ADP
fuelectenerg-1426	191	2	each	each	DET
fuelectenerg-1426	191	3	qudt	qudt	NOUN
fuelectenerg-1426	191	4	in	in	ADP
fuelectenerg-1426	191	5	figures	figure	NOUN
fuelectenerg-1426	191	6	5(a	5(a	NUM
fuelectenerg-1426	191	7	)	)	PUNCT
fuelectenerg-1426	191	8	and	and	CCONJ
fuelectenerg-1426	191	9	6(a	6(a	NUM
fuelectenerg-1426	191	10	)	)	PUNCT
fuelectenerg-1426	191	11	,	,	PUNCT
fuelectenerg-1426	191	12	there	there	PRON
fuelectenerg-1426	191	13	are	be	VERB
fuelectenerg-1426	191	14	as	as	ADV
fuelectenerg-1426	191	15	many	many	ADJ
fuelectenerg-1426	191	16	if	if	SCONJ
fuelectenerg-1426	191	17	forms	form	NOUN
fuelectenerg-1426	191	18	obtained	obtain	VERB
fuelectenerg-1426	191	19	for	for	ADP
fuelectenerg-1426	191	20	the	the	DET
fuelectenerg-1426	191	21	function	function	NOUN
fuelectenerg-1426	191	22	f	f	PROPN
fuelectenerg-1426	191	23	as	as	ADP
fuelectenerg-1426	191	24	the	the	DET
fuelectenerg-1426	191	25	number	number	NOUN
fuelectenerg-1426	191	26	of	of	ADP
fuelectenerg-1426	191	27	all	all	DET
fuelectenerg-1426	191	28	possible	possible	ADJ
fuelectenerg-1426	191	29	permutations	permutation	NOUN
fuelectenerg-1426	191	30	of	of	ADP
fuelectenerg-1426	191	31	the	the	DET
fuelectenerg-1426	191	32	polarities	polarity	NOUN
fuelectenerg-1426	191	33	of	of	ADP
fuelectenerg-1426	191	34	the	the	DET
fuelectenerg-1426	191	35	variables	variable	NOUN
fuelectenerg-1426	191	36	in	in	ADP
fuelectenerg-1426	191	37	the	the	DET
fuelectenerg-1426	191	38	second	second	ADJ
fuelectenerg-1426	191	39	level	level	NOUN
fuelectenerg-1426	191	40	branches	branch	NOUN
fuelectenerg-1426	191	41	of	of	ADP
fuelectenerg-1426	191	42	each	each	DET
fuelectenerg-1426	191	43	qudt	qudt	NOUN
fuelectenerg-1426	191	44	.	.	PUNCT
fuelectenerg-1426	192	1	4	4	NUM
fuelectenerg-1426	192	2	count	count	NOUN
fuelectenerg-1426	192	3	of	of	ADP
fuelectenerg-1426	192	4	the	the	DET
fuelectenerg-1426	192	5	number	number	NOUN
fuelectenerg-1426	192	6	of	of	ADP
fuelectenerg-1426	192	7	s	s	PROPN
fuelectenerg-1426	192	8	/	/	SYM
fuelectenerg-1426	192	9	d	d	NOUN
fuelectenerg-1426	192	10	inclusive	inclusive	ADJ
fuelectenerg-1426	192	11	forms	form	NOUN
fuelectenerg-1426	192	12	over	over	ADP
fuelectenerg-1426	192	13	gf(pk	gf(pk	NOUN
fuelectenerg-1426	192	14	)	)	PUNCT
fuelectenerg-1426	192	15	and	and	CCONJ
fuelectenerg-1426	192	16	the	the	DET
fuelectenerg-1426	192	17	new	new	ADJ
fuelectenerg-1426	192	18	ifn,2	ifn,2	ADJ
fuelectenerg-1426	192	19	triangles	triangle	NOUN
fuelectenerg-1426	192	20	this	this	DET
fuelectenerg-1426	192	21	section	section	NOUN
fuelectenerg-1426	192	22	provides	provide	VERB
fuelectenerg-1426	192	23	the	the	DET
fuelectenerg-1426	192	24	count	count	NOUN
fuelectenerg-1426	192	25	for	for	ADP
fuelectenerg-1426	192	26	the	the	DET
fuelectenerg-1426	192	27	numbers	number	NOUN
fuelectenerg-1426	192	28	of	of	ADP
fuelectenerg-1426	192	29	inclusive	inclusive	ADJ
fuelectenerg-1426	192	30	forms	form	NOUN
fuelectenerg-1426	192	31	,	,	PUNCT
fuelectenerg-1426	192	32	which	which	PRON
fuelectenerg-1426	192	33	are	be	AUX
fuelectenerg-1426	192	34	flattened	flatten	VERB
fuelectenerg-1426	192	35	expressions	expression	NOUN
fuelectenerg-1426	192	36	generated	generate	VERB
fuelectenerg-1426	192	37	by	by	ADP
fuelectenerg-1426	192	38	the	the	DET
fuelectenerg-1426	192	39	corresponding	correspond	VERB
fuelectenerg-1426	192	40	s	s	PROPN
fuelectenerg-1426	192	41	/	/	SYM
fuelectenerg-1426	192	42	d	d	NOUN
fuelectenerg-1426	192	43	trees	tree	NOUN
fuelectenerg-1426	192	44	,	,	PUNCT
fuelectenerg-1426	192	45	where	where	SCONJ
fuelectenerg-1426	192	46	these	these	DET
fuelectenerg-1426	192	47	counts	count	NOUN
fuelectenerg-1426	192	48	can	can	AUX
fuelectenerg-1426	192	49	be	be	AUX
fuelectenerg-1426	192	50	used	use	VERB
fuelectenerg-1426	192	51	as	as	ADP
fuelectenerg-1426	192	52	numerical	numerical	ADJ
fuelectenerg-1426	192	53	parameters	parameter	NOUN
fuelectenerg-1426	192	54	for	for	ADP
fuelectenerg-1426	192	55	upper	upper	ADJ
fuelectenerg-1426	192	56	-	-	PUNCT
fuelectenerg-1426	192	57	bounds	bound	NOUN
fuelectenerg-1426	192	58	in	in	ADP
fuelectenerg-1426	192	59	search	search	NOUN
fuelectenerg-1426	192	60	heuristics	heuristic	NOUN
fuelectenerg-1426	192	61	that	that	PRON
fuelectenerg-1426	192	62	search	search	VERB
fuelectenerg-1426	192	63	for	for	ADP
fuelectenerg-1426	192	64	minimum	minimum	ADJ
fuelectenerg-1426	192	65	gfsop	gfsop	NOUN
fuelectenerg-1426	192	66	expressions	expression	NOUN
fuelectenerg-1426	192	67	.	.	PUNCT
fuelectenerg-1426	193	1	theorem	theorem	NOUN
fuelectenerg-1426	193	2	1	1	NUM
fuelectenerg-1426	193	3	.	.	X
fuelectenerg-1426	193	4	for	for	ADP
fuelectenerg-1426	193	5	gf(3	gf(3	PROPN
fuelectenerg-1426	193	6	)	)	PUNCT
fuelectenerg-1426	193	7	and	and	CCONJ
fuelectenerg-1426	193	8	n	n	NUM
fuelectenerg-1426	193	9	variables	variable	NOUN
fuelectenerg-1426	193	10	,	,	PUNCT
fuelectenerg-1426	193	11	the	the	DET
fuelectenerg-1426	193	12	total	total	ADJ
fuelectenerg-1426	193	13	number	number	NOUN
fuelectenerg-1426	193	14	of	of	ADP
fuelectenerg-1426	193	15	ternary	ternary	ADJ
fuelectenerg-1426	193	16	ifs	ifs	PROPN
fuelectenerg-1426	193	17	(	(	PUNCT
fuelectenerg-1426	193	18	tifs	tifs	PROPN
fuelectenerg-1426	193	19	)	)	PUNCT
fuelectenerg-1426	193	20	per	per	ADP
fuelectenerg-1426	193	21	variable	variable	ADJ
fuelectenerg-1426	193	22	order	order	NOUN
fuelectenerg-1426	193	23	is	be	AUX
fuelectenerg-1426	193	24	:	:	PUNCT
fuelectenerg-1426	193	25	#	#	X
fuelectenerg-1426	193	26	tifs	tif	NOUN
fuelectenerg-1426	193	27	=	=	PUNCT
fuelectenerg-1426	193	28	(	(	PUNCT
fuelectenerg-1426	193	29	3)n−1	3)n−1	PROPN
fuelectenerg-1426	193	30	∑	∑	PROPN
fuelectenerg-1426	193	31	k1=0	k1=0	PROPN
fuelectenerg-1426	193	32	(	(	PUNCT
fuelectenerg-1426	193	33	3)n−2	3)n−2	NUM
fuelectenerg-1426	193	34	∑	∑	PUNCT
fuelectenerg-1426	193	35	k2=0	k2=0	PROPN
fuelectenerg-1426	193	36	(	(	PUNCT
fuelectenerg-1426	193	37	3)n−3	3)n−3	NUM
fuelectenerg-1426	193	38	∑	∑	SYM
fuelectenerg-1426	193	39	k3=0	k3=0	PROPN
fuelectenerg-1426	193	40	·	·	PUNCT
fuelectenerg-1426	193	41	·	·	PUNCT
fuelectenerg-1426	193	42	·	·	PUNCT
fuelectenerg-1426	194	1	(	(	PUNCT
fuelectenerg-1426	194	2	3)0	3)0	NUM
fuelectenerg-1426	194	3	∑	∑	PUNCT
fuelectenerg-1426	194	4	kn=0	kn=0	X
fuelectenerg-1426	194	5	{	{	PUNCT
fuelectenerg-1426	194	6	[	[	PUNCT
fuelectenerg-1426	194	7	3(n−1	3(n−1	NOUN
fuelectenerg-1426	194	8	)	)	PUNCT
fuelectenerg-1426	194	9	!	!	PUNCT
fuelectenerg-1426	195	1	(	(	PUNCT
fuelectenerg-1426	195	2	3(n−1)−	3(n−1)−	NOUN
fuelectenerg-1426	195	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	195	4	!	!	PUNCT
fuelectenerg-1426	196	1	3(n−2	3(n−2	NUM
fuelectenerg-1426	196	2	)	)	PUNCT
fuelectenerg-1426	196	3	!	!	PUNCT
fuelectenerg-1426	197	1	(	(	PUNCT
fuelectenerg-1426	197	2	3(n−2)−	3(n−2)−	ADJ
fuelectenerg-1426	197	3	k2)!k2	k2)!k2	PROPN
fuelectenerg-1426	197	4	!	!	PUNCT
fuelectenerg-1426	197	5	3(n−3	3(n−3	NUM
fuelectenerg-1426	197	6	)	)	PUNCT
fuelectenerg-1426	197	7	!	!	PUNCT
fuelectenerg-1426	198	1	(	(	PUNCT
fuelectenerg-1426	198	2	3(n−3)−	3(n−3)−	PROPN
fuelectenerg-1426	198	3	k3)!k3	k3)!k3	PROPN
fuelectenerg-1426	198	4	!	!	PUNCT
fuelectenerg-1426	198	5	·	·	PUNCT
fuelectenerg-1426	198	6	·	·	PUNCT
fuelectenerg-1426	198	7	·	·	PUNCT
fuelectenerg-1426	199	1	3(0	3(0	NUM
fuelectenerg-1426	199	2	)	)	PUNCT
fuelectenerg-1426	199	3	!	!	PUNCT
fuelectenerg-1426	200	1	(	(	PUNCT
fuelectenerg-1426	200	2	3(0)−	3(0)−	NUM
fuelectenerg-1426	200	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	200	4	!	!	PUNCT
fuelectenerg-1426	200	5	]	]	PUNCT
fuelectenerg-1426	201	1	[	[	PUNCT
fuelectenerg-1426	201	2	(	(	PUNCT
fuelectenerg-1426	201	3	32(3)0	32(3)0	NUM
fuelectenerg-1426	201	4	)	)	PUNCT
fuelectenerg-1426	201	5	k1(32(3)1	k1(32(3)1	NOUN
fuelectenerg-1426	201	6	)	)	PUNCT
fuelectenerg-1426	201	7	k2(32(3)2	k2(32(3)2	PROPN
fuelectenerg-1426	201	8	)	)	PUNCT
fuelectenerg-1426	201	9	k3	k3	PROPN
fuelectenerg-1426	201	10	·	·	PUNCT
fuelectenerg-1426	201	11	·	·	PUNCT
fuelectenerg-1426	201	12	·	·	PUNCT
fuelectenerg-1426	202	1	(	(	PUNCT
fuelectenerg-1426	202	2	32(3)n−1	32(3)n−1	NUM
fuelectenerg-1426	202	3	)	)	PUNCT
fuelectenerg-1426	202	4	kn	kn	NOUN
fuelectenerg-1426	202	5	]	]	X
fuelectenerg-1426	202	6	}	}	PUNCT
fuelectenerg-1426	202	7	.	.	PUNCT
fuelectenerg-1426	203	1	(	(	PUNCT
fuelectenerg-1426	203	2	38	38	NUM
fuelectenerg-1426	203	3	)	)	PUNCT
fuelectenerg-1426	203	4	proof	proof	NOUN
fuelectenerg-1426	203	5	.	.	PUNCT
fuelectenerg-1426	204	1	the	the	DET
fuelectenerg-1426	204	2	following	follow	VERB
fuelectenerg-1426	204	3	is	be	AUX
fuelectenerg-1426	204	4	the	the	DET
fuelectenerg-1426	204	5	derivation	derivation	NOUN
fuelectenerg-1426	204	6	of	of	ADP
fuelectenerg-1426	204	7	equation	equation	NOUN
fuelectenerg-1426	204	8	(	(	PUNCT
fuelectenerg-1426	204	9	38	38	NUM
fuelectenerg-1426	204	10	)	)	PUNCT
fuelectenerg-1426	204	11	to	to	PART
fuelectenerg-1426	204	12	calculate	calculate	VERB
fuelectenerg-1426	204	13	#	#	SYM
fuelectenerg-1426	204	14	tifs	tif	NOUN
fuelectenerg-1426	204	15	per	per	ADP
fuelectenerg-1426	204	16	variable	variable	ADJ
fuelectenerg-1426	204	17	order	order	NOUN
fuelectenerg-1426	204	18	.	.	PUNCT
fuelectenerg-1426	205	1	the	the	DET
fuelectenerg-1426	205	2	total	total	ADJ
fuelectenerg-1426	205	3	number	number	NOUN
fuelectenerg-1426	205	4	of	of	ADP
fuelectenerg-1426	205	5	nodes	node	NOUN
fuelectenerg-1426	205	6	for	for	ADP
fuelectenerg-1426	205	7	any	any	DET
fuelectenerg-1426	205	8	gf(3	gf(3	NOUN
fuelectenerg-1426	205	9	)	)	PUNCT
fuelectenerg-1426	205	10	tree	tree	NOUN
fuelectenerg-1426	205	11	with	with	ADP
fuelectenerg-1426	205	12	n	n	PROPN
fuelectenerg-1426	205	13	levels	level	NOUN
fuelectenerg-1426	205	14	(	(	PUNCT
fuelectenerg-1426	205	15	n	n	CCONJ
fuelectenerg-1426	205	16	variables	variable	NOUN
fuelectenerg-1426	205	17	)	)	PUNCT
fuelectenerg-1426	205	18	equals	equal	VERB
fuelectenerg-1426	205	19	:	:	PUNCT
fuelectenerg-1426	205	20	n−1	n−1	PROPN
fuelectenerg-1426	205	21	∑	∑	ADP
fuelectenerg-1426	205	22	k=0	k=0	PROPN
fuelectenerg-1426	205	23	(	(	PUNCT
fuelectenerg-1426	205	24	3)k	3)k	ADV
fuelectenerg-1426	205	25	.	.	PUNCT
fuelectenerg-1426	206	1	(	(	PUNCT
fuelectenerg-1426	206	2	39	39	NUM
fuelectenerg-1426	206	3	)	)	PUNCT
fuelectenerg-1426	206	4	for	for	ADP
fuelectenerg-1426	206	5	any	any	DET
fuelectenerg-1426	206	6	s	s	NOUN
fuelectenerg-1426	206	7	-	-	PUNCT
fuelectenerg-1426	206	8	type	type	NOUN
fuelectenerg-1426	206	9	node	node	NOUN
fuelectenerg-1426	206	10	there	there	PRON
fuelectenerg-1426	206	11	is	be	VERB
fuelectenerg-1426	206	12	only	only	ADV
fuelectenerg-1426	206	13	one	one	NUM
fuelectenerg-1426	206	14	type	type	NOUN
fuelectenerg-1426	206	15	of	of	ADP
fuelectenerg-1426	206	16	nodes	node	NOUN
fuelectenerg-1426	206	17	as	as	SCONJ
fuelectenerg-1426	206	18	the	the	DET
fuelectenerg-1426	206	19	branches	branch	NOUN
fuelectenerg-1426	206	20	have	have	VERB
fuelectenerg-1426	206	21	the	the	DET
fuelectenerg-1426	206	22	possibility	possibility	NOUN
fuelectenerg-1426	206	23	of	of	ADP
fuelectenerg-1426	206	24	single	single	ADJ
fuelectenerg-1426	206	25	value	value	NOUN
fuelectenerg-1426	206	26	each	each	PRON
fuelectenerg-1426	206	27	.	.	PUNCT
fuelectenerg-1426	207	1	yet	yet	ADV
fuelectenerg-1426	207	2	,	,	PUNCT
fuelectenerg-1426	207	3	for	for	ADP
fuelectenerg-1426	207	4	d	d	NOUN
fuelectenerg-1426	207	5	-	-	PUNCT
fuelectenerg-1426	207	6	type	type	ADJ
fuelectenerg-1426	207	7	node	node	NOUN
fuelectenerg-1426	207	8	there	there	PRON
fuelectenerg-1426	207	9	are	be	VERB
fuelectenerg-1426	207	10	n	n	PRON
fuelectenerg-1426	207	11	possible	possible	ADJ
fuelectenerg-1426	207	12	types	type	NOUN
fuelectenerg-1426	207	13	of	of	ADP
fuelectenerg-1426	207	14	nodes	node	NOUN
fuelectenerg-1426	207	15	where	where	SCONJ
fuelectenerg-1426	207	16	n	n	X
fuelectenerg-1426	207	17	is	be	AUX
fuelectenerg-1426	207	18	the	the	DET
fuelectenerg-1426	207	19	109	109	NUM
fuelectenerg-1426	207	20	710	710	NUM
fuelectenerg-1426	207	21	a.	a.	NOUN
fuelectenerg-1426	207	22	n.	n.	PROPN
fuelectenerg-1426	207	23	al	al	PROPN
fuelectenerg-1426	207	24	-	-	PUNCT
fuelectenerg-1426	207	25	rabadi	rabadi	PROPN
fuelectenerg-1426	207	26	multi	multi	ADJ
fuelectenerg-1426	207	27	-	-	ADJ
fuelectenerg-1426	207	28	valued	value	VERB
fuelectenerg-1426	207	29	galois	galois	PROPN
fuelectenerg-1426	207	30	shannon	shannon	PROPN
fuelectenerg-1426	207	31	davio	davio	PROPN
fuelectenerg-1426	207	32	trees	tree	NOUN
fuelectenerg-1426	207	33	and	and	CCONJ
fuelectenerg-1426	207	34	their	their	PRON
fuelectenerg-1426	207	35	complexity	complexity	NOUN
fuelectenerg-1426	207	36	711	711	NUM
fuelectenerg-1426	207	37	multi	multi	ADV
fuelectenerg-1426	207	38	-	-	ADJ
fuelectenerg-1426	207	39	valued	value	VERB
fuelectenerg-1426	207	40	galois	galois	PROPN
fuelectenerg-1426	207	41	shannon	shannon	PROPN
fuelectenerg-1426	207	42	davio	davio	PROPN
fuelectenerg-1426	207	43	trees	tree	NOUN
fuelectenerg-1426	207	44	and	and	CCONJ
fuelectenerg-1426	207	45	their	their	PRON
fuelectenerg-1426	207	46	complexity	complexity	NOUN
fuelectenerg-1426	208	1	1	1	NUM
fuelectenerg-1426	208	2	1	1	NUM
fuelectenerg-1426	208	3	1	1	NUM
fuelectenerg-1426	208	4	1	1	NUM
fuelectenerg-1426	208	5	1	1	NUM
fuelectenerg-1426	208	6	1	1	NUM
fuelectenerg-1426	208	7	0	0	NUM
fuelectenerg-1426	208	8	b	b	NOUN
fuelectenerg-1426	208	9	0	0	NUM
fuelectenerg-1426	208	10	b	b	NOUN
fuelectenerg-1426	208	11	0	0	NUM
fuelectenerg-1426	208	12	b	b	NOUN
fuelectenerg-1426	208	13	0	0	NUM
fuelectenerg-1426	208	14	b	b	NOUN
fuelectenerg-1426	208	15	0	0	NUM
fuelectenerg-1426	208	16	b	b	PROPN
fuelectenerg-1426	208	17	0	0	NUM
fuelectenerg-1426	208	18	b	b	PROPN
fuelectenerg-1426	208	19	b	b	PROPN
fuelectenerg-1426	208	20	b	b	PROPN
fuelectenerg-1426	208	21	b	b	PROPN
fuelectenerg-1426	208	22	b	b	PROPN
fuelectenerg-1426	208	23	b	b	PROPN
fuelectenerg-1426	208	24	’’	’'	PUNCT
fuelectenerg-1426	208	25	b	b	NOUN
fuelectenerg-1426	208	26	’	'	PUNCT
fuelectenerg-1426	208	27	b	b	PROPN
fuelectenerg-1426	208	28	1	1	NUM
fuelectenerg-1426	208	29	b	b	SYM
fuelectenerg-1426	208	30	1	1	NUM
fuelectenerg-1426	208	31	b	b	SYM
fuelectenerg-1426	208	32	b	b	PROPN
fuelectenerg-1426	208	33	1	1	NUM
fuelectenerg-1426	208	34	b	b	SYM
fuelectenerg-1426	208	35	1	1	NUM
fuelectenerg-1426	208	36	b	b	PROPN
fuelectenerg-1426	208	37	(	(	PUNCT
fuelectenerg-1426	208	38	)	)	PUNCT
fuelectenerg-1426	208	39	b	b	X
fuelectenerg-1426	208	40	2	2	NUM
fuelectenerg-1426	208	41	(	(	PUNCT
fuelectenerg-1426	208	42	b	b	NOUN
fuelectenerg-1426	208	43	’	'	PUNCT
fuelectenerg-1426	208	44	)	)	PUNCT
fuelectenerg-1426	208	45	2	2	NUM
fuelectenerg-1426	208	46	(	(	PUNCT
fuelectenerg-1426	208	47	b	b	NOUN
fuelectenerg-1426	208	48	)	)	PUNCT
fuelectenerg-1426	208	49	2	2	NUM
fuelectenerg-1426	208	50	(	(	PUNCT
fuelectenerg-1426	208	51	)	)	PUNCT
fuelectenerg-1426	208	52	b	b	X
fuelectenerg-1426	208	53	2	2	NUM
fuelectenerg-1426	208	54	(	(	PUNCT
fuelectenerg-1426	208	55	b	b	NOUN
fuelectenerg-1426	208	56	’	'	PUNCT
fuelectenerg-1426	208	57	)	)	PUNCT
fuelectenerg-1426	208	58	2	2	NUM
fuelectenerg-1426	208	59	(	(	PUNCT
fuelectenerg-1426	208	60	b	b	NOUN
fuelectenerg-1426	208	61	)	)	PUNCT
fuelectenerg-1426	208	62	2	2	NUM
fuelectenerg-1426	208	63	2	2	NUM
fuelectenerg-1426	208	64	b	b	SYM
fuelectenerg-1426	208	65	2	2	NUM
fuelectenerg-1426	208	66	b	b	SYM
fuelectenerg-1426	208	67	2	2	NUM
fuelectenerg-1426	208	68	b	b	SYM
fuelectenerg-1426	208	69	2	2	NUM
fuelectenerg-1426	208	70	b	b	SYM
fuelectenerg-1426	208	71	2	2	NUM
fuelectenerg-1426	208	72	b	b	SYM
fuelectenerg-1426	208	73	2	2	NUM
fuelectenerg-1426	208	74	b	b	PROPN
fuelectenerg-1426	208	75	(	(	PUNCT
fuelectenerg-1426	208	76	)	)	PUNCT
fuelectenerg-1426	208	77	b	b	X
fuelectenerg-1426	208	78	3	3	NUM
fuelectenerg-1426	208	79	(	(	PUNCT
fuelectenerg-1426	208	80	b	b	NOUN
fuelectenerg-1426	208	81	’	'	PUNCT
fuelectenerg-1426	208	82	)	)	PUNCT
fuelectenerg-1426	208	83	3	3	NUM
fuelectenerg-1426	208	84	(	(	PUNCT
fuelectenerg-1426	208	85	b	b	NOUN
fuelectenerg-1426	208	86	’’	’'	PUNCT
fuelectenerg-1426	208	87	)	)	PUNCT
fuelectenerg-1426	208	88	3	3	NUM
fuelectenerg-1426	208	89	(	(	PUNCT
fuelectenerg-1426	208	90	)	)	PUNCT
fuelectenerg-1426	208	91	b	b	X
fuelectenerg-1426	208	92	3	3	NUM
fuelectenerg-1426	208	93	(	(	PUNCT
fuelectenerg-1426	208	94	b	b	NOUN
fuelectenerg-1426	208	95	)	)	PUNCT
fuelectenerg-1426	208	96	3	3	NUM
fuelectenerg-1426	208	97	(	(	PUNCT
fuelectenerg-1426	208	98	b	b	NOUN
fuelectenerg-1426	208	99	)	)	PUNCT
fuelectenerg-1426	208	100	3	3	NUM
fuelectenerg-1426	208	101	3	3	NUM
fuelectenerg-1426	208	102	b	b	SYM
fuelectenerg-1426	208	103	3	3	NUM
fuelectenerg-1426	208	104	b	b	SYM
fuelectenerg-1426	208	105	3	3	NUM
fuelectenerg-1426	208	106	b	b	SYM
fuelectenerg-1426	208	107	3	3	NUM
fuelectenerg-1426	208	108	b	b	SYM
fuelectenerg-1426	208	109	3	3	NUM
fuelectenerg-1426	208	110	b	b	SYM
fuelectenerg-1426	208	111	3	3	NUM
fuelectenerg-1426	208	112	b	b	NOUN
fuelectenerg-1426	208	113	s	s	X
fuelectenerg-1426	208	114	s	s	X
fuelectenerg-1426	208	115	s	s	X
fuelectenerg-1426	208	116	s	s	X
fuelectenerg-1426	208	117	s	s	X
fuelectenerg-1426	208	118	s	s	X
fuelectenerg-1426	208	119	s	s	X
fuelectenerg-1426	208	120	s	s	X
fuelectenerg-1426	208	121	s	s	X
fuelectenerg-1426	208	122	d	d	X
fuelectenerg-1426	208	123	d	d	PROPN
fuelectenerg-1426	208	124	d	d	PROPN
fuelectenerg-1426	208	125	d	d	PROPN
fuelectenerg-1426	208	126	d	d	PROPN
fuelectenerg-1426	208	127	d	d	X
fuelectenerg-1426	208	128	(	(	PUNCT
fuelectenerg-1426	208	129	a	a	NOUN
fuelectenerg-1426	208	130	)	)	PUNCT
fuelectenerg-1426	208	131	(	(	PUNCT
fuelectenerg-1426	208	132	b	b	NOUN
fuelectenerg-1426	208	133	)	)	PUNCT
fuelectenerg-1426	208	134	(	(	PUNCT
fuelectenerg-1426	208	135	)	)	PUNCT
fuelectenerg-1426	208	136	n=	n=	ADV
fuelectenerg-1426	208	137	4,096	4,096	NUM
fuelectenerg-1426	208	138	0	0	NUM
fuelectenerg-1426	208	139	a	a	DET
fuelectenerg-1426	208	140	0	0	NUM
fuelectenerg-1426	208	141	a	a	DET
fuelectenerg-1426	208	142	0	0	NUM
fuelectenerg-1426	208	143	a	a	DET
fuelectenerg-1426	208	144	1	1	NUM
fuelectenerg-1426	208	145	a	a	DET
fuelectenerg-1426	208	146	1	1	NUM
fuelectenerg-1426	208	147	a	a	DET
fuelectenerg-1426	208	148	1	1	NUM
fuelectenerg-1426	208	149	a	a	DET
fuelectenerg-1426	208	150	2	2	NUM
fuelectenerg-1426	208	151	a	a	DET
fuelectenerg-1426	208	152	2	2	NUM
fuelectenerg-1426	208	153	a	a	DET
fuelectenerg-1426	208	154	2	2	NUM
fuelectenerg-1426	208	155	a	a	DET
fuelectenerg-1426	208	156	3	3	NUM
fuelectenerg-1426	208	157	a	a	DET
fuelectenerg-1426	208	158	3	3	NUM
fuelectenerg-1426	208	159	a	a	DET
fuelectenerg-1426	208	160	3	3	NUM
fuelectenerg-1426	208	161	a	a	DET
fuelectenerg-1426	208	162	c	c	NOUN
fuelectenerg-1426	208	163	fig	fig	NOUN
fuelectenerg-1426	208	164	.	.	PUNCT
fuelectenerg-1426	209	1	5	5	NUM
fuelectenerg-1426	209	2	:	:	PUNCT
fuelectenerg-1426	209	3	examples	example	NOUN
fuelectenerg-1426	209	4	of	of	ADP
fuelectenerg-1426	209	5	s	s	PROPN
fuelectenerg-1426	209	6	/	/	SYM
fuelectenerg-1426	209	7	d	d	NOUN
fuelectenerg-1426	209	8	trees	tree	NOUN
fuelectenerg-1426	209	9	:	:	PUNCT
fuelectenerg-1426	209	10	(	(	PUNCT
fuelectenerg-1426	209	11	a	a	X
fuelectenerg-1426	209	12	)	)	PUNCT
fuelectenerg-1426	209	13	quaternary	quaternary	ADJ
fuelectenerg-1426	209	14	s	s	PROPN
fuelectenerg-1426	209	15	/	/	SYM
fuelectenerg-1426	209	16	d	d	NOUN
fuelectenerg-1426	209	17	tree	tree	NOUN
fuelectenerg-1426	209	18	for	for	ADP
fuelectenerg-1426	209	19	two	two	NUM
fuelectenerg-1426	209	20	variables	variable	NOUN
fuelectenerg-1426	209	21	of	of	ADP
fuelectenerg-1426	209	22	order	order	NOUN
fuelectenerg-1426	209	23	{	{	PUNCT
fuelectenerg-1426	209	24	a	a	DET
fuelectenerg-1426	209	25	,	,	PUNCT
fuelectenerg-1426	209	26	b	b	NOUN
fuelectenerg-1426	209	27	}	}	PUNCT
fuelectenerg-1426	209	28	with	with	ADP
fuelectenerg-1426	209	29	three	three	NUM
fuelectenerg-1426	209	30	shannon	shannon	PROPN
fuelectenerg-1426	209	31	nodes	node	NOUN
fuelectenerg-1426	209	32	and	and	CCONJ
fuelectenerg-1426	209	33	two	two	NUM
fuelectenerg-1426	209	34	generalized	generalized	ADJ
fuelectenerg-1426	209	35	davio	davio	NOUN
fuelectenerg-1426	209	36	nodes	node	NOUN
fuelectenerg-1426	209	37	,	,	PUNCT
fuelectenerg-1426	209	38	and	and	CCONJ
fuelectenerg-1426	209	39	(	(	PUNCT
fuelectenerg-1426	209	40	b	b	NOUN
fuelectenerg-1426	209	41	)	)	PUNCT
fuelectenerg-1426	209	42	(	(	PUNCT
fuelectenerg-1426	209	43	c	c	X
fuelectenerg-1426	209	44	)	)	PUNCT
fuelectenerg-1426	209	45	some	some	PRON
fuelectenerg-1426	209	46	of	of	ADP
fuelectenerg-1426	209	47	the	the	DET
fuelectenerg-1426	209	48	quaternary	quaternary	ADJ
fuelectenerg-1426	209	49	trees	tree	NOUN
fuelectenerg-1426	209	50	that	that	PRON
fuelectenerg-1426	209	51	it	it	PRON
fuelectenerg-1426	209	52	generates	generate	VERB
fuelectenerg-1426	209	53	.	.	PUNCT
fuelectenerg-1426	210	1	number	number	NOUN
fuelectenerg-1426	210	2	of	of	ADP
fuelectenerg-1426	210	3	variables	variable	NOUN
fuelectenerg-1426	210	4	which	which	PRON
fuelectenerg-1426	210	5	is	be	AUX
fuelectenerg-1426	210	6	equal	equal	ADJ
fuelectenerg-1426	210	7	to	to	ADP
fuelectenerg-1426	210	8	the	the	DET
fuelectenerg-1426	210	9	number	number	NOUN
fuelectenerg-1426	210	10	of	of	ADP
fuelectenerg-1426	210	11	levels	level	NOUN
fuelectenerg-1426	210	12	.	.	PUNCT
fuelectenerg-1426	211	1	the	the	DET
fuelectenerg-1426	211	2	highest	high	ADJ
fuelectenerg-1426	211	3	possible	possible	ADJ
fuelectenerg-1426	211	4	number	number	NOUN
fuelectenerg-1426	211	5	of	of	ADP
fuelectenerg-1426	211	6	forms	form	NOUN
fuelectenerg-1426	211	7	for	for	ADP
fuelectenerg-1426	211	8	the	the	DET
fuelectenerg-1426	211	9	d	d	ADJ
fuelectenerg-1426	211	10	-	-	PUNCT
fuelectenerg-1426	211	11	type	type	NOUN
fuelectenerg-1426	211	12	node	node	NOUN
fuelectenerg-1426	211	13	is	be	AUX
fuelectenerg-1426	211	14	when	when	SCONJ
fuelectenerg-1426	211	15	the	the	DET
fuelectenerg-1426	211	16	d	d	ADJ
fuelectenerg-1426	211	17	-	-	PUNCT
fuelectenerg-1426	211	18	type	type	NOUN
fuelectenerg-1426	211	19	node	node	NOUN
fuelectenerg-1426	211	20	exists	exist	VERB
fuelectenerg-1426	211	21	in	in	ADP
fuelectenerg-1426	211	22	the	the	DET
fuelectenerg-1426	211	23	first	first	ADJ
fuelectenerg-1426	211	24	(	(	PUNCT
fuelectenerg-1426	211	25	highest	high	ADJ
fuelectenerg-1426	211	26	)	)	PUNCT
fuelectenerg-1426	211	27	level	level	NOUN
fuelectenerg-1426	211	28	,	,	PUNCT
fuelectenerg-1426	211	29	and	and	CCONJ
fuelectenerg-1426	211	30	the	the	DET
fuelectenerg-1426	211	31	lowest	low	ADJ
fuelectenerg-1426	211	32	possible	possible	ADJ
fuelectenerg-1426	211	33	number	number	NOUN
fuelectenerg-1426	211	34	of	of	ADP
fuelectenerg-1426	211	35	forms	form	NOUN
fuelectenerg-1426	211	36	for	for	ADP
fuelectenerg-1426	211	37	the	the	DET
fuelectenerg-1426	211	38	d	d	ADJ
fuelectenerg-1426	211	39	-	-	PUNCT
fuelectenerg-1426	211	40	type	type	NOUN
fuelectenerg-1426	211	41	node	node	NOUN
fuelectenerg-1426	211	42	is	be	AUX
fuelectenerg-1426	211	43	when	when	SCONJ
fuelectenerg-1426	211	44	the	the	DET
fuelectenerg-1426	211	45	d	d	ADJ
fuelectenerg-1426	211	46	-	-	PUNCT
fuelectenerg-1426	211	47	type	type	NOUN
fuelectenerg-1426	211	48	node	node	NOUN
fuelectenerg-1426	211	49	exists	exist	VERB
fuelectenerg-1426	211	50	in	in	ADP
fuelectenerg-1426	211	51	the	the	DET
fuelectenerg-1426	211	52	n	n	NOUN
fuelectenerg-1426	211	53	-	-	PUNCT
fuelectenerg-1426	211	54	level	level	NOUN
fuelectenerg-1426	211	55	(	(	PUNCT
fuelectenerg-1426	211	56	lowest	low	ADJ
fuelectenerg-1426	211	57	level	level	NOUN
fuelectenerg-1426	211	58	)	)	PUNCT
fuelectenerg-1426	211	59	.	.	PUNCT
fuelectenerg-1426	212	1	therefore	therefore	ADV
fuelectenerg-1426	212	2	,	,	PUNCT
fuelectenerg-1426	212	3	for	for	ADP
fuelectenerg-1426	212	4	certain	certain	ADJ
fuelectenerg-1426	212	5	number	number	NOUN
fuelectenerg-1426	212	6	m	m	NOUN
fuelectenerg-1426	212	7	of	of	ADP
fuelectenerg-1426	212	8	s	s	NOUN
fuelectenerg-1426	212	9	-	-	PUNCT
fuelectenerg-1426	212	10	type	type	NOUN
fuelectenerg-1426	212	11	nodes	node	NOUN
fuelectenerg-1426	212	12	the	the	DET
fuelectenerg-1426	212	13	following	follow	VERB
fuelectenerg-1426	212	14	equation	equation	NOUN
fuelectenerg-1426	212	15	describes	describe	VERB
fuelectenerg-1426	212	16	the	the	DET
fuelectenerg-1426	212	17	number	number	NOUN
fuelectenerg-1426	212	18	of	of	ADP
fuelectenerg-1426	212	19	the	the	DET
fuelectenerg-1426	212	20	d	d	ADJ
fuelectenerg-1426	212	21	-	-	PUNCT
fuelectenerg-1426	212	22	type	type	NOUN
fuelectenerg-1426	212	23	nodes	node	NOUN
fuelectenerg-1426	212	24	for	for	ADP
fuelectenerg-1426	212	25	n	n	DET
fuelectenerg-1426	212	26	variables	variable	NOUN
fuelectenerg-1426	212	27	:	:	PUNCT
fuelectenerg-1426	213	1	#	#	SYM
fuelectenerg-1426	213	2	s	s	NOUN
fuelectenerg-1426	213	3	=	=	NOUN
fuelectenerg-1426	213	4	m	m	NOUN
fuelectenerg-1426	213	5	⇒	⇒	NOUN
fuelectenerg-1426	213	6	#	#	SYM
fuelectenerg-1426	213	7	d	d	NOUN
fuelectenerg-1426	213	8	=	=	SYM
fuelectenerg-1426	213	9	[	[	PUNCT
fuelectenerg-1426	213	10	n−1	n−1	PROPN
fuelectenerg-1426	213	11	∑	∑	PUNCT
fuelectenerg-1426	213	12	k	k	X
fuelectenerg-1426	213	13	=	=	NOUN
fuelectenerg-1426	213	14	o	o	X
fuelectenerg-1426	213	15	(	(	PUNCT
fuelectenerg-1426	213	16	3)k	3)k	NUM
fuelectenerg-1426	213	17	−m	−m	NOUN
fuelectenerg-1426	213	18	]	]	PUNCT
fuelectenerg-1426	213	19	.	.	PUNCT
fuelectenerg-1426	214	1	(	(	PUNCT
fuelectenerg-1426	214	2	40	40	NUM
fuelectenerg-1426	214	3	)	)	PUNCT
fuelectenerg-1426	214	4	it	it	PRON
fuelectenerg-1426	214	5	can	can	AUX
fuelectenerg-1426	214	6	be	be	AUX
fuelectenerg-1426	214	7	shown	show	VERB
fuelectenerg-1426	214	8	that	that	SCONJ
fuelectenerg-1426	214	9	for	for	ADP
fuelectenerg-1426	214	10	gf(3	gf(3	PROPN
fuelectenerg-1426	214	11	)	)	PUNCT
fuelectenerg-1426	214	12	(	(	PUNCT
fuelectenerg-1426	214	13	i.e.	i.e.	X
fuelectenerg-1426	214	14	,	,	PUNCT
fuelectenerg-1426	214	15	ternary	ternary	ADJ
fuelectenerg-1426	214	16	decision	decision	NOUN
fuelectenerg-1426	214	17	tree	tree	NOUN
fuelectenerg-1426	214	18	(	(	PUNCT
fuelectenerg-1426	214	19	tdt	tdt	PROPN
fuelectenerg-1426	214	20	)	)	PUNCT
fuelectenerg-1426	214	21	)	)	PUNCT
fuelectenerg-1426	214	22	and	and	CCONJ
fuelectenerg-1426	214	23	n	n	CCONJ
fuelectenerg-1426	214	24	-	-	PUNCT
fuelectenerg-1426	214	25	levels	level	NOUN
fuelectenerg-1426	214	26	(	(	PUNCT
fuelectenerg-1426	214	27	n	n	CCONJ
fuelectenerg-1426	214	28	-	-	PUNCT
fuelectenerg-1426	214	29	variables	variable	NOUN
fuelectenerg-1426	214	30	)	)	PUNCT
fuelectenerg-1426	214	31	,	,	PUNCT
fuelectenerg-1426	214	32	the	the	DET
fuelectenerg-1426	214	33	general	general	ADJ
fuelectenerg-1426	214	34	formulas	formula	NOUN
fuelectenerg-1426	214	35	that	that	PRON
fuelectenerg-1426	214	36	count	count	VERB
fuelectenerg-1426	214	37	the	the	DET
fuelectenerg-1426	214	38	number	number	NOUN
fuelectenerg-1426	214	39	of	of	ADP
fuelectenerg-1426	214	40	d	d	ADJ
fuelectenerg-1426	214	41	-	-	PUNCT
fuelectenerg-1426	214	42	type	type	NOUN
fuelectenerg-1426	214	43	nodes	node	NOUN
fuelectenerg-1426	214	44	,	,	PUNCT
fuelectenerg-1426	214	45	and	and	CCONJ
fuelectenerg-1426	214	46	the	the	DET
fuelectenerg-1426	214	47	number	number	NOUN
fuelectenerg-1426	214	48	of	of	ADP
fuelectenerg-1426	214	49	all	all	DET
fuelectenerg-1426	214	50	possible	possible	ADJ
fuelectenerg-1426	214	51	110	110	NUM
fuelectenerg-1426	214	52	1	1	NUM
fuelectenerg-1426	214	53	1	1	NUM
fuelectenerg-1426	214	54	710	710	NUM
fuelectenerg-1426	214	55	a.	a.	NOUN
fuelectenerg-1426	214	56	n.	n.	PROPN
fuelectenerg-1426	214	57	al	al	PROPN
fuelectenerg-1426	214	58	-	-	PUNCT
fuelectenerg-1426	214	59	rabadi	rabadi	PROPN
fuelectenerg-1426	214	60	multi	multi	ADJ
fuelectenerg-1426	214	61	-	-	ADJ
fuelectenerg-1426	214	62	valued	value	VERB
fuelectenerg-1426	214	63	galois	galois	PROPN
fuelectenerg-1426	214	64	shannon	shannon	PROPN
fuelectenerg-1426	214	65	davio	davio	PROPN
fuelectenerg-1426	214	66	trees	tree	NOUN
fuelectenerg-1426	214	67	and	and	CCONJ
fuelectenerg-1426	214	68	their	their	PRON
fuelectenerg-1426	214	69	complexity	complexity	NOUN
fuelectenerg-1426	214	70	711	711	NUM
fuelectenerg-1426	214	71	multi	multi	ADV
fuelectenerg-1426	214	72	-	-	ADJ
fuelectenerg-1426	214	73	valued	value	VERB
fuelectenerg-1426	214	74	galois	galois	PROPN
fuelectenerg-1426	214	75	shannon	shannon	PROPN
fuelectenerg-1426	214	76	davio	davio	PROPN
fuelectenerg-1426	214	77	trees	tree	NOUN
fuelectenerg-1426	214	78	and	and	CCONJ
fuelectenerg-1426	214	79	their	their	PRON
fuelectenerg-1426	214	80	complexity	complexity	NOUN
fuelectenerg-1426	214	81	1	1	NUM
fuelectenerg-1426	214	82	1	1	NUM
fuelectenerg-1426	214	83	1	1	NUM
fuelectenerg-1426	214	84	1	1	NUM
fuelectenerg-1426	214	85	1	1	NUM
fuelectenerg-1426	214	86	1	1	NUM
fuelectenerg-1426	214	87	0	0	NUM
fuelectenerg-1426	214	88	a	a	DET
fuelectenerg-1426	214	89	0	0	NUM
fuelectenerg-1426	214	90	a	a	DET
fuelectenerg-1426	214	91	0	0	NUM
fuelectenerg-1426	214	92	a	a	DET
fuelectenerg-1426	214	93	1	1	NUM
fuelectenerg-1426	214	94	1	1	NUM
fuelectenerg-1426	214	95	1	1	NUM
fuelectenerg-1426	214	96	a	a	DET
fuelectenerg-1426	214	97	a	a	DET
fuelectenerg-1426	214	98	aa	aa	NOUN
fuelectenerg-1426	214	99	a	a	PRON
fuelectenerg-1426	214	100	’	'	PUNCT
fuelectenerg-1426	214	101	a	a	DET
fuelectenerg-1426	214	102	1	1	NUM
fuelectenerg-1426	214	103	a	a	DET
fuelectenerg-1426	214	104	1	1	NUM
fuelectenerg-1426	214	105	a	a	DET
fuelectenerg-1426	214	106	1	1	NUM
fuelectenerg-1426	214	107	a	a	DET
fuelectenerg-1426	214	108	a	a	DET
fuelectenerg-1426	214	109	a	a	DET
fuelectenerg-1426	214	110	’’	’'	PUNCT
fuelectenerg-1426	214	111	a	a	PRON
fuelectenerg-1426	214	112	’’	’'	PUNCT
fuelectenerg-1426	214	113	(	(	PUNCT
fuelectenerg-1426	214	114	)	)	PUNCT
fuelectenerg-1426	214	115	a	a	DET
fuelectenerg-1426	214	116	2	2	NUM
fuelectenerg-1426	214	117	(	(	PUNCT
fuelectenerg-1426	214	118	a	a	NOUN
fuelectenerg-1426	214	119	)	)	PUNCT
fuelectenerg-1426	214	120	2	2	NUM
fuelectenerg-1426	214	121	(	(	PUNCT
fuelectenerg-1426	214	122	a	a	X
fuelectenerg-1426	214	123	)	)	PUNCT
fuelectenerg-1426	214	124	2	2	NUM
fuelectenerg-1426	214	125	(	(	PUNCT
fuelectenerg-1426	214	126	)	)	PUNCT
fuelectenerg-1426	214	127	a	a	DET
fuelectenerg-1426	214	128	2	2	NUM
fuelectenerg-1426	214	129	(	(	PUNCT
fuelectenerg-1426	214	130	a	a	DET
fuelectenerg-1426	214	131	’’	’'	PUNCT
fuelectenerg-1426	214	132	)	)	PUNCT
fuelectenerg-1426	214	133	2	2	NUM
fuelectenerg-1426	214	134	(	(	PUNCT
fuelectenerg-1426	214	135	a	a	DET
fuelectenerg-1426	214	136	’’	’'	PUNCT
fuelectenerg-1426	214	137	)	)	PUNCT
fuelectenerg-1426	214	138	2	2	NUM
fuelectenerg-1426	214	139	2	2	NUM
fuelectenerg-1426	214	140	a	a	DET
fuelectenerg-1426	214	141	2	2	NUM
fuelectenerg-1426	214	142	a	a	DET
fuelectenerg-1426	214	143	2	2	NUM
fuelectenerg-1426	214	144	a	a	PRON
fuelectenerg-1426	214	145	(	(	PUNCT
fuelectenerg-1426	214	146	a	a	NOUN
fuelectenerg-1426	214	147	)	)	PUNCT
fuelectenerg-1426	214	148	2	2	NUM
fuelectenerg-1426	214	149	(	(	PUNCT
fuelectenerg-1426	214	150	a	a	DET
fuelectenerg-1426	214	151	’’	’'	PUNCT
fuelectenerg-1426	214	152	’	'	PUNCT
fuelectenerg-1426	214	153	)	)	PUNCT
fuelectenerg-1426	214	154	2	2	NUM
fuelectenerg-1426	214	155	(	(	PUNCT
fuelectenerg-1426	214	156	a	a	X
fuelectenerg-1426	214	157	)	)	PUNCT
fuelectenerg-1426	214	158	2	2	NUM
fuelectenerg-1426	214	159	(	(	PUNCT
fuelectenerg-1426	214	160	)	)	PUNCT
fuelectenerg-1426	214	161	a	a	DET
fuelectenerg-1426	214	162	3	3	NUM
fuelectenerg-1426	214	163	(	(	PUNCT
fuelectenerg-1426	214	164	a	a	NOUN
fuelectenerg-1426	214	165	)	)	PUNCT
fuelectenerg-1426	214	166	3	3	NUM
fuelectenerg-1426	214	167	(	(	PUNCT
fuelectenerg-1426	214	168	a	a	PRON
fuelectenerg-1426	214	169	’	'	PUNCT
fuelectenerg-1426	214	170	)	)	PUNCT
fuelectenerg-1426	214	171	3	3	NUM
fuelectenerg-1426	214	172	(	(	PUNCT
fuelectenerg-1426	214	173	)	)	PUNCT
fuelectenerg-1426	214	174	a	a	DET
fuelectenerg-1426	214	175	3	3	NUM
fuelectenerg-1426	214	176	(	(	PUNCT
fuelectenerg-1426	214	177	a	a	DET
fuelectenerg-1426	214	178	’’	’'	PUNCT
fuelectenerg-1426	214	179	’	'	PUNCT
fuelectenerg-1426	214	180	)	)	PUNCT
fuelectenerg-1426	214	181	3	3	NUM
fuelectenerg-1426	214	182	(	(	PUNCT
fuelectenerg-1426	214	183	a	a	DET
fuelectenerg-1426	214	184	’’	’'	PUNCT
fuelectenerg-1426	214	185	)	)	PUNCT
fuelectenerg-1426	214	186	3	3	NUM
fuelectenerg-1426	214	187	3	3	NUM
fuelectenerg-1426	214	188	a	a	DET
fuelectenerg-1426	214	189	3	3	NUM
fuelectenerg-1426	214	190	a	a	DET
fuelectenerg-1426	214	191	3	3	NUM
fuelectenerg-1426	214	192	a	a	DET
fuelectenerg-1426	214	193	(	(	PUNCT
fuelectenerg-1426	214	194	a	a	NOUN
fuelectenerg-1426	214	195	)	)	PUNCT
fuelectenerg-1426	214	196	3	3	NUM
fuelectenerg-1426	214	197	(	(	PUNCT
fuelectenerg-1426	214	198	a	a	PRON
fuelectenerg-1426	214	199	’	'	PUNCT
fuelectenerg-1426	214	200	)	)	PUNCT
fuelectenerg-1426	214	201	3	3	NUM
fuelectenerg-1426	214	202	(	(	PUNCT
fuelectenerg-1426	214	203	a	a	PRON
fuelectenerg-1426	214	204	’	'	PUNCT
fuelectenerg-1426	214	205	)	)	PUNCT
fuelectenerg-1426	215	1	3	3	NUM
fuelectenerg-1426	215	2	s	s	NOUN
fuelectenerg-1426	215	3	s	s	NOUN
fuelectenerg-1426	215	4	s	s	NOUN
fuelectenerg-1426	215	5	d	d	X
fuelectenerg-1426	215	6	d	d	X
fuelectenerg-1426	215	7	s	s	X
fuelectenerg-1426	215	8	s	s	X
fuelectenerg-1426	215	9	s	s	X
fuelectenerg-1426	215	10	s	s	X
fuelectenerg-1426	215	11	d	d	X
fuelectenerg-1426	215	12	d	d	PROPN
fuelectenerg-1426	215	13	d	d	PROPN
fuelectenerg-1426	215	14	d	d	PROPN
fuelectenerg-1426	215	15	d	d	PROPN
fuelectenerg-1426	215	16	d	d	X
fuelectenerg-1426	215	17	(	(	PUNCT
fuelectenerg-1426	215	18	a	a	NOUN
fuelectenerg-1426	215	19	)	)	PUNCT
fuelectenerg-1426	215	20	(	(	PUNCT
fuelectenerg-1426	215	21	b	b	NOUN
fuelectenerg-1426	215	22	)	)	PUNCT
fuelectenerg-1426	215	23	n=	n=	ADJ
fuelectenerg-1426	215	24	262,144	262,144	NUM
fuelectenerg-1426	215	25	0	0	NUM
fuelectenerg-1426	215	26	b	b	NOUN
fuelectenerg-1426	215	27	0	0	NUM
fuelectenerg-1426	215	28	b	b	NOUN
fuelectenerg-1426	215	29	0	0	NUM
fuelectenerg-1426	215	30	b	b	SYM
fuelectenerg-1426	215	31	1	1	NUM
fuelectenerg-1426	215	32	b	b	SYM
fuelectenerg-1426	215	33	1	1	NUM
fuelectenerg-1426	215	34	b	b	SYM
fuelectenerg-1426	215	35	1	1	NUM
fuelectenerg-1426	215	36	b	b	SYM
fuelectenerg-1426	215	37	2	2	NUM
fuelectenerg-1426	215	38	b	b	SYM
fuelectenerg-1426	215	39	2	2	NUM
fuelectenerg-1426	215	40	b	b	SYM
fuelectenerg-1426	215	41	2	2	NUM
fuelectenerg-1426	215	42	b	b	SYM
fuelectenerg-1426	215	43	3	3	NUM
fuelectenerg-1426	215	44	b	b	SYM
fuelectenerg-1426	215	45	3	3	NUM
fuelectenerg-1426	215	46	b	b	SYM
fuelectenerg-1426	215	47	3	3	NUM
fuelectenerg-1426	215	48	b	b	PROPN
fuelectenerg-1426	215	49	(	(	PUNCT
fuelectenerg-1426	215	50	c	c	NOUN
fuelectenerg-1426	215	51	)	)	PUNCT
fuelectenerg-1426	215	52	fig	fig	NOUN
fuelectenerg-1426	215	53	.	.	PUNCT
fuelectenerg-1426	216	1	6	6	NUM
fuelectenerg-1426	216	2	:	:	PUNCT
fuelectenerg-1426	216	3	examples	example	NOUN
fuelectenerg-1426	216	4	of	of	ADP
fuelectenerg-1426	216	5	s	s	PROPN
fuelectenerg-1426	216	6	/	/	SYM
fuelectenerg-1426	216	7	d	d	NOUN
fuelectenerg-1426	216	8	trees	tree	NOUN
fuelectenerg-1426	216	9	:	:	PUNCT
fuelectenerg-1426	216	10	(	(	PUNCT
fuelectenerg-1426	216	11	a	a	X
fuelectenerg-1426	216	12	)	)	PUNCT
fuelectenerg-1426	216	13	quaternary	quaternary	ADJ
fuelectenerg-1426	216	14	s	s	PROPN
fuelectenerg-1426	216	15	/	/	SYM
fuelectenerg-1426	216	16	d	d	NOUN
fuelectenerg-1426	216	17	tree	tree	NOUN
fuelectenerg-1426	216	18	for	for	ADP
fuelectenerg-1426	216	19	two	two	NUM
fuelectenerg-1426	216	20	variables	variable	NOUN
fuelectenerg-1426	216	21	of	of	ADP
fuelectenerg-1426	216	22	order	order	NOUN
fuelectenerg-1426	216	23	{	{	PUNCT
fuelectenerg-1426	216	24	b	b	NOUN
fuelectenerg-1426	216	25	,	,	PUNCT
fuelectenerg-1426	216	26	a	a	PRON
fuelectenerg-1426	216	27	}	}	PUNCT
fuelectenerg-1426	216	28	with	with	ADP
fuelectenerg-1426	216	29	two	two	NUM
fuelectenerg-1426	216	30	shannon	shannon	PROPN
fuelectenerg-1426	216	31	nodes	node	NOUN
fuelectenerg-1426	216	32	and	and	CCONJ
fuelectenerg-1426	216	33	three	three	NUM
fuelectenerg-1426	216	34	generalized	generalized	ADJ
fuelectenerg-1426	216	35	davio	davio	NOUN
fuelectenerg-1426	216	36	nodes	node	NOUN
fuelectenerg-1426	216	37	,	,	PUNCT
fuelectenerg-1426	216	38	and	and	CCONJ
fuelectenerg-1426	216	39	(	(	PUNCT
fuelectenerg-1426	216	40	b	b	NOUN
fuelectenerg-1426	216	41	)	)	PUNCT
fuelectenerg-1426	216	42	(	(	PUNCT
fuelectenerg-1426	216	43	c	c	X
fuelectenerg-1426	216	44	)	)	PUNCT
fuelectenerg-1426	216	45	some	some	PRON
fuelectenerg-1426	216	46	of	of	ADP
fuelectenerg-1426	216	47	the	the	DET
fuelectenerg-1426	216	48	quaternary	quaternary	ADJ
fuelectenerg-1426	216	49	trees	tree	NOUN
fuelectenerg-1426	216	50	that	that	PRON
fuelectenerg-1426	216	51	it	it	PRON
fuelectenerg-1426	216	52	generates	generate	VERB
fuelectenerg-1426	216	53	.	.	PUNCT
fuelectenerg-1426	217	1	forms	form	NOUN
fuelectenerg-1426	217	2	for	for	ADP
fuelectenerg-1426	217	3	the	the	DET
fuelectenerg-1426	217	4	d	d	ADJ
fuelectenerg-1426	217	5	-	-	PUNCT
fuelectenerg-1426	217	6	type	type	NOUN
fuelectenerg-1426	217	7	node	node	NOUN
fuelectenerg-1426	217	8	in	in	ADP
fuelectenerg-1426	217	9	the	the	DET
fuelectenerg-1426	217	10	k	k	PROPN
fuelectenerg-1426	217	11	level	level	NOUN
fuelectenerg-1426	217	12	of	of	ADP
fuelectenerg-1426	217	13	the	the	DET
fuelectenerg-1426	217	14	n	n	CCONJ
fuelectenerg-1426	217	15	-	-	PUNCT
fuelectenerg-1426	217	16	level	level	NOUN
fuelectenerg-1426	217	17	tdt	tdt	PROPN
fuelectenerg-1426	217	18	are	be	AUX
fuelectenerg-1426	217	19	:	:	PUNCT
fuelectenerg-1426	217	20	#	#	SYM
fuelectenerg-1426	217	21	dk	dk	PROPN
fuelectenerg-1426	217	22	=(	=(	NOUN
fuelectenerg-1426	217	23	3)(k−1	3)(k−1	NUM
fuelectenerg-1426	217	24	)	)	PUNCT
fuelectenerg-1426	217	25	,	,	PUNCT
fuelectenerg-1426	217	26	(	(	PUNCT
fuelectenerg-1426	217	27	41	41	NUM
fuelectenerg-1426	217	28	)	)	PUNCT
fuelectenerg-1426	217	29	|dk|per	|dk|per	NOUN
fuelectenerg-1426	217	30	node	node	PROPN
fuelectenerg-1426	217	31	=(	=(	PROPN
fuelectenerg-1426	217	32	3)2(3)(n−k	3)2(3)(n−k	PROPN
fuelectenerg-1426	217	33	)	)	PUNCT
fuelectenerg-1426	217	34	,	,	PUNCT
fuelectenerg-1426	217	35	(	(	PUNCT
fuelectenerg-1426	217	36	42	42	NUM
fuelectenerg-1426	217	37	)	)	PUNCT
fuelectenerg-1426	217	38	where	where	SCONJ
fuelectenerg-1426	217	39	#	#	SYM
fuelectenerg-1426	217	40	dk	dk	NOUN
fuelectenerg-1426	217	41	is	be	AUX
fuelectenerg-1426	217	42	the	the	DET
fuelectenerg-1426	217	43	number	number	NOUN
fuelectenerg-1426	217	44	of	of	ADP
fuelectenerg-1426	217	45	d	d	ADJ
fuelectenerg-1426	217	46	-	-	PUNCT
fuelectenerg-1426	217	47	type	type	NOUN
fuelectenerg-1426	217	48	nodes	node	NOUN
fuelectenerg-1426	217	49	in	in	ADP
fuelectenerg-1426	217	50	k	k	PROPN
fuelectenerg-1426	217	51	level	level	NOUN
fuelectenerg-1426	217	52	,	,	PUNCT
fuelectenerg-1426	217	53	and	and	CCONJ
fuelectenerg-1426	217	54	|dk|	|dk|	NOUN
fuelectenerg-1426	217	55	is	be	AUX
fuelectenerg-1426	217	56	the	the	DET
fuelectenerg-1426	217	57	number	number	NOUN
fuelectenerg-1426	217	58	of	of	ADP
fuelectenerg-1426	217	59	all	all	DET
fuelectenerg-1426	217	60	possible	possible	ADJ
fuelectenerg-1426	217	61	forms	form	NOUN
fuelectenerg-1426	217	62	for	for	ADP
fuelectenerg-1426	217	63	the	the	DET
fuelectenerg-1426	217	64	d	d	ADJ
fuelectenerg-1426	217	65	-	-	PUNCT
fuelectenerg-1426	217	66	type	type	NOUN
fuelectenerg-1426	217	67	node	node	NOUN
fuelectenerg-1426	217	68	in	in	ADP
fuelectenerg-1426	217	69	the	the	DET
fuelectenerg-1426	217	70	k	k	PROPN
fuelectenerg-1426	217	71	level	level	NOUN
fuelectenerg-1426	217	72	.	.	PUNCT
fuelectenerg-1426	218	1	let	let	VERB
fuelectenerg-1426	218	2	us	we	PRON
fuelectenerg-1426	218	3	define	define	VERB
fuelectenerg-1426	218	4	s	s	NOUN
fuelectenerg-1426	218	5	/	/	SYM
fuelectenerg-1426	218	6	d	d	NOUN
fuelectenerg-1426	218	7	tree	tree	NOUN
fuelectenerg-1426	218	8	category	category	NOUN
fuelectenerg-1426	218	9	to	to	PART
fuelectenerg-1426	218	10	be	be	AUX
fuelectenerg-1426	218	11	the	the	DET
fuelectenerg-1426	218	12	s	s	PROPN
fuelectenerg-1426	218	13	/	/	SYM
fuelectenerg-1426	218	14	d	d	NOUN
fuelectenerg-1426	218	15	trees	tree	NOUN
fuelectenerg-1426	218	16	that	that	PRON
fuelectenerg-1426	218	17	have	have	VERB
fuelectenerg-1426	218	18	in	in	ADP
fuelectenerg-1426	218	19	common	common	ADJ
fuelectenerg-1426	218	20	the	the	DET
fuelectenerg-1426	218	21	same	same	ADJ
fuelectenerg-1426	218	22	number	number	NOUN
fuelectenerg-1426	218	23	of	of	ADP
fuelectenerg-1426	218	24	s	s	NOUN
fuelectenerg-1426	218	25	-	-	PUNCT
fuelectenerg-1426	218	26	type	type	NOUN
fuelectenerg-1426	218	27	nodes	node	NOUN
fuelectenerg-1426	218	28	and	and	CCONJ
fuelectenerg-1426	218	29	same	same	ADJ
fuelectenerg-1426	218	30	number	number	NOUN
fuelectenerg-1426	218	31	of	of	ADP
fuelectenerg-1426	218	32	111	111	NUM
fuelectenerg-1426	218	33	(	(	PUNCT
fuelectenerg-1426	218	34	a)2	a)2	PROPN
fuelectenerg-1426	218	35	(	(	PUNCT
fuelectenerg-1426	218	36	a)3	a)3	ADJ
fuelectenerg-1426	218	37	d	d	PROPN
fuelectenerg-1426	218	38	712	712	NUM
fuelectenerg-1426	218	39	a.	a.	NOUN
fuelectenerg-1426	218	40	n.	n.	PROPN
fuelectenerg-1426	218	41	al	al	PROPN
fuelectenerg-1426	218	42	-	-	PUNCT
fuelectenerg-1426	218	43	rabadi	rabadi	PROPN
fuelectenerg-1426	218	44	multi	multi	ADJ
fuelectenerg-1426	218	45	-	-	ADJ
fuelectenerg-1426	218	46	valued	value	VERB
fuelectenerg-1426	218	47	galois	galois	PROPN
fuelectenerg-1426	218	48	shannon	shannon	PROPN
fuelectenerg-1426	218	49	davio	davio	PROPN
fuelectenerg-1426	218	50	trees	tree	NOUN
fuelectenerg-1426	218	51	and	and	CCONJ
fuelectenerg-1426	218	52	their	their	PRON
fuelectenerg-1426	218	53	complexity	complexity	NOUN
fuelectenerg-1426	218	54	713	713	NUM
fuelectenerg-1426	218	55	multi	multi	ADJ
fuelectenerg-1426	218	56	-	-	ADJ
fuelectenerg-1426	218	57	valued	value	VERB
fuelectenerg-1426	218	58	galois	galois	PROPN
fuelectenerg-1426	218	59	shannon	shannon	PROPN
fuelectenerg-1426	218	60	davio	davio	PROPN
fuelectenerg-1426	218	61	trees	tree	NOUN
fuelectenerg-1426	218	62	and	and	CCONJ
fuelectenerg-1426	218	63	their	their	PRON
fuelectenerg-1426	218	64	complexity	complexity	NOUN
fuelectenerg-1426	218	65	d	d	NOUN
fuelectenerg-1426	218	66	-	-	PUNCT
fuelectenerg-1426	218	67	type	type	NOUN
fuelectenerg-1426	218	68	nodes	node	NOUN
fuelectenerg-1426	218	69	within	within	ADP
fuelectenerg-1426	218	70	the	the	DET
fuelectenerg-1426	218	71	same	same	ADJ
fuelectenerg-1426	218	72	variable	variable	ADJ
fuelectenerg-1426	218	73	order	order	NOUN
fuelectenerg-1426	218	74	.	.	PUNCT
fuelectenerg-1426	219	1	also	also	ADV
fuelectenerg-1426	219	2	,	,	PUNCT
fuelectenerg-1426	219	3	define	define	VERB
fuelectenerg-1426	219	4	:	:	PUNCT
fuelectenerg-1426	219	5	ψ	ψ	X
fuelectenerg-1426	219	6	≡	≡	ADJ
fuelectenerg-1426	219	7	number	number	NOUN
fuelectenerg-1426	219	8	of	of	ADP
fuelectenerg-1426	219	9	variable	variable	ADJ
fuelectenerg-1426	219	10	orders	order	NOUN
fuelectenerg-1426	219	11	,	,	PUNCT
fuelectenerg-1426	219	12	(	(	PUNCT
fuelectenerg-1426	219	13	43	43	NUM
fuelectenerg-1426	219	14	)	)	PUNCT
fuelectenerg-1426	219	15	ω	ω	PROPN
fuelectenerg-1426	219	16	≡	≡	ADJ
fuelectenerg-1426	219	17	number	number	NOUN
fuelectenerg-1426	219	18	of	of	ADP
fuelectenerg-1426	219	19	s	s	PROPN
fuelectenerg-1426	219	20	/	/	SYM
fuelectenerg-1426	219	21	d	d	NOUN
fuelectenerg-1426	219	22	tree	tree	NOUN
fuelectenerg-1426	219	23	categories	category	NOUN
fuelectenerg-1426	219	24	per	per	ADP
fuelectenerg-1426	219	25	variable	variable	ADJ
fuelectenerg-1426	219	26	order	order	NOUN
fuelectenerg-1426	219	27	,	,	PUNCT
fuelectenerg-1426	219	28	(	(	PUNCT
fuelectenerg-1426	219	29	44	44	NUM
fuelectenerg-1426	219	30	)	)	PUNCT
fuelectenerg-1426	219	31	φ	φ	PROPN
fuelectenerg-1426	219	32	≡	≡	PROPN
fuelectenerg-1426	219	33	number	number	NOUN
fuelectenerg-1426	219	34	of	of	ADP
fuelectenerg-1426	219	35	s	s	PROPN
fuelectenerg-1426	219	36	/	/	SYM
fuelectenerg-1426	219	37	d	d	NOUN
fuelectenerg-1426	219	38	trees	tree	NOUN
fuelectenerg-1426	219	39	per	per	ADP
fuelectenerg-1426	219	40	category	category	NOUN
fuelectenerg-1426	219	41	,	,	PUNCT
fuelectenerg-1426	219	42	(	(	PUNCT
fuelectenerg-1426	219	43	45	45	NUM
fuelectenerg-1426	219	44	)	)	PUNCT
fuelectenerg-1426	219	45	φ	φ	PROPN
fuelectenerg-1426	219	46	≡	≡	PROPN
fuelectenerg-1426	219	47	number	number	NOUN
fuelectenerg-1426	219	48	of	of	ADP
fuelectenerg-1426	219	49	tifs	tifs	PROPN
fuelectenerg-1426	219	50	per	per	ADP
fuelectenerg-1426	219	51	variable	variable	ADJ
fuelectenerg-1426	219	52	order	order	NOUN
fuelectenerg-1426	219	53	.	.	PUNCT
fuelectenerg-1426	220	1	(	(	PUNCT
fuelectenerg-1426	220	2	46	46	NUM
fuelectenerg-1426	220	3	)	)	PUNCT
fuelectenerg-1426	220	4	from	from	ADP
fuelectenerg-1426	220	5	equations	equation	NOUN
fuelectenerg-1426	220	6	(	(	PUNCT
fuelectenerg-1426	220	7	39	39	NUM
fuelectenerg-1426	220	8	)	)	PUNCT
fuelectenerg-1426	220	9	(	(	PUNCT
fuelectenerg-1426	220	10	42	42	NUM
fuelectenerg-1426	220	11	)	)	PUNCT
fuelectenerg-1426	220	12	,	,	PUNCT
fuelectenerg-1426	220	13	and	and	CCONJ
fuelectenerg-1426	220	14	using	use	VERB
fuelectenerg-1426	220	15	some	some	DET
fuelectenerg-1426	220	16	elementary	elementary	ADJ
fuelectenerg-1426	220	17	count	count	NOUN
fuelectenerg-1426	220	18	rules	rule	NOUN
fuelectenerg-1426	220	19	,	,	PUNCT
fuelectenerg-1426	220	20	we	we	PRON
fuelectenerg-1426	220	21	can	can	AUX
fuelectenerg-1426	220	22	derive	derive	VERB
fuelectenerg-1426	220	23	by	by	ADP
fuelectenerg-1426	220	24	mathematical	mathematical	ADJ
fuelectenerg-1426	220	25	induction	induction	NOUN
fuelectenerg-1426	220	26	the	the	DET
fuelectenerg-1426	220	27	following	follow	VERB
fuelectenerg-1426	220	28	general	general	ADJ
fuelectenerg-1426	220	29	formulas	formula	NOUN
fuelectenerg-1426	220	30	for	for	ADP
fuelectenerg-1426	220	31	n	n	PRON
fuelectenerg-1426	220	32	being	be	AUX
fuelectenerg-1426	220	33	the	the	DET
fuelectenerg-1426	220	34	number	number	NOUN
fuelectenerg-1426	220	35	of	of	ADP
fuelectenerg-1426	220	36	variables	variable	NOUN
fuelectenerg-1426	220	37	:	:	PUNCT
fuelectenerg-1426	220	38	ψ	ψ	X
fuelectenerg-1426	220	39	=	=	X
fuelectenerg-1426	220	40	n	n	X
fuelectenerg-1426	220	41	!	!	NUM
fuelectenerg-1426	220	42	,	,	PUNCT
fuelectenerg-1426	220	43	(	(	PUNCT
fuelectenerg-1426	220	44	47	47	NUM
fuelectenerg-1426	220	45	)	)	PUNCT
fuelectenerg-1426	220	46	ω	ω	PROPN
fuelectenerg-1426	221	1	=	=	SYM
fuelectenerg-1426	221	2	n−1	n−1	PROPN
fuelectenerg-1426	221	3	∑	∑	ADP
fuelectenerg-1426	221	4	k=0	k=0	PROPN
fuelectenerg-1426	221	5	(	(	PUNCT
fuelectenerg-1426	221	6	3)k	3)k	NUM
fuelectenerg-1426	221	7	+1	+1	PROPN
fuelectenerg-1426	221	8	,	,	PUNCT
fuelectenerg-1426	221	9	(	(	PUNCT
fuelectenerg-1426	221	10	48	48	NUM
fuelectenerg-1426	221	11	)	)	PUNCT
fuelectenerg-1426	221	12	φ	φ	NOUN
fuelectenerg-1426	221	13	=	=	PUNCT
fuelectenerg-1426	222	1	[	[	X
fuelectenerg-1426	222	2	∑n−1	∑n−1	ADP
fuelectenerg-1426	222	3	k=0	k=0	PROPN
fuelectenerg-1426	222	4	(	(	PUNCT
fuelectenerg-1426	222	5	3	3	X
fuelectenerg-1426	222	6	)	)	PUNCT
fuelectenerg-1426	222	7	k	k	NOUN
fuelectenerg-1426	222	8	]	]	X
fuelectenerg-1426	222	9	!	!	PUNCT
fuelectenerg-1426	223	1	[	[	X
fuelectenerg-1426	223	2	∑n−1	∑n−1	X
fuelectenerg-1426	223	3	k=0	k=0	PROPN
fuelectenerg-1426	223	4	(	(	PUNCT
fuelectenerg-1426	223	5	3)k	3)k	NUM
fuelectenerg-1426	223	6	−	−	PROPN
fuelectenerg-1426	223	7	k]!k	k]!k	PROPN
fuelectenerg-1426	223	8	!	!	PUNCT
fuelectenerg-1426	223	9	,	,	PUNCT
fuelectenerg-1426	223	10	where	where	SCONJ
fuelectenerg-1426	223	11	k	k	NOUN
fuelectenerg-1426	223	12	=	=	PUNCT
fuelectenerg-1426	223	13	0,1,2,3	0,1,2,3	NUM
fuelectenerg-1426	223	14	,	,	PUNCT
fuelectenerg-1426	223	15	.	.	PUNCT
fuelectenerg-1426	223	16	.	.	PUNCT
fuelectenerg-1426	224	1	.	.	PUNCT
fuelectenerg-1426	225	1	,	,	PUNCT
fuelectenerg-1426	225	2	n−1	n−1	PROPN
fuelectenerg-1426	225	3	∑	∑	PUNCT
fuelectenerg-1426	225	4	k=0	k=0	PROPN
fuelectenerg-1426	225	5	(	(	PUNCT
fuelectenerg-1426	225	6	3)k	3)k	ADV
fuelectenerg-1426	225	7	,	,	PUNCT
fuelectenerg-1426	225	8	(	(	PUNCT
fuelectenerg-1426	225	9	49	49	NUM
fuelectenerg-1426	225	10	)	)	PUNCT
fuelectenerg-1426	225	11	φ	φ	NOUN
fuelectenerg-1426	225	12	=	=	SYM
fuelectenerg-1426	225	13	(	(	PUNCT
fuelectenerg-1426	225	14	3)n−1	3)n−1	PROPN
fuelectenerg-1426	225	15	∑	∑	PROPN
fuelectenerg-1426	225	16	k1=0	k1=0	PROPN
fuelectenerg-1426	225	17	(	(	PUNCT
fuelectenerg-1426	225	18	3)n−2	3)n−2	NUM
fuelectenerg-1426	225	19	∑	∑	PUNCT
fuelectenerg-1426	225	20	k2=0	k2=0	PROPN
fuelectenerg-1426	225	21	(	(	PUNCT
fuelectenerg-1426	225	22	3)n−3	3)n−3	NUM
fuelectenerg-1426	225	23	∑	∑	SYM
fuelectenerg-1426	225	24	k3=0	k3=0	PROPN
fuelectenerg-1426	225	25	·	·	PUNCT
fuelectenerg-1426	225	26	·	·	PUNCT
fuelectenerg-1426	225	27	·	·	PUNCT
fuelectenerg-1426	226	1	(	(	PUNCT
fuelectenerg-1426	226	2	3)0	3)0	NUM
fuelectenerg-1426	226	3	∑	∑	PUNCT
fuelectenerg-1426	226	4	kn=0	kn=0	X
fuelectenerg-1426	226	5	{	{	PUNCT
fuelectenerg-1426	226	6	[	[	PUNCT
fuelectenerg-1426	226	7	3(n−1	3(n−1	NOUN
fuelectenerg-1426	226	8	)	)	PUNCT
fuelectenerg-1426	226	9	!	!	PUNCT
fuelectenerg-1426	227	1	(	(	PUNCT
fuelectenerg-1426	227	2	3(n−1)−	3(n−1)−	NOUN
fuelectenerg-1426	227	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	227	4	!	!	PUNCT
fuelectenerg-1426	228	1	3(n−2	3(n−2	NUM
fuelectenerg-1426	228	2	)	)	PUNCT
fuelectenerg-1426	228	3	!	!	PUNCT
fuelectenerg-1426	229	1	(	(	PUNCT
fuelectenerg-1426	229	2	3(n−2)−	3(n−2)−	ADJ
fuelectenerg-1426	229	3	k2)!k2	k2)!k2	PROPN
fuelectenerg-1426	229	4	!	!	PUNCT
fuelectenerg-1426	229	5	3(n−3	3(n−3	NUM
fuelectenerg-1426	229	6	)	)	PUNCT
fuelectenerg-1426	229	7	!	!	PUNCT
fuelectenerg-1426	230	1	(	(	PUNCT
fuelectenerg-1426	230	2	3(n−3)−	3(n−3)−	PROPN
fuelectenerg-1426	230	3	k3)!k3	k3)!k3	PROPN
fuelectenerg-1426	230	4	!	!	PUNCT
fuelectenerg-1426	230	5	·	·	PUNCT
fuelectenerg-1426	230	6	·	·	PUNCT
fuelectenerg-1426	230	7	·	·	PUNCT
fuelectenerg-1426	231	1	3(0	3(0	NUM
fuelectenerg-1426	231	2	)	)	PUNCT
fuelectenerg-1426	231	3	!	!	PUNCT
fuelectenerg-1426	232	1	(	(	PUNCT
fuelectenerg-1426	232	2	3(0)−	3(0)−	NUM
fuelectenerg-1426	232	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	232	4	!	!	PUNCT
fuelectenerg-1426	233	1	]	]	PUNCT
fuelectenerg-1426	233	2	[	[	PUNCT
fuelectenerg-1426	233	3	(	(	PUNCT
fuelectenerg-1426	233	4	32(3)0	32(3)0	NUM
fuelectenerg-1426	233	5	)	)	PUNCT
fuelectenerg-1426	233	6	k1(32(3)1	k1(32(3)1	NOUN
fuelectenerg-1426	233	7	)	)	PUNCT
fuelectenerg-1426	233	8	k2(32(3)2	k2(32(3)2	PROPN
fuelectenerg-1426	233	9	)	)	PUNCT
fuelectenerg-1426	233	10	k3	k3	PROPN
fuelectenerg-1426	233	11	·	·	PUNCT
fuelectenerg-1426	233	12	·	·	PUNCT
fuelectenerg-1426	233	13	·	·	PUNCT
fuelectenerg-1426	233	14	(	(	PUNCT
fuelectenerg-1426	233	15	32(3)(n−1	32(3)(n−1	NUM
fuelectenerg-1426	233	16	)	)	PUNCT
fuelectenerg-1426	233	17	)	)	PUNCT
fuelectenerg-1426	234	1	kn	kn	NOUN
fuelectenerg-1426	234	2	]	]	PUNCT
fuelectenerg-1426	234	3	}	}	PUNCT
fuelectenerg-1426	234	4	.	.	PUNCT
fuelectenerg-1426	235	1	(	(	PUNCT
fuelectenerg-1426	235	2	50	50	NUM
fuelectenerg-1426	235	3	)	)	PUNCT
fuelectenerg-1426	235	4	from	from	ADP
fuelectenerg-1426	235	5	equations	equation	NOUN
fuelectenerg-1426	235	6	(	(	PUNCT
fuelectenerg-1426	235	7	47	47	NUM
fuelectenerg-1426	235	8	)	)	PUNCT
fuelectenerg-1426	235	9	(	(	PUNCT
fuelectenerg-1426	235	10	50	50	NUM
fuelectenerg-1426	235	11	)	)	PUNCT
fuelectenerg-1426	235	12	,	,	PUNCT
fuelectenerg-1426	235	13	it	it	PRON
fuelectenerg-1426	235	14	can	can	AUX
fuelectenerg-1426	235	15	be	be	AUX
fuelectenerg-1426	235	16	noticed	notice	VERB
fuelectenerg-1426	235	17	that	that	SCONJ
fuelectenerg-1426	235	18	the	the	DET
fuelectenerg-1426	235	19	total	total	ADJ
fuelectenerg-1426	235	20	number	number	NOUN
fuelectenerg-1426	235	21	of	of	ADP
fuelectenerg-1426	235	22	tifs	tifs	PROPN
fuelectenerg-1426	235	23	for	for	ADP
fuelectenerg-1426	235	24	all	all	DET
fuelectenerg-1426	235	25	variable	variable	ADJ
fuelectenerg-1426	235	26	orders	order	NOUN
fuelectenerg-1426	235	27	is	be	AUX
fuelectenerg-1426	235	28	equal	equal	ADJ
fuelectenerg-1426	235	29	to	to	ADP
fuelectenerg-1426	235	30	[	[	X
fuelectenerg-1426	235	31	n!][#tifs	n!][#tif	NOUN
fuelectenerg-1426	235	32	per	per	ADP
fuelectenerg-1426	235	33	order	order	NOUN
fuelectenerg-1426	235	34	]	]	PUNCT
fuelectenerg-1426	235	35	.	.	PUNCT
fuelectenerg-1426	236	1	example	example	NOUN
fuelectenerg-1426	237	1	4	4	NUM
fuelectenerg-1426	237	2	.	.	X
fuelectenerg-1426	238	1	for	for	ADP
fuelectenerg-1426	238	2	number	number	NOUN
fuelectenerg-1426	238	3	of	of	ADP
fuelectenerg-1426	238	4	variables	variable	NOUN
fuelectenerg-1426	238	5	equal	equal	ADJ
fuelectenerg-1426	238	6	to	to	ADP
fuelectenerg-1426	238	7	two	two	NUM
fuelectenerg-1426	238	8	(	(	PUNCT
fuelectenerg-1426	238	9	n	n	NOUN
fuelectenerg-1426	238	10	=	=	SYM
fuelectenerg-1426	238	11	2	2	NUM
fuelectenerg-1426	238	12	)	)	PUNCT
fuelectenerg-1426	238	13	,	,	PUNCT
fuelectenerg-1426	238	14	φ	φ	PROPN
fuelectenerg-1426	238	15	reduces	reduce	VERB
fuelectenerg-1426	238	16	to	to	ADP
fuelectenerg-1426	238	17	:	:	PUNCT
fuelectenerg-1426	238	18	φ	φ	PROPN
fuelectenerg-1426	238	19	=	=	SYM
fuelectenerg-1426	238	20	(	(	PUNCT
fuelectenerg-1426	238	21	3)1	3)1	NUM
fuelectenerg-1426	238	22	∑	∑	PUNCT
fuelectenerg-1426	238	23	k1=0	k1=0	PROPN
fuelectenerg-1426	238	24	1	1	NUM
fuelectenerg-1426	238	25	∑	∑	ADP
fuelectenerg-1426	238	26	k2=0	k2=0	PROPN
fuelectenerg-1426	238	27	{	{	PUNCT
fuelectenerg-1426	238	28	31	31	NUM
fuelectenerg-1426	238	29	!	!	PUNCT
fuelectenerg-1426	239	1	(	(	PUNCT
fuelectenerg-1426	239	2	31	31	NUM
fuelectenerg-1426	239	3	−	−	PROPN
fuelectenerg-1426	239	4	k1)!k1	k1)!k1	PROPN
fuelectenerg-1426	239	5	!	!	PUNCT
fuelectenerg-1426	239	6	30	30	NUM
fuelectenerg-1426	239	7	!	!	PUNCT
fuelectenerg-1426	240	1	(	(	PUNCT
fuelectenerg-1426	240	2	30	30	NUM
fuelectenerg-1426	240	3	−	−	NOUN
fuelectenerg-1426	240	4	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	240	5	!	!	PUNCT
fuelectenerg-1426	241	1	(	(	PUNCT
fuelectenerg-1426	241	2	32(3)0	32(3)0	NUM
fuelectenerg-1426	241	3	)	)	PUNCT
fuelectenerg-1426	241	4	k1(32(3)1	k1(32(3)1	PROPN
fuelectenerg-1426	241	5	)	)	PUNCT
fuelectenerg-1426	241	6	k2	k2	PROPN
fuelectenerg-1426	241	7	}	}	PUNCT
fuelectenerg-1426	241	8	φ	φ	PROPN
fuelectenerg-1426	241	9	=	=	SYM
fuelectenerg-1426	241	10	φ|k1=0,k2=0	φ|k1=0,k2=0	PROPN
fuelectenerg-1426	242	1	+	+	X
fuelectenerg-1426	242	2	φ|k1=1,k2=0	φ|k1=1,k2=0	X
fuelectenerg-1426	242	3	+	+	ADJ
fuelectenerg-1426	242	4	φ|k1=2,k2=0	φ|k1=2,k2=0	ADJ
fuelectenerg-1426	242	5	+	+	ADJ
fuelectenerg-1426	242	6	φ|k1=3,k2=0	φ|k1=3,k2=0	X
fuelectenerg-1426	242	7	+	+	ADJ
fuelectenerg-1426	242	8	φ|k1=0,k2=1	φ|k1=0,k2=1	ADJ
fuelectenerg-1426	242	9	+	+	ADJ
fuelectenerg-1426	242	10	φ|k1=1,k2=1	φ|k1=1,k2=1	PROPN
fuelectenerg-1426	242	11	+	+	NOUN
fuelectenerg-1426	242	12	φ|k1=2,k2=1	φ|k1=2,k2=1	PROPN
fuelectenerg-1426	242	13	+	+	ADJ
fuelectenerg-1426	242	14	φ|k1=3,k2=1	φ|k1=3,k2=1	NUM
fuelectenerg-1426	242	15	=	=	ADJ
fuelectenerg-1426	242	16	φ00	φ00	NOUN
fuelectenerg-1426	242	17	+	+	NOUN
fuelectenerg-1426	242	18	φ10	φ10	NOUN
fuelectenerg-1426	243	1	+	+	NOUN
fuelectenerg-1426	243	2	φ20	φ20	NOUN
fuelectenerg-1426	243	3	+	+	NOUN
fuelectenerg-1426	243	4	φ30	φ30	NOUN
fuelectenerg-1426	243	5	+	+	NOUN
fuelectenerg-1426	243	6	φ01	φ01	NOUN
fuelectenerg-1426	243	7	+	+	NOUN
fuelectenerg-1426	243	8	φ11	φ11	ADJ
fuelectenerg-1426	243	9	+	+	ADJ
fuelectenerg-1426	243	10	φ21	φ21	NOUN
fuelectenerg-1426	243	11	+	+	ADV
fuelectenerg-1426	243	12	φ31	φ31	ADJ
fuelectenerg-1426	243	13	=	=	NOUN
fuelectenerg-1426	243	14	1	1	NUM
fuelectenerg-1426	243	15	+	+	NUM
fuelectenerg-1426	243	16	27	27	NUM
fuelectenerg-1426	243	17	+	+	NUM
fuelectenerg-1426	243	18	243	243	NUM
fuelectenerg-1426	244	1	+	+	NOUN
fuelectenerg-1426	244	2	729	729	NUM
fuelectenerg-1426	244	3	+	+	ADJ
fuelectenerg-1426	244	4	729	729	NUM
fuelectenerg-1426	244	5	+	+	NOUN
fuelectenerg-1426	244	6	19683	19683	NUM
fuelectenerg-1426	244	7	+	+	ADJ
fuelectenerg-1426	244	8	177147	177147	NUM
fuelectenerg-1426	244	9	+	+	ADJ
fuelectenerg-1426	244	10	531441=	531441=	NUM
fuelectenerg-1426	244	11	730,000	730,000	NUM
fuelectenerg-1426	244	12	.	.	PUNCT
fuelectenerg-1426	245	1	utilizing	utilize	VERB
fuelectenerg-1426	245	2	multi	multi	ADJ
fuelectenerg-1426	245	3	-	-	ADJ
fuelectenerg-1426	245	4	valued	value	VERB
fuelectenerg-1426	245	5	map	map	NOUN
fuelectenerg-1426	245	6	representation	representation	NOUN
fuelectenerg-1426	245	7	,	,	PUNCT
fuelectenerg-1426	245	8	there	there	PRON
fuelectenerg-1426	245	9	are	be	VERB
fuelectenerg-1426	245	10	n#minterms	n#minterm	NOUN
fuelectenerg-1426	245	11	different	different	ADJ
fuelectenerg-1426	245	12	functions	function	NOUN
fuelectenerg-1426	245	13	for	for	ADP
fuelectenerg-1426	245	14	n	n	ADV
fuelectenerg-1426	245	15	-	-	PUNCT
fuelectenerg-1426	245	16	valued	value	VERB
fuelectenerg-1426	245	17	input	input	NOUN
fuelectenerg-1426	245	18	-	-	PUNCT
fuelectenerg-1426	245	19	output	output	NOUN
fuelectenerg-1426	245	20	logic	logic	NOUN
fuelectenerg-1426	245	21	.	.	PUNCT
fuelectenerg-1426	246	1	therefore	therefore	ADV
fuelectenerg-1426	246	2	,	,	PUNCT
fuelectenerg-1426	246	3	for	for	ADP
fuelectenerg-1426	246	4	ternary	ternary	ADJ
fuelectenerg-1426	246	5	logic	logic	NOUN
fuelectenerg-1426	246	6	,	,	PUNCT
fuelectenerg-1426	246	7	there	there	PRON
fuelectenerg-1426	246	8	are	be	VERB
fuelectenerg-1426	246	9	39	39	NUM
fuelectenerg-1426	246	10	=	=	SYM
fuelectenerg-1426	246	11	19,683	19,683	NUM
fuelectenerg-1426	246	12	different	different	ADJ
fuelectenerg-1426	246	13	ternary	ternary	ADJ
fuelectenerg-1426	246	14	functions	function	NOUN
fuelectenerg-1426	246	15	of	of	ADP
fuelectenerg-1426	246	16	two	two	NUM
fuelectenerg-1426	246	17	variables	variable	NOUN
fuelectenerg-1426	246	18	,	,	PUNCT
fuelectenerg-1426	246	19	and	and	CCONJ
fuelectenerg-1426	246	20	730,000	730,000	NUM
fuelectenerg-1426	246	21	ternary	ternary	ADJ
fuelectenerg-1426	246	22	inclusive	inclusive	ADJ
fuelectenerg-1426	246	23	forms	form	NOUN
fuelectenerg-1426	246	24	generated	generate	VERB
fuelectenerg-1426	246	25	by	by	ADP
fuelectenerg-1426	246	26	the	the	DET
fuelectenerg-1426	246	27	s	s	PROPN
fuelectenerg-1426	246	28	/	/	SYM
fuelectenerg-1426	246	29	d	d	NOUN
fuelectenerg-1426	246	30	trees	tree	NOUN
fuelectenerg-1426	246	31	.	.	PUNCT
fuelectenerg-1426	247	1	thus	thus	ADV
fuelectenerg-1426	247	2	,	,	PUNCT
fuelectenerg-1426	247	3	on	on	ADP
fuelectenerg-1426	247	4	the	the	DET
fuelectenerg-1426	247	5	average	average	ADJ
fuelectenerg-1426	247	6	every	every	DET
fuelectenerg-1426	247	7	function	function	NOUN
fuelectenerg-1426	247	8	of	of	ADP
fuelectenerg-1426	247	9	two	two	NUM
fuelectenerg-1426	247	10	variables	variable	NOUN
fuelectenerg-1426	247	11	can	can	AUX
fuelectenerg-1426	247	12	be	be	AUX
fuelectenerg-1426	247	13	realized	realize	VERB
fuelectenerg-1426	247	14	in	in	ADP
fuelectenerg-1426	247	15	approximately	approximately	ADV
fuelectenerg-1426	247	16	37	37	NUM
fuelectenerg-1426	247	17	ways	way	NOUN
fuelectenerg-1426	247	18	.	.	PUNCT
fuelectenerg-1426	248	1	112	112	NUM
fuelectenerg-1426	248	2	712	712	NUM
fuelectenerg-1426	248	3	a.	a.	NOUN
fuelectenerg-1426	248	4	n.	n.	PROPN
fuelectenerg-1426	248	5	al	al	PROPN
fuelectenerg-1426	248	6	-	-	PUNCT
fuelectenerg-1426	248	7	rabadi	rabadi	PROPN
fuelectenerg-1426	248	8	multi	multi	ADJ
fuelectenerg-1426	248	9	-	-	ADJ
fuelectenerg-1426	248	10	valued	value	VERB
fuelectenerg-1426	248	11	galois	galois	PROPN
fuelectenerg-1426	248	12	shannon	shannon	PROPN
fuelectenerg-1426	248	13	davio	davio	PROPN
fuelectenerg-1426	248	14	trees	tree	NOUN
fuelectenerg-1426	248	15	and	and	CCONJ
fuelectenerg-1426	248	16	their	their	PRON
fuelectenerg-1426	248	17	complexity	complexity	NOUN
fuelectenerg-1426	248	18	713	713	NUM
fuelectenerg-1426	248	19	multi	multi	ADJ
fuelectenerg-1426	248	20	-	-	ADJ
fuelectenerg-1426	248	21	valued	value	VERB
fuelectenerg-1426	248	22	galois	galois	PROPN
fuelectenerg-1426	248	23	shannon	shannon	PROPN
fuelectenerg-1426	248	24	davio	davio	PROPN
fuelectenerg-1426	248	25	trees	tree	NOUN
fuelectenerg-1426	248	26	and	and	CCONJ
fuelectenerg-1426	248	27	their	their	PRON
fuelectenerg-1426	248	28	complexity	complexity	NOUN
fuelectenerg-1426	248	29	d	d	NOUN
fuelectenerg-1426	248	30	-	-	PUNCT
fuelectenerg-1426	248	31	type	type	NOUN
fuelectenerg-1426	248	32	nodes	node	NOUN
fuelectenerg-1426	248	33	within	within	ADP
fuelectenerg-1426	248	34	the	the	DET
fuelectenerg-1426	248	35	same	same	ADJ
fuelectenerg-1426	248	36	variable	variable	ADJ
fuelectenerg-1426	248	37	order	order	NOUN
fuelectenerg-1426	248	38	.	.	PUNCT
fuelectenerg-1426	249	1	also	also	ADV
fuelectenerg-1426	249	2	,	,	PUNCT
fuelectenerg-1426	249	3	define	define	VERB
fuelectenerg-1426	249	4	:	:	PUNCT
fuelectenerg-1426	249	5	ψ	ψ	X
fuelectenerg-1426	249	6	≡	≡	ADJ
fuelectenerg-1426	249	7	number	number	NOUN
fuelectenerg-1426	249	8	of	of	ADP
fuelectenerg-1426	249	9	variable	variable	ADJ
fuelectenerg-1426	249	10	orders	order	NOUN
fuelectenerg-1426	249	11	,	,	PUNCT
fuelectenerg-1426	249	12	(	(	PUNCT
fuelectenerg-1426	249	13	43	43	NUM
fuelectenerg-1426	249	14	)	)	PUNCT
fuelectenerg-1426	249	15	ω	ω	PROPN
fuelectenerg-1426	249	16	≡	≡	ADJ
fuelectenerg-1426	249	17	number	number	NOUN
fuelectenerg-1426	249	18	of	of	ADP
fuelectenerg-1426	249	19	s	s	PROPN
fuelectenerg-1426	249	20	/	/	SYM
fuelectenerg-1426	249	21	d	d	NOUN
fuelectenerg-1426	249	22	tree	tree	NOUN
fuelectenerg-1426	249	23	categories	category	NOUN
fuelectenerg-1426	249	24	per	per	ADP
fuelectenerg-1426	249	25	variable	variable	ADJ
fuelectenerg-1426	249	26	order	order	NOUN
fuelectenerg-1426	249	27	,	,	PUNCT
fuelectenerg-1426	249	28	(	(	PUNCT
fuelectenerg-1426	249	29	44	44	NUM
fuelectenerg-1426	249	30	)	)	PUNCT
fuelectenerg-1426	249	31	φ	φ	PROPN
fuelectenerg-1426	249	32	≡	≡	PROPN
fuelectenerg-1426	249	33	number	number	NOUN
fuelectenerg-1426	249	34	of	of	ADP
fuelectenerg-1426	249	35	s	s	PROPN
fuelectenerg-1426	249	36	/	/	SYM
fuelectenerg-1426	249	37	d	d	NOUN
fuelectenerg-1426	249	38	trees	tree	NOUN
fuelectenerg-1426	249	39	per	per	ADP
fuelectenerg-1426	249	40	category	category	NOUN
fuelectenerg-1426	249	41	,	,	PUNCT
fuelectenerg-1426	249	42	(	(	PUNCT
fuelectenerg-1426	249	43	45	45	NUM
fuelectenerg-1426	249	44	)	)	PUNCT
fuelectenerg-1426	249	45	φ	φ	PROPN
fuelectenerg-1426	249	46	≡	≡	PROPN
fuelectenerg-1426	249	47	number	number	NOUN
fuelectenerg-1426	249	48	of	of	ADP
fuelectenerg-1426	249	49	tifs	tifs	PROPN
fuelectenerg-1426	249	50	per	per	ADP
fuelectenerg-1426	249	51	variable	variable	ADJ
fuelectenerg-1426	249	52	order	order	NOUN
fuelectenerg-1426	249	53	.	.	PUNCT
fuelectenerg-1426	250	1	(	(	PUNCT
fuelectenerg-1426	250	2	46	46	NUM
fuelectenerg-1426	250	3	)	)	PUNCT
fuelectenerg-1426	250	4	from	from	ADP
fuelectenerg-1426	250	5	equations	equation	NOUN
fuelectenerg-1426	250	6	(	(	PUNCT
fuelectenerg-1426	250	7	39	39	NUM
fuelectenerg-1426	250	8	)	)	PUNCT
fuelectenerg-1426	250	9	(	(	PUNCT
fuelectenerg-1426	250	10	42	42	NUM
fuelectenerg-1426	250	11	)	)	PUNCT
fuelectenerg-1426	250	12	,	,	PUNCT
fuelectenerg-1426	250	13	and	and	CCONJ
fuelectenerg-1426	250	14	using	use	VERB
fuelectenerg-1426	250	15	some	some	DET
fuelectenerg-1426	250	16	elementary	elementary	ADJ
fuelectenerg-1426	250	17	count	count	NOUN
fuelectenerg-1426	250	18	rules	rule	NOUN
fuelectenerg-1426	250	19	,	,	PUNCT
fuelectenerg-1426	250	20	we	we	PRON
fuelectenerg-1426	250	21	can	can	AUX
fuelectenerg-1426	250	22	derive	derive	VERB
fuelectenerg-1426	250	23	by	by	ADP
fuelectenerg-1426	250	24	mathematical	mathematical	ADJ
fuelectenerg-1426	250	25	induction	induction	NOUN
fuelectenerg-1426	250	26	the	the	DET
fuelectenerg-1426	250	27	following	follow	VERB
fuelectenerg-1426	250	28	general	general	ADJ
fuelectenerg-1426	250	29	formulas	formula	NOUN
fuelectenerg-1426	250	30	for	for	ADP
fuelectenerg-1426	250	31	n	n	PRON
fuelectenerg-1426	250	32	being	be	AUX
fuelectenerg-1426	250	33	the	the	DET
fuelectenerg-1426	250	34	number	number	NOUN
fuelectenerg-1426	250	35	of	of	ADP
fuelectenerg-1426	250	36	variables	variable	NOUN
fuelectenerg-1426	250	37	:	:	PUNCT
fuelectenerg-1426	250	38	ψ	ψ	X
fuelectenerg-1426	250	39	=	=	X
fuelectenerg-1426	250	40	n	n	X
fuelectenerg-1426	250	41	!	!	NUM
fuelectenerg-1426	250	42	,	,	PUNCT
fuelectenerg-1426	250	43	(	(	PUNCT
fuelectenerg-1426	250	44	47	47	NUM
fuelectenerg-1426	250	45	)	)	PUNCT
fuelectenerg-1426	250	46	ω	ω	PROPN
fuelectenerg-1426	251	1	=	=	SYM
fuelectenerg-1426	251	2	n−1	n−1	PROPN
fuelectenerg-1426	251	3	∑	∑	ADP
fuelectenerg-1426	251	4	k=0	k=0	PROPN
fuelectenerg-1426	251	5	(	(	PUNCT
fuelectenerg-1426	251	6	3)k	3)k	NUM
fuelectenerg-1426	251	7	+1	+1	PROPN
fuelectenerg-1426	251	8	,	,	PUNCT
fuelectenerg-1426	251	9	(	(	PUNCT
fuelectenerg-1426	251	10	48	48	NUM
fuelectenerg-1426	251	11	)	)	PUNCT
fuelectenerg-1426	251	12	φ	φ	NOUN
fuelectenerg-1426	251	13	=	=	PUNCT
fuelectenerg-1426	252	1	[	[	X
fuelectenerg-1426	252	2	∑n−1	∑n−1	ADP
fuelectenerg-1426	252	3	k=0	k=0	PROPN
fuelectenerg-1426	252	4	(	(	PUNCT
fuelectenerg-1426	252	5	3	3	X
fuelectenerg-1426	252	6	)	)	PUNCT
fuelectenerg-1426	252	7	k	k	NOUN
fuelectenerg-1426	252	8	]	]	X
fuelectenerg-1426	252	9	!	!	PUNCT
fuelectenerg-1426	253	1	[	[	X
fuelectenerg-1426	253	2	∑n−1	∑n−1	X
fuelectenerg-1426	253	3	k=0	k=0	PROPN
fuelectenerg-1426	253	4	(	(	PUNCT
fuelectenerg-1426	253	5	3)k	3)k	NUM
fuelectenerg-1426	253	6	−	−	PROPN
fuelectenerg-1426	253	7	k]!k	k]!k	PROPN
fuelectenerg-1426	253	8	!	!	PUNCT
fuelectenerg-1426	253	9	,	,	PUNCT
fuelectenerg-1426	253	10	where	where	SCONJ
fuelectenerg-1426	253	11	k	k	NOUN
fuelectenerg-1426	253	12	=	=	PUNCT
fuelectenerg-1426	253	13	0,1,2,3	0,1,2,3	NUM
fuelectenerg-1426	253	14	,	,	PUNCT
fuelectenerg-1426	253	15	.	.	PUNCT
fuelectenerg-1426	253	16	.	.	PUNCT
fuelectenerg-1426	254	1	.	.	PUNCT
fuelectenerg-1426	255	1	,	,	PUNCT
fuelectenerg-1426	255	2	n−1	n−1	PROPN
fuelectenerg-1426	255	3	∑	∑	PUNCT
fuelectenerg-1426	255	4	k=0	k=0	PROPN
fuelectenerg-1426	255	5	(	(	PUNCT
fuelectenerg-1426	255	6	3)k	3)k	ADV
fuelectenerg-1426	255	7	,	,	PUNCT
fuelectenerg-1426	255	8	(	(	PUNCT
fuelectenerg-1426	255	9	49	49	NUM
fuelectenerg-1426	255	10	)	)	PUNCT
fuelectenerg-1426	255	11	φ	φ	NOUN
fuelectenerg-1426	255	12	=	=	SYM
fuelectenerg-1426	255	13	(	(	PUNCT
fuelectenerg-1426	255	14	3)n−1	3)n−1	PROPN
fuelectenerg-1426	255	15	∑	∑	PROPN
fuelectenerg-1426	255	16	k1=0	k1=0	PROPN
fuelectenerg-1426	255	17	(	(	PUNCT
fuelectenerg-1426	255	18	3)n−2	3)n−2	NUM
fuelectenerg-1426	255	19	∑	∑	PUNCT
fuelectenerg-1426	255	20	k2=0	k2=0	PROPN
fuelectenerg-1426	255	21	(	(	PUNCT
fuelectenerg-1426	255	22	3)n−3	3)n−3	NUM
fuelectenerg-1426	255	23	∑	∑	SYM
fuelectenerg-1426	255	24	k3=0	k3=0	PROPN
fuelectenerg-1426	255	25	·	·	PUNCT
fuelectenerg-1426	255	26	·	·	PUNCT
fuelectenerg-1426	255	27	·	·	PUNCT
fuelectenerg-1426	256	1	(	(	PUNCT
fuelectenerg-1426	256	2	3)0	3)0	NUM
fuelectenerg-1426	256	3	∑	∑	PUNCT
fuelectenerg-1426	256	4	kn=0	kn=0	X
fuelectenerg-1426	256	5	{	{	PUNCT
fuelectenerg-1426	256	6	[	[	PUNCT
fuelectenerg-1426	256	7	3(n−1	3(n−1	NOUN
fuelectenerg-1426	256	8	)	)	PUNCT
fuelectenerg-1426	256	9	!	!	PUNCT
fuelectenerg-1426	257	1	(	(	PUNCT
fuelectenerg-1426	257	2	3(n−1)−	3(n−1)−	NOUN
fuelectenerg-1426	257	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	257	4	!	!	PUNCT
fuelectenerg-1426	258	1	3(n−2	3(n−2	NUM
fuelectenerg-1426	258	2	)	)	PUNCT
fuelectenerg-1426	258	3	!	!	PUNCT
fuelectenerg-1426	259	1	(	(	PUNCT
fuelectenerg-1426	259	2	3(n−2)−	3(n−2)−	ADJ
fuelectenerg-1426	259	3	k2)!k2	k2)!k2	PROPN
fuelectenerg-1426	259	4	!	!	PUNCT
fuelectenerg-1426	259	5	3(n−3	3(n−3	NUM
fuelectenerg-1426	259	6	)	)	PUNCT
fuelectenerg-1426	259	7	!	!	PUNCT
fuelectenerg-1426	260	1	(	(	PUNCT
fuelectenerg-1426	260	2	3(n−3)−	3(n−3)−	PROPN
fuelectenerg-1426	260	3	k3)!k3	k3)!k3	PROPN
fuelectenerg-1426	260	4	!	!	PUNCT
fuelectenerg-1426	260	5	·	·	PUNCT
fuelectenerg-1426	260	6	·	·	PUNCT
fuelectenerg-1426	260	7	·	·	PUNCT
fuelectenerg-1426	261	1	3(0	3(0	NUM
fuelectenerg-1426	261	2	)	)	PUNCT
fuelectenerg-1426	261	3	!	!	PUNCT
fuelectenerg-1426	262	1	(	(	PUNCT
fuelectenerg-1426	262	2	3(0)−	3(0)−	NUM
fuelectenerg-1426	262	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	262	4	!	!	PUNCT
fuelectenerg-1426	263	1	]	]	PUNCT
fuelectenerg-1426	263	2	[	[	PUNCT
fuelectenerg-1426	263	3	(	(	PUNCT
fuelectenerg-1426	263	4	32(3)0	32(3)0	NUM
fuelectenerg-1426	263	5	)	)	PUNCT
fuelectenerg-1426	263	6	k1(32(3)1	k1(32(3)1	NOUN
fuelectenerg-1426	263	7	)	)	PUNCT
fuelectenerg-1426	263	8	k2(32(3)2	k2(32(3)2	PROPN
fuelectenerg-1426	263	9	)	)	PUNCT
fuelectenerg-1426	263	10	k3	k3	PROPN
fuelectenerg-1426	263	11	·	·	PUNCT
fuelectenerg-1426	263	12	·	·	PUNCT
fuelectenerg-1426	263	13	·	·	PUNCT
fuelectenerg-1426	263	14	(	(	PUNCT
fuelectenerg-1426	263	15	32(3)(n−1	32(3)(n−1	NUM
fuelectenerg-1426	263	16	)	)	PUNCT
fuelectenerg-1426	263	17	)	)	PUNCT
fuelectenerg-1426	264	1	kn	kn	NOUN
fuelectenerg-1426	264	2	]	]	PUNCT
fuelectenerg-1426	264	3	}	}	PUNCT
fuelectenerg-1426	264	4	.	.	PUNCT
fuelectenerg-1426	265	1	(	(	PUNCT
fuelectenerg-1426	265	2	50	50	NUM
fuelectenerg-1426	265	3	)	)	PUNCT
fuelectenerg-1426	265	4	from	from	ADP
fuelectenerg-1426	265	5	equations	equation	NOUN
fuelectenerg-1426	265	6	(	(	PUNCT
fuelectenerg-1426	265	7	47	47	NUM
fuelectenerg-1426	265	8	)	)	PUNCT
fuelectenerg-1426	265	9	(	(	PUNCT
fuelectenerg-1426	265	10	50	50	NUM
fuelectenerg-1426	265	11	)	)	PUNCT
fuelectenerg-1426	265	12	,	,	PUNCT
fuelectenerg-1426	265	13	it	it	PRON
fuelectenerg-1426	265	14	can	can	AUX
fuelectenerg-1426	265	15	be	be	AUX
fuelectenerg-1426	265	16	noticed	notice	VERB
fuelectenerg-1426	265	17	that	that	SCONJ
fuelectenerg-1426	265	18	the	the	DET
fuelectenerg-1426	265	19	total	total	ADJ
fuelectenerg-1426	265	20	number	number	NOUN
fuelectenerg-1426	265	21	of	of	ADP
fuelectenerg-1426	265	22	tifs	tifs	PROPN
fuelectenerg-1426	265	23	for	for	ADP
fuelectenerg-1426	265	24	all	all	DET
fuelectenerg-1426	265	25	variable	variable	ADJ
fuelectenerg-1426	265	26	orders	order	NOUN
fuelectenerg-1426	265	27	is	be	AUX
fuelectenerg-1426	265	28	equal	equal	ADJ
fuelectenerg-1426	265	29	to	to	ADP
fuelectenerg-1426	265	30	[	[	X
fuelectenerg-1426	265	31	n!][#tifs	n!][#tif	NOUN
fuelectenerg-1426	265	32	per	per	ADP
fuelectenerg-1426	265	33	order	order	NOUN
fuelectenerg-1426	265	34	]	]	PUNCT
fuelectenerg-1426	265	35	.	.	PUNCT
fuelectenerg-1426	266	1	example	example	NOUN
fuelectenerg-1426	267	1	4	4	NUM
fuelectenerg-1426	267	2	.	.	X
fuelectenerg-1426	268	1	for	for	ADP
fuelectenerg-1426	268	2	number	number	NOUN
fuelectenerg-1426	268	3	of	of	ADP
fuelectenerg-1426	268	4	variables	variable	NOUN
fuelectenerg-1426	268	5	equal	equal	ADJ
fuelectenerg-1426	268	6	to	to	ADP
fuelectenerg-1426	268	7	two	two	NUM
fuelectenerg-1426	268	8	(	(	PUNCT
fuelectenerg-1426	268	9	n	n	NOUN
fuelectenerg-1426	268	10	=	=	SYM
fuelectenerg-1426	268	11	2	2	NUM
fuelectenerg-1426	268	12	)	)	PUNCT
fuelectenerg-1426	268	13	,	,	PUNCT
fuelectenerg-1426	268	14	φ	φ	PROPN
fuelectenerg-1426	268	15	reduces	reduce	VERB
fuelectenerg-1426	268	16	to	to	ADP
fuelectenerg-1426	268	17	:	:	PUNCT
fuelectenerg-1426	268	18	φ	φ	PROPN
fuelectenerg-1426	268	19	=	=	SYM
fuelectenerg-1426	268	20	(	(	PUNCT
fuelectenerg-1426	268	21	3)1	3)1	NUM
fuelectenerg-1426	268	22	∑	∑	PUNCT
fuelectenerg-1426	268	23	k1=0	k1=0	PROPN
fuelectenerg-1426	268	24	1	1	NUM
fuelectenerg-1426	268	25	∑	∑	ADP
fuelectenerg-1426	268	26	k2=0	k2=0	PROPN
fuelectenerg-1426	268	27	{	{	PUNCT
fuelectenerg-1426	268	28	31	31	NUM
fuelectenerg-1426	268	29	!	!	PUNCT
fuelectenerg-1426	269	1	(	(	PUNCT
fuelectenerg-1426	269	2	31	31	NUM
fuelectenerg-1426	269	3	−	−	PROPN
fuelectenerg-1426	269	4	k1)!k1	k1)!k1	PROPN
fuelectenerg-1426	269	5	!	!	PUNCT
fuelectenerg-1426	269	6	30	30	NUM
fuelectenerg-1426	269	7	!	!	PUNCT
fuelectenerg-1426	270	1	(	(	PUNCT
fuelectenerg-1426	270	2	30	30	NUM
fuelectenerg-1426	270	3	−	−	NOUN
fuelectenerg-1426	270	4	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	270	5	!	!	PUNCT
fuelectenerg-1426	271	1	(	(	PUNCT
fuelectenerg-1426	271	2	32(3)0	32(3)0	NUM
fuelectenerg-1426	271	3	)	)	PUNCT
fuelectenerg-1426	271	4	k1(32(3)1	k1(32(3)1	PROPN
fuelectenerg-1426	271	5	)	)	PUNCT
fuelectenerg-1426	271	6	k2	k2	PROPN
fuelectenerg-1426	271	7	}	}	PUNCT
fuelectenerg-1426	271	8	φ	φ	PROPN
fuelectenerg-1426	271	9	=	=	SYM
fuelectenerg-1426	271	10	φ|k1=0,k2=0	φ|k1=0,k2=0	PROPN
fuelectenerg-1426	272	1	+	+	X
fuelectenerg-1426	272	2	φ|k1=1,k2=0	φ|k1=1,k2=0	X
fuelectenerg-1426	272	3	+	+	ADJ
fuelectenerg-1426	272	4	φ|k1=2,k2=0	φ|k1=2,k2=0	ADJ
fuelectenerg-1426	272	5	+	+	ADJ
fuelectenerg-1426	272	6	φ|k1=3,k2=0	φ|k1=3,k2=0	X
fuelectenerg-1426	272	7	+	+	ADJ
fuelectenerg-1426	272	8	φ|k1=0,k2=1	φ|k1=0,k2=1	ADJ
fuelectenerg-1426	272	9	+	+	ADJ
fuelectenerg-1426	272	10	φ|k1=1,k2=1	φ|k1=1,k2=1	PROPN
fuelectenerg-1426	272	11	+	+	NOUN
fuelectenerg-1426	272	12	φ|k1=2,k2=1	φ|k1=2,k2=1	PROPN
fuelectenerg-1426	272	13	+	+	ADJ
fuelectenerg-1426	272	14	φ|k1=3,k2=1	φ|k1=3,k2=1	NUM
fuelectenerg-1426	272	15	=	=	ADJ
fuelectenerg-1426	272	16	φ00	φ00	NOUN
fuelectenerg-1426	272	17	+	+	NOUN
fuelectenerg-1426	272	18	φ10	φ10	NOUN
fuelectenerg-1426	273	1	+	+	NOUN
fuelectenerg-1426	273	2	φ20	φ20	NOUN
fuelectenerg-1426	273	3	+	+	NOUN
fuelectenerg-1426	273	4	φ30	φ30	NOUN
fuelectenerg-1426	273	5	+	+	NOUN
fuelectenerg-1426	273	6	φ01	φ01	NOUN
fuelectenerg-1426	273	7	+	+	NOUN
fuelectenerg-1426	273	8	φ11	φ11	ADJ
fuelectenerg-1426	273	9	+	+	ADJ
fuelectenerg-1426	273	10	φ21	φ21	NOUN
fuelectenerg-1426	273	11	+	+	ADV
fuelectenerg-1426	273	12	φ31	φ31	ADJ
fuelectenerg-1426	273	13	=	=	ADJ
fuelectenerg-1426	273	14	1	1	NUM
fuelectenerg-1426	273	15	+	+	NOUN
fuelectenerg-1426	273	16	27	27	NUM
fuelectenerg-1426	273	17	+	+	SYM
fuelectenerg-1426	273	18	243	243	NUM
fuelectenerg-1426	273	19	+	+	NOUN
fuelectenerg-1426	273	20	729	729	NUM
fuelectenerg-1426	273	21	+	+	ADJ
fuelectenerg-1426	273	22	729	729	NUM
fuelectenerg-1426	273	23	+	+	NOUN
fuelectenerg-1426	273	24	19683	19683	NUM
fuelectenerg-1426	273	25	+	+	ADJ
fuelectenerg-1426	273	26	177147	177147	NUM
fuelectenerg-1426	273	27	+	+	ADJ
fuelectenerg-1426	273	28	531441=	531441=	NUM
fuelectenerg-1426	273	29	730,000	730,000	NUM
fuelectenerg-1426	273	30	.	.	PUNCT
fuelectenerg-1426	274	1	utilizing	utilize	VERB
fuelectenerg-1426	274	2	multi	multi	ADJ
fuelectenerg-1426	274	3	-	-	ADJ
fuelectenerg-1426	274	4	valued	value	VERB
fuelectenerg-1426	274	5	map	map	NOUN
fuelectenerg-1426	274	6	representation	representation	NOUN
fuelectenerg-1426	274	7	,	,	PUNCT
fuelectenerg-1426	274	8	there	there	PRON
fuelectenerg-1426	274	9	are	be	VERB
fuelectenerg-1426	274	10	n#minterms	n#minterm	NOUN
fuelectenerg-1426	274	11	different	different	ADJ
fuelectenerg-1426	274	12	functions	function	NOUN
fuelectenerg-1426	274	13	for	for	ADP
fuelectenerg-1426	274	14	n	n	ADV
fuelectenerg-1426	274	15	-	-	PUNCT
fuelectenerg-1426	274	16	valued	value	VERB
fuelectenerg-1426	274	17	input	input	NOUN
fuelectenerg-1426	274	18	-	-	PUNCT
fuelectenerg-1426	274	19	output	output	NOUN
fuelectenerg-1426	274	20	logic	logic	NOUN
fuelectenerg-1426	274	21	.	.	PUNCT
fuelectenerg-1426	275	1	therefore	therefore	ADV
fuelectenerg-1426	275	2	,	,	PUNCT
fuelectenerg-1426	275	3	for	for	ADP
fuelectenerg-1426	275	4	ternary	ternary	ADJ
fuelectenerg-1426	275	5	logic	logic	NOUN
fuelectenerg-1426	275	6	,	,	PUNCT
fuelectenerg-1426	275	7	there	there	PRON
fuelectenerg-1426	275	8	are	be	VERB
fuelectenerg-1426	275	9	39	39	NUM
fuelectenerg-1426	275	10	=	=	SYM
fuelectenerg-1426	275	11	19,683	19,683	NUM
fuelectenerg-1426	275	12	different	different	ADJ
fuelectenerg-1426	275	13	ternary	ternary	ADJ
fuelectenerg-1426	275	14	functions	function	NOUN
fuelectenerg-1426	275	15	of	of	ADP
fuelectenerg-1426	275	16	two	two	NUM
fuelectenerg-1426	275	17	variables	variable	NOUN
fuelectenerg-1426	275	18	,	,	PUNCT
fuelectenerg-1426	275	19	and	and	CCONJ
fuelectenerg-1426	275	20	730,000	730,000	NUM
fuelectenerg-1426	275	21	ternary	ternary	ADJ
fuelectenerg-1426	275	22	inclusive	inclusive	ADJ
fuelectenerg-1426	275	23	forms	form	NOUN
fuelectenerg-1426	275	24	generated	generate	VERB
fuelectenerg-1426	275	25	by	by	ADP
fuelectenerg-1426	275	26	the	the	DET
fuelectenerg-1426	275	27	s	s	PROPN
fuelectenerg-1426	275	28	/	/	SYM
fuelectenerg-1426	275	29	d	d	NOUN
fuelectenerg-1426	275	30	trees	tree	NOUN
fuelectenerg-1426	275	31	.	.	PUNCT
fuelectenerg-1426	276	1	thus	thus	ADV
fuelectenerg-1426	276	2	,	,	PUNCT
fuelectenerg-1426	276	3	on	on	ADP
fuelectenerg-1426	276	4	the	the	DET
fuelectenerg-1426	276	5	average	average	ADJ
fuelectenerg-1426	276	6	every	every	DET
fuelectenerg-1426	276	7	function	function	NOUN
fuelectenerg-1426	276	8	of	of	ADP
fuelectenerg-1426	276	9	two	two	NUM
fuelectenerg-1426	276	10	variables	variable	NOUN
fuelectenerg-1426	276	11	can	can	AUX
fuelectenerg-1426	276	12	be	be	AUX
fuelectenerg-1426	276	13	realized	realize	VERB
fuelectenerg-1426	276	14	in	in	ADP
fuelectenerg-1426	276	15	approximately	approximately	ADV
fuelectenerg-1426	276	16	37	37	NUM
fuelectenerg-1426	276	17	ways	way	NOUN
fuelectenerg-1426	276	18	.	.	PUNCT
fuelectenerg-1426	277	1	112	112	NUM
fuelectenerg-1426	277	2	multi	multi	ADJ
fuelectenerg-1426	277	3	-	-	ADJ
fuelectenerg-1426	277	4	valued	value	VERB
fuelectenerg-1426	277	5	galois	galois	PROPN
fuelectenerg-1426	277	6	shannon	shannon	PROPN
fuelectenerg-1426	277	7	davio	davio	PROPN
fuelectenerg-1426	277	8	trees	tree	NOUN
fuelectenerg-1426	277	9	and	and	CCONJ
fuelectenerg-1426	277	10	their	their	PRON
fuelectenerg-1426	277	11	complexity	complexity	NOUN
fuelectenerg-1426	277	12	theorem	theorem	NOUN
fuelectenerg-1426	277	13	2	2	NUM
fuelectenerg-1426	277	14	.	.	X
fuelectenerg-1426	277	15	for	for	ADP
fuelectenerg-1426	277	16	gf(4	gf(4	NOUN
fuelectenerg-1426	277	17	)	)	PUNCT
fuelectenerg-1426	277	18	and	and	CCONJ
fuelectenerg-1426	277	19	n	n	NUM
fuelectenerg-1426	277	20	variables	variable	NOUN
fuelectenerg-1426	277	21	,	,	PUNCT
fuelectenerg-1426	277	22	the	the	DET
fuelectenerg-1426	277	23	total	total	ADJ
fuelectenerg-1426	277	24	number	number	NOUN
fuelectenerg-1426	277	25	of	of	ADP
fuelectenerg-1426	277	26	quaternary	quaternary	ADJ
fuelectenerg-1426	277	27	ifs	ifs	PROPN
fuelectenerg-1426	277	28	(	(	PUNCT
fuelectenerg-1426	277	29	qifs	qifs	PROPN
fuelectenerg-1426	277	30	)	)	PUNCT
fuelectenerg-1426	277	31	per	per	ADP
fuelectenerg-1426	277	32	variable	variable	ADJ
fuelectenerg-1426	277	33	order	order	NOUN
fuelectenerg-1426	277	34	is	be	AUX
fuelectenerg-1426	277	35	:	:	PUNCT
fuelectenerg-1426	277	36	#	#	SYM
fuelectenerg-1426	277	37	qifs	qifs	NOUN
fuelectenerg-1426	277	38	=	=	X
fuelectenerg-1426	277	39	φ	φ	NOUN
fuelectenerg-1426	277	40	=	=	SYM
fuelectenerg-1426	277	41	(	(	PUNCT
fuelectenerg-1426	277	42	4)n−1	4)n−1	NUM
fuelectenerg-1426	277	43	∑	∑	PROPN
fuelectenerg-1426	277	44	k1=0	k1=0	PROPN
fuelectenerg-1426	277	45	(	(	PUNCT
fuelectenerg-1426	277	46	4)n−2	4)n−2	NUM
fuelectenerg-1426	277	47	∑	∑	PUNCT
fuelectenerg-1426	277	48	k2=0	k2=0	PROPN
fuelectenerg-1426	277	49	·	·	PUNCT
fuelectenerg-1426	277	50	·	·	PUNCT
fuelectenerg-1426	277	51	·	·	PUNCT
fuelectenerg-1426	277	52	(	(	PUNCT
fuelectenerg-1426	277	53	4)0	4)0	NUM
fuelectenerg-1426	277	54	∑	∑	PUNCT
fuelectenerg-1426	277	55	kn=0	kn=0	X
fuelectenerg-1426	277	56	{	{	PUNCT
fuelectenerg-1426	277	57	4(n−1	4(n−1	NOUN
fuelectenerg-1426	277	58	)	)	PUNCT
fuelectenerg-1426	277	59	!	!	PUNCT
fuelectenerg-1426	278	1	(	(	PUNCT
fuelectenerg-1426	278	2	4(n−1)−	4(n−1)−	NOUN
fuelectenerg-1426	278	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	278	4	!	!	PUNCT
fuelectenerg-1426	279	1	4(n−2	4(n−2	NOUN
fuelectenerg-1426	279	2	)	)	PUNCT
fuelectenerg-1426	279	3	!	!	PUNCT
fuelectenerg-1426	280	1	(	(	PUNCT
fuelectenerg-1426	280	2	4(n−2)−	4(n−2)−	ADJ
fuelectenerg-1426	280	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	280	4	!	!	PUNCT
fuelectenerg-1426	280	5	·	·	PUNCT
fuelectenerg-1426	280	6	·	·	PUNCT
fuelectenerg-1426	280	7	·	·	PUNCT
fuelectenerg-1426	280	8	4(0	4(0	NUM
fuelectenerg-1426	280	9	)	)	PUNCT
fuelectenerg-1426	280	10	!	!	PUNCT
fuelectenerg-1426	281	1	(	(	PUNCT
fuelectenerg-1426	281	2	4(0)−	4(0)−	NUM
fuelectenerg-1426	281	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	281	4	!	!	PUNCT
fuelectenerg-1426	282	1	(	(	PUNCT
fuelectenerg-1426	282	2	43(4)0	43(4)0	NUM
fuelectenerg-1426	282	3	)	)	PUNCT
fuelectenerg-1426	282	4	k1(43(4)1	k1(43(4)1	NOUN
fuelectenerg-1426	282	5	)	)	PUNCT
fuelectenerg-1426	282	6	k2(43(4)2	k2(43(4)2	X
fuelectenerg-1426	282	7	)	)	PUNCT
fuelectenerg-1426	282	8	k3	k3	VERB
fuelectenerg-1426	282	9	·	·	PUNCT
fuelectenerg-1426	282	10	·	·	PUNCT
fuelectenerg-1426	282	11	·	·	PUNCT
fuelectenerg-1426	282	12	(	(	PUNCT
fuelectenerg-1426	282	13	43(4)(n−1	43(4)(n−1	NUM
fuelectenerg-1426	282	14	)	)	PUNCT
fuelectenerg-1426	282	15	)	)	PUNCT
fuelectenerg-1426	283	1	kn	kn	NOUN
fuelectenerg-1426	283	2	}	}	PUNCT
fuelectenerg-1426	283	3	.	.	PUNCT
fuelectenerg-1426	284	1	(	(	PUNCT
fuelectenerg-1426	284	2	51	51	NUM
fuelectenerg-1426	284	3	)	)	PUNCT
fuelectenerg-1426	284	4	proof	proof	NOUN
fuelectenerg-1426	284	5	.	.	PUNCT
fuelectenerg-1426	285	1	a	a	DET
fuelectenerg-1426	285	2	general	general	ADJ
fuelectenerg-1426	285	3	proof	proof	NOUN
fuelectenerg-1426	285	4	that	that	PRON
fuelectenerg-1426	285	5	includes	include	VERB
fuelectenerg-1426	285	6	gf(4	gf(4	NOUN
fuelectenerg-1426	285	7	)	)	PUNCT
fuelectenerg-1426	285	8	as	as	SCONJ
fuelectenerg-1426	285	9	special	special	ADJ
fuelectenerg-1426	285	10	case	case	NOUN
fuelectenerg-1426	285	11	will	will	AUX
fuelectenerg-1426	285	12	be	be	AUX
fuelectenerg-1426	285	13	provided	provide	VERB
fuelectenerg-1426	285	14	later	later	ADV
fuelectenerg-1426	285	15	in	in	ADP
fuelectenerg-1426	285	16	this	this	DET
fuelectenerg-1426	285	17	section	section	NOUN
fuelectenerg-1426	285	18	.	.	PUNCT
fuelectenerg-1426	286	1	the	the	DET
fuelectenerg-1426	286	2	extension	extension	NOUN
fuelectenerg-1426	286	3	of	of	ADP
fuelectenerg-1426	286	4	the	the	DET
fuelectenerg-1426	286	5	concept	concept	NOUN
fuelectenerg-1426	286	6	of	of	ADP
fuelectenerg-1426	286	7	s	s	PROPN
fuelectenerg-1426	286	8	/	/	SYM
fuelectenerg-1426	286	9	d	d	NOUN
fuelectenerg-1426	286	10	trees	tree	NOUN
fuelectenerg-1426	286	11	to	to	ADP
fuelectenerg-1426	286	12	higher	high	ADJ
fuelectenerg-1426	286	13	radices	radix	NOUN
fuelectenerg-1426	286	14	of	of	ADP
fuelectenerg-1426	286	15	galois	galois	PROPN
fuelectenerg-1426	286	16	fields	field	NOUN
fuelectenerg-1426	286	17	(	(	PUNCT
fuelectenerg-1426	286	18	i.e.	i.e.	X
fuelectenerg-1426	286	19	,	,	PUNCT
fuelectenerg-1426	286	20	higher	high	ADJ
fuelectenerg-1426	286	21	than	than	ADP
fuelectenerg-1426	286	22	four	four	NUM
fuelectenerg-1426	286	23	)	)	PUNCT
fuelectenerg-1426	286	24	is	be	AUX
fuelectenerg-1426	286	25	a	a	DET
fuelectenerg-1426	286	26	systematic	systematic	ADJ
fuelectenerg-1426	286	27	and	and	CCONJ
fuelectenerg-1426	286	28	direct	direct	ADJ
fuelectenerg-1426	286	29	process	process	NOUN
fuelectenerg-1426	286	30	that	that	PRON
fuelectenerg-1426	286	31	follows	follow	VERB
fuelectenerg-1426	286	32	the	the	DET
fuelectenerg-1426	286	33	same	same	ADJ
fuelectenerg-1426	286	34	method	method	NOUN
fuelectenerg-1426	286	35	developed	develop	VERB
fuelectenerg-1426	286	36	for	for	ADP
fuelectenerg-1426	286	37	the	the	DET
fuelectenerg-1426	286	38	ternary	ternary	ADJ
fuelectenerg-1426	286	39	case	case	NOUN
fuelectenerg-1426	286	40	and	and	CCONJ
fuelectenerg-1426	286	41	the	the	DET
fuelectenerg-1426	286	42	quaternary	quaternary	ADJ
fuelectenerg-1426	286	43	case	case	NOUN
fuelectenerg-1426	286	44	.	.	PUNCT
fuelectenerg-1426	287	1	the	the	DET
fuelectenerg-1426	287	2	following	follow	VERB
fuelectenerg-1426	287	3	example	example	NOUN
fuelectenerg-1426	287	4	demonstrates	demonstrate	VERB
fuelectenerg-1426	287	5	the	the	DET
fuelectenerg-1426	287	6	counts	count	NOUN
fuelectenerg-1426	287	7	of	of	ADP
fuelectenerg-1426	287	8	qifs	qif	NOUN
fuelectenerg-1426	287	9	using	use	VERB
fuelectenerg-1426	287	10	theorem	theorem	NOUN
fuelectenerg-1426	287	11	2	2	NUM
fuelectenerg-1426	287	12	.	.	NOUN
fuelectenerg-1426	287	13	example	example	NOUN
fuelectenerg-1426	287	14	5	5	NUM
fuelectenerg-1426	287	15	.	.	X
fuelectenerg-1426	288	1	for	for	ADP
fuelectenerg-1426	288	2	number	number	NOUN
fuelectenerg-1426	288	3	of	of	ADP
fuelectenerg-1426	288	4	variables	variable	NOUN
fuelectenerg-1426	288	5	equal	equal	ADJ
fuelectenerg-1426	288	6	to	to	ADP
fuelectenerg-1426	288	7	two	two	NUM
fuelectenerg-1426	288	8	(	(	PUNCT
fuelectenerg-1426	288	9	n	n	NOUN
fuelectenerg-1426	288	10	=	=	SYM
fuelectenerg-1426	288	11	2	2	NUM
fuelectenerg-1426	288	12	)	)	PUNCT
fuelectenerg-1426	288	13	,	,	PUNCT
fuelectenerg-1426	288	14	equation	equation	NOUN
fuelectenerg-1426	288	15	(	(	PUNCT
fuelectenerg-1426	288	16	51	51	NUM
fuelectenerg-1426	288	17	)	)	PUNCT
fuelectenerg-1426	288	18	reduces	reduce	VERB
fuelectenerg-1426	288	19	to	to	ADP
fuelectenerg-1426	288	20	:	:	PUNCT
fuelectenerg-1426	288	21	φ	φ	PROPN
fuelectenerg-1426	288	22	=	=	SYM
fuelectenerg-1426	288	23	(	(	PUNCT
fuelectenerg-1426	288	24	4)1	4)1	NOUN
fuelectenerg-1426	288	25	∑	∑	PROPN
fuelectenerg-1426	288	26	k1=0	k1=0	PROPN
fuelectenerg-1426	288	27	(	(	PUNCT
fuelectenerg-1426	288	28	4)0	4)0	NUM
fuelectenerg-1426	288	29	∑	∑	PUNCT
fuelectenerg-1426	288	30	k2=0	k2=0	PROPN
fuelectenerg-1426	288	31	{	{	PUNCT
fuelectenerg-1426	288	32	4(1	4(1	NOUN
fuelectenerg-1426	288	33	)	)	PUNCT
fuelectenerg-1426	288	34	!	!	PUNCT
fuelectenerg-1426	289	1	(	(	PUNCT
fuelectenerg-1426	289	2	4(1)−	4(1)−	PROPN
fuelectenerg-1426	289	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	289	4	!	!	PUNCT
fuelectenerg-1426	289	5	4(0	4(0	NUM
fuelectenerg-1426	289	6	)	)	PUNCT
fuelectenerg-1426	289	7	!	!	PUNCT
fuelectenerg-1426	290	1	(	(	PUNCT
fuelectenerg-1426	290	2	4(0)−	4(0)−	NOUN
fuelectenerg-1426	290	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	290	4	!	!	PUNCT
fuelectenerg-1426	291	1	(	(	PUNCT
fuelectenerg-1426	291	2	43(4)0	43(4)0	NUM
fuelectenerg-1426	291	3	)	)	PUNCT
fuelectenerg-1426	291	4	k1(43(4)1	k1(43(4)1	NOUN
fuelectenerg-1426	291	5	)	)	PUNCT
fuelectenerg-1426	291	6	k2	k2	NOUN
fuelectenerg-1426	291	7	}	}	PUNCT
fuelectenerg-1426	292	1	=	=	SYM
fuelectenerg-1426	292	2	φ|k1=0,k2=0	φ|k1=0,k2=0	PROPN
fuelectenerg-1426	292	3	+	+	ADJ
fuelectenerg-1426	292	4	φ|k1=1,k2=0	φ|k1=1,k2=0	X
fuelectenerg-1426	292	5	+	+	ADJ
fuelectenerg-1426	292	6	φ|k1=2,k2=0	φ|k1=2,k2=0	ADJ
fuelectenerg-1426	292	7	+	+	ADJ
fuelectenerg-1426	292	8	φ|k1=3,k2=0	φ|k1=3,k2=0	X
fuelectenerg-1426	292	9	+	+	ADJ
fuelectenerg-1426	292	10	φ|k1=4,k2=0	φ|k1=4,k2=0	X
fuelectenerg-1426	292	11	+	+	ADJ
fuelectenerg-1426	292	12	φ|k1=0,k2=1	φ|k1=0,k2=1	PROPN
fuelectenerg-1426	292	13	+	+	ADJ
fuelectenerg-1426	292	14	φ|k1=1,k2=1	φ|k1=1,k2=1	PROPN
fuelectenerg-1426	292	15	+	+	NOUN
fuelectenerg-1426	292	16	φ|k1=2,k2=1	φ|k1=2,k2=1	X
fuelectenerg-1426	292	17	+	+	ADJ
fuelectenerg-1426	292	18	φ|k1=3,k2=1	φ|k1=3,k2=1	NUM
fuelectenerg-1426	292	19	+	+	ADJ
fuelectenerg-1426	292	20	φ|k1=4,k2=1	φ|k1=4,k2=1	X
fuelectenerg-1426	292	21	=	=	NOUN
fuelectenerg-1426	292	22	φ00	φ00	NOUN
fuelectenerg-1426	292	23	+	+	NOUN
fuelectenerg-1426	292	24	φ10	φ10	NOUN
fuelectenerg-1426	292	25	+	+	NOUN
fuelectenerg-1426	292	26	φ20	φ20	NOUN
fuelectenerg-1426	292	27	+	+	ADJ
fuelectenerg-1426	292	28	φ30	φ30	NOUN
fuelectenerg-1426	292	29	+	+	NOUN
fuelectenerg-1426	292	30	φ40	φ40	NOUN
fuelectenerg-1426	292	31	+	+	NOUN
fuelectenerg-1426	292	32	φ01	φ01	NOUN
fuelectenerg-1426	292	33	+	+	NOUN
fuelectenerg-1426	292	34	φ11	φ11	ADJ
fuelectenerg-1426	292	35	+	+	ADJ
fuelectenerg-1426	292	36	φ21	φ21	NOUN
fuelectenerg-1426	292	37	+	+	ADV
fuelectenerg-1426	292	38	φ31	φ31	ADJ
fuelectenerg-1426	292	39	+	+	ADJ
fuelectenerg-1426	292	40	φ41	φ41	ADJ
fuelectenerg-1426	292	41	=	=	SYM
fuelectenerg-1426	292	42	1	1	NUM
fuelectenerg-1426	292	43	+	+	NUM
fuelectenerg-1426	292	44	256	256	NUM
fuelectenerg-1426	292	45	+	+	NUM
fuelectenerg-1426	292	46	24,576	24,576	NUM
fuelectenerg-1426	292	47	+	+	NOUN
fuelectenerg-1426	292	48	1,048,576	1,048,576	NUM
fuelectenerg-1426	292	49	+	+	NOUN
fuelectenerg-1426	292	50	16,777,216	16,777,216	NUM
fuelectenerg-1426	292	51	+	+	NUM
fuelectenerg-1426	292	52	16,777,216	16,777,216	NUM
fuelectenerg-1426	292	53	+	+	NOUN
fuelectenerg-1426	292	54	4,294,967,296	4,294,967,296	NUM
fuelectenerg-1426	292	55	+	+	NOUN
fuelectenerg-1426	292	56	412,316,860,416	412,316,860,416	NUM
fuelectenerg-1426	292	57	+	+	SYM
fuelectenerg-1426	292	58	1.75921860444×1013	1.75921860444×1013	NUM
fuelectenerg-1426	292	59	+	+	NOUN
fuelectenerg-1426	292	60	2.81477976711×1014	2.81477976711×1014	NUM
fuelectenerg-1426	292	61	=	=	SYM
fuelectenerg-1426	292	62	2.99483809211×1014	2.99483809211×1014	NOUN
fuelectenerg-1426	292	63	.	.	PUNCT
fuelectenerg-1426	293	1	utilizing	utilize	VERB
fuelectenerg-1426	293	2	multi	multi	ADJ
fuelectenerg-1426	293	3	-	-	ADJ
fuelectenerg-1426	293	4	valued	value	VERB
fuelectenerg-1426	293	5	map	map	NOUN
fuelectenerg-1426	293	6	representation	representation	NOUN
fuelectenerg-1426	293	7	,	,	PUNCT
fuelectenerg-1426	293	8	we	we	PRON
fuelectenerg-1426	293	9	can	can	AUX
fuelectenerg-1426	293	10	easily	easily	ADV
fuelectenerg-1426	293	11	prove	prove	VERB
fuelectenerg-1426	293	12	that	that	SCONJ
fuelectenerg-1426	293	13	there	there	PRON
fuelectenerg-1426	293	14	are	be	VERB
fuelectenerg-1426	293	15	416	416	NUM
fuelectenerg-1426	293	16	=	=	SYM
fuelectenerg-1426	293	17	4,294,967,296	4,294,967,296	NUM
fuelectenerg-1426	293	18	quaternary	quaternary	ADJ
fuelectenerg-1426	293	19	functions	function	NOUN
fuelectenerg-1426	293	20	of	of	ADP
fuelectenerg-1426	293	21	two	two	NUM
fuelectenerg-1426	293	22	variables	variable	NOUN
fuelectenerg-1426	293	23	,	,	PUNCT
fuelectenerg-1426	293	24	and	and	CCONJ
fuelectenerg-1426	293	25	2.99483809211×	2.99483809211×	NUM
fuelectenerg-1426	293	26	1014	1014	NUM
fuelectenerg-1426	293	27	quaternary	quaternary	ADJ
fuelectenerg-1426	293	28	inclusive	inclusive	ADJ
fuelectenerg-1426	293	29	forms	form	NOUN
fuelectenerg-1426	293	30	generated	generate	VERB
fuelectenerg-1426	293	31	by	by	ADP
fuelectenerg-1426	293	32	the	the	DET
fuelectenerg-1426	293	33	s	s	PROPN
fuelectenerg-1426	293	34	/	/	SYM
fuelectenerg-1426	293	35	d	d	NOUN
fuelectenerg-1426	293	36	trees	tree	NOUN
fuelectenerg-1426	293	37	.	.	PUNCT
fuelectenerg-1426	294	1	thus	thus	ADV
fuelectenerg-1426	294	2	,	,	PUNCT
fuelectenerg-1426	294	3	on	on	ADP
fuelectenerg-1426	294	4	the	the	DET
fuelectenerg-1426	294	5	average	average	NOUN
fuelectenerg-1426	294	6	,	,	PUNCT
fuelectenerg-1426	294	7	every	every	DET
fuelectenerg-1426	294	8	function	function	NOUN
fuelectenerg-1426	294	9	of	of	ADP
fuelectenerg-1426	294	10	two	two	NUM
fuelectenerg-1426	294	11	variables	variable	NOUN
fuelectenerg-1426	294	12	can	can	AUX
fuelectenerg-1426	294	13	be	be	AUX
fuelectenerg-1426	294	14	synthesized	synthesize	VERB
fuelectenerg-1426	294	15	(	(	PUNCT
fuelectenerg-1426	294	16	realized	realize	VERB
fuelectenerg-1426	294	17	)	)	PUNCT
fuelectenerg-1426	294	18	in	in	ADP
fuelectenerg-1426	294	19	approximately	approximately	ADV
fuelectenerg-1426	294	20	69,729	69,729	NUM
fuelectenerg-1426	294	21	ways	way	NOUN
fuelectenerg-1426	294	22	.	.	PUNCT
fuelectenerg-1426	295	1	this	this	DET
fuelectenerg-1426	295	2	high	high	ADJ
fuelectenerg-1426	295	3	number	number	NOUN
fuelectenerg-1426	295	4	of	of	ADP
fuelectenerg-1426	295	5	realizations	realization	NOUN
fuelectenerg-1426	295	6	means	mean	VERB
fuelectenerg-1426	295	7	that	that	SCONJ
fuelectenerg-1426	295	8	most	most	ADJ
fuelectenerg-1426	295	9	functions	function	NOUN
fuelectenerg-1426	295	10	of	of	ADP
fuelectenerg-1426	295	11	two	two	NUM
fuelectenerg-1426	295	12	variables	variable	NOUN
fuelectenerg-1426	295	13	are	be	AUX
fuelectenerg-1426	295	14	realized	realize	VERB
fuelectenerg-1426	295	15	with	with	ADP
fuelectenerg-1426	295	16	less	less	ADJ
fuelectenerg-1426	295	17	than	than	ADP
fuelectenerg-1426	295	18	five	five	NUM
fuelectenerg-1426	295	19	expansions	expansion	NOUN
fuelectenerg-1426	295	20	,	,	PUNCT
fuelectenerg-1426	295	21	and	and	CCONJ
fuelectenerg-1426	295	22	all	all	DET
fuelectenerg-1426	295	23	functions	function	NOUN
fuelectenerg-1426	295	24	with	with	ADP
fuelectenerg-1426	295	25	at	at	ADP
fuelectenerg-1426	295	26	most	most	ADJ
fuelectenerg-1426	295	27	five	five	NUM
fuelectenerg-1426	295	28	expansions	expansion	NOUN
fuelectenerg-1426	295	29	.	.	PUNCT
fuelectenerg-1426	296	1	4.1	4.1	NUM
fuelectenerg-1426	296	2	general	general	ADJ
fuelectenerg-1426	296	3	formula	formula	NOUN
fuelectenerg-1426	296	4	to	to	PART
fuelectenerg-1426	296	5	compute	compute	VERB
fuelectenerg-1426	296	6	the	the	DET
fuelectenerg-1426	296	7	number	number	NOUN
fuelectenerg-1426	296	8	of	of	ADP
fuelectenerg-1426	296	9	ifs	ifs	PROPN
fuelectenerg-1426	296	10	for	for	ADP
fuelectenerg-1426	296	11	an	an	DET
fuelectenerg-1426	296	12	arbitrary	arbitrary	ADJ
fuelectenerg-1426	296	13	variable	variable	ADJ
fuelectenerg-1426	296	14	number	number	NOUN
fuelectenerg-1426	296	15	and	and	CCONJ
fuelectenerg-1426	296	16	arbitrary	arbitrary	ADJ
fuelectenerg-1426	296	17	galois	galois	PROPN
fuelectenerg-1426	296	18	radix	radix	PROPN
fuelectenerg-1426	296	19	gf(pk	gf(pk	PROPN
fuelectenerg-1426	296	20	)	)	PUNCT
fuelectenerg-1426	296	21	although	although	SCONJ
fuelectenerg-1426	296	22	the	the	DET
fuelectenerg-1426	296	23	s	s	PROPN
fuelectenerg-1426	296	24	/	/	SYM
fuelectenerg-1426	296	25	d	d	NOUN
fuelectenerg-1426	296	26	trees	tree	NOUN
fuelectenerg-1426	296	27	and	and	CCONJ
fuelectenerg-1426	296	28	inclusive	inclusive	ADJ
fuelectenerg-1426	296	29	forms	form	NOUN
fuelectenerg-1426	296	30	that	that	PRON
fuelectenerg-1426	296	31	were	be	AUX
fuelectenerg-1426	296	32	developed	develop	VERB
fuelectenerg-1426	296	33	are	be	AUX
fuelectenerg-1426	296	34	for	for	ADP
fuelectenerg-1426	296	35	gf(4	gf(4	NOUN
fuelectenerg-1426	296	36	)	)	PUNCT
fuelectenerg-1426	296	37	,	,	PUNCT
fuelectenerg-1426	296	38	the	the	DET
fuelectenerg-1426	296	39	same	same	ADJ
fuelectenerg-1426	296	40	concept	concept	NOUN
fuelectenerg-1426	296	41	can	can	AUX
fuelectenerg-1426	296	42	be	be	AUX
fuelectenerg-1426	296	43	directly	directly	ADV
fuelectenerg-1426	296	44	and	and	CCONJ
fuelectenerg-1426	296	45	systematically	systematically	ADV
fuelectenerg-1426	296	46	extended	extend	VERB
fuelectenerg-1426	296	47	to	to	ADP
fuelectenerg-1426	296	48	the	the	DET
fuelectenerg-1426	296	49	case	case	NOUN
fuelectenerg-1426	296	50	of	of	ADP
fuelectenerg-1426	296	51	n	n	PROPN
fuelectenerg-1426	296	52	radix	radix	NOUN
fuelectenerg-1426	296	53	of	of	ADP
fuelectenerg-1426	296	54	galois	galois	PROPN
fuelectenerg-1426	296	55	fields	field	NOUN
fuelectenerg-1426	296	56	and	and	CCONJ
fuelectenerg-1426	296	57	n	n	NUM
fuelectenerg-1426	296	58	variables	variable	NOUN
fuelectenerg-1426	296	59	.	.	PUNCT
fuelectenerg-1426	297	1	theorem	theorem	NOUN
fuelectenerg-1426	297	2	3	3	NUM
fuelectenerg-1426	297	3	provides	provide	VERB
fuelectenerg-1426	297	4	the	the	DET
fuelectenerg-1426	297	5	total	total	ADJ
fuelectenerg-1426	297	6	number	number	NOUN
fuelectenerg-1426	297	7	of	of	ADP
fuelectenerg-1426	297	8	ifs	ifs	PROPN
fuelectenerg-1426	297	9	per	per	ADP
fuelectenerg-1426	297	10	variable	variable	ADJ
fuelectenerg-1426	297	11	order	order	NOUN
fuelectenerg-1426	297	12	for	for	ADP
fuelectenerg-1426	297	13	n	n	DET
fuelectenerg-1426	297	14	variables	variable	NOUN
fuelectenerg-1426	297	15	(	(	PUNCT
fuelectenerg-1426	297	16	i.e.	i.e.	X
fuelectenerg-1426	297	17	,	,	PUNCT
fuelectenerg-1426	297	18	n	n	PRON
fuelectenerg-1426	297	19	decision	decision	NOUN
fuelectenerg-1426	297	20	tree	tree	NOUN
fuelectenerg-1426	297	21	levels	level	NOUN
fuelectenerg-1426	297	22	)	)	PUNCT
fuelectenerg-1426	297	23	and	and	CCONJ
fuelectenerg-1426	297	24	n	n	PROPN
fuelectenerg-1426	297	25	radix	radix	NOUN
fuelectenerg-1426	297	26	of	of	ADP
fuelectenerg-1426	297	27	any	any	DET
fuelectenerg-1426	297	28	arbitrary	arbitrary	ADJ
fuelectenerg-1426	297	29	algebraic	algebraic	ADJ
fuelectenerg-1426	297	30	field	field	NOUN
fuelectenerg-1426	297	31	,	,	PUNCT
fuelectenerg-1426	297	32	including	include	VERB
fuelectenerg-1426	297	33	gf(pk	gf(pk	NOUN
fuelectenerg-1426	297	34	)	)	PUNCT
fuelectenerg-1426	297	35	where	where	SCONJ
fuelectenerg-1426	297	36	p	p	NOUN
fuelectenerg-1426	297	37	is	be	AUX
fuelectenerg-1426	297	38	a	a	DET
fuelectenerg-1426	297	39	prime	prime	ADJ
fuelectenerg-1426	297	40	number	number	NOUN
fuelectenerg-1426	297	41	and	and	CCONJ
fuelectenerg-1426	297	42	k	k	PROPN
fuelectenerg-1426	297	43	is	be	AUX
fuelectenerg-1426	297	44	a	a	DET
fuelectenerg-1426	297	45	natural	natural	ADJ
fuelectenerg-1426	297	46	number	number	NOUN
fuelectenerg-1426	297	47	≥	≥	NOUN
fuelectenerg-1426	297	48	1	1	NUM
fuelectenerg-1426	297	49	.	.	PUNCT
fuelectenerg-1426	298	1	the	the	DET
fuelectenerg-1426	298	2	generality	generality	NOUN
fuelectenerg-1426	298	3	of	of	ADP
fuelectenerg-1426	298	4	theorem	theorem	ADJ
fuelectenerg-1426	298	5	3	3	NUM
fuelectenerg-1426	298	6	comes	come	VERB
fuelectenerg-1426	298	7	from	from	ADP
fuelectenerg-1426	298	8	the	the	DET
fuelectenerg-1426	298	9	fact	fact	NOUN
fuelectenerg-1426	298	10	that	that	SCONJ
fuelectenerg-1426	298	11	algebraic	algebraic	ADJ
fuelectenerg-1426	298	12	structures	structure	NOUN
fuelectenerg-1426	298	13	specify	specify	VERB
fuelectenerg-1426	298	14	the	the	DET
fuelectenerg-1426	298	15	type	type	NOUN
fuelectenerg-1426	298	16	of	of	ADP
fuelectenerg-1426	298	17	operations	operation	NOUN
fuelectenerg-1426	298	18	113	113	NUM
fuelectenerg-1426	298	19	714	714	NUM
fuelectenerg-1426	298	20	a.	a.	NOUN
fuelectenerg-1426	298	21	n.	n.	PROPN
fuelectenerg-1426	298	22	al	al	PROPN
fuelectenerg-1426	298	23	-	-	PUNCT
fuelectenerg-1426	298	24	rabadi	rabadi	PROPN
fuelectenerg-1426	298	25	multi	multi	ADJ
fuelectenerg-1426	298	26	-	-	ADJ
fuelectenerg-1426	298	27	valued	value	VERB
fuelectenerg-1426	298	28	galois	galois	PROPN
fuelectenerg-1426	298	29	shannon	shannon	PROPN
fuelectenerg-1426	298	30	davio	davio	PROPN
fuelectenerg-1426	298	31	trees	tree	NOUN
fuelectenerg-1426	298	32	and	and	CCONJ
fuelectenerg-1426	298	33	their	their	PRON
fuelectenerg-1426	298	34	complexity	complexity	NOUN
fuelectenerg-1426	298	35	715	715	NUM
fuelectenerg-1426	298	36	multi	multi	ADJ
fuelectenerg-1426	298	37	-	-	ADJ
fuelectenerg-1426	298	38	valued	value	VERB
fuelectenerg-1426	298	39	galois	galois	PROPN
fuelectenerg-1426	298	40	shannon	shannon	PROPN
fuelectenerg-1426	298	41	davio	davio	PROPN
fuelectenerg-1426	298	42	trees	tree	NOUN
fuelectenerg-1426	298	43	and	and	CCONJ
fuelectenerg-1426	298	44	their	their	PRON
fuelectenerg-1426	298	45	complexity	complexity	NOUN
fuelectenerg-1426	298	46	(	(	PUNCT
fuelectenerg-1426	298	47	e.g.	e.g.	ADV
fuelectenerg-1426	298	48	,	,	PUNCT
fuelectenerg-1426	298	49	addition	addition	NOUN
fuelectenerg-1426	298	50	and	and	CCONJ
fuelectenerg-1426	298	51	multiplication	multiplication	NOUN
fuelectenerg-1426	298	52	operations	operation	NOUN
fuelectenerg-1426	298	53	)	)	PUNCT
fuelectenerg-1426	298	54	in	in	ADP
fuelectenerg-1426	298	55	the	the	DET
fuelectenerg-1426	298	56	functional	functional	ADJ
fuelectenerg-1426	298	57	expansions	expansion	NOUN
fuelectenerg-1426	298	58	but	but	CCONJ
fuelectenerg-1426	298	59	do	do	AUX
fuelectenerg-1426	298	60	not	not	PART
fuelectenerg-1426	298	61	specify	specify	VERB
fuelectenerg-1426	298	62	the	the	DET
fuelectenerg-1426	298	63	counts	count	NOUN
fuelectenerg-1426	298	64	which	which	PRON
fuelectenerg-1426	298	65	are	be	AUX
fuelectenerg-1426	298	66	an	an	DET
fuelectenerg-1426	298	67	intrinsic	intrinsic	ADJ
fuelectenerg-1426	298	68	property	property	NOUN
fuelectenerg-1426	298	69	of	of	ADP
fuelectenerg-1426	298	70	the	the	DET
fuelectenerg-1426	298	71	tree	tree	NOUN
fuelectenerg-1426	298	72	structure	structure	NOUN
fuelectenerg-1426	298	73	and	and	CCONJ
fuelectenerg-1426	298	74	are	be	AUX
fuelectenerg-1426	298	75	independent	independent	ADJ
fuelectenerg-1426	298	76	of	of	ADP
fuelectenerg-1426	298	77	the	the	DET
fuelectenerg-1426	298	78	algebraic	algebraic	ADJ
fuelectenerg-1426	298	79	operations	operation	NOUN
fuelectenerg-1426	298	80	performed	perform	VERB
fuelectenerg-1426	298	81	.	.	PUNCT
fuelectenerg-1426	299	1	thus	thus	ADV
fuelectenerg-1426	299	2	,	,	PUNCT
fuelectenerg-1426	299	3	theorem	theorem	VERB
fuelectenerg-1426	299	4	3	3	NUM
fuelectenerg-1426	299	5	is	be	AUX
fuelectenerg-1426	299	6	valid	valid	ADJ
fuelectenerg-1426	299	7	,	,	PUNCT
fuelectenerg-1426	299	8	among	among	ADP
fuelectenerg-1426	299	9	others	other	NOUN
fuelectenerg-1426	299	10	,	,	PUNCT
fuelectenerg-1426	299	11	for	for	ADP
fuelectenerg-1426	299	12	galois	galois	PROPN
fuelectenerg-1426	299	13	fields	field	NOUN
fuelectenerg-1426	299	14	of	of	ADP
fuelectenerg-1426	299	15	arbitrary	arbitrary	ADJ
fuelectenerg-1426	299	16	radix	radix	NOUN
fuelectenerg-1426	299	17	.	.	PUNCT
fuelectenerg-1426	300	1	theorem	theorem	VERB
fuelectenerg-1426	300	2	3	3	NUM
fuelectenerg-1426	300	3	.	.	PUNCT
fuelectenerg-1426	301	1	the	the	DET
fuelectenerg-1426	301	2	total	total	ADJ
fuelectenerg-1426	301	3	number	number	NOUN
fuelectenerg-1426	301	4	of	of	ADP
fuelectenerg-1426	301	5	inclusive	inclusive	ADJ
fuelectenerg-1426	301	6	forms	form	NOUN
fuelectenerg-1426	301	7	for	for	ADP
fuelectenerg-1426	301	8	n	n	CCONJ
fuelectenerg-1426	301	9	variables	variable	NOUN
fuelectenerg-1426	301	10	and	and	CCONJ
fuelectenerg-1426	301	11	n	n	CCONJ
fuelectenerg-1426	301	12	-	-	PUNCT
fuelectenerg-1426	301	13	radix	radix	NOUN
fuelectenerg-1426	301	14	galois	galois	PROPN
fuelectenerg-1426	301	15	field	field	NOUN
fuelectenerg-1426	301	16	logic	logic	NOUN
fuelectenerg-1426	301	17	is	be	AUX
fuelectenerg-1426	301	18	equal	equal	ADJ
fuelectenerg-1426	301	19	to	to	ADP
fuelectenerg-1426	301	20	:	:	PUNCT
fuelectenerg-1426	301	21	#	#	SYM
fuelectenerg-1426	301	22	nifs	nifs	NOUN
fuelectenerg-1426	301	23	=	=	SYM
fuelectenerg-1426	301	24	φn	φn	PROPN
fuelectenerg-1426	301	25	,	,	PUNCT
fuelectenerg-1426	301	26	n	n	NOUN
fuelectenerg-1426	301	27	=	=	SYM
fuelectenerg-1426	301	28	(	(	PUNCT
fuelectenerg-1426	301	29	n)n−1	n)n−1	INTJ
fuelectenerg-1426	301	30	∑	∑	PROPN
fuelectenerg-1426	301	31	k1=0	k1=0	PROPN
fuelectenerg-1426	301	32	(	(	PUNCT
fuelectenerg-1426	301	33	n)n−2	n)n−2	ADP
fuelectenerg-1426	301	34	∑	∑	ADP
fuelectenerg-1426	301	35	k2=0	k2=0	PROPN
fuelectenerg-1426	301	36	·	·	PUNCT
fuelectenerg-1426	301	37	·	·	PUNCT
fuelectenerg-1426	301	38	·	·	PUNCT
fuelectenerg-1426	301	39	(	(	PUNCT
fuelectenerg-1426	301	40	n)0	n)0	X
fuelectenerg-1426	301	41	∑	∑	PUNCT
fuelectenerg-1426	301	42	kn=0	kn=0	X
fuelectenerg-1426	301	43	{	{	PUNCT
fuelectenerg-1426	301	44	n(n−1	n(n−1	NUM
fuelectenerg-1426	301	45	)	)	PUNCT
fuelectenerg-1426	301	46	!	!	PUNCT
fuelectenerg-1426	302	1	(	(	PUNCT
fuelectenerg-1426	302	2	n(n−1)−	n(n−1)−	ADV
fuelectenerg-1426	302	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	302	4	!	!	PUNCT
fuelectenerg-1426	303	1	n(n−2	n(n−2	PROPN
fuelectenerg-1426	303	2	)	)	PUNCT
fuelectenerg-1426	303	3	!	!	PUNCT
fuelectenerg-1426	304	1	(	(	PUNCT
fuelectenerg-1426	304	2	n(n−2)−	n(n−2)−	ADV
fuelectenerg-1426	304	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	304	4	!	!	PUNCT
fuelectenerg-1426	305	1	·	·	PUNCT
fuelectenerg-1426	305	2	·	·	PUNCT
fuelectenerg-1426	305	3	·	·	PUNCT
fuelectenerg-1426	305	4	n(0	n(0	PROPN
fuelectenerg-1426	305	5	)	)	PUNCT
fuelectenerg-1426	305	6	!	!	PUNCT
fuelectenerg-1426	306	1	(	(	PUNCT
fuelectenerg-1426	306	2	n(0)−	n(0)−	NUM
fuelectenerg-1426	306	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	306	4	!	!	PUNCT
fuelectenerg-1426	306	5	(	(	PUNCT
fuelectenerg-1426	306	6	n(n−1)(n)0	n(n−1)(n)0	NOUN
fuelectenerg-1426	306	7	)	)	PUNCT
fuelectenerg-1426	306	8	k1(n(n−1)(n)1	k1(n(n−1)(n)1	PROPN
fuelectenerg-1426	306	9	)	)	PUNCT
fuelectenerg-1426	306	10	k2(n(n−1)(n)2	k2(n(n−1)(n)2	NOUN
fuelectenerg-1426	306	11	)	)	PUNCT
fuelectenerg-1426	306	12	k3	k3	VERB
fuelectenerg-1426	306	13	·	·	PUNCT
fuelectenerg-1426	306	14	·	·	PUNCT
fuelectenerg-1426	306	15	·	·	PUNCT
fuelectenerg-1426	306	16	(	(	PUNCT
fuelectenerg-1426	306	17	n(n−1)(n)n−1	n(n−1)(n)n−1	PROPN
fuelectenerg-1426	306	18	)	)	PUNCT
fuelectenerg-1426	306	19	kn	kn	PROPN
fuelectenerg-1426	306	20	}	}	PUNCT
fuelectenerg-1426	306	21	.	.	PUNCT
fuelectenerg-1426	307	1	(	(	PUNCT
fuelectenerg-1426	307	2	52	52	NUM
fuelectenerg-1426	307	3	)	)	PUNCT
fuelectenerg-1426	307	4	proof	proof	NOUN
fuelectenerg-1426	307	5	.	.	PUNCT
fuelectenerg-1426	308	1	the	the	DET
fuelectenerg-1426	308	2	following	follow	VERB
fuelectenerg-1426	308	3	is	be	AUX
fuelectenerg-1426	308	4	the	the	DET
fuelectenerg-1426	308	5	derivation	derivation	NOUN
fuelectenerg-1426	308	6	of	of	ADP
fuelectenerg-1426	308	7	the	the	DET
fuelectenerg-1426	308	8	general	general	ADJ
fuelectenerg-1426	308	9	equation	equation	NOUN
fuelectenerg-1426	308	10	(	(	PUNCT
fuelectenerg-1426	308	11	52	52	NUM
fuelectenerg-1426	308	12	)	)	PUNCT
fuelectenerg-1426	308	13	to	to	PART
fuelectenerg-1426	308	14	calculate	calculate	VERB
fuelectenerg-1426	308	15	the	the	DET
fuelectenerg-1426	308	16	number	number	NOUN
fuelectenerg-1426	308	17	of	of	ADP
fuelectenerg-1426	308	18	ifs	ifs	PROPN
fuelectenerg-1426	308	19	per	per	ADP
fuelectenerg-1426	308	20	variable	variable	ADJ
fuelectenerg-1426	308	21	order	order	NOUN
fuelectenerg-1426	308	22	.	.	PUNCT
fuelectenerg-1426	309	1	the	the	DET
fuelectenerg-1426	309	2	total	total	ADJ
fuelectenerg-1426	309	3	number	number	NOUN
fuelectenerg-1426	309	4	of	of	ADP
fuelectenerg-1426	309	5	nodes	node	NOUN
fuelectenerg-1426	309	6	for	for	ADP
fuelectenerg-1426	309	7	any	any	DET
fuelectenerg-1426	309	8	gf(n	gf(n	NOUN
fuelectenerg-1426	309	9	)	)	PUNCT
fuelectenerg-1426	309	10	tree	tree	NOUN
fuelectenerg-1426	309	11	with	with	ADP
fuelectenerg-1426	309	12	n	n	PROPN
fuelectenerg-1426	309	13	levels	level	NOUN
fuelectenerg-1426	309	14	(	(	PUNCT
fuelectenerg-1426	309	15	i.e.	i.e.	X
fuelectenerg-1426	309	16	,	,	PUNCT
fuelectenerg-1426	309	17	n	n	PRON
fuelectenerg-1426	309	18	variables	variable	NOUN
fuelectenerg-1426	309	19	)	)	PUNCT
fuelectenerg-1426	309	20	equals	equal	VERB
fuelectenerg-1426	309	21	to	to	ADP
fuelectenerg-1426	309	22	:	:	PUNCT
fuelectenerg-1426	309	23	n−1	n−1	PROPN
fuelectenerg-1426	309	24	∑	∑	PUNCT
fuelectenerg-1426	309	25	k=0	k=0	X
fuelectenerg-1426	309	26	(	(	PUNCT
fuelectenerg-1426	309	27	n)k	n)k	ADV
fuelectenerg-1426	309	28	.	.	PUNCT
fuelectenerg-1426	310	1	(	(	PUNCT
fuelectenerg-1426	310	2	53	53	NUM
fuelectenerg-1426	310	3	)	)	PUNCT
fuelectenerg-1426	310	4	for	for	ADP
fuelectenerg-1426	310	5	any	any	DET
fuelectenerg-1426	310	6	s	s	NOUN
fuelectenerg-1426	310	7	-	-	PUNCT
fuelectenerg-1426	310	8	type	type	NOUN
fuelectenerg-1426	310	9	(	(	PUNCT
fuelectenerg-1426	310	10	i.e.	i.e.	X
fuelectenerg-1426	310	11	,	,	PUNCT
fuelectenerg-1426	310	12	shannon	shannon	PROPN
fuelectenerg-1426	310	13	type	type	PROPN
fuelectenerg-1426	310	14	)	)	PUNCT
fuelectenerg-1426	310	15	node	node	NOUN
fuelectenerg-1426	310	16	there	there	PRON
fuelectenerg-1426	310	17	is	be	VERB
fuelectenerg-1426	310	18	only	only	ADV
fuelectenerg-1426	310	19	one	one	NUM
fuelectenerg-1426	310	20	type	type	NOUN
fuelectenerg-1426	310	21	of	of	ADP
fuelectenerg-1426	310	22	nodes	node	NOUN
fuelectenerg-1426	310	23	as	as	SCONJ
fuelectenerg-1426	310	24	the	the	DET
fuelectenerg-1426	310	25	branches	branch	NOUN
fuelectenerg-1426	310	26	of	of	ADP
fuelectenerg-1426	310	27	the	the	DET
fuelectenerg-1426	310	28	shannon	shannon	PROPN
fuelectenerg-1426	310	29	node	node	PROPN
fuelectenerg-1426	310	30	have	have	VERB
fuelectenerg-1426	310	31	the	the	DET
fuelectenerg-1426	310	32	possibility	possibility	NOUN
fuelectenerg-1426	310	33	of	of	ADP
fuelectenerg-1426	310	34	single	single	ADJ
fuelectenerg-1426	310	35	value	value	NOUN
fuelectenerg-1426	310	36	each	each	PRON
fuelectenerg-1426	310	37	.	.	PUNCT
fuelectenerg-1426	311	1	yet	yet	ADV
fuelectenerg-1426	311	2	,	,	PUNCT
fuelectenerg-1426	311	3	for	for	ADP
fuelectenerg-1426	311	4	d	d	NOUN
fuelectenerg-1426	311	5	-	-	PUNCT
fuelectenerg-1426	311	6	type	type	NOUN
fuelectenerg-1426	311	7	(	(	PUNCT
fuelectenerg-1426	311	8	i.e.	i.e.	X
fuelectenerg-1426	311	9	,	,	PUNCT
fuelectenerg-1426	311	10	davio	davio	NOUN
fuelectenerg-1426	311	11	type	type	NOUN
fuelectenerg-1426	311	12	)	)	PUNCT
fuelectenerg-1426	311	13	node	node	NOUN
fuelectenerg-1426	311	14	there	there	PRON
fuelectenerg-1426	311	15	are	be	VERB
fuelectenerg-1426	311	16	n	n	PRON
fuelectenerg-1426	311	17	possible	possible	ADJ
fuelectenerg-1426	311	18	types	type	NOUN
fuelectenerg-1426	311	19	of	of	ADP
fuelectenerg-1426	311	20	nodes	node	NOUN
fuelectenerg-1426	311	21	where	where	SCONJ
fuelectenerg-1426	311	22	n	n	X
fuelectenerg-1426	311	23	is	be	AUX
fuelectenerg-1426	311	24	the	the	DET
fuelectenerg-1426	311	25	number	number	NOUN
fuelectenerg-1426	311	26	of	of	ADP
fuelectenerg-1426	311	27	variables	variable	NOUN
fuelectenerg-1426	311	28	which	which	PRON
fuelectenerg-1426	311	29	is	be	AUX
fuelectenerg-1426	311	30	equal	equal	ADJ
fuelectenerg-1426	311	31	to	to	ADP
fuelectenerg-1426	311	32	the	the	DET
fuelectenerg-1426	311	33	number	number	NOUN
fuelectenerg-1426	311	34	of	of	ADP
fuelectenerg-1426	311	35	levels	level	NOUN
fuelectenerg-1426	311	36	.	.	PUNCT
fuelectenerg-1426	312	1	the	the	DET
fuelectenerg-1426	312	2	highest	high	ADJ
fuelectenerg-1426	312	3	possible	possible	ADJ
fuelectenerg-1426	312	4	number	number	NOUN
fuelectenerg-1426	312	5	of	of	ADP
fuelectenerg-1426	312	6	forms	form	NOUN
fuelectenerg-1426	312	7	for	for	ADP
fuelectenerg-1426	312	8	the	the	DET
fuelectenerg-1426	312	9	d	d	ADJ
fuelectenerg-1426	312	10	-	-	PUNCT
fuelectenerg-1426	312	11	type	type	NOUN
fuelectenerg-1426	312	12	node	node	NOUN
fuelectenerg-1426	312	13	exists	exist	VERB
fuelectenerg-1426	312	14	when	when	SCONJ
fuelectenerg-1426	312	15	the	the	DET
fuelectenerg-1426	312	16	davio	davio	NOUN
fuelectenerg-1426	312	17	node	node	NOUN
fuelectenerg-1426	312	18	exists	exist	VERB
fuelectenerg-1426	312	19	in	in	ADP
fuelectenerg-1426	312	20	the	the	DET
fuelectenerg-1426	312	21	first	first	ADJ
fuelectenerg-1426	312	22	(	(	PUNCT
fuelectenerg-1426	312	23	highest	high	ADJ
fuelectenerg-1426	312	24	)	)	PUNCT
fuelectenerg-1426	312	25	level	level	NOUN
fuelectenerg-1426	312	26	,	,	PUNCT
fuelectenerg-1426	312	27	and	and	CCONJ
fuelectenerg-1426	312	28	the	the	DET
fuelectenerg-1426	312	29	lowest	low	ADJ
fuelectenerg-1426	312	30	possible	possible	ADJ
fuelectenerg-1426	312	31	number	number	NOUN
fuelectenerg-1426	312	32	of	of	ADP
fuelectenerg-1426	312	33	forms	form	NOUN
fuelectenerg-1426	312	34	for	for	ADP
fuelectenerg-1426	312	35	the	the	DET
fuelectenerg-1426	312	36	d	d	ADJ
fuelectenerg-1426	312	37	-	-	PUNCT
fuelectenerg-1426	312	38	type	type	NOUN
fuelectenerg-1426	312	39	node	node	NOUN
fuelectenerg-1426	312	40	is	be	AUX
fuelectenerg-1426	312	41	when	when	SCONJ
fuelectenerg-1426	312	42	the	the	DET
fuelectenerg-1426	312	43	davio	davio	NOUN
fuelectenerg-1426	312	44	node	node	NOUN
fuelectenerg-1426	312	45	exists	exist	VERB
fuelectenerg-1426	312	46	in	in	ADP
fuelectenerg-1426	312	47	the	the	DET
fuelectenerg-1426	312	48	n	n	NOUN
fuelectenerg-1426	312	49	-	-	PUNCT
fuelectenerg-1426	312	50	level	level	NOUN
fuelectenerg-1426	312	51	(	(	PUNCT
fuelectenerg-1426	312	52	lowest	low	ADJ
fuelectenerg-1426	312	53	level	level	NOUN
fuelectenerg-1426	312	54	)	)	PUNCT
fuelectenerg-1426	312	55	.	.	PUNCT
fuelectenerg-1426	313	1	therefore	therefore	ADV
fuelectenerg-1426	313	2	,	,	PUNCT
fuelectenerg-1426	313	3	for	for	ADP
fuelectenerg-1426	313	4	certain	certain	ADJ
fuelectenerg-1426	313	5	number	number	NOUN
fuelectenerg-1426	313	6	m	m	NOUN
fuelectenerg-1426	313	7	of	of	ADP
fuelectenerg-1426	313	8	s	s	NOUN
fuelectenerg-1426	313	9	-	-	PUNCT
fuelectenerg-1426	313	10	type	type	NOUN
fuelectenerg-1426	313	11	nodes	node	NOUN
fuelectenerg-1426	313	12	the	the	DET
fuelectenerg-1426	313	13	following	follow	VERB
fuelectenerg-1426	313	14	formula	formula	NOUN
fuelectenerg-1426	313	15	describes	describe	VERB
fuelectenerg-1426	313	16	the	the	DET
fuelectenerg-1426	313	17	number	number	NOUN
fuelectenerg-1426	313	18	of	of	ADP
fuelectenerg-1426	313	19	the	the	DET
fuelectenerg-1426	313	20	d	d	ADJ
fuelectenerg-1426	313	21	-	-	PUNCT
fuelectenerg-1426	313	22	type	type	NOUN
fuelectenerg-1426	313	23	nodes	node	NOUN
fuelectenerg-1426	313	24	for	for	ADP
fuelectenerg-1426	313	25	n	n	DET
fuelectenerg-1426	313	26	variables	variable	NOUN
fuelectenerg-1426	313	27	:	:	PUNCT
fuelectenerg-1426	313	28	#	#	SYM
fuelectenerg-1426	313	29	s	s	AUX
fuelectenerg-1426	313	30	=	=	NOUN
fuelectenerg-1426	313	31	m	m	NOUN
fuelectenerg-1426	313	32	⇒	⇒	NOUN
fuelectenerg-1426	313	33	#	#	SYM
fuelectenerg-1426	313	34	d	d	NOUN
fuelectenerg-1426	313	35	=	=	SYM
fuelectenerg-1426	313	36	n−1	n−1	PROPN
fuelectenerg-1426	313	37	∑	∑	ADP
fuelectenerg-1426	313	38	k=0	k=0	X
fuelectenerg-1426	313	39	(	(	PUNCT
fuelectenerg-1426	313	40	n)k	n)k	ADJ
fuelectenerg-1426	313	41	−m	−m	NOUN
fuelectenerg-1426	313	42	.	.	PUNCT
fuelectenerg-1426	314	1	(	(	PUNCT
fuelectenerg-1426	314	2	54	54	NUM
fuelectenerg-1426	314	3	)	)	PUNCT
fuelectenerg-1426	314	4	it	it	PRON
fuelectenerg-1426	314	5	can	can	AUX
fuelectenerg-1426	314	6	be	be	AUX
fuelectenerg-1426	314	7	shown	show	VERB
fuelectenerg-1426	314	8	that	that	SCONJ
fuelectenerg-1426	314	9	for	for	ADP
fuelectenerg-1426	314	10	gf(n	gf(n	NOUN
fuelectenerg-1426	314	11	)	)	PUNCT
fuelectenerg-1426	314	12	(	(	PUNCT
fuelectenerg-1426	314	13	n	n	CCONJ
fuelectenerg-1426	314	14	-	-	PUNCT
fuelectenerg-1426	314	15	ary	ary	PROPN
fuelectenerg-1426	314	16	decision	decision	NOUN
fuelectenerg-1426	314	17	tree	tree	NOUN
fuelectenerg-1426	314	18	with	with	ADP
fuelectenerg-1426	314	19	n	n	NOUN
fuelectenerg-1426	314	20	-	-	PUNCT
fuelectenerg-1426	314	21	levels	level	NOUN
fuelectenerg-1426	314	22	,	,	PUNCT
fuelectenerg-1426	314	23	i.e.	i.e.	X
fuelectenerg-1426	314	24	,	,	PUNCT
fuelectenerg-1426	314	25	n	n	DET
fuelectenerg-1426	314	26	variables	variable	NOUN
fuelectenerg-1426	314	27	)	)	PUNCT
fuelectenerg-1426	314	28	,	,	PUNCT
fuelectenerg-1426	314	29	the	the	DET
fuelectenerg-1426	314	30	general	general	ADJ
fuelectenerg-1426	314	31	formulas	formula	NOUN
fuelectenerg-1426	314	32	that	that	PRON
fuelectenerg-1426	314	33	count	count	VERB
fuelectenerg-1426	314	34	the	the	DET
fuelectenerg-1426	314	35	number	number	NOUN
fuelectenerg-1426	314	36	of	of	ADP
fuelectenerg-1426	314	37	d	d	ADJ
fuelectenerg-1426	314	38	-	-	PUNCT
fuelectenerg-1426	314	39	type	type	NOUN
fuelectenerg-1426	314	40	nodes	node	NOUN
fuelectenerg-1426	314	41	,	,	PUNCT
fuelectenerg-1426	314	42	and	and	CCONJ
fuelectenerg-1426	314	43	the	the	DET
fuelectenerg-1426	314	44	number	number	NOUN
fuelectenerg-1426	314	45	of	of	ADP
fuelectenerg-1426	314	46	all	all	DET
fuelectenerg-1426	314	47	possible	possible	ADJ
fuelectenerg-1426	314	48	forms	form	NOUN
fuelectenerg-1426	314	49	for	for	ADP
fuelectenerg-1426	314	50	the	the	DET
fuelectenerg-1426	314	51	d	d	ADJ
fuelectenerg-1426	314	52	-	-	PUNCT
fuelectenerg-1426	314	53	type	type	NOUN
fuelectenerg-1426	314	54	node	node	NOUN
fuelectenerg-1426	314	55	in	in	ADP
fuelectenerg-1426	314	56	the	the	DET
fuelectenerg-1426	314	57	k	k	PROPN
fuelectenerg-1426	314	58	level	level	NOUN
fuelectenerg-1426	314	59	(	(	PUNCT
fuelectenerg-1426	314	60	where	where	SCONJ
fuelectenerg-1426	314	61	k	k	PROPN
fuelectenerg-1426	314	62	is	be	AUX
fuelectenerg-1426	314	63	less	less	ADJ
fuelectenerg-1426	314	64	than	than	ADP
fuelectenerg-1426	314	65	or	or	CCONJ
fuelectenerg-1426	314	66	equal	equal	VERB
fuelectenerg-1426	314	67	the	the	DET
fuelectenerg-1426	314	68	total	total	ADJ
fuelectenerg-1426	314	69	number	number	NOUN
fuelectenerg-1426	314	70	of	of	ADP
fuelectenerg-1426	314	71	levels	level	NOUN
fuelectenerg-1426	314	72	n	n	CCONJ
fuelectenerg-1426	314	73	)	)	PUNCT
fuelectenerg-1426	314	74	are	be	AUX
fuelectenerg-1426	314	75	,	,	PUNCT
fuelectenerg-1426	314	76	respectively	respectively	ADV
fuelectenerg-1426	314	77	:	:	PUNCT
fuelectenerg-1426	314	78	#	#	ADP
fuelectenerg-1426	314	79	dk	dk	NOUN
fuelectenerg-1426	314	80	=(	=(	NOUN
fuelectenerg-1426	314	81	n)k−1	n)k−1	PROPN
fuelectenerg-1426	314	82	,	,	PUNCT
fuelectenerg-1426	314	83	(	(	PUNCT
fuelectenerg-1426	314	84	55	55	NUM
fuelectenerg-1426	314	85	)	)	PUNCT
fuelectenerg-1426	314	86	|dk|=(n)(n−1)(n)(n−k	|dk|=(n)(n−1)(n)(n−k	NOUN
fuelectenerg-1426	314	87	)	)	PUNCT
fuelectenerg-1426	314	88	,	,	PUNCT
fuelectenerg-1426	314	89	(	(	PUNCT
fuelectenerg-1426	314	90	56	56	NUM
fuelectenerg-1426	314	91	)	)	PUNCT
fuelectenerg-1426	314	92	where	where	SCONJ
fuelectenerg-1426	314	93	#	#	SYM
fuelectenerg-1426	314	94	dk	dk	NOUN
fuelectenerg-1426	314	95	is	be	AUX
fuelectenerg-1426	314	96	the	the	DET
fuelectenerg-1426	314	97	number	number	NOUN
fuelectenerg-1426	314	98	of	of	ADP
fuelectenerg-1426	314	99	d	d	ADJ
fuelectenerg-1426	314	100	-	-	PUNCT
fuelectenerg-1426	314	101	type	type	NOUN
fuelectenerg-1426	314	102	nodes	node	NOUN
fuelectenerg-1426	314	103	in	in	ADP
fuelectenerg-1426	314	104	the	the	DET
fuelectenerg-1426	314	105	k	k	PROPN
fuelectenerg-1426	314	106	level	level	NOUN
fuelectenerg-1426	314	107	and	and	CCONJ
fuelectenerg-1426	314	108	|dk|	|dk|	NOUN
fuelectenerg-1426	314	109	is	be	AUX
fuelectenerg-1426	314	110	the	the	DET
fuelectenerg-1426	314	111	number	number	NOUN
fuelectenerg-1426	314	112	of	of	ADP
fuelectenerg-1426	314	113	all	all	DET
fuelectenerg-1426	314	114	possible	possible	ADJ
fuelectenerg-1426	314	115	forms	form	NOUN
fuelectenerg-1426	314	116	(	(	PUNCT
fuelectenerg-1426	314	117	per	per	ADP
fuelectenerg-1426	314	118	node	node	NOUN
fuelectenerg-1426	314	119	)	)	PUNCT
fuelectenerg-1426	314	120	for	for	ADP
fuelectenerg-1426	314	121	the	the	DET
fuelectenerg-1426	314	122	d	d	ADJ
fuelectenerg-1426	314	123	-	-	PUNCT
fuelectenerg-1426	314	124	type	type	NOUN
fuelectenerg-1426	314	125	node	node	NOUN
fuelectenerg-1426	314	126	in	in	ADP
fuelectenerg-1426	314	127	the	the	DET
fuelectenerg-1426	314	128	k	k	PROPN
fuelectenerg-1426	314	129	level	level	NOUN
fuelectenerg-1426	314	130	.	.	PUNCT
fuelectenerg-1426	315	1	let	let	VERB
fuelectenerg-1426	315	2	us	we	PRON
fuelectenerg-1426	315	3	define	define	VERB
fuelectenerg-1426	315	4	the	the	DET
fuelectenerg-1426	315	5	s	s	PROPN
fuelectenerg-1426	315	6	/	/	SYM
fuelectenerg-1426	315	7	d	d	NOUN
fuelectenerg-1426	315	8	tree	tree	NOUN
fuelectenerg-1426	315	9	category	category	NOUN
fuelectenerg-1426	315	10	to	to	PART
fuelectenerg-1426	315	11	be	be	AUX
fuelectenerg-1426	315	12	the	the	DET
fuelectenerg-1426	315	13	s	s	PROPN
fuelectenerg-1426	315	14	/	/	SYM
fuelectenerg-1426	315	15	d	d	NOUN
fuelectenerg-1426	315	16	trees	tree	NOUN
fuelectenerg-1426	315	17	that	that	PRON
fuelectenerg-1426	315	18	have	have	VERB
fuelectenerg-1426	315	19	in	in	ADP
fuelectenerg-1426	315	20	common	common	ADJ
fuelectenerg-1426	315	21	the	the	DET
fuelectenerg-1426	315	22	same	same	ADJ
fuelectenerg-1426	315	23	number	number	NOUN
fuelectenerg-1426	315	24	of	of	ADP
fuelectenerg-1426	315	25	s	s	NOUN
fuelectenerg-1426	315	26	-	-	PUNCT
fuelectenerg-1426	315	27	type	type	NOUN
fuelectenerg-1426	315	28	nodes	node	NOUN
fuelectenerg-1426	315	29	and	and	CCONJ
fuelectenerg-1426	315	30	the	the	DET
fuelectenerg-1426	315	31	same	same	ADJ
fuelectenerg-1426	315	32	number	number	NOUN
fuelectenerg-1426	315	33	of	of	ADP
fuelectenerg-1426	315	34	d	d	ADJ
fuelectenerg-1426	315	35	-	-	PUNCT
fuelectenerg-1426	315	36	type	type	NOUN
fuelectenerg-1426	315	37	nodes	node	NOUN
fuelectenerg-1426	315	38	within	within	ADP
fuelectenerg-1426	315	39	the	the	DET
fuelectenerg-1426	315	40	same	same	ADJ
fuelectenerg-1426	315	41	variable	variable	ADJ
fuelectenerg-1426	315	42	order	order	NOUN
fuelectenerg-1426	315	43	.	.	PUNCT
fuelectenerg-1426	316	1	let	let	VERB
fuelectenerg-1426	316	2	us	we	PRON
fuelectenerg-1426	316	3	define	define	VERB
fuelectenerg-1426	316	4	the	the	DET
fuelectenerg-1426	316	5	following	follow	VERB
fuelectenerg-1426	316	6	114	114	NUM
fuelectenerg-1426	316	7	714	714	NUM
fuelectenerg-1426	316	8	a.	a.	NOUN
fuelectenerg-1426	316	9	n.	n.	PROPN
fuelectenerg-1426	316	10	al	al	PROPN
fuelectenerg-1426	316	11	-	-	PUNCT
fuelectenerg-1426	316	12	rabadi	rabadi	PROPN
fuelectenerg-1426	316	13	multi	multi	ADJ
fuelectenerg-1426	316	14	-	-	ADJ
fuelectenerg-1426	316	15	valued	value	VERB
fuelectenerg-1426	316	16	galois	galois	PROPN
fuelectenerg-1426	316	17	shannon	shannon	PROPN
fuelectenerg-1426	316	18	davio	davio	PROPN
fuelectenerg-1426	316	19	trees	tree	NOUN
fuelectenerg-1426	316	20	and	and	CCONJ
fuelectenerg-1426	316	21	their	their	PRON
fuelectenerg-1426	316	22	complexity	complexity	NOUN
fuelectenerg-1426	316	23	715	715	NUM
fuelectenerg-1426	316	24	multi	multi	ADJ
fuelectenerg-1426	316	25	-	-	ADJ
fuelectenerg-1426	316	26	valued	value	VERB
fuelectenerg-1426	316	27	galois	galois	PROPN
fuelectenerg-1426	316	28	shannon	shannon	PROPN
fuelectenerg-1426	316	29	davio	davio	PROPN
fuelectenerg-1426	316	30	trees	tree	NOUN
fuelectenerg-1426	316	31	and	and	CCONJ
fuelectenerg-1426	316	32	their	their	PRON
fuelectenerg-1426	316	33	complexity	complexity	NOUN
fuelectenerg-1426	316	34	entities	entity	NOUN
fuelectenerg-1426	316	35	for	for	ADP
fuelectenerg-1426	316	36	n	n	PRON
fuelectenerg-1426	316	37	radix	radix	PROPN
fuelectenerg-1426	316	38	galois	galois	PROPN
fuelectenerg-1426	316	39	field	field	NOUN
fuelectenerg-1426	316	40	and	and	CCONJ
fuelectenerg-1426	316	41	n	n	NUM
fuelectenerg-1426	316	42	variables	variable	NOUN
fuelectenerg-1426	316	43	(	(	PUNCT
fuelectenerg-1426	316	44	i.e.	i.e.	X
fuelectenerg-1426	316	45	,	,	PUNCT
fuelectenerg-1426	316	46	n	n	PRON
fuelectenerg-1426	316	47	decision	decision	NOUN
fuelectenerg-1426	316	48	tree	tree	NOUN
fuelectenerg-1426	316	49	levels	level	NOUN
fuelectenerg-1426	316	50	):	):	PUNCT
fuelectenerg-1426	316	51	ψn	ψn	X
fuelectenerg-1426	316	52	,	,	PUNCT
fuelectenerg-1426	316	53	n	n	PRON
fuelectenerg-1426	316	54	≡	≡	ADJ
fuelectenerg-1426	316	55	number	number	NOUN
fuelectenerg-1426	316	56	of	of	ADP
fuelectenerg-1426	316	57	variable	variable	ADJ
fuelectenerg-1426	316	58	orders	order	NOUN
fuelectenerg-1426	316	59	,	,	PUNCT
fuelectenerg-1426	316	60	(	(	PUNCT
fuelectenerg-1426	316	61	57	57	NUM
fuelectenerg-1426	316	62	)	)	PUNCT
fuelectenerg-1426	316	63	ωn	ωn	PROPN
fuelectenerg-1426	316	64	,	,	PUNCT
fuelectenerg-1426	316	65	n	n	CCONJ
fuelectenerg-1426	316	66	≡	≡	ADJ
fuelectenerg-1426	316	67	number	number	NOUN
fuelectenerg-1426	316	68	of	of	ADP
fuelectenerg-1426	316	69	s	s	PROPN
fuelectenerg-1426	316	70	/	/	SYM
fuelectenerg-1426	316	71	d	d	NOUN
fuelectenerg-1426	316	72	tree	tree	NOUN
fuelectenerg-1426	316	73	categories	category	NOUN
fuelectenerg-1426	316	74	per	per	ADP
fuelectenerg-1426	316	75	variable	variable	ADJ
fuelectenerg-1426	316	76	order	order	NOUN
fuelectenerg-1426	316	77	,	,	PUNCT
fuelectenerg-1426	316	78	(	(	PUNCT
fuelectenerg-1426	316	79	58	58	X
fuelectenerg-1426	316	80	)	)	PUNCT
fuelectenerg-1426	316	81	φn	φn	NOUN
fuelectenerg-1426	316	82	,	,	PUNCT
fuelectenerg-1426	316	83	n	n	PRON
fuelectenerg-1426	316	84	≡	≡	ADJ
fuelectenerg-1426	316	85	number	number	NOUN
fuelectenerg-1426	316	86	of	of	ADP
fuelectenerg-1426	316	87	s	s	PROPN
fuelectenerg-1426	316	88	/	/	SYM
fuelectenerg-1426	316	89	d	d	NOUN
fuelectenerg-1426	316	90	trees	tree	NOUN
fuelectenerg-1426	316	91	per	per	ADP
fuelectenerg-1426	316	92	category	category	NOUN
fuelectenerg-1426	316	93	,	,	PUNCT
fuelectenerg-1426	316	94	(	(	PUNCT
fuelectenerg-1426	316	95	59	59	NUM
fuelectenerg-1426	316	96	)	)	PUNCT
fuelectenerg-1426	316	97	φn	φn	NOUN
fuelectenerg-1426	316	98	,	,	PUNCT
fuelectenerg-1426	316	99	n	n	PRON
fuelectenerg-1426	316	100	≡	≡	ADJ
fuelectenerg-1426	316	101	number	number	NOUN
fuelectenerg-1426	316	102	of	of	ADP
fuelectenerg-1426	316	103	ifs	ifs	PROPN
fuelectenerg-1426	316	104	per	per	ADP
fuelectenerg-1426	316	105	variable	variable	ADJ
fuelectenerg-1426	316	106	order	order	NOUN
fuelectenerg-1426	316	107	.	.	PUNCT
fuelectenerg-1426	317	1	(	(	PUNCT
fuelectenerg-1426	317	2	60	60	NUM
fuelectenerg-1426	317	3	)	)	PUNCT
fuelectenerg-1426	317	4	from	from	ADP
fuelectenerg-1426	317	5	the	the	DET
fuelectenerg-1426	317	6	previous	previous	ADJ
fuelectenerg-1426	317	7	equations	equation	NOUN
fuelectenerg-1426	317	8	,	,	PUNCT
fuelectenerg-1426	317	9	and	and	CCONJ
fuelectenerg-1426	317	10	using	use	VERB
fuelectenerg-1426	317	11	elementary	elementary	ADJ
fuelectenerg-1426	317	12	count	count	NOUN
fuelectenerg-1426	317	13	rules	rule	NOUN
fuelectenerg-1426	317	14	,	,	PUNCT
fuelectenerg-1426	317	15	one	one	PRON
fuelectenerg-1426	317	16	can	can	AUX
fuelectenerg-1426	317	17	derive	derive	VERB
fuelectenerg-1426	317	18	by	by	ADP
fuelectenerg-1426	317	19	mathematical	mathematical	ADJ
fuelectenerg-1426	317	20	induction	induction	NOUN
fuelectenerg-1426	317	21	the	the	DET
fuelectenerg-1426	317	22	following	follow	VERB
fuelectenerg-1426	317	23	general	general	ADJ
fuelectenerg-1426	317	24	formulas	formula	NOUN
fuelectenerg-1426	317	25	for	for	ADP
fuelectenerg-1426	317	26	n	n	PRON
fuelectenerg-1426	317	27	being	be	AUX
fuelectenerg-1426	317	28	the	the	DET
fuelectenerg-1426	317	29	number	number	NOUN
fuelectenerg-1426	317	30	of	of	ADP
fuelectenerg-1426	317	31	variables	variable	NOUN
fuelectenerg-1426	317	32	and	and	CCONJ
fuelectenerg-1426	317	33	n	n	PRON
fuelectenerg-1426	317	34	being	be	AUX
fuelectenerg-1426	317	35	the	the	DET
fuelectenerg-1426	317	36	field	field	NOUN
fuelectenerg-1426	317	37	radix	radix	NOUN
fuelectenerg-1426	317	38	:	:	PUNCT
fuelectenerg-1426	317	39	ψn	ψn	PROPN
fuelectenerg-1426	317	40	,	,	PUNCT
fuelectenerg-1426	317	41	n	n	NOUN
fuelectenerg-1426	317	42	=	=	SYM
fuelectenerg-1426	317	43	n	n	X
fuelectenerg-1426	317	44	!	!	NUM
fuelectenerg-1426	317	45	,	,	PUNCT
fuelectenerg-1426	317	46	(	(	PUNCT
fuelectenerg-1426	317	47	61	61	NUM
fuelectenerg-1426	317	48	)	)	PUNCT
fuelectenerg-1426	317	49	ωn	ωn	PROPN
fuelectenerg-1426	317	50	,	,	PUNCT
fuelectenerg-1426	317	51	n	n	PROPN
fuelectenerg-1426	317	52	=	=	SYM
fuelectenerg-1426	317	53	n−1	n−1	PROPN
fuelectenerg-1426	317	54	∑	∑	ADP
fuelectenerg-1426	317	55	k=0	k=0	PROPN
fuelectenerg-1426	317	56	(	(	PUNCT
fuelectenerg-1426	317	57	n)k	n)k	X
fuelectenerg-1426	317	58	+1	+1	PROPN
fuelectenerg-1426	317	59	,	,	PUNCT
fuelectenerg-1426	317	60	(	(	PUNCT
fuelectenerg-1426	317	61	62	62	NUM
fuelectenerg-1426	317	62	)	)	PUNCT
fuelectenerg-1426	317	63	φn	φn	NOUN
fuelectenerg-1426	317	64	,	,	PUNCT
fuelectenerg-1426	317	65	n	n	NOUN
fuelectenerg-1426	317	66	=	=	SYM
fuelectenerg-1426	318	1	[	[	X
fuelectenerg-1426	318	2	∑n−1	∑n−1	ADP
fuelectenerg-1426	318	3	k=0	k=0	PROPN
fuelectenerg-1426	318	4	(	(	PUNCT
fuelectenerg-1426	318	5	n	n	CCONJ
fuelectenerg-1426	318	6	)	)	PUNCT
fuelectenerg-1426	318	7	k	k	NOUN
fuelectenerg-1426	318	8	]	]	X
fuelectenerg-1426	318	9	!	!	PUNCT
fuelectenerg-1426	319	1	[	[	X
fuelectenerg-1426	319	2	∑n−1	∑n−1	X
fuelectenerg-1426	319	3	k=0	k=0	PROPN
fuelectenerg-1426	319	4	(	(	PUNCT
fuelectenerg-1426	319	5	n)k	n)k	X
fuelectenerg-1426	319	6	−	−	ADP
fuelectenerg-1426	319	7	k]!k	k]!k	PROPN
fuelectenerg-1426	319	8	!	!	PUNCT
fuelectenerg-1426	320	1	,	,	PUNCT
fuelectenerg-1426	320	2	where	where	SCONJ
fuelectenerg-1426	320	3	k	k	NOUN
fuelectenerg-1426	320	4	=	=	PUNCT
fuelectenerg-1426	320	5	0,1,2,3	0,1,2,3	NUM
fuelectenerg-1426	320	6	,	,	PUNCT
fuelectenerg-1426	320	7	.	.	PUNCT
fuelectenerg-1426	320	8	.	.	PUNCT
fuelectenerg-1426	321	1	.	.	PUNCT
fuelectenerg-1426	322	1	,	,	PUNCT
fuelectenerg-1426	322	2	n	n	PRON
fuelectenerg-1426	322	3	−1	−1	NOUN
fuelectenerg-1426	322	4	,	,	PUNCT
fuelectenerg-1426	322	5	(	(	PUNCT
fuelectenerg-1426	322	6	63	63	NUM
fuelectenerg-1426	322	7	)	)	PUNCT
fuelectenerg-1426	322	8	φn	φn	NOUN
fuelectenerg-1426	322	9	,	,	PUNCT
fuelectenerg-1426	322	10	n	n	NOUN
fuelectenerg-1426	322	11	=	=	SYM
fuelectenerg-1426	322	12	(	(	PUNCT
fuelectenerg-1426	322	13	n)n−1	n)n−1	INTJ
fuelectenerg-1426	322	14	∑	∑	PROPN
fuelectenerg-1426	322	15	k1=0	k1=0	PROPN
fuelectenerg-1426	322	16	(	(	PUNCT
fuelectenerg-1426	322	17	n)n−2	n)n−2	ADP
fuelectenerg-1426	322	18	∑	∑	ADP
fuelectenerg-1426	322	19	k2=0	k2=0	PROPN
fuelectenerg-1426	322	20	·	·	PUNCT
fuelectenerg-1426	322	21	·	·	PUNCT
fuelectenerg-1426	322	22	·	·	PUNCT
fuelectenerg-1426	323	1	(	(	PUNCT
fuelectenerg-1426	323	2	n)0	n)0	X
fuelectenerg-1426	323	3	∑	∑	PUNCT
fuelectenerg-1426	323	4	kn=0	kn=0	X
fuelectenerg-1426	323	5	{	{	PUNCT
fuelectenerg-1426	323	6	n(n−1	n(n−1	NUM
fuelectenerg-1426	323	7	)	)	PUNCT
fuelectenerg-1426	323	8	!	!	PUNCT
fuelectenerg-1426	324	1	(	(	PUNCT
fuelectenerg-1426	324	2	n(n−1)−	n(n−1)−	ADV
fuelectenerg-1426	324	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	324	4	!	!	PUNCT
fuelectenerg-1426	325	1	n(n−2	n(n−2	PROPN
fuelectenerg-1426	325	2	)	)	PUNCT
fuelectenerg-1426	325	3	!	!	PUNCT
fuelectenerg-1426	326	1	(	(	PUNCT
fuelectenerg-1426	326	2	n(n−2)−	n(n−2)−	ADV
fuelectenerg-1426	326	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	326	4	!	!	PUNCT
fuelectenerg-1426	327	1	·	·	PUNCT
fuelectenerg-1426	327	2	·	·	PUNCT
fuelectenerg-1426	327	3	·	·	PUNCT
fuelectenerg-1426	327	4	n(0	n(0	PROPN
fuelectenerg-1426	327	5	)	)	PUNCT
fuelectenerg-1426	327	6	!	!	PUNCT
fuelectenerg-1426	328	1	(	(	PUNCT
fuelectenerg-1426	328	2	n(0)−	n(0)−	NUM
fuelectenerg-1426	328	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	328	4	!	!	PUNCT
fuelectenerg-1426	328	5	(	(	PUNCT
fuelectenerg-1426	328	6	n(n−1)(n)0	n(n−1)(n)0	NOUN
fuelectenerg-1426	328	7	)	)	PUNCT
fuelectenerg-1426	328	8	k1(n(n−1)(n)1	k1(n(n−1)(n)1	PROPN
fuelectenerg-1426	328	9	)	)	PUNCT
fuelectenerg-1426	328	10	k2	k2	X
fuelectenerg-1426	328	11	·	·	PUNCT
fuelectenerg-1426	328	12	·	·	PUNCT
fuelectenerg-1426	328	13	·	·	PUNCT
fuelectenerg-1426	328	14	(	(	PUNCT
fuelectenerg-1426	328	15	n(n−1)(n)(n−1	n(n−1)(n)(n−1	NOUN
fuelectenerg-1426	328	16	)	)	PUNCT
fuelectenerg-1426	328	17	)	)	PUNCT
fuelectenerg-1426	329	1	kn	kn	NOUN
fuelectenerg-1426	329	2	}	}	PUNCT
fuelectenerg-1426	329	3	.	.	PUNCT
fuelectenerg-1426	330	1	(	(	PUNCT
fuelectenerg-1426	330	2	64	64	NUM
fuelectenerg-1426	330	3	)	)	PUNCT
fuelectenerg-1426	330	4	one	one	NOUN
fuelectenerg-1426	330	5	can	can	AUX
fuelectenerg-1426	330	6	note	note	VERB
fuelectenerg-1426	330	7	that	that	SCONJ
fuelectenerg-1426	330	8	the	the	DET
fuelectenerg-1426	330	9	formula	formula	NOUN
fuelectenerg-1426	330	10	in	in	ADP
fuelectenerg-1426	330	11	equation	equation	NOUN
fuelectenerg-1426	330	12	(	(	PUNCT
fuelectenerg-1426	330	13	52	52	NUM
fuelectenerg-1426	330	14	)	)	PUNCT
fuelectenerg-1426	330	15	used	use	VERB
fuelectenerg-1426	330	16	to	to	PART
fuelectenerg-1426	330	17	obtain	obtain	VERB
fuelectenerg-1426	330	18	the	the	DET
fuelectenerg-1426	330	19	total	total	ADJ
fuelectenerg-1426	330	20	number	number	NOUN
fuelectenerg-1426	330	21	of	of	ADP
fuelectenerg-1426	330	22	inclusive	inclusive	ADJ
fuelectenerg-1426	330	23	forms	form	NOUN
fuelectenerg-1426	330	24	for	for	ADP
fuelectenerg-1426	330	25	n	n	NOUN
fuelectenerg-1426	330	26	variables	variable	NOUN
fuelectenerg-1426	330	27	and	and	CCONJ
fuelectenerg-1426	330	28	n	n	DET
fuelectenerg-1426	330	29	radix	radix	NOUN
fuelectenerg-1426	330	30	of	of	ADP
fuelectenerg-1426	330	31	galois	galois	PROPN
fuelectenerg-1426	330	32	field	field	NOUN
fuelectenerg-1426	330	33	is	be	AUX
fuelectenerg-1426	330	34	a	a	DET
fuelectenerg-1426	330	35	very	very	ADV
fuelectenerg-1426	330	36	general	general	ADJ
fuelectenerg-1426	330	37	formula	formula	NOUN
fuelectenerg-1426	330	38	that	that	PRON
fuelectenerg-1426	330	39	includes	include	VERB
fuelectenerg-1426	330	40	the	the	DET
fuelectenerg-1426	330	41	ternary	ternary	ADJ
fuelectenerg-1426	330	42	case	case	NOUN
fuelectenerg-1426	330	43	in	in	ADP
fuelectenerg-1426	330	44	equation	equation	NOUN
fuelectenerg-1426	330	45	(	(	PUNCT
fuelectenerg-1426	330	46	38	38	NUM
fuelectenerg-1426	330	47	)	)	PUNCT
fuelectenerg-1426	330	48	and	and	CCONJ
fuelectenerg-1426	330	49	the	the	DET
fuelectenerg-1426	330	50	quaternary	quaternary	ADJ
fuelectenerg-1426	330	51	case	case	NOUN
fuelectenerg-1426	330	52	in	in	ADP
fuelectenerg-1426	330	53	equation	equation	NOUN
fuelectenerg-1426	330	54	(	(	PUNCT
fuelectenerg-1426	330	55	51	51	NUM
fuelectenerg-1426	330	56	)	)	PUNCT
fuelectenerg-1426	330	57	as	as	ADP
fuelectenerg-1426	330	58	special	special	ADJ
fuelectenerg-1426	330	59	cases	case	NOUN
fuelectenerg-1426	330	60	.	.	PUNCT
fuelectenerg-1426	331	1	numerical	numerical	ADJ
fuelectenerg-1426	331	2	counting	counting	NOUN
fuelectenerg-1426	331	3	results	result	NOUN
fuelectenerg-1426	331	4	that	that	PRON
fuelectenerg-1426	331	5	are	be	AUX
fuelectenerg-1426	331	6	obtained	obtain	VERB
fuelectenerg-1426	331	7	from	from	ADP
fuelectenerg-1426	331	8	equation	equation	NOUN
fuelectenerg-1426	331	9	(	(	PUNCT
fuelectenerg-1426	331	10	52	52	NUM
fuelectenerg-1426	331	11	)	)	PUNCT
fuelectenerg-1426	331	12	can	can	AUX
fuelectenerg-1426	331	13	be	be	AUX
fuelectenerg-1426	331	14	used	use	VERB
fuelectenerg-1426	331	15	in	in	ADP
fuelectenerg-1426	331	16	search	search	NOUN
fuelectenerg-1426	331	17	heuristics	heuristic	NOUN
fuelectenerg-1426	331	18	as	as	ADP
fuelectenerg-1426	331	19	numerical	numerical	ADJ
fuelectenerg-1426	331	20	bounds	bound	NOUN
fuelectenerg-1426	331	21	that	that	PRON
fuelectenerg-1426	331	22	could	could	AUX
fuelectenerg-1426	331	23	be	be	AUX
fuelectenerg-1426	331	24	incorporated	incorporate	VERB
fuelectenerg-1426	331	25	into	into	ADP
fuelectenerg-1426	331	26	efficient	efficient	ADJ
fuelectenerg-1426	331	27	search	search	NOUN
fuelectenerg-1426	331	28	of	of	ADP
fuelectenerg-1426	331	29	s	s	NOUN
fuelectenerg-1426	331	30	/	/	SYM
fuelectenerg-1426	331	31	d	d	NOUN
fuelectenerg-1426	331	32	trees	tree	NOUN
fuelectenerg-1426	331	33	in	in	ADP
fuelectenerg-1426	331	34	order	order	NOUN
fuelectenerg-1426	331	35	to	to	PART
fuelectenerg-1426	331	36	obtain	obtain	VERB
fuelectenerg-1426	331	37	minimal	minimal	ADJ
fuelectenerg-1426	331	38	gfsop	gfsop	NOUN
fuelectenerg-1426	331	39	forms	form	NOUN
fuelectenerg-1426	331	40	for	for	ADP
fuelectenerg-1426	331	41	specific	specific	ADJ
fuelectenerg-1426	331	42	multi	multi	ADJ
fuelectenerg-1426	331	43	-	-	ADJ
fuelectenerg-1426	331	44	valued	value	VERB
fuelectenerg-1426	331	45	logic	logic	NOUN
fuelectenerg-1426	331	46	functions	function	NOUN
fuelectenerg-1426	331	47	.	.	PUNCT
fuelectenerg-1426	332	1	since	since	SCONJ
fuelectenerg-1426	332	2	such	such	ADJ
fuelectenerg-1426	332	3	search	search	NOUN
fuelectenerg-1426	332	4	for	for	ADP
fuelectenerg-1426	332	5	minimal	minimal	ADJ
fuelectenerg-1426	332	6	forms	form	NOUN
fuelectenerg-1426	332	7	is	be	AUX
fuelectenerg-1426	332	8	already	already	ADV
fuelectenerg-1426	332	9	a	a	DET
fuelectenerg-1426	332	10	difficult	difficult	ADJ
fuelectenerg-1426	332	11	problem	problem	NOUN
fuelectenerg-1426	332	12	in	in	ADP
fuelectenerg-1426	332	13	two	two	NUM
fuelectenerg-1426	332	14	-	-	PUNCT
fuelectenerg-1426	332	15	valued	value	VERB
fuelectenerg-1426	332	16	logic	logic	NOUN
fuelectenerg-1426	332	17	for	for	ADP
fuelectenerg-1426	332	18	example	example	NOUN
fuelectenerg-1426	332	19	using	use	VERB
fuelectenerg-1426	332	20	binary	binary	PROPN
fuelectenerg-1426	332	21	s	s	PROPN
fuelectenerg-1426	332	22	/	/	SYM
fuelectenerg-1426	332	23	d	d	NOUN
fuelectenerg-1426	332	24	trees	tree	NOUN
fuelectenerg-1426	332	25	especially	especially	ADV
fuelectenerg-1426	332	26	when	when	SCONJ
fuelectenerg-1426	332	27	the	the	DET
fuelectenerg-1426	332	28	number	number	NOUN
fuelectenerg-1426	332	29	of	of	ADP
fuelectenerg-1426	332	30	variables	variable	NOUN
fuelectenerg-1426	332	31	is	be	AUX
fuelectenerg-1426	332	32	large	large	ADJ
fuelectenerg-1426	332	33	,	,	PUNCT
fuelectenerg-1426	332	34	the	the	DET
fuelectenerg-1426	332	35	search	search	NOUN
fuelectenerg-1426	332	36	for	for	ADP
fuelectenerg-1426	332	37	minimal	minimal	ADJ
fuelectenerg-1426	332	38	gfsop	gfsop	NOUN
fuelectenerg-1426	332	39	forms	form	NOUN
fuelectenerg-1426	332	40	in	in	ADP
fuelectenerg-1426	332	41	multi	multi	ADJ
fuelectenerg-1426	332	42	-	-	ADJ
fuelectenerg-1426	332	43	valued	value	VERB
fuelectenerg-1426	332	44	galois	galois	PROPN
fuelectenerg-1426	332	45	logic	logic	NOUN
fuelectenerg-1426	332	46	will	will	AUX
fuelectenerg-1426	332	47	be	be	AUX
fuelectenerg-1426	332	48	very	very	ADV
fuelectenerg-1426	332	49	difficult	difficult	ADJ
fuelectenerg-1426	332	50	.	.	PUNCT
fuelectenerg-1426	333	1	thus	thus	ADV
fuelectenerg-1426	333	2	,	,	PUNCT
fuelectenerg-1426	333	3	further	further	PROPN
fuelectenerg-1426	333	4	numerical	numerical	ADJ
fuelectenerg-1426	333	5	evaluations	evaluation	NOUN
fuelectenerg-1426	333	6	have	have	VERB
fuelectenerg-1426	333	7	to	to	PART
fuelectenerg-1426	333	8	be	be	AUX
fuelectenerg-1426	333	9	conducted	conduct	VERB
fuelectenerg-1426	333	10	in	in	ADP
fuelectenerg-1426	333	11	order	order	NOUN
fuelectenerg-1426	333	12	to	to	PART
fuelectenerg-1426	333	13	estimate	estimate	VERB
fuelectenerg-1426	333	14	the	the	DET
fuelectenerg-1426	333	15	usefulness	usefulness	NOUN
fuelectenerg-1426	333	16	of	of	ADP
fuelectenerg-1426	333	17	the	the	DET
fuelectenerg-1426	333	18	utilizations	utilization	NOUN
fuelectenerg-1426	333	19	of	of	ADP
fuelectenerg-1426	333	20	the	the	DET
fuelectenerg-1426	333	21	numerical	numerical	ADJ
fuelectenerg-1426	333	22	bounds	bound	NOUN
fuelectenerg-1426	333	23	obtained	obtain	VERB
fuelectenerg-1426	333	24	from	from	ADP
fuelectenerg-1426	333	25	equation	equation	NOUN
fuelectenerg-1426	333	26	(	(	PUNCT
fuelectenerg-1426	333	27	52	52	NUM
fuelectenerg-1426	333	28	)	)	PUNCT
fuelectenerg-1426	333	29	in	in	ADP
fuelectenerg-1426	333	30	such	such	ADJ
fuelectenerg-1426	333	31	extended	extended	ADJ
fuelectenerg-1426	333	32	multi	multi	ADJ
fuelectenerg-1426	333	33	-	-	ADJ
fuelectenerg-1426	333	34	valued	value	VERB
fuelectenerg-1426	333	35	search	search	NOUN
fuelectenerg-1426	333	36	heuristics	heuristic	NOUN
fuelectenerg-1426	333	37	.	.	PUNCT
fuelectenerg-1426	334	1	example	example	NOUN
fuelectenerg-1426	334	2	6	6	NUM
fuelectenerg-1426	334	3	.	.	PUNCT
fuelectenerg-1426	335	1	the	the	DET
fuelectenerg-1426	335	2	number	number	NOUN
fuelectenerg-1426	335	3	of	of	ADP
fuelectenerg-1426	335	4	qifs	qifs	PROPN
fuelectenerg-1426	335	5	over	over	ADP
fuelectenerg-1426	335	6	gf(4	gf(4	NOUN
fuelectenerg-1426	335	7	)	)	PUNCT
fuelectenerg-1426	335	8	for	for	ADP
fuelectenerg-1426	335	9	two	two	NUM
fuelectenerg-1426	335	10	variables	variable	NOUN
fuelectenerg-1426	335	11	(	(	PUNCT
fuelectenerg-1426	335	12	i.e.	i.e.	X
fuelectenerg-1426	335	13	,	,	PUNCT
fuelectenerg-1426	335	14	n	n	NOUN
fuelectenerg-1426	335	15	=	=	SYM
fuelectenerg-1426	335	16	2	2	NUM
fuelectenerg-1426	335	17	and	and	CCONJ
fuelectenerg-1426	335	18	n	n	NOUN
fuelectenerg-1426	335	19	=	=	NOUN
fuelectenerg-1426	335	20	4	4	X
fuelectenerg-1426	335	21	)	)	PUNCT
fuelectenerg-1426	335	22	is	be	AUX
fuelectenerg-1426	335	23	:	:	PUNCT
fuelectenerg-1426	335	24	115	115	NUM
fuelectenerg-1426	335	25	716	716	NUM
fuelectenerg-1426	335	26	a.	a.	NOUN
fuelectenerg-1426	335	27	n.	n.	PROPN
fuelectenerg-1426	335	28	al	al	PROPN
fuelectenerg-1426	335	29	-	-	PUNCT
fuelectenerg-1426	335	30	rabadi	rabadi	PROPN
fuelectenerg-1426	335	31	multi	multi	ADJ
fuelectenerg-1426	335	32	-	-	ADJ
fuelectenerg-1426	335	33	valued	value	VERB
fuelectenerg-1426	335	34	galois	galois	PROPN
fuelectenerg-1426	335	35	shannon	shannon	PROPN
fuelectenerg-1426	335	36	davio	davio	PROPN
fuelectenerg-1426	335	37	trees	tree	NOUN
fuelectenerg-1426	335	38	and	and	CCONJ
fuelectenerg-1426	335	39	their	their	PRON
fuelectenerg-1426	335	40	complexity	complexity	NOUN
fuelectenerg-1426	335	41	717	717	NUM
fuelectenerg-1426	335	42	multi	multi	ADV
fuelectenerg-1426	335	43	-	-	ADJ
fuelectenerg-1426	335	44	valued	value	VERB
fuelectenerg-1426	335	45	galois	galois	PROPN
fuelectenerg-1426	335	46	shannon	shannon	PROPN
fuelectenerg-1426	335	47	davio	davio	PROPN
fuelectenerg-1426	335	48	trees	tree	NOUN
fuelectenerg-1426	335	49	and	and	CCONJ
fuelectenerg-1426	335	50	their	their	PRON
fuelectenerg-1426	335	51	complexity	complexity	NOUN
fuelectenerg-1426	335	52	φ4,2	φ4,2	PROPN
fuelectenerg-1426	335	53	=	=	SYM
fuelectenerg-1426	335	54	(	(	PUNCT
fuelectenerg-1426	335	55	4)2−1	4)2−1	NOUN
fuelectenerg-1426	335	56	∑	∑	PROPN
fuelectenerg-1426	335	57	k1=0	k1=0	PROPN
fuelectenerg-1426	335	58	(	(	PUNCT
fuelectenerg-1426	335	59	4)2−2	4)2−2	INTJ
fuelectenerg-1426	335	60	∑	∑	PUNCT
fuelectenerg-1426	335	61	k2=0	k2=0	PROPN
fuelectenerg-1426	335	62	{	{	PUNCT
fuelectenerg-1426	335	63	4(2−1	4(2−1	NOUN
fuelectenerg-1426	335	64	)	)	PUNCT
fuelectenerg-1426	335	65	!	!	PUNCT
fuelectenerg-1426	336	1	(	(	PUNCT
fuelectenerg-1426	336	2	4(2−1)−	4(2−1)−	ADJ
fuelectenerg-1426	336	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	336	4	!	!	PUNCT
fuelectenerg-1426	336	5	4(2−2	4(2−2	NOUN
fuelectenerg-1426	336	6	)	)	PUNCT
fuelectenerg-1426	336	7	!	!	PUNCT
fuelectenerg-1426	337	1	(	(	PUNCT
fuelectenerg-1426	337	2	4(2−2)−	4(2−2)−	ADJ
fuelectenerg-1426	337	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	337	4	!	!	PUNCT
fuelectenerg-1426	338	1	(	(	PUNCT
fuelectenerg-1426	338	2	4(4−1)(4)0	4(4−1)(4)0	NOUN
fuelectenerg-1426	338	3	)	)	PUNCT
fuelectenerg-1426	338	4	k1(4(4−1)(4)1	k1(4(4−1)(4)1	NOUN
fuelectenerg-1426	338	5	)	)	PUNCT
fuelectenerg-1426	338	6	k2	k2	PROPN
fuelectenerg-1426	338	7	}	}	PUNCT
fuelectenerg-1426	338	8	,	,	PUNCT
fuelectenerg-1426	338	9	=	=	PUNCT
fuelectenerg-1426	338	10	φ00|4,2	φ00|4,2	NOUN
fuelectenerg-1426	338	11	+	+	ADJ
fuelectenerg-1426	338	12	φ10|4,2	φ10|4,2	NOUN
fuelectenerg-1426	338	13	+	+	ADP
fuelectenerg-1426	338	14	φ20|4,2	φ20|4,2	PROPN
fuelectenerg-1426	338	15	+	+	PROPN
fuelectenerg-1426	338	16	φ30|4,2	φ30|4,2	PROPN
fuelectenerg-1426	338	17	+	+	ADJ
fuelectenerg-1426	338	18	φ40|4,2	φ40|4,2	PROPN
fuelectenerg-1426	338	19	+	+	ADJ
fuelectenerg-1426	338	20	φ01|4,2	φ01|4,2	PROPN
fuelectenerg-1426	338	21	+	+	ADJ
fuelectenerg-1426	338	22	φ11|4,2	φ11|4,2	NOUN
fuelectenerg-1426	338	23	+	+	PROPN
fuelectenerg-1426	338	24	φ21|4,2	φ21|4,2	PROPN
fuelectenerg-1426	338	25	+	+	PROPN
fuelectenerg-1426	338	26	φ31|4,2	φ31|4,2	PROPN
fuelectenerg-1426	338	27	+	+	NOUN
fuelectenerg-1426	338	28	φ41|4,2	φ41|4,2	PROPN
fuelectenerg-1426	338	29	=	=	SYM
fuelectenerg-1426	338	30	1	1	NUM
fuelectenerg-1426	338	31	+	+	NUM
fuelectenerg-1426	338	32	256	256	NUM
fuelectenerg-1426	338	33	+	+	NUM
fuelectenerg-1426	338	34	24,576	24,576	NUM
fuelectenerg-1426	338	35	+	+	NOUN
fuelectenerg-1426	338	36	1,048,576	1,048,576	NUM
fuelectenerg-1426	338	37	+	+	NOUN
fuelectenerg-1426	338	38	16,777,216	16,777,216	NUM
fuelectenerg-1426	338	39	+	+	NUM
fuelectenerg-1426	338	40	16,777,216	16,777,216	NUM
fuelectenerg-1426	338	41	+	+	NOUN
fuelectenerg-1426	338	42	4,294,967,296	4,294,967,296	NUM
fuelectenerg-1426	338	43	+	+	NOUN
fuelectenerg-1426	338	44	412,316,860,416	412,316,860,416	NUM
fuelectenerg-1426	339	1	+	+	SYM
fuelectenerg-1426	339	2	1.75921860444×1013	1.75921860444×1013	NUM
fuelectenerg-1426	339	3	+	+	NOUN
fuelectenerg-1426	339	4	2.81477976711×1014	2.81477976711×1014	NUM
fuelectenerg-1426	339	5	=	=	SYM
fuelectenerg-1426	339	6	2.99483809211×1014	2.99483809211×1014	NOUN
fuelectenerg-1426	339	7	.	.	PUNCT
fuelectenerg-1426	340	1	corollary	corollary	ADJ
fuelectenerg-1426	340	2	1	1	NUM
fuelectenerg-1426	340	3	.	.	PUNCT
fuelectenerg-1426	341	1	from	from	ADP
fuelectenerg-1426	341	2	equation	equation	NOUN
fuelectenerg-1426	341	3	(	(	PUNCT
fuelectenerg-1426	341	4	52	52	NUM
fuelectenerg-1426	341	5	)	)	PUNCT
fuelectenerg-1426	341	6	,	,	PUNCT
fuelectenerg-1426	341	7	the	the	DET
fuelectenerg-1426	341	8	count	count	NOUN
fuelectenerg-1426	341	9	of	of	ADP
fuelectenerg-1426	341	10	ifs	ifs	PROPN
fuelectenerg-1426	341	11	for	for	ADP
fuelectenerg-1426	341	12	n	n	NOUN
fuelectenerg-1426	341	13	variables	variable	NOUN
fuelectenerg-1426	341	14	and	and	CCONJ
fuelectenerg-1426	341	15	second	second	ADJ
fuelectenerg-1426	341	16	radix	radix	NOUN
fuelectenerg-1426	341	17	is	be	AUX
fuelectenerg-1426	341	18	:	:	PUNCT
fuelectenerg-1426	341	19	n−1	n−1	PROPN
fuelectenerg-1426	341	20	∏	∏	PROPN
fuelectenerg-1426	341	21	k=0	k=0	X
fuelectenerg-1426	341	22	(	(	PUNCT
fuelectenerg-1426	341	23	1	1	NUM
fuelectenerg-1426	341	24	+	+	NUM
fuelectenerg-1426	341	25	22n−k−1	22n−k−1	NUM
fuelectenerg-1426	341	26	)	)	PUNCT
fuelectenerg-1426	341	27	2k	2k	NOUN
fuelectenerg-1426	341	28	=	=	SYM
fuelectenerg-1426	341	29	(	(	PUNCT
fuelectenerg-1426	341	30	2)n−1	2)n−1	NUM
fuelectenerg-1426	341	31	∑	∑	PROPN
fuelectenerg-1426	341	32	k1=0	k1=0	PROPN
fuelectenerg-1426	341	33	(	(	PUNCT
fuelectenerg-1426	341	34	2)n−2	2)n−2	NUM
fuelectenerg-1426	341	35	∑	∑	PROPN
fuelectenerg-1426	341	36	k2=0	k2=0	PROPN
fuelectenerg-1426	341	37	·	·	PUNCT
fuelectenerg-1426	341	38	·	·	PUNCT
fuelectenerg-1426	341	39	·	·	PUNCT
fuelectenerg-1426	342	1	(	(	PUNCT
fuelectenerg-1426	342	2	2)0	2)0	NUM
fuelectenerg-1426	342	3	∑	∑	PROPN
fuelectenerg-1426	342	4	kn=0	kn=0	X
fuelectenerg-1426	342	5	{	{	PUNCT
fuelectenerg-1426	342	6	2(n−1	2(n−1	ADJ
fuelectenerg-1426	342	7	)	)	PUNCT
fuelectenerg-1426	342	8	!	!	PUNCT
fuelectenerg-1426	343	1	(	(	PUNCT
fuelectenerg-1426	343	2	2(n−1)−	2(n−1)−	NOUN
fuelectenerg-1426	343	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	343	4	!	!	PUNCT
fuelectenerg-1426	343	5	2(n−2	2(n−2	PROPN
fuelectenerg-1426	343	6	)	)	PUNCT
fuelectenerg-1426	343	7	!	!	PUNCT
fuelectenerg-1426	344	1	(	(	PUNCT
fuelectenerg-1426	344	2	2(n−2)−	2(n−2)−	X
fuelectenerg-1426	344	3	k2)!k2	k2)!k2	X
fuelectenerg-1426	344	4	!	!	PUNCT
fuelectenerg-1426	344	5	·	·	PUNCT
fuelectenerg-1426	344	6	·	·	PUNCT
fuelectenerg-1426	344	7	·	·	PUNCT
fuelectenerg-1426	344	8	2(0	2(0	NUM
fuelectenerg-1426	344	9	)	)	PUNCT
fuelectenerg-1426	344	10	!	!	PUNCT
fuelectenerg-1426	345	1	(	(	PUNCT
fuelectenerg-1426	345	2	2(0)−	2(0)−	NUM
fuelectenerg-1426	345	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	345	4	!	!	PUNCT
fuelectenerg-1426	346	1	(	(	PUNCT
fuelectenerg-1426	346	2	2(2−1)(2)0	2(2−1)(2)0	X
fuelectenerg-1426	346	3	)	)	PUNCT
fuelectenerg-1426	346	4	k1(2(2−1)(2)1	k1(2(2−1)(2)1	PROPN
fuelectenerg-1426	346	5	)	)	PUNCT
fuelectenerg-1426	346	6	k2	k2	X
fuelectenerg-1426	346	7	·	·	PUNCT
fuelectenerg-1426	346	8	·	·	PUNCT
fuelectenerg-1426	346	9	·	·	PUNCT
fuelectenerg-1426	346	10	(	(	PUNCT
fuelectenerg-1426	346	11	2(2−1)(2)(n−1	2(2−1)(2)(n−1	NUM
fuelectenerg-1426	346	12	)	)	PUNCT
fuelectenerg-1426	346	13	)	)	PUNCT
fuelectenerg-1426	347	1	kn	kn	NOUN
fuelectenerg-1426	347	2	}	}	PUNCT
fuelectenerg-1426	347	3	.	.	PUNCT
fuelectenerg-1426	348	1	(	(	PUNCT
fuelectenerg-1426	348	2	65	65	NUM
fuelectenerg-1426	348	3	)	)	PUNCT
fuelectenerg-1426	348	4	as	as	SCONJ
fuelectenerg-1426	348	5	previously	previously	ADV
fuelectenerg-1426	348	6	mentioned	mention	VERB
fuelectenerg-1426	348	7	,	,	PUNCT
fuelectenerg-1426	348	8	this	this	DET
fuelectenerg-1426	348	9	enumeration	enumeration	NOUN
fuelectenerg-1426	348	10	can	can	AUX
fuelectenerg-1426	348	11	be	be	AUX
fuelectenerg-1426	348	12	useful	useful	ADJ
fuelectenerg-1426	348	13	as	as	ADP
fuelectenerg-1426	348	14	a	a	DET
fuelectenerg-1426	348	15	terminating	terminate	VERB
fuelectenerg-1426	348	16	point	point	NOUN
fuelectenerg-1426	348	17	of	of	ADP
fuelectenerg-1426	348	18	minimization	minimization	NOUN
fuelectenerg-1426	348	19	algorithms	algorithm	NOUN
fuelectenerg-1426	348	20	for	for	ADP
fuelectenerg-1426	348	21	multi	multi	ADJ
fuelectenerg-1426	348	22	-	-	ADJ
fuelectenerg-1426	348	23	valued	value	VERB
fuelectenerg-1426	348	24	functions	function	NOUN
fuelectenerg-1426	348	25	.	.	PUNCT
fuelectenerg-1426	349	1	yet	yet	ADV
fuelectenerg-1426	349	2	,	,	PUNCT
fuelectenerg-1426	349	3	as	as	SCONJ
fuelectenerg-1426	349	4	shown	show	VERB
fuelectenerg-1426	349	5	,	,	PUNCT
fuelectenerg-1426	349	6	the	the	DET
fuelectenerg-1426	349	7	number	number	NOUN
fuelectenerg-1426	349	8	of	of	ADP
fuelectenerg-1426	349	9	combinations	combination	NOUN
fuelectenerg-1426	349	10	is	be	AUX
fuelectenerg-1426	349	11	so	so	ADV
fuelectenerg-1426	349	12	large	large	ADJ
fuelectenerg-1426	349	13	that	that	DET
fuelectenerg-1426	349	14	restriction	restriction	NOUN
fuelectenerg-1426	349	15	to	to	ADP
fuelectenerg-1426	349	16	some	some	DET
fuelectenerg-1426	349	17	particular	particular	ADJ
fuelectenerg-1426	349	18	cases	case	NOUN
fuelectenerg-1426	349	19	of	of	ADP
fuelectenerg-1426	349	20	functional	functional	ADJ
fuelectenerg-1426	349	21	expressions	expression	NOUN
fuelectenerg-1426	349	22	can	can	AUX
fuelectenerg-1426	349	23	be	be	AUX
fuelectenerg-1426	349	24	more	more	ADV
fuelectenerg-1426	349	25	feasible	feasible	ADJ
fuelectenerg-1426	349	26	.	.	PUNCT
fuelectenerg-1426	350	1	the	the	DET
fuelectenerg-1426	350	2	following	follow	VERB
fuelectenerg-1426	350	3	section	section	NOUN
fuelectenerg-1426	350	4	introduces	introduce	VERB
fuelectenerg-1426	350	5	a	a	DET
fuelectenerg-1426	350	6	fast	fast	ADJ
fuelectenerg-1426	350	7	method	method	NOUN
fuelectenerg-1426	350	8	to	to	PART
fuelectenerg-1426	350	9	calculate	calculate	VERB
fuelectenerg-1426	350	10	the	the	DET
fuelectenerg-1426	350	11	number	number	NOUN
fuelectenerg-1426	350	12	of	of	ADP
fuelectenerg-1426	350	13	ifs	ifs	PROPN
fuelectenerg-1426	350	14	for	for	ADP
fuelectenerg-1426	350	15	an	an	DET
fuelectenerg-1426	350	16	arbitrary	arbitrary	ADJ
fuelectenerg-1426	350	17	galois	galois	NOUN
fuelectenerg-1426	350	18	field	field	NOUN
fuelectenerg-1426	350	19	logic	logic	NOUN
fuelectenerg-1426	350	20	for	for	ADP
fuelectenerg-1426	350	21	functions	function	NOUN
fuelectenerg-1426	350	22	with	with	ADP
fuelectenerg-1426	350	23	two	two	NUM
fuelectenerg-1426	350	24	variables	variable	NOUN
fuelectenerg-1426	350	25	.	.	PUNCT
fuelectenerg-1426	351	1	4.2	4.2	NUM
fuelectenerg-1426	351	2	the	the	DET
fuelectenerg-1426	351	3	ifn,2	ifn,2	ADJ
fuelectenerg-1426	351	4	triangles	triangle	NOUN
fuelectenerg-1426	351	5	:	:	PUNCT
fuelectenerg-1426	351	6	fast	fast	ADJ
fuelectenerg-1426	351	7	count	count	NOUN
fuelectenerg-1426	351	8	calculations	calculation	NOUN
fuelectenerg-1426	351	9	of	of	ADP
fuelectenerg-1426	351	10	ifs	ifs	PROPN
fuelectenerg-1426	351	11	for	for	ADP
fuelectenerg-1426	351	12	gf(pk	gf(pk	NOUN
fuelectenerg-1426	351	13	)	)	PUNCT
fuelectenerg-1426	351	14	and	and	CCONJ
fuelectenerg-1426	351	15	two	two	NUM
fuelectenerg-1426	351	16	-	-	PUNCT
fuelectenerg-1426	351	17	variable	variable	NOUN
fuelectenerg-1426	351	18	functions	function	NOUN
fuelectenerg-1426	351	19	the	the	DET
fuelectenerg-1426	351	20	count	count	NOUN
fuelectenerg-1426	351	21	of	of	ADP
fuelectenerg-1426	351	22	the	the	DET
fuelectenerg-1426	351	23	number	number	NOUN
fuelectenerg-1426	351	24	of	of	ADP
fuelectenerg-1426	351	25	ifs	ifs	PROPN
fuelectenerg-1426	351	26	can	can	AUX
fuelectenerg-1426	351	27	be	be	AUX
fuelectenerg-1426	351	28	important	important	ADJ
fuelectenerg-1426	351	29	in	in	ADP
fuelectenerg-1426	351	30	many	many	ADJ
fuelectenerg-1426	351	31	applications	application	NOUN
fuelectenerg-1426	351	32	,	,	PUNCT
fuelectenerg-1426	351	33	especially	especially	ADV
fuelectenerg-1426	351	34	in	in	ADP
fuelectenerg-1426	351	35	providing	provide	VERB
fuelectenerg-1426	351	36	upper	upper	ADJ
fuelectenerg-1426	351	37	numerical	numerical	ADJ
fuelectenerg-1426	351	38	boundaries	boundary	NOUN
fuelectenerg-1426	351	39	for	for	ADP
fuelectenerg-1426	351	40	efficient	efficient	ADJ
fuelectenerg-1426	351	41	search	search	NOUN
fuelectenerg-1426	351	42	of	of	ADP
fuelectenerg-1426	351	43	a	a	DET
fuelectenerg-1426	351	44	minimum	minimum	ADJ
fuelectenerg-1426	351	45	gfsop	gfsop	NOUN
fuelectenerg-1426	351	46	.	.	PUNCT
fuelectenerg-1426	352	1	calculating	calculate	VERB
fuelectenerg-1426	352	2	the	the	DET
fuelectenerg-1426	352	3	numbers	number	NOUN
fuelectenerg-1426	352	4	of	of	ADP
fuelectenerg-1426	352	5	inclusive	inclusive	ADJ
fuelectenerg-1426	352	6	forms	form	NOUN
fuelectenerg-1426	352	7	can	can	AUX
fuelectenerg-1426	352	8	be	be	AUX
fuelectenerg-1426	352	9	very	very	ADV
fuelectenerg-1426	352	10	time	time	NOUN
fuelectenerg-1426	352	11	consuming	consume	VERB
fuelectenerg-1426	352	12	due	due	ADP
fuelectenerg-1426	352	13	to	to	ADP
fuelectenerg-1426	352	14	the	the	DET
fuelectenerg-1426	352	15	time	time	NOUN
fuelectenerg-1426	352	16	required	require	VERB
fuelectenerg-1426	352	17	to	to	PART
fuelectenerg-1426	352	18	perform	perform	VERB
fuelectenerg-1426	352	19	the	the	DET
fuelectenerg-1426	352	20	mathematical	mathematical	ADJ
fuelectenerg-1426	352	21	operations	operation	NOUN
fuelectenerg-1426	352	22	in	in	ADP
fuelectenerg-1426	352	23	the	the	DET
fuelectenerg-1426	352	24	general	general	ADJ
fuelectenerg-1426	352	25	equation	equation	NOUN
fuelectenerg-1426	352	26	(	(	PUNCT
fuelectenerg-1426	352	27	52	52	NUM
fuelectenerg-1426	352	28	)	)	PUNCT
fuelectenerg-1426	352	29	.	.	PUNCT
fuelectenerg-1426	353	1	this	this	PRON
fuelectenerg-1426	353	2	is	be	AUX
fuelectenerg-1426	353	3	why	why	SCONJ
fuelectenerg-1426	353	4	a	a	DET
fuelectenerg-1426	353	5	fast	fast	ADJ
fuelectenerg-1426	353	6	method	method	NOUN
fuelectenerg-1426	353	7	to	to	PART
fuelectenerg-1426	353	8	generate	generate	VERB
fuelectenerg-1426	353	9	the	the	DET
fuelectenerg-1426	353	10	number	number	NOUN
fuelectenerg-1426	353	11	of	of	ADP
fuelectenerg-1426	353	12	ifs	ifs	PROPN
fuelectenerg-1426	353	13	is	be	AUX
fuelectenerg-1426	353	14	needed	need	VERB
fuelectenerg-1426	353	15	.	.	PUNCT
fuelectenerg-1426	354	1	because	because	SCONJ
fuelectenerg-1426	354	2	functions	function	NOUN
fuelectenerg-1426	354	3	with	with	ADP
fuelectenerg-1426	354	4	two	two	NUM
fuelectenerg-1426	354	5	variables	variable	NOUN
fuelectenerg-1426	354	6	find	find	VERB
fuelectenerg-1426	354	7	an	an	DET
fuelectenerg-1426	354	8	important	important	ADJ
fuelectenerg-1426	354	9	application	application	NOUN
fuelectenerg-1426	354	10	such	such	ADJ
fuelectenerg-1426	354	11	as	as	ADP
fuelectenerg-1426	354	12	in	in	ADP
fuelectenerg-1426	354	13	universal	universal	ADJ
fuelectenerg-1426	354	14	logic	logic	NOUN
fuelectenerg-1426	354	15	modules	module	NOUN
fuelectenerg-1426	354	16	(	(	PUNCT
fuelectenerg-1426	354	17	ulms	ulm	NOUN
fuelectenerg-1426	354	18	)	)	PUNCT
fuelectenerg-1426	354	19	for	for	ADP
fuelectenerg-1426	354	20	pairs	pair	NOUN
fuelectenerg-1426	354	21	of	of	ADP
fuelectenerg-1426	354	22	control	control	NOUN
fuelectenerg-1426	354	23	variables	variable	NOUN
fuelectenerg-1426	354	24	that	that	PRON
fuelectenerg-1426	354	25	generalize	generalize	VERB
fuelectenerg-1426	354	26	shannon	shannon	PROPN
fuelectenerg-1426	354	27	and	and	CCONJ
fuelectenerg-1426	354	28	davio	davio	NOUN
fuelectenerg-1426	354	29	expansion	expansion	NOUN
fuelectenerg-1426	354	30	modules	module	NOUN
fuelectenerg-1426	354	31	[	[	X
fuelectenerg-1426	354	32	2	2	NUM
fuelectenerg-1426	354	33	]	]	PUNCT
fuelectenerg-1426	354	34	,	,	PUNCT
fuelectenerg-1426	354	35	and	and	CCONJ
fuelectenerg-1426	354	36	since	since	SCONJ
fuelectenerg-1426	354	37	two	two	NUM
fuelectenerg-1426	354	38	-	-	PUNCT
fuelectenerg-1426	354	39	variable	variable	NOUN
fuelectenerg-1426	354	40	functions	function	NOUN
fuelectenerg-1426	354	41	are	be	AUX
fuelectenerg-1426	354	42	attractive	attractive	ADJ
fuelectenerg-1426	354	43	in	in	ADP
fuelectenerg-1426	354	44	logic	logic	ADJ
fuelectenerg-1426	354	45	synthesis	synthesis	NOUN
fuelectenerg-1426	354	46	since	since	SCONJ
fuelectenerg-1426	354	47	many	many	ADJ
fuelectenerg-1426	354	48	functional	functional	ADJ
fuelectenerg-1426	354	49	decomposition	decomposition	NOUN
fuelectenerg-1426	354	50	methods	method	NOUN
fuelectenerg-1426	354	51	exist	exist	VERB
fuelectenerg-1426	354	52	that	that	PRON
fuelectenerg-1426	354	53	produce	produce	VERB
fuelectenerg-1426	354	54	two	two	NUM
fuelectenerg-1426	354	55	control	control	NOUN
fuelectenerg-1426	354	56	inputs	input	NOUN
fuelectenerg-1426	354	57	for	for	ADP
fuelectenerg-1426	354	58	primitive	primitive	ADJ
fuelectenerg-1426	354	59	cells	cell	NOUN
fuelectenerg-1426	354	60	in	in	ADP
fuelectenerg-1426	354	61	a	a	DET
fuelectenerg-1426	354	62	standard	standard	ADJ
fuelectenerg-1426	354	63	library	library	NOUN
fuelectenerg-1426	354	64	of	of	ADP
fuelectenerg-1426	354	65	standard	standard	ADJ
fuelectenerg-1426	354	66	cells	cell	NOUN
fuelectenerg-1426	354	67	such	such	ADJ
fuelectenerg-1426	354	68	as	as	ADP
fuelectenerg-1426	354	69	in	in	ADP
fuelectenerg-1426	354	70	a	a	DET
fuelectenerg-1426	354	71	multiplexer	multiplexer	NOUN
fuelectenerg-1426	354	72	with	with	ADP
fuelectenerg-1426	354	73	two	two	NUM
fuelectenerg-1426	354	74	address	address	NOUN
fuelectenerg-1426	354	75	lines	line	NOUN
fuelectenerg-1426	354	76	,	,	PUNCT
fuelectenerg-1426	354	77	theorem	theorem	VERB
fuelectenerg-1426	354	78	4	4	NUM
fuelectenerg-1426	354	79	provides	provide	VERB
fuelectenerg-1426	354	80	a	a	DET
fuelectenerg-1426	354	81	fast	fast	ADJ
fuelectenerg-1426	354	82	computational	computational	ADJ
fuelectenerg-1426	354	83	method	method	NOUN
fuelectenerg-1426	354	84	to	to	PART
fuelectenerg-1426	354	85	calculate	calculate	VERB
fuelectenerg-1426	354	86	the	the	DET
fuelectenerg-1426	354	87	number	number	NOUN
fuelectenerg-1426	354	88	of	of	ADP
fuelectenerg-1426	354	89	ifs	ifs	PROPN
fuelectenerg-1426	354	90	over	over	ADP
fuelectenerg-1426	354	91	an	an	DET
fuelectenerg-1426	354	92	arbitrary	arbitrary	ADJ
fuelectenerg-1426	354	93	radix	radix	NOUN
fuelectenerg-1426	354	94	of	of	ADP
fuelectenerg-1426	354	95	galois	galois	PROPN
fuelectenerg-1426	354	96	field	field	NOUN
fuelectenerg-1426	354	97	gf(pk	gf(pk	PROPN
fuelectenerg-1426	354	98	)	)	PUNCT
fuelectenerg-1426	354	99	for	for	ADP
fuelectenerg-1426	354	100	two	two	NUM
fuelectenerg-1426	354	101	-	-	PUNCT
fuelectenerg-1426	354	102	variable	variable	NOUN
fuelectenerg-1426	354	103	functions	function	NOUN
fuelectenerg-1426	354	104	(	(	PUNCT
fuelectenerg-1426	354	105	i.e.	i.e.	X
fuelectenerg-1426	354	106	,	,	PUNCT
fuelectenerg-1426	354	107	n	n	NOUN
fuelectenerg-1426	354	108	=	=	SYM
fuelectenerg-1426	354	109	2	2	NUM
fuelectenerg-1426	354	110	)	)	PUNCT
fuelectenerg-1426	354	111	.	.	PUNCT
fuelectenerg-1426	355	1	theorem	theorem	ADJ
fuelectenerg-1426	355	2	4	4	NUM
fuelectenerg-1426	355	3	.	.	PUNCT
fuelectenerg-1426	356	1	the	the	DET
fuelectenerg-1426	356	2	following	follow	VERB
fuelectenerg-1426	356	3	ifn,2	ifn,2	ADJ
fuelectenerg-1426	356	4	triangles	triangle	NOUN
fuelectenerg-1426	356	5	provide	provide	VERB
fuelectenerg-1426	356	6	a	a	DET
fuelectenerg-1426	356	7	fast	fast	ADJ
fuelectenerg-1426	356	8	computational	computational	ADJ
fuelectenerg-1426	356	9	method	method	NOUN
fuelectenerg-1426	356	10	to	to	PART
fuelectenerg-1426	356	11	calculate	calculate	VERB
fuelectenerg-1426	356	12	the	the	DET
fuelectenerg-1426	356	13	number	number	NOUN
fuelectenerg-1426	356	14	of	of	ADP
fuelectenerg-1426	356	15	ifs	ifs	PROPN
fuelectenerg-1426	356	16	over	over	ADP
fuelectenerg-1426	356	17	an	an	DET
fuelectenerg-1426	356	18	arbitrary	arbitrary	ADJ
fuelectenerg-1426	356	19	n	n	X
fuelectenerg-1426	356	20	radix	radix	NOUN
fuelectenerg-1426	356	21	of	of	ADP
fuelectenerg-1426	356	22	galois	galois	PROPN
fuelectenerg-1426	356	23	field	field	NOUN
fuelectenerg-1426	356	24	gf(pk	gf(pk	PROPN
fuelectenerg-1426	356	25	)	)	PUNCT
fuelectenerg-1426	356	26	for	for	ADP
fuelectenerg-1426	356	27	two	two	NUM
fuelectenerg-1426	356	28	-	-	PUNCT
fuelectenerg-1426	356	29	variable	variable	NOUN
fuelectenerg-1426	356	30	functions	function	NOUN
fuelectenerg-1426	356	31	(	(	PUNCT
fuelectenerg-1426	356	32	n	n	NOUN
fuelectenerg-1426	356	33	=	=	SYM
fuelectenerg-1426	356	34	2	2	NUM
fuelectenerg-1426	356	35	)	)	PUNCT
fuelectenerg-1426	356	36	.	.	PUNCT
fuelectenerg-1426	357	1	116	116	NUM
fuelectenerg-1426	357	2	716	716	NUM
fuelectenerg-1426	357	3	a.	a.	NOUN
fuelectenerg-1426	357	4	n.	n.	PROPN
fuelectenerg-1426	357	5	al	al	PROPN
fuelectenerg-1426	357	6	-	-	PUNCT
fuelectenerg-1426	357	7	rabadi	rabadi	PROPN
fuelectenerg-1426	357	8	multi	multi	ADJ
fuelectenerg-1426	357	9	-	-	ADJ
fuelectenerg-1426	357	10	valued	value	VERB
fuelectenerg-1426	357	11	galois	galois	PROPN
fuelectenerg-1426	357	12	shannon	shannon	PROPN
fuelectenerg-1426	357	13	davio	davio	PROPN
fuelectenerg-1426	357	14	trees	tree	NOUN
fuelectenerg-1426	357	15	and	and	CCONJ
fuelectenerg-1426	357	16	their	their	PRON
fuelectenerg-1426	357	17	complexity	complexity	NOUN
fuelectenerg-1426	357	18	717	717	NUM
fuelectenerg-1426	357	19	multi	multi	ADV
fuelectenerg-1426	357	20	-	-	ADJ
fuelectenerg-1426	357	21	valued	value	VERB
fuelectenerg-1426	357	22	galois	galois	PROPN
fuelectenerg-1426	357	23	shannon	shannon	PROPN
fuelectenerg-1426	357	24	davio	davio	PROPN
fuelectenerg-1426	357	25	trees	tree	NOUN
fuelectenerg-1426	357	26	and	and	CCONJ
fuelectenerg-1426	357	27	their	their	PRON
fuelectenerg-1426	357	28	complexity	complexity	NOUN
fuelectenerg-1426	357	29	φ4,2	φ4,2	PROPN
fuelectenerg-1426	357	30	=	=	SYM
fuelectenerg-1426	357	31	(	(	PUNCT
fuelectenerg-1426	357	32	4)2−1	4)2−1	NOUN
fuelectenerg-1426	357	33	∑	∑	PROPN
fuelectenerg-1426	357	34	k1=0	k1=0	PROPN
fuelectenerg-1426	357	35	(	(	PUNCT
fuelectenerg-1426	357	36	4)2−2	4)2−2	INTJ
fuelectenerg-1426	357	37	∑	∑	PUNCT
fuelectenerg-1426	357	38	k2=0	k2=0	PROPN
fuelectenerg-1426	357	39	{	{	PUNCT
fuelectenerg-1426	357	40	4(2−1	4(2−1	NOUN
fuelectenerg-1426	357	41	)	)	PUNCT
fuelectenerg-1426	357	42	!	!	PUNCT
fuelectenerg-1426	358	1	(	(	PUNCT
fuelectenerg-1426	358	2	4(2−1)−	4(2−1)−	ADJ
fuelectenerg-1426	358	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	358	4	!	!	PUNCT
fuelectenerg-1426	358	5	4(2−2	4(2−2	NOUN
fuelectenerg-1426	358	6	)	)	PUNCT
fuelectenerg-1426	358	7	!	!	PUNCT
fuelectenerg-1426	359	1	(	(	PUNCT
fuelectenerg-1426	359	2	4(2−2)−	4(2−2)−	ADJ
fuelectenerg-1426	359	3	k2)!k2	k2)!k2	NOUN
fuelectenerg-1426	359	4	!	!	PUNCT
fuelectenerg-1426	360	1	(	(	PUNCT
fuelectenerg-1426	360	2	4(4−1)(4)0	4(4−1)(4)0	NOUN
fuelectenerg-1426	360	3	)	)	PUNCT
fuelectenerg-1426	360	4	k1(4(4−1)(4)1	k1(4(4−1)(4)1	NOUN
fuelectenerg-1426	360	5	)	)	PUNCT
fuelectenerg-1426	360	6	k2	k2	PROPN
fuelectenerg-1426	360	7	}	}	PUNCT
fuelectenerg-1426	360	8	,	,	PUNCT
fuelectenerg-1426	360	9	=	=	PUNCT
fuelectenerg-1426	360	10	φ00|4,2	φ00|4,2	NOUN
fuelectenerg-1426	360	11	+	+	ADJ
fuelectenerg-1426	360	12	φ10|4,2	φ10|4,2	NOUN
fuelectenerg-1426	360	13	+	+	ADP
fuelectenerg-1426	360	14	φ20|4,2	φ20|4,2	PROPN
fuelectenerg-1426	360	15	+	+	PROPN
fuelectenerg-1426	360	16	φ30|4,2	φ30|4,2	PROPN
fuelectenerg-1426	360	17	+	+	ADJ
fuelectenerg-1426	360	18	φ40|4,2	φ40|4,2	PROPN
fuelectenerg-1426	360	19	+	+	ADJ
fuelectenerg-1426	360	20	φ01|4,2	φ01|4,2	PROPN
fuelectenerg-1426	360	21	+	+	ADJ
fuelectenerg-1426	360	22	φ11|4,2	φ11|4,2	NOUN
fuelectenerg-1426	360	23	+	+	PROPN
fuelectenerg-1426	360	24	φ21|4,2	φ21|4,2	PROPN
fuelectenerg-1426	360	25	+	+	PROPN
fuelectenerg-1426	360	26	φ31|4,2	φ31|4,2	PROPN
fuelectenerg-1426	360	27	+	+	NOUN
fuelectenerg-1426	360	28	φ41|4,2	φ41|4,2	X
fuelectenerg-1426	360	29	=	=	SYM
fuelectenerg-1426	360	30	1	1	NUM
fuelectenerg-1426	360	31	+	+	NOUN
fuelectenerg-1426	360	32	256	256	NUM
fuelectenerg-1426	360	33	+	+	NUM
fuelectenerg-1426	360	34	24,576	24,576	NUM
fuelectenerg-1426	360	35	+	+	NOUN
fuelectenerg-1426	360	36	1,048,576	1,048,576	NUM
fuelectenerg-1426	360	37	+	+	NOUN
fuelectenerg-1426	360	38	16,777,216	16,777,216	NUM
fuelectenerg-1426	360	39	+	+	NUM
fuelectenerg-1426	360	40	16,777,216	16,777,216	NUM
fuelectenerg-1426	360	41	+	+	SYM
fuelectenerg-1426	360	42	4,294,967,296	4,294,967,296	NUM
fuelectenerg-1426	360	43	+412,316,860,416	+412,316,860,416	X
fuelectenerg-1426	360	44	+	+	PROPN
fuelectenerg-1426	360	45	1.75921860444×1013	1.75921860444×1013	NUM
fuelectenerg-1426	360	46	+	+	NUM
fuelectenerg-1426	360	47	2.81477976711×1014	2.81477976711×1014	NUM
fuelectenerg-1426	360	48	=	=	NOUN
fuelectenerg-1426	360	49	2.99483809211×1014	2.99483809211×1014	NOUN
fuelectenerg-1426	360	50	.	.	PUNCT
fuelectenerg-1426	361	1	corollary	corollary	ADJ
fuelectenerg-1426	361	2	1	1	NUM
fuelectenerg-1426	361	3	.	.	PUNCT
fuelectenerg-1426	362	1	from	from	ADP
fuelectenerg-1426	362	2	equation	equation	NOUN
fuelectenerg-1426	362	3	(	(	PUNCT
fuelectenerg-1426	362	4	52	52	NUM
fuelectenerg-1426	362	5	)	)	PUNCT
fuelectenerg-1426	362	6	,	,	PUNCT
fuelectenerg-1426	362	7	the	the	DET
fuelectenerg-1426	362	8	count	count	NOUN
fuelectenerg-1426	362	9	of	of	ADP
fuelectenerg-1426	362	10	ifs	ifs	PROPN
fuelectenerg-1426	362	11	for	for	ADP
fuelectenerg-1426	362	12	n	n	NOUN
fuelectenerg-1426	362	13	variables	variable	NOUN
fuelectenerg-1426	362	14	and	and	CCONJ
fuelectenerg-1426	362	15	second	second	ADJ
fuelectenerg-1426	362	16	radix	radix	NOUN
fuelectenerg-1426	362	17	is	be	AUX
fuelectenerg-1426	362	18	:	:	PUNCT
fuelectenerg-1426	362	19	n−1	n−1	PROPN
fuelectenerg-1426	362	20	∏	∏	PROPN
fuelectenerg-1426	362	21	k=0	k=0	X
fuelectenerg-1426	362	22	(	(	PUNCT
fuelectenerg-1426	362	23	1	1	NUM
fuelectenerg-1426	362	24	+	+	NOUN
fuelectenerg-1426	362	25	22n−k−1	22n−k−1	NUM
fuelectenerg-1426	362	26	)	)	PUNCT
fuelectenerg-1426	362	27	2k	2k	NOUN
fuelectenerg-1426	362	28	=	=	SYM
fuelectenerg-1426	362	29	(	(	PUNCT
fuelectenerg-1426	362	30	2)n−1	2)n−1	NUM
fuelectenerg-1426	362	31	∑	∑	PROPN
fuelectenerg-1426	362	32	k1=0	k1=0	PROPN
fuelectenerg-1426	362	33	(	(	PUNCT
fuelectenerg-1426	362	34	2)n−2	2)n−2	NUM
fuelectenerg-1426	362	35	∑	∑	PROPN
fuelectenerg-1426	362	36	k2=0	k2=0	PROPN
fuelectenerg-1426	362	37	·	·	PUNCT
fuelectenerg-1426	362	38	·	·	PUNCT
fuelectenerg-1426	362	39	·	·	PUNCT
fuelectenerg-1426	363	1	(	(	PUNCT
fuelectenerg-1426	363	2	2)0	2)0	NUM
fuelectenerg-1426	363	3	∑	∑	PROPN
fuelectenerg-1426	363	4	kn=0	kn=0	X
fuelectenerg-1426	363	5	{	{	PUNCT
fuelectenerg-1426	363	6	2(n−1	2(n−1	ADJ
fuelectenerg-1426	363	7	)	)	PUNCT
fuelectenerg-1426	363	8	!	!	PUNCT
fuelectenerg-1426	364	1	(	(	PUNCT
fuelectenerg-1426	364	2	2(n−1)−	2(n−1)−	NOUN
fuelectenerg-1426	364	3	k1)!k1	k1)!k1	NOUN
fuelectenerg-1426	364	4	!	!	PUNCT
fuelectenerg-1426	364	5	2(n−2	2(n−2	PROPN
fuelectenerg-1426	364	6	)	)	PUNCT
fuelectenerg-1426	364	7	!	!	PUNCT
fuelectenerg-1426	365	1	(	(	PUNCT
fuelectenerg-1426	365	2	2(n−2)−	2(n−2)−	X
fuelectenerg-1426	365	3	k2)!k2	k2)!k2	X
fuelectenerg-1426	365	4	!	!	PUNCT
fuelectenerg-1426	365	5	·	·	PUNCT
fuelectenerg-1426	365	6	·	·	PUNCT
fuelectenerg-1426	365	7	·	·	PUNCT
fuelectenerg-1426	365	8	2(0	2(0	NUM
fuelectenerg-1426	365	9	)	)	PUNCT
fuelectenerg-1426	365	10	!	!	PUNCT
fuelectenerg-1426	366	1	(	(	PUNCT
fuelectenerg-1426	366	2	2(0)−	2(0)−	NUM
fuelectenerg-1426	366	3	kn)!kn	kn)!kn	PROPN
fuelectenerg-1426	366	4	!	!	PUNCT
fuelectenerg-1426	367	1	(	(	PUNCT
fuelectenerg-1426	367	2	2(2−1)(2)0	2(2−1)(2)0	X
fuelectenerg-1426	367	3	)	)	PUNCT
fuelectenerg-1426	367	4	k1(2(2−1)(2)1	k1(2(2−1)(2)1	PROPN
fuelectenerg-1426	367	5	)	)	PUNCT
fuelectenerg-1426	367	6	k2	k2	X
fuelectenerg-1426	367	7	·	·	PUNCT
fuelectenerg-1426	367	8	·	·	PUNCT
fuelectenerg-1426	367	9	·	·	PUNCT
fuelectenerg-1426	367	10	(	(	PUNCT
fuelectenerg-1426	367	11	2(2−1)(2)(n−1	2(2−1)(2)(n−1	NUM
fuelectenerg-1426	367	12	)	)	PUNCT
fuelectenerg-1426	367	13	)	)	PUNCT
fuelectenerg-1426	368	1	kn	kn	NOUN
fuelectenerg-1426	368	2	}	}	PUNCT
fuelectenerg-1426	368	3	.	.	PUNCT
fuelectenerg-1426	369	1	(	(	PUNCT
fuelectenerg-1426	369	2	65	65	NUM
fuelectenerg-1426	369	3	)	)	PUNCT
fuelectenerg-1426	369	4	as	as	SCONJ
fuelectenerg-1426	369	5	previously	previously	ADV
fuelectenerg-1426	369	6	mentioned	mention	VERB
fuelectenerg-1426	369	7	,	,	PUNCT
fuelectenerg-1426	369	8	this	this	DET
fuelectenerg-1426	369	9	enumeration	enumeration	NOUN
fuelectenerg-1426	369	10	can	can	AUX
fuelectenerg-1426	369	11	be	be	AUX
fuelectenerg-1426	369	12	useful	useful	ADJ
fuelectenerg-1426	369	13	as	as	ADP
fuelectenerg-1426	369	14	a	a	DET
fuelectenerg-1426	369	15	terminating	terminate	VERB
fuelectenerg-1426	369	16	point	point	NOUN
fuelectenerg-1426	369	17	of	of	ADP
fuelectenerg-1426	369	18	minimization	minimization	NOUN
fuelectenerg-1426	369	19	algorithms	algorithm	NOUN
fuelectenerg-1426	369	20	for	for	ADP
fuelectenerg-1426	369	21	multi	multi	ADJ
fuelectenerg-1426	369	22	-	-	ADJ
fuelectenerg-1426	369	23	valued	value	VERB
fuelectenerg-1426	369	24	functions	function	NOUN
fuelectenerg-1426	369	25	.	.	PUNCT
fuelectenerg-1426	370	1	yet	yet	ADV
fuelectenerg-1426	370	2	,	,	PUNCT
fuelectenerg-1426	370	3	as	as	SCONJ
fuelectenerg-1426	370	4	shown	show	VERB
fuelectenerg-1426	370	5	,	,	PUNCT
fuelectenerg-1426	370	6	the	the	DET
fuelectenerg-1426	370	7	number	number	NOUN
fuelectenerg-1426	370	8	of	of	ADP
fuelectenerg-1426	370	9	combinations	combination	NOUN
fuelectenerg-1426	370	10	is	be	AUX
fuelectenerg-1426	370	11	so	so	ADV
fuelectenerg-1426	370	12	large	large	ADJ
fuelectenerg-1426	370	13	that	that	DET
fuelectenerg-1426	370	14	restriction	restriction	NOUN
fuelectenerg-1426	370	15	to	to	ADP
fuelectenerg-1426	370	16	some	some	DET
fuelectenerg-1426	370	17	particular	particular	ADJ
fuelectenerg-1426	370	18	cases	case	NOUN
fuelectenerg-1426	370	19	of	of	ADP
fuelectenerg-1426	370	20	functional	functional	ADJ
fuelectenerg-1426	370	21	expressions	expression	NOUN
fuelectenerg-1426	370	22	can	can	AUX
fuelectenerg-1426	370	23	be	be	AUX
fuelectenerg-1426	370	24	more	more	ADV
fuelectenerg-1426	370	25	feasible	feasible	ADJ
fuelectenerg-1426	370	26	.	.	PUNCT
fuelectenerg-1426	371	1	the	the	DET
fuelectenerg-1426	371	2	following	follow	VERB
fuelectenerg-1426	371	3	section	section	NOUN
fuelectenerg-1426	371	4	introduces	introduce	VERB
fuelectenerg-1426	371	5	a	a	DET
fuelectenerg-1426	371	6	fast	fast	ADJ
fuelectenerg-1426	371	7	method	method	NOUN
fuelectenerg-1426	371	8	to	to	PART
fuelectenerg-1426	371	9	calculate	calculate	VERB
fuelectenerg-1426	371	10	the	the	DET
fuelectenerg-1426	371	11	number	number	NOUN
fuelectenerg-1426	371	12	of	of	ADP
fuelectenerg-1426	371	13	ifs	ifs	PROPN
fuelectenerg-1426	371	14	for	for	ADP
fuelectenerg-1426	371	15	an	an	DET
fuelectenerg-1426	371	16	arbitrary	arbitrary	ADJ
fuelectenerg-1426	371	17	galois	galois	NOUN
fuelectenerg-1426	371	18	field	field	NOUN
fuelectenerg-1426	371	19	logic	logic	NOUN
fuelectenerg-1426	371	20	for	for	ADP
fuelectenerg-1426	371	21	functions	function	NOUN
fuelectenerg-1426	371	22	with	with	ADP
fuelectenerg-1426	371	23	two	two	NUM
fuelectenerg-1426	371	24	variables	variable	NOUN
fuelectenerg-1426	371	25	.	.	PUNCT
fuelectenerg-1426	372	1	4.2	4.2	NUM
fuelectenerg-1426	372	2	the	the	DET
fuelectenerg-1426	372	3	ifn,2	ifn,2	ADJ
fuelectenerg-1426	372	4	triangles	triangle	NOUN
fuelectenerg-1426	372	5	:	:	PUNCT
fuelectenerg-1426	372	6	fast	fast	ADJ
fuelectenerg-1426	372	7	count	count	NOUN
fuelectenerg-1426	372	8	calculations	calculation	NOUN
fuelectenerg-1426	372	9	of	of	ADP
fuelectenerg-1426	372	10	ifs	ifs	PROPN
fuelectenerg-1426	372	11	for	for	ADP
fuelectenerg-1426	372	12	gf(pk	gf(pk	NOUN
fuelectenerg-1426	372	13	)	)	PUNCT
fuelectenerg-1426	372	14	and	and	CCONJ
fuelectenerg-1426	372	15	two	two	NUM
fuelectenerg-1426	372	16	-	-	PUNCT
fuelectenerg-1426	372	17	variable	variable	NOUN
fuelectenerg-1426	372	18	functions	function	NOUN
fuelectenerg-1426	372	19	the	the	DET
fuelectenerg-1426	372	20	count	count	NOUN
fuelectenerg-1426	372	21	of	of	ADP
fuelectenerg-1426	372	22	the	the	DET
fuelectenerg-1426	372	23	number	number	NOUN
fuelectenerg-1426	372	24	of	of	ADP
fuelectenerg-1426	372	25	ifs	ifs	PROPN
fuelectenerg-1426	372	26	can	can	AUX
fuelectenerg-1426	372	27	be	be	AUX
fuelectenerg-1426	372	28	important	important	ADJ
fuelectenerg-1426	372	29	in	in	ADP
fuelectenerg-1426	372	30	many	many	ADJ
fuelectenerg-1426	372	31	applications	application	NOUN
fuelectenerg-1426	372	32	,	,	PUNCT
fuelectenerg-1426	372	33	especially	especially	ADV
fuelectenerg-1426	372	34	in	in	ADP
fuelectenerg-1426	372	35	providing	provide	VERB
fuelectenerg-1426	372	36	upper	upper	ADJ
fuelectenerg-1426	372	37	numerical	numerical	ADJ
fuelectenerg-1426	372	38	boundaries	boundary	NOUN
fuelectenerg-1426	372	39	for	for	ADP
fuelectenerg-1426	372	40	efficient	efficient	ADJ
fuelectenerg-1426	372	41	search	search	NOUN
fuelectenerg-1426	372	42	of	of	ADP
fuelectenerg-1426	372	43	a	a	DET
fuelectenerg-1426	372	44	minimum	minimum	ADJ
fuelectenerg-1426	372	45	gfsop	gfsop	NOUN
fuelectenerg-1426	372	46	.	.	PUNCT
fuelectenerg-1426	373	1	calculating	calculate	VERB
fuelectenerg-1426	373	2	the	the	DET
fuelectenerg-1426	373	3	numbers	number	NOUN
fuelectenerg-1426	373	4	of	of	ADP
fuelectenerg-1426	373	5	inclusive	inclusive	ADJ
fuelectenerg-1426	373	6	forms	form	NOUN
fuelectenerg-1426	373	7	can	can	AUX
fuelectenerg-1426	373	8	be	be	AUX
fuelectenerg-1426	373	9	very	very	ADV
fuelectenerg-1426	373	10	time	time	NOUN
fuelectenerg-1426	373	11	consuming	consume	VERB
fuelectenerg-1426	373	12	due	due	ADP
fuelectenerg-1426	373	13	to	to	ADP
fuelectenerg-1426	373	14	the	the	DET
fuelectenerg-1426	373	15	time	time	NOUN
fuelectenerg-1426	373	16	required	require	VERB
fuelectenerg-1426	373	17	to	to	PART
fuelectenerg-1426	373	18	perform	perform	VERB
fuelectenerg-1426	373	19	the	the	DET
fuelectenerg-1426	373	20	mathematical	mathematical	ADJ
fuelectenerg-1426	373	21	operations	operation	NOUN
fuelectenerg-1426	373	22	in	in	ADP
fuelectenerg-1426	373	23	the	the	DET
fuelectenerg-1426	373	24	general	general	ADJ
fuelectenerg-1426	373	25	equation	equation	NOUN
fuelectenerg-1426	373	26	(	(	PUNCT
fuelectenerg-1426	373	27	52	52	NUM
fuelectenerg-1426	373	28	)	)	PUNCT
fuelectenerg-1426	373	29	.	.	PUNCT
fuelectenerg-1426	374	1	this	this	PRON
fuelectenerg-1426	374	2	is	be	AUX
fuelectenerg-1426	374	3	why	why	SCONJ
fuelectenerg-1426	374	4	a	a	DET
fuelectenerg-1426	374	5	fast	fast	ADJ
fuelectenerg-1426	374	6	method	method	NOUN
fuelectenerg-1426	374	7	to	to	PART
fuelectenerg-1426	374	8	generate	generate	VERB
fuelectenerg-1426	374	9	the	the	DET
fuelectenerg-1426	374	10	number	number	NOUN
fuelectenerg-1426	374	11	of	of	ADP
fuelectenerg-1426	374	12	ifs	ifs	PROPN
fuelectenerg-1426	374	13	is	be	AUX
fuelectenerg-1426	374	14	needed	need	VERB
fuelectenerg-1426	374	15	.	.	PUNCT
fuelectenerg-1426	375	1	because	because	SCONJ
fuelectenerg-1426	375	2	functions	function	NOUN
fuelectenerg-1426	375	3	with	with	ADP
fuelectenerg-1426	375	4	two	two	NUM
fuelectenerg-1426	375	5	variables	variable	NOUN
fuelectenerg-1426	375	6	find	find	VERB
fuelectenerg-1426	375	7	an	an	DET
fuelectenerg-1426	375	8	important	important	ADJ
fuelectenerg-1426	375	9	application	application	NOUN
fuelectenerg-1426	375	10	such	such	ADJ
fuelectenerg-1426	375	11	as	as	ADP
fuelectenerg-1426	375	12	in	in	ADP
fuelectenerg-1426	375	13	universal	universal	ADJ
fuelectenerg-1426	375	14	logic	logic	NOUN
fuelectenerg-1426	375	15	modules	module	NOUN
fuelectenerg-1426	375	16	(	(	PUNCT
fuelectenerg-1426	375	17	ulms	ulm	NOUN
fuelectenerg-1426	375	18	)	)	PUNCT
fuelectenerg-1426	375	19	for	for	ADP
fuelectenerg-1426	375	20	pairs	pair	NOUN
fuelectenerg-1426	375	21	of	of	ADP
fuelectenerg-1426	375	22	control	control	NOUN
fuelectenerg-1426	375	23	variables	variable	NOUN
fuelectenerg-1426	375	24	that	that	PRON
fuelectenerg-1426	375	25	generalize	generalize	VERB
fuelectenerg-1426	375	26	shannon	shannon	PROPN
fuelectenerg-1426	375	27	and	and	CCONJ
fuelectenerg-1426	375	28	davio	davio	NOUN
fuelectenerg-1426	375	29	expansion	expansion	NOUN
fuelectenerg-1426	375	30	modules	module	NOUN
fuelectenerg-1426	375	31	[	[	X
fuelectenerg-1426	375	32	2	2	NUM
fuelectenerg-1426	375	33	]	]	PUNCT
fuelectenerg-1426	375	34	,	,	PUNCT
fuelectenerg-1426	375	35	and	and	CCONJ
fuelectenerg-1426	375	36	since	since	SCONJ
fuelectenerg-1426	375	37	two	two	NUM
fuelectenerg-1426	375	38	-	-	PUNCT
fuelectenerg-1426	375	39	variable	variable	NOUN
fuelectenerg-1426	375	40	functions	function	NOUN
fuelectenerg-1426	375	41	are	be	AUX
fuelectenerg-1426	375	42	attractive	attractive	ADJ
fuelectenerg-1426	375	43	in	in	ADP
fuelectenerg-1426	375	44	logic	logic	ADJ
fuelectenerg-1426	375	45	synthesis	synthesis	NOUN
fuelectenerg-1426	375	46	since	since	SCONJ
fuelectenerg-1426	375	47	many	many	ADJ
fuelectenerg-1426	375	48	functional	functional	ADJ
fuelectenerg-1426	375	49	decomposition	decomposition	NOUN
fuelectenerg-1426	375	50	methods	method	NOUN
fuelectenerg-1426	375	51	exist	exist	VERB
fuelectenerg-1426	375	52	that	that	PRON
fuelectenerg-1426	375	53	produce	produce	VERB
fuelectenerg-1426	375	54	two	two	NUM
fuelectenerg-1426	375	55	control	control	NOUN
fuelectenerg-1426	375	56	inputs	input	NOUN
fuelectenerg-1426	375	57	for	for	ADP
fuelectenerg-1426	375	58	primitive	primitive	ADJ
fuelectenerg-1426	375	59	cells	cell	NOUN
fuelectenerg-1426	375	60	in	in	ADP
fuelectenerg-1426	375	61	a	a	DET
fuelectenerg-1426	375	62	standard	standard	ADJ
fuelectenerg-1426	375	63	library	library	NOUN
fuelectenerg-1426	375	64	of	of	ADP
fuelectenerg-1426	375	65	standard	standard	ADJ
fuelectenerg-1426	375	66	cells	cell	NOUN
fuelectenerg-1426	375	67	such	such	ADJ
fuelectenerg-1426	375	68	as	as	ADP
fuelectenerg-1426	375	69	in	in	ADP
fuelectenerg-1426	375	70	a	a	DET
fuelectenerg-1426	375	71	multiplexer	multiplexer	NOUN
fuelectenerg-1426	375	72	with	with	ADP
fuelectenerg-1426	375	73	two	two	NUM
fuelectenerg-1426	375	74	address	address	NOUN
fuelectenerg-1426	375	75	lines	line	NOUN
fuelectenerg-1426	375	76	,	,	PUNCT
fuelectenerg-1426	375	77	theorem	theorem	VERB
fuelectenerg-1426	375	78	4	4	NUM
fuelectenerg-1426	375	79	provides	provide	VERB
fuelectenerg-1426	375	80	a	a	DET
fuelectenerg-1426	375	81	fast	fast	ADJ
fuelectenerg-1426	375	82	computational	computational	ADJ
fuelectenerg-1426	375	83	method	method	NOUN
fuelectenerg-1426	375	84	to	to	PART
fuelectenerg-1426	375	85	calculate	calculate	VERB
fuelectenerg-1426	375	86	the	the	DET
fuelectenerg-1426	375	87	number	number	NOUN
fuelectenerg-1426	375	88	of	of	ADP
fuelectenerg-1426	375	89	ifs	ifs	PROPN
fuelectenerg-1426	375	90	over	over	ADP
fuelectenerg-1426	375	91	an	an	DET
fuelectenerg-1426	375	92	arbitrary	arbitrary	ADJ
fuelectenerg-1426	375	93	radix	radix	NOUN
fuelectenerg-1426	375	94	of	of	ADP
fuelectenerg-1426	375	95	galois	galois	PROPN
fuelectenerg-1426	375	96	field	field	NOUN
fuelectenerg-1426	375	97	gf(pk	gf(pk	PROPN
fuelectenerg-1426	375	98	)	)	PUNCT
fuelectenerg-1426	375	99	for	for	ADP
fuelectenerg-1426	375	100	two	two	NUM
fuelectenerg-1426	375	101	-	-	PUNCT
fuelectenerg-1426	375	102	variable	variable	NOUN
fuelectenerg-1426	375	103	functions	function	NOUN
fuelectenerg-1426	375	104	(	(	PUNCT
fuelectenerg-1426	375	105	i.e.	i.e.	X
fuelectenerg-1426	375	106	,	,	PUNCT
fuelectenerg-1426	375	107	n	n	NOUN
fuelectenerg-1426	375	108	=	=	SYM
fuelectenerg-1426	375	109	2	2	NUM
fuelectenerg-1426	375	110	)	)	PUNCT
fuelectenerg-1426	375	111	.	.	PUNCT
fuelectenerg-1426	376	1	theorem	theorem	ADJ
fuelectenerg-1426	376	2	4	4	NUM
fuelectenerg-1426	376	3	.	.	PUNCT
fuelectenerg-1426	377	1	the	the	DET
fuelectenerg-1426	377	2	following	follow	VERB
fuelectenerg-1426	377	3	ifn,2	ifn,2	ADJ
fuelectenerg-1426	377	4	triangles	triangle	NOUN
fuelectenerg-1426	377	5	provide	provide	VERB
fuelectenerg-1426	377	6	a	a	DET
fuelectenerg-1426	377	7	fast	fast	ADJ
fuelectenerg-1426	377	8	computational	computational	ADJ
fuelectenerg-1426	377	9	method	method	NOUN
fuelectenerg-1426	377	10	to	to	PART
fuelectenerg-1426	377	11	calculate	calculate	VERB
fuelectenerg-1426	377	12	the	the	DET
fuelectenerg-1426	377	13	number	number	NOUN
fuelectenerg-1426	377	14	of	of	ADP
fuelectenerg-1426	377	15	ifs	ifs	PROPN
fuelectenerg-1426	377	16	over	over	ADP
fuelectenerg-1426	377	17	an	an	DET
fuelectenerg-1426	377	18	arbitrary	arbitrary	ADJ
fuelectenerg-1426	377	19	n	n	X
fuelectenerg-1426	377	20	radix	radix	NOUN
fuelectenerg-1426	377	21	of	of	ADP
fuelectenerg-1426	377	22	galois	galois	PROPN
fuelectenerg-1426	377	23	field	field	NOUN
fuelectenerg-1426	377	24	gf(pk	gf(pk	PROPN
fuelectenerg-1426	377	25	)	)	PUNCT
fuelectenerg-1426	377	26	for	for	ADP
fuelectenerg-1426	377	27	two	two	NUM
fuelectenerg-1426	377	28	-	-	PUNCT
fuelectenerg-1426	377	29	variable	variable	NOUN
fuelectenerg-1426	377	30	functions	function	NOUN
fuelectenerg-1426	377	31	(	(	PUNCT
fuelectenerg-1426	377	32	n	n	NOUN
fuelectenerg-1426	377	33	=	=	SYM
fuelectenerg-1426	377	34	2	2	NUM
fuelectenerg-1426	377	35	)	)	PUNCT
fuelectenerg-1426	377	36	.	.	PUNCT
fuelectenerg-1426	378	1	116	116	NUM
fuelectenerg-1426	378	2	multi	multi	ADJ
fuelectenerg-1426	378	3	-	-	ADJ
fuelectenerg-1426	378	4	valued	value	VERB
fuelectenerg-1426	378	5	galois	galois	PROPN
fuelectenerg-1426	378	6	shannon	shannon	PROPN
fuelectenerg-1426	378	7	davio	davio	PROPN
fuelectenerg-1426	378	8	trees	tree	NOUN
fuelectenerg-1426	378	9	and	and	CCONJ
fuelectenerg-1426	378	10	their	their	PRON
fuelectenerg-1426	378	11	complexity	complexity	NOUN
fuelectenerg-1426	378	12	1	1	NUM
fuelectenerg-1426	378	13	2	2	NUM
fuelectenerg-1426	378	14	1	1	NUM
fuelectenerg-1426	378	15	1	1	NUM
fuelectenerg-1426	378	16	2	2	NUM
fuelectenerg-1426	378	17	1	1	NUM
fuelectenerg-1426	378	18	1	1	NUM
fuelectenerg-1426	378	19	3	3	NUM
fuelectenerg-1426	378	20	3	3	NUM
fuelectenerg-1426	378	21	1	1	NUM
fuelectenerg-1426	378	22	1	1	NUM
fuelectenerg-1426	378	23	3	3	NUM
fuelectenerg-1426	378	24	3	3	NUM
fuelectenerg-1426	378	25	1	1	NUM
fuelectenerg-1426	378	26	1	1	NUM
fuelectenerg-1426	378	27	4	4	NUM
fuelectenerg-1426	378	28	6	6	NUM
fuelectenerg-1426	378	29	4	4	NUM
fuelectenerg-1426	378	30	1	1	NUM
fuelectenerg-1426	378	31	1	1	NUM
fuelectenerg-1426	378	32	4	4	NUM
fuelectenerg-1426	378	33	6	6	NUM
fuelectenerg-1426	378	34	4	4	NUM
fuelectenerg-1426	378	35	1	1	NUM
fuelectenerg-1426	378	36	1	1	NUM
fuelectenerg-1426	378	37	5	5	NUM
fuelectenerg-1426	378	38	10	10	NUM
fuelectenerg-1426	378	39	10	10	NUM
fuelectenerg-1426	378	40	5	5	NUM
fuelectenerg-1426	378	41	1	1	NUM
fuelectenerg-1426	378	42	1	1	NUM
fuelectenerg-1426	378	43	5	5	NUM
fuelectenerg-1426	378	44	10	10	NUM
fuelectenerg-1426	378	45	10	10	NUM
fuelectenerg-1426	378	46	5	5	NUM
fuelectenerg-1426	378	47	1	1	NUM
fuelectenerg-1426	378	48	1	1	NUM
fuelectenerg-1426	378	49	6	6	NUM
fuelectenerg-1426	378	50	15	15	NUM
fuelectenerg-1426	378	51	20	20	NUM
fuelectenerg-1426	378	52	15	15	NUM
fuelectenerg-1426	378	53	6	6	NUM
fuelectenerg-1426	378	54	1	1	NUM
fuelectenerg-1426	378	55	1	1	NUM
fuelectenerg-1426	378	56	6	6	NUM
fuelectenerg-1426	378	57	15	15	NUM
fuelectenerg-1426	378	58	20	20	NUM
fuelectenerg-1426	378	59	15	15	NUM
fuelectenerg-1426	378	60	6	6	NUM
fuelectenerg-1426	378	61	1	1	NUM
fuelectenerg-1426	378	62	1	1	NUM
fuelectenerg-1426	378	63	7	7	NUM
fuelectenerg-1426	378	64	21	21	NUM
fuelectenerg-1426	378	65	35	35	NUM
fuelectenerg-1426	378	66	35	35	NUM
fuelectenerg-1426	378	67	21	21	NUM
fuelectenerg-1426	378	68	7	7	NUM
fuelectenerg-1426	378	69	1	1	NUM
fuelectenerg-1426	378	70	1	1	NUM
fuelectenerg-1426	378	71	7	7	NUM
fuelectenerg-1426	378	72	21	21	NUM
fuelectenerg-1426	378	73	35	35	NUM
fuelectenerg-1426	378	74	35	35	NUM
fuelectenerg-1426	378	75	21	21	NUM
fuelectenerg-1426	378	76	7	7	NUM
fuelectenerg-1426	378	77	1	1	NUM
fuelectenerg-1426	378	78	2	2	NUM
fuelectenerg-1426	378	79	0	0	NUM
fuelectenerg-1426	378	80	2	2	NUM
fuelectenerg-1426	378	81	1	1	NUM
fuelectenerg-1426	378	82	2	2	NUM
fuelectenerg-1426	378	83	2	2	NUM
fuelectenerg-1426	378	84	2	2	NUM
fuelectenerg-1426	378	85	2	2	NUM
fuelectenerg-1426	378	86	2	2	NUM
fuelectenerg-1426	378	87	3	3	NUM
fuelectenerg-1426	378	88	2	2	NUM
fuelectenerg-1426	378	89	4	4	NUM
fuelectenerg-1426	378	90	3	3	NUM
fuelectenerg-1426	378	91	0	0	NUM
fuelectenerg-1426	378	92	3	3	NUM
fuelectenerg-1426	378	93	2	2	NUM
fuelectenerg-1426	378	94	3	3	NUM
fuelectenerg-1426	378	95	4	4	NUM
fuelectenerg-1426	378	96	3	3	NUM
fuelectenerg-1426	378	97	6	6	NUM
fuelectenerg-1426	378	98	3	3	NUM
fuelectenerg-1426	378	99	6	6	NUM
fuelectenerg-1426	378	100	3	3	NUM
fuelectenerg-1426	378	101	8	8	NUM
fuelectenerg-1426	378	102	3	3	NUM
fuelectenerg-1426	378	103	10	10	NUM
fuelectenerg-1426	378	104	3	3	NUM
fuelectenerg-1426	378	105	12	12	NUM
fuelectenerg-1426	378	106	4	4	NUM
fuelectenerg-1426	378	107	0	0	NUM
fuelectenerg-1426	378	108	4	4	NUM
fuelectenerg-1426	378	109	3	3	NUM
fuelectenerg-1426	378	110	4	4	NUM
fuelectenerg-1426	378	111	6	6	NUM
fuelectenerg-1426	378	112	4	4	NUM
fuelectenerg-1426	378	113	9	9	NUM
fuelectenerg-1426	378	114	4	4	NUM
fuelectenerg-1426	378	115	12	12	NUM
fuelectenerg-1426	378	116	4	4	NUM
fuelectenerg-1426	378	117	12	12	NUM
fuelectenerg-1426	378	118	4	4	NUM
fuelectenerg-1426	378	119	15	15	NUM
fuelectenerg-1426	378	120	4	4	NUM
fuelectenerg-1426	378	121	18	18	NUM
fuelectenerg-1426	378	122	4	4	NUM
fuelectenerg-1426	378	123	21	21	NUM
fuelectenerg-1426	378	124	4	4	NUM
fuelectenerg-1426	378	125	24	24	NUM
fuelectenerg-1426	378	126	5	5	NUM
fuelectenerg-1426	378	127	0	0	NUM
fuelectenerg-1426	378	128	5	5	NUM
fuelectenerg-1426	378	129	4	4	NUM
fuelectenerg-1426	378	130	5	5	NUM
fuelectenerg-1426	378	131	8	8	NUM
fuelectenerg-1426	378	132	5	5	NUM
fuelectenerg-1426	378	133	12	12	NUM
fuelectenerg-1426	378	134	5	5	NUM
fuelectenerg-1426	378	135	16	16	NUM
fuelectenerg-1426	378	136	5	5	NUM
fuelectenerg-1426	378	137	20	20	NUM
fuelectenerg-1426	378	138	5	5	NUM
fuelectenerg-1426	378	139	20	20	NUM
fuelectenerg-1426	378	140	5	5	NUM
fuelectenerg-1426	378	141	24	24	NUM
fuelectenerg-1426	378	142	5	5	NUM
fuelectenerg-1426	378	143	28	28	NUM
fuelectenerg-1426	378	144	5	5	NUM
fuelectenerg-1426	378	145	32	32	NUM
fuelectenerg-1426	378	146	5	5	NUM
fuelectenerg-1426	378	147	36	36	NUM
fuelectenerg-1426	378	148	5	5	NUM
fuelectenerg-1426	378	149	40	40	NUM
fuelectenerg-1426	378	150	n	n	NUM
fuelectenerg-1426	378	151	0(n-1	0(n-1	NOUN
fuelectenerg-1426	378	152	)	)	PUNCT
fuelectenerg-1426	378	153	n	n	PRON
fuelectenerg-1426	378	154	1(n-1	1(n-1	NUM
fuelectenerg-1426	378	155	)	)	PUNCT
fuelectenerg-1426	378	156	n	n	PRON
fuelectenerg-1426	378	157	2(n-1	2(n-1	NUM
fuelectenerg-1426	378	158	)	)	PUNCT
fuelectenerg-1426	378	159	n	n	PRON
fuelectenerg-1426	378	160	3(n-1	3(n-1	NUM
fuelectenerg-1426	378	161	)	)	PUNCT
fuelectenerg-1426	378	162	...	...	PUNCT
fuelectenerg-1426	379	1	n	n	X
fuelectenerg-1426	379	2	...	...	PUNCT
fuelectenerg-1426	379	3	(	(	PUNCT
fuelectenerg-1426	379	4	n-1)(n-1	n-1)(n-1	PROPN
fuelectenerg-1426	379	5	)	)	PUNCT
fuelectenerg-1426	379	6	n	n	PRON
fuelectenerg-1426	379	7	n(n-1	n(n-1	NOUN
fuelectenerg-1426	379	8	)	)	PUNCT
fuelectenerg-1426	379	9	n	n	PRON
fuelectenerg-1426	379	10	n(n-1	n(n-1	NOUN
fuelectenerg-1426	379	11	)	)	PUNCT
fuelectenerg-1426	379	12	n	n	CCONJ
fuelectenerg-1426	379	13	(	(	PUNCT
fuelectenerg-1426	379	14	n+1)(n-1	n+1)(n-1	NOUN
fuelectenerg-1426	379	15	)	)	PUNCT
fuelectenerg-1426	379	16	n	n	CCONJ
fuelectenerg-1426	379	17	(	(	PUNCT
fuelectenerg-1426	379	18	n+2)(n-1	n+2)(n-1	PROPN
fuelectenerg-1426	379	19	)	)	PUNCT
fuelectenerg-1426	379	20	n	n	PRON
fuelectenerg-1426	379	21	2n(n-1	2n(n-1	NUM
fuelectenerg-1426	379	22	)	)	PUNCT
fuelectenerg-1426	379	23	(	(	PUNCT
fuelectenerg-1426	379	24	)	)	PUNCT
fuelectenerg-1426	379	25	a	a	DET
fuelectenerg-1426	379	26	(	(	PUNCT
fuelectenerg-1426	379	27	)	)	PUNCT
fuelectenerg-1426	379	28	b	b	NOUN
fuelectenerg-1426	379	29	fig	fig	NOUN
fuelectenerg-1426	379	30	.	.	PUNCT
fuelectenerg-1426	380	1	7	7	NUM
fuelectenerg-1426	380	2	:	:	PUNCT
fuelectenerg-1426	380	3	the	the	DET
fuelectenerg-1426	380	4	ifn,2	ifn,2	ADJ
fuelectenerg-1426	380	5	triangles	triangle	NOUN
fuelectenerg-1426	380	6	:	:	PUNCT
fuelectenerg-1426	380	7	(	(	PUNCT
fuelectenerg-1426	380	8	a	a	X
fuelectenerg-1426	380	9	)	)	PUNCT
fuelectenerg-1426	380	10	triangle	triangle	NOUN
fuelectenerg-1426	380	11	of	of	ADP
fuelectenerg-1426	380	12	coefficients	coefficient	NOUN
fuelectenerg-1426	380	13	,	,	PUNCT
fuelectenerg-1426	380	14	and	and	CCONJ
fuelectenerg-1426	380	15	(	(	PUNCT
fuelectenerg-1426	380	16	b	b	NOUN
fuelectenerg-1426	380	17	)	)	PUNCT
fuelectenerg-1426	380	18	triangle	triangle	NOUN
fuelectenerg-1426	380	19	of	of	ADP
fuelectenerg-1426	380	20	values	value	NOUN
fuelectenerg-1426	380	21	for	for	ADP
fuelectenerg-1426	380	22	fast	fast	ADJ
fuelectenerg-1426	380	23	calculation	calculation	NOUN
fuelectenerg-1426	380	24	of	of	ADP
fuelectenerg-1426	380	25	the	the	DET
fuelectenerg-1426	380	26	number	number	NOUN
fuelectenerg-1426	380	27	of	of	ADP
fuelectenerg-1426	380	28	inclusive	inclusive	ADJ
fuelectenerg-1426	380	29	forms	form	NOUN
fuelectenerg-1426	380	30	for	for	ADP
fuelectenerg-1426	380	31	arbitrary	arbitrary	ADJ
fuelectenerg-1426	380	32	radix	radix	PROPN
fuelectenerg-1426	380	33	galois	galois	PROPN
fuelectenerg-1426	380	34	field	field	NOUN
fuelectenerg-1426	380	35	and	and	CCONJ
fuelectenerg-1426	380	36	functions	function	NOUN
fuelectenerg-1426	380	37	of	of	ADP
fuelectenerg-1426	380	38	two	two	NUM
fuelectenerg-1426	380	39	-	-	PUNCT
fuelectenerg-1426	380	40	input	input	NOUN
fuelectenerg-1426	380	41	variables	variable	NOUN
fuelectenerg-1426	380	42	.	.	PUNCT
fuelectenerg-1426	381	1	proof	proof	NOUN
fuelectenerg-1426	381	2	.	.	PUNCT
fuelectenerg-1426	381	3	.	.	PUNCT
fuelectenerg-1426	382	1	the	the	DET
fuelectenerg-1426	382	2	proof	proof	NOUN
fuelectenerg-1426	382	3	follows	follow	VERB
fuelectenerg-1426	382	4	directly	directly	ADV
fuelectenerg-1426	382	5	from	from	ADP
fuelectenerg-1426	382	6	mathematical	mathematical	ADJ
fuelectenerg-1426	382	7	induction	induction	NOUN
fuelectenerg-1426	382	8	of	of	ADP
fuelectenerg-1426	382	9	the	the	DET
fuelectenerg-1426	382	10	number	number	NOUN
fuelectenerg-1426	382	11	of	of	ADP
fuelectenerg-1426	382	12	ifs	ifs	PROPN
fuelectenerg-1426	382	13	over	over	ADP
fuelectenerg-1426	382	14	gf(pk	gf(pk	NOUN
fuelectenerg-1426	382	15	)	)	PUNCT
fuelectenerg-1426	382	16	for	for	ADP
fuelectenerg-1426	382	17	twovariable	twovariable	ADJ
fuelectenerg-1426	382	18	functions	function	NOUN
fuelectenerg-1426	382	19	.	.	PUNCT
fuelectenerg-1426	383	1	this	this	PRON
fuelectenerg-1426	383	2	is	be	AUX
fuelectenerg-1426	383	3	deduced	deduce	VERB
fuelectenerg-1426	383	4	from	from	ADP
fuelectenerg-1426	383	5	the	the	DET
fuelectenerg-1426	383	6	general	general	ADJ
fuelectenerg-1426	383	7	equation	equation	NOUN
fuelectenerg-1426	383	8	(	(	PUNCT
fuelectenerg-1426	383	9	52	52	NUM
fuelectenerg-1426	383	10	)	)	PUNCT
fuelectenerg-1426	383	11	;	;	PUNCT
fuelectenerg-1426	383	12	if	if	SCONJ
fuelectenerg-1426	383	13	the	the	DET
fuelectenerg-1426	383	14	ifn,2	ifn,2	ADJ
fuelectenerg-1426	383	15	triangles	triangle	NOUN
fuelectenerg-1426	383	16	are	be	AUX
fuelectenerg-1426	383	17	valid	valid	ADJ
fuelectenerg-1426	383	18	for	for	ADP
fuelectenerg-1426	383	19	n	n	NOUN
fuelectenerg-1426	383	20	=	=	PRON
fuelectenerg-1426	384	1	q	q	NOUN
fuelectenerg-1426	384	2	then	then	ADV
fuelectenerg-1426	384	3	they	they	PRON
fuelectenerg-1426	384	4	will	will	AUX
fuelectenerg-1426	384	5	be	be	AUX
fuelectenerg-1426	384	6	also	also	ADV
fuelectenerg-1426	384	7	valid	valid	ADJ
fuelectenerg-1426	384	8	for	for	ADP
fuelectenerg-1426	384	9	n	n	NOUN
fuelectenerg-1426	384	10	=	=	PUNCT
fuelectenerg-1426	384	11	q+	q+	ADP
fuelectenerg-1426	384	12	1	1	NUM
fuelectenerg-1426	384	13	,	,	PUNCT
fuelectenerg-1426	384	14	for	for	ADP
fuelectenerg-1426	384	15	n	n	NOUN
fuelectenerg-1426	384	16	=	=	SYM
fuelectenerg-1426	384	17	pk	pk	NOUN
fuelectenerg-1426	384	18	where	where	SCONJ
fuelectenerg-1426	384	19	p	p	NOUN
fuelectenerg-1426	384	20	is	be	AUX
fuelectenerg-1426	384	21	a	a	DET
fuelectenerg-1426	384	22	prime	prime	ADJ
fuelectenerg-1426	384	23	number	number	NOUN
fuelectenerg-1426	384	24	and	and	CCONJ
fuelectenerg-1426	384	25	k	k	PROPN
fuelectenerg-1426	384	26	≥	≥	NUM
fuelectenerg-1426	384	27	1	1	NUM
fuelectenerg-1426	384	28	.	.	PUNCT
fuelectenerg-1426	385	1	these	these	DET
fuelectenerg-1426	385	2	triangles	triangle	NOUN
fuelectenerg-1426	385	3	are	be	AUX
fuelectenerg-1426	385	4	important	important	ADJ
fuelectenerg-1426	385	5	because	because	SCONJ
fuelectenerg-1426	385	6	the	the	DET
fuelectenerg-1426	385	7	count	count	NOUN
fuelectenerg-1426	385	8	complexity	complexity	NOUN
fuelectenerg-1426	385	9	using	use	VERB
fuelectenerg-1426	385	10	equation	equation	NOUN
fuelectenerg-1426	385	11	(	(	PUNCT
fuelectenerg-1426	385	12	52	52	NUM
fuelectenerg-1426	385	13	)	)	PUNCT
fuelectenerg-1426	385	14	for	for	ADP
fuelectenerg-1426	385	15	high	high	ADJ
fuelectenerg-1426	385	16	dimensions	dimension	NOUN
fuelectenerg-1426	385	17	is	be	AUX
fuelectenerg-1426	385	18	very	very	ADV
fuelectenerg-1426	385	19	high	high	ADJ
fuelectenerg-1426	385	20	,	,	PUNCT
fuelectenerg-1426	385	21	and	and	CCONJ
fuelectenerg-1426	385	22	thus	thus	ADV
fuelectenerg-1426	385	23	the	the	DET
fuelectenerg-1426	385	24	ability	ability	NOUN
fuelectenerg-1426	385	25	of	of	ADP
fuelectenerg-1426	385	26	a	a	DET
fuelectenerg-1426	385	27	computer	computer	NOUN
fuelectenerg-1426	385	28	to	to	PART
fuelectenerg-1426	385	29	compute	compute	VERB
fuelectenerg-1426	385	30	the	the	DET
fuelectenerg-1426	385	31	counts	count	NOUN
fuelectenerg-1426	385	32	for	for	ADP
fuelectenerg-1426	385	33	number	number	NOUN
fuelectenerg-1426	385	34	of	of	ADP
fuelectenerg-1426	385	35	variables	variable	NOUN
fuelectenerg-1426	385	36	greater	great	ADJ
fuelectenerg-1426	385	37	than	than	ADP
fuelectenerg-1426	385	38	five	five	NUM
fuelectenerg-1426	385	39	in	in	ADP
fuelectenerg-1426	385	40	a	a	DET
fuelectenerg-1426	385	41	reasonable	reasonable	ADJ
fuelectenerg-1426	385	42	amount	amount	NOUN
fuelectenerg-1426	385	43	of	of	ADP
fuelectenerg-1426	385	44	time	time	NOUN
fuelectenerg-1426	385	45	becomes	become	VERB
fuelectenerg-1426	385	46	difficult	difficult	ADJ
fuelectenerg-1426	385	47	.	.	PUNCT
fuelectenerg-1426	386	1	consequently	consequently	ADV
fuelectenerg-1426	386	2	,	,	PUNCT
fuelectenerg-1426	386	3	the	the	DET
fuelectenerg-1426	386	4	ifn,2	ifn,2	ADJ
fuelectenerg-1426	386	5	triangles	triangle	NOUN
fuelectenerg-1426	386	6	provide	provide	VERB
fuelectenerg-1426	386	7	an	an	DET
fuelectenerg-1426	386	8	alternative	alternative	ADJ
fuelectenerg-1426	386	9	numerical	numerical	ADJ
fuelectenerg-1426	386	10	and	and	CCONJ
fuelectenerg-1426	386	11	geometrical	geometrical	ADJ
fuelectenerg-1426	386	12	pattern	pattern	NOUN
fuelectenerg-1426	386	13	of	of	ADP
fuelectenerg-1426	386	14	computing	computing	NOUN
fuelectenerg-1426	386	15	.	.	PUNCT
fuelectenerg-1426	387	1	it	it	PRON
fuelectenerg-1426	387	2	can	can	AUX
fuelectenerg-1426	387	3	be	be	AUX
fuelectenerg-1426	387	4	observed	observe	VERB
fuelectenerg-1426	387	5	that	that	SCONJ
fuelectenerg-1426	387	6	the	the	DET
fuelectenerg-1426	387	7	ifn,2	ifn,2	ADJ
fuelectenerg-1426	387	8	triangle	triangle	NOUN
fuelectenerg-1426	387	9	of	of	ADP
fuelectenerg-1426	387	10	coefficients	coefficient	NOUN
fuelectenerg-1426	387	11	possesses	possess	VERB
fuelectenerg-1426	387	12	a	a	DET
fuelectenerg-1426	387	13	close	close	ADJ
fuelectenerg-1426	387	14	similarity	similarity	NOUN
fuelectenerg-1426	387	15	to	to	ADP
fuelectenerg-1426	387	16	the	the	DET
fuelectenerg-1426	387	17	well	well	ADV
fuelectenerg-1426	387	18	-	-	PUNCT
fuelectenerg-1426	387	19	known	know	VERB
fuelectenerg-1426	387	20	pascal	pascal	ADJ
fuelectenerg-1426	387	21	triangle	triangle	NOUN
fuelectenerg-1426	387	22	.	.	PUNCT
fuelectenerg-1426	388	1	this	this	PRON
fuelectenerg-1426	388	2	occurs	occur	VERB
fuelectenerg-1426	388	3	as	as	SCONJ
fuelectenerg-1426	388	4	follows	follow	VERB
fuelectenerg-1426	388	5	:	:	PUNCT
fuelectenerg-1426	388	6	if	if	SCONJ
fuelectenerg-1426	388	7	one	one	PRON
fuelectenerg-1426	388	8	omits	omit	VERB
fuelectenerg-1426	388	9	the	the	DET
fuelectenerg-1426	388	10	first	first	ADJ
fuelectenerg-1426	388	11	two	two	NUM
fuelectenerg-1426	388	12	rows	row	NOUN
fuelectenerg-1426	388	13	of	of	ADP
fuelectenerg-1426	388	14	the	the	DET
fuelectenerg-1426	388	15	pascal	pascal	ADJ
fuelectenerg-1426	388	16	triangle	triangle	NOUN
fuelectenerg-1426	388	17	and	and	CCONJ
fuelectenerg-1426	388	18	duplicates	duplicate	VERB
fuelectenerg-1426	388	19	each	each	DET
fuelectenerg-1426	388	20	row	row	NOUN
fuelectenerg-1426	388	21	into	into	ADP
fuelectenerg-1426	388	22	another	another	DET
fuelectenerg-1426	388	23	horizontally	horizontally	ADV
fuelectenerg-1426	388	24	adjacent	adjacent	ADJ
fuelectenerg-1426	388	25	row	row	NOUN
fuelectenerg-1426	388	26	,	,	PUNCT
fuelectenerg-1426	388	27	the	the	DET
fuelectenerg-1426	388	28	ifn,2	ifn,2	ADJ
fuelectenerg-1426	388	29	triangle	triangle	NOUN
fuelectenerg-1426	388	30	of	of	ADP
fuelectenerg-1426	388	31	coefficients	coefficient	NOUN
fuelectenerg-1426	388	32	will	will	AUX
fuelectenerg-1426	388	33	be	be	AUX
fuelectenerg-1426	388	34	obtained	obtain	VERB
fuelectenerg-1426	388	35	.	.	PUNCT
fuelectenerg-1426	389	1	this	this	DET
fuelectenerg-1426	389	2	observation	observation	NOUN
fuelectenerg-1426	389	3	helps	help	VERB
fuelectenerg-1426	389	4	in	in	ADP
fuelectenerg-1426	389	5	creating	create	VERB
fuelectenerg-1426	389	6	algorithms	algorithm	NOUN
fuelectenerg-1426	389	7	that	that	PRON
fuelectenerg-1426	389	8	generates	generate	VERB
fuelectenerg-1426	389	9	the	the	DET
fuelectenerg-1426	389	10	ifn,2	ifn,2	ADJ
fuelectenerg-1426	389	11	triangle	triangle	NOUN
fuelectenerg-1426	389	12	of	of	ADP
fuelectenerg-1426	389	13	coefficients	coefficient	NOUN
fuelectenerg-1426	389	14	since	since	SCONJ
fuelectenerg-1426	389	15	many	many	ADJ
fuelectenerg-1426	389	16	efficient	efficient	ADJ
fuelectenerg-1426	389	17	algorithms	algorithm	NOUN
fuelectenerg-1426	389	18	exist	exist	VERB
fuelectenerg-1426	389	19	to	to	PART
fuelectenerg-1426	389	20	generate	generate	VERB
fuelectenerg-1426	389	21	the	the	DET
fuelectenerg-1426	389	22	pascal	pascal	ADJ
fuelectenerg-1426	389	23	triangle	triangle	NOUN
fuelectenerg-1426	389	24	example	example	NOUN
fuelectenerg-1426	389	25	7	7	NUM
fuelectenerg-1426	389	26	.	.	PUNCT
fuelectenerg-1426	389	27	utilizing	utilize	VERB
fuelectenerg-1426	389	28	ifn,2	ifn,2	ADJ
fuelectenerg-1426	389	29	triangles	triangle	NOUN
fuelectenerg-1426	389	30	from	from	ADP
fuelectenerg-1426	389	31	figure	figure	NOUN
fuelectenerg-1426	389	32	7	7	NUM
fuelectenerg-1426	389	33	,	,	PUNCT
fuelectenerg-1426	389	34	one	one	NUM
fuelectenerg-1426	389	35	calculates	calculate	VERB
fuelectenerg-1426	389	36	the	the	DET
fuelectenerg-1426	389	37	following	follow	VERB
fuelectenerg-1426	389	38	number	number	NOUN
fuelectenerg-1426	389	39	of	of	ADP
fuelectenerg-1426	389	40	inclusive	inclusive	ADJ
fuelectenerg-1426	389	41	forms	form	NOUN
fuelectenerg-1426	389	42	for	for	ADP
fuelectenerg-1426	389	43	gf(2	gf(2	PROPN
fuelectenerg-1426	389	44	)	)	PUNCT
fuelectenerg-1426	389	45	,	,	PUNCT
fuelectenerg-1426	389	46	gf(3	gf(3	PROPN
fuelectenerg-1426	389	47	)	)	PUNCT
fuelectenerg-1426	389	48	and	and	CCONJ
fuelectenerg-1426	389	49	gf(4	gf(4	NOUN
fuelectenerg-1426	389	50	)	)	PUNCT
fuelectenerg-1426	389	51	for	for	ADP
fuelectenerg-1426	389	52	two	two	NUM
fuelectenerg-1426	389	53	variables	variable	NOUN
fuelectenerg-1426	389	54	,	,	PUNCT
fuelectenerg-1426	389	55	where	where	SCONJ
fuelectenerg-1426	389	56	the	the	DET
fuelectenerg-1426	389	57	results	result	NOUN
fuelectenerg-1426	389	58	are	be	AUX
fuelectenerg-1426	389	59	117	117	NUM
fuelectenerg-1426	389	60	(	(	PUNCT
fuelectenerg-1426	389	61	a	a	NOUN
fuelectenerg-1426	389	62	)	)	PUNCT
fuelectenerg-1426	389	63	(	(	PUNCT
fuelectenerg-1426	389	64	b	b	NOUN
fuelectenerg-1426	389	65	)	)	PUNCT
fuelectenerg-1426	389	66	.	.	PUNCT
fuelectenerg-1426	390	1	718	718	NUM
fuelectenerg-1426	390	2	a.	a.	PROPN
fuelectenerg-1426	390	3	n.	n.	PROPN
fuelectenerg-1426	390	4	al	al	PROPN
fuelectenerg-1426	390	5	-	-	PUNCT
fuelectenerg-1426	390	6	rabadi	rabadi	PROPN
fuelectenerg-1426	390	7	multi	multi	ADJ
fuelectenerg-1426	390	8	-	-	ADJ
fuelectenerg-1426	390	9	valued	value	VERB
fuelectenerg-1426	390	10	galois	galois	PROPN
fuelectenerg-1426	390	11	shannon	shannon	PROPN
fuelectenerg-1426	390	12	davio	davio	PROPN
fuelectenerg-1426	390	13	trees	tree	NOUN
fuelectenerg-1426	390	14	and	and	CCONJ
fuelectenerg-1426	390	15	their	their	PRON
fuelectenerg-1426	390	16	complexity	complexity	NOUN
fuelectenerg-1426	390	17	719	719	NUM
fuelectenerg-1426	390	18	multi	multi	ADJ
fuelectenerg-1426	390	19	-	-	ADJ
fuelectenerg-1426	390	20	valued	value	VERB
fuelectenerg-1426	390	21	galois	galois	PROPN
fuelectenerg-1426	390	22	shannon	shannon	PROPN
fuelectenerg-1426	390	23	davio	davio	PROPN
fuelectenerg-1426	390	24	trees	tree	NOUN
fuelectenerg-1426	390	25	and	and	CCONJ
fuelectenerg-1426	390	26	their	their	PRON
fuelectenerg-1426	390	27	complexity	complexity	NOUN
fuelectenerg-1426	390	28	identical	identical	ADJ
fuelectenerg-1426	390	29	to	to	ADP
fuelectenerg-1426	390	30	those	those	PRON
fuelectenerg-1426	390	31	obtained	obtain	VERB
fuelectenerg-1426	390	32	previously	previously	ADV
fuelectenerg-1426	390	33	:	:	PUNCT
fuelectenerg-1426	391	1	φ2,2	φ2,2	PROPN
fuelectenerg-1426	391	2	=	=	SYM
fuelectenerg-1426	391	3	1	1	NUM
fuelectenerg-1426	391	4	·	·	SYM
fuelectenerg-1426	391	5	20	20	NUM
fuelectenerg-1426	391	6	+	+	NUM
fuelectenerg-1426	391	7	2	2	NUM
fuelectenerg-1426	391	8	·	·	SYM
fuelectenerg-1426	391	9	21	21	NUM
fuelectenerg-1426	391	10	+	+	SYM
fuelectenerg-1426	391	11	1	1	NUM
fuelectenerg-1426	391	12	·	·	SYM
fuelectenerg-1426	391	13	22	22	NUM
fuelectenerg-1426	391	14	+	+	NUM
fuelectenerg-1426	391	15	1	1	NUM
fuelectenerg-1426	391	16	·	·	SYM
fuelectenerg-1426	391	17	22	22	NUM
fuelectenerg-1426	391	18	+	+	NUM
fuelectenerg-1426	391	19	2	2	NUM
fuelectenerg-1426	391	20	·	·	SYM
fuelectenerg-1426	391	21	23	23	NUM
fuelectenerg-1426	391	22	+	+	SYM
fuelectenerg-1426	391	23	1	1	NUM
fuelectenerg-1426	391	24	·	·	SYM
fuelectenerg-1426	391	25	24	24	NUM
fuelectenerg-1426	391	26	=	=	SYM
fuelectenerg-1426	391	27	1	1	NUM
fuelectenerg-1426	391	28	+	+	NOUN
fuelectenerg-1426	391	29	4	4	NUM
fuelectenerg-1426	391	30	+	+	SYM
fuelectenerg-1426	391	31	4	4	NUM
fuelectenerg-1426	391	32	+	+	SYM
fuelectenerg-1426	391	33	4	4	NUM
fuelectenerg-1426	391	34	+	+	SYM
fuelectenerg-1426	391	35	16	16	NUM
fuelectenerg-1426	391	36	+	+	ADJ
fuelectenerg-1426	391	37	16=	16=	NUM
fuelectenerg-1426	391	38	45	45	NUM
fuelectenerg-1426	391	39	.	.	PUNCT
fuelectenerg-1426	391	40	φ3,2	φ3,2	NOUN
fuelectenerg-1426	391	41	=	=	SYM
fuelectenerg-1426	391	42	1	1	NUM
fuelectenerg-1426	391	43	·	·	SYM
fuelectenerg-1426	391	44	30	30	NUM
fuelectenerg-1426	391	45	+	+	NUM
fuelectenerg-1426	391	46	3	3	NUM
fuelectenerg-1426	391	47	·	·	SYM
fuelectenerg-1426	391	48	32	32	NUM
fuelectenerg-1426	391	49	+	+	SYM
fuelectenerg-1426	391	50	3	3	NUM
fuelectenerg-1426	391	51	·	·	SYM
fuelectenerg-1426	391	52	34	34	NUM
fuelectenerg-1426	391	53	+	+	SYM
fuelectenerg-1426	391	54	1	1	NUM
fuelectenerg-1426	391	55	·	·	SYM
fuelectenerg-1426	391	56	36	36	NUM
fuelectenerg-1426	391	57	+	+	SYM
fuelectenerg-1426	391	58	1	1	NUM
fuelectenerg-1426	391	59	·	·	SYM
fuelectenerg-1426	391	60	36	36	NUM
fuelectenerg-1426	391	61	+	+	SYM
fuelectenerg-1426	391	62	3	3	NUM
fuelectenerg-1426	391	63	·	·	SYM
fuelectenerg-1426	391	64	38	38	NUM
fuelectenerg-1426	391	65	+	+	SYM
fuelectenerg-1426	391	66	3	3	NUM
fuelectenerg-1426	391	67	·	·	SYM
fuelectenerg-1426	391	68	310	310	NUM
fuelectenerg-1426	391	69	+	+	SYM
fuelectenerg-1426	391	70	1	1	NUM
fuelectenerg-1426	391	71	·	·	SYM
fuelectenerg-1426	391	72	312	312	NUM
fuelectenerg-1426	391	73	=	=	SYM
fuelectenerg-1426	391	74	730,000	730,000	NUM
fuelectenerg-1426	391	75	.	.	PUNCT
fuelectenerg-1426	392	1	φ4,2	φ4,2	PROPN
fuelectenerg-1426	392	2	=	=	SYM
fuelectenerg-1426	392	3	1	1	NUM
fuelectenerg-1426	392	4	·	·	SYM
fuelectenerg-1426	392	5	40	40	NUM
fuelectenerg-1426	392	6	+	+	NUM
fuelectenerg-1426	392	7	4	4	NUM
fuelectenerg-1426	392	8	·	·	SYM
fuelectenerg-1426	392	9	43	43	NUM
fuelectenerg-1426	392	10	+	+	NUM
fuelectenerg-1426	392	11	6	6	NUM
fuelectenerg-1426	392	12	·	·	SYM
fuelectenerg-1426	392	13	46	46	NUM
fuelectenerg-1426	392	14	+	+	SYM
fuelectenerg-1426	392	15	4	4	NUM
fuelectenerg-1426	392	16	·	·	SYM
fuelectenerg-1426	392	17	49	49	NUM
fuelectenerg-1426	392	18	+	+	SYM
fuelectenerg-1426	392	19	1	1	NUM
fuelectenerg-1426	392	20	·	·	SYM
fuelectenerg-1426	392	21	412	412	NUM
fuelectenerg-1426	392	22	+	+	SYM
fuelectenerg-1426	392	23	1	1	NUM
fuelectenerg-1426	392	24	·	·	SYM
fuelectenerg-1426	392	25	412	412	NUM
fuelectenerg-1426	392	26	+	+	SYM
fuelectenerg-1426	392	27	4	4	NUM
fuelectenerg-1426	392	28	·	·	SYM
fuelectenerg-1426	392	29	415	415	NUM
fuelectenerg-1426	392	30	+	+	NOUN
fuelectenerg-1426	392	31	6	6	NUM
fuelectenerg-1426	392	32	·	·	SYM
fuelectenerg-1426	392	33	418	418	NUM
fuelectenerg-1426	392	34	+	+	SYM
fuelectenerg-1426	392	35	4	4	NUM
fuelectenerg-1426	392	36	·	·	SYM
fuelectenerg-1426	392	37	421	421	NUM
fuelectenerg-1426	392	38	+	+	SYM
fuelectenerg-1426	392	39	1	1	NUM
fuelectenerg-1426	392	40	·	·	SYM
fuelectenerg-1426	392	41	424	424	NUM
fuelectenerg-1426	392	42	=	=	SYM
fuelectenerg-1426	392	43	2.99483809211×1014	2.99483809211×1014	NOUN
fuelectenerg-1426	392	44	.	.	PUNCT
fuelectenerg-1426	393	1	the	the	DET
fuelectenerg-1426	393	2	ifn,2	ifn,2	ADJ
fuelectenerg-1426	393	3	triangles	triangle	NOUN
fuelectenerg-1426	393	4	,	,	PUNCT
fuelectenerg-1426	393	5	for	for	ADP
fuelectenerg-1426	393	6	n	n	PRON
fuelectenerg-1426	393	7	is	be	AUX
fuelectenerg-1426	393	8	the	the	DET
fuelectenerg-1426	393	9	number	number	NOUN
fuelectenerg-1426	393	10	of	of	ADP
fuelectenerg-1426	393	11	variables	variable	NOUN
fuelectenerg-1426	393	12	,	,	PUNCT
fuelectenerg-1426	393	13	possess	possess	VERB
fuelectenerg-1426	393	14	the	the	DET
fuelectenerg-1426	393	15	following	follow	VERB
fuelectenerg-1426	393	16	interesting	interesting	ADJ
fuelectenerg-1426	393	17	properties	property	NOUN
fuelectenerg-1426	393	18	:	:	PUNCT
fuelectenerg-1426	393	19	1	1	X
fuelectenerg-1426	393	20	.	.	X
fuelectenerg-1426	393	21	number	number	NOUN
fuelectenerg-1426	393	22	of	of	ADP
fuelectenerg-1426	393	23	positions	position	NOUN
fuelectenerg-1426	393	24	(	(	PUNCT
fuelectenerg-1426	393	25	elements	element	NOUN
fuelectenerg-1426	393	26	)	)	PUNCT
fuelectenerg-1426	393	27	in	in	ADP
fuelectenerg-1426	393	28	each	each	DET
fuelectenerg-1426	393	29	row	row	NOUN
fuelectenerg-1426	393	30	of	of	ADP
fuelectenerg-1426	393	31	the	the	DET
fuelectenerg-1426	393	32	triangles	triangle	NOUN
fuelectenerg-1426	393	33	in	in	ADP
fuelectenerg-1426	393	34	figure	figure	NOUN
fuelectenerg-1426	393	35	7	7	NUM
fuelectenerg-1426	393	36	are	be	AUX
fuelectenerg-1426	393	37	even	even	ADV
fuelectenerg-1426	393	38	starting	start	VERB
fuelectenerg-1426	393	39	from	from	ADP
fuelectenerg-1426	393	40	six	six	NUM
fuelectenerg-1426	393	41	.	.	NOUN
fuelectenerg-1426	394	1	2	2	NUM
fuelectenerg-1426	394	2	.	.	X
fuelectenerg-1426	394	3	sum	sum	NOUN
fuelectenerg-1426	394	4	of	of	ADP
fuelectenerg-1426	394	5	elements	element	NOUN
fuelectenerg-1426	394	6	in	in	ADP
fuelectenerg-1426	394	7	each	each	DET
fuelectenerg-1426	394	8	row	row	NOUN
fuelectenerg-1426	394	9	in	in	ADP
fuelectenerg-1426	394	10	figure	figure	NOUN
fuelectenerg-1426	394	11	7(a	7(a	NUM
fuelectenerg-1426	394	12	)	)	PUNCT
fuelectenerg-1426	394	13	equals	equal	VERB
fuelectenerg-1426	394	14	to	to	ADP
fuelectenerg-1426	394	15	the	the	DET
fuelectenerg-1426	394	16	number	number	NOUN
fuelectenerg-1426	394	17	of	of	ADP
fuelectenerg-1426	394	18	s	s	PROPN
fuelectenerg-1426	394	19	/	/	SYM
fuelectenerg-1426	394	20	d	d	NOUN
fuelectenerg-1426	394	21	trees	tree	NOUN
fuelectenerg-1426	394	22	per	per	ADP
fuelectenerg-1426	394	23	variable	variable	ADJ
fuelectenerg-1426	394	24	order	order	NOUN
fuelectenerg-1426	394	25	.	.	PUNCT
fuelectenerg-1426	395	1	3	3	X
fuelectenerg-1426	395	2	.	.	X
fuelectenerg-1426	395	3	triangle	triangle	NOUN
fuelectenerg-1426	395	4	in	in	ADP
fuelectenerg-1426	395	5	figure	figure	NOUN
fuelectenerg-1426	395	6	7(a	7(a	NUM
fuelectenerg-1426	395	7	)	)	PUNCT
fuelectenerg-1426	395	8	possesses	possess	VERB
fuelectenerg-1426	395	9	even	even	ADV
fuelectenerg-1426	395	10	symmetry	symmetry	VERB
fuelectenerg-1426	395	11	around	around	ADP
fuelectenerg-1426	395	12	an	an	DET
fuelectenerg-1426	395	13	imaginary	imaginary	ADJ
fuelectenerg-1426	395	14	vertical	vertical	ADJ
fuelectenerg-1426	395	15	axis	axis	NOUN
fuelectenerg-1426	395	16	in	in	ADP
fuelectenerg-1426	395	17	the	the	DET
fuelectenerg-1426	395	18	middle	middle	NOUN
fuelectenerg-1426	395	19	.	.	PUNCT
fuelectenerg-1426	396	1	4	4	X
fuelectenerg-1426	396	2	.	.	X
fuelectenerg-1426	396	3	the	the	DET
fuelectenerg-1426	396	4	minimum	minimum	ADJ
fuelectenerg-1426	396	5	number	number	NOUN
fuelectenerg-1426	396	6	of	of	ADP
fuelectenerg-1426	396	7	columns	column	NOUN
fuelectenerg-1426	396	8	required	require	VERB
fuelectenerg-1426	396	9	to	to	PART
fuelectenerg-1426	396	10	generate	generate	VERB
fuelectenerg-1426	396	11	the	the	DET
fuelectenerg-1426	396	12	whole	whole	ADJ
fuelectenerg-1426	396	13	triangle	triangle	NOUN
fuelectenerg-1426	396	14	in	in	ADP
fuelectenerg-1426	396	15	figure	figure	NOUN
fuelectenerg-1426	396	16	7(a	7(a	NUM
fuelectenerg-1426	396	17	)	)	PUNCT
fuelectenerg-1426	396	18	is	be	AUX
fuelectenerg-1426	396	19	equal	equal	ADJ
fuelectenerg-1426	396	20	to	to	ADP
fuelectenerg-1426	396	21	three	three	NUM
fuelectenerg-1426	396	22	due	due	ADJ
fuelectenerg-1426	396	23	to	to	ADP
fuelectenerg-1426	396	24	even	even	ADV
fuelectenerg-1426	396	25	symmetry	symmetry	NOUN
fuelectenerg-1426	396	26	:	:	PUNCT
fuelectenerg-1426	396	27	one	one	NUM
fuelectenerg-1426	396	28	wing	wing	NOUN
fuelectenerg-1426	396	29	,	,	PUNCT
fuelectenerg-1426	396	30	one	one	NUM
fuelectenerg-1426	396	31	column	column	NOUN
fuelectenerg-1426	396	32	neighbor	neighbor	NOUN
fuelectenerg-1426	396	33	to	to	ADP
fuelectenerg-1426	396	34	the	the	DET
fuelectenerg-1426	396	35	middle	middle	ADJ
fuelectenerg-1426	396	36	column	column	NOUN
fuelectenerg-1426	396	37	and	and	CCONJ
fuelectenerg-1426	396	38	one	one	NUM
fuelectenerg-1426	396	39	middle	middle	ADJ
fuelectenerg-1426	396	40	column	column	NOUN
fuelectenerg-1426	396	41	.	.	PUNCT
fuelectenerg-1426	397	1	5	5	X
fuelectenerg-1426	397	2	.	.	X
fuelectenerg-1426	397	3	the	the	DET
fuelectenerg-1426	397	4	triangle	triangle	NOUN
fuelectenerg-1426	397	5	in	in	ADP
fuelectenerg-1426	397	6	figure	figure	NOUN
fuelectenerg-1426	397	7	7(a	7(a	NUM
fuelectenerg-1426	397	8	)	)	PUNCT
fuelectenerg-1426	397	9	can	can	AUX
fuelectenerg-1426	397	10	be	be	AUX
fuelectenerg-1426	397	11	generated	generate	VERB
fuelectenerg-1426	397	12	by	by	ADP
fuelectenerg-1426	397	13	the	the	DET
fuelectenerg-1426	397	14	process	process	NOUN
fuelectenerg-1426	397	15	of	of	ADP
fuelectenerg-1426	397	16	"	"	PUNCT
fuelectenerg-1426	397	17	shift	shift	VERB
fuelectenerg-1426	397	18	diagonally	diagonally	ADV
fuelectenerg-1426	397	19	and	and	CCONJ
fuelectenerg-1426	397	20	add	add	VERB
fuelectenerg-1426	397	21	diagonally	diagonally	ADV
fuelectenerg-1426	397	22	"	"	PUNCT
fuelectenerg-1426	397	23	(	(	PUNCT
fuelectenerg-1426	397	24	sdaad	sdaad	VERB
fuelectenerg-1426	397	25	):	):	PUNCT
fuelectenerg-1426	397	26	shift	shift	VERB
fuelectenerg-1426	397	27	the	the	DET
fuelectenerg-1426	397	28	left	left	ADJ
fuelectenerg-1426	397	29	wing	wing	NOUN
fuelectenerg-1426	397	30	diagonally	diagonally	ADV
fuelectenerg-1426	397	31	from	from	ADP
fuelectenerg-1426	397	32	west	west	PROPN
fuelectenerg-1426	397	33	to	to	ADP
fuelectenerg-1426	397	34	southeast	southeast	ADJ
fuelectenerg-1426	397	35	direction	direction	NOUN
fuelectenerg-1426	397	36	and	and	CCONJ
fuelectenerg-1426	397	37	add	add	VERB
fuelectenerg-1426	397	38	two	two	NUM
fuelectenerg-1426	397	39	numbers	number	NOUN
fuelectenerg-1426	397	40	diagonally	diagonally	ADV
fuelectenerg-1426	397	41	from	from	ADP
fuelectenerg-1426	397	42	east	east	PROPN
fuelectenerg-1426	397	43	to	to	ADP
fuelectenerg-1426	397	44	southwest	southwest	NOUN
fuelectenerg-1426	397	45	direction	direction	NOUN
fuelectenerg-1426	397	46	,	,	PUNCT
fuelectenerg-1426	397	47	and	and	CCONJ
fuelectenerg-1426	397	48	shift	shift	VERB
fuelectenerg-1426	397	49	the	the	DET
fuelectenerg-1426	397	50	right	right	ADJ
fuelectenerg-1426	397	51	wing	wing	NOUN
fuelectenerg-1426	397	52	diagonally	diagonally	ADV
fuelectenerg-1426	397	53	from	from	ADP
fuelectenerg-1426	397	54	east	east	PROPN
fuelectenerg-1426	397	55	to	to	ADP
fuelectenerg-1426	397	56	southwest	southwest	NOUN
fuelectenerg-1426	397	57	direction	direction	NOUN
fuelectenerg-1426	397	58	and	and	CCONJ
fuelectenerg-1426	397	59	add	add	VERB
fuelectenerg-1426	397	60	two	two	NUM
fuelectenerg-1426	397	61	numbers	number	NOUN
fuelectenerg-1426	397	62	diagonally	diagonally	ADV
fuelectenerg-1426	397	63	from	from	ADP
fuelectenerg-1426	397	64	west	west	NOUN
fuelectenerg-1426	397	65	to	to	ADP
fuelectenerg-1426	397	66	southeast	southeast	ADJ
fuelectenerg-1426	397	67	direction	direction	NOUN
fuelectenerg-1426	397	68	.	.	PUNCT
fuelectenerg-1426	398	1	6	6	X
fuelectenerg-1426	398	2	.	.	X
fuelectenerg-1426	398	3	the	the	DET
fuelectenerg-1426	398	4	difference	difference	NOUN
fuelectenerg-1426	398	5	in	in	ADP
fuelectenerg-1426	398	6	powers	power	NOUN
fuelectenerg-1426	398	7	in	in	ADP
fuelectenerg-1426	398	8	the	the	DET
fuelectenerg-1426	398	9	triangle	triangle	NOUN
fuelectenerg-1426	398	10	in	in	ADP
fuelectenerg-1426	398	11	figure	figure	NOUN
fuelectenerg-1426	398	12	7(b	7(b	NOUN
fuelectenerg-1426	398	13	)	)	PUNCT
fuelectenerg-1426	398	14	per	per	ADP
fuelectenerg-1426	398	15	row	row	NOUN
fuelectenerg-1426	398	16	element	element	NOUN
fuelectenerg-1426	398	17	is	be	AUX
fuelectenerg-1426	398	18	(	(	PUNCT
fuelectenerg-1426	398	19	n	n	X
fuelectenerg-1426	398	20	−1	−1	NOUN
fuelectenerg-1426	398	21	)	)	PUNCT
fuelectenerg-1426	398	22	.	.	PUNCT
fuelectenerg-1426	399	1	7	7	X
fuelectenerg-1426	399	2	.	.	X
fuelectenerg-1426	399	3	the	the	DET
fuelectenerg-1426	399	4	first	first	ADJ
fuelectenerg-1426	399	5	number	number	NOUN
fuelectenerg-1426	399	6	in	in	ADP
fuelectenerg-1426	399	7	each	each	DET
fuelectenerg-1426	399	8	row	row	NOUN
fuelectenerg-1426	399	9	of	of	ADP
fuelectenerg-1426	399	10	the	the	DET
fuelectenerg-1426	399	11	triangle	triangle	NOUN
fuelectenerg-1426	399	12	in	in	ADP
fuelectenerg-1426	399	13	figure	figure	NOUN
fuelectenerg-1426	399	14	7(b	7(b	NUM
fuelectenerg-1426	399	15	)	)	PUNCT
fuelectenerg-1426	399	16	is	be	AUX
fuelectenerg-1426	399	17	n0	n0	ADJ
fuelectenerg-1426	399	18	and	and	CCONJ
fuelectenerg-1426	399	19	the	the	DET
fuelectenerg-1426	399	20	last	last	ADJ
fuelectenerg-1426	399	21	number	number	NOUN
fuelectenerg-1426	399	22	per	per	ADP
fuelectenerg-1426	399	23	row	row	NOUN
fuelectenerg-1426	399	24	is	be	AUX
fuelectenerg-1426	399	25	n2n(n−1	n2n(n−1	PROPN
fuelectenerg-1426	399	26	)	)	PUNCT
fuelectenerg-1426	399	27	.	.	PUNCT
fuelectenerg-1426	400	1	8	8	X
fuelectenerg-1426	400	2	.	.	PUNCT
fuelectenerg-1426	401	1	the	the	DET
fuelectenerg-1426	401	2	middle	middle	ADJ
fuelectenerg-1426	401	3	two	two	NUM
fuelectenerg-1426	401	4	numbers	number	NOUN
fuelectenerg-1426	401	5	in	in	ADP
fuelectenerg-1426	401	6	each	each	DET
fuelectenerg-1426	401	7	row	row	NOUN
fuelectenerg-1426	401	8	of	of	ADP
fuelectenerg-1426	401	9	the	the	DET
fuelectenerg-1426	401	10	triangle	triangle	NOUN
fuelectenerg-1426	401	11	in	in	ADP
fuelectenerg-1426	401	12	figure	figure	NOUN
fuelectenerg-1426	401	13	7(b	7(b	NUM
fuelectenerg-1426	401	14	)	)	PUNCT
fuelectenerg-1426	401	15	are	be	AUX
fuelectenerg-1426	401	16	always	always	ADV
fuelectenerg-1426	401	17	equal	equal	ADJ
fuelectenerg-1426	401	18	to	to	ADP
fuelectenerg-1426	401	19	nn(n−1	nn(n−1	PROPN
fuelectenerg-1426	401	20	)	)	PUNCT
fuelectenerg-1426	401	21	.	.	PUNCT
fuelectenerg-1426	402	1	5	5	NUM
fuelectenerg-1426	402	2	conclusions	conclusion	NOUN
fuelectenerg-1426	402	3	and	and	CCONJ
fuelectenerg-1426	402	4	future	future	ADJ
fuelectenerg-1426	402	5	work	work	NOUN
fuelectenerg-1426	402	6	trees	tree	NOUN
fuelectenerg-1426	402	7	for	for	ADP
fuelectenerg-1426	402	8	generalized	generalized	ADJ
fuelectenerg-1426	402	9	shannon	shannon	NOUN
fuelectenerg-1426	402	10	-	-	PUNCT
fuelectenerg-1426	402	11	davio	davio	NOUN
fuelectenerg-1426	402	12	(	(	PUNCT
fuelectenerg-1426	402	13	s	s	NOUN
fuelectenerg-1426	402	14	/	/	SYM
fuelectenerg-1426	402	15	d	d	NOUN
fuelectenerg-1426	402	16	)	)	PUNCT
fuelectenerg-1426	402	17	expansions	expansion	NOUN
fuelectenerg-1426	402	18	over	over	ADP
fuelectenerg-1426	402	19	quaternary	quaternary	ADJ
fuelectenerg-1426	402	20	galois	galois	PROPN
fuelectenerg-1426	402	21	radix	radix	NOUN
fuelectenerg-1426	402	22	is	be	AUX
fuelectenerg-1426	402	23	presented	present	VERB
fuelectenerg-1426	402	24	,	,	PUNCT
fuelectenerg-1426	402	25	and	and	CCONJ
fuelectenerg-1426	402	26	the	the	DET
fuelectenerg-1426	402	27	corresponding	corresponding	ADJ
fuelectenerg-1426	402	28	count	count	NOUN
fuelectenerg-1426	402	29	for	for	ADP
fuelectenerg-1426	402	30	the	the	DET
fuelectenerg-1426	402	31	number	number	NOUN
fuelectenerg-1426	402	32	of	of	ADP
fuelectenerg-1426	402	33	inclusive	inclusive	ADJ
fuelectenerg-1426	402	34	forms	form	NOUN
fuelectenerg-1426	402	35	(	(	PUNCT
fuelectenerg-1426	402	36	ifs	ifs	PROPN
fuelectenerg-1426	402	37	)	)	PUNCT
fuelectenerg-1426	402	38	per	per	ADP
fuelectenerg-1426	402	39	variable	variable	ADJ
fuelectenerg-1426	402	40	order	order	NOUN
fuelectenerg-1426	402	41	for	for	ADP
fuelectenerg-1426	402	42	arbitrary	arbitrary	ADJ
fuelectenerg-1426	402	43	galois	galois	PROPN
fuelectenerg-1426	402	44	radix	radix	NOUN
fuelectenerg-1426	402	45	and	and	CCONJ
fuelectenerg-1426	402	46	arbitrary	arbitrary	ADJ
fuelectenerg-1426	402	47	number	number	NOUN
fuelectenerg-1426	402	48	of	of	ADP
fuelectenerg-1426	402	49	variables	variable	NOUN
fuelectenerg-1426	402	50	is	be	AUX
fuelectenerg-1426	402	51	introduced	introduce	VERB
fuelectenerg-1426	402	52	.	.	PUNCT
fuelectenerg-1426	403	1	also	also	ADV
fuelectenerg-1426	403	2	,	,	PUNCT
fuelectenerg-1426	403	3	the	the	DET
fuelectenerg-1426	403	4	ifn,2	ifn,2	ADJ
fuelectenerg-1426	403	5	triangles	triangle	NOUN
fuelectenerg-1426	403	6	as	as	ADP
fuelectenerg-1426	403	7	a	a	DET
fuelectenerg-1426	403	8	new	new	ADJ
fuelectenerg-1426	403	9	fast	fast	ADJ
fuelectenerg-1426	403	10	computational	computational	ADJ
fuelectenerg-1426	403	11	method	method	NOUN
fuelectenerg-1426	403	12	to	to	PART
fuelectenerg-1426	403	13	count	count	VERB
fuelectenerg-1426	403	14	the	the	DET
fuelectenerg-1426	403	15	number	number	NOUN
fuelectenerg-1426	403	16	of	of	ADP
fuelectenerg-1426	403	17	ifs	ifs	PROPN
fuelectenerg-1426	403	18	for	for	ADP
fuelectenerg-1426	403	19	an	an	DET
fuelectenerg-1426	403	20	arbitrary	arbitrary	ADJ
fuelectenerg-1426	403	21	galois	galois	PROPN
fuelectenerg-1426	403	22	radix	radix	NOUN
fuelectenerg-1426	403	23	and	and	CCONJ
fuelectenerg-1426	403	24	functions	function	NOUN
fuelectenerg-1426	403	25	of	of	ADP
fuelectenerg-1426	403	26	two	two	NUM
fuelectenerg-1426	403	27	variables	variable	NOUN
fuelectenerg-1426	403	28	is	be	AUX
fuelectenerg-1426	403	29	introduced	introduce	VERB
fuelectenerg-1426	403	30	.	.	PUNCT
fuelectenerg-1426	404	1	since	since	SCONJ
fuelectenerg-1426	404	2	galois	galois	PROPN
fuelectenerg-1426	404	3	field	field	NOUN
fuelectenerg-1426	404	4	of	of	ADP
fuelectenerg-1426	404	5	quaternary	quaternary	ADJ
fuelectenerg-1426	404	6	radix	radix	NOUN
fuelectenerg-1426	404	7	has	have	VERB
fuelectenerg-1426	404	8	some	some	DET
fuelectenerg-1426	404	9	interesting	interesting	ADJ
fuelectenerg-1426	404	10	properties	property	NOUN
fuelectenerg-1426	404	11	including	include	VERB
fuelectenerg-1426	404	12	its	its	PRON
fuelectenerg-1426	404	13	implementation	implementation	NOUN
fuelectenerg-1426	404	14	utilizing	utilize	VERB
fuelectenerg-1426	404	15	the	the	DET
fuelectenerg-1426	404	16	well	well	ADV
fuelectenerg-1426	404	17	-	-	PUNCT
fuelectenerg-1426	404	18	established	establish	VERB
fuelectenerg-1426	404	19	two	two	NUM
fuelectenerg-1426	404	20	-	-	PUNCT
fuelectenerg-1426	404	21	valued	value	VERB
fuelectenerg-1426	404	22	logic	logic	NOUN
fuelectenerg-1426	404	23	synthesis	synthesis	NOUN
fuelectenerg-1426	404	24	methods	method	NOUN
fuelectenerg-1426	404	25	,	,	PUNCT
fuelectenerg-1426	404	26	the	the	DET
fuelectenerg-1426	404	27	extension	extension	NOUN
fuelectenerg-1426	404	28	of	of	ADP
fuelectenerg-1426	404	29	the	the	DET
fuelectenerg-1426	404	30	s	s	PROPN
fuelectenerg-1426	404	31	/	/	SYM
fuelectenerg-1426	404	32	d	d	NOUN
fuelectenerg-1426	404	33	trees	tree	NOUN
fuelectenerg-1426	404	34	to	to	ADP
fuelectenerg-1426	404	35	gf(4	gf(4	NOUN
fuelectenerg-1426	404	36	)	)	PUNCT
fuelectenerg-1426	404	37	is	be	AUX
fuelectenerg-1426	404	38	presented	present	VERB
fuelectenerg-1426	404	39	.	.	PUNCT
fuelectenerg-1426	405	1	in	in	ADP
fuelectenerg-1426	405	2	addition	addition	NOUN
fuelectenerg-1426	405	3	,	,	PUNCT
fuelectenerg-1426	405	4	the	the	DET
fuelectenerg-1426	405	5	form	form	NOUN
fuelectenerg-1426	405	6	of	of	ADP
fuelectenerg-1426	405	7	s	s	PROPN
fuelectenerg-1426	405	8	/	/	SYM
fuelectenerg-1426	405	9	d	d	NOUN
fuelectenerg-1426	405	10	trees	tree	NOUN
fuelectenerg-1426	405	11	is	be	AUX
fuelectenerg-1426	405	12	a	a	DET
fuelectenerg-1426	405	13	general	general	ADJ
fuelectenerg-1426	405	14	concept	concept	NOUN
fuelectenerg-1426	405	15	that	that	PRON
fuelectenerg-1426	405	16	can	can	AUX
fuelectenerg-1426	405	17	be	be	AUX
fuelectenerg-1426	405	18	used	use	VERB
fuelectenerg-1426	405	19	in	in	ADP
fuelectenerg-1426	405	20	applications	application	NOUN
fuelectenerg-1426	405	21	for	for	ADP
fuelectenerg-1426	405	22	the	the	DET
fuelectenerg-1426	405	23	generation	generation	NOUN
fuelectenerg-1426	405	24	of	of	ADP
fuelectenerg-1426	405	25	new	new	ADJ
fuelectenerg-1426	405	26	diagrams	diagram	NOUN
fuelectenerg-1426	405	27	and	and	CCONJ
fuelectenerg-1426	405	28	canonical	canonical	ADJ
fuelectenerg-1426	405	29	forms	form	NOUN
fuelectenerg-1426	405	30	,	,	PUNCT
fuelectenerg-1426	405	31	and	and	CCONJ
fuelectenerg-1426	405	32	in	in	ADP
fuelectenerg-1426	405	33	the	the	DET
fuelectenerg-1426	405	34	sumof	sumof	NOUN
fuelectenerg-1426	405	35	-	-	PUNCT
fuelectenerg-1426	405	36	product	product	NOUN
fuelectenerg-1426	405	37	(	(	PUNCT
fuelectenerg-1426	405	38	sop	sop	PROPN
fuelectenerg-1426	405	39	)	)	PUNCT
fuelectenerg-1426	405	40	minimization	minimization	NOUN
fuelectenerg-1426	405	41	where	where	SCONJ
fuelectenerg-1426	405	42	s	s	X
fuelectenerg-1426	405	43	/	/	SYM
fuelectenerg-1426	405	44	d	d	NOUN
fuelectenerg-1426	405	45	trees	tree	NOUN
fuelectenerg-1426	405	46	can	can	AUX
fuelectenerg-1426	405	47	be	be	AUX
fuelectenerg-1426	405	48	utilized	utilize	VERB
fuelectenerg-1426	405	49	for	for	ADP
fuelectenerg-1426	405	50	generating	generate	VERB
fuelectenerg-1426	405	51	forms	form	NOUN
fuelectenerg-1426	405	52	that	that	PRON
fuelectenerg-1426	405	53	include	include	VERB
fuelectenerg-1426	405	54	minimum	minimum	ADJ
fuelectenerg-1426	405	55	galois	galois	PROPN
fuelectenerg-1426	405	56	field	field	NOUN
fuelectenerg-1426	405	57	sum	sum	NOUN
fuelectenerg-1426	405	58	-	-	PUNCT
fuelectenerg-1426	405	59	of	of	ADP
fuelectenerg-1426	405	60	-	-	PUNCT
fuelectenerg-1426	405	61	products	product	NOUN
fuelectenerg-1426	405	62	(	(	PUNCT
fuelectenerg-1426	405	63	gfsop	gfsop	NOUN
fuelectenerg-1426	405	64	)	)	PUNCT
fuelectenerg-1426	405	65	circuits	circuit	NOUN
fuelectenerg-1426	405	66	for	for	ADP
fuelectenerg-1426	405	67	binary	binary	ADJ
fuelectenerg-1426	405	68	and	and	CCONJ
fuelectenerg-1426	405	69	m	m	PROPN
fuelectenerg-1426	405	70	-	-	ADJ
fuelectenerg-1426	405	71	ary	ary	PROPN
fuelectenerg-1426	405	72	radices	radix	NOUN
fuelectenerg-1426	405	73	.	.	PUNCT
fuelectenerg-1426	406	1	118	118	NUM
fuelectenerg-1426	406	2	718	718	NUM
fuelectenerg-1426	406	3	a.	a.	NOUN
fuelectenerg-1426	406	4	n.	n.	PROPN
fuelectenerg-1426	406	5	al	al	PROPN
fuelectenerg-1426	406	6	-	-	PUNCT
fuelectenerg-1426	406	7	rabadi	rabadi	PROPN
fuelectenerg-1426	406	8	multi	multi	ADJ
fuelectenerg-1426	406	9	-	-	ADJ
fuelectenerg-1426	406	10	valued	value	VERB
fuelectenerg-1426	406	11	galois	galois	PROPN
fuelectenerg-1426	406	12	shannon	shannon	PROPN
fuelectenerg-1426	406	13	davio	davio	PROPN
fuelectenerg-1426	406	14	trees	tree	NOUN
fuelectenerg-1426	406	15	and	and	CCONJ
fuelectenerg-1426	406	16	their	their	PRON
fuelectenerg-1426	406	17	complexity	complexity	NOUN
fuelectenerg-1426	406	18	719	719	NUM
fuelectenerg-1426	406	19	multi	multi	ADJ
fuelectenerg-1426	406	20	-	-	ADJ
fuelectenerg-1426	406	21	valued	value	VERB
fuelectenerg-1426	406	22	galois	galois	PROPN
fuelectenerg-1426	406	23	shannon	shannon	PROPN
fuelectenerg-1426	406	24	davio	davio	PROPN
fuelectenerg-1426	406	25	trees	tree	NOUN
fuelectenerg-1426	406	26	and	and	CCONJ
fuelectenerg-1426	406	27	their	their	PRON
fuelectenerg-1426	406	28	complexity	complexity	NOUN
fuelectenerg-1426	406	29	future	future	ADJ
fuelectenerg-1426	406	30	work	work	NOUN
fuelectenerg-1426	406	31	will	will	AUX
fuelectenerg-1426	406	32	investigate	investigate	VERB
fuelectenerg-1426	406	33	using	use	VERB
fuelectenerg-1426	406	34	other	other	ADJ
fuelectenerg-1426	406	35	complex	complex	ADJ
fuelectenerg-1426	406	36	types	type	NOUN
fuelectenerg-1426	406	37	of	of	ADP
fuelectenerg-1426	406	38	literals	literal	NOUN
fuelectenerg-1426	406	39	such	such	ADJ
fuelectenerg-1426	406	40	as	as	ADP
fuelectenerg-1426	406	41	the	the	DET
fuelectenerg-1426	406	42	presented	present	VERB
fuelectenerg-1426	406	43	post	post	NOUN
fuelectenerg-1426	406	44	literal	literal	ADJ
fuelectenerg-1426	406	45	(	(	PUNCT
fuelectenerg-1426	406	46	pl	pl	NOUN
fuelectenerg-1426	406	47	)	)	PUNCT
fuelectenerg-1426	406	48	and	and	CCONJ
fuelectenerg-1426	406	49	window	window	NOUN
fuelectenerg-1426	406	50	literal	literal	NOUN
fuelectenerg-1426	406	51	(	(	PUNCT
fuelectenerg-1426	406	52	wl	wl	NOUN
fuelectenerg-1426	406	53	)	)	PUNCT
fuelectenerg-1426	406	54	to	to	PART
fuelectenerg-1426	406	55	expand	expand	VERB
fuelectenerg-1426	406	56	upon	upon	SCONJ
fuelectenerg-1426	406	57	and	and	CCONJ
fuelectenerg-1426	406	58	consequently	consequently	ADV
fuelectenerg-1426	406	59	construct	construct	VERB
fuelectenerg-1426	406	60	the	the	DET
fuelectenerg-1426	406	61	corresponding	correspond	VERB
fuelectenerg-1426	406	62	new	new	ADJ
fuelectenerg-1426	406	63	s	s	PROPN
fuelectenerg-1426	406	64	/	/	SYM
fuelectenerg-1426	406	65	d	d	NOUN
fuelectenerg-1426	406	66	trees	tree	NOUN
fuelectenerg-1426	406	67	.	.	PUNCT
fuelectenerg-1426	407	1	the	the	DET
fuelectenerg-1426	407	2	utilization	utilization	NOUN
fuelectenerg-1426	407	3	of	of	ADP
fuelectenerg-1426	407	4	the	the	DET
fuelectenerg-1426	407	5	results	result	NOUN
fuelectenerg-1426	407	6	from	from	ADP
fuelectenerg-1426	407	7	this	this	DET
fuelectenerg-1426	407	8	research	research	NOUN
fuelectenerg-1426	407	9	to	to	PART
fuelectenerg-1426	407	10	create	create	VERB
fuelectenerg-1426	407	11	an	an	DET
fuelectenerg-1426	407	12	efficient	efficient	ADJ
fuelectenerg-1426	407	13	gfsop	gfsop	NOUN
fuelectenerg-1426	407	14	minimizer	minimizer	NOUN
fuelectenerg-1426	407	15	for	for	ADP
fuelectenerg-1426	407	16	synthesis	synthesis	NOUN
fuelectenerg-1426	407	17	applications	application	NOUN
fuelectenerg-1426	407	18	within	within	ADP
fuelectenerg-1426	407	19	the	the	DET
fuelectenerg-1426	407	20	spaces	space	NOUN
fuelectenerg-1426	407	21	of	of	ADP
fuelectenerg-1426	407	22	classical	classical	ADJ
fuelectenerg-1426	407	23	and	and	CCONJ
fuelectenerg-1426	407	24	reversible	reversible	ADJ
fuelectenerg-1426	407	25	logic	logic	NOUN
fuelectenerg-1426	407	26	will	will	AUX
fuelectenerg-1426	407	27	also	also	ADV
fuelectenerg-1426	407	28	be	be	AUX
fuelectenerg-1426	407	29	conducted	conduct	VERB
fuelectenerg-1426	407	30	.	.	PUNCT
fuelectenerg-1426	408	1	references	reference	NOUN
fuelectenerg-1426	408	2	[	[	X
fuelectenerg-1426	408	3	1	1	X
fuelectenerg-1426	408	4	]	]	PUNCT
fuelectenerg-1426	408	5	s.	s.	PROPN
fuelectenerg-1426	408	6	b.	b.	PROPN
fuelectenerg-1426	408	7	akers	akers	PROPN
fuelectenerg-1426	408	8	,	,	PUNCT
fuelectenerg-1426	408	9	"	"	PUNCT
fuelectenerg-1426	408	10	binary	binary	ADJ
fuelectenerg-1426	408	11	decision	decision	NOUN
fuelectenerg-1426	408	12	diagrams	diagram	NOUN
fuelectenerg-1426	408	13	,	,	PUNCT
fuelectenerg-1426	408	14	"	"	PUNCT
fuelectenerg-1426	408	15	ieee	ieee	NOUN
fuelectenerg-1426	408	16	trans	tran	NOUN
fuelectenerg-1426	408	17	.	.	PUNCT
fuelectenerg-1426	409	1	comp	comp	PROPN
fuelectenerg-1426	409	2	.	.	PUNCT
fuelectenerg-1426	409	3	,	,	PUNCT
fuelectenerg-1426	409	4	vol	vol	NOUN
fuelectenerg-1426	409	5	.	.	PUNCT
fuelectenerg-1426	410	1	c-27	c-27	PROPN
fuelectenerg-1426	410	2	,	,	PUNCT
fuelectenerg-1426	410	3	no	no	INTJ
fuelectenerg-1426	410	4	.	.	NOUN
fuelectenerg-1426	410	5	6	6	NUM
fuelectenerg-1426	410	6	,	,	PUNCT
fuelectenerg-1426	410	7	pp	pp	ADJ
fuelectenerg-1426	410	8	.	.	PUNCT
fuelectenerg-1426	411	1	509	509	NUM
fuelectenerg-1426	411	2	-	-	SYM
fuelectenerg-1426	411	3	516	516	NUM
fuelectenerg-1426	411	4	,	,	PUNCT
fuelectenerg-1426	411	5	june	june	PROPN
fuelectenerg-1426	411	6	1978	1978	NUM
fuelectenerg-1426	411	7	.	.	PUNCT
fuelectenerg-1426	412	1	[	[	X
fuelectenerg-1426	412	2	2	2	NUM
fuelectenerg-1426	412	3	]	]	PUNCT
fuelectenerg-1426	412	4	a.	a.	NOUN
fuelectenerg-1426	412	5	n.	n.	PROPN
fuelectenerg-1426	412	6	al	al	PROPN
fuelectenerg-1426	412	7	-	-	PUNCT
fuelectenerg-1426	412	8	rabadi	rabadi	PROPN
fuelectenerg-1426	412	9	,	,	PUNCT
fuelectenerg-1426	412	10	reversible	reversible	ADJ
fuelectenerg-1426	412	11	logic	logic	NOUN
fuelectenerg-1426	412	12	synthesis	synthesis	NOUN
fuelectenerg-1426	412	13	:	:	PUNCT
fuelectenerg-1426	412	14	from	from	ADP
fuelectenerg-1426	412	15	fundamentals	fundamental	NOUN
fuelectenerg-1426	412	16	to	to	ADP
fuelectenerg-1426	412	17	quantum	quantum	ADJ
fuelectenerg-1426	412	18	computing	computing	NOUN
fuelectenerg-1426	412	19	,	,	PUNCT
fuelectenerg-1426	412	20	springer	springer	NOUN
fuelectenerg-1426	412	21	-	-	PUNCT
fuelectenerg-1426	412	22	verlag	verlag	PROPN
fuelectenerg-1426	412	23	,	,	PUNCT
fuelectenerg-1426	412	24	2004	2004	NUM
fuelectenerg-1426	412	25	.	.	PUNCT
fuelectenerg-1426	413	1	[	[	X
fuelectenerg-1426	413	2	3	3	NUM
fuelectenerg-1426	413	3	]	]	PUNCT
fuelectenerg-1426	413	4	a.	a.	NOUN
fuelectenerg-1426	413	5	n.	n.	PROPN
fuelectenerg-1426	413	6	al	al	PROPN
fuelectenerg-1426	413	7	-	-	PUNCT
fuelectenerg-1426	413	8	rabadi	rabadi	PROPN
fuelectenerg-1426	413	9	,	,	PUNCT
fuelectenerg-1426	413	10	"	"	PUNCT
fuelectenerg-1426	413	11	reversible	reversible	ADJ
fuelectenerg-1426	413	12	fast	fast	ADJ
fuelectenerg-1426	413	13	permutation	permutation	NOUN
fuelectenerg-1426	413	14	transforms	transform	VERB
fuelectenerg-1426	413	15	for	for	ADP
fuelectenerg-1426	413	16	quantum	quantum	ADJ
fuelectenerg-1426	413	17	circuit	circuit	NOUN
fuelectenerg-1426	413	18	synthesis	synthesis	NOUN
fuelectenerg-1426	413	19	,	,	PUNCT
fuelectenerg-1426	413	20	"	"	PUNCT
fuelectenerg-1426	413	21	proc	proc	NOUN
fuelectenerg-1426	413	22	.	.	PUNCT
fuelectenerg-1426	414	1	ieee	ieee	PROPN
fuelectenerg-1426	414	2	int	int	PROPN
fuelectenerg-1426	414	3	.	.	PUNCT
fuelectenerg-1426	415	1	symposium	symposium	NOUN
fuelectenerg-1426	415	2	on	on	ADP
fuelectenerg-1426	415	3	multiple	multiple	ADV
fuelectenerg-1426	415	4	-	-	PUNCT
fuelectenerg-1426	415	5	valued	value	VERB
fuelectenerg-1426	415	6	logic	logic	NOUN
fuelectenerg-1426	415	7	(	(	PUNCT
fuelectenerg-1426	415	8	ismvl	ismvl	PROPN
fuelectenerg-1426	415	9	)	)	PUNCT
fuelectenerg-1426	415	10	,	,	PUNCT
fuelectenerg-1426	415	11	toronto	toronto	PROPN
fuelectenerg-1426	415	12	,	,	PUNCT
fuelectenerg-1426	415	13	2004	2004	NUM
fuelectenerg-1426	415	14	,	,	PUNCT
fuelectenerg-1426	415	15	pp	pp	PROPN
fuelectenerg-1426	415	16	.	.	PUNCT
fuelectenerg-1426	416	1	81	81	NUM
fuelectenerg-1426	416	2	-	-	SYM
fuelectenerg-1426	416	3	86	86	NUM
fuelectenerg-1426	416	4	.	.	PUNCT
fuelectenerg-1426	417	1	[	[	X
fuelectenerg-1426	417	2	4	4	NUM
fuelectenerg-1426	417	3	]	]	PUNCT
fuelectenerg-1426	417	4	a.	a.	NOUN
fuelectenerg-1426	417	5	n.	n.	PROPN
fuelectenerg-1426	417	6	al	al	PROPN
fuelectenerg-1426	417	7	-	-	PUNCT
fuelectenerg-1426	417	8	rabadi	rabadi	PROPN
fuelectenerg-1426	417	9	,	,	PUNCT
fuelectenerg-1426	417	10	"	"	PUNCT
fuelectenerg-1426	417	11	quantum	quantum	ADJ
fuelectenerg-1426	417	12	circuit	circuit	NOUN
fuelectenerg-1426	417	13	synthesis	synthesis	NOUN
fuelectenerg-1426	417	14	using	use	VERB
fuelectenerg-1426	417	15	classes	class	NOUN
fuelectenerg-1426	417	16	of	of	ADP
fuelectenerg-1426	417	17	gf(3	gf(3	NOUN
fuelectenerg-1426	417	18	)	)	PUNCT
fuelectenerg-1426	417	19	reversible	reversible	ADJ
fuelectenerg-1426	417	20	fast	fast	ADJ
fuelectenerg-1426	417	21	spectral	spectral	ADJ
fuelectenerg-1426	417	22	transforms	transform	NOUN
fuelectenerg-1426	417	23	,	,	PUNCT
fuelectenerg-1426	417	24	"	"	PUNCT
fuelectenerg-1426	417	25	proc	proc	NOUN
fuelectenerg-1426	417	26	.	.	PUNCT
fuelectenerg-1426	418	1	ieee	ieee	PROPN
fuelectenerg-1426	418	2	int	int	PROPN
fuelectenerg-1426	418	3	.	.	PUNCT
fuelectenerg-1426	419	1	symposium	symposium	NOUN
fuelectenerg-1426	419	2	on	on	ADP
fuelectenerg-1426	419	3	multiple	multiple	ADV
fuelectenerg-1426	419	4	-	-	PUNCT
fuelectenerg-1426	419	5	valued	value	VERB
fuelectenerg-1426	419	6	logic	logic	NOUN
fuelectenerg-1426	419	7	(	(	PUNCT
fuelectenerg-1426	419	8	ismvl	ismvl	PROPN
fuelectenerg-1426	419	9	)	)	PUNCT
fuelectenerg-1426	419	10	,	,	PUNCT
fuelectenerg-1426	419	11	toronto	toronto	PROPN
fuelectenerg-1426	419	12	,	,	PUNCT
fuelectenerg-1426	419	13	2004	2004	NUM
fuelectenerg-1426	419	14	,	,	PUNCT
fuelectenerg-1426	419	15	pp	pp	ADV
fuelectenerg-1426	419	16	.	.	PUNCT
fuelectenerg-1426	420	1	87	87	NUM
fuelectenerg-1426	420	2	-	-	SYM
fuelectenerg-1426	420	3	93	93	NUM
fuelectenerg-1426	420	4	.	.	PUNCT
fuelectenerg-1426	421	1	[	[	PUNCT
fuelectenerg-1426	421	2	5	5	NUM
fuelectenerg-1426	421	3	]	]	PUNCT
fuelectenerg-1426	421	4	a.	a.	NOUN
fuelectenerg-1426	421	5	n.	n.	PROPN
fuelectenerg-1426	421	6	al	al	PROPN
fuelectenerg-1426	421	7	-	-	PUNCT
fuelectenerg-1426	421	8	rabadi	rabadi	PROPN
fuelectenerg-1426	421	9	,	,	PUNCT
fuelectenerg-1426	421	10	"	"	PUNCT
fuelectenerg-1426	421	11	quantum	quantum	ADJ
fuelectenerg-1426	421	12	logic	logic	NOUN
fuelectenerg-1426	421	13	circuit	circuit	NOUN
fuelectenerg-1426	421	14	design	design	NOUN
fuelectenerg-1426	421	15	of	of	ADP
fuelectenerg-1426	421	16	many	many	ADV
fuelectenerg-1426	421	17	-	-	PUNCT
fuelectenerg-1426	421	18	valued	value	VERB
fuelectenerg-1426	421	19	galois	galois	PROPN
fuelectenerg-1426	421	20	reversible	reversible	ADJ
fuelectenerg-1426	421	21	expansions	expansion	NOUN
fuelectenerg-1426	421	22	and	and	CCONJ
fuelectenerg-1426	421	23	fast	fast	ADJ
fuelectenerg-1426	421	24	transforms	transform	NOUN
fuelectenerg-1426	421	25	,	,	PUNCT
fuelectenerg-1426	421	26	"	"	PUNCT
fuelectenerg-1426	421	27	j.	j.	PROPN
fuelectenerg-1426	421	28	circuits	circuits	PROPN
fuelectenerg-1426	421	29	,	,	PUNCT
fuelectenerg-1426	421	30	systems	system	NOUN
fuelectenerg-1426	421	31	,	,	PUNCT
fuelectenerg-1426	421	32	and	and	CCONJ
fuelectenerg-1426	421	33	computers	computer	NOUN
fuelectenerg-1426	421	34	,	,	PUNCT
fuelectenerg-1426	421	35	world	world	NOUN
fuelectenerg-1426	421	36	scientific	scientific	PROPN
fuelectenerg-1426	421	37	,	,	PUNCT
fuelectenerg-1426	421	38	singapore	singapore	PROPN
fuelectenerg-1426	421	39	,	,	PUNCT
fuelectenerg-1426	421	40	vol	vol	NOUN
fuelectenerg-1426	421	41	.	.	PROPN
fuelectenerg-1426	421	42	16	16	NUM
fuelectenerg-1426	421	43	,	,	PUNCT
fuelectenerg-1426	421	44	no	no	INTJ
fuelectenerg-1426	421	45	.	.	NOUN
fuelectenerg-1426	421	46	5	5	NUM
fuelectenerg-1426	421	47	,	,	PUNCT
fuelectenerg-1426	421	48	pp	pp	ADJ
fuelectenerg-1426	421	49	.	.	PUNCT
fuelectenerg-1426	422	1	641	641	NUM
fuelectenerg-1426	422	2	671	671	NUM
fuelectenerg-1426	422	3	,	,	PUNCT
fuelectenerg-1426	422	4	2007	2007	NUM
fuelectenerg-1426	422	5	.	.	PUNCT
fuelectenerg-1426	423	1	[	[	PUNCT
fuelectenerg-1426	423	2	6	6	NUM
fuelectenerg-1426	423	3	]	]	PUNCT
fuelectenerg-1426	423	4	a.	a.	NOUN
fuelectenerg-1426	423	5	n.	n.	PROPN
fuelectenerg-1426	423	6	al	al	PROPN
fuelectenerg-1426	423	7	-	-	PUNCT
fuelectenerg-1426	423	8	rabadi	rabadi	PROPN
fuelectenerg-1426	423	9	,	,	PUNCT
fuelectenerg-1426	423	10	"	"	PUNCT
fuelectenerg-1426	423	11	representations	representation	NOUN
fuelectenerg-1426	423	12	,	,	PUNCT
fuelectenerg-1426	423	13	operations	operation	NOUN
fuelectenerg-1426	423	14	,	,	PUNCT
fuelectenerg-1426	423	15	and	and	CCONJ
fuelectenerg-1426	423	16	applications	application	NOUN
fuelectenerg-1426	423	17	of	of	ADP
fuelectenerg-1426	423	18	switching	switch	VERB
fuelectenerg-1426	423	19	circuits	circuit	NOUN
fuelectenerg-1426	423	20	in	in	ADP
fuelectenerg-1426	423	21	the	the	DET
fuelectenerg-1426	423	22	reversible	reversible	ADJ
fuelectenerg-1426	423	23	and	and	CCONJ
fuelectenerg-1426	423	24	quantum	quantum	ADJ
fuelectenerg-1426	423	25	spaces	space	NOUN
fuelectenerg-1426	423	26	,	,	PUNCT
fuelectenerg-1426	423	27	"	"	PUNCT
fuelectenerg-1426	423	28	facta	facta	PROPN
fuelectenerg-1426	423	29	universitatis	universitatis	PROPN
fuelectenerg-1426	423	30	(	(	PUNCT
fuelectenerg-1426	423	31	fu	fu	NOUN
fuelectenerg-1426	423	32	)	)	PUNCT
fuelectenerg-1426	423	33	electronics	electronic	NOUN
fuelectenerg-1426	423	34	and	and	CCONJ
fuelectenerg-1426	423	35	energetics	energetic	NOUN
fuelectenerg-1426	423	36	,	,	PUNCT
fuelectenerg-1426	423	37	vol	vol	NOUN
fuelectenerg-1426	423	38	.	.	PROPN
fuelectenerg-1426	423	39	20	20	NUM
fuelectenerg-1426	423	40	,	,	PUNCT
fuelectenerg-1426	423	41	no	no	INTJ
fuelectenerg-1426	423	42	.	.	NOUN
fuelectenerg-1426	424	1	3	3	NUM
fuelectenerg-1426	424	2	,	,	PUNCT
fuelectenerg-1426	424	3	pp	pp	ADJ
fuelectenerg-1426	424	4	.	.	PUNCT
fuelectenerg-1426	425	1	507	507	NUM
fuelectenerg-1426	425	2	539	539	NUM
fuelectenerg-1426	425	3	,	,	PUNCT
fuelectenerg-1426	425	4	2007	2007	NUM
fuelectenerg-1426	425	5	.	.	PUNCT
fuelectenerg-1426	426	1	[	[	X
fuelectenerg-1426	426	2	7	7	X
fuelectenerg-1426	426	3	]	]	X
fuelectenerg-1426	426	4	r.	r.	PROPN
fuelectenerg-1426	426	5	e.	e.	PROPN
fuelectenerg-1426	426	6	bryant	bryant	PROPN
fuelectenerg-1426	426	7	,	,	PUNCT
fuelectenerg-1426	426	8	"	"	PUNCT
fuelectenerg-1426	426	9	graph	graph	NOUN
fuelectenerg-1426	426	10	-	-	PUNCT
fuelectenerg-1426	426	11	based	base	VERB
fuelectenerg-1426	426	12	algorithms	algorithm	NOUN
fuelectenerg-1426	426	13	for	for	ADP
fuelectenerg-1426	426	14	boolean	boolean	ADJ
fuelectenerg-1426	426	15	functions	function	NOUN
fuelectenerg-1426	426	16	manipulation	manipulation	NOUN
fuelectenerg-1426	426	17	,	,	PUNCT
fuelectenerg-1426	426	18	"	"	PUNCT
fuelectenerg-1426	426	19	ieee	ieee	NOUN
fuelectenerg-1426	426	20	trans	tran	NOUN
fuelectenerg-1426	426	21	.	.	PUNCT
fuelectenerg-1426	427	1	on	on	ADP
fuelectenerg-1426	427	2	comp	comp	PROPN
fuelectenerg-1426	427	3	.	.	PUNCT
fuelectenerg-1426	427	4	,	,	PUNCT
fuelectenerg-1426	427	5	vol	vol	NOUN
fuelectenerg-1426	427	6	.	.	PUNCT
fuelectenerg-1426	428	1	c-35	c-35	PROPN
fuelectenerg-1426	428	2	,	,	PUNCT
fuelectenerg-1426	428	3	no.8	no.8	PROPN
fuelectenerg-1426	428	4	,	,	PUNCT
fuelectenerg-1426	428	5	pp	pp	ADV
fuelectenerg-1426	428	6	.	.	PUNCT
fuelectenerg-1426	429	1	667	667	NUM
fuelectenerg-1426	429	2	-	-	SYM
fuelectenerg-1426	429	3	691	691	NUM
fuelectenerg-1426	429	4	,	,	PUNCT
fuelectenerg-1426	429	5	1986	1986	NUM
fuelectenerg-1426	429	6	.	.	PUNCT
fuelectenerg-1426	430	1	[	[	X
fuelectenerg-1426	430	2	8	8	NUM
fuelectenerg-1426	430	3	]	]	X
fuelectenerg-1426	430	4	m.	m.	NOUN
fuelectenerg-1426	430	5	cohn	cohn	PROPN
fuelectenerg-1426	430	6	,	,	PUNCT
fuelectenerg-1426	430	7	switching	switch	VERB
fuelectenerg-1426	430	8	function	function	NOUN
fuelectenerg-1426	430	9	canonical	canonical	ADJ
fuelectenerg-1426	430	10	form	form	NOUN
fuelectenerg-1426	430	11	over	over	ADP
fuelectenerg-1426	430	12	integer	integer	NOUN
fuelectenerg-1426	430	13	fields	field	NOUN
fuelectenerg-1426	430	14	,	,	PUNCT
fuelectenerg-1426	430	15	ph.d	ph.d	PROPN
fuelectenerg-1426	430	16	.	.	PUNCT
fuelectenerg-1426	430	17	dissertation	dissertation	PROPN
fuelectenerg-1426	430	18	,	,	PUNCT
fuelectenerg-1426	430	19	harvard	harvard	PROPN
fuelectenerg-1426	430	20	university	university	PROPN
fuelectenerg-1426	430	21	,	,	PUNCT
fuelectenerg-1426	430	22	1960	1960	NUM
fuelectenerg-1426	430	23	.	.	PUNCT
fuelectenerg-1426	431	1	[	[	X
fuelectenerg-1426	431	2	9	9	NUM
fuelectenerg-1426	431	3	]	]	X
fuelectenerg-1426	431	4	r.	r.	NOUN
fuelectenerg-1426	431	5	drechsler	drechsler	PROPN
fuelectenerg-1426	431	6	,	,	PUNCT
fuelectenerg-1426	431	7	a.	a.	NOUN
fuelectenerg-1426	431	8	sarabi	sarabi	PROPN
fuelectenerg-1426	431	9	,	,	PUNCT
fuelectenerg-1426	431	10	m.	m.	NOUN
fuelectenerg-1426	431	11	theobald	theobald	PROPN
fuelectenerg-1426	431	12	,	,	PUNCT
fuelectenerg-1426	431	13	b.	b.	PROPN
fuelectenerg-1426	431	14	becker	becker	PROPN
fuelectenerg-1426	431	15	,	,	PUNCT
fuelectenerg-1426	431	16	and	and	CCONJ
fuelectenerg-1426	431	17	m.	m.	PROPN
fuelectenerg-1426	431	18	a.	a.	PROPN
fuelectenerg-1426	431	19	perkowski	perkowski	PROPN
fuelectenerg-1426	431	20	,	,	PUNCT
fuelectenerg-1426	431	21	"	"	PUNCT
fuelectenerg-1426	431	22	efficient	efficient	ADJ
fuelectenerg-1426	431	23	representation	representation	NOUN
fuelectenerg-1426	431	24	and	and	CCONJ
fuelectenerg-1426	431	25	manipulation	manipulation	NOUN
fuelectenerg-1426	431	26	of	of	ADP
fuelectenerg-1426	431	27	switching	switch	VERB
fuelectenerg-1426	431	28	functions	function	NOUN
fuelectenerg-1426	431	29	based	base	VERB
fuelectenerg-1426	431	30	on	on	ADP
fuelectenerg-1426	431	31	ordered	order	VERB
fuelectenerg-1426	431	32	kronecker	kronecker	NOUN
fuelectenerg-1426	431	33	functional	functional	ADJ
fuelectenerg-1426	431	34	decision	decision	NOUN
fuelectenerg-1426	431	35	diagrams	diagram	NOUN
fuelectenerg-1426	431	36	,	,	PUNCT
fuelectenerg-1426	431	37	"	"	PUNCT
fuelectenerg-1426	431	38	proc	proc	NOUN
fuelectenerg-1426	431	39	.	.	PUNCT
fuelectenerg-1426	431	40	dac	dac	PROPN
fuelectenerg-1426	431	41	,	,	PUNCT
fuelectenerg-1426	431	42	1994	1994	NUM
fuelectenerg-1426	431	43	,	,	PUNCT
fuelectenerg-1426	431	44	pp	pp	ADJ
fuelectenerg-1426	431	45	.	.	PUNCT
fuelectenerg-1426	431	46	415	415	NUM
fuelectenerg-1426	431	47	-	-	SYM
fuelectenerg-1426	431	48	419	419	NUM
fuelectenerg-1426	431	49	.	.	PUNCT
fuelectenerg-1426	432	1	[	[	X
fuelectenerg-1426	432	2	10	10	NUM
fuelectenerg-1426	432	3	]	]	PUNCT
fuelectenerg-1426	432	4	m.	m.	NOUN
fuelectenerg-1426	432	5	escobar	escobar	PROPN
fuelectenerg-1426	432	6	and	and	CCONJ
fuelectenerg-1426	432	7	f.	f.	PROPN
fuelectenerg-1426	432	8	somenzi	somenzi	PROPN
fuelectenerg-1426	432	9	,	,	PUNCT
fuelectenerg-1426	432	10	"	"	PUNCT
fuelectenerg-1426	432	11	synthesis	synthesis	NOUN
fuelectenerg-1426	432	12	of	of	ADP
fuelectenerg-1426	432	13	and	and	CCONJ
fuelectenerg-1426	432	14	/	/	SYM
fuelectenerg-1426	432	15	exor	exor	PROPN
fuelectenerg-1426	432	16	expressions	expression	NOUN
fuelectenerg-1426	432	17	via	via	ADP
fuelectenerg-1426	432	18	satisfiability	satisfiability	NOUN
fuelectenerg-1426	432	19	,	,	PUNCT
fuelectenerg-1426	432	20	"	"	PUNCT
fuelectenerg-1426	432	21	proc	proc	NOUN
fuelectenerg-1426	432	22	.	.	PUNCT
fuelectenerg-1426	433	1	reed	reed	NOUN
fuelectenerg-1426	433	2	-	-	PUNCT
fuelectenerg-1426	433	3	muller	muller	NOUN
fuelectenerg-1426	433	4	,	,	PUNCT
fuelectenerg-1426	433	5	1995	1995	NUM
fuelectenerg-1426	433	6	,	,	PUNCT
fuelectenerg-1426	433	7	pp	pp	PROPN
fuelectenerg-1426	433	8	.	.	PUNCT
fuelectenerg-1426	434	1	80	80	NUM
fuelectenerg-1426	434	2	-	-	SYM
fuelectenerg-1426	434	3	87	87	NUM
fuelectenerg-1426	434	4	.	.	PUNCT
fuelectenerg-1426	435	1	[	[	X
fuelectenerg-1426	435	2	11	11	NUM
fuelectenerg-1426	435	3	]	]	X
fuelectenerg-1426	435	4	b.	b.	PROPN
fuelectenerg-1426	435	5	j.	j.	PROPN
fuelectenerg-1426	435	6	falkowski	falkowski	PROPN
fuelectenerg-1426	435	7	and	and	CCONJ
fuelectenerg-1426	435	8	s.	s.	PROPN
fuelectenerg-1426	435	9	rahardja	rahardja	PROPN
fuelectenerg-1426	435	10	,	,	PUNCT
fuelectenerg-1426	435	11	"	"	PUNCT
fuelectenerg-1426	435	12	classification	classification	NOUN
fuelectenerg-1426	435	13	and	and	CCONJ
fuelectenerg-1426	435	14	properties	property	NOUN
fuelectenerg-1426	435	15	of	of	ADP
fuelectenerg-1426	435	16	fast	fast	ADJ
fuelectenerg-1426	435	17	linearly	linearly	ADV
fuelectenerg-1426	435	18	independent	independent	ADJ
fuelectenerg-1426	435	19	logic	logic	NOUN
fuelectenerg-1426	435	20	transformations	transformation	NOUN
fuelectenerg-1426	435	21	,	,	PUNCT
fuelectenerg-1426	435	22	"	"	PUNCT
fuelectenerg-1426	435	23	ieee	ieee	NOUN
fuelectenerg-1426	435	24	trans	tran	NOUN
fuelectenerg-1426	435	25	.	.	PUNCT
fuelectenerg-1426	436	1	on	on	ADP
fuelectenerg-1426	436	2	circuits	circuit	NOUN
fuelectenerg-1426	436	3	and	and	CCONJ
fuelectenerg-1426	436	4	systems	system	NOUN
fuelectenerg-1426	436	5	-	-	PUNCT
fuelectenerg-1426	436	6	ii	ii	NOUN
fuelectenerg-1426	436	7	,	,	PUNCT
fuelectenerg-1426	436	8	vol	vol	NOUN
fuelectenerg-1426	436	9	.	.	PROPN
fuelectenerg-1426	436	10	44	44	NUM
fuelectenerg-1426	436	11	,	,	PUNCT
fuelectenerg-1426	436	12	no	no	INTJ
fuelectenerg-1426	436	13	.	.	NOUN
fuelectenerg-1426	436	14	8	8	NUM
fuelectenerg-1426	436	15	,	,	PUNCT
fuelectenerg-1426	436	16	pp	pp	ADJ
fuelectenerg-1426	436	17	.	.	PUNCT
fuelectenerg-1426	436	18	646	646	NUM
fuelectenerg-1426	436	19	-	-	SYM
fuelectenerg-1426	436	20	655	655	NUM
fuelectenerg-1426	436	21	,	,	PUNCT
fuelectenerg-1426	436	22	august	august	PROPN
fuelectenerg-1426	436	23	1997	1997	NUM
fuelectenerg-1426	436	24	.	.	PUNCT
fuelectenerg-1426	437	1	[	[	X
fuelectenerg-1426	437	2	12	12	NUM
fuelectenerg-1426	437	3	]	]	PUNCT
fuelectenerg-1426	437	4	b.	b.	PROPN
fuelectenerg-1426	437	5	falkowski	falkowski	NOUN
fuelectenerg-1426	437	6	and	and	CCONJ
fuelectenerg-1426	437	7	l.-s	l.-s	PROPN
fuelectenerg-1426	437	8	.	.	PUNCT
fuelectenerg-1426	438	1	lim	lim	PROPN
fuelectenerg-1426	438	2	,	,	PUNCT
fuelectenerg-1426	438	3	"	"	PUNCT
fuelectenerg-1426	438	4	gray	gray	ADJ
fuelectenerg-1426	438	5	scale	scale	NOUN
fuelectenerg-1426	438	6	image	image	NOUN
fuelectenerg-1426	438	7	compression	compression	NOUN
fuelectenerg-1426	438	8	based	base	VERB
fuelectenerg-1426	438	9	on	on	ADP
fuelectenerg-1426	438	10	multiple	multiple	ADV
fuelectenerg-1426	438	11	-	-	PUNCT
fuelectenerg-1426	438	12	valued	value	VERB
fuelectenerg-1426	438	13	input	input	NOUN
fuelectenerg-1426	438	14	binary	binary	NOUN
fuelectenerg-1426	438	15	functions	function	NOUN
fuelectenerg-1426	438	16	,	,	PUNCT
fuelectenerg-1426	438	17	walsh	walsh	NOUN
fuelectenerg-1426	438	18	and	and	CCONJ
fuelectenerg-1426	438	19	reed	reed	PROPN
fuelectenerg-1426	438	20	-	-	PUNCT
fuelectenerg-1426	438	21	muller	muller	PROPN
fuelectenerg-1426	438	22	spectra	spectra	PROPN
fuelectenerg-1426	438	23	,	,	PUNCT
fuelectenerg-1426	438	24	"	"	PUNCT
fuelectenerg-1426	438	25	proc	proc	NOUN
fuelectenerg-1426	438	26	.	.	PUNCT
fuelectenerg-1426	439	1	ismvl	ismvl	PROPN
fuelectenerg-1426	439	2	,	,	PUNCT
fuelectenerg-1426	439	3	2000	2000	NUM
fuelectenerg-1426	439	4	,	,	PUNCT
fuelectenerg-1426	439	5	pp	pp	ADJ
fuelectenerg-1426	439	6	.	.	PUNCT
fuelectenerg-1426	440	1	279	279	NUM
fuelectenerg-1426	440	2	-	-	SYM
fuelectenerg-1426	440	3	284	284	NUM
fuelectenerg-1426	440	4	.	.	PUNCT
fuelectenerg-1426	441	1	[	[	X
fuelectenerg-1426	441	2	13	13	NUM
fuelectenerg-1426	441	3	]	]	X
fuelectenerg-1426	441	4	h.	h.	PROPN
fuelectenerg-1426	441	5	fujiwara	fujiwara	PROPN
fuelectenerg-1426	441	6	,	,	PUNCT
fuelectenerg-1426	441	7	logic	logic	NOUN
fuelectenerg-1426	441	8	testing	testing	NOUN
fuelectenerg-1426	441	9	and	and	CCONJ
fuelectenerg-1426	441	10	design	design	NOUN
fuelectenerg-1426	441	11	for	for	ADP
fuelectenerg-1426	441	12	testability	testability	NOUN
fuelectenerg-1426	441	13	,	,	PUNCT
fuelectenerg-1426	441	14	mit	mit	NOUN
fuelectenerg-1426	441	15	press	press	NOUN
fuelectenerg-1426	441	16	,	,	PUNCT
fuelectenerg-1426	441	17	1985	1985	NUM
fuelectenerg-1426	441	18	.	.	PUNCT
fuelectenerg-1426	442	1	[	[	X
fuelectenerg-1426	442	2	14	14	NUM
fuelectenerg-1426	442	3	]	]	X
fuelectenerg-1426	442	4	d.	d.	PROPN
fuelectenerg-1426	442	5	h.	h.	PROPN
fuelectenerg-1426	442	6	green	green	PROPN
fuelectenerg-1426	442	7	,	,	PUNCT
fuelectenerg-1426	442	8	"	"	PUNCT
fuelectenerg-1426	442	9	families	family	NOUN
fuelectenerg-1426	442	10	of	of	ADP
fuelectenerg-1426	442	11	reed	reed	NOUN
fuelectenerg-1426	442	12	-	-	PUNCT
fuelectenerg-1426	442	13	muller	muller	NOUN
fuelectenerg-1426	442	14	canonical	canonical	ADJ
fuelectenerg-1426	442	15	forms	form	NOUN
fuelectenerg-1426	442	16	,	,	PUNCT
fuelectenerg-1426	442	17	"	"	PUNCT
fuelectenerg-1426	442	18	int	int	NOUN
fuelectenerg-1426	442	19	.	.	PUNCT
fuelectenerg-1426	443	1	j.	j.	PROPN
fuelectenerg-1426	443	2	of	of	ADP
fuelectenerg-1426	443	3	electronics	electronics	PROPN
fuelectenerg-1426	443	4	,	,	PUNCT
fuelectenerg-1426	443	5	no	no	INTJ
fuelectenerg-1426	443	6	.	.	NOUN
fuelectenerg-1426	443	7	2	2	NUM
fuelectenerg-1426	443	8	,	,	PUNCT
fuelectenerg-1426	443	9	pp	pp	ADJ
fuelectenerg-1426	443	10	.	.	PUNCT
fuelectenerg-1426	444	1	259	259	NUM
fuelectenerg-1426	444	2	-	-	SYM
fuelectenerg-1426	444	3	280	280	NUM
fuelectenerg-1426	444	4	,	,	PUNCT
fuelectenerg-1426	444	5	1991	1991	NUM
fuelectenerg-1426	444	6	.	.	PUNCT
fuelectenerg-1426	445	1	[	[	X
fuelectenerg-1426	445	2	15	15	NUM
fuelectenerg-1426	445	3	]	]	X
fuelectenerg-1426	445	4	s.	s.	PROPN
fuelectenerg-1426	445	5	hassoun	hassoun	PROPN
fuelectenerg-1426	445	6	,	,	PUNCT
fuelectenerg-1426	445	7	t.	t.	PROPN
fuelectenerg-1426	445	8	sasao	sasao	PROPN
fuelectenerg-1426	445	9	,	,	PUNCT
fuelectenerg-1426	445	10	and	and	CCONJ
fuelectenerg-1426	445	11	r.	r.	PROPN
fuelectenerg-1426	445	12	brayton	brayton	PROPN
fuelectenerg-1426	445	13	(	(	PUNCT
fuelectenerg-1426	445	14	editors	editor	NOUN
fuelectenerg-1426	445	15	)	)	PUNCT
fuelectenerg-1426	445	16	,	,	PUNCT
fuelectenerg-1426	445	17	logic	logic	NOUN
fuelectenerg-1426	445	18	synthesis	synthesis	NOUN
fuelectenerg-1426	445	19	and	and	CCONJ
fuelectenerg-1426	445	20	verification	verification	NOUN
fuelectenerg-1426	445	21	,	,	PUNCT
fuelectenerg-1426	445	22	kluwer	kluwer	NOUN
fuelectenerg-1426	445	23	acad	acad	PROPN
fuelectenerg-1426	445	24	.	.	PUNCT
fuelectenerg-1426	446	1	publishers	publisher	NOUN
fuelectenerg-1426	446	2	,	,	PUNCT
fuelectenerg-1426	446	3	2001	2001	NUM
fuelectenerg-1426	446	4	.	.	PUNCT
fuelectenerg-1426	447	1	[	[	X
fuelectenerg-1426	447	2	16	16	NUM
fuelectenerg-1426	447	3	]	]	PUNCT
fuelectenerg-1426	447	4	m.	m.	NOUN
fuelectenerg-1426	447	5	helliwell	helliwell	NOUN
fuelectenerg-1426	447	6	and	and	CCONJ
fuelectenerg-1426	447	7	m.	m.	PROPN
fuelectenerg-1426	447	8	a.	a.	PROPN
fuelectenerg-1426	447	9	perkowski	perkowski	PROPN
fuelectenerg-1426	447	10	,	,	PUNCT
fuelectenerg-1426	447	11	"	"	PUNCT
fuelectenerg-1426	447	12	a	a	DET
fuelectenerg-1426	447	13	fast	fast	ADJ
fuelectenerg-1426	447	14	algorithm	algorithm	NOUN
fuelectenerg-1426	447	15	to	to	PART
fuelectenerg-1426	447	16	minimize	minimize	VERB
fuelectenerg-1426	447	17	multi	multi	ADJ
fuelectenerg-1426	447	18	-	-	ADJ
fuelectenerg-1426	447	19	output	output	ADJ
fuelectenerg-1426	447	20	mixed	mix	VERB
fuelectenerg-1426	447	21	-	-	PUNCT
fuelectenerg-1426	447	22	polarity	polarity	NOUN
fuelectenerg-1426	447	23	generalized	generalize	VERB
fuelectenerg-1426	447	24	reed	reed	NOUN
fuelectenerg-1426	447	25	-	-	PUNCT
fuelectenerg-1426	447	26	muller	muller	NOUN
fuelectenerg-1426	447	27	forms	form	NOUN
fuelectenerg-1426	447	28	,	,	PUNCT
fuelectenerg-1426	447	29	"	"	PUNCT
fuelectenerg-1426	447	30	proc	proc	NOUN
fuelectenerg-1426	447	31	.	.	PUNCT
fuelectenerg-1426	448	1	design	design	NOUN
fuelectenerg-1426	448	2	automation	automation	NOUN
fuelectenerg-1426	448	3	conference	conference	NOUN
fuelectenerg-1426	448	4	,	,	PUNCT
fuelectenerg-1426	448	5	1988	1988	NUM
fuelectenerg-1426	448	6	,	,	PUNCT
fuelectenerg-1426	448	7	pp	pp	ADV
fuelectenerg-1426	448	8	.	.	PUNCT
fuelectenerg-1426	449	1	427	427	NUM
fuelectenerg-1426	449	2	-	-	SYM
fuelectenerg-1426	449	3	432	432	NUM
fuelectenerg-1426	449	4	.	.	PUNCT
fuelectenerg-1426	450	1	[	[	X
fuelectenerg-1426	450	2	17	17	NUM
fuelectenerg-1426	450	3	]	]	PUNCT
fuelectenerg-1426	450	4	s.	s.	PROPN
fuelectenerg-1426	450	5	l.	l.	PROPN
fuelectenerg-1426	450	6	hurst	hurst	PROPN
fuelectenerg-1426	450	7	,	,	PUNCT
fuelectenerg-1426	450	8	d.	d.	PROPN
fuelectenerg-1426	450	9	m.	m.	PROPN
fuelectenerg-1426	450	10	miller	miller	PROPN
fuelectenerg-1426	450	11	,	,	PUNCT
fuelectenerg-1426	450	12	and	and	CCONJ
fuelectenerg-1426	450	13	j.	j.	PROPN
fuelectenerg-1426	450	14	c.	c.	PROPN
fuelectenerg-1426	450	15	muzio	muzio	PROPN
fuelectenerg-1426	450	16	,	,	PUNCT
fuelectenerg-1426	450	17	spectral	spectral	ADJ
fuelectenerg-1426	450	18	techniques	technique	NOUN
fuelectenerg-1426	450	19	in	in	ADP
fuelectenerg-1426	450	20	digital	digital	ADJ
fuelectenerg-1426	450	21	logic	logic	NOUN
fuelectenerg-1426	450	22	,	,	PUNCT
fuelectenerg-1426	450	23	academic	academic	ADJ
fuelectenerg-1426	450	24	119	119	NUM
fuelectenerg-1426	450	25	multi	multi	ADJ
fuelectenerg-1426	450	26	-	-	ADJ
fuelectenerg-1426	450	27	valued	value	VERB
fuelectenerg-1426	450	28	galois	galois	PROPN
fuelectenerg-1426	450	29	shannon	shannon	PROPN
fuelectenerg-1426	450	30	davio	davio	PROPN
fuelectenerg-1426	450	31	trees	tree	NOUN
fuelectenerg-1426	450	32	and	and	CCONJ
fuelectenerg-1426	450	33	their	their	PRON
fuelectenerg-1426	450	34	complexity	complexity	NOUN
fuelectenerg-1426	450	35	future	future	ADJ
fuelectenerg-1426	450	36	work	work	NOUN
fuelectenerg-1426	450	37	will	will	AUX
fuelectenerg-1426	450	38	investigate	investigate	VERB
fuelectenerg-1426	450	39	using	use	VERB
fuelectenerg-1426	450	40	other	other	ADJ
fuelectenerg-1426	450	41	complex	complex	ADJ
fuelectenerg-1426	450	42	types	type	NOUN
fuelectenerg-1426	450	43	of	of	ADP
fuelectenerg-1426	450	44	literals	literal	NOUN
fuelectenerg-1426	450	45	such	such	ADJ
fuelectenerg-1426	450	46	as	as	ADP
fuelectenerg-1426	450	47	the	the	DET
fuelectenerg-1426	450	48	presented	present	VERB
fuelectenerg-1426	450	49	post	post	NOUN
fuelectenerg-1426	450	50	literal	literal	ADJ
fuelectenerg-1426	450	51	(	(	PUNCT
fuelectenerg-1426	450	52	pl	pl	NOUN
fuelectenerg-1426	450	53	)	)	PUNCT
fuelectenerg-1426	450	54	and	and	CCONJ
fuelectenerg-1426	450	55	window	window	NOUN
fuelectenerg-1426	450	56	literal	literal	NOUN
fuelectenerg-1426	450	57	(	(	PUNCT
fuelectenerg-1426	450	58	wl	wl	NOUN
fuelectenerg-1426	450	59	)	)	PUNCT
fuelectenerg-1426	450	60	to	to	PART
fuelectenerg-1426	450	61	expand	expand	VERB
fuelectenerg-1426	450	62	upon	upon	SCONJ
fuelectenerg-1426	450	63	and	and	CCONJ
fuelectenerg-1426	450	64	consequently	consequently	ADV
fuelectenerg-1426	450	65	construct	construct	VERB
fuelectenerg-1426	450	66	the	the	DET
fuelectenerg-1426	450	67	corresponding	correspond	VERB
fuelectenerg-1426	450	68	new	new	ADJ
fuelectenerg-1426	450	69	s	s	PROPN
fuelectenerg-1426	450	70	/	/	SYM
fuelectenerg-1426	450	71	d	d	NOUN
fuelectenerg-1426	450	72	trees	tree	NOUN
fuelectenerg-1426	450	73	.	.	PUNCT
fuelectenerg-1426	451	1	the	the	DET
fuelectenerg-1426	451	2	utilization	utilization	NOUN
fuelectenerg-1426	451	3	of	of	ADP
fuelectenerg-1426	451	4	the	the	DET
fuelectenerg-1426	451	5	results	result	NOUN
fuelectenerg-1426	451	6	from	from	ADP
fuelectenerg-1426	451	7	this	this	DET
fuelectenerg-1426	451	8	research	research	NOUN
fuelectenerg-1426	451	9	to	to	PART
fuelectenerg-1426	451	10	create	create	VERB
fuelectenerg-1426	451	11	an	an	DET
fuelectenerg-1426	451	12	efficient	efficient	ADJ
fuelectenerg-1426	451	13	gfsop	gfsop	NOUN
fuelectenerg-1426	451	14	minimizer	minimizer	NOUN
fuelectenerg-1426	451	15	for	for	ADP
fuelectenerg-1426	451	16	synthesis	synthesis	NOUN
fuelectenerg-1426	451	17	applications	application	NOUN
fuelectenerg-1426	451	18	within	within	ADP
fuelectenerg-1426	451	19	the	the	DET
fuelectenerg-1426	451	20	spaces	space	NOUN
fuelectenerg-1426	451	21	of	of	ADP
fuelectenerg-1426	451	22	classical	classical	ADJ
fuelectenerg-1426	451	23	and	and	CCONJ
fuelectenerg-1426	451	24	reversible	reversible	ADJ
fuelectenerg-1426	451	25	logic	logic	NOUN
fuelectenerg-1426	451	26	will	will	AUX
fuelectenerg-1426	451	27	also	also	ADV
fuelectenerg-1426	451	28	be	be	AUX
fuelectenerg-1426	451	29	conducted	conduct	VERB
fuelectenerg-1426	451	30	.	.	PUNCT
fuelectenerg-1426	452	1	references	reference	NOUN
fuelectenerg-1426	452	2	[	[	X
fuelectenerg-1426	452	3	1	1	X
fuelectenerg-1426	452	4	]	]	PUNCT
fuelectenerg-1426	452	5	s.	s.	PROPN
fuelectenerg-1426	452	6	b.	b.	PROPN
fuelectenerg-1426	452	7	akers	akers	PROPN
fuelectenerg-1426	452	8	,	,	PUNCT
fuelectenerg-1426	452	9	"	"	PUNCT
fuelectenerg-1426	452	10	binary	binary	ADJ
fuelectenerg-1426	452	11	decision	decision	NOUN
fuelectenerg-1426	452	12	diagrams	diagram	NOUN
fuelectenerg-1426	452	13	,	,	PUNCT
fuelectenerg-1426	452	14	"	"	PUNCT
fuelectenerg-1426	452	15	ieee	ieee	NOUN
fuelectenerg-1426	452	16	trans	tran	NOUN
fuelectenerg-1426	452	17	.	.	PUNCT
fuelectenerg-1426	453	1	comp	comp	PROPN
fuelectenerg-1426	453	2	.	.	PUNCT
fuelectenerg-1426	453	3	,	,	PUNCT
fuelectenerg-1426	453	4	vol	vol	NOUN
fuelectenerg-1426	453	5	.	.	PUNCT
fuelectenerg-1426	454	1	c-27	c-27	PROPN
fuelectenerg-1426	454	2	,	,	PUNCT
fuelectenerg-1426	454	3	no	no	INTJ
fuelectenerg-1426	454	4	.	.	NOUN
fuelectenerg-1426	454	5	6	6	NUM
fuelectenerg-1426	454	6	,	,	PUNCT
fuelectenerg-1426	454	7	pp	pp	ADJ
fuelectenerg-1426	454	8	.	.	PUNCT
fuelectenerg-1426	455	1	509	509	NUM
fuelectenerg-1426	455	2	-	-	SYM
fuelectenerg-1426	455	3	516	516	NUM
fuelectenerg-1426	455	4	,	,	PUNCT
fuelectenerg-1426	455	5	june	june	PROPN
fuelectenerg-1426	455	6	1978	1978	NUM
fuelectenerg-1426	455	7	.	.	PUNCT
fuelectenerg-1426	456	1	[	[	X
fuelectenerg-1426	456	2	2	2	NUM
fuelectenerg-1426	456	3	]	]	PUNCT
fuelectenerg-1426	456	4	a.	a.	NOUN
fuelectenerg-1426	456	5	n.	n.	PROPN
fuelectenerg-1426	456	6	al	al	PROPN
fuelectenerg-1426	456	7	-	-	PUNCT
fuelectenerg-1426	456	8	rabadi	rabadi	PROPN
fuelectenerg-1426	456	9	,	,	PUNCT
fuelectenerg-1426	456	10	reversible	reversible	ADJ
fuelectenerg-1426	456	11	logic	logic	NOUN
fuelectenerg-1426	456	12	synthesis	synthesis	NOUN
fuelectenerg-1426	456	13	:	:	PUNCT
fuelectenerg-1426	456	14	from	from	ADP
fuelectenerg-1426	456	15	fundamentals	fundamental	NOUN
fuelectenerg-1426	456	16	to	to	ADP
fuelectenerg-1426	456	17	quantum	quantum	ADJ
fuelectenerg-1426	456	18	computing	computing	NOUN
fuelectenerg-1426	456	19	,	,	PUNCT
fuelectenerg-1426	456	20	springer	springer	NOUN
fuelectenerg-1426	456	21	-	-	PUNCT
fuelectenerg-1426	456	22	verlag	verlag	PROPN
fuelectenerg-1426	456	23	,	,	PUNCT
fuelectenerg-1426	456	24	2004	2004	NUM
fuelectenerg-1426	456	25	.	.	PUNCT
fuelectenerg-1426	457	1	[	[	X
fuelectenerg-1426	457	2	3	3	NUM
fuelectenerg-1426	457	3	]	]	PUNCT
fuelectenerg-1426	457	4	a.	a.	NOUN
fuelectenerg-1426	457	5	n.	n.	PROPN
fuelectenerg-1426	457	6	al	al	PROPN
fuelectenerg-1426	457	7	-	-	PUNCT
fuelectenerg-1426	457	8	rabadi	rabadi	PROPN
fuelectenerg-1426	457	9	,	,	PUNCT
fuelectenerg-1426	457	10	"	"	PUNCT
fuelectenerg-1426	457	11	reversible	reversible	ADJ
fuelectenerg-1426	457	12	fast	fast	ADJ
fuelectenerg-1426	457	13	permutation	permutation	NOUN
fuelectenerg-1426	457	14	transforms	transform	VERB
fuelectenerg-1426	457	15	for	for	ADP
fuelectenerg-1426	457	16	quantum	quantum	ADJ
fuelectenerg-1426	457	17	circuit	circuit	NOUN
fuelectenerg-1426	457	18	synthesis	synthesis	NOUN
fuelectenerg-1426	457	19	,	,	PUNCT
fuelectenerg-1426	457	20	"	"	PUNCT
fuelectenerg-1426	457	21	proc	proc	NOUN
fuelectenerg-1426	457	22	.	.	PUNCT
fuelectenerg-1426	458	1	ieee	ieee	PROPN
fuelectenerg-1426	458	2	int	int	PROPN
fuelectenerg-1426	458	3	.	.	PUNCT
fuelectenerg-1426	459	1	symposium	symposium	NOUN
fuelectenerg-1426	459	2	on	on	ADP
fuelectenerg-1426	459	3	multiple	multiple	ADV
fuelectenerg-1426	459	4	-	-	PUNCT
fuelectenerg-1426	459	5	valued	value	VERB
fuelectenerg-1426	459	6	logic	logic	NOUN
fuelectenerg-1426	459	7	(	(	PUNCT
fuelectenerg-1426	459	8	ismvl	ismvl	PROPN
fuelectenerg-1426	459	9	)	)	PUNCT
fuelectenerg-1426	459	10	,	,	PUNCT
fuelectenerg-1426	459	11	toronto	toronto	PROPN
fuelectenerg-1426	459	12	,	,	PUNCT
fuelectenerg-1426	459	13	2004	2004	NUM
fuelectenerg-1426	459	14	,	,	PUNCT
fuelectenerg-1426	459	15	pp	pp	PROPN
fuelectenerg-1426	459	16	.	.	PUNCT
fuelectenerg-1426	460	1	81	81	NUM
fuelectenerg-1426	460	2	-	-	SYM
fuelectenerg-1426	460	3	86	86	NUM
fuelectenerg-1426	460	4	.	.	PUNCT
fuelectenerg-1426	461	1	[	[	X
fuelectenerg-1426	461	2	4	4	NUM
fuelectenerg-1426	461	3	]	]	PUNCT
fuelectenerg-1426	461	4	a.	a.	NOUN
fuelectenerg-1426	461	5	n.	n.	PROPN
fuelectenerg-1426	461	6	al	al	PROPN
fuelectenerg-1426	461	7	-	-	PUNCT
fuelectenerg-1426	461	8	rabadi	rabadi	PROPN
fuelectenerg-1426	461	9	,	,	PUNCT
fuelectenerg-1426	461	10	"	"	PUNCT
fuelectenerg-1426	461	11	quantum	quantum	ADJ
fuelectenerg-1426	461	12	circuit	circuit	NOUN
fuelectenerg-1426	461	13	synthesis	synthesis	NOUN
fuelectenerg-1426	461	14	using	use	VERB
fuelectenerg-1426	461	15	classes	class	NOUN
fuelectenerg-1426	461	16	of	of	ADP
fuelectenerg-1426	461	17	gf(3	gf(3	NOUN
fuelectenerg-1426	461	18	)	)	PUNCT
fuelectenerg-1426	461	19	reversible	reversible	ADJ
fuelectenerg-1426	461	20	fast	fast	ADJ
fuelectenerg-1426	461	21	spectral	spectral	ADJ
fuelectenerg-1426	461	22	transforms	transform	NOUN
fuelectenerg-1426	461	23	,	,	PUNCT
fuelectenerg-1426	461	24	"	"	PUNCT
fuelectenerg-1426	461	25	proc	proc	NOUN
fuelectenerg-1426	461	26	.	.	PUNCT
fuelectenerg-1426	462	1	ieee	ieee	PROPN
fuelectenerg-1426	462	2	int	int	PROPN
fuelectenerg-1426	462	3	.	.	PUNCT
fuelectenerg-1426	463	1	symposium	symposium	NOUN
fuelectenerg-1426	463	2	on	on	ADP
fuelectenerg-1426	463	3	multiple	multiple	ADV
fuelectenerg-1426	463	4	-	-	PUNCT
fuelectenerg-1426	463	5	valued	value	VERB
fuelectenerg-1426	463	6	logic	logic	NOUN
fuelectenerg-1426	463	7	(	(	PUNCT
fuelectenerg-1426	463	8	ismvl	ismvl	PROPN
fuelectenerg-1426	463	9	)	)	PUNCT
fuelectenerg-1426	463	10	,	,	PUNCT
fuelectenerg-1426	463	11	toronto	toronto	PROPN
fuelectenerg-1426	463	12	,	,	PUNCT
fuelectenerg-1426	463	13	2004	2004	NUM
fuelectenerg-1426	463	14	,	,	PUNCT
fuelectenerg-1426	463	15	pp	pp	ADV
fuelectenerg-1426	463	16	.	.	PUNCT
fuelectenerg-1426	464	1	87	87	NUM
fuelectenerg-1426	464	2	-	-	SYM
fuelectenerg-1426	464	3	93	93	NUM
fuelectenerg-1426	464	4	.	.	PUNCT
fuelectenerg-1426	465	1	[	[	PUNCT
fuelectenerg-1426	465	2	5	5	NUM
fuelectenerg-1426	465	3	]	]	PUNCT
fuelectenerg-1426	465	4	a.	a.	NOUN
fuelectenerg-1426	465	5	n.	n.	PROPN
fuelectenerg-1426	465	6	al	al	PROPN
fuelectenerg-1426	465	7	-	-	PUNCT
fuelectenerg-1426	465	8	rabadi	rabadi	PROPN
fuelectenerg-1426	465	9	,	,	PUNCT
fuelectenerg-1426	465	10	"	"	PUNCT
fuelectenerg-1426	465	11	quantum	quantum	ADJ
fuelectenerg-1426	465	12	logic	logic	NOUN
fuelectenerg-1426	465	13	circuit	circuit	NOUN
fuelectenerg-1426	465	14	design	design	NOUN
fuelectenerg-1426	465	15	of	of	ADP
fuelectenerg-1426	465	16	many	many	ADV
fuelectenerg-1426	465	17	-	-	PUNCT
fuelectenerg-1426	465	18	valued	value	VERB
fuelectenerg-1426	465	19	galois	galois	PROPN
fuelectenerg-1426	465	20	reversible	reversible	ADJ
fuelectenerg-1426	465	21	expansions	expansion	NOUN
fuelectenerg-1426	465	22	and	and	CCONJ
fuelectenerg-1426	465	23	fast	fast	ADJ
fuelectenerg-1426	465	24	transforms	transform	NOUN
fuelectenerg-1426	465	25	,	,	PUNCT
fuelectenerg-1426	465	26	"	"	PUNCT
fuelectenerg-1426	465	27	j.	j.	PROPN
fuelectenerg-1426	465	28	circuits	circuits	PROPN
fuelectenerg-1426	465	29	,	,	PUNCT
fuelectenerg-1426	465	30	systems	system	NOUN
fuelectenerg-1426	465	31	,	,	PUNCT
fuelectenerg-1426	465	32	and	and	CCONJ
fuelectenerg-1426	465	33	computers	computer	NOUN
fuelectenerg-1426	465	34	,	,	PUNCT
fuelectenerg-1426	465	35	world	world	NOUN
fuelectenerg-1426	465	36	scientific	scientific	PROPN
fuelectenerg-1426	465	37	,	,	PUNCT
fuelectenerg-1426	465	38	singapore	singapore	PROPN
fuelectenerg-1426	465	39	,	,	PUNCT
fuelectenerg-1426	465	40	vol	vol	NOUN
fuelectenerg-1426	465	41	.	.	PROPN
fuelectenerg-1426	465	42	16	16	NUM
fuelectenerg-1426	465	43	,	,	PUNCT
fuelectenerg-1426	465	44	no	no	INTJ
fuelectenerg-1426	465	45	.	.	NOUN
fuelectenerg-1426	465	46	5	5	NUM
fuelectenerg-1426	465	47	,	,	PUNCT
fuelectenerg-1426	465	48	pp	pp	ADJ
fuelectenerg-1426	465	49	.	.	PUNCT
fuelectenerg-1426	466	1	641	641	NUM
fuelectenerg-1426	466	2	671	671	NUM
fuelectenerg-1426	466	3	,	,	PUNCT
fuelectenerg-1426	466	4	2007	2007	NUM
fuelectenerg-1426	466	5	.	.	PUNCT
fuelectenerg-1426	467	1	[	[	PUNCT
fuelectenerg-1426	467	2	6	6	NUM
fuelectenerg-1426	467	3	]	]	PUNCT
fuelectenerg-1426	467	4	a.	a.	NOUN
fuelectenerg-1426	467	5	n.	n.	PROPN
fuelectenerg-1426	467	6	al	al	PROPN
fuelectenerg-1426	467	7	-	-	PUNCT
fuelectenerg-1426	467	8	rabadi	rabadi	PROPN
fuelectenerg-1426	467	9	,	,	PUNCT
fuelectenerg-1426	467	10	"	"	PUNCT
fuelectenerg-1426	467	11	representations	representation	NOUN
fuelectenerg-1426	467	12	,	,	PUNCT
fuelectenerg-1426	467	13	operations	operation	NOUN
fuelectenerg-1426	467	14	,	,	PUNCT
fuelectenerg-1426	467	15	and	and	CCONJ
fuelectenerg-1426	467	16	applications	application	NOUN
fuelectenerg-1426	467	17	of	of	ADP
fuelectenerg-1426	467	18	switching	switch	VERB
fuelectenerg-1426	467	19	circuits	circuit	NOUN
fuelectenerg-1426	467	20	in	in	ADP
fuelectenerg-1426	467	21	the	the	DET
fuelectenerg-1426	467	22	reversible	reversible	ADJ
fuelectenerg-1426	467	23	and	and	CCONJ
fuelectenerg-1426	467	24	quantum	quantum	ADJ
fuelectenerg-1426	467	25	spaces	space	NOUN
fuelectenerg-1426	467	26	,	,	PUNCT
fuelectenerg-1426	467	27	"	"	PUNCT
fuelectenerg-1426	467	28	facta	facta	PROPN
fuelectenerg-1426	467	29	universitatis	universitatis	PROPN
fuelectenerg-1426	467	30	(	(	PUNCT
fuelectenerg-1426	467	31	fu	fu	NOUN
fuelectenerg-1426	467	32	)	)	PUNCT
fuelectenerg-1426	467	33	electronics	electronic	NOUN
fuelectenerg-1426	467	34	and	and	CCONJ
fuelectenerg-1426	467	35	energetics	energetic	NOUN
fuelectenerg-1426	467	36	,	,	PUNCT
fuelectenerg-1426	467	37	vol	vol	NOUN
fuelectenerg-1426	467	38	.	.	PROPN
fuelectenerg-1426	467	39	20	20	NUM
fuelectenerg-1426	467	40	,	,	PUNCT
fuelectenerg-1426	467	41	no	no	INTJ
fuelectenerg-1426	467	42	.	.	NOUN
fuelectenerg-1426	468	1	3	3	NUM
fuelectenerg-1426	468	2	,	,	PUNCT
fuelectenerg-1426	468	3	pp	pp	ADJ
fuelectenerg-1426	468	4	.	.	PUNCT
fuelectenerg-1426	469	1	507	507	NUM
fuelectenerg-1426	469	2	539	539	NUM
fuelectenerg-1426	469	3	,	,	PUNCT
fuelectenerg-1426	469	4	2007	2007	NUM
fuelectenerg-1426	469	5	.	.	PUNCT
fuelectenerg-1426	470	1	[	[	X
fuelectenerg-1426	470	2	7	7	X
fuelectenerg-1426	470	3	]	]	X
fuelectenerg-1426	470	4	r.	r.	PROPN
fuelectenerg-1426	470	5	e.	e.	PROPN
fuelectenerg-1426	470	6	bryant	bryant	PROPN
fuelectenerg-1426	470	7	,	,	PUNCT
fuelectenerg-1426	470	8	"	"	PUNCT
fuelectenerg-1426	470	9	graph	graph	NOUN
fuelectenerg-1426	470	10	-	-	PUNCT
fuelectenerg-1426	470	11	based	base	VERB
fuelectenerg-1426	470	12	algorithms	algorithm	NOUN
fuelectenerg-1426	470	13	for	for	ADP
fuelectenerg-1426	470	14	boolean	boolean	ADJ
fuelectenerg-1426	470	15	functions	function	NOUN
fuelectenerg-1426	470	16	manipulation	manipulation	NOUN
fuelectenerg-1426	470	17	,	,	PUNCT
fuelectenerg-1426	470	18	"	"	PUNCT
fuelectenerg-1426	470	19	ieee	ieee	NOUN
fuelectenerg-1426	470	20	trans	tran	NOUN
fuelectenerg-1426	470	21	.	.	PUNCT
fuelectenerg-1426	471	1	on	on	ADP
fuelectenerg-1426	471	2	comp	comp	PROPN
fuelectenerg-1426	471	3	.	.	PUNCT
fuelectenerg-1426	471	4	,	,	PUNCT
fuelectenerg-1426	471	5	vol	vol	NOUN
fuelectenerg-1426	471	6	.	.	PUNCT
fuelectenerg-1426	472	1	c-35	c-35	PROPN
fuelectenerg-1426	472	2	,	,	PUNCT
fuelectenerg-1426	472	3	no.8	no.8	PROPN
fuelectenerg-1426	472	4	,	,	PUNCT
fuelectenerg-1426	472	5	pp	pp	ADV
fuelectenerg-1426	472	6	.	.	PUNCT
fuelectenerg-1426	473	1	667	667	NUM
fuelectenerg-1426	473	2	-	-	SYM
fuelectenerg-1426	473	3	691	691	NUM
fuelectenerg-1426	473	4	,	,	PUNCT
fuelectenerg-1426	473	5	1986	1986	NUM
fuelectenerg-1426	473	6	.	.	PUNCT
fuelectenerg-1426	474	1	[	[	X
fuelectenerg-1426	474	2	8	8	NUM
fuelectenerg-1426	474	3	]	]	X
fuelectenerg-1426	474	4	m.	m.	NOUN
fuelectenerg-1426	474	5	cohn	cohn	PROPN
fuelectenerg-1426	474	6	,	,	PUNCT
fuelectenerg-1426	474	7	switching	switch	VERB
fuelectenerg-1426	474	8	function	function	NOUN
fuelectenerg-1426	474	9	canonical	canonical	ADJ
fuelectenerg-1426	474	10	form	form	NOUN
fuelectenerg-1426	474	11	over	over	ADP
fuelectenerg-1426	474	12	integer	integer	NOUN
fuelectenerg-1426	474	13	fields	field	NOUN
fuelectenerg-1426	474	14	,	,	PUNCT
fuelectenerg-1426	474	15	ph.d	ph.d	PROPN
fuelectenerg-1426	474	16	.	.	PUNCT
fuelectenerg-1426	474	17	dissertation	dissertation	PROPN
fuelectenerg-1426	474	18	,	,	PUNCT
fuelectenerg-1426	474	19	harvard	harvard	PROPN
fuelectenerg-1426	474	20	university	university	PROPN
fuelectenerg-1426	474	21	,	,	PUNCT
fuelectenerg-1426	474	22	1960	1960	NUM
fuelectenerg-1426	474	23	.	.	PUNCT
fuelectenerg-1426	475	1	[	[	X
fuelectenerg-1426	475	2	9	9	NUM
fuelectenerg-1426	475	3	]	]	X
fuelectenerg-1426	475	4	r.	r.	NOUN
fuelectenerg-1426	475	5	drechsler	drechsler	PROPN
fuelectenerg-1426	475	6	,	,	PUNCT
fuelectenerg-1426	475	7	a.	a.	NOUN
fuelectenerg-1426	475	8	sarabi	sarabi	PROPN
fuelectenerg-1426	475	9	,	,	PUNCT
fuelectenerg-1426	475	10	m.	m.	NOUN
fuelectenerg-1426	475	11	theobald	theobald	PROPN
fuelectenerg-1426	475	12	,	,	PUNCT
fuelectenerg-1426	475	13	b.	b.	PROPN
fuelectenerg-1426	475	14	becker	becker	PROPN
fuelectenerg-1426	475	15	,	,	PUNCT
fuelectenerg-1426	475	16	and	and	CCONJ
fuelectenerg-1426	475	17	m.	m.	PROPN
fuelectenerg-1426	475	18	a.	a.	PROPN
fuelectenerg-1426	475	19	perkowski	perkowski	PROPN
fuelectenerg-1426	475	20	,	,	PUNCT
fuelectenerg-1426	475	21	"	"	PUNCT
fuelectenerg-1426	475	22	efficient	efficient	ADJ
fuelectenerg-1426	475	23	representation	representation	NOUN
fuelectenerg-1426	475	24	and	and	CCONJ
fuelectenerg-1426	475	25	manipulation	manipulation	NOUN
fuelectenerg-1426	475	26	of	of	ADP
fuelectenerg-1426	475	27	switching	switch	VERB
fuelectenerg-1426	475	28	functions	function	NOUN
fuelectenerg-1426	475	29	based	base	VERB
fuelectenerg-1426	475	30	on	on	ADP
fuelectenerg-1426	475	31	ordered	order	VERB
fuelectenerg-1426	475	32	kronecker	kronecker	NOUN
fuelectenerg-1426	475	33	functional	functional	ADJ
fuelectenerg-1426	475	34	decision	decision	NOUN
fuelectenerg-1426	475	35	diagrams	diagram	NOUN
fuelectenerg-1426	475	36	,	,	PUNCT
fuelectenerg-1426	475	37	"	"	PUNCT
fuelectenerg-1426	475	38	proc	proc	NOUN
fuelectenerg-1426	475	39	.	.	PUNCT
fuelectenerg-1426	475	40	dac	dac	PROPN
fuelectenerg-1426	475	41	,	,	PUNCT
fuelectenerg-1426	475	42	1994	1994	NUM
fuelectenerg-1426	475	43	,	,	PUNCT
fuelectenerg-1426	475	44	pp	pp	ADJ
fuelectenerg-1426	475	45	.	.	PUNCT
fuelectenerg-1426	475	46	415	415	NUM
fuelectenerg-1426	475	47	-	-	SYM
fuelectenerg-1426	475	48	419	419	NUM
fuelectenerg-1426	475	49	.	.	PUNCT
fuelectenerg-1426	476	1	[	[	X
fuelectenerg-1426	476	2	10	10	NUM
fuelectenerg-1426	476	3	]	]	PUNCT
fuelectenerg-1426	476	4	m.	m.	NOUN
fuelectenerg-1426	476	5	escobar	escobar	PROPN
fuelectenerg-1426	476	6	and	and	CCONJ
fuelectenerg-1426	476	7	f.	f.	PROPN
fuelectenerg-1426	476	8	somenzi	somenzi	PROPN
fuelectenerg-1426	476	9	,	,	PUNCT
fuelectenerg-1426	476	10	"	"	PUNCT
fuelectenerg-1426	476	11	synthesis	synthesis	NOUN
fuelectenerg-1426	476	12	of	of	ADP
fuelectenerg-1426	476	13	and	and	CCONJ
fuelectenerg-1426	476	14	/	/	SYM
fuelectenerg-1426	476	15	exor	exor	PROPN
fuelectenerg-1426	476	16	expressions	expression	NOUN
fuelectenerg-1426	476	17	via	via	ADP
fuelectenerg-1426	476	18	satisfiability	satisfiability	NOUN
fuelectenerg-1426	476	19	,	,	PUNCT
fuelectenerg-1426	476	20	"	"	PUNCT
fuelectenerg-1426	476	21	proc	proc	NOUN
fuelectenerg-1426	476	22	.	.	PUNCT
fuelectenerg-1426	477	1	reed	reed	NOUN
fuelectenerg-1426	477	2	-	-	PUNCT
fuelectenerg-1426	477	3	muller	muller	NOUN
fuelectenerg-1426	477	4	,	,	PUNCT
fuelectenerg-1426	477	5	1995	1995	NUM
fuelectenerg-1426	477	6	,	,	PUNCT
fuelectenerg-1426	477	7	pp	pp	PROPN
fuelectenerg-1426	477	8	.	.	PUNCT
fuelectenerg-1426	478	1	80	80	NUM
fuelectenerg-1426	478	2	-	-	SYM
fuelectenerg-1426	478	3	87	87	NUM
fuelectenerg-1426	478	4	.	.	PUNCT
fuelectenerg-1426	479	1	[	[	X
fuelectenerg-1426	479	2	11	11	NUM
fuelectenerg-1426	479	3	]	]	X
fuelectenerg-1426	479	4	b.	b.	PROPN
fuelectenerg-1426	479	5	j.	j.	PROPN
fuelectenerg-1426	479	6	falkowski	falkowski	PROPN
fuelectenerg-1426	479	7	and	and	CCONJ
fuelectenerg-1426	479	8	s.	s.	PROPN
fuelectenerg-1426	479	9	rahardja	rahardja	PROPN
fuelectenerg-1426	479	10	,	,	PUNCT
fuelectenerg-1426	479	11	"	"	PUNCT
fuelectenerg-1426	479	12	classification	classification	NOUN
fuelectenerg-1426	479	13	and	and	CCONJ
fuelectenerg-1426	479	14	properties	property	NOUN
fuelectenerg-1426	479	15	of	of	ADP
fuelectenerg-1426	479	16	fast	fast	ADJ
fuelectenerg-1426	479	17	linearly	linearly	ADV
fuelectenerg-1426	479	18	independent	independent	ADJ
fuelectenerg-1426	479	19	logic	logic	NOUN
fuelectenerg-1426	479	20	transformations	transformation	NOUN
fuelectenerg-1426	479	21	,	,	PUNCT
fuelectenerg-1426	479	22	"	"	PUNCT
fuelectenerg-1426	479	23	ieee	ieee	NOUN
fuelectenerg-1426	479	24	trans	tran	NOUN
fuelectenerg-1426	479	25	.	.	PUNCT
fuelectenerg-1426	480	1	on	on	ADP
fuelectenerg-1426	480	2	circuits	circuit	NOUN
fuelectenerg-1426	480	3	and	and	CCONJ
fuelectenerg-1426	480	4	systems	system	NOUN
fuelectenerg-1426	480	5	-	-	PUNCT
fuelectenerg-1426	480	6	ii	ii	NOUN
fuelectenerg-1426	480	7	,	,	PUNCT
fuelectenerg-1426	480	8	vol	vol	NOUN
fuelectenerg-1426	480	9	.	.	PROPN
fuelectenerg-1426	480	10	44	44	NUM
fuelectenerg-1426	480	11	,	,	PUNCT
fuelectenerg-1426	480	12	no	no	INTJ
fuelectenerg-1426	480	13	.	.	NOUN
fuelectenerg-1426	480	14	8	8	NUM
fuelectenerg-1426	480	15	,	,	PUNCT
fuelectenerg-1426	480	16	pp	pp	ADJ
fuelectenerg-1426	480	17	.	.	PUNCT
fuelectenerg-1426	480	18	646	646	NUM
fuelectenerg-1426	480	19	-	-	SYM
fuelectenerg-1426	480	20	655	655	NUM
fuelectenerg-1426	480	21	,	,	PUNCT
fuelectenerg-1426	480	22	august	august	PROPN
fuelectenerg-1426	480	23	1997	1997	NUM
fuelectenerg-1426	480	24	.	.	PUNCT
fuelectenerg-1426	481	1	[	[	X
fuelectenerg-1426	481	2	12	12	NUM
fuelectenerg-1426	481	3	]	]	PUNCT
fuelectenerg-1426	481	4	b.	b.	PROPN
fuelectenerg-1426	481	5	falkowski	falkowski	NOUN
fuelectenerg-1426	481	6	and	and	CCONJ
fuelectenerg-1426	481	7	l.-s	l.-s	PROPN
fuelectenerg-1426	481	8	.	.	PUNCT
fuelectenerg-1426	482	1	lim	lim	PROPN
fuelectenerg-1426	482	2	,	,	PUNCT
fuelectenerg-1426	482	3	"	"	PUNCT
fuelectenerg-1426	482	4	gray	gray	ADJ
fuelectenerg-1426	482	5	scale	scale	NOUN
fuelectenerg-1426	482	6	image	image	NOUN
fuelectenerg-1426	482	7	compression	compression	NOUN
fuelectenerg-1426	482	8	based	base	VERB
fuelectenerg-1426	482	9	on	on	ADP
fuelectenerg-1426	482	10	multiple	multiple	ADV
fuelectenerg-1426	482	11	-	-	PUNCT
fuelectenerg-1426	482	12	valued	value	VERB
fuelectenerg-1426	482	13	input	input	NOUN
fuelectenerg-1426	482	14	binary	binary	NOUN
fuelectenerg-1426	482	15	functions	function	NOUN
fuelectenerg-1426	482	16	,	,	PUNCT
fuelectenerg-1426	482	17	walsh	walsh	NOUN
fuelectenerg-1426	482	18	and	and	CCONJ
fuelectenerg-1426	482	19	reed	reed	PROPN
fuelectenerg-1426	482	20	-	-	PUNCT
fuelectenerg-1426	482	21	muller	muller	PROPN
fuelectenerg-1426	482	22	spectra	spectra	PROPN
fuelectenerg-1426	482	23	,	,	PUNCT
fuelectenerg-1426	482	24	"	"	PUNCT
fuelectenerg-1426	482	25	proc	proc	NOUN
fuelectenerg-1426	482	26	.	.	PUNCT
fuelectenerg-1426	483	1	ismvl	ismvl	PROPN
fuelectenerg-1426	483	2	,	,	PUNCT
fuelectenerg-1426	483	3	2000	2000	NUM
fuelectenerg-1426	483	4	,	,	PUNCT
fuelectenerg-1426	483	5	pp	pp	ADJ
fuelectenerg-1426	483	6	.	.	PUNCT
fuelectenerg-1426	484	1	279	279	NUM
fuelectenerg-1426	484	2	-	-	SYM
fuelectenerg-1426	484	3	284	284	NUM
fuelectenerg-1426	484	4	.	.	PUNCT
fuelectenerg-1426	485	1	[	[	X
fuelectenerg-1426	485	2	13	13	NUM
fuelectenerg-1426	485	3	]	]	X
fuelectenerg-1426	485	4	h.	h.	PROPN
fuelectenerg-1426	485	5	fujiwara	fujiwara	PROPN
fuelectenerg-1426	485	6	,	,	PUNCT
fuelectenerg-1426	485	7	logic	logic	NOUN
fuelectenerg-1426	485	8	testing	testing	NOUN
fuelectenerg-1426	485	9	and	and	CCONJ
fuelectenerg-1426	485	10	design	design	NOUN
fuelectenerg-1426	485	11	for	for	ADP
fuelectenerg-1426	485	12	testability	testability	NOUN
fuelectenerg-1426	485	13	,	,	PUNCT
fuelectenerg-1426	485	14	mit	mit	NOUN
fuelectenerg-1426	485	15	press	press	NOUN
fuelectenerg-1426	485	16	,	,	PUNCT
fuelectenerg-1426	485	17	1985	1985	NUM
fuelectenerg-1426	485	18	.	.	PUNCT
fuelectenerg-1426	486	1	[	[	X
fuelectenerg-1426	486	2	14	14	NUM
fuelectenerg-1426	486	3	]	]	X
fuelectenerg-1426	486	4	d.	d.	PROPN
fuelectenerg-1426	486	5	h.	h.	PROPN
fuelectenerg-1426	486	6	green	green	PROPN
fuelectenerg-1426	486	7	,	,	PUNCT
fuelectenerg-1426	486	8	"	"	PUNCT
fuelectenerg-1426	486	9	families	family	NOUN
fuelectenerg-1426	486	10	of	of	ADP
fuelectenerg-1426	486	11	reed	reed	NOUN
fuelectenerg-1426	486	12	-	-	PUNCT
fuelectenerg-1426	486	13	muller	muller	NOUN
fuelectenerg-1426	486	14	canonical	canonical	ADJ
fuelectenerg-1426	486	15	forms	form	NOUN
fuelectenerg-1426	486	16	,	,	PUNCT
fuelectenerg-1426	486	17	"	"	PUNCT
fuelectenerg-1426	486	18	int	int	NOUN
fuelectenerg-1426	486	19	.	.	PUNCT
fuelectenerg-1426	487	1	j.	j.	PROPN
fuelectenerg-1426	487	2	of	of	ADP
fuelectenerg-1426	487	3	electronics	electronics	PROPN
fuelectenerg-1426	487	4	,	,	PUNCT
fuelectenerg-1426	487	5	no	no	INTJ
fuelectenerg-1426	487	6	.	.	NOUN
fuelectenerg-1426	487	7	2	2	NUM
fuelectenerg-1426	487	8	,	,	PUNCT
fuelectenerg-1426	487	9	pp	pp	ADJ
fuelectenerg-1426	487	10	.	.	PUNCT
fuelectenerg-1426	488	1	259	259	NUM
fuelectenerg-1426	488	2	-	-	SYM
fuelectenerg-1426	488	3	280	280	NUM
fuelectenerg-1426	488	4	,	,	PUNCT
fuelectenerg-1426	488	5	1991	1991	NUM
fuelectenerg-1426	488	6	.	.	PUNCT
fuelectenerg-1426	489	1	[	[	X
fuelectenerg-1426	489	2	15	15	NUM
fuelectenerg-1426	489	3	]	]	X
fuelectenerg-1426	489	4	s.	s.	PROPN
fuelectenerg-1426	489	5	hassoun	hassoun	PROPN
fuelectenerg-1426	489	6	,	,	PUNCT
fuelectenerg-1426	489	7	t.	t.	PROPN
fuelectenerg-1426	489	8	sasao	sasao	PROPN
fuelectenerg-1426	489	9	,	,	PUNCT
fuelectenerg-1426	489	10	and	and	CCONJ
fuelectenerg-1426	489	11	r.	r.	PROPN
fuelectenerg-1426	489	12	brayton	brayton	PROPN
fuelectenerg-1426	489	13	(	(	PUNCT
fuelectenerg-1426	489	14	editors	editor	NOUN
fuelectenerg-1426	489	15	)	)	PUNCT
fuelectenerg-1426	489	16	,	,	PUNCT
fuelectenerg-1426	489	17	logic	logic	NOUN
fuelectenerg-1426	489	18	synthesis	synthesis	NOUN
fuelectenerg-1426	489	19	and	and	CCONJ
fuelectenerg-1426	489	20	verification	verification	NOUN
fuelectenerg-1426	489	21	,	,	PUNCT
fuelectenerg-1426	489	22	kluwer	kluwer	NOUN
fuelectenerg-1426	489	23	acad	acad	PROPN
fuelectenerg-1426	489	24	.	.	PUNCT
fuelectenerg-1426	490	1	publishers	publisher	NOUN
fuelectenerg-1426	490	2	,	,	PUNCT
fuelectenerg-1426	490	3	2001	2001	NUM
fuelectenerg-1426	490	4	.	.	PUNCT
fuelectenerg-1426	491	1	[	[	X
fuelectenerg-1426	491	2	16	16	NUM
fuelectenerg-1426	491	3	]	]	PUNCT
fuelectenerg-1426	491	4	m.	m.	NOUN
fuelectenerg-1426	491	5	helliwell	helliwell	NOUN
fuelectenerg-1426	491	6	and	and	CCONJ
fuelectenerg-1426	491	7	m.	m.	PROPN
fuelectenerg-1426	491	8	a.	a.	PROPN
fuelectenerg-1426	491	9	perkowski	perkowski	PROPN
fuelectenerg-1426	491	10	,	,	PUNCT
fuelectenerg-1426	491	11	"	"	PUNCT
fuelectenerg-1426	491	12	a	a	DET
fuelectenerg-1426	491	13	fast	fast	ADJ
fuelectenerg-1426	491	14	algorithm	algorithm	NOUN
fuelectenerg-1426	491	15	to	to	PART
fuelectenerg-1426	491	16	minimize	minimize	VERB
fuelectenerg-1426	491	17	multi	multi	ADJ
fuelectenerg-1426	491	18	-	-	ADJ
fuelectenerg-1426	491	19	output	output	ADJ
fuelectenerg-1426	491	20	mixed	mix	VERB
fuelectenerg-1426	491	21	-	-	PUNCT
fuelectenerg-1426	491	22	polarity	polarity	NOUN
fuelectenerg-1426	491	23	generalized	generalize	VERB
fuelectenerg-1426	491	24	reed	reed	NOUN
fuelectenerg-1426	491	25	-	-	PUNCT
fuelectenerg-1426	491	26	muller	muller	NOUN
fuelectenerg-1426	491	27	forms	form	NOUN
fuelectenerg-1426	491	28	,	,	PUNCT
fuelectenerg-1426	491	29	"	"	PUNCT
fuelectenerg-1426	491	30	proc	proc	NOUN
fuelectenerg-1426	491	31	.	.	PUNCT
fuelectenerg-1426	492	1	design	design	NOUN
fuelectenerg-1426	492	2	automation	automation	NOUN
fuelectenerg-1426	492	3	conference	conference	NOUN
fuelectenerg-1426	492	4	,	,	PUNCT
fuelectenerg-1426	492	5	1988	1988	NUM
fuelectenerg-1426	492	6	,	,	PUNCT
fuelectenerg-1426	492	7	pp	pp	ADV
fuelectenerg-1426	492	8	.	.	PUNCT
fuelectenerg-1426	493	1	427	427	NUM
fuelectenerg-1426	493	2	-	-	SYM
fuelectenerg-1426	493	3	432	432	NUM
fuelectenerg-1426	493	4	.	.	PUNCT
fuelectenerg-1426	494	1	[	[	X
fuelectenerg-1426	494	2	17	17	NUM
fuelectenerg-1426	494	3	]	]	PUNCT
fuelectenerg-1426	494	4	s.	s.	PROPN
fuelectenerg-1426	494	5	l.	l.	PROPN
fuelectenerg-1426	494	6	hurst	hurst	PROPN
fuelectenerg-1426	494	7	,	,	PUNCT
fuelectenerg-1426	494	8	d.	d.	PROPN
fuelectenerg-1426	494	9	m.	m.	PROPN
fuelectenerg-1426	494	10	miller	miller	PROPN
fuelectenerg-1426	494	11	,	,	PUNCT
fuelectenerg-1426	494	12	and	and	CCONJ
fuelectenerg-1426	494	13	j.	j.	PROPN
fuelectenerg-1426	494	14	c.	c.	PROPN
fuelectenerg-1426	494	15	muzio	muzio	PROPN
fuelectenerg-1426	494	16	,	,	PUNCT
fuelectenerg-1426	494	17	spectral	spectral	ADJ
fuelectenerg-1426	494	18	techniques	technique	NOUN
fuelectenerg-1426	494	19	in	in	ADP
fuelectenerg-1426	494	20	digital	digital	ADJ
fuelectenerg-1426	494	21	logic	logic	NOUN
fuelectenerg-1426	494	22	,	,	PUNCT
fuelectenerg-1426	494	23	academic	academic	ADJ
fuelectenerg-1426	494	24	119	119	NUM
fuelectenerg-1426	494	25	acknowledgement	acknowledgement	NOUN
fuelectenerg-1426	494	26	:	:	PUNCT
fuelectenerg-1426	494	27	this	this	DET
fuelectenerg-1426	494	28	research	research	NOUN
fuelectenerg-1426	494	29	was	be	AUX
fuelectenerg-1426	494	30	performed	perform	VERB
fuelectenerg-1426	494	31	during	during	ADP
fuelectenerg-1426	494	32	sabbatical	sabbatical	ADJ
fuelectenerg-1426	494	33	leave	leave	NOUN
fuelectenerg-1426	494	34	in	in	ADP
fuelectenerg-1426	494	35	2015	2015	NUM
fuelectenerg-1426	494	36	-	-	SYM
fuelectenerg-1426	494	37	2016	2016	NUM
fuelectenerg-1426	494	38	granted	grant	VERB
fuelectenerg-1426	494	39	from	from	ADP
fuelectenerg-1426	494	40	the	the	DET
fuelectenerg-1426	494	41	university	university	PROPN
fuelectenerg-1426	494	42	of	of	ADP
fuelectenerg-1426	494	43	jordan	jordan	PROPN
fuelectenerg-1426	494	44	and	and	CCONJ
fuelectenerg-1426	494	45	spent	spend	VERB
fuelectenerg-1426	494	46	at	at	ADP
fuelectenerg-1426	494	47	philadelphia	philadelphia	PROPN
fuelectenerg-1426	494	48	university	university	NOUN
fuelectenerg-1426	494	49	.	.	PUNCT
fuelectenerg-1426	495	1	720	720	NUM
fuelectenerg-1426	495	2	a.	a.	NOUN
fuelectenerg-1426	495	3	n.	n.	PROPN
fuelectenerg-1426	495	4	al	al	PROPN
fuelectenerg-1426	495	5	-	-	PUNCT
fuelectenerg-1426	495	6	rabadi	rabadi	PROPN
fuelectenerg-1426	495	7	multi	multi	ADJ
fuelectenerg-1426	495	8	-	-	ADJ
fuelectenerg-1426	495	9	valued	value	VERB
fuelectenerg-1426	495	10	galois	galois	PROPN
fuelectenerg-1426	495	11	shannon	shannon	PROPN
fuelectenerg-1426	495	12	davio	davio	PROPN
fuelectenerg-1426	495	13	trees	tree	NOUN
fuelectenerg-1426	495	14	and	and	CCONJ
fuelectenerg-1426	495	15	their	their	PRON
fuelectenerg-1426	495	16	complexity	complexity	NOUN
fuelectenerg-1426	495	17	pb	pb	ADP
fuelectenerg-1426	495	18	multi	multi	ADJ
fuelectenerg-1426	495	19	-	-	ADJ
fuelectenerg-1426	495	20	valued	value	VERB
fuelectenerg-1426	495	21	galois	galois	PROPN
fuelectenerg-1426	495	22	shannon	shannon	PROPN
fuelectenerg-1426	495	23	davio	davio	PROPN
fuelectenerg-1426	495	24	trees	tree	NOUN
fuelectenerg-1426	495	25	and	and	CCONJ
fuelectenerg-1426	495	26	their	their	PRON
fuelectenerg-1426	495	27	complexity	complexity	NOUN
fuelectenerg-1426	495	28	press	press	PROPN
fuelectenerg-1426	495	29	inc	inc	PROPN
fuelectenerg-1426	495	30	.	.	PROPN
fuelectenerg-1426	495	31	,	,	PUNCT
fuelectenerg-1426	495	32	1985	1985	NUM
fuelectenerg-1426	495	33	.	.	PUNCT
fuelectenerg-1426	496	1	[	[	X
fuelectenerg-1426	496	2	18	18	NUM
fuelectenerg-1426	496	3	]	]	PUNCT
fuelectenerg-1426	496	4	m.	m.	NOUN
fuelectenerg-1426	496	5	g.	g.	PROPN
fuelectenerg-1426	496	6	karpovski	karpovski	PROPN
fuelectenerg-1426	496	7	,	,	PUNCT
fuelectenerg-1426	496	8	finite	finite	PROPN
fuelectenerg-1426	496	9	orthogonal	orthogonal	ADJ
fuelectenerg-1426	496	10	series	series	NOUN
fuelectenerg-1426	496	11	in	in	ADP
fuelectenerg-1426	496	12	the	the	DET
fuelectenerg-1426	496	13	design	design	NOUN
fuelectenerg-1426	496	14	of	of	ADP
fuelectenerg-1426	496	15	digital	digital	ADJ
fuelectenerg-1426	496	16	devices	device	NOUN
fuelectenerg-1426	496	17	,	,	PUNCT
fuelectenerg-1426	496	18	wiley	wiley	NOUN
fuelectenerg-1426	496	19	,	,	PUNCT
fuelectenerg-1426	496	20	1976	1976	NUM
fuelectenerg-1426	496	21	.	.	PUNCT
fuelectenerg-1426	497	1	[	[	X
fuelectenerg-1426	497	2	19	19	NUM
fuelectenerg-1426	497	3	]	]	X
fuelectenerg-1426	497	4	c.	c.	PROPN
fuelectenerg-1426	497	5	y.	y.	PROPN
fuelectenerg-1426	497	6	lee	lee	PROPN
fuelectenerg-1426	497	7	,	,	PUNCT
fuelectenerg-1426	497	8	"	"	PUNCT
fuelectenerg-1426	497	9	representation	representation	NOUN
fuelectenerg-1426	497	10	of	of	ADP
fuelectenerg-1426	497	11	switching	switch	VERB
fuelectenerg-1426	497	12	circuits	circuit	NOUN
fuelectenerg-1426	497	13	by	by	ADP
fuelectenerg-1426	497	14	binary	binary	ADJ
fuelectenerg-1426	497	15	decision	decision	NOUN
fuelectenerg-1426	497	16	diagrams	diagram	NOUN
fuelectenerg-1426	497	17	,	,	PUNCT
fuelectenerg-1426	497	18	"	"	PUNCT
fuelectenerg-1426	497	19	bell	bell	NOUN
fuelectenerg-1426	497	20	syst	syst	NOUN
fuelectenerg-1426	497	21	.	.	PUNCT
fuelectenerg-1426	498	1	tech	tech	PROPN
fuelectenerg-1426	498	2	.	.	PUNCT
fuelectenerg-1426	499	1	j.	j.	PROPN
fuelectenerg-1426	499	2	,	,	PUNCT
fuelectenerg-1426	499	3	vol	vol	NOUN
fuelectenerg-1426	499	4	.	.	PROPN
fuelectenerg-1426	499	5	38	38	NUM
fuelectenerg-1426	499	6	,	,	PUNCT
fuelectenerg-1426	499	7	pp	pp	ADJ
fuelectenerg-1426	499	8	.	.	PUNCT
fuelectenerg-1426	500	1	985	985	NUM
fuelectenerg-1426	500	2	-	-	SYM
fuelectenerg-1426	500	3	999	999	NUM
fuelectenerg-1426	500	4	,	,	PUNCT
fuelectenerg-1426	500	5	1959	1959	NUM
fuelectenerg-1426	500	6	.	.	PUNCT
fuelectenerg-1426	501	1	[	[	X
fuelectenerg-1426	501	2	20	20	NUM
fuelectenerg-1426	501	3	]	]	X
fuelectenerg-1426	501	4	c.	c.	PROPN
fuelectenerg-1426	501	5	moraga	moraga	PROPN
fuelectenerg-1426	501	6	,	,	PUNCT
fuelectenerg-1426	501	7	"	"	PUNCT
fuelectenerg-1426	501	8	ternary	ternary	ADJ
fuelectenerg-1426	501	9	spectral	spectral	ADJ
fuelectenerg-1426	501	10	logic	logic	NOUN
fuelectenerg-1426	501	11	,	,	PUNCT
fuelectenerg-1426	501	12	"	"	PUNCT
fuelectenerg-1426	501	13	proc	proc	NOUN
fuelectenerg-1426	501	14	.	.	PUNCT
fuelectenerg-1426	502	1	ismvl	ismvl	PROPN
fuelectenerg-1426	502	2	,	,	PUNCT
fuelectenerg-1426	502	3	pp	pp	ADJ
fuelectenerg-1426	502	4	.	.	PUNCT
fuelectenerg-1426	503	1	7	7	NUM
fuelectenerg-1426	503	2	-	-	SYM
fuelectenerg-1426	503	3	12	12	NUM
fuelectenerg-1426	503	4	,	,	PUNCT
fuelectenerg-1426	503	5	1977	1977	NUM
fuelectenerg-1426	503	6	.	.	PUNCT
fuelectenerg-1426	504	1	[	[	X
fuelectenerg-1426	504	2	21	21	NUM
fuelectenerg-1426	504	3	]	]	X
fuelectenerg-1426	504	4	j.	j.	PROPN
fuelectenerg-1426	504	5	c.	c.	PROPN
fuelectenerg-1426	504	6	muzio	muzio	PROPN
fuelectenerg-1426	504	7	and	and	CCONJ
fuelectenerg-1426	504	8	t.	t.	PROPN
fuelectenerg-1426	504	9	wesselkamper	wesselkamper	NOUN
fuelectenerg-1426	504	10	,	,	PUNCT
fuelectenerg-1426	504	11	multiple	multiple	ADV
fuelectenerg-1426	504	12	-	-	PUNCT
fuelectenerg-1426	504	13	valued	value	VERB
fuelectenerg-1426	504	14	switching	switching	NOUN
fuelectenerg-1426	504	15	theory	theory	NOUN
fuelectenerg-1426	504	16	,	,	PUNCT
fuelectenerg-1426	504	17	adam	adam	NOUN
fuelectenerg-1426	504	18	-	-	PUNCT
fuelectenerg-1426	504	19	hilger	hilger	NOUN
fuelectenerg-1426	504	20	,	,	PUNCT
fuelectenerg-1426	504	21	1985	1985	NUM
fuelectenerg-1426	504	22	.	.	PUNCT
fuelectenerg-1426	505	1	[	[	X
fuelectenerg-1426	505	2	22	22	NUM
fuelectenerg-1426	505	3	]	]	PUNCT
fuelectenerg-1426	505	4	d.	d.	PROPN
fuelectenerg-1426	505	5	k.	k.	PROPN
fuelectenerg-1426	505	6	pradhan	pradhan	PROPN
fuelectenerg-1426	505	7	,	,	PUNCT
fuelectenerg-1426	505	8	"	"	PUNCT
fuelectenerg-1426	505	9	universal	universal	ADJ
fuelectenerg-1426	505	10	test	test	NOUN
fuelectenerg-1426	505	11	sets	set	NOUN
fuelectenerg-1426	505	12	for	for	ADP
fuelectenerg-1426	505	13	multiple	multiple	ADJ
fuelectenerg-1426	505	14	fault	fault	NOUN
fuelectenerg-1426	505	15	detection	detection	NOUN
fuelectenerg-1426	505	16	in	in	ADP
fuelectenerg-1426	505	17	and	and	CCONJ
fuelectenerg-1426	505	18	-	-	PUNCT
fuelectenerg-1426	505	19	exor	exor	PROPN
fuelectenerg-1426	505	20	arrays	array	VERB
fuelectenerg-1426	505	21	,	,	PUNCT
fuelectenerg-1426	505	22	"	"	PUNCT
fuelectenerg-1426	505	23	ieee	ieee	NOUN
fuelectenerg-1426	505	24	trans	tran	NOUN
fuelectenerg-1426	505	25	.	.	PUNCT
fuelectenerg-1426	506	1	comp	comp	PROPN
fuelectenerg-1426	506	2	.	.	PUNCT
fuelectenerg-1426	506	3	,	,	PUNCT
fuelectenerg-1426	506	4	vol	vol	NOUN
fuelectenerg-1426	506	5	.	.	PROPN
fuelectenerg-1426	507	1	27	27	NUM
fuelectenerg-1426	507	2	,	,	PUNCT
fuelectenerg-1426	507	3	pp	pp	ADJ
fuelectenerg-1426	507	4	.	.	PUNCT
fuelectenerg-1426	508	1	181	181	NUM
fuelectenerg-1426	508	2	-	-	SYM
fuelectenerg-1426	508	3	187	187	NUM
fuelectenerg-1426	508	4	,	,	PUNCT
fuelectenerg-1426	508	5	1978	1978	NUM
fuelectenerg-1426	508	6	.	.	PUNCT
fuelectenerg-1426	509	1	[	[	X
fuelectenerg-1426	509	2	23	23	NUM
fuelectenerg-1426	509	3	]	]	X
fuelectenerg-1426	509	4	d.	d.	PROPN
fuelectenerg-1426	509	5	k.	k.	PROPN
fuelectenerg-1426	509	6	pradhan	pradhan	PROPN
fuelectenerg-1426	509	7	,	,	PUNCT
fuelectenerg-1426	509	8	fault	fault	NOUN
fuelectenerg-1426	509	9	-	-	PUNCT
fuelectenerg-1426	509	10	tolerant	tolerant	ADJ
fuelectenerg-1426	509	11	computing	computing	NOUN
fuelectenerg-1426	509	12	:	:	PUNCT
fuelectenerg-1426	509	13	theory	theory	NOUN
fuelectenerg-1426	509	14	and	and	CCONJ
fuelectenerg-1426	509	15	techniques	technique	NOUN
fuelectenerg-1426	509	16	,	,	PUNCT
fuelectenerg-1426	509	17	vol	vol	NOUN
fuelectenerg-1426	509	18	.	.	PUNCT
fuelectenerg-1426	510	1	i	i	PRON
fuelectenerg-1426	510	2	,	,	PUNCT
fuelectenerg-1426	510	3	prentice	prentice	NOUN
fuelectenerg-1426	510	4	-	-	PUNCT
fuelectenerg-1426	510	5	hall	hall	NOUN
fuelectenerg-1426	510	6	,	,	PUNCT
fuelectenerg-1426	510	7	1987	1987	NUM
fuelectenerg-1426	510	8	.	.	PUNCT
fuelectenerg-1426	511	1	[	[	X
fuelectenerg-1426	511	2	24	24	NUM
fuelectenerg-1426	511	3	]	]	X
fuelectenerg-1426	511	4	s.	s.	PROPN
fuelectenerg-1426	511	5	m.	m.	PROPN
fuelectenerg-1426	511	6	reddy	reddy	PROPN
fuelectenerg-1426	511	7	,	,	PUNCT
fuelectenerg-1426	511	8	"	"	PUNCT
fuelectenerg-1426	511	9	easily	easily	ADV
fuelectenerg-1426	511	10	testable	testable	ADJ
fuelectenerg-1426	511	11	realizations	realization	NOUN
fuelectenerg-1426	511	12	of	of	ADP
fuelectenerg-1426	511	13	logic	logic	NOUN
fuelectenerg-1426	511	14	functions	function	NOUN
fuelectenerg-1426	511	15	,	,	PUNCT
fuelectenerg-1426	511	16	"	"	PUNCT
fuelectenerg-1426	511	17	ieee	ieee	NOUN
fuelectenerg-1426	511	18	trans	tran	NOUN
fuelectenerg-1426	511	19	.	.	PUNCT
fuelectenerg-1426	512	1	comp	comp	PROPN
fuelectenerg-1426	512	2	.	.	PUNCT
fuelectenerg-1426	512	3	,	,	PUNCT
fuelectenerg-1426	512	4	c-21	c-21	PROPN
fuelectenerg-1426	512	5	,	,	PUNCT
fuelectenerg-1426	512	6	pp	pp	ADV
fuelectenerg-1426	512	7	.	.	PUNCT
fuelectenerg-1426	513	1	1183	1183	NUM
fuelectenerg-1426	513	2	-	-	SYM
fuelectenerg-1426	513	3	1188	1188	NUM
fuelectenerg-1426	513	4	,	,	PUNCT
fuelectenerg-1426	513	5	1972	1972	NUM
fuelectenerg-1426	513	6	.	.	PUNCT
fuelectenerg-1426	514	1	[	[	X
fuelectenerg-1426	514	2	25	25	NUM
fuelectenerg-1426	514	3	]	]	PUNCT
fuelectenerg-1426	514	4	t.	t.	PROPN
fuelectenerg-1426	514	5	sasao	sasao	PROPN
fuelectenerg-1426	514	6	(	(	PUNCT
fuelectenerg-1426	514	7	editor	editor	NOUN
fuelectenerg-1426	514	8	)	)	PUNCT
fuelectenerg-1426	514	9	,	,	PUNCT
fuelectenerg-1426	514	10	logic	logic	NOUN
fuelectenerg-1426	514	11	synthesis	synthesis	NOUN
fuelectenerg-1426	514	12	and	and	CCONJ
fuelectenerg-1426	514	13	optimization	optimization	NOUN
fuelectenerg-1426	514	14	,	,	PUNCT
fuelectenerg-1426	514	15	kluwer	kluwer	NOUN
fuelectenerg-1426	514	16	academic	academic	ADJ
fuelectenerg-1426	514	17	publishers	publisher	NOUN
fuelectenerg-1426	514	18	,	,	PUNCT
fuelectenerg-1426	514	19	1993	1993	NUM
fuelectenerg-1426	514	20	.	.	PUNCT
fuelectenerg-1426	515	1	[	[	X
fuelectenerg-1426	515	2	26	26	NUM
fuelectenerg-1426	515	3	]	]	PUNCT
fuelectenerg-1426	515	4	t.	t.	PROPN
fuelectenerg-1426	515	5	sasao	sasao	PROPN
fuelectenerg-1426	515	6	,	,	PUNCT
fuelectenerg-1426	515	7	"	"	PUNCT
fuelectenerg-1426	515	8	exmin2	exmin2	PROPN
fuelectenerg-1426	515	9	:	:	PUNCT
fuelectenerg-1426	515	10	a	a	DET
fuelectenerg-1426	515	11	simplified	simplified	ADJ
fuelectenerg-1426	515	12	algorithm	algorithm	NOUN
fuelectenerg-1426	515	13	for	for	ADP
fuelectenerg-1426	515	14	exclusive	exclusive	ADJ
fuelectenerg-1426	515	15	-	-	PUNCT
fuelectenerg-1426	515	16	or	or	CCONJ
fuelectenerg-1426	515	17	-	-	PUNCT
fuelectenerg-1426	515	18	sum	sum	NOUN
fuelectenerg-1426	515	19	-	-	PUNCT
fuelectenerg-1426	515	20	of	of	ADP
fuelectenerg-1426	515	21	-	-	PUNCT
fuelectenerg-1426	515	22	products	product	NOUN
fuelectenerg-1426	515	23	expressions	expression	NOUN
fuelectenerg-1426	515	24	for	for	ADP
fuelectenerg-1426	515	25	muliptle	muliptle	NOUN
fuelectenerg-1426	515	26	-	-	PUNCT
fuelectenerg-1426	515	27	valued	value	VERB
fuelectenerg-1426	515	28	input	input	NOUN
fuelectenerg-1426	515	29	two	two	NUM
fuelectenerg-1426	515	30	-	-	PUNCT
fuelectenerg-1426	515	31	valued	value	VERB
fuelectenerg-1426	515	32	output	output	NOUN
fuelectenerg-1426	515	33	functions	function	NOUN
fuelectenerg-1426	515	34	,	,	PUNCT
fuelectenerg-1426	515	35	"	"	PUNCT
fuelectenerg-1426	515	36	ieee	ieee	NOUN
fuelectenerg-1426	515	37	trans	tran	NOUN
fuelectenerg-1426	515	38	.	.	PUNCT
fuelectenerg-1426	516	1	computer	computer	NOUN
fuelectenerg-1426	516	2	aided	aid	VERB
fuelectenerg-1426	516	3	design	design	NOUN
fuelectenerg-1426	516	4	,	,	PUNCT
fuelectenerg-1426	516	5	vol	vol	NOUN
fuelectenerg-1426	516	6	.	.	PROPN
fuelectenerg-1426	517	1	12	12	NUM
fuelectenerg-1426	517	2	,	,	PUNCT
fuelectenerg-1426	517	3	no	no	INTJ
fuelectenerg-1426	517	4	.	.	NOUN
fuelectenerg-1426	517	5	5	5	NUM
fuelectenerg-1426	517	6	,	,	PUNCT
fuelectenerg-1426	517	7	pp	pp	ADJ
fuelectenerg-1426	517	8	.	.	PUNCT
fuelectenerg-1426	518	1	621	621	NUM
fuelectenerg-1426	518	2	-	-	SYM
fuelectenerg-1426	518	3	632	632	NUM
fuelectenerg-1426	518	4	,	,	PUNCT
fuelectenerg-1426	518	5	1993	1993	NUM
fuelectenerg-1426	518	6	.	.	PUNCT
fuelectenerg-1426	519	1	[	[	X
fuelectenerg-1426	519	2	27	27	NUM
fuelectenerg-1426	519	3	]	]	PUNCT
fuelectenerg-1426	519	4	t.	t.	PROPN
fuelectenerg-1426	519	5	sasao	sasao	PROPN
fuelectenerg-1426	519	6	and	and	CCONJ
fuelectenerg-1426	519	7	m.	m.	PROPN
fuelectenerg-1426	519	8	fujita	fujita	PROPN
fuelectenerg-1426	519	9	(	(	PUNCT
fuelectenerg-1426	519	10	editors	editor	NOUN
fuelectenerg-1426	519	11	)	)	PUNCT
fuelectenerg-1426	519	12	,	,	PUNCT
fuelectenerg-1426	519	13	representations	representation	NOUN
fuelectenerg-1426	519	14	of	of	ADP
fuelectenerg-1426	519	15	discrete	discrete	ADJ
fuelectenerg-1426	519	16	functions	function	NOUN
fuelectenerg-1426	519	17	,	,	PUNCT
fuelectenerg-1426	519	18	kluwer	kluwer	NOUN
fuelectenerg-1426	519	19	academic	academic	ADJ
fuelectenerg-1426	519	20	publishers	publisher	NOUN
fuelectenerg-1426	519	21	,	,	PUNCT
fuelectenerg-1426	519	22	1996	1996	NUM
fuelectenerg-1426	519	23	.	.	PUNCT
fuelectenerg-1426	520	1	[	[	X
fuelectenerg-1426	520	2	28	28	NUM
fuelectenerg-1426	520	3	]	]	X
fuelectenerg-1426	520	4	t.	t.	PROPN
fuelectenerg-1426	520	5	sasao	sasao	PROPN
fuelectenerg-1426	520	6	,	,	PUNCT
fuelectenerg-1426	520	7	"	"	PUNCT
fuelectenerg-1426	520	8	easily	easily	ADV
fuelectenerg-1426	520	9	testable	testable	ADJ
fuelectenerg-1426	520	10	realizations	realization	NOUN
fuelectenerg-1426	520	11	for	for	ADP
fuelectenerg-1426	520	12	generalized	generalized	ADJ
fuelectenerg-1426	520	13	reed	reed	NOUN
fuelectenerg-1426	520	14	-	-	PUNCT
fuelectenerg-1426	520	15	muller	muller	NOUN
fuelectenerg-1426	520	16	expressions	expression	NOUN
fuelectenerg-1426	520	17	,	,	PUNCT
fuelectenerg-1426	520	18	"	"	PUNCT
fuelectenerg-1426	520	19	ieee	ieee	NOUN
fuelectenerg-1426	520	20	trans	tran	NOUN
fuelectenerg-1426	520	21	.	.	PUNCT
fuelectenerg-1426	521	1	comp	comp	PROPN
fuelectenerg-1426	521	2	.	.	PUNCT
fuelectenerg-1426	521	3	,	,	PUNCT
fuelectenerg-1426	521	4	vol	vol	NOUN
fuelectenerg-1426	521	5	.	.	PROPN
fuelectenerg-1426	522	1	46	46	NUM
fuelectenerg-1426	522	2	,	,	PUNCT
fuelectenerg-1426	522	3	pp	pp	ADJ
fuelectenerg-1426	522	4	.	.	PUNCT
fuelectenerg-1426	523	1	709	709	NUM
fuelectenerg-1426	523	2	-	-	PUNCT
fuelectenerg-1426	523	3	716	716	NUM
fuelectenerg-1426	523	4	,	,	PUNCT
fuelectenerg-1426	523	5	1997	1997	NUM
fuelectenerg-1426	523	6	.	.	PUNCT
fuelectenerg-1426	524	1	[	[	X
fuelectenerg-1426	524	2	29	29	NUM
fuelectenerg-1426	524	3	]	]	X
fuelectenerg-1426	524	4	t.	t.	PROPN
fuelectenerg-1426	524	5	sasao	sasao	PROPN
fuelectenerg-1426	524	6	,	,	PUNCT
fuelectenerg-1426	524	7	switching	switch	VERB
fuelectenerg-1426	524	8	theory	theory	NOUN
fuelectenerg-1426	524	9	for	for	ADP
fuelectenerg-1426	524	10	logic	logic	NOUN
fuelectenerg-1426	524	11	synthesis	synthesis	NOUN
fuelectenerg-1426	524	12	,	,	PUNCT
fuelectenerg-1426	524	13	kluwer	kluwer	NOUN
fuelectenerg-1426	524	14	academic	academic	ADJ
fuelectenerg-1426	524	15	publishers	publisher	NOUN
fuelectenerg-1426	524	16	,	,	PUNCT
fuelectenerg-1426	524	17	1999	1999	NUM
fuelectenerg-1426	524	18	.	.	PUNCT
fuelectenerg-1426	525	1	[	[	X
fuelectenerg-1426	525	2	30	30	NUM
fuelectenerg-1426	525	3	]	]	X
fuelectenerg-1426	525	4	n.	n.	NOUN
fuelectenerg-1426	525	5	song	song	NOUN
fuelectenerg-1426	525	6	and	and	CCONJ
fuelectenerg-1426	525	7	m.	m.	NOUN
fuelectenerg-1426	525	8	perkowski	perkowski	PROPN
fuelectenerg-1426	525	9	,	,	PUNCT
fuelectenerg-1426	525	10	"	"	PUNCT
fuelectenerg-1426	525	11	minimization	minimization	NOUN
fuelectenerg-1426	525	12	of	of	ADP
fuelectenerg-1426	525	13	exclusive	exclusive	ADJ
fuelectenerg-1426	525	14	sum	sum	NOUN
fuelectenerg-1426	525	15	of	of	ADP
fuelectenerg-1426	525	16	products	product	NOUN
fuelectenerg-1426	525	17	expressions	expression	NOUN
fuelectenerg-1426	525	18	for	for	ADP
fuelectenerg-1426	525	19	multioutput	multioutput	ADJ
fuelectenerg-1426	525	20	multiple	multiple	ADV
fuelectenerg-1426	525	21	-	-	PUNCT
fuelectenerg-1426	525	22	valued	value	VERB
fuelectenerg-1426	525	23	input	input	NOUN
fuelectenerg-1426	525	24	incompletely	incompletely	ADV
fuelectenerg-1426	525	25	specified	specify	VERB
fuelectenerg-1426	525	26	functions	function	NOUN
fuelectenerg-1426	525	27	,	,	PUNCT
fuelectenerg-1426	525	28	"	"	PUNCT
fuelectenerg-1426	525	29	ieee	ieee	NOUN
fuelectenerg-1426	525	30	trans	tran	NOUN
fuelectenerg-1426	525	31	.	.	PUNCT
fuelectenerg-1426	526	1	computer	computer	NOUN
fuelectenerg-1426	526	2	aided	aid	VERB
fuelectenerg-1426	526	3	design	design	NOUN
fuelectenerg-1426	526	4	,	,	PUNCT
fuelectenerg-1426	526	5	vol	vol	NOUN
fuelectenerg-1426	526	6	.	.	PROPN
fuelectenerg-1426	526	7	15	15	NUM
fuelectenerg-1426	526	8	,	,	PUNCT
fuelectenerg-1426	526	9	no	no	INTJ
fuelectenerg-1426	526	10	.	.	NOUN
fuelectenerg-1426	526	11	4	4	NUM
fuelectenerg-1426	526	12	,	,	PUNCT
fuelectenerg-1426	526	13	pp	pp	ADJ
fuelectenerg-1426	526	14	.	.	PUNCT
fuelectenerg-1426	527	1	385	385	NUM
fuelectenerg-1426	527	2	-	-	SYM
fuelectenerg-1426	527	3	395	395	NUM
fuelectenerg-1426	527	4	,	,	PUNCT
fuelectenerg-1426	527	5	1996	1996	NUM
fuelectenerg-1426	527	6	.	.	PUNCT
fuelectenerg-1426	528	1	[	[	X
fuelectenerg-1426	528	2	31	31	NUM
fuelectenerg-1426	528	3	]	]	PUNCT
fuelectenerg-1426	528	4	r.	r.	PROPN
fuelectenerg-1426	528	5	s.	s.	PROPN
fuelectenerg-1426	528	6	stanković	stanković	PROPN
fuelectenerg-1426	528	7	,	,	PUNCT
fuelectenerg-1426	528	8	"	"	PUNCT
fuelectenerg-1426	528	9	functional	functional	ADJ
fuelectenerg-1426	528	10	decision	decision	NOUN
fuelectenerg-1426	528	11	diagrams	diagram	NOUN
fuelectenerg-1426	528	12	for	for	ADP
fuelectenerg-1426	528	13	multiple	multiple	ADV
fuelectenerg-1426	528	14	-	-	PUNCT
fuelectenerg-1426	528	15	valued	value	VERB
fuelectenerg-1426	528	16	functions	function	NOUN
fuelectenerg-1426	528	17	,	,	PUNCT
fuelectenerg-1426	528	18	"	"	PUNCT
fuelectenerg-1426	528	19	proc	proc	NOUN
fuelectenerg-1426	528	20	.	.	PUNCT
fuelectenerg-1426	529	1	ismvl	ismvl	PROPN
fuelectenerg-1426	529	2	,	,	PUNCT
fuelectenerg-1426	529	3	1995	1995	NUM
fuelectenerg-1426	529	4	,	,	PUNCT
fuelectenerg-1426	529	5	pp	pp	ADJ
fuelectenerg-1426	529	6	.	.	PUNCT
fuelectenerg-1426	530	1	284	284	NUM
fuelectenerg-1426	530	2	-	-	SYM
fuelectenerg-1426	530	3	289	289	NUM
fuelectenerg-1426	530	4	.	.	PUNCT
fuelectenerg-1426	531	1	[	[	X
fuelectenerg-1426	531	2	32	32	NUM
fuelectenerg-1426	531	3	]	]	PUNCT
fuelectenerg-1426	531	4	r.	r.	PROPN
fuelectenerg-1426	531	5	s.	s.	PROPN
fuelectenerg-1426	531	6	stankovic	stankovic	PROPN
fuelectenerg-1426	531	7	,	,	PUNCT
fuelectenerg-1426	531	8	spectral	spectral	ADJ
fuelectenerg-1426	531	9	transform	transform	VERB
fuelectenerg-1426	531	10	decision	decision	NOUN
fuelectenerg-1426	531	11	diagrams	diagram	NOUN
fuelectenerg-1426	531	12	in	in	ADP
fuelectenerg-1426	531	13	simple	simple	ADJ
fuelectenerg-1426	531	14	questions	question	NOUN
fuelectenerg-1426	531	15	and	and	CCONJ
fuelectenerg-1426	531	16	simple	simple	ADJ
fuelectenerg-1426	531	17	answers	answer	NOUN
fuelectenerg-1426	531	18	,	,	PUNCT
fuelectenerg-1426	531	19	nauka	nauka	PROPN
fuelectenerg-1426	531	20	,	,	PUNCT
fuelectenerg-1426	531	21	1998	1998	NUM
fuelectenerg-1426	531	22	.	.	PUNCT
fuelectenerg-1426	532	1	[	[	X
fuelectenerg-1426	532	2	33	33	NUM
fuelectenerg-1426	532	3	]	]	PUNCT
fuelectenerg-1426	532	4	r.	r.	PROPN
fuelectenerg-1426	532	5	s.	s.	PROPN
fuelectenerg-1426	532	6	stanković	stanković	PROPN
fuelectenerg-1426	532	7	,	,	PUNCT
fuelectenerg-1426	532	8	c.	c.	PROPN
fuelectenerg-1426	532	9	moraga	moraga	PROPN
fuelectenerg-1426	532	10	,	,	PUNCT
fuelectenerg-1426	532	11	and	and	CCONJ
fuelectenerg-1426	532	12	j.	j.	PROPN
fuelectenerg-1426	532	13	t.	t.	PROPN
fuelectenerg-1426	532	14	astola	astola	PROPN
fuelectenerg-1426	532	15	,	,	PUNCT
fuelectenerg-1426	532	16	"	"	PUNCT
fuelectenerg-1426	532	17	reed	reed	NOUN
fuelectenerg-1426	532	18	-	-	PUNCT
fuelectenerg-1426	532	19	muller	muller	NOUN
fuelectenerg-1426	532	20	expressions	expression	NOUN
fuelectenerg-1426	532	21	in	in	ADP
fuelectenerg-1426	532	22	the	the	DET
fuelectenerg-1426	532	23	previous	previous	ADJ
fuelectenerg-1426	532	24	decade	decade	NOUN
fuelectenerg-1426	532	25	,	,	PUNCT
fuelectenerg-1426	532	26	"	"	PUNCT
fuelectenerg-1426	532	27	proc	proc	NOUN
fuelectenerg-1426	532	28	.	.	PUNCT
fuelectenerg-1426	533	1	reed	reed	NOUN
fuelectenerg-1426	533	2	-	-	PUNCT
fuelectenerg-1426	533	3	muller	muller	NOUN
fuelectenerg-1426	533	4	,	,	PUNCT
fuelectenerg-1426	533	5	starkville	starkville	PROPN
fuelectenerg-1426	533	6	,	,	PUNCT
fuelectenerg-1426	533	7	2001	2001	NUM
fuelectenerg-1426	533	8	,	,	PUNCT
fuelectenerg-1426	533	9	pp	pp	ADJ
fuelectenerg-1426	533	10	.	.	PUNCT
fuelectenerg-1426	534	1	7	7	NUM
fuelectenerg-1426	534	2	-	-	SYM
fuelectenerg-1426	534	3	26	26	NUM
fuelectenerg-1426	534	4	.	.	PUNCT
fuelectenerg-1426	535	1	[	[	X
fuelectenerg-1426	535	2	34	34	NUM
fuelectenerg-1426	535	3	]	]	PUNCT
fuelectenerg-1426	535	4	b.	b.	PROPN
fuelectenerg-1426	535	5	steinbach	steinbach	PROPN
fuelectenerg-1426	535	6	and	and	CCONJ
fuelectenerg-1426	535	7	a.	a.	NOUN
fuelectenerg-1426	535	8	mishchenko	mishchenko	PROPN
fuelectenerg-1426	535	9	,	,	PUNCT
fuelectenerg-1426	535	10	"	"	PUNCT
fuelectenerg-1426	535	11	a	a	DET
fuelectenerg-1426	535	12	new	new	ADJ
fuelectenerg-1426	535	13	approach	approach	NOUN
fuelectenerg-1426	535	14	to	to	PART
fuelectenerg-1426	535	15	exact	exact	VERB
fuelectenerg-1426	535	16	esop	esop	PROPN
fuelectenerg-1426	535	17	minimization	minimization	NOUN
fuelectenerg-1426	535	18	,	,	PUNCT
fuelectenerg-1426	535	19	"	"	PUNCT
fuelectenerg-1426	535	20	proc	proc	NOUN
fuelectenerg-1426	535	21	.	.	PUNCT
fuelectenerg-1426	536	1	reedmuller	reedmuller	PROPN
fuelectenerg-1426	536	2	,	,	PUNCT
fuelectenerg-1426	536	3	starkville	starkville	PROPN
fuelectenerg-1426	536	4	,	,	PUNCT
fuelectenerg-1426	536	5	2001	2001	NUM
fuelectenerg-1426	536	6	,	,	PUNCT
fuelectenerg-1426	536	7	pp	pp	ADJ
fuelectenerg-1426	536	8	.	.	PUNCT
fuelectenerg-1426	537	1	66	66	NUM
fuelectenerg-1426	537	2	-	-	SYM
fuelectenerg-1426	537	3	81	81	NUM
fuelectenerg-1426	537	4	.	.	PUNCT
fuelectenerg-1426	538	1	[	[	X
fuelectenerg-1426	538	2	35	35	NUM
fuelectenerg-1426	538	3	]	]	PUNCT
fuelectenerg-1426	538	4	s.	s.	PROPN
fuelectenerg-1426	538	5	n.	n.	PROPN
fuelectenerg-1426	538	6	yanushkevich	yanushkevich	PROPN
fuelectenerg-1426	538	7	,	,	PUNCT
fuelectenerg-1426	538	8	logic	logic	NOUN
fuelectenerg-1426	538	9	differential	differential	NOUN
fuelectenerg-1426	538	10	calculus	calculus	NOUN
fuelectenerg-1426	538	11	in	in	ADP
fuelectenerg-1426	538	12	multi	multi	ADJ
fuelectenerg-1426	538	13	-	-	ADJ
fuelectenerg-1426	538	14	valued	value	VERB
fuelectenerg-1426	538	15	logic	logic	NOUN
fuelectenerg-1426	538	16	design	design	NOUN
fuelectenerg-1426	538	17	,	,	PUNCT
fuelectenerg-1426	538	18	technical	technical	PROPN
fuelectenerg-1426	538	19	univ	univ	PROPN
fuelectenerg-1426	538	20	.	.	PUNCT
fuelectenerg-1426	539	1	szczecin	szczecin	PROPN
fuelectenerg-1426	539	2	,	,	PUNCT
fuelectenerg-1426	539	3	1998	1998	NUM
fuelectenerg-1426	539	4	.	.	PUNCT
fuelectenerg-1426	540	1	[	[	X
fuelectenerg-1426	540	2	36	36	NUM
fuelectenerg-1426	540	3	]	]	X
fuelectenerg-1426	540	4	i.	i.	NOUN
fuelectenerg-1426	540	5	zhegalkin	zhegalkin	PROPN
fuelectenerg-1426	540	6	,	,	PUNCT
fuelectenerg-1426	540	7	"	"	PUNCT
fuelectenerg-1426	540	8	on	on	ADP
fuelectenerg-1426	540	9	the	the	DET
fuelectenerg-1426	540	10	techniques	technique	NOUN
fuelectenerg-1426	540	11	of	of	ADP
fuelectenerg-1426	540	12	calculating	calculate	VERB
fuelectenerg-1426	540	13	sentences	sentence	NOUN
fuelectenerg-1426	540	14	in	in	ADP
fuelectenerg-1426	540	15	symbolic	symbolic	ADJ
fuelectenerg-1426	540	16	logic	logic	NOUN
fuelectenerg-1426	540	17	,	,	PUNCT
fuelectenerg-1426	540	18	"	"	PUNCT
fuelectenerg-1426	540	19	math	math	NOUN
fuelectenerg-1426	540	20	.	.	PUNCT
fuelectenerg-1426	541	1	sb	sb	PROPN
fuelectenerg-1426	541	2	.	.	PROPN
fuelectenerg-1426	541	3	,	,	PUNCT
fuelectenerg-1426	541	4	vol	vol	NOUN
fuelectenerg-1426	541	5	.	.	PROPN
fuelectenerg-1426	542	1	34	34	NUM
fuelectenerg-1426	542	2	,	,	PUNCT
fuelectenerg-1426	542	3	pp	pp	ADJ
fuelectenerg-1426	542	4	.	.	PUNCT
fuelectenerg-1426	543	1	9	9	NUM
fuelectenerg-1426	543	2	-	-	SYM
fuelectenerg-1426	543	3	28	28	NUM
fuelectenerg-1426	543	4	,	,	PUNCT
fuelectenerg-1426	543	5	1927	1927	NUM
fuelectenerg-1426	543	6	.	.	PUNCT
fuelectenerg-1426	544	1	[	[	X
fuelectenerg-1426	544	2	37	37	NUM
fuelectenerg-1426	544	3	]	]	X
fuelectenerg-1426	544	4	i.	i.	NOUN
fuelectenerg-1426	544	5	zhegalkin	zhegalkin	PROPN
fuelectenerg-1426	544	6	,	,	PUNCT
fuelectenerg-1426	544	7	"	"	PUNCT
fuelectenerg-1426	544	8	arithmetic	arithmetic	ADJ
fuelectenerg-1426	544	9	representations	representation	NOUN
fuelectenerg-1426	544	10	for	for	ADP
fuelectenerg-1426	544	11	symbolic	symbolic	ADJ
fuelectenerg-1426	544	12	logic	logic	NOUN
fuelectenerg-1426	544	13	,	,	PUNCT
fuelectenerg-1426	544	14	"	"	PUNCT
fuelectenerg-1426	544	15	math	math	NOUN
fuelectenerg-1426	544	16	.	.	PUNCT
fuelectenerg-1426	545	1	sb	sb	PROPN
fuelectenerg-1426	545	2	.	.	PROPN
fuelectenerg-1426	545	3	,	,	PUNCT
fuelectenerg-1426	545	4	vol	vol	NOUN
fuelectenerg-1426	545	5	.	.	PROPN
fuelectenerg-1426	545	6	35	35	NUM
fuelectenerg-1426	545	7	,	,	PUNCT
fuelectenerg-1426	546	1	pp	pp	ADJ
fuelectenerg-1426	546	2	.	.	PUNCT
fuelectenerg-1426	547	1	311	311	NUM
fuelectenerg-1426	547	2	-	-	SYM
fuelectenerg-1426	547	3	377	377	NUM
fuelectenerg-1426	547	4	,	,	PUNCT
fuelectenerg-1426	547	5	1928	1928	NUM
fuelectenerg-1426	547	6	.	.	PUNCT
fuelectenerg-1426	548	1	120	120	NUM
fuelectenerg-1426	548	2	multi	multi	ADJ
fuelectenerg-1426	548	3	-	-	ADJ
fuelectenerg-1426	548	4	valued	value	VERB
fuelectenerg-1426	548	5	galois	galois	PROPN
fuelectenerg-1426	548	6	shannon	shannon	PROPN
fuelectenerg-1426	548	7	davio	davio	PROPN
fuelectenerg-1426	548	8	trees	tree	NOUN
fuelectenerg-1426	548	9	and	and	CCONJ
fuelectenerg-1426	548	10	their	their	PRON
fuelectenerg-1426	548	11	complexity	complexity	NOUN
fuelectenerg-1426	548	12	future	future	ADJ
fuelectenerg-1426	548	13	work	work	NOUN
fuelectenerg-1426	548	14	will	will	AUX
fuelectenerg-1426	548	15	investigate	investigate	VERB
fuelectenerg-1426	548	16	using	use	VERB
fuelectenerg-1426	548	17	other	other	ADJ
fuelectenerg-1426	548	18	complex	complex	ADJ
fuelectenerg-1426	548	19	types	type	NOUN
fuelectenerg-1426	548	20	of	of	ADP
fuelectenerg-1426	548	21	literals	literal	NOUN
fuelectenerg-1426	548	22	such	such	ADJ
fuelectenerg-1426	548	23	as	as	ADP
fuelectenerg-1426	548	24	the	the	DET
fuelectenerg-1426	548	25	presented	present	VERB
fuelectenerg-1426	548	26	post	post	NOUN
fuelectenerg-1426	548	27	literal	literal	ADJ
fuelectenerg-1426	548	28	(	(	PUNCT
fuelectenerg-1426	548	29	pl	pl	NOUN
fuelectenerg-1426	548	30	)	)	PUNCT
fuelectenerg-1426	548	31	and	and	CCONJ
fuelectenerg-1426	548	32	window	window	NOUN
fuelectenerg-1426	548	33	literal	literal	NOUN
fuelectenerg-1426	548	34	(	(	PUNCT
fuelectenerg-1426	548	35	wl	wl	NOUN
fuelectenerg-1426	548	36	)	)	PUNCT
fuelectenerg-1426	548	37	to	to	PART
fuelectenerg-1426	548	38	expand	expand	VERB
fuelectenerg-1426	548	39	upon	upon	SCONJ
fuelectenerg-1426	548	40	and	and	CCONJ
fuelectenerg-1426	548	41	consequently	consequently	ADV
fuelectenerg-1426	548	42	construct	construct	VERB
fuelectenerg-1426	548	43	the	the	DET
fuelectenerg-1426	548	44	corresponding	correspond	VERB
fuelectenerg-1426	548	45	new	new	ADJ
fuelectenerg-1426	548	46	s	s	PROPN
fuelectenerg-1426	548	47	/	/	SYM
fuelectenerg-1426	548	48	d	d	NOUN
fuelectenerg-1426	548	49	trees	tree	NOUN
fuelectenerg-1426	548	50	.	.	PUNCT
fuelectenerg-1426	549	1	the	the	DET
fuelectenerg-1426	549	2	utilization	utilization	NOUN
fuelectenerg-1426	549	3	of	of	ADP
fuelectenerg-1426	549	4	the	the	DET
fuelectenerg-1426	549	5	results	result	NOUN
fuelectenerg-1426	549	6	from	from	ADP
fuelectenerg-1426	549	7	this	this	DET
fuelectenerg-1426	549	8	research	research	NOUN
fuelectenerg-1426	549	9	to	to	PART
fuelectenerg-1426	549	10	create	create	VERB
fuelectenerg-1426	549	11	an	an	DET
fuelectenerg-1426	549	12	efficient	efficient	ADJ
fuelectenerg-1426	549	13	gfsop	gfsop	NOUN
fuelectenerg-1426	549	14	minimizer	minimizer	NOUN
fuelectenerg-1426	549	15	for	for	ADP
fuelectenerg-1426	549	16	synthesis	synthesis	NOUN
fuelectenerg-1426	549	17	applications	application	NOUN
fuelectenerg-1426	549	18	within	within	ADP
fuelectenerg-1426	549	19	the	the	DET
fuelectenerg-1426	549	20	spaces	space	NOUN
fuelectenerg-1426	549	21	of	of	ADP
fuelectenerg-1426	549	22	classical	classical	ADJ
fuelectenerg-1426	549	23	and	and	CCONJ
fuelectenerg-1426	549	24	reversible	reversible	ADJ
fuelectenerg-1426	549	25	logic	logic	NOUN
fuelectenerg-1426	549	26	will	will	AUX
fuelectenerg-1426	549	27	also	also	ADV
fuelectenerg-1426	549	28	be	be	AUX
fuelectenerg-1426	549	29	conducted	conduct	VERB
fuelectenerg-1426	549	30	.	.	PUNCT
fuelectenerg-1426	550	1	references	reference	NOUN
fuelectenerg-1426	550	2	[	[	X
fuelectenerg-1426	550	3	1	1	X
fuelectenerg-1426	550	4	]	]	PUNCT
fuelectenerg-1426	550	5	s.	s.	PROPN
fuelectenerg-1426	550	6	b.	b.	PROPN
fuelectenerg-1426	550	7	akers	akers	PROPN
fuelectenerg-1426	550	8	,	,	PUNCT
fuelectenerg-1426	550	9	"	"	PUNCT
fuelectenerg-1426	550	10	binary	binary	ADJ
fuelectenerg-1426	550	11	decision	decision	NOUN
fuelectenerg-1426	550	12	diagrams	diagram	NOUN
fuelectenerg-1426	550	13	,	,	PUNCT
fuelectenerg-1426	550	14	"	"	PUNCT
fuelectenerg-1426	550	15	ieee	ieee	NOUN
fuelectenerg-1426	550	16	trans	tran	NOUN
fuelectenerg-1426	550	17	.	.	PUNCT
fuelectenerg-1426	551	1	comp	comp	PROPN
fuelectenerg-1426	551	2	.	.	PUNCT
fuelectenerg-1426	551	3	,	,	PUNCT
fuelectenerg-1426	551	4	vol	vol	NOUN
fuelectenerg-1426	551	5	.	.	PUNCT
fuelectenerg-1426	552	1	c-27	c-27	PROPN
fuelectenerg-1426	552	2	,	,	PUNCT
fuelectenerg-1426	552	3	no	no	INTJ
fuelectenerg-1426	552	4	.	.	NOUN
fuelectenerg-1426	552	5	6	6	NUM
fuelectenerg-1426	552	6	,	,	PUNCT
fuelectenerg-1426	552	7	pp	pp	ADJ
fuelectenerg-1426	552	8	.	.	PUNCT
fuelectenerg-1426	553	1	509	509	NUM
fuelectenerg-1426	553	2	-	-	SYM
fuelectenerg-1426	553	3	516	516	NUM
fuelectenerg-1426	553	4	,	,	PUNCT
fuelectenerg-1426	553	5	june	june	PROPN
fuelectenerg-1426	553	6	1978	1978	NUM
fuelectenerg-1426	553	7	.	.	PUNCT
fuelectenerg-1426	554	1	[	[	X
fuelectenerg-1426	554	2	2	2	NUM
fuelectenerg-1426	554	3	]	]	PUNCT
fuelectenerg-1426	554	4	a.	a.	NOUN
fuelectenerg-1426	554	5	n.	n.	PROPN
fuelectenerg-1426	554	6	al	al	PROPN
fuelectenerg-1426	554	7	-	-	PUNCT
fuelectenerg-1426	554	8	rabadi	rabadi	PROPN
fuelectenerg-1426	554	9	,	,	PUNCT
fuelectenerg-1426	554	10	reversible	reversible	ADJ
fuelectenerg-1426	554	11	logic	logic	NOUN
fuelectenerg-1426	554	12	synthesis	synthesis	NOUN
fuelectenerg-1426	554	13	:	:	PUNCT
fuelectenerg-1426	554	14	from	from	ADP
fuelectenerg-1426	554	15	fundamentals	fundamental	NOUN
fuelectenerg-1426	554	16	to	to	ADP
fuelectenerg-1426	554	17	quantum	quantum	ADJ
fuelectenerg-1426	554	18	computing	computing	NOUN
fuelectenerg-1426	554	19	,	,	PUNCT
fuelectenerg-1426	554	20	springer	springer	NOUN
fuelectenerg-1426	554	21	-	-	PUNCT
fuelectenerg-1426	554	22	verlag	verlag	PROPN
fuelectenerg-1426	554	23	,	,	PUNCT
fuelectenerg-1426	554	24	2004	2004	NUM
fuelectenerg-1426	554	25	.	.	PUNCT
fuelectenerg-1426	555	1	[	[	X
fuelectenerg-1426	555	2	3	3	NUM
fuelectenerg-1426	555	3	]	]	PUNCT
fuelectenerg-1426	555	4	a.	a.	NOUN
fuelectenerg-1426	555	5	n.	n.	PROPN
fuelectenerg-1426	555	6	al	al	PROPN
fuelectenerg-1426	555	7	-	-	PUNCT
fuelectenerg-1426	555	8	rabadi	rabadi	PROPN
fuelectenerg-1426	555	9	,	,	PUNCT
fuelectenerg-1426	555	10	"	"	PUNCT
fuelectenerg-1426	555	11	reversible	reversible	ADJ
fuelectenerg-1426	555	12	fast	fast	ADJ
fuelectenerg-1426	555	13	permutation	permutation	NOUN
fuelectenerg-1426	555	14	transforms	transform	VERB
fuelectenerg-1426	555	15	for	for	ADP
fuelectenerg-1426	555	16	quantum	quantum	ADJ
fuelectenerg-1426	555	17	circuit	circuit	NOUN
fuelectenerg-1426	555	18	synthesis	synthesis	NOUN
fuelectenerg-1426	555	19	,	,	PUNCT
fuelectenerg-1426	555	20	"	"	PUNCT
fuelectenerg-1426	555	21	proc	proc	NOUN
fuelectenerg-1426	555	22	.	.	PUNCT
fuelectenerg-1426	556	1	ieee	ieee	PROPN
fuelectenerg-1426	556	2	int	int	PROPN
fuelectenerg-1426	556	3	.	.	PUNCT
fuelectenerg-1426	557	1	symposium	symposium	NOUN
fuelectenerg-1426	557	2	on	on	ADP
fuelectenerg-1426	557	3	multiple	multiple	ADV
fuelectenerg-1426	557	4	-	-	PUNCT
fuelectenerg-1426	557	5	valued	value	VERB
fuelectenerg-1426	557	6	logic	logic	NOUN
fuelectenerg-1426	557	7	(	(	PUNCT
fuelectenerg-1426	557	8	ismvl	ismvl	PROPN
fuelectenerg-1426	557	9	)	)	PUNCT
fuelectenerg-1426	557	10	,	,	PUNCT
fuelectenerg-1426	557	11	toronto	toronto	PROPN
fuelectenerg-1426	557	12	,	,	PUNCT
fuelectenerg-1426	557	13	2004	2004	NUM
fuelectenerg-1426	557	14	,	,	PUNCT
fuelectenerg-1426	557	15	pp	pp	PROPN
fuelectenerg-1426	557	16	.	.	PUNCT
fuelectenerg-1426	558	1	81	81	NUM
fuelectenerg-1426	558	2	-	-	SYM
fuelectenerg-1426	558	3	86	86	NUM
fuelectenerg-1426	558	4	.	.	PUNCT
fuelectenerg-1426	559	1	[	[	X
fuelectenerg-1426	559	2	4	4	NUM
fuelectenerg-1426	559	3	]	]	PUNCT
fuelectenerg-1426	559	4	a.	a.	NOUN
fuelectenerg-1426	559	5	n.	n.	PROPN
fuelectenerg-1426	559	6	al	al	PROPN
fuelectenerg-1426	559	7	-	-	PUNCT
fuelectenerg-1426	559	8	rabadi	rabadi	PROPN
fuelectenerg-1426	559	9	,	,	PUNCT
fuelectenerg-1426	559	10	"	"	PUNCT
fuelectenerg-1426	559	11	quantum	quantum	ADJ
fuelectenerg-1426	559	12	circuit	circuit	NOUN
fuelectenerg-1426	559	13	synthesis	synthesis	NOUN
fuelectenerg-1426	559	14	using	use	VERB
fuelectenerg-1426	559	15	classes	class	NOUN
fuelectenerg-1426	559	16	of	of	ADP
fuelectenerg-1426	559	17	gf(3	gf(3	NOUN
fuelectenerg-1426	559	18	)	)	PUNCT
fuelectenerg-1426	559	19	reversible	reversible	ADJ
fuelectenerg-1426	559	20	fast	fast	ADJ
fuelectenerg-1426	559	21	spectral	spectral	ADJ
fuelectenerg-1426	559	22	transforms	transform	NOUN
fuelectenerg-1426	559	23	,	,	PUNCT
fuelectenerg-1426	559	24	"	"	PUNCT
fuelectenerg-1426	559	25	proc	proc	NOUN
fuelectenerg-1426	559	26	.	.	PUNCT
fuelectenerg-1426	560	1	ieee	ieee	PROPN
fuelectenerg-1426	560	2	int	int	PROPN
fuelectenerg-1426	560	3	.	.	PUNCT
fuelectenerg-1426	561	1	symposium	symposium	NOUN
fuelectenerg-1426	561	2	on	on	ADP
fuelectenerg-1426	561	3	multiple	multiple	ADV
fuelectenerg-1426	561	4	-	-	PUNCT
fuelectenerg-1426	561	5	valued	value	VERB
fuelectenerg-1426	561	6	logic	logic	NOUN
fuelectenerg-1426	561	7	(	(	PUNCT
fuelectenerg-1426	561	8	ismvl	ismvl	PROPN
fuelectenerg-1426	561	9	)	)	PUNCT
fuelectenerg-1426	561	10	,	,	PUNCT
fuelectenerg-1426	561	11	toronto	toronto	PROPN
fuelectenerg-1426	561	12	,	,	PUNCT
fuelectenerg-1426	561	13	2004	2004	NUM
fuelectenerg-1426	561	14	,	,	PUNCT
fuelectenerg-1426	561	15	pp	pp	ADV
fuelectenerg-1426	561	16	.	.	PUNCT
fuelectenerg-1426	562	1	87	87	NUM
fuelectenerg-1426	562	2	-	-	SYM
fuelectenerg-1426	562	3	93	93	NUM
fuelectenerg-1426	562	4	.	.	PUNCT
fuelectenerg-1426	563	1	[	[	PUNCT
fuelectenerg-1426	563	2	5	5	NUM
fuelectenerg-1426	563	3	]	]	PUNCT
fuelectenerg-1426	563	4	a.	a.	NOUN
fuelectenerg-1426	563	5	n.	n.	PROPN
fuelectenerg-1426	563	6	al	al	PROPN
fuelectenerg-1426	563	7	-	-	PUNCT
fuelectenerg-1426	563	8	rabadi	rabadi	PROPN
fuelectenerg-1426	563	9	,	,	PUNCT
fuelectenerg-1426	563	10	"	"	PUNCT
fuelectenerg-1426	563	11	quantum	quantum	ADJ
fuelectenerg-1426	563	12	logic	logic	NOUN
fuelectenerg-1426	563	13	circuit	circuit	NOUN
fuelectenerg-1426	563	14	design	design	NOUN
fuelectenerg-1426	563	15	of	of	ADP
fuelectenerg-1426	563	16	many	many	ADV
fuelectenerg-1426	563	17	-	-	PUNCT
fuelectenerg-1426	563	18	valued	value	VERB
fuelectenerg-1426	563	19	galois	galois	PROPN
fuelectenerg-1426	563	20	reversible	reversible	ADJ
fuelectenerg-1426	563	21	expansions	expansion	NOUN
fuelectenerg-1426	563	22	and	and	CCONJ
fuelectenerg-1426	563	23	fast	fast	ADJ
fuelectenerg-1426	563	24	transforms	transform	NOUN
fuelectenerg-1426	563	25	,	,	PUNCT
fuelectenerg-1426	563	26	"	"	PUNCT
fuelectenerg-1426	563	27	j.	j.	PROPN
fuelectenerg-1426	563	28	circuits	circuits	PROPN
fuelectenerg-1426	563	29	,	,	PUNCT
fuelectenerg-1426	563	30	systems	system	NOUN
fuelectenerg-1426	563	31	,	,	PUNCT
fuelectenerg-1426	563	32	and	and	CCONJ
fuelectenerg-1426	563	33	computers	computer	NOUN
fuelectenerg-1426	563	34	,	,	PUNCT
fuelectenerg-1426	563	35	world	world	NOUN
fuelectenerg-1426	563	36	scientific	scientific	PROPN
fuelectenerg-1426	563	37	,	,	PUNCT
fuelectenerg-1426	563	38	singapore	singapore	PROPN
fuelectenerg-1426	563	39	,	,	PUNCT
fuelectenerg-1426	563	40	vol	vol	NOUN
fuelectenerg-1426	563	41	.	.	PROPN
fuelectenerg-1426	563	42	16	16	NUM
fuelectenerg-1426	563	43	,	,	PUNCT
fuelectenerg-1426	563	44	no	no	INTJ
fuelectenerg-1426	563	45	.	.	NOUN
fuelectenerg-1426	563	46	5	5	NUM
fuelectenerg-1426	563	47	,	,	PUNCT
fuelectenerg-1426	563	48	pp	pp	ADJ
fuelectenerg-1426	563	49	.	.	PUNCT
fuelectenerg-1426	564	1	641	641	NUM
fuelectenerg-1426	564	2	671	671	NUM
fuelectenerg-1426	564	3	,	,	PUNCT
fuelectenerg-1426	564	4	2007	2007	NUM
fuelectenerg-1426	564	5	.	.	PUNCT
fuelectenerg-1426	565	1	[	[	PUNCT
fuelectenerg-1426	565	2	6	6	NUM
fuelectenerg-1426	565	3	]	]	PUNCT
fuelectenerg-1426	565	4	a.	a.	NOUN
fuelectenerg-1426	565	5	n.	n.	PROPN
fuelectenerg-1426	565	6	al	al	PROPN
fuelectenerg-1426	565	7	-	-	PUNCT
fuelectenerg-1426	565	8	rabadi	rabadi	PROPN
fuelectenerg-1426	565	9	,	,	PUNCT
fuelectenerg-1426	565	10	"	"	PUNCT
fuelectenerg-1426	565	11	representations	representation	NOUN
fuelectenerg-1426	565	12	,	,	PUNCT
fuelectenerg-1426	565	13	operations	operation	NOUN
fuelectenerg-1426	565	14	,	,	PUNCT
fuelectenerg-1426	565	15	and	and	CCONJ
fuelectenerg-1426	565	16	applications	application	NOUN
fuelectenerg-1426	565	17	of	of	ADP
fuelectenerg-1426	565	18	switching	switch	VERB
fuelectenerg-1426	565	19	circuits	circuit	NOUN
fuelectenerg-1426	565	20	in	in	ADP
fuelectenerg-1426	565	21	the	the	DET
fuelectenerg-1426	565	22	reversible	reversible	ADJ
fuelectenerg-1426	565	23	and	and	CCONJ
fuelectenerg-1426	565	24	quantum	quantum	ADJ
fuelectenerg-1426	565	25	spaces	space	NOUN
fuelectenerg-1426	565	26	,	,	PUNCT
fuelectenerg-1426	565	27	"	"	PUNCT
fuelectenerg-1426	565	28	facta	facta	PROPN
fuelectenerg-1426	565	29	universitatis	universitatis	PROPN
fuelectenerg-1426	565	30	(	(	PUNCT
fuelectenerg-1426	565	31	fu	fu	NOUN
fuelectenerg-1426	565	32	)	)	PUNCT
fuelectenerg-1426	565	33	electronics	electronic	NOUN
fuelectenerg-1426	565	34	and	and	CCONJ
fuelectenerg-1426	565	35	energetics	energetic	NOUN
fuelectenerg-1426	565	36	,	,	PUNCT
fuelectenerg-1426	565	37	vol	vol	NOUN
fuelectenerg-1426	565	38	.	.	PROPN
fuelectenerg-1426	565	39	20	20	NUM
fuelectenerg-1426	565	40	,	,	PUNCT
fuelectenerg-1426	565	41	no	no	INTJ
fuelectenerg-1426	565	42	.	.	NOUN
fuelectenerg-1426	566	1	3	3	NUM
fuelectenerg-1426	566	2	,	,	PUNCT
fuelectenerg-1426	566	3	pp	pp	ADJ
fuelectenerg-1426	566	4	.	.	PUNCT
fuelectenerg-1426	567	1	507	507	NUM
fuelectenerg-1426	567	2	539	539	NUM
fuelectenerg-1426	567	3	,	,	PUNCT
fuelectenerg-1426	567	4	2007	2007	NUM
fuelectenerg-1426	567	5	.	.	PUNCT
fuelectenerg-1426	568	1	[	[	X
fuelectenerg-1426	568	2	7	7	X
fuelectenerg-1426	568	3	]	]	X
fuelectenerg-1426	568	4	r.	r.	PROPN
fuelectenerg-1426	568	5	e.	e.	PROPN
fuelectenerg-1426	568	6	bryant	bryant	PROPN
fuelectenerg-1426	568	7	,	,	PUNCT
fuelectenerg-1426	568	8	"	"	PUNCT
fuelectenerg-1426	568	9	graph	graph	NOUN
fuelectenerg-1426	568	10	-	-	PUNCT
fuelectenerg-1426	568	11	based	base	VERB
fuelectenerg-1426	568	12	algorithms	algorithm	NOUN
fuelectenerg-1426	568	13	for	for	ADP
fuelectenerg-1426	568	14	boolean	boolean	ADJ
fuelectenerg-1426	568	15	functions	function	NOUN
fuelectenerg-1426	568	16	manipulation	manipulation	NOUN
fuelectenerg-1426	568	17	,	,	PUNCT
fuelectenerg-1426	568	18	"	"	PUNCT
fuelectenerg-1426	568	19	ieee	ieee	NOUN
fuelectenerg-1426	568	20	trans	tran	NOUN
fuelectenerg-1426	568	21	.	.	PUNCT
fuelectenerg-1426	569	1	on	on	ADP
fuelectenerg-1426	569	2	comp	comp	PROPN
fuelectenerg-1426	569	3	.	.	PUNCT
fuelectenerg-1426	569	4	,	,	PUNCT
fuelectenerg-1426	569	5	vol	vol	NOUN
fuelectenerg-1426	569	6	.	.	PUNCT
fuelectenerg-1426	570	1	c-35	c-35	PROPN
fuelectenerg-1426	570	2	,	,	PUNCT
fuelectenerg-1426	570	3	no.8	no.8	PROPN
fuelectenerg-1426	570	4	,	,	PUNCT
fuelectenerg-1426	570	5	pp	pp	ADV
fuelectenerg-1426	570	6	.	.	PUNCT
fuelectenerg-1426	571	1	667	667	NUM
fuelectenerg-1426	571	2	-	-	SYM
fuelectenerg-1426	571	3	691	691	NUM
fuelectenerg-1426	571	4	,	,	PUNCT
fuelectenerg-1426	571	5	1986	1986	NUM
fuelectenerg-1426	571	6	.	.	PUNCT
fuelectenerg-1426	572	1	[	[	X
fuelectenerg-1426	572	2	8	8	NUM
fuelectenerg-1426	572	3	]	]	X
fuelectenerg-1426	572	4	m.	m.	NOUN
fuelectenerg-1426	572	5	cohn	cohn	PROPN
fuelectenerg-1426	572	6	,	,	PUNCT
fuelectenerg-1426	572	7	switching	switch	VERB
fuelectenerg-1426	572	8	function	function	NOUN
fuelectenerg-1426	572	9	canonical	canonical	ADJ
fuelectenerg-1426	572	10	form	form	NOUN
fuelectenerg-1426	572	11	over	over	ADP
fuelectenerg-1426	572	12	integer	integer	NOUN
fuelectenerg-1426	572	13	fields	field	NOUN
fuelectenerg-1426	572	14	,	,	PUNCT
fuelectenerg-1426	572	15	ph.d	ph.d	PROPN
fuelectenerg-1426	572	16	.	.	PUNCT
fuelectenerg-1426	572	17	dissertation	dissertation	PROPN
fuelectenerg-1426	572	18	,	,	PUNCT
fuelectenerg-1426	572	19	harvard	harvard	PROPN
fuelectenerg-1426	572	20	university	university	PROPN
fuelectenerg-1426	572	21	,	,	PUNCT
fuelectenerg-1426	572	22	1960	1960	NUM
fuelectenerg-1426	572	23	.	.	PUNCT
fuelectenerg-1426	573	1	[	[	X
fuelectenerg-1426	573	2	9	9	NUM
fuelectenerg-1426	573	3	]	]	X
fuelectenerg-1426	573	4	r.	r.	NOUN
fuelectenerg-1426	573	5	drechsler	drechsler	PROPN
fuelectenerg-1426	573	6	,	,	PUNCT
fuelectenerg-1426	573	7	a.	a.	NOUN
fuelectenerg-1426	573	8	sarabi	sarabi	PROPN
fuelectenerg-1426	573	9	,	,	PUNCT
fuelectenerg-1426	573	10	m.	m.	NOUN
fuelectenerg-1426	573	11	theobald	theobald	PROPN
fuelectenerg-1426	573	12	,	,	PUNCT
fuelectenerg-1426	573	13	b.	b.	PROPN
fuelectenerg-1426	573	14	becker	becker	PROPN
fuelectenerg-1426	573	15	,	,	PUNCT
fuelectenerg-1426	573	16	and	and	CCONJ
fuelectenerg-1426	573	17	m.	m.	PROPN
fuelectenerg-1426	573	18	a.	a.	PROPN
fuelectenerg-1426	573	19	perkowski	perkowski	PROPN
fuelectenerg-1426	573	20	,	,	PUNCT
fuelectenerg-1426	573	21	"	"	PUNCT
fuelectenerg-1426	573	22	efficient	efficient	ADJ
fuelectenerg-1426	573	23	representation	representation	NOUN
fuelectenerg-1426	573	24	and	and	CCONJ
fuelectenerg-1426	573	25	manipulation	manipulation	NOUN
fuelectenerg-1426	573	26	of	of	ADP
fuelectenerg-1426	573	27	switching	switch	VERB
fuelectenerg-1426	573	28	functions	function	NOUN
fuelectenerg-1426	573	29	based	base	VERB
fuelectenerg-1426	573	30	on	on	ADP
fuelectenerg-1426	573	31	ordered	order	VERB
fuelectenerg-1426	573	32	kronecker	kronecker	NOUN
fuelectenerg-1426	573	33	functional	functional	ADJ
fuelectenerg-1426	573	34	decision	decision	NOUN
fuelectenerg-1426	573	35	diagrams	diagram	NOUN
fuelectenerg-1426	573	36	,	,	PUNCT
fuelectenerg-1426	573	37	"	"	PUNCT
fuelectenerg-1426	573	38	proc	proc	NOUN
fuelectenerg-1426	573	39	.	.	PUNCT
fuelectenerg-1426	573	40	dac	dac	PROPN
fuelectenerg-1426	573	41	,	,	PUNCT
fuelectenerg-1426	573	42	1994	1994	NUM
fuelectenerg-1426	573	43	,	,	PUNCT
fuelectenerg-1426	573	44	pp	pp	ADJ
fuelectenerg-1426	573	45	.	.	PUNCT
fuelectenerg-1426	573	46	415	415	NUM
fuelectenerg-1426	573	47	-	-	SYM
fuelectenerg-1426	573	48	419	419	NUM
fuelectenerg-1426	573	49	.	.	PUNCT
fuelectenerg-1426	574	1	[	[	X
fuelectenerg-1426	574	2	10	10	NUM
fuelectenerg-1426	574	3	]	]	PUNCT
fuelectenerg-1426	574	4	m.	m.	NOUN
fuelectenerg-1426	574	5	escobar	escobar	PROPN
fuelectenerg-1426	574	6	and	and	CCONJ
fuelectenerg-1426	574	7	f.	f.	PROPN
fuelectenerg-1426	574	8	somenzi	somenzi	PROPN
fuelectenerg-1426	574	9	,	,	PUNCT
fuelectenerg-1426	574	10	"	"	PUNCT
fuelectenerg-1426	574	11	synthesis	synthesis	NOUN
fuelectenerg-1426	574	12	of	of	ADP
fuelectenerg-1426	574	13	and	and	CCONJ
fuelectenerg-1426	574	14	/	/	SYM
fuelectenerg-1426	574	15	exor	exor	PROPN
fuelectenerg-1426	574	16	expressions	expression	NOUN
fuelectenerg-1426	574	17	via	via	ADP
fuelectenerg-1426	574	18	satisfiability	satisfiability	NOUN
fuelectenerg-1426	574	19	,	,	PUNCT
fuelectenerg-1426	574	20	"	"	PUNCT
fuelectenerg-1426	574	21	proc	proc	NOUN
fuelectenerg-1426	574	22	.	.	PUNCT
fuelectenerg-1426	575	1	reed	reed	NOUN
fuelectenerg-1426	575	2	-	-	PUNCT
fuelectenerg-1426	575	3	muller	muller	NOUN
fuelectenerg-1426	575	4	,	,	PUNCT
fuelectenerg-1426	575	5	1995	1995	NUM
fuelectenerg-1426	575	6	,	,	PUNCT
fuelectenerg-1426	575	7	pp	pp	PROPN
fuelectenerg-1426	575	8	.	.	PUNCT
fuelectenerg-1426	576	1	80	80	NUM
fuelectenerg-1426	576	2	-	-	SYM
fuelectenerg-1426	576	3	87	87	NUM
fuelectenerg-1426	576	4	.	.	PUNCT
fuelectenerg-1426	577	1	[	[	X
fuelectenerg-1426	577	2	11	11	NUM
fuelectenerg-1426	577	3	]	]	X
fuelectenerg-1426	577	4	b.	b.	PROPN
fuelectenerg-1426	577	5	j.	j.	PROPN
fuelectenerg-1426	577	6	falkowski	falkowski	PROPN
fuelectenerg-1426	577	7	and	and	CCONJ
fuelectenerg-1426	577	8	s.	s.	PROPN
fuelectenerg-1426	577	9	rahardja	rahardja	PROPN
fuelectenerg-1426	577	10	,	,	PUNCT
fuelectenerg-1426	577	11	"	"	PUNCT
fuelectenerg-1426	577	12	classification	classification	NOUN
fuelectenerg-1426	577	13	and	and	CCONJ
fuelectenerg-1426	577	14	properties	property	NOUN
fuelectenerg-1426	577	15	of	of	ADP
fuelectenerg-1426	577	16	fast	fast	ADJ
fuelectenerg-1426	577	17	linearly	linearly	ADV
fuelectenerg-1426	577	18	independent	independent	ADJ
fuelectenerg-1426	577	19	logic	logic	NOUN
fuelectenerg-1426	577	20	transformations	transformation	NOUN
fuelectenerg-1426	577	21	,	,	PUNCT
fuelectenerg-1426	577	22	"	"	PUNCT
fuelectenerg-1426	577	23	ieee	ieee	NOUN
fuelectenerg-1426	577	24	trans	tran	NOUN
fuelectenerg-1426	577	25	.	.	PUNCT
fuelectenerg-1426	578	1	on	on	ADP
fuelectenerg-1426	578	2	circuits	circuit	NOUN
fuelectenerg-1426	578	3	and	and	CCONJ
fuelectenerg-1426	578	4	systems	system	NOUN
fuelectenerg-1426	578	5	-	-	PUNCT
fuelectenerg-1426	578	6	ii	ii	NOUN
fuelectenerg-1426	578	7	,	,	PUNCT
fuelectenerg-1426	578	8	vol	vol	NOUN
fuelectenerg-1426	578	9	.	.	PROPN
fuelectenerg-1426	578	10	44	44	NUM
fuelectenerg-1426	578	11	,	,	PUNCT
fuelectenerg-1426	578	12	no	no	INTJ
fuelectenerg-1426	578	13	.	.	NOUN
fuelectenerg-1426	578	14	8	8	NUM
fuelectenerg-1426	578	15	,	,	PUNCT
fuelectenerg-1426	578	16	pp	pp	ADJ
fuelectenerg-1426	578	17	.	.	PUNCT
fuelectenerg-1426	578	18	646	646	NUM
fuelectenerg-1426	578	19	-	-	SYM
fuelectenerg-1426	578	20	655	655	NUM
fuelectenerg-1426	578	21	,	,	PUNCT
fuelectenerg-1426	578	22	august	august	PROPN
fuelectenerg-1426	578	23	1997	1997	NUM
fuelectenerg-1426	578	24	.	.	PUNCT
fuelectenerg-1426	579	1	[	[	X
fuelectenerg-1426	579	2	12	12	NUM
fuelectenerg-1426	579	3	]	]	PUNCT
fuelectenerg-1426	579	4	b.	b.	PROPN
fuelectenerg-1426	579	5	falkowski	falkowski	NOUN
fuelectenerg-1426	579	6	and	and	CCONJ
fuelectenerg-1426	579	7	l.-s	l.-s	PROPN
fuelectenerg-1426	579	8	.	.	PUNCT
fuelectenerg-1426	580	1	lim	lim	PROPN
fuelectenerg-1426	580	2	,	,	PUNCT
fuelectenerg-1426	580	3	"	"	PUNCT
fuelectenerg-1426	580	4	gray	gray	ADJ
fuelectenerg-1426	580	5	scale	scale	NOUN
fuelectenerg-1426	580	6	image	image	NOUN
fuelectenerg-1426	580	7	compression	compression	NOUN
fuelectenerg-1426	580	8	based	base	VERB
fuelectenerg-1426	580	9	on	on	ADP
fuelectenerg-1426	580	10	multiple	multiple	ADV
fuelectenerg-1426	580	11	-	-	PUNCT
fuelectenerg-1426	580	12	valued	value	VERB
fuelectenerg-1426	580	13	input	input	NOUN
fuelectenerg-1426	580	14	binary	binary	NOUN
fuelectenerg-1426	580	15	functions	function	NOUN
fuelectenerg-1426	580	16	,	,	PUNCT
fuelectenerg-1426	580	17	walsh	walsh	NOUN
fuelectenerg-1426	580	18	and	and	CCONJ
fuelectenerg-1426	580	19	reed	reed	PROPN
fuelectenerg-1426	580	20	-	-	PUNCT
fuelectenerg-1426	580	21	muller	muller	PROPN
fuelectenerg-1426	580	22	spectra	spectra	PROPN
fuelectenerg-1426	580	23	,	,	PUNCT
fuelectenerg-1426	580	24	"	"	PUNCT
fuelectenerg-1426	580	25	proc	proc	NOUN
fuelectenerg-1426	580	26	.	.	PUNCT
fuelectenerg-1426	581	1	ismvl	ismvl	PROPN
fuelectenerg-1426	581	2	,	,	PUNCT
fuelectenerg-1426	581	3	2000	2000	NUM
fuelectenerg-1426	581	4	,	,	PUNCT
fuelectenerg-1426	581	5	pp	pp	ADJ
fuelectenerg-1426	581	6	.	.	PUNCT
fuelectenerg-1426	582	1	279	279	NUM
fuelectenerg-1426	582	2	-	-	SYM
fuelectenerg-1426	582	3	284	284	NUM
fuelectenerg-1426	582	4	.	.	PUNCT
fuelectenerg-1426	583	1	[	[	X
fuelectenerg-1426	583	2	13	13	NUM
fuelectenerg-1426	583	3	]	]	X
fuelectenerg-1426	583	4	h.	h.	PROPN
fuelectenerg-1426	583	5	fujiwara	fujiwara	PROPN
fuelectenerg-1426	583	6	,	,	PUNCT
fuelectenerg-1426	583	7	logic	logic	NOUN
fuelectenerg-1426	583	8	testing	testing	NOUN
fuelectenerg-1426	583	9	and	and	CCONJ
fuelectenerg-1426	583	10	design	design	NOUN
fuelectenerg-1426	583	11	for	for	ADP
fuelectenerg-1426	583	12	testability	testability	NOUN
fuelectenerg-1426	583	13	,	,	PUNCT
fuelectenerg-1426	583	14	mit	mit	NOUN
fuelectenerg-1426	583	15	press	press	NOUN
fuelectenerg-1426	583	16	,	,	PUNCT
fuelectenerg-1426	583	17	1985	1985	NUM
fuelectenerg-1426	583	18	.	.	PUNCT
fuelectenerg-1426	584	1	[	[	X
fuelectenerg-1426	584	2	14	14	NUM
fuelectenerg-1426	584	3	]	]	X
fuelectenerg-1426	584	4	d.	d.	PROPN
fuelectenerg-1426	584	5	h.	h.	PROPN
fuelectenerg-1426	584	6	green	green	PROPN
fuelectenerg-1426	584	7	,	,	PUNCT
fuelectenerg-1426	584	8	"	"	PUNCT
fuelectenerg-1426	584	9	families	family	NOUN
fuelectenerg-1426	584	10	of	of	ADP
fuelectenerg-1426	584	11	reed	reed	NOUN
fuelectenerg-1426	584	12	-	-	PUNCT
fuelectenerg-1426	584	13	muller	muller	NOUN
fuelectenerg-1426	584	14	canonical	canonical	ADJ
fuelectenerg-1426	584	15	forms	form	NOUN
fuelectenerg-1426	584	16	,	,	PUNCT
fuelectenerg-1426	584	17	"	"	PUNCT
fuelectenerg-1426	584	18	int	int	NOUN
fuelectenerg-1426	584	19	.	.	PUNCT
fuelectenerg-1426	585	1	j.	j.	PROPN
fuelectenerg-1426	585	2	of	of	ADP
fuelectenerg-1426	585	3	electronics	electronics	PROPN
fuelectenerg-1426	585	4	,	,	PUNCT
fuelectenerg-1426	585	5	no	no	INTJ
fuelectenerg-1426	585	6	.	.	NOUN
fuelectenerg-1426	585	7	2	2	NUM
fuelectenerg-1426	585	8	,	,	PUNCT
fuelectenerg-1426	585	9	pp	pp	ADJ
fuelectenerg-1426	585	10	.	.	PUNCT
fuelectenerg-1426	586	1	259	259	NUM
fuelectenerg-1426	586	2	-	-	SYM
fuelectenerg-1426	586	3	280	280	NUM
fuelectenerg-1426	586	4	,	,	PUNCT
fuelectenerg-1426	586	5	1991	1991	NUM
fuelectenerg-1426	586	6	.	.	PUNCT
fuelectenerg-1426	587	1	[	[	X
fuelectenerg-1426	587	2	15	15	NUM
fuelectenerg-1426	587	3	]	]	X
fuelectenerg-1426	587	4	s.	s.	PROPN
fuelectenerg-1426	587	5	hassoun	hassoun	PROPN
fuelectenerg-1426	587	6	,	,	PUNCT
fuelectenerg-1426	587	7	t.	t.	PROPN
fuelectenerg-1426	587	8	sasao	sasao	PROPN
fuelectenerg-1426	587	9	,	,	PUNCT
fuelectenerg-1426	587	10	and	and	CCONJ
fuelectenerg-1426	587	11	r.	r.	PROPN
fuelectenerg-1426	587	12	brayton	brayton	PROPN
fuelectenerg-1426	587	13	(	(	PUNCT
fuelectenerg-1426	587	14	editors	editor	NOUN
fuelectenerg-1426	587	15	)	)	PUNCT
fuelectenerg-1426	587	16	,	,	PUNCT
fuelectenerg-1426	587	17	logic	logic	NOUN
fuelectenerg-1426	587	18	synthesis	synthesis	NOUN
fuelectenerg-1426	587	19	and	and	CCONJ
fuelectenerg-1426	587	20	verification	verification	NOUN
fuelectenerg-1426	587	21	,	,	PUNCT
fuelectenerg-1426	587	22	kluwer	kluwer	NOUN
fuelectenerg-1426	587	23	acad	acad	PROPN
fuelectenerg-1426	587	24	.	.	PUNCT
fuelectenerg-1426	588	1	publishers	publisher	NOUN
fuelectenerg-1426	588	2	,	,	PUNCT
fuelectenerg-1426	588	3	2001	2001	NUM
fuelectenerg-1426	588	4	.	.	PUNCT
fuelectenerg-1426	589	1	[	[	X
fuelectenerg-1426	589	2	16	16	NUM
fuelectenerg-1426	589	3	]	]	PUNCT
fuelectenerg-1426	589	4	m.	m.	NOUN
fuelectenerg-1426	589	5	helliwell	helliwell	NOUN
fuelectenerg-1426	589	6	and	and	CCONJ
fuelectenerg-1426	589	7	m.	m.	PROPN
fuelectenerg-1426	589	8	a.	a.	PROPN
fuelectenerg-1426	589	9	perkowski	perkowski	PROPN
fuelectenerg-1426	589	10	,	,	PUNCT
fuelectenerg-1426	589	11	"	"	PUNCT
fuelectenerg-1426	589	12	a	a	DET
fuelectenerg-1426	589	13	fast	fast	ADJ
fuelectenerg-1426	589	14	algorithm	algorithm	NOUN
fuelectenerg-1426	589	15	to	to	PART
fuelectenerg-1426	589	16	minimize	minimize	VERB
fuelectenerg-1426	589	17	multi	multi	ADJ
fuelectenerg-1426	589	18	-	-	ADJ
fuelectenerg-1426	589	19	output	output	ADJ
fuelectenerg-1426	589	20	mixed	mix	VERB
fuelectenerg-1426	589	21	-	-	PUNCT
fuelectenerg-1426	589	22	polarity	polarity	NOUN
fuelectenerg-1426	589	23	generalized	generalize	VERB
fuelectenerg-1426	589	24	reed	reed	NOUN
fuelectenerg-1426	589	25	-	-	PUNCT
fuelectenerg-1426	589	26	muller	muller	NOUN
fuelectenerg-1426	589	27	forms	form	NOUN
fuelectenerg-1426	589	28	,	,	PUNCT
fuelectenerg-1426	589	29	"	"	PUNCT
fuelectenerg-1426	589	30	proc	proc	NOUN
fuelectenerg-1426	589	31	.	.	PUNCT
fuelectenerg-1426	590	1	design	design	NOUN
fuelectenerg-1426	590	2	automation	automation	NOUN
fuelectenerg-1426	590	3	conference	conference	NOUN
fuelectenerg-1426	590	4	,	,	PUNCT
fuelectenerg-1426	590	5	1988	1988	NUM
fuelectenerg-1426	590	6	,	,	PUNCT
fuelectenerg-1426	590	7	pp	pp	ADV
fuelectenerg-1426	590	8	.	.	PUNCT
fuelectenerg-1426	591	1	427	427	NUM
fuelectenerg-1426	591	2	-	-	SYM
fuelectenerg-1426	591	3	432	432	NUM
fuelectenerg-1426	591	4	.	.	PUNCT
fuelectenerg-1426	592	1	[	[	X
fuelectenerg-1426	592	2	17	17	NUM
fuelectenerg-1426	592	3	]	]	PUNCT
fuelectenerg-1426	592	4	s.	s.	PROPN
fuelectenerg-1426	592	5	l.	l.	PROPN
fuelectenerg-1426	592	6	hurst	hurst	PROPN
fuelectenerg-1426	592	7	,	,	PUNCT
fuelectenerg-1426	592	8	d.	d.	PROPN
fuelectenerg-1426	592	9	m.	m.	PROPN
fuelectenerg-1426	592	10	miller	miller	PROPN
fuelectenerg-1426	592	11	,	,	PUNCT
fuelectenerg-1426	592	12	and	and	CCONJ
fuelectenerg-1426	592	13	j.	j.	PROPN
fuelectenerg-1426	592	14	c.	c.	PROPN
fuelectenerg-1426	592	15	muzio	muzio	PROPN
fuelectenerg-1426	592	16	,	,	PUNCT
fuelectenerg-1426	592	17	spectral	spectral	ADJ
fuelectenerg-1426	592	18	techniques	technique	NOUN
fuelectenerg-1426	592	19	in	in	ADP
fuelectenerg-1426	592	20	digital	digital	ADJ
fuelectenerg-1426	592	21	logic	logic	NOUN
fuelectenerg-1426	592	22	,	,	PUNCT
fuelectenerg-1426	592	23	academic	academic	NOUN
fuelectenerg-1426	592	24	119	119	NUM