id	sid	tid	token	lemma	pos
ijassa-419	1	1	advances	advance	NOUN
ijassa-419	1	2	in	in	ADP
ijassa-419	1	3	systems	system	NOUN
ijassa-419	1	4	science	science	NOUN
ijassa-419	1	5	and	and	CCONJ
ijassa-419	1	6	applications	application	NOUN
ijassa-419	1	7	(	(	PUNCT
ijassa-419	1	8	2013	2013	NUM
ijassa-419	1	9	)	)	PUNCT
ijassa-419	2	1	vol.13	vol.13	NOUN
ijassa-419	2	2	no.2	no.2	PROPN
ijassa-419	2	3	100	100	NUM
ijassa-419	2	4	-	-	SYM
ijassa-419	2	5	115	115	NUM
ijassa-419	2	6	set	set	NOUN
ijassa-419	2	7	-	-	PUNCT
ijassa-419	2	8	theoretic	theoretic	NOUN
ijassa-419	2	9	design	design	NOUN
ijassa-419	2	10	and	and	CCONJ
ijassa-419	2	11	analysis	analysis	NOUN
ijassa-419	2	12	of	of	ADP
ijassa-419	2	13	l	l	NOUN
ijassa-419	2	14	systems	system	NOUN
ijassa-419	2	15	xiaojun	xiaojun	PROPN
ijassa-419	2	16	duan1	duan1	PROPN
ijassa-419	2	17	,	,	PUNCT
ijassa-419	2	18	bing	bing	VERB
ijassa-419	2	19	ju1	ju1	NOUN
ijassa-419	2	20	and	and	CCONJ
ijassa-419	2	21	yi	yi	PROPN
ijassa-419	2	22	lin2	lin2	PROPN
ijassa-419	2	23	1department	1department	NUM
ijassa-419	2	24	of	of	ADP
ijassa-419	2	25	mathematics	mathematic	NOUN
ijassa-419	2	26	and	and	CCONJ
ijassa-419	2	27	systems	system	NOUN
ijassa-419	2	28	science	science	NOUN
ijassa-419	2	29	,	,	PUNCT
ijassa-419	2	30	national	national	ADJ
ijassa-419	2	31	university	university	PROPN
ijassa-419	2	32	of	of	ADP
ijassa-419	2	33	defense	defense	PROPN
ijassa-419	2	34	technology	technology	NOUN
ijassa-419	2	35	,	,	PUNCT
ijassa-419	2	36	changsha	changsha	PROPN
ijassa-419	2	37	410073	410073	NUM
ijassa-419	2	38	,	,	PUNCT
ijassa-419	2	39	pr	pr	ADP
ijassa-419	2	40	china	china	PROPN
ijassa-419	3	1	2department	2department	NUM
ijassa-419	3	2	of	of	ADP
ijassa-419	3	3	mathematics	mathematic	NOUN
ijassa-419	3	4	,	,	PUNCT
ijassa-419	3	5	slippery	slippery	ADJ
ijassa-419	3	6	rock	rock	NOUN
ijassa-419	3	7	university	university	NOUN
ijassa-419	3	8	,	,	PUNCT
ijassa-419	3	9	slippery	slippery	ADJ
ijassa-419	3	10	rock	rock	NOUN
ijassa-419	3	11	,	,	PUNCT
ijassa-419	3	12	pa	pa	PROPN
ijassa-419	3	13	16057	16057	NUM
ijassa-419	3	14	usa	usa	PROPN
ijassa-419	3	15	abstract	abstract	NOUN
ijassa-419	3	16	from	from	ADP
ijassa-419	3	17	the	the	DET
ijassa-419	3	18	perspective	perspective	NOUN
ijassa-419	3	19	of	of	ADP
ijassa-419	3	20	set	set	NOUN
ijassa-419	3	21	theory	theory	NOUN
ijassa-419	3	22	,	,	PUNCT
ijassa-419	3	23	this	this	DET
ijassa-419	3	24	paper	paper	NOUN
ijassa-419	3	25	establishes	establish	VERB
ijassa-419	3	26	a	a	DET
ijassa-419	3	27	rigorous	rigorous	ADJ
ijassa-419	3	28	mathematical	mathematical	ADJ
ijassa-419	3	29	definition	definition	NOUN
ijassa-419	3	30	of	of	ADP
ijassa-419	3	31	l	l	NOUN
ijassa-419	3	32	systems	system	NOUN
ijassa-419	3	33	,	,	PUNCT
ijassa-419	3	34	and	and	CCONJ
ijassa-419	3	35	proves	prove	VERB
ijassa-419	3	36	the	the	DET
ijassa-419	3	37	common	common	ADJ
ijassa-419	3	38	characteristics	characteristic	NOUN
ijassa-419	3	39	of	of	ADP
ijassa-419	3	40	simple	simple	ADJ
ijassa-419	3	41	l	l	NOUN
ijassa-419	3	42	systems	system	NOUN
ijassa-419	3	43	by	by	ADP
ijassa-419	3	44	providing	provide	VERB
ijassa-419	3	45	a	a	DET
ijassa-419	3	46	theoretical	theoretical	ADJ
ijassa-419	3	47	framework	framework	NOUN
ijassa-419	3	48	for	for	ADP
ijassa-419	3	49	a	a	DET
ijassa-419	3	50	systematic	systematic	ADJ
ijassa-419	3	51	research	research	NOUN
ijassa-419	3	52	of	of	ADP
ijassa-419	3	53	l	l	NOUN
ijassa-419	3	54	systems	system	NOUN
ijassa-419	3	55	.	.	PUNCT
ijassa-419	4	1	additionally	additionally	ADV
ijassa-419	4	2	,	,	PUNCT
ijassa-419	4	3	explanations	explanation	NOUN
ijassa-419	4	4	for	for	ADP
ijassa-419	4	5	the	the	DET
ijassa-419	4	6	characteristics	characteristic	NOUN
ijassa-419	4	7	of	of	ADP
ijassa-419	4	8	systems	system	NOUN
ijassa-419	4	9	’	'	PUNCT
ijassa-419	4	10	emergence	emergence	NOUN
ijassa-419	4	11	based	base	VERB
ijassa-419	4	12	on	on	ADP
ijassa-419	4	13	l	l	PROPN
ijassa-419	4	14	systems	system	NOUN
ijassa-419	4	15	are	be	AUX
ijassa-419	4	16	provided	provide	VERB
ijassa-419	4	17	,	,	PUNCT
ijassa-419	4	18	and	and	CCONJ
ijassa-419	4	19	some	some	DET
ijassa-419	4	20	design	design	NOUN
ijassa-419	4	21	methods	method	NOUN
ijassa-419	4	22	of	of	ADP
ijassa-419	4	23	l	l	NOUN
ijassa-419	4	24	systems	system	NOUN
ijassa-419	4	25	are	be	AUX
ijassa-419	4	26	developed	develop	VERB
ijassa-419	4	27	and	and	CCONJ
ijassa-419	4	28	interesting	interesting	ADJ
ijassa-419	4	29	cases	case	NOUN
ijassa-419	4	30	of	of	ADP
ijassa-419	4	31	design	design	NOUN
ijassa-419	4	32	are	be	AUX
ijassa-419	4	33	constructed	construct	VERB
ijassa-419	4	34	.	.	PUNCT
ijassa-419	5	1	this	this	DET
ijassa-419	5	2	work	work	NOUN
ijassa-419	5	3	is	be	AUX
ijassa-419	5	4	the	the	DET
ijassa-419	5	5	first	first	ADJ
ijassa-419	5	6	of	of	ADP
ijassa-419	5	7	its	its	PRON
ijassa-419	5	8	kind	kind	NOUN
ijassa-419	5	9	that	that	PRON
ijassa-419	5	10	investigates	investigate	VERB
ijassa-419	5	11	the	the	DET
ijassa-419	5	12	l	l	NOUN
ijassa-419	5	13	system	system	NOUN
ijassa-419	5	14	using	use	VERB
ijassa-419	5	15	a	a	DET
ijassa-419	5	16	rigorous	rigorous	ADJ
ijassa-419	5	17	mathematical	mathematical	ADJ
ijassa-419	5	18	definition	definition	NOUN
ijassa-419	5	19	based	base	VERB
ijassa-419	5	20	on	on	ADP
ijassa-419	5	21	set	set	NOUN
ijassa-419	5	22	theory	theory	NOUN
ijassa-419	5	23	.	.	PUNCT
ijassa-419	6	1	keywords	keyword	NOUN
ijassa-419	6	2	set	set	VERB
ijassa-419	6	3	theory	theory	NOUN
ijassa-419	6	4	,	,	PUNCT
ijassa-419	6	5	l	l	NOUN
ijassa-419	6	6	system	system	NOUN
ijassa-419	6	7	,	,	PUNCT
ijassa-419	6	8	characteristics	characteristic	NOUN
ijassa-419	6	9	of	of	ADP
ijassa-419	6	10	systems	system	NOUN
ijassa-419	6	11	1	1	NUM
ijassa-419	6	12	introduction	introduction	NOUN
ijassa-419	6	13	although	although	SCONJ
ijassa-419	6	14	the	the	DET
ijassa-419	6	15	figures	figure	NOUN
ijassa-419	6	16	produced	produce	VERB
ijassa-419	6	17	out	out	ADP
ijassa-419	6	18	of	of	ADP
ijassa-419	6	19	fractals	fractal	NOUN
ijassa-419	6	20	are	be	AUX
ijassa-419	6	21	generally	generally	ADV
ijassa-419	6	22	complicated	complicate	VERB
ijassa-419	6	23	,	,	PUNCT
ijassa-419	6	24	the	the	DET
ijassa-419	6	25	description	description	NOUN
ijassa-419	6	26	of	of	ADP
ijassa-419	6	27	fractals	fractal	NOUN
ijassa-419	6	28	can	can	AUX
ijassa-419	6	29	be	be	AUX
ijassa-419	6	30	quite	quite	ADV
ijassa-419	6	31	straightforward	straightforward	ADJ
ijassa-419	6	32	.	.	PUNCT
ijassa-419	7	1	among	among	ADP
ijassa-419	7	2	the	the	DET
ijassa-419	7	3	commonly	commonly	ADV
ijassa-419	7	4	utilized	utilize	VERB
ijassa-419	7	5	methods	method	NOUN
ijassa-419	7	6	are	be	AUX
ijassa-419	7	7	the	the	DET
ijassa-419	7	8	l	l	NOUN
ijassa-419	7	9	-	-	NOUN
ijassa-419	7	10	system	system	NOUN
ijassa-419	7	11	and	and	CCONJ
ijassa-419	7	12	the	the	DET
ijassa-419	7	13	ifs	ifs	PROPN
ijassa-419	7	14	(	(	PUNCT
ijassa-419	7	15	iterated	iterate	VERB
ijassa-419	7	16	function	function	NOUN
ijassa-419	7	17	system	system	NOUN
ijassa-419	7	18	)	)	PUNCT
ijassa-419	7	19	.	.	PUNCT
ijassa-419	8	1	in	in	ADP
ijassa-419	8	2	terms	term	NOUN
ijassa-419	8	3	of	of	ADP
ijassa-419	8	4	the	the	DET
ijassa-419	8	5	fractals	fractal	NOUN
ijassa-419	8	6	they	they	PRON
ijassa-419	8	7	respectively	respectively	ADV
ijassa-419	8	8	describe	describe	VERB
ijassa-419	8	9	,	,	PUNCT
ijassa-419	8	10	the	the	DET
ijassa-419	8	11	l	l	NOUN
ijassa-419	8	12	-	-	NOUN
ijassa-419	8	13	system	system	NOUN
ijassa-419	8	14	is	be	AUX
ijassa-419	8	15	simpler	simple	ADJ
ijassa-419	8	16	than	than	ADP
ijassa-419	8	17	the	the	DET
ijassa-419	8	18	if	if	SCONJ
ijassa-419	8	19	system	system	NOUN
ijassa-419	8	20	,	,	PUNCT
ijassa-419	8	21	where	where	SCONJ
ijassa-419	8	22	the	the	DET
ijassa-419	8	23	former	former	NOUN
ijassa-419	8	24	contains	contain	VERB
ijassa-419	8	25	simple	simple	ADJ
ijassa-419	8	26	iterations	iteration	NOUN
ijassa-419	8	27	of	of	ADP
ijassa-419	8	28	character	character	NOUN
ijassa-419	8	29	strings	string	NOUN
ijassa-419	8	30	,	,	PUNCT
ijassa-419	8	31	while	while	SCONJ
ijassa-419	8	32	the	the	DET
ijassa-419	8	33	latter	latter	ADJ
ijassa-419	8	34	is	be	AUX
ijassa-419	8	35	much	much	ADV
ijassa-419	8	36	more	more	ADV
ijassa-419	8	37	complicated	complicated	ADJ
ijassa-419	8	38	in	in	ADP
ijassa-419	8	39	this	this	DET
ijassa-419	8	40	regard	regard	NOUN
ijassa-419	8	41	.	.	PUNCT
ijassa-419	9	1	aristid	aristid	NOUN
ijassa-419	9	2	lindenmayer	lindenmayer	NOUN
ijassa-419	9	3	,	,	PUNCT
ijassa-419	9	4	a	a	DET
ijassa-419	9	5	hungary	hungary	PROPN
ijassa-419	9	6	biologist	biologist	NOUN
ijassa-419	9	7	,	,	PUNCT
ijassa-419	9	8	introduced	introduce	VERB
ijassa-419	9	9	the	the	DET
ijassa-419	9	10	lindenmayer	lindenmayer	NOUN
ijassa-419	9	11	system	system	NOUN
ijassa-419	9	12	,	,	PUNCT
ijassa-419	9	13	or	or	CCONJ
ijassa-419	9	14	l	l	NOUN
ijassa-419	9	15	system	system	NOUN
ijassa-419	9	16	in	in	ADP
ijassa-419	9	17	short	short	ADJ
ijassa-419	9	18	,	,	PUNCT
ijassa-419	9	19	as	as	ADP
ijassa-419	9	20	the	the	DET
ijassa-419	9	21	mathematics	mathematics	NOUN
ijassa-419	9	22	theory	theory	NOUN
ijassa-419	9	23	for	for	ADP
ijassa-419	9	24	describing	describe	VERB
ijassa-419	9	25	the	the	DET
ijassa-419	9	26	growth	growth	NOUN
ijassa-419	9	27	of	of	ADP
ijassa-419	9	28	a	a	DET
ijassa-419	9	29	plant[1	plant[1	NOUN
ijassa-419	9	30	]	]	X
ijassa-419	9	31	.	.	PUNCT
ijassa-419	10	1	it	it	PRON
ijassa-419	10	2	is	be	AUX
ijassa-419	10	3	a	a	DET
ijassa-419	10	4	kind	kind	NOUN
ijassa-419	10	5	of	of	ADP
ijassa-419	10	6	subsequent	subsequent	ADJ
ijassa-419	10	7	string	string	NOUN
ijassa-419	10	8	replacement	replacement	NOUN
ijassa-419	10	9	system	system	NOUN
ijassa-419	10	10	;	;	PUNCT
ijassa-419	10	11	its	its	PRON
ijassa-419	10	12	theory	theory	NOUN
ijassa-419	10	13	focuses	focus	VERB
ijassa-419	10	14	on	on	ADP
ijassa-419	10	15	the	the	DET
ijassa-419	10	16	topology	topology	NOUN
ijassa-419	10	17	of	of	ADP
ijassa-419	10	18	plants	plant	NOUN
ijassa-419	10	19	,	,	PUNCT
ijassa-419	10	20	and	and	CCONJ
ijassa-419	10	21	attempts	attempt	VERB
ijassa-419	10	22	to	to	PART
ijassa-419	10	23	describe	describe	VERB
ijassa-419	10	24	the	the	DET
ijassa-419	10	25	adjacency	adjacency	NOUN
ijassa-419	10	26	relations	relation	NOUN
ijassa-419	10	27	between	between	ADP
ijassa-419	10	28	cells	cell	NOUN
ijassa-419	10	29	or	or	CCONJ
ijassa-419	10	30	between	between	ADP
ijassa-419	10	31	larger	large	ADJ
ijassa-419	10	32	plant	plant	NOUN
ijassa-419	10	33	modules	module	NOUN
ijassa-419	10	34	.	.	PUNCT
ijassa-419	11	1	while	while	SCONJ
ijassa-419	11	2	lindenmayer	lindenmayer	NOUN
ijassa-419	11	3	and	and	CCONJ
ijassa-419	11	4	others	other	NOUN
ijassa-419	11	5	proposed	propose	VERB
ijassa-419	11	6	the	the	DET
ijassa-419	11	7	initial	initial	ADJ
ijassa-419	11	8	solution[1	solution[1	PROPN
ijassa-419	11	9	]	]	PUNCT
ijassa-419	11	10	,	,	PUNCT
ijassa-419	11	11	prusinkiewicz	prusinkiewicz	PROPN
ijassa-419	11	12	used	use	VERB
ijassa-419	11	13	turtle	turtle	NOUN
ijassa-419	11	14	graphics	graphic	NOUN
ijassa-419	11	15	to	to	PART
ijassa-419	11	16	implement	implement	VERB
ijassa-419	11	17	a	a	DET
ijassa-419	11	18	lot	lot	NOUN
ijassa-419	11	19	of	of	ADP
ijassa-419	11	20	fractal	fractal	ADJ
ijassa-419	11	21	shapes	shape	NOUN
ijassa-419	11	22	and	and	CCONJ
ijassa-419	11	23	herb	herb	NOUN
ijassa-419	11	24	model	model	NOUN
ijassa-419	11	25	based	base	VERB
ijassa-419	11	26	on	on	ADP
ijassa-419	11	27	turtle	turtle	NOUN
ijassa-419	11	28	shapes[2	shapes[2	NOUN
ijassa-419	11	29	]	]	PUNCT
ijassa-419	11	30	.	.	PUNCT
ijassa-419	12	1	his	his	PRON
ijassa-419	12	2	works	work	NOUN
ijassa-419	12	3	made	make	VERB
ijassa-419	12	4	turtle	turtle	NOUN
ijassa-419	12	5	the	the	DET
ijassa-419	12	6	most	most	ADV
ijassa-419	12	7	commonly	commonly	ADV
ijassa-419	12	8	used	use	VERB
ijassa-419	12	9	form	form	NOUN
ijassa-419	12	10	and	and	CCONJ
ijassa-419	12	11	explanatory	explanatory	ADJ
ijassa-419	12	12	schemes	scheme	NOUN
ijassa-419	12	13	of	of	ADP
ijassa-419	12	14	l	l	NOUN
ijassa-419	12	15	systems	system	NOUN
ijassa-419	12	16	.	.	PUNCT
ijassa-419	13	1	in	in	ADP
ijassa-419	13	2	order	order	NOUN
ijassa-419	13	3	to	to	PART
ijassa-419	13	4	avoid	avoid	VERB
ijassa-419	13	5	the	the	DET
ijassa-419	13	6	models	model	NOUN
ijassa-419	13	7	constructed	construct	VERB
ijassa-419	13	8	using	use	VERB
ijassa-419	13	9	l	l	PROPN
ijassa-419	13	10	systems	system	NOUN
ijassa-419	13	11	inflexible	inflexible	ADJ
ijassa-419	13	12	,	,	PUNCT
ijassa-419	13	13	eichhorst	eichhorst	NOUN
ijassa-419	13	14	and	and	CCONJ
ijassa-419	13	15	others	other	NOUN
ijassa-419	13	16	proposed	propose	VERB
ijassa-419	13	17	the	the	DET
ijassa-419	13	18	concept	concept	NOUN
ijassa-419	13	19	of	of	ADP
ijassa-419	13	20	stochastic	stochastic	ADJ
ijassa-419	13	21	l	l	NOUN
ijassa-419	13	22	-	-	NOUN
ijassa-419	13	23	systems	system	NOUN
ijassa-419	13	24	to	to	PART
ijassa-419	13	25	enhance	enhance	VERB
ijassa-419	13	26	the	the	DET
ijassa-419	13	27	flexibility	flexibility	NOUN
ijassa-419	13	28	of	of	ADP
ijassa-419	13	29	the	the	DET
ijassa-419	13	30	earlier	early	ADJ
ijassa-419	13	31	l	l	NOUN
ijassa-419	13	32	-	-	PUNCT
ijassa-419	13	33	models[3	models[3	ADJ
ijassa-419	13	34	]	]	PUNCT
ijassa-419	13	35	.	.	PUNCT
ijassa-419	14	1	herman	herman	PROPN
ijassa-419	14	2	generalized	generalize	VERB
ijassa-419	14	3	the	the	DET
ijassa-419	14	4	concept	concept	NOUN
ijassa-419	14	5	of	of	ADP
ijassa-419	14	6	l	l	NOUN
ijassa-419	14	7	-	-	NOUN
ijassa-419	14	8	systems	system	NOUN
ijassa-419	14	9	to	to	ADP
ijassa-419	14	10	a	a	DET
ijassa-419	14	11	context	context	NOUN
ijassa-419	14	12	sensitive	sensitive	ADJ
ijassa-419	14	13	model	model	NOUN
ijassa-419	14	14	in	in	ADP
ijassa-419	14	15	order	order	NOUN
ijassa-419	14	16	to	to	PART
ijassa-419	14	17	establish	establish	VERB
ijassa-419	14	18	associations	association	NOUN
ijassa-419	14	19	between	between	ADP
ijassa-419	14	20	different	different	ADJ
ijassa-419	14	21	modules	module	NOUN
ijassa-419	14	22	of	of	ADP
ijassa-419	14	23	the	the	DET
ijassa-419	14	24	plant	plant	NOUN
ijassa-419	14	25	model[4	model[4	VERB
ijassa-419	14	26	]	]	PUNCT
ijassa-419	14	27	.	.	PUNCT
ijassa-419	15	1	then	then	ADV
ijassa-419	15	2	,	,	PUNCT
ijassa-419	15	3	lindenmayer	lindenmayer	PROPN
ijassa-419	15	4	introduced	introduce	VERB
ijassa-419	15	5	parameters	parameter	NOUN
ijassa-419	15	6	to	to	PART
ijassa-419	15	7	make	make	VERB
ijassa-419	15	8	l	l	NOUN
ijassa-419	15	9	-	-	NOUN
ijassa-419	15	10	systems	system	NOUN
ijassa-419	15	11	even	even	ADV
ijassa-419	15	12	more	more	ADV
ijassa-419	15	13	forthright	forthright	ADJ
ijassa-419	15	14	and	and	CCONJ
ijassa-419	15	15	efficient	efficient	ADJ
ijassa-419	15	16	.	.	PUNCT
ijassa-419	16	1	the	the	DET
ijassa-419	16	2	most	most	ADV
ijassa-419	16	3	typical	typical	ADJ
ijassa-419	16	4	applications	application	NOUN
ijassa-419	16	5	of	of	ADP
ijassa-419	16	6	l	l	NOUN
ijassa-419	16	7	-	-	NOUN
ijassa-419	16	8	systems	system	NOUN
ijassa-419	16	9	are	be	AUX
ijassa-419	16	10	done	do	VERB
ijassa-419	16	11	by	by	ADP
ijassa-419	16	12	scholars	scholar	NOUN
ijassa-419	16	13	at	at	ADP
ijassa-419	16	14	calgary	calgary	PROPN
ijassa-419	16	15	university	university	PROPN
ijassa-419	16	16	,	,	PUNCT
ijassa-419	16	17	canada	canada	PROPN
ijassa-419	16	18	.	.	PUNCT
ijassa-419	17	1	they	they	PRON
ijassa-419	17	2	were	be	AUX
ijassa-419	17	3	involved	involve	VERB
ijassa-419	17	4	in	in	ADP
ijassa-419	17	5	the	the	DET
ijassa-419	17	6	parametricalization	parametricalization	NOUN
ijassa-419	17	7	of	of	ADP
ijassa-419	17	8	l	l	NOUN
ijassa-419	17	9	-	-	NOUN
ijassa-419	17	10	systems	system	NOUN
ijassa-419	17	11	,	,	PUNCT
ijassa-419	17	12	the	the	DET
ijassa-419	17	13	establishment	establishment	NOUN
ijassa-419	17	14	of	of	ADP
ijassa-419	17	15	differential	differential	ADJ
ijassa-419	17	16	l	l	NOUN
ijassa-419	17	17	-	-	NOUN
ijassa-419	17	18	system	system	NOUN
ijassa-419	17	19	,	,	PUNCT
ijassa-419	17	20	open	open	ADJ
ijassa-419	17	21	advances	advance	NOUN
ijassa-419	17	22	in	in	ADP
ijassa-419	17	23	systems	system	NOUN
ijassa-419	17	24	science	science	NOUN
ijassa-419	17	25	and	and	CCONJ
ijassa-419	17	26	applications	application	NOUN
ijassa-419	17	27	(	(	PUNCT
ijassa-419	17	28	2013	2013	NUM
ijassa-419	17	29	)	)	PUNCT
ijassa-419	17	30	vol.13	vol.13	NOUN
ijassa-419	17	31	no.2	no.2	PROPN
ijassa-419	17	32	101	101	NUM
ijassa-419	17	33	l	l	NOUN
ijassa-419	17	34	-	-	NOUN
ijassa-419	17	35	system	system	NOUN
ijassa-419	17	36	,	,	PUNCT
ijassa-419	17	37	and	and	CCONJ
ijassa-419	17	38	other	other	ADJ
ijassa-419	17	39	relevant	relevant	ADJ
ijassa-419	17	40	theoretical	theoretical	ADJ
ijassa-419	17	41	researches[2	researches[2	PROPN
ijassa-419	17	42	]	]	PUNCT
ijassa-419	17	43	.	.	PUNCT
ijassa-419	18	1	additionally	additionally	ADV
ijassa-419	18	2	,	,	PUNCT
ijassa-419	18	3	they	they	PRON
ijassa-419	18	4	developed	develop	VERB
ijassa-419	18	5	the	the	DET
ijassa-419	18	6	plant	plant	NOUN
ijassa-419	18	7	simulation	simulation	NOUN
ijassa-419	18	8	software	software	PROPN
ijassa-419	18	9	l	l	PROPN
ijassa-419	18	10	-	-	PUNCT
ijassa-419	18	11	studio[2,5	studio[2,5	NOUN
ijassa-419	18	12	]	]	PUNCT
ijassa-419	18	13	.	.	PUNCT
ijassa-419	19	1	because	because	SCONJ
ijassa-419	19	2	there	there	PRON
ijassa-419	19	3	has	have	AUX
ijassa-419	19	4	not	not	PART
ijassa-419	19	5	been	be	AUX
ijassa-419	19	6	any	any	DET
ijassa-419	19	7	rigorous	rigorous	ADJ
ijassa-419	19	8	mathematical	mathematical	ADJ
ijassa-419	19	9	definition	definition	NOUN
ijassa-419	19	10	established	establish	VERB
ijassa-419	19	11	for	for	ADP
ijassa-419	19	12	l	l	NOUN
ijassa-419	19	13	systems	system	NOUN
ijassa-419	19	14	,	,	PUNCT
ijassa-419	19	15	all	all	PRON
ijassa-419	19	16	published	publish	VERB
ijassa-419	19	17	studies	study	NOUN
ijassa-419	19	18	on	on	ADP
ijassa-419	19	19	the	the	DET
ijassa-419	19	20	subject	subject	NOUN
ijassa-419	19	21	have	have	AUX
ijassa-419	19	22	stayed	stay	VERB
ijassa-419	19	23	only	only	ADV
ijassa-419	19	24	at	at	ADP
ijassa-419	19	25	the	the	DET
ijassa-419	19	26	level	level	NOUN
ijassa-419	19	27	of	of	ADP
ijassa-419	19	28	innovative	innovative	ADJ
ijassa-419	19	29	designs	design	NOUN
ijassa-419	19	30	without	without	ADP
ijassa-419	19	31	much	much	ADJ
ijassa-419	19	32	theoretical	theoretical	ADJ
ijassa-419	19	33	support	support	NOUN
ijassa-419	19	34	.	.	PUNCT
ijassa-419	20	1	on	on	ADP
ijassa-419	20	2	the	the	DET
ijassa-419	20	3	other	other	ADJ
ijassa-419	20	4	hand	hand	NOUN
ijassa-419	20	5	,	,	PUNCT
ijassa-419	20	6	as	as	SCONJ
ijassa-419	20	7	shown	show	VERB
ijassa-419	20	8	in	in	ADP
ijassa-419	20	9	(	(	PUNCT
ijassa-419	20	10	lin	lin	PROPN
ijassa-419	20	11	,	,	PUNCT
ijassa-419	20	12	1999)[6	1999)[6	NUM
ijassa-419	20	13	]	]	PUNCT
ijassa-419	20	14	,	,	PUNCT
ijassa-419	20	15	set	set	VERB
ijassa-419	20	16	theory	theory	NOUN
ijassa-419	20	17	is	be	AUX
ijassa-419	20	18	a	a	DET
ijassa-419	20	19	good	good	ADJ
ijassa-419	20	20	tool	tool	NOUN
ijassa-419	20	21	for	for	ADP
ijassa-419	20	22	the	the	DET
ijassa-419	20	23	theoretical	theoretical	ADJ
ijassa-419	20	24	framework	framework	NOUN
ijassa-419	20	25	of	of	ADP
ijassa-419	20	26	systemics	systemic	NOUN
ijassa-419	20	27	.	.	PUNCT
ijassa-419	21	1	in	in	ADP
ijassa-419	21	2	this	this	DET
ijassa-419	21	3	paper	paper	NOUN
ijassa-419	21	4	,	,	PUNCT
ijassa-419	21	5	starting	start	VERB
ijassa-419	21	6	from	from	ADP
ijassa-419	21	7	the	the	DET
ijassa-419	21	8	basics	basic	NOUN
ijassa-419	21	9	of	of	ADP
ijassa-419	21	10	set	set	NOUN
ijassa-419	21	11	theory	theory	NOUN
ijassa-419	21	12	,	,	PUNCT
ijassa-419	21	13	we	we	PRON
ijassa-419	21	14	will	will	AUX
ijassa-419	21	15	develop	develop	VERB
ijassa-419	21	16	a	a	DET
ijassa-419	21	17	rigorous	rigorous	ADJ
ijassa-419	21	18	mathematical	mathematical	ADJ
ijassa-419	21	19	definition	definition	NOUN
ijassa-419	21	20	for	for	ADP
ijassa-419	21	21	simple	simple	ADJ
ijassa-419	21	22	l	l	NOUN
ijassa-419	21	23	systems	system	NOUN
ijassa-419	21	24	.	.	PUNCT
ijassa-419	22	1	on	on	ADP
ijassa-419	22	2	the	the	DET
ijassa-419	22	3	basis	basis	NOUN
ijassa-419	22	4	of	of	ADP
ijassa-419	22	5	this	this	DET
ijassa-419	22	6	definition	definition	NOUN
ijassa-419	22	7	,	,	PUNCT
ijassa-419	22	8	we	we	PRON
ijassa-419	22	9	establish	establish	VERB
ijassa-419	22	10	some	some	PRON
ijassa-419	22	11	of	of	ADP
ijassa-419	22	12	the	the	DET
ijassa-419	22	13	general	general	ADJ
ijassa-419	22	14	properties	property	NOUN
ijassa-419	22	15	simple	simple	ADJ
ijassa-419	22	16	l	l	NOUN
ijassa-419	22	17	systems	system	NOUN
ijassa-419	22	18	satisfy	satisfy	VERB
ijassa-419	22	19	so	so	SCONJ
ijassa-419	22	20	that	that	SCONJ
ijassa-419	22	21	our	our	PRON
ijassa-419	22	22	constructed	construct	VERB
ijassa-419	22	23	theoretical	theoretical	ADJ
ijassa-419	22	24	framework	framework	NOUN
ijassa-419	22	25	is	be	AUX
ijassa-419	22	26	expected	expect	VERB
ijassa-419	22	27	to	to	PART
ijassa-419	22	28	provide	provide	VERB
ijassa-419	22	29	the	the	DET
ijassa-419	22	30	needed	need	VERB
ijassa-419	22	31	fundamental	fundamental	ADJ
ijassa-419	22	32	ground	ground	NOUN
ijassa-419	22	33	for	for	ADP
ijassa-419	22	34	further	further	ADJ
ijassa-419	22	35	investigation	investigation	NOUN
ijassa-419	22	36	of	of	ADP
ijassa-419	22	37	l	l	NOUN
ijassa-419	22	38	systems	system	NOUN
ijassa-419	22	39	.	.	PUNCT
ijassa-419	23	1	2	2	NUM
ijassa-419	23	2	the	the	DET
ijassa-419	23	3	definition	definition	NOUN
ijassa-419	23	4	of	of	ADP
ijassa-419	23	5	simple	simple	ADJ
ijassa-419	23	6	l	l	NOUN
ijassa-419	23	7	systems	system	NOUN
ijassa-419	23	8	the	the	DET
ijassa-419	23	9	fact	fact	NOUN
ijassa-419	23	10	is	be	AUX
ijassa-419	23	11	that	that	SCONJ
ijassa-419	23	12	l	l	NOUN
ijassa-419	23	13	-	-	NOUN
ijassa-419	23	14	systems	system	NOUN
ijassa-419	23	15	represent	represent	VERB
ijassa-419	23	16	a	a	DET
ijassa-419	23	17	formal	formal	ADJ
ijassa-419	23	18	language	language	NOUN
ijassa-419	23	19	;	;	PUNCT
ijassa-419	23	20	it	it	PRON
ijassa-419	23	21	can	can	AUX
ijassa-419	23	22	be	be	AUX
ijassa-419	23	23	divided	divide	VERB
ijassa-419	23	24	into	into	ADP
ijassa-419	23	25	three	three	NUM
ijassa-419	23	26	classes	class	NOUN
ijassa-419	23	27	:	:	PUNCT
ijassa-419	23	28	0l	0l	NUM
ijassa-419	23	29	system	system	NOUN
ijassa-419	23	30	,	,	PUNCT
ijassa-419	23	31	1l	1l	NUM
ijassa-419	23	32	system	system	NOUN
ijassa-419	23	33	,	,	PUNCT
ijassa-419	23	34	and	and	CCONJ
ijassa-419	23	35	2l	2l	NUM
ijassa-419	23	36	system	system	NOUN
ijassa-419	23	37	.	.	PUNCT
ijassa-419	24	1	a	a	DET
ijassa-419	24	2	0l	0l	NUM
ijassa-419	24	3	system	system	NOUN
ijassa-419	24	4	stands	stand	VERB
ijassa-419	24	5	for	for	ADP
ijassa-419	24	6	an	an	DET
ijassa-419	24	7	l	l	NOUN
ijassa-419	24	8	system	system	NOUN
ijassa-419	24	9	that	that	PRON
ijassa-419	24	10	is	be	AUX
ijassa-419	24	11	context	context	ADV
ijassa-419	24	12	free	free	ADJ
ijassa-419	24	13	.	.	PUNCT
ijassa-419	25	1	that	that	PRON
ijassa-419	25	2	is	is	ADV
ijassa-419	25	3	,	,	PUNCT
ijassa-419	25	4	the	the	DET
ijassa-419	25	5	behavior	behavior	NOUN
ijassa-419	25	6	of	of	ADP
ijassa-419	25	7	each	each	DET
ijassa-419	25	8	element	element	NOUN
ijassa-419	25	9	is	be	AUX
ijassa-419	25	10	solely	solely	ADV
ijassa-419	25	11	determined	determine	VERB
ijassa-419	25	12	by	by	ADP
ijassa-419	25	13	the	the	DET
ijassa-419	25	14	rewriting	rewrite	VERB
ijassa-419	25	15	rule	rule	NOUN
ijassa-419	25	16	;	;	PUNCT
ijassa-419	25	17	the	the	DET
ijassa-419	25	18	current	current	ADJ
ijassa-419	25	19	state	state	NOUN
ijassa-419	25	20	of	of	ADP
ijassa-419	25	21	the	the	DET
ijassa-419	25	22	system	system	NOUN
ijassa-419	25	23	has	have	VERB
ijassa-419	25	24	something	something	PRON
ijassa-419	25	25	to	to	PART
ijassa-419	25	26	do	do	VERB
ijassa-419	25	27	only	only	ADV
ijassa-419	25	28	with	with	ADP
ijassa-419	25	29	the	the	DET
ijassa-419	25	30	state	state	NOUN
ijassa-419	25	31	of	of	ADP
ijassa-419	25	32	the	the	DET
ijassa-419	25	33	immediate	immediate	ADJ
ijassa-419	25	34	previous	previous	ADJ
ijassa-419	25	35	time	time	NOUN
ijassa-419	25	36	moment	moment	NOUN
ijassa-419	25	37	and	and	CCONJ
ijassa-419	25	38	has	have	VERB
ijassa-419	25	39	nothing	nothing	PRON
ijassa-419	25	40	to	to	PART
ijassa-419	25	41	do	do	VERB
ijassa-419	25	42	with	with	ADP
ijassa-419	25	43	any	any	DET
ijassa-419	25	44	surrounding	surround	VERB
ijassa-419	25	45	element	element	NOUN
ijassa-419	25	46	.	.	PUNCT
ijassa-419	26	1	among	among	ADP
ijassa-419	26	2	l	l	PROPN
ijassa-419	26	3	systems	system	NOUN
ijassa-419	26	4	are	be	AUX
ijassa-419	26	5	0l	0l	NUM
ijassa-419	26	6	systems	system	NOUN
ijassa-419	26	7	the	the	DET
ijassa-419	26	8	simplest	simplest	NOUN
ijassa-419	26	9	;	;	PUNCT
ijassa-419	26	10	that	that	PRON
ijassa-419	26	11	is	be	AUX
ijassa-419	26	12	why	why	SCONJ
ijassa-419	26	13	each	each	DET
ijassa-419	26	14	0l	0l	NUM
ijassa-419	26	15	system	system	NOUN
ijassa-419	26	16	is	be	AUX
ijassa-419	26	17	also	also	ADV
ijassa-419	26	18	referred	refer	VERB
ijassa-419	26	19	to	to	ADP
ijassa-419	26	20	as	as	ADP
ijassa-419	26	21	a	a	DET
ijassa-419	26	22	simple	simple	ADJ
ijassa-419	26	23	l	l	NOUN
ijassa-419	26	24	system	system	NOUN
ijassa-419	26	25	.	.	PUNCT
ijassa-419	27	1	each	each	DET
ijassa-419	27	2	1l	1l	NUM
ijassa-419	27	3	system	system	NOUN
ijassa-419	27	4	stands	stand	VERB
ijassa-419	27	5	for	for	ADP
ijassa-419	27	6	a	a	DET
ijassa-419	27	7	context	context	NOUN
ijassa-419	27	8	sensitive	sensitive	ADJ
ijassa-419	27	9	l	l	NOUN
ijassa-419	27	10	system	system	NOUN
ijassa-419	27	11	that	that	PRON
ijassa-419	27	12	considers	consider	VERB
ijassa-419	27	13	only	only	ADV
ijassa-419	27	14	one	one	NUM
ijassa-419	27	15	single	single	ADJ
ijassa-419	27	16	-	-	PUNCT
ijassa-419	27	17	sided	sided	ADJ
ijassa-419	27	18	grammatical	grammatical	ADJ
ijassa-419	27	19	relationship	relationship	NOUN
ijassa-419	27	20	.	.	PUNCT
ijassa-419	28	1	the	the	DET
ijassa-419	28	2	current	current	ADJ
ijassa-419	28	3	state	state	NOUN
ijassa-419	28	4	of	of	ADP
ijassa-419	28	5	the	the	DET
ijassa-419	28	6	system	system	NOUN
ijassa-419	28	7	has	have	VERB
ijassa-419	28	8	something	something	PRON
ijassa-419	28	9	to	to	PART
ijassa-419	28	10	do	do	VERB
ijassa-419	28	11	with	with	ADP
ijassa-419	28	12	not	not	PART
ijassa-419	28	13	only	only	ADV
ijassa-419	28	14	the	the	DET
ijassa-419	28	15	state	state	NOUN
ijassa-419	28	16	of	of	ADP
ijassa-419	28	17	the	the	DET
ijassa-419	28	18	immediate	immediate	ADJ
ijassa-419	28	19	previous	previous	ADJ
ijassa-419	28	20	time	time	NOUN
ijassa-419	28	21	moment	moment	NOUN
ijassa-419	28	22	but	but	CCONJ
ijassa-419	28	23	also	also	ADV
ijassa-419	28	24	the	the	DET
ijassa-419	28	25	state	state	NOUN
ijassa-419	28	26	of	of	ADP
ijassa-419	28	27	the	the	DET
ijassa-419	28	28	elements	element	NOUN
ijassa-419	28	29	on	on	ADP
ijassa-419	28	30	one	one	NUM
ijassa-419	28	31	side	side	NOUN
ijassa-419	28	32	,	,	PUNCT
ijassa-419	28	33	either	either	CCONJ
ijassa-419	28	34	left	leave	VERB
ijassa-419	28	35	associated	associated	ADJ
ijassa-419	28	36	or	or	CCONJ
ijassa-419	28	37	right	right	ADV
ijassa-419	28	38	associated	associate	VERB
ijassa-419	28	39	.	.	PUNCT
ijassa-419	29	1	each	each	DET
ijassa-419	29	2	2l	2l	NUM
ijassa-419	29	3	system	system	NOUN
ijassa-419	29	4	is	be	AUX
ijassa-419	29	5	also	also	ADV
ijassa-419	29	6	a	a	DET
ijassa-419	29	7	context	context	NOUN
ijassa-419	29	8	sensitive	sensitive	ADJ
ijassa-419	29	9	l	l	NOUN
ijassa-419	29	10	system	system	NOUN
ijassa-419	29	11	that	that	PRON
ijassa-419	29	12	,	,	PUNCT
ijassa-419	29	13	different	different	ADJ
ijassa-419	29	14	of	of	ADP
ijassa-419	29	15	1l	1l	NUM
ijassa-419	29	16	systems	system	NOUN
ijassa-419	29	17	,	,	PUNCT
ijassa-419	29	18	it	it	PRON
ijassa-419	29	19	considers	consider	VERB
ijassa-419	29	20	grammatical	grammatical	ADJ
ijassa-419	29	21	relationships	relationship	NOUN
ijassa-419	29	22	from	from	ADP
ijassa-419	29	23	both	both	DET
ijassa-419	29	24	sides	side	NOUN
ijassa-419	29	25	.	.	PUNCT
ijassa-419	30	1	that	that	PRON
ijassa-419	30	2	is	is	ADV
ijassa-419	30	3	,	,	PUNCT
ijassa-419	30	4	the	the	DET
ijassa-419	30	5	current	current	ADJ
ijassa-419	30	6	state	state	NOUN
ijassa-419	30	7	of	of	ADP
ijassa-419	30	8	the	the	DET
ijassa-419	30	9	system	system	NOUN
ijassa-419	30	10	is	be	AUX
ijassa-419	30	11	related	relate	VERB
ijassa-419	30	12	to	to	ADP
ijassa-419	30	13	not	not	PART
ijassa-419	30	14	only	only	ADV
ijassa-419	30	15	the	the	DET
ijassa-419	30	16	state	state	NOUN
ijassa-419	30	17	of	of	ADP
ijassa-419	30	18	the	the	DET
ijassa-419	30	19	immediate	immediate	ADJ
ijassa-419	30	20	previous	previous	ADJ
ijassa-419	30	21	time	time	NOUN
ijassa-419	30	22	moment	moment	NOUN
ijassa-419	30	23	,	,	PUNCT
ijassa-419	30	24	but	but	CCONJ
ijassa-419	30	25	also	also	ADV
ijassa-419	30	26	the	the	DET
ijassa-419	30	27	states	state	NOUN
ijassa-419	30	28	of	of	ADP
ijassa-419	30	29	the	the	DET
ijassa-419	30	30	surrounding	surround	VERB
ijassa-419	30	31	elements	element	NOUN
ijassa-419	30	32	.	.	PUNCT
ijassa-419	31	1	it	it	PRON
ijassa-419	31	2	represents	represent	VERB
ijassa-419	31	3	a	a	DET
ijassa-419	31	4	method	method	NOUN
ijassa-419	31	5	that	that	PRON
ijassa-419	31	6	is	be	AUX
ijassa-419	31	7	most	most	ADV
ijassa-419	31	8	sensitive	sensitive	ADJ
ijassa-419	31	9	to	to	ADP
ijassa-419	31	10	the	the	DET
ijassa-419	31	11	context	context	NOUN
ijassa-419	31	12	.	.	PUNCT
ijassa-419	32	1	these	these	DET
ijassa-419	32	2	three	three	NUM
ijassa-419	32	3	classes	class	NOUN
ijassa-419	32	4	of	of	ADP
ijassa-419	32	5	l	l	PROPN
ijassa-419	32	6	systems	system	NOUN
ijassa-419	32	7	are	be	AUX
ijassa-419	32	8	further	far	ADV
ijassa-419	32	9	divided	divide	VERB
ijassa-419	32	10	into	into	ADP
ijassa-419	32	11	deterministic	deterministic	ADJ
ijassa-419	32	12	and	and	CCONJ
ijassa-419	32	13	random	random	ADJ
ijassa-419	32	14	l	l	NOUN
ijassa-419	32	15	systems	system	NOUN
ijassa-419	32	16	depending	depend	VERB
ijassa-419	32	17	on	on	ADP
ijassa-419	32	18	whether	whether	SCONJ
ijassa-419	32	19	or	or	CCONJ
ijassa-419	32	20	not	not	PART
ijassa-419	32	21	the	the	DET
ijassa-419	32	22	rewrite	rewrite	NOUN
ijassa-419	32	23	rules	rule	NOUN
ijassa-419	32	24	are	be	AUX
ijassa-419	32	25	deterministic	deterministic	ADJ
ijassa-419	32	26	.	.	PUNCT
ijassa-419	33	1	let	let	VERB
ijassa-419	33	2	s	s	VERB
ijassa-419	33	3	=	=	NOUN
ijassa-419	33	4	{	{	PUNCT
ijassa-419	33	5	s1	s1	NOUN
ijassa-419	33	6	,	,	PUNCT
ijassa-419	33	7	s2	s2	NOUN
ijassa-419	33	8	,	,	PUNCT
ijassa-419	33	9	.	.	PUNCT
ijassa-419	33	10	.	.	PUNCT
ijassa-419	34	1	.	.	PUNCT
ijassa-419	35	1	,	,	PUNCT
ijassa-419	35	2	sn	sn	AUX
ijassa-419	35	3	}	}	PUNCT
ijassa-419	35	4	be	be	AUX
ijassa-419	35	5	a	a	DET
ijassa-419	35	6	finite	finite	ADJ
ijassa-419	35	7	set	set	NOUN
ijassa-419	35	8	of	of	ADP
ijassa-419	35	9	characters	character	NOUN
ijassa-419	35	10	of	of	ADP
ijassa-419	35	11	a	a	DET
ijassa-419	35	12	language	language	NOUN
ijassa-419	35	13	,	,	PUNCT
ijassa-419	35	14	say	say	INTJ
ijassa-419	35	15	,	,	PUNCT
ijassa-419	35	16	english	english	PROPN
ijassa-419	35	17	,	,	PUNCT
ijassa-419	35	18	and	and	CCONJ
ijassa-419	35	19	s∗	s∗	VERB
ijassa-419	35	20	the	the	DET
ijassa-419	35	21	set	set	NOUN
ijassa-419	35	22	of	of	ADP
ijassa-419	35	23	all	all	DET
ijassa-419	35	24	strings	string	NOUN
ijassa-419	35	25	of	of	ADP
ijassa-419	35	26	characters	character	NOUN
ijassa-419	35	27	from	from	ADP
ijassa-419	35	28	s.	s.	PROPN
ijassa-419	35	29	because	because	SCONJ
ijassa-419	35	30	s	s	PROPN
ijassa-419	35	31	⊂	⊂	PROPN
ijassa-419	35	32	s∗	s∗	PROPN
ijassa-419	35	33	,	,	PUNCT
ijassa-419	35	34	s∗	s∗	PROPN
ijassa-419	35	35	is	be	AUX
ijassa-419	35	36	a	a	DET
ijassa-419	35	37	non	non	ADJ
ijassa-419	35	38	-	-	ADJ
ijassa-419	35	39	empty	empty	ADJ
ijassa-419	35	40	set	set	NOUN
ijassa-419	35	41	.	.	PUNCT
ijassa-419	36	1	∀α	∀α	NOUN
ijassa-419	36	2	,	,	PUNCT
ijassa-419	36	3	β	β	X
ijassa-419	36	4	∈	∈	PROPN
ijassa-419	36	5	s∗	s∗	PROPN
ijassa-419	36	6	,	,	PUNCT
ijassa-419	36	7	define	define	VERB
ijassa-419	36	8	that	that	SCONJ
ijassa-419	36	9	α	α	NOUN
ijassa-419	36	10	=	=	X
ijassa-419	36	11	β	β	X
ijassa-419	36	12	⇔	⇔	PROPN
ijassa-419	36	13	both	both	CCONJ
ijassa-419	36	14	α	α	PROPN
ijassa-419	36	15	and	and	CCONJ
ijassa-419	36	16	β	β	X
ijassa-419	36	17	are	be	AUX
ijassa-419	36	18	identical	identical	ADJ
ijassa-419	36	19	,	,	PUNCT
ijassa-419	36	20	meanings	meaning	NOUN
ijassa-419	36	21	that	that	PRON
ijassa-419	36	22	they	they	PRON
ijassa-419	36	23	have	have	VERB
ijassa-419	36	24	the	the	DET
ijassa-419	36	25	same	same	ADJ
ijassa-419	36	26	length	length	NOUN
ijassa-419	36	27	and	and	CCONJ
ijassa-419	36	28	order	order	NOUN
ijassa-419	36	29	of	of	ADP
ijassa-419	36	30	the	the	DET
ijassa-419	36	31	same	same	ADJ
ijassa-419	36	32	characters	character	NOUN
ijassa-419	36	33	.	.	PUNCT
ijassa-419	37	1	now	now	ADV
ijassa-419	37	2	,	,	PUNCT
ijassa-419	37	3	define	define	VERB
ijassa-419	37	4	the	the	DET
ijassa-419	37	5	addition	addition	NOUN
ijassa-419	37	6	operation	operation	NOUN
ijassa-419	37	7	⊕	⊕	PROPN
ijassa-419	37	8	on	on	ADP
ijassa-419	37	9	s∗	s∗	PROPN
ijassa-419	37	10	as	as	SCONJ
ijassa-419	37	11	follows	follow	VERB
ijassa-419	37	12	:	:	PUNCT
ijassa-419	37	13	α	α	X
ijassa-419	37	14	⊕	⊕	NOUN
ijassa-419	37	15	β	β	X
ijassa-419	37	16	=	=	PUNCT
ijassa-419	38	1	αβ	αβ	INTJ
ijassa-419	38	2	=	=	PUNCT
ijassa-419	38	3	the	the	DET
ijassa-419	38	4	string	string	NOUN
ijassa-419	38	5	of	of	ADP
ijassa-419	38	6	characters	character	NOUN
ijassa-419	38	7	of	of	ADP
ijassa-419	38	8	those	those	PRON
ijassa-419	38	9	in	in	ADP
ijassa-419	38	10	α	α	NOUN
ijassa-419	38	11	followed	follow	VERB
ijassa-419	38	12	by	by	ADP
ijassa-419	38	13	those	those	PRON
ijassa-419	38	14	in	in	ADP
ijassa-419	38	15	β	β	NOUN
ijassa-419	38	16	,	,	PUNCT
ijassa-419	38	17	∀α	∀α	NOUN
ijassa-419	38	18	,	,	PUNCT
ijassa-419	38	19	β	β	X
ijassa-419	38	20	∈	∈	PROPN
ijassa-419	38	21	s∗.	s∗.	VERB
ijassa-419	38	22	the	the	DET
ijassa-419	38	23	scalar	scalar	ADJ
ijassa-419	38	24	multiplication	multiplication	NOUN
ijassa-419	38	25	on	on	ADP
ijassa-419	38	26	s∗	s∗	PROPN
ijassa-419	38	27	is	be	AUX
ijassa-419	38	28	defined	define	VERB
ijassa-419	38	29	as	as	SCONJ
ijassa-419	38	30	follows	follow	VERB
ijassa-419	38	31	:	:	PUNCT
ijassa-419	38	32	∀α	∀α	X
ijassa-419	38	33	∈	∈	PROPN
ijassa-419	38	34	s∗	s∗	NOUN
ijassa-419	38	35	,	,	PUNCT
ijassa-419	38	36	k	k	PROPN
ijassa-419	38	37	∈	∈	PROPN
ijassa-419	38	38	z+	z+	NUM
ijassa-419	38	39	=	=	NOUN
ijassa-419	38	40	the	the	DET
ijassa-419	38	41	set	set	NOUN
ijassa-419	38	42	of	of	ADP
ijassa-419	38	43	all	all	PRON
ijassa-419	38	44	whole	whole	ADJ
ijassa-419	38	45	102	102	NUM
ijassa-419	38	46	xiaojun	xiaojun	PROPN
ijassa-419	38	47	duan	duan	PROPN
ijassa-419	38	48	:	:	PUNCT
ijassa-419	38	49	set	set	VERB
ijassa-419	38	50	-	-	PUNCT
ijassa-419	38	51	theoretic	theoretic	NOUN
ijassa-419	38	52	design	design	NOUN
ijassa-419	38	53	and	and	CCONJ
ijassa-419	38	54	analysis	analysis	NOUN
ijassa-419	38	55	of	of	ADP
ijassa-419	38	56	l	l	NOUN
ijassa-419	38	57	systems	system	NOUN
ijassa-419	38	58	numbers	number	NOUN
ijassa-419	38	59	,	,	PUNCT
ijassa-419	38	60	kα	kα	PROPN
ijassa-419	38	61	=	=	NOUN
ijassa-419	38	62	αα	αα	PROPN
ijassa-419	38	63	.	.	PUNCT
ijassa-419	38	64	.	.	PUNCT
ijassa-419	38	65	.	.	PUNCT
ijassa-419	39	1	α︸	α︸	NOUN
ijassa-419	39	2	︷︷	︷︷	PROPN
ijassa-419	39	3	︸	︸	X
ijassa-419	39	4	k	k	PROPN
ijassa-419	39	5	times	times	PROPN
ijassa-419	39	6	.	.	PUNCT
ijassa-419	40	1	then	then	ADV
ijassa-419	40	2	,	,	PUNCT
ijassa-419	40	3	the	the	DET
ijassa-419	40	4	following	follow	VERB
ijassa-419	40	5	properties	property	NOUN
ijassa-419	40	6	can	can	AUX
ijassa-419	40	7	be	be	AUX
ijassa-419	40	8	shown	show	VERB
ijassa-419	40	9	:	:	PUNCT
ijassa-419	40	10	(	(	PUNCT
ijassa-419	40	11	1)both	1)both	NUM
ijassa-419	40	12	addition	addition	NOUN
ijassa-419	40	13	and	and	CCONJ
ijassa-419	40	14	scalar	scalar	ADJ
ijassa-419	40	15	multiplication	multiplication	NOUN
ijassa-419	40	16	defined	define	VERB
ijassa-419	40	17	on	on	ADP
ijassa-419	40	18	s∗	s∗	PROPN
ijassa-419	40	19	are	be	AUX
ijassa-419	40	20	closed	close	VERB
ijassa-419	40	21	;	;	PUNCT
ijassa-419	40	22	(	(	PUNCT
ijassa-419	40	23	2)(α⊕	2)(α⊕	NUM
ijassa-419	40	24	β)⊕	β)⊕	NOUN
ijassa-419	40	25	γ	γ	X
ijassa-419	40	26	=	=	PUNCT
ijassa-419	40	27	α⊕	α⊕	PROPN
ijassa-419	40	28	(	(	PUNCT
ijassa-419	40	29	β	β	PROPN
ijassa-419	40	30	⊕	⊕	PROPN
ijassa-419	40	31	γ),∀α	γ),∀α	PROPN
ijassa-419	40	32	,	,	PUNCT
ijassa-419	40	33	β	β	X
ijassa-419	40	34	,	,	PUNCT
ijassa-419	40	35	γ	γ	PROPN
ijassa-419	40	36	∈	∈	PROPN
ijassa-419	40	37	s∗	s∗	PROPN
ijassa-419	40	38	;	;	PUNCT
ijassa-419	40	39	(	(	PUNCT
ijassa-419	40	40	3)k(lα	3)k(lα	NUM
ijassa-419	40	41	)	)	PUNCT
ijassa-419	40	42	=	=	PUNCT
ijassa-419	41	1	(	(	PUNCT
ijassa-419	41	2	kl)α,(α⊕	kl)α,(α⊕	INTJ
ijassa-419	41	3	β)⊕	β)⊕	X
ijassa-419	41	4	γ	γ	X
ijassa-419	41	5	=	=	PUNCT
ijassa-419	41	6	α⊕	α⊕	PROPN
ijassa-419	41	7	(	(	PUNCT
ijassa-419	41	8	β	β	PROPN
ijassa-419	41	9	⊕	⊕	PROPN
ijassa-419	41	10	γ),∀α	γ),∀α	PROPN
ijassa-419	41	11	,	,	PUNCT
ijassa-419	41	12	β	β	X
ijassa-419	41	13	,	,	PUNCT
ijassa-419	41	14	γ	γ	PROPN
ijassa-419	41	15	∈	∈	PROPN
ijassa-419	41	16	s∗;and	s∗;and	NOUN
ijassa-419	41	17	(	(	PUNCT
ijassa-419	41	18	4)(k	4)(k	NUM
ijassa-419	41	19	+	+	CCONJ
ijassa-419	41	20	l)α	l)α	ADJ
ijassa-419	41	21	=	=	PUNCT
ijassa-419	41	22	kα⊕	kα⊕	PROPN
ijassa-419	42	1	lα,∀α	lα,∀α	PROPN
ijassa-419	42	2	∈	∈	PROPN
ijassa-419	42	3	s∗	s∗	PROPN
ijassa-419	42	4	,	,	PUNCT
ijassa-419	42	5	k	k	NOUN
ijassa-419	42	6	,	,	PUNCT
ijassa-419	42	7	l	l	PROPN
ijassa-419	42	8	∈	∈	PROPN
ijassa-419	42	9	z+	z+	PUNCT
ijassa-419	42	10	.	.	PUNCT
ijassa-419	43	1	before	before	SCONJ
ijassa-419	43	2	we	we	PRON
ijassa-419	43	3	develop	develop	VERB
ijassa-419	43	4	a	a	DET
ijassa-419	43	5	rigorous	rigorous	ADJ
ijassa-419	43	6	definition	definition	NOUN
ijassa-419	43	7	of	of	ADP
ijassa-419	43	8	simple	simple	ADJ
ijassa-419	43	9	l	l	NOUN
ijassa-419	43	10	systems	system	NOUN
ijassa-419	43	11	,	,	PUNCT
ijassa-419	43	12	let	let	VERB
ijassa-419	43	13	us	we	PRON
ijassa-419	43	14	first	first	ADV
ijassa-419	43	15	look	look	VERB
ijassa-419	43	16	at	at	ADP
ijassa-419	43	17	a	a	DET
ijassa-419	43	18	specific	specific	ADJ
ijassa-419	43	19	mapping	mapping	NOUN
ijassa-419	43	20	s∗	s∗	PROPN
ijassa-419	43	21	→	→	SYM
ijassa-419	43	22	s∗	s∗	PROPN
ijassa-419	43	23	,	,	PUNCT
ijassa-419	43	24	known	know	VERB
ijassa-419	43	25	as	as	ADP
ijassa-419	43	26	l	l	NOUN
ijassa-419	43	27	mapping	mapping	NOUN
ijassa-419	43	28	.	.	PUNCT
ijassa-419	44	1	2.1	2.1	NUM
ijassa-419	44	2	the	the	DET
ijassa-419	44	3	l	l	NOUN
ijassa-419	44	4	mapping	mapping	NOUN
ijassa-419	44	5	definition	definition	NOUN
ijassa-419	44	6	2.1(production	2.1(production	NUM
ijassa-419	44	7	rules	rule	NOUN
ijassa-419	44	8	)	)	PUNCT
ijassa-419	44	9	.	.	PUNCT
ijassa-419	45	1	for	for	ADP
ijassa-419	45	2	any	any	DET
ijassa-419	45	3	si	si	PROPN
ijassa-419	45	4	∈	∈	PROPN
ijassa-419	45	5	s	s	PROPN
ijassa-419	45	6	,	,	PUNCT
ijassa-419	45	7	1	1	NUM
ijassa-419	45	8	≤	≤	NUM
ijassa-419	45	9	i	i	PRON
ijassa-419	45	10	≤	≤	PROPN
ijassa-419	45	11	n	n	CCONJ
ijassa-419	45	12	,	,	PUNCT
ijassa-419	45	13	if	if	SCONJ
ijassa-419	45	14	an	an	DET
ijassa-419	45	15	ordered	order	VERB
ijassa-419	45	16	pair	pair	NOUN
ijassa-419	45	17	(	(	PUNCT
ijassa-419	45	18	si	si	X
ijassa-419	45	19	,	,	PUNCT
ijassa-419	45	20	α	α	NOUN
ijassa-419	45	21	)	)	PUNCT
ijassa-419	45	22	∈	∈	PROPN
ijassa-419	45	23	s	s	PART
ijassa-419	45	24	×	×	NOUN
ijassa-419	45	25	s∗	s∗	NOUN
ijassa-419	45	26	can	can	AUX
ijassa-419	45	27	be	be	AUX
ijassa-419	45	28	defined	define	VERB
ijassa-419	45	29	,	,	PUNCT
ijassa-419	45	30	then	then	ADV
ijassa-419	45	31	this	this	DET
ijassa-419	45	32	pair	pair	NOUN
ijassa-419	45	33	defines	define	VERB
ijassa-419	45	34	a	a	DET
ijassa-419	45	35	relation	relation	NOUN
ijassa-419	45	36	pi	pi	NOUN
ijassa-419	45	37	from	from	ADP
ijassa-419	45	38	si	si	PROPN
ijassa-419	45	39	to	to	ADP
ijassa-419	45	40	α	α	PRON
ijassa-419	45	41	,	,	PUNCT
ijassa-419	45	42	known	know	VERB
ijassa-419	45	43	as	as	ADP
ijassa-419	45	44	a	a	DET
ijassa-419	45	45	production	production	NOUN
ijassa-419	45	46	rule	rule	NOUN
ijassa-419	45	47	from	from	ADP
ijassa-419	45	48	s	s	PRON
ijassa-419	45	49	to	to	PART
ijassa-419	45	50	s∗.	s∗.	ADJ
ijassa-419	45	51	definition	definition	NOUN
ijassa-419	45	52	2.2	2.2	NUM
ijassa-419	45	53	(	(	PUNCT
ijassa-419	45	54	same	same	ADJ
ijassa-419	45	55	class	class	NOUN
ijassa-419	45	56	production	production	NOUN
ijassa-419	45	57	rules	rule	NOUN
ijassa-419	45	58	)	)	PUNCT
ijassa-419	45	59	.	.	PUNCT
ijassa-419	46	1	for	for	ADP
ijassa-419	46	2	a	a	DET
ijassa-419	46	3	given	give	VERB
ijassa-419	46	4	si	si	NOUN
ijassa-419	46	5	∈	∈	PROPN
ijassa-419	46	6	s	s	NOUN
ijassa-419	46	7	,	,	PUNCT
ijassa-419	46	8	if	if	SCONJ
ijassa-419	46	9	there	there	PRON
ijassa-419	46	10	are	be	VERB
ijassa-419	46	11	r	r	NOUN
ijassa-419	46	12	≥	≥	NUM
ijassa-419	46	13	1	1	NUM
ijassa-419	46	14	production	production	NOUN
ijassa-419	46	15	rules	rule	NOUN
ijassa-419	46	16	p	p	X
ijassa-419	46	17	(	(	PUNCT
ijassa-419	46	18	1	1	NUM
ijassa-419	46	19	)	)	PUNCT
ijassa-419	46	20	i	i	PRON
ijassa-419	46	21	,	,	PUNCT
ijassa-419	46	22	p	p	X
ijassa-419	46	23	(	(	PUNCT
ijassa-419	46	24	2	2	NUM
ijassa-419	46	25	)	)	PUNCT
ijassa-419	46	26	i	i	PRON
ijassa-419	46	27	,	,	PUNCT
ijassa-419	46	28	.	.	PUNCT
ijassa-419	46	29	.	.	PUNCT
ijassa-419	47	1	.	.	PUNCT
ijassa-419	48	1	,	,	PUNCT
ijassa-419	48	2	p	p	X
ijassa-419	48	3	(	(	PUNCT
ijassa-419	48	4	r	r	NOUN
ijassa-419	48	5	)	)	PUNCT
ijassa-419	48	6	i	i	PRON
ijassa-419	48	7	defined	define	VERB
ijassa-419	48	8	for	for	ADP
ijassa-419	48	9	si	si	INTJ
ijassa-419	48	10	such	such	ADJ
ijassa-419	48	11	that	that	SCONJ
ijassa-419	48	12	∀j	∀j	PROPN
ijassa-419	48	13	̸=	̸=	PROPN
ijassa-419	48	14	k(1	k(1	PROPN
ijassa-419	48	15	≤	≤	PROPN
ijassa-419	48	16	j	j	PROPN
ijassa-419	48	17	,	,	PUNCT
ijassa-419	48	18	k	k	PROPN
ijassa-419	48	19	≤	≤	NUM
ijassa-419	48	20	r	r	NOUN
ijassa-419	48	21	)	)	PUNCT
ijassa-419	48	22	,	,	PUNCT
ijassa-419	48	23	p	p	X
ijassa-419	48	24	(	(	PUNCT
ijassa-419	48	25	j	j	NOUN
ijassa-419	48	26	)	)	PUNCT
ijassa-419	48	27	i	i	PRON
ijassa-419	48	28	(	(	PUNCT
ijassa-419	48	29	si	si	X
ijassa-419	48	30	)	)	PUNCT
ijassa-419	48	31	̸=	̸=	PROPN
ijassa-419	48	32	p	p	NOUN
ijassa-419	48	33	(	(	PUNCT
ijassa-419	48	34	k	k	NOUN
ijassa-419	48	35	)	)	PUNCT
ijassa-419	48	36	i	i	PRON
ijassa-419	48	37	(	(	PUNCT
ijassa-419	48	38	si	si	X
ijassa-419	48	39	)	)	PUNCT
ijassa-419	48	40	,	,	PUNCT
ijassa-419	48	41	then	then	ADV
ijassa-419	48	42	p	p	X
ijassa-419	48	43	(	(	PUNCT
ijassa-419	48	44	1	1	NUM
ijassa-419	48	45	)	)	PUNCT
ijassa-419	48	46	i	i	PRON
ijassa-419	48	47	,	,	PUNCT
ijassa-419	48	48	p	p	X
ijassa-419	48	49	(	(	PUNCT
ijassa-419	48	50	2	2	NUM
ijassa-419	48	51	)	)	PUNCT
ijassa-419	48	52	i	i	PRON
ijassa-419	48	53	,	,	PUNCT
ijassa-419	48	54	.	.	PUNCT
ijassa-419	48	55	.	.	PUNCT
ijassa-419	48	56	.	.	PUNCT
ijassa-419	49	1	,	,	PUNCT
ijassa-419	49	2	p	p	X
ijassa-419	49	3	(	(	PUNCT
ijassa-419	49	4	r	r	NOUN
ijassa-419	49	5	)	)	PUNCT
ijassa-419	49	6	i	i	PRON
ijassa-419	49	7	are	be	AUX
ijassa-419	49	8	referred	refer	VERB
ijassa-419	49	9	to	to	ADP
ijassa-419	49	10	as	as	ADP
ijassa-419	49	11	r	r	NOUN
ijassa-419	49	12	same	same	ADJ
ijassa-419	49	13	class	class	NOUN
ijassa-419	49	14	production	production	NOUN
ijassa-419	49	15	rules	rule	NOUN
ijassa-419	49	16	of	of	ADP
ijassa-419	49	17	the	the	DET
ijassa-419	49	18	character	character	NOUN
ijassa-419	49	19	si	si	NOUN
ijassa-419	49	20	,	,	PUNCT
ijassa-419	49	21	and	and	CCONJ
ijassa-419	49	22	pi	pi	NOUN
ijassa-419	49	23	=	=	SYM
ijassa-419	49	24	{	{	PUNCT
ijassa-419	49	25	p(1)i	p(1)i	PROPN
ijassa-419	49	26	,	,	PUNCT
ijassa-419	49	27	p	p	X
ijassa-419	49	28	(	(	PUNCT
ijassa-419	49	29	2	2	NUM
ijassa-419	49	30	)	)	PUNCT
ijassa-419	49	31	i	i	PRON
ijassa-419	49	32	,	,	PUNCT
ijassa-419	49	33	.	.	PUNCT
ijassa-419	49	34	.	.	PUNCT
ijassa-419	50	1	.	.	PUNCT
ijassa-419	51	1	,	,	PUNCT
ijassa-419	51	2	p	p	X
ijassa-419	51	3	(	(	PUNCT
ijassa-419	51	4	r	r	NOUN
ijassa-419	51	5	)	)	PUNCT
ijassa-419	51	6	i	i	NOUN
ijassa-419	51	7	}	}	PUNCT
ijassa-419	51	8	the	the	DET
ijassa-419	51	9	set	set	NOUN
ijassa-419	51	10	of	of	ADP
ijassa-419	51	11	same	same	ADJ
ijassa-419	51	12	class	class	NOUN
ijassa-419	51	13	production	production	NOUN
ijassa-419	51	14	rules	rule	NOUN
ijassa-419	51	15	of	of	ADP
ijassa-419	51	16	the	the	DET
ijassa-419	51	17	character	character	NOUN
ijassa-419	51	18	si	si	PROPN
ijassa-419	51	19	.	.	PROPN
ijassa-419	51	20	definition	definition	NOUN
ijassa-419	51	21	2.3	2.3	NUM
ijassa-419	51	22	(	(	PUNCT
ijassa-419	51	23	l	l	NOUN
ijassa-419	51	24	mapping	mapping	NOUN
ijassa-419	51	25	)	)	PUNCT
ijassa-419	51	26	.	.	PUNCT
ijassa-419	52	1	suppose	suppose	VERB
ijassa-419	52	2	that	that	SCONJ
ijassa-419	52	3	m(≥	m(≥	ADJ
ijassa-419	52	4	n	n	CCONJ
ijassa-419	52	5	)	)	PUNCT
ijassa-419	52	6	production	production	NOUN
ijassa-419	52	7	rules	rule	NOUN
ijassa-419	52	8	p	p	X
ijassa-419	52	9	=	=	PUNCT
ijassa-419	52	10	n∪	n∪	PROPN
ijassa-419	52	11	i=1	i=1	PROPN
ijassa-419	52	12	pi	pi	NOUN
ijassa-419	52	13	from	from	ADP
ijassa-419	52	14	s	s	PRON
ijassa-419	52	15	to	to	PART
ijassa-419	52	16	s∗	s∗	PROPN
ijassa-419	52	17	are	be	AUX
ijassa-419	52	18	given	give	VERB
ijassa-419	52	19	,	,	PUNCT
ijassa-419	52	20	where	where	SCONJ
ijassa-419	52	21	each	each	DET
ijassa-419	52	22	pi	pi	NOUN
ijassa-419	52	23	is	be	AUX
ijassa-419	52	24	non	non	ADJ
ijassa-419	52	25	-	-	ADJ
ijassa-419	52	26	empty	empty	ADJ
ijassa-419	52	27	and	and	CCONJ
ijassa-419	52	28	stands	stand	VERB
ijassa-419	52	29	for	for	ADP
ijassa-419	52	30	the	the	DET
ijassa-419	52	31	same	same	ADJ
ijassa-419	52	32	class	class	NOUN
ijassa-419	52	33	production	production	NOUN
ijassa-419	52	34	rules	rule	NOUN
ijassa-419	52	35	of	of	ADP
ijassa-419	52	36	the	the	DET
ijassa-419	52	37	character	character	NOUN
ijassa-419	52	38	si	si	PROPN
ijassa-419	52	39	∈	∈	PROPN
ijassa-419	52	40	s	s	PROPN
ijassa-419	52	41	,	,	PUNCT
ijassa-419	52	42	1	1	NUM
ijassa-419	52	43	≤	≤	NUM
ijassa-419	52	44	i	i	PRON
ijassa-419	52	45	≤	≤	ADJ
ijassa-419	52	46	n.	n.	NOUN
ijassa-419	52	47	for	for	ADP
ijassa-419	52	48	any	any	DET
ijassa-419	52	49	group	group	NOUN
ijassa-419	52	50	of	of	ADP
ijassa-419	52	51	production	production	NOUN
ijassa-419	52	52	rules	rule	NOUN
ijassa-419	52	53	p1	p1	PROPN
ijassa-419	52	54	,	,	PUNCT
ijassa-419	52	55	p2	p2	NOUN
ijassa-419	52	56	,	,	PUNCT
ijassa-419	52	57	.	.	PUNCT
ijassa-419	52	58	.	.	PUNCT
ijassa-419	53	1	.	.	PUNCT
ijassa-419	54	1	,	,	PUNCT
ijassa-419	54	2	pn	pn	PROPN
ijassa-419	54	3	∈	∈	PROPN
ijassa-419	54	4	p	p	PROPN
ijassa-419	54	5	,	,	PUNCT
ijassa-419	54	6	satisfying	satisfy	VERB
ijassa-419	54	7	pi	pi	NOUN
ijassa-419	54	8	∈	∈	PROPN
ijassa-419	54	9	pi	pi	NOUN
ijassa-419	54	10	,	,	PUNCT
ijassa-419	54	11	i	i	PRON
ijassa-419	54	12	=	=	NOUN
ijassa-419	54	13	1	1	NUM
ijassa-419	54	14	,	,	PUNCT
ijassa-419	54	15	2	2	NUM
ijassa-419	54	16	,	,	PUNCT
ijassa-419	54	17	.	.	PUNCT
ijassa-419	54	18	.	.	PUNCT
ijassa-419	55	1	.	.	PUNCT
ijassa-419	56	1	,	,	PUNCT
ijassa-419	56	2	n	n	CCONJ
ijassa-419	56	3	,	,	PUNCT
ijassa-419	56	4	the	the	DET
ijassa-419	56	5	set	set	NOUN
ijassa-419	56	6	φ	φ	PROPN
ijassa-419	56	7	=	=	SYM
ijassa-419	56	8	{	{	PUNCT
ijassa-419	56	9	p1	p1	NOUN
ijassa-419	56	10	,	,	PUNCT
ijassa-419	56	11	p2	p2	NOUN
ijassa-419	56	12	,	,	PUNCT
ijassa-419	56	13	.	.	PUNCT
ijassa-419	56	14	.	.	PUNCT
ijassa-419	57	1	.	.	PUNCT
ijassa-419	58	1	,	,	PUNCT
ijassa-419	58	2	pn	pn	PROPN
ijassa-419	58	3	}	}	PUNCT
ijassa-419	58	4	defines	define	VERB
ijassa-419	58	5	a	a	DET
ijassa-419	58	6	mapping	mapping	NOUN
ijassa-419	58	7	s∗	s∗	PROPN
ijassa-419	58	8	→	→	SYM
ijassa-419	58	9	s∗	s∗	PROPN
ijassa-419	58	10	,	,	PUNCT
ijassa-419	58	11	still	still	ADV
ijassa-419	58	12	denoted	denote	VERB
ijassa-419	58	13	φ	φ	NUM
ijassa-419	58	14	,	,	PUNCT
ijassa-419	58	15	by	by	ADP
ijassa-419	58	16	φ	φ	PROPN
ijassa-419	58	17	:	:	PUNCT
ijassa-419	58	18	sk1sk2	sk1sk2	NOUN
ijassa-419	58	19	.	.	PUNCT
ijassa-419	58	20	.	.	PUNCT
ijassa-419	58	21	.	.	PUNCT
ijassa-419	59	1	skr	skr	PROPN
ijassa-419	59	2	→	→	SYM
ijassa-419	59	3	pk1(sk1)pk2(sk2	pk1(sk1)pk2(sk2	PROPN
ijassa-419	59	4	)	)	PUNCT
ijassa-419	59	5	.	.	PUNCT
ijassa-419	59	6	.	.	PUNCT
ijassa-419	59	7	.	.	PUNCT
ijassa-419	60	1	pkr(skr	pkr(skr	PROPN
ijassa-419	60	2	)	)	PUNCT
ijassa-419	61	1	(	(	PUNCT
ijassa-419	61	2	1	1	X
ijassa-419	61	3	)	)	PUNCT
ijassa-419	61	4	∀sk1sk2	∀sk1sk2	PROPN
ijassa-419	61	5	.	.	PUNCT
ijassa-419	61	6	.	.	PUNCT
ijassa-419	61	7	.	.	PUNCT
ijassa-419	62	1	skr	skr	PROPN
ijassa-419	62	2	∈	∈	PROPN
ijassa-419	62	3	s∗	s∗	PROPN
ijassa-419	62	4	,	,	PUNCT
ijassa-419	62	5	ki	ki	PROPN
ijassa-419	62	6	∈	∈	PROPN
ijassa-419	62	7	{	{	PUNCT
ijassa-419	62	8	1	1	NUM
ijassa-419	62	9	,	,	PUNCT
ijassa-419	62	10	2	2	NUM
ijassa-419	62	11	,	,	PUNCT
ijassa-419	62	12	.	.	PUNCT
ijassa-419	62	13	.	.	PUNCT
ijassa-419	62	14	.	.	PUNCT
ijassa-419	62	15	,	,	PUNCT
ijassa-419	62	16	n	n	CCONJ
ijassa-419	62	17	}	}	PUNCT
ijassa-419	62	18	,	,	PUNCT
ijassa-419	62	19	1	1	NUM
ijassa-419	62	20	≤	≤	NUM
ijassa-419	62	21	i	i	X
ijassa-419	62	22	≤	≤	ADJ
ijassa-419	62	23	r	r	NOUN
ijassa-419	62	24	,	,	PUNCT
ijassa-419	62	25	and	and	CCONJ
ijassa-419	62	26	r	r	NOUN
ijassa-419	62	27	stands	stand	VERB
ijassa-419	62	28	for	for	ADP
ijassa-419	62	29	the	the	DET
ijassa-419	62	30	length	length	NOUN
ijassa-419	62	31	of	of	ADP
ijassa-419	62	32	the	the	DET
ijassa-419	62	33	character	character	NOUN
ijassa-419	62	34	string	string	NOUN
ijassa-419	62	35	.	.	PUNCT
ijassa-419	63	1	then	then	ADV
ijassa-419	63	2	,	,	PUNCT
ijassa-419	63	3	this	this	DET
ijassa-419	63	4	mapping	mapping	NOUN
ijassa-419	63	5	φ	φ	PROPN
ijassa-419	63	6	:	:	PUNCT
ijassa-419	63	7	s∗	s∗	PROPN
ijassa-419	63	8	→	→	SYM
ijassa-419	63	9	s∗	s∗	PROPN
ijassa-419	63	10	is	be	AUX
ijassa-419	63	11	referred	refer	VERB
ijassa-419	63	12	to	to	ADP
ijassa-419	63	13	as	as	ADP
ijassa-419	63	14	an	an	DET
ijassa-419	63	15	l	l	NOUN
ijassa-419	63	16	mapping	mapping	NOUN
ijassa-419	63	17	.	.	PUNCT
ijassa-419	64	1	note	note	NOUN
ijassa-419	64	2	:	:	PUNCT
ijassa-419	64	3	from	from	ADP
ijassa-419	64	4	the	the	DET
ijassa-419	64	5	definition	definition	NOUN
ijassa-419	64	6	of	of	ADP
ijassa-419	64	7	l	l	NOUN
ijassa-419	64	8	mappings	mapping	NOUN
ijassa-419	64	9	,	,	PUNCT
ijassa-419	64	10	it	it	PRON
ijassa-419	64	11	follows	follow	VERB
ijassa-419	64	12	that	that	SCONJ
ijassa-419	64	13	the	the	DET
ijassa-419	64	14	set	set	NOUN
ijassa-419	64	15	of	of	ADP
ijassa-419	64	16	m(≥	m(≥	ADJ
ijassa-419	64	17	n	n	CCONJ
ijassa-419	64	18	)	)	PUNCT
ijassa-419	64	19	production	production	NOUN
ijassa-419	64	20	rules	rule	NOUN
ijassa-419	64	21	from	from	ADP
ijassa-419	64	22	s	s	PRON
ijassa-419	64	23	to	to	PART
ijassa-419	64	24	s∗	s∗	PROPN
ijassa-419	64	25	:	:	PUNCT
ijassa-419	64	26	p	p	X
ijassa-419	64	27	=	=	X
ijassa-419	64	28	{	{	PUNCT
ijassa-419	64	29	p(1)1	p(1)1	NOUN
ijassa-419	64	30	,	,	PUNCT
ijassa-419	64	31	.	.	PUNCT
ijassa-419	64	32	.	.	PUNCT
ijassa-419	65	1	.	.	PUNCT
ijassa-419	66	1	,	,	PUNCT
ijassa-419	66	2	p	p	X
ijassa-419	66	3	(	(	PUNCT
ijassa-419	66	4	r1	r1	PROPN
ijassa-419	66	5	)	)	PUNCT
ijassa-419	66	6	1	1	NUM
ijassa-419	66	7	,	,	PUNCT
ijassa-419	66	8	p	p	X
ijassa-419	66	9	(	(	PUNCT
ijassa-419	66	10	1	1	NUM
ijassa-419	66	11	)	)	PUNCT
ijassa-419	66	12	2	2	NUM
ijassa-419	66	13	,	,	PUNCT
ijassa-419	66	14	.	.	PUNCT
ijassa-419	66	15	.	.	PUNCT
ijassa-419	67	1	.	.	PUNCT
ijassa-419	68	1	,	,	PUNCT
ijassa-419	68	2	p	p	X
ijassa-419	68	3	(	(	PUNCT
ijassa-419	68	4	r2	r2	PROPN
ijassa-419	68	5	)	)	PUNCT
ijassa-419	68	6	2	2	NUM
ijassa-419	68	7	,	,	PUNCT
ijassa-419	68	8	.	.	PUNCT
ijassa-419	68	9	.	.	PUNCT
ijassa-419	69	1	.	.	PUNCT
ijassa-419	70	1	,	,	PUNCT
ijassa-419	70	2	p(1)n	p(1)n	X
ijassa-419	70	3	,	,	PUNCT
ijassa-419	70	4	.	.	PUNCT
ijassa-419	70	5	.	.	PUNCT
ijassa-419	70	6	.	.	PUNCT
ijassa-419	71	1	,	,	PUNCT
ijassa-419	71	2	p(rn)n	p(rn)n	NOUN
ijassa-419	71	3	}	}	PUNCT
ijassa-419	71	4	(	(	PUNCT
ijassa-419	71	5	2	2	X
ijassa-419	71	6	)	)	PUNCT
ijassa-419	71	7	can	can	AUX
ijassa-419	71	8	define	define	VERB
ijassa-419	71	9	(	(	PUNCT
ijassa-419	71	10	r1r2	r1r2	ADJ
ijassa-419	71	11	.	.	PUNCT
ijassa-419	71	12	.	.	PUNCT
ijassa-419	71	13	.	.	PUNCT
ijassa-419	72	1	rn	rn	X
ijassa-419	72	2	)	)	PUNCT
ijassa-419	72	3	many	many	ADJ
ijassa-419	72	4	l	l	NOUN
ijassa-419	72	5	mappings	mapping	NOUN
ijassa-419	72	6	from	from	ADP
ijassa-419	72	7	s	s	PRON
ijassa-419	72	8	to	to	ADP
ijassa-419	72	9	s∗	s∗	PROPN
ijassa-419	72	10	,	,	PUNCT
ijassa-419	72	11	where	where	SCONJ
ijassa-419	72	12	n∑	n∑	PROPN
ijassa-419	72	13	i=1	i=1	PROPN
ijassa-419	72	14	ri	ri	PROPN
ijassa-419	73	1	=	=	PUNCT
ijassa-419	73	2	m.	m.	NOUN
ijassa-419	73	3	the	the	DET
ijassa-419	73	4	set	set	NOUN
ijassa-419	73	5	of	of	ADP
ijassa-419	73	6	all	all	DET
ijassa-419	73	7	l	l	NOUN
ijassa-419	73	8	mappings	mapping	NOUN
ijassa-419	73	9	determined	determine	VERB
ijassa-419	73	10	by	by	ADP
ijassa-419	73	11	the	the	DET
ijassa-419	73	12	set	set	NOUN
ijassa-419	73	13	p	p	NOUN
ijassa-419	73	14	is	be	AUX
ijassa-419	73	15	denoted	denote	VERB
ijassa-419	73	16	by	by	ADP
ijassa-419	73	17	φ	φ	PROPN
ijassa-419	73	18	=	=	SYM
ijassa-419	73	19	{	{	PUNCT
ijassa-419	73	20	φ1	φ1	PROPN
ijassa-419	73	21	,	,	PUNCT
ijassa-419	73	22	φ2	φ2	PROPN
ijassa-419	73	23	,	,	PUNCT
ijassa-419	73	24	.	.	PUNCT
ijassa-419	73	25	.	.	PUNCT
ijassa-419	74	1	.	.	PUNCT
ijassa-419	75	1	,	,	PUNCT
ijassa-419	75	2	φr1r2	φr1r2	PROPN
ijassa-419	75	3	...	...	SYM
ijassa-419	75	4	rn	rn	NOUN
ijassa-419	75	5	}	}	PUNCT
ijassa-419	75	6	.	.	PUNCT
ijassa-419	76	1	proposition	proposition	NOUN
ijassa-419	76	2	2.1	2.1	NUM
ijassa-419	76	3	(	(	PUNCT
ijassa-419	76	4	properties	property	NOUN
ijassa-419	76	5	of	of	ADP
ijassa-419	76	6	l	l	NOUN
ijassa-419	76	7	mappings	mapping	NOUN
ijassa-419	76	8	)	)	PUNCT
ijassa-419	76	9	.	.	PUNCT
ijassa-419	77	1	for	for	ADP
ijassa-419	77	2	any	any	DET
ijassa-419	77	3	α	α	NOUN
ijassa-419	77	4	,	,	PUNCT
ijassa-419	77	5	β	β	PROPN
ijassa-419	77	6	∈	∈	NOUN
ijassa-419	77	7	s∗	s∗	PROPN
ijassa-419	77	8	and	and	CCONJ
ijassa-419	77	9	m	m	PROPN
ijassa-419	77	10	,	,	PUNCT
ijassa-419	77	11	n	n	PROPN
ijassa-419	77	12	∈	∈	PROPN
ijassa-419	77	13	z+	z+	NUM
ijassa-419	77	14	,	,	PUNCT
ijassa-419	77	15	each	each	DET
ijassa-419	77	16	l	l	NOUN
ijassa-419	77	17	mapping	mapping	NOUN
ijassa-419	77	18	φ	φ	PROPN
ijassa-419	77	19	satisfies	satisfy	VERB
ijassa-419	77	20	the	the	DET
ijassa-419	77	21	following	follow	VERB
ijassa-419	77	22	properties	property	NOUN
ijassa-419	77	23	:	:	PUNCT
ijassa-419	77	24	(	(	PUNCT
ijassa-419	77	25	i	i	NOUN
ijassa-419	77	26	)	)	PUNCT
ijassa-419	77	27	φ(α	φ(α	ADJ
ijassa-419	77	28	)	)	PUNCT
ijassa-419	77	29	∈	∈	PROPN
ijassa-419	77	30	s∗	s∗	NOUN
ijassa-419	77	31	is	be	AUX
ijassa-419	77	32	uniquely	uniquely	ADV
ijassa-419	77	33	defined	define	VERB
ijassa-419	77	34	;	;	PUNCT
ijassa-419	77	35	(	(	PUNCT
ijassa-419	77	36	ii	ii	NOUN
ijassa-419	77	37	)	)	PUNCT
ijassa-419	77	38	if	if	SCONJ
ijassa-419	77	39	φ|s	φ|s	PROPN
ijassa-419	77	40	is	be	AUX
ijassa-419	77	41	surjective	surjective	PROPN
ijassa-419	77	42	s	s	X
ijassa-419	77	43	→	→	SYM
ijassa-419	77	44	s	s	PROPN
ijassa-419	77	45	,	,	PUNCT
ijassa-419	77	46	then	then	ADV
ijassa-419	77	47	φ|s	φ|s	PROPN
ijassa-419	77	48	must	must	AUX
ijassa-419	77	49	be	be	AUX
ijassa-419	77	50	bijective	bijective	ADJ
ijassa-419	77	51	;	;	PUNCT
ijassa-419	77	52	advances	advance	NOUN
ijassa-419	77	53	in	in	ADP
ijassa-419	77	54	systems	system	NOUN
ijassa-419	77	55	science	science	NOUN
ijassa-419	77	56	and	and	CCONJ
ijassa-419	77	57	applications	application	NOUN
ijassa-419	77	58	(	(	PUNCT
ijassa-419	77	59	2013	2013	NUM
ijassa-419	77	60	)	)	PUNCT
ijassa-419	77	61	vol.13	vol.13	NOUN
ijassa-419	77	62	no.2	no.2	PROPN
ijassa-419	77	63	103	103	NUM
ijassa-419	77	64	(	(	PUNCT
ijassa-419	77	65	iii	iii	NOUN
ijassa-419	77	66	)	)	PUNCT
ijassa-419	77	67	if	if	SCONJ
ijassa-419	77	68	α	α	NOUN
ijassa-419	77	69	=	=	NOUN
ijassa-419	77	70	sk1sk2	sk1sk2	NOUN
ijassa-419	77	71	.	.	PUNCT
ijassa-419	77	72	.	.	PUNCT
ijassa-419	77	73	.	.	PUNCT
ijassa-419	78	1	skp	skp	PROPN
ijassa-419	78	2	∈	∈	PROPN
ijassa-419	78	3	s∗	s∗	PROPN
ijassa-419	78	4	,	,	PUNCT
ijassa-419	78	5	then	then	ADV
ijassa-419	78	6	φ(α	φ(α	ADJ
ijassa-419	78	7	)	)	PUNCT
ijassa-419	78	8	=	=	SYM
ijassa-419	78	9	φ(sk1)φ(sk2	φ(sk1)φ(sk2	PROPN
ijassa-419	78	10	)	)	PUNCT
ijassa-419	78	11	.	.	PUNCT
ijassa-419	78	12	.	.	PUNCT
ijassa-419	78	13	.	.	PUNCT
ijassa-419	79	1	φ(skp	φ(skp	PROPN
ijassa-419	79	2	)	)	PUNCT
ijassa-419	79	3	;	;	PUNCT
ijassa-419	79	4	(	(	PUNCT
ijassa-419	79	5	iv	iv	X
ijassa-419	79	6	)	)	PUNCT
ijassa-419	79	7	φ(α⊕	φ(α⊕	ADV
ijassa-419	79	8	β	β	X
ijassa-419	79	9	)	)	PUNCT
ijassa-419	79	10	=	=	SYM
ijassa-419	79	11	φ(α)⊕	φ(α)⊕	NOUN
ijassa-419	79	12	φ(β	φ(β	PROPN
ijassa-419	79	13	)	)	PUNCT
ijassa-419	79	14	;	;	PUNCT
ijassa-419	79	15	(	(	PUNCT
ijassa-419	79	16	v	v	NOUN
ijassa-419	79	17	)	)	PUNCT
ijassa-419	79	18	φ(mα	φ(mα	PROPN
ijassa-419	79	19	)	)	PUNCT
ijassa-419	79	20	=	=	SYM
ijassa-419	79	21	mφ(α	mφ(α	NOUN
ijassa-419	79	22	)	)	PUNCT
ijassa-419	79	23	;	;	PUNCT
ijassa-419	79	24	(	(	PUNCT
ijassa-419	79	25	vi	vi	NOUN
ijassa-419	79	26	)	)	PUNCT
ijassa-419	79	27	∀φ	∀φ	PROPN
ijassa-419	79	28	,	,	PUNCT
ijassa-419	79	29	ϕ	ϕ	PROPN
ijassa-419	79	30	∈	∈	PROPN
ijassa-419	79	31	φ	φ	PROPN
ijassa-419	79	32	,	,	PUNCT
ijassa-419	79	33	φϕ(mα⊕	φϕ(mα⊕	PROPN
ijassa-419	79	34	nβ	nβ	NUM
ijassa-419	79	35	)	)	PUNCT
ijassa-419	79	36	=	=	NOUN
ijassa-419	79	37	mφϕ(α)⊕	mφϕ(α)⊕	NOUN
ijassa-419	79	38	nφϕ(β	nφϕ(β	PROPN
ijassa-419	79	39	)	)	PUNCT
ijassa-419	79	40	;	;	PUNCT
ijassa-419	79	41	proof	proof	NOUN
ijassa-419	79	42	.	.	PUNCT
ijassa-419	80	1	because	because	SCONJ
ijassa-419	80	2	both	both	PRON
ijassa-419	80	3	(	(	PUNCT
ijassa-419	80	4	i	i	NOUN
ijassa-419	80	5	)	)	PUNCT
ijassa-419	80	6	and	and	CCONJ
ijassa-419	80	7	(	(	PUNCT
ijassa-419	80	8	ii	ii	NOUN
ijassa-419	80	9	)	)	PUNCT
ijassa-419	80	10	are	be	AUX
ijassa-419	80	11	evident	evident	ADJ
ijassa-419	80	12	,	,	PUNCT
ijassa-419	80	13	it	it	PRON
ijassa-419	80	14	suffices	suffice	VERB
ijassa-419	80	15	to	to	PART
ijassa-419	80	16	show	show	VERB
ijassa-419	80	17	(	(	PUNCT
ijassa-419	80	18	iii	iii	NOUN
ijassa-419	80	19	)	)	PUNCT
ijassa-419	80	20	(	(	PUNCT
ijassa-419	80	21	vi	vi	NOUN
ijassa-419	80	22	)	)	PUNCT
ijassa-419	80	23	.	.	PUNCT
ijassa-419	81	1	(	(	PUNCT
ijassa-419	81	2	iii	iii	X
ijassa-419	81	3	)	)	PUNCT
ijassa-419	81	4	for	for	ADP
ijassa-419	81	5	any	any	DET
ijassa-419	81	6	α	α	NOUN
ijassa-419	81	7	=	=	NOUN
ijassa-419	81	8	sk1sk2	sk1sk2	NOUN
ijassa-419	81	9	.	.	PUNCT
ijassa-419	81	10	.	.	PUNCT
ijassa-419	81	11	.	.	PUNCT
ijassa-419	82	1	skp	skp	PROPN
ijassa-419	82	2	∈	∈	PROPN
ijassa-419	82	3	s∗	s∗	PROPN
ijassa-419	82	4	,	,	PUNCT
ijassa-419	82	5	the	the	DET
ijassa-419	82	6	definition	definition	NOUN
ijassa-419	82	7	of	of	ADP
ijassa-419	82	8	the	the	DET
ijassa-419	82	9	l	l	NOUN
ijassa-419	82	10	mappings	mapping	NOUN
ijassa-419	82	11	implies	imply	VERB
ijassa-419	82	12	that	that	SCONJ
ijassa-419	82	13	φ(sk1sk2	φ(sk1sk2	NUM
ijassa-419	82	14	.	.	PUNCT
ijassa-419	82	15	.	.	PUNCT
ijassa-419	82	16	.	.	PUNCT
ijassa-419	83	1	skp	skp	X
ijassa-419	83	2	)	)	PUNCT
ijassa-419	83	3	=	=	SYM
ijassa-419	83	4	pk1(sk1)pk2(sk2	pk1(sk1)pk2(sk2	PROPN
ijassa-419	83	5	)	)	PUNCT
ijassa-419	83	6	.	.	PUNCT
ijassa-419	83	7	.	.	PUNCT
ijassa-419	83	8	.	.	PUNCT
ijassa-419	84	1	pkp(skp	pkp(skp	PROPN
ijassa-419	84	2	)	)	PUNCT
ijassa-419	85	1	(	(	PUNCT
ijassa-419	85	2	3	3	X
ijassa-419	85	3	)	)	PUNCT
ijassa-419	85	4	and	and	CCONJ
ijassa-419	85	5	,	,	PUNCT
ijassa-419	85	6	∀ski	∀ski	PROPN
ijassa-419	85	7	∈	∈	PROPN
ijassa-419	85	8	s∗(1	s∗(1	NOUN
ijassa-419	85	9	≤	≤	NUM
ijassa-419	86	1	i	i	PRON
ijassa-419	86	2	≤	≤	NOUN
ijassa-419	87	1	p	p	X
ijassa-419	87	2	)	)	PUNCT
ijassa-419	87	3	,	,	PUNCT
ijassa-419	87	4	we	we	PRON
ijassa-419	87	5	have	have	VERB
ijassa-419	87	6	φ(ski	φ(ski	ADJ
ijassa-419	87	7	)	)	PUNCT
ijassa-419	87	8	=	=	SYM
ijassa-419	87	9	p(ski	p(ski	NOUN
ijassa-419	87	10	)	)	PUNCT
ijassa-419	87	11	(	(	PUNCT
ijassa-419	87	12	4	4	X
ijassa-419	87	13	)	)	PUNCT
ijassa-419	87	14	hence	hence	ADV
ijassa-419	87	15	,	,	PUNCT
ijassa-419	87	16	φ(α	φ(α	ADJ
ijassa-419	87	17	)	)	PUNCT
ijassa-419	88	1	=	=	SYM
ijassa-419	88	2	φ(sk1sk2	φ(sk1sk2	PROPN
ijassa-419	88	3	.	.	PUNCT
ijassa-419	88	4	.	.	PUNCT
ijassa-419	88	5	.	.	PUNCT
ijassa-419	89	1	skp	skp	X
ijassa-419	89	2	)	)	PUNCT
ijassa-419	89	3	=	=	SYM
ijassa-419	89	4	pk1(sk1)pk2(sk2	pk1(sk1)pk2(sk2	PROPN
ijassa-419	89	5	)	)	PUNCT
ijassa-419	89	6	.	.	PUNCT
ijassa-419	89	7	.	.	PUNCT
ijassa-419	89	8	.	.	PUNCT
ijassa-419	90	1	pkp(skp	pkp(skp	PROPN
ijassa-419	90	2	)	)	PUNCT
ijassa-419	90	3	=	=	SYM
ijassa-419	90	4	φ(sk1)φ(sk2	φ(sk1)φ(sk2	PROPN
ijassa-419	90	5	)	)	PUNCT
ijassa-419	90	6	.	.	PUNCT
ijassa-419	90	7	.	.	PUNCT
ijassa-419	90	8	.	.	PUNCT
ijassa-419	91	1	φ(skp	φ(skp	PROPN
ijassa-419	91	2	)	)	PUNCT
ijassa-419	91	3	.	.	PUNCT
ijassa-419	92	1	(	(	PUNCT
ijassa-419	92	2	iv	iv	X
ijassa-419	92	3	)	)	PUNCT
ijassa-419	92	4	for	for	ADP
ijassa-419	92	5	any	any	DET
ijassa-419	92	6	α	α	NOUN
ijassa-419	92	7	,	,	PUNCT
ijassa-419	92	8	β	β	PROPN
ijassa-419	92	9	∈	∈	PROPN
ijassa-419	92	10	s∗	s∗	PROPN
ijassa-419	92	11	,	,	PUNCT
ijassa-419	92	12	from	from	ADP
ijassa-419	92	13	the	the	DET
ijassa-419	92	14	addition	addition	NOUN
ijassa-419	92	15	operation	operation	NOUN
ijassa-419	92	16	on	on	ADP
ijassa-419	92	17	s∗	s∗	PROPN
ijassa-419	92	18	and	and	CCONJ
ijassa-419	92	19	property	property	NOUN
ijassa-419	92	20	(	(	PUNCT
ijassa-419	92	21	iii	iii	NOUN
ijassa-419	92	22	)	)	PUNCT
ijassa-419	92	23	,	,	PUNCT
ijassa-419	92	24	it	it	PRON
ijassa-419	92	25	follows	follow	VERB
ijassa-419	92	26	that	that	SCONJ
ijassa-419	92	27	φ(α⊕	φ(α⊕	ADJ
ijassa-419	92	28	β	β	X
ijassa-419	92	29	)	)	PUNCT
ijassa-419	92	30	=	=	SYM
ijassa-419	92	31	φ(αβ	φ(αβ	NUM
ijassa-419	92	32	)	)	PUNCT
ijassa-419	92	33	=	=	NOUN
ijassa-419	92	34	φ(α)φ(β	φ(α)φ(β	NOUN
ijassa-419	92	35	)	)	PUNCT
ijassa-419	92	36	=	=	SYM
ijassa-419	92	37	φ(α)⊕	φ(α)⊕	NOUN
ijassa-419	92	38	φ(β	φ(β	PROPN
ijassa-419	92	39	)	)	PUNCT
ijassa-419	92	40	(	(	PUNCT
ijassa-419	92	41	5	5	NUM
ijassa-419	92	42	)	)	PUNCT
ijassa-419	92	43	(	(	PUNCT
ijassa-419	92	44	v	v	NOUN
ijassa-419	92	45	)	)	PUNCT
ijassa-419	92	46	for	for	ADP
ijassa-419	92	47	any	any	DET
ijassa-419	92	48	α	α	PROPN
ijassa-419	92	49	∈	∈	PROPN
ijassa-419	92	50	s∗	s∗	NOUN
ijassa-419	92	51	and	and	CCONJ
ijassa-419	92	52	m	m	PROPN
ijassa-419	92	53	∈	∈	NOUN
ijassa-419	92	54	z+	z+	NOUN
ijassa-419	92	55	,	,	PUNCT
ijassa-419	92	56	from	from	ADP
ijassa-419	92	57	the	the	DET
ijassa-419	92	58	definition	definition	NOUN
ijassa-419	92	59	of	of	ADP
ijassa-419	92	60	scalar	scalar	ADJ
ijassa-419	92	61	multiplication	multiplication	NOUN
ijassa-419	92	62	on	on	ADP
ijassa-419	92	63	s∗	s∗	PROPN
ijassa-419	92	64	and	and	CCONJ
ijassa-419	92	65	property	property	NOUN
ijassa-419	92	66	(	(	PUNCT
ijassa-419	92	67	ii	ii	NOUN
ijassa-419	92	68	)	)	PUNCT
ijassa-419	92	69	,	,	PUNCT
ijassa-419	92	70	it	it	PRON
ijassa-419	92	71	following	follow	VERB
ijassa-419	92	72	that	that	SCONJ
ijassa-419	92	73	φ(mα	φ(mα	NOUN
ijassa-419	92	74	)	)	PUNCT
ijassa-419	92	75	=	=	PUNCT
ijassa-419	92	76	φ(αα	φ(αα	PROPN
ijassa-419	92	77	...	...	PUNCT
ijassa-419	92	78	α︸	α︸	NOUN
ijassa-419	92	79	︷︷	︷︷	PROPN
ijassa-419	92	80	︸	︸	ADP
ijassa-419	92	81	m	m	PROPN
ijassa-419	92	82	times	time	NOUN
ijassa-419	92	83	)	)	PUNCT
ijassa-419	93	1	=	=	SYM
ijassa-419	93	2	φ(α)φ(α)	φ(α)φ(α)	X
ijassa-419	93	3	...	...	PUNCT
ijassa-419	93	4	φ(α)︸	φ(α)︸	X
ijassa-419	93	5	︷︷	︷︷	PROPN
ijassa-419	93	6	︸	︸	ADP
ijassa-419	93	7	m	m	PROPN
ijassa-419	93	8	times	time	NOUN
ijassa-419	93	9	=	=	SYM
ijassa-419	93	10	mφ(α	mφ(α	X
ijassa-419	93	11	)	)	PUNCT
ijassa-419	93	12	(	(	PUNCT
ijassa-419	93	13	6	6	NUM
ijassa-419	93	14	)	)	PUNCT
ijassa-419	93	15	(	(	PUNCT
ijassa-419	93	16	vi	vi	NOUN
ijassa-419	93	17	)	)	PUNCT
ijassa-419	93	18	for	for	ADP
ijassa-419	93	19	any	any	DET
ijassa-419	93	20	φ	φ	NOUN
ijassa-419	93	21	,	,	PUNCT
ijassa-419	93	22	ϕ	ϕ	PROPN
ijassa-419	93	23	∈	∈	PROPN
ijassa-419	93	24	φ	φ	PROPN
ijassa-419	93	25	,	,	PUNCT
ijassa-419	93	26	by	by	ADP
ijassa-419	93	27	employing	employ	VERB
ijassa-419	93	28	properties	property	NOUN
ijassa-419	93	29	(	(	PUNCT
ijassa-419	93	30	iv	iv	X
ijassa-419	93	31	)	)	PUNCT
ijassa-419	93	32	and	and	CCONJ
ijassa-419	93	33	(	(	PUNCT
ijassa-419	93	34	v	v	NOUN
ijassa-419	93	35	)	)	PUNCT
ijassa-419	93	36	,	,	PUNCT
ijassa-419	93	37	we	we	PRON
ijassa-419	93	38	obtain	obtain	VERB
ijassa-419	93	39	:	:	PUNCT
ijassa-419	93	40	φϕ(mα⊕	φϕ(mα⊕	PROPN
ijassa-419	93	41	nβ	nβ	NUM
ijassa-419	93	42	)	)	PUNCT
ijassa-419	93	43	=	=	NOUN
ijassa-419	93	44	φ(mϕ(α)⊕	φ(mϕ(α)⊕	NOUN
ijassa-419	93	45	nϕ(β	nϕ(β	NOUN
ijassa-419	93	46	)	)	PUNCT
ijassa-419	93	47	)	)	PUNCT
ijassa-419	94	1	=	=	SYM
ijassa-419	94	2	mφϕ(α)⊕	mφϕ(α)⊕	ADJ
ijassa-419	94	3	nφϕ(β	nφϕ(β	NOUN
ijassa-419	94	4	)	)	PUNCT
ijassa-419	94	5	(	(	PUNCT
ijassa-419	94	6	7	7	X
ijassa-419	94	7	)	)	PUNCT
ijassa-419	94	8	qed	qed	PROPN
ijassa-419	94	9	.	.	PUNCT
ijassa-419	95	1	2.2	2.2	NUM
ijassa-419	95	2	simple	simple	ADJ
ijassa-419	95	3	l	l	NOUN
ijassa-419	95	4	-	-	NOUN
ijassa-419	95	5	systems	system	NOUN
ijassa-419	95	6	with	with	ADP
ijassa-419	95	7	the	the	DET
ijassa-419	95	8	concept	concept	NOUN
ijassa-419	95	9	of	of	ADP
ijassa-419	95	10	l	l	NOUN
ijassa-419	95	11	-	-	NOUN
ijassa-419	95	12	mappings	mapping	NOUN
ijassa-419	95	13	in	in	ADP
ijassa-419	95	14	place	place	NOUN
ijassa-419	95	15	,	,	PUNCT
ijassa-419	95	16	let	let	VERB
ijassa-419	95	17	us	we	PRON
ijassa-419	95	18	now	now	ADV
ijassa-419	95	19	look	look	VERB
ijassa-419	95	20	at	at	ADP
ijassa-419	95	21	how	how	SCONJ
ijassa-419	95	22	to	to	PART
ijassa-419	95	23	define	define	VERB
ijassa-419	95	24	simple	simple	ADJ
ijassa-419	95	25	l	l	NOUN
ijassa-419	95	26	-	-	NOUN
ijassa-419	95	27	systems	system	NOUN
ijassa-419	95	28	.	.	PUNCT
ijassa-419	96	1	according	accord	VERB
ijassa-419	96	2	to	to	ADP
ijassa-419	96	3	the	the	DET
ijassa-419	96	4	classification	classification	NOUN
ijassa-419	96	5	of	of	ADP
ijassa-419	96	6	simple	simple	ADJ
ijassa-419	96	7	l	l	NOUN
ijassa-419	96	8	systems	system	NOUN
ijassa-419	96	9	,	,	PUNCT
ijassa-419	96	10	deterministic	deterministic	ADJ
ijassa-419	96	11	and	and	CCONJ
ijassa-419	96	12	random	random	ADJ
ijassa-419	96	13	simple	simple	ADJ
ijassa-419	96	14	l	l	NOUN
ijassa-419	96	15	systems	system	NOUN
ijassa-419	96	16	,	,	PUNCT
ijassa-419	96	17	we	we	PRON
ijassa-419	96	18	now	now	ADV
ijassa-419	96	19	establish	establish	VERB
ijassa-419	96	20	the	the	DET
ijassa-419	96	21	relevant	relevant	ADJ
ijassa-419	96	22	definitions	definition	NOUN
ijassa-419	96	23	by	by	ADP
ijassa-419	96	24	using	use	VERB
ijassa-419	96	25	the	the	DET
ijassa-419	96	26	concept	concept	NOUN
ijassa-419	96	27	of	of	ADP
ijassa-419	96	28	l	l	NOUN
ijassa-419	96	29	mappings	mapping	NOUN
ijassa-419	96	30	.	.	PUNCT
ijassa-419	97	1	definition	definition	NOUN
ijassa-419	97	2	2.4(deterministic	2.4(deterministic	ADJ
ijassa-419	97	3	simple	simple	ADJ
ijassa-419	97	4	l	l	NOUN
ijassa-419	97	5	systems	system	NOUN
ijassa-419	97	6	)	)	PUNCT
ijassa-419	97	7	.	.	PUNCT
ijassa-419	98	1	let	let	AUX
ijassa-419	98	2	s	s	VERB
ijassa-419	98	3	=	=	NOUN
ijassa-419	98	4	{	{	PUNCT
ijassa-419	98	5	s1	s1	NOUN
ijassa-419	98	6	,	,	PUNCT
ijassa-419	98	7	s2	s2	PROPN
ijassa-419	98	8	,	,	PUNCT
ijassa-419	98	9	...	...	PUNCT
ijassa-419	98	10	,	,	PUNCT
ijassa-419	98	11	sn	sn	PROPN
ijassa-419	98	12	}	}	PUNCT
ijassa-419	98	13	be	be	AUX
ijassa-419	98	14	a	a	DET
ijassa-419	98	15	finite	finite	ADJ
ijassa-419	98	16	set	set	NOUN
ijassa-419	98	17	of	of	ADP
ijassa-419	98	18	characters	character	NOUN
ijassa-419	98	19	and	and	CCONJ
ijassa-419	98	20	s∗	s∗	VERB
ijassa-419	98	21	the	the	DET
ijassa-419	98	22	set	set	NOUN
ijassa-419	98	23	of	of	ADP
ijassa-419	98	24	all	all	DET
ijassa-419	98	25	strings	string	NOUN
ijassa-419	98	26	of	of	ADP
ijassa-419	98	27	characters	character	NOUN
ijassa-419	98	28	from	from	ADP
ijassa-419	98	29	s.	s.	PROPN
ijassa-419	98	30	assume	assume	VERB
ijassa-419	98	31	that	that	SCONJ
ijassa-419	98	32	φ	φ	PROPN
ijassa-419	98	33	:	:	PUNCT
ijassa-419	98	34	s∗	s∗	PROPN
ijassa-419	98	35	→	→	SYM
ijassa-419	98	36	s∗	s∗	PROPN
ijassa-419	98	37	is	be	AUX
ijassa-419	98	38	a	a	DET
ijassa-419	98	39	given	give	VERB
ijassa-419	98	40	l	l	NOUN
ijassa-419	98	41	mapping	mapping	NOUN
ijassa-419	98	42	.	.	PUNCT
ijassa-419	99	1	for	for	ADP
ijassa-419	99	2	any	any	DET
ijassa-419	99	3	given	give	VERB
ijassa-419	99	4	initial	initial	ADJ
ijassa-419	99	5	string	string	NOUN
ijassa-419	99	6	ω	ω	PROPN
ijassa-419	99	7	∈	∈	PROPN
ijassa-419	99	8	s∗	s∗	PROPN
ijassa-419	99	9	,	,	PUNCT
ijassa-419	99	10	the	the	DET
ijassa-419	99	11	system	system	NOUN
ijassa-419	99	12	that	that	PRON
ijassa-419	99	13	is	be	AUX
ijassa-419	99	14	made	make	VERB
ijassa-419	99	15	up	up	ADP
ijassa-419	99	16	of	of	ADP
ijassa-419	99	17	the	the	DET
ijassa-419	99	18	nth	nth	NOUN
ijassa-419	99	19	iterations	iteration	NOUN
ijassa-419	99	20	φn(ω	φn(ω	NOUN
ijassa-419	99	21	)	)	PUNCT
ijassa-419	99	22	,	,	PUNCT
ijassa-419	99	23	n	n	PRON
ijassa-419	99	24	≥	≥	NOUN
ijassa-419	99	25	1	1	NUM
ijassa-419	99	26	,	,	PUNCT
ijassa-419	99	27	is	be	AUX
ijassa-419	99	28	referred	refer	VERB
ijassa-419	99	29	to	to	ADP
ijassa-419	99	30	a	a	DET
ijassa-419	99	31	deterministic	deterministic	ADJ
ijassa-419	99	32	simple	simple	ADJ
ijassa-419	99	33	l	l	NOUN
ijassa-419	99	34	(	(	PUNCT
ijassa-419	99	35	d0l	d0l	PROPN
ijassa-419	99	36	)	)	PUNCT
ijassa-419	99	37	system	system	NOUN
ijassa-419	99	38	(	(	PUNCT
ijassa-419	99	39	of	of	ADP
ijassa-419	99	40	order	order	NOUN
ijassa-419	99	41	n	n	CCONJ
ijassa-419	99	42	)	)	PUNCT
ijassa-419	99	43	,	,	PUNCT
ijassa-419	99	44	denoted	denote	VERB
ijassa-419	99	45	by	by	ADP
ijassa-419	99	46	the	the	DET
ijassa-419	99	47	ordered	order	VERB
ijassa-419	99	48	triplet	triplet	NOUN
ijassa-419	99	49	⟨s	⟨s	PROPN
ijassa-419	99	50	,	,	PUNCT
ijassa-419	99	51	ω	ω	PROPN
ijassa-419	99	52	,	,	PUNCT
ijassa-419	99	53	φ⟩.	φ⟩.	PRON
ijassa-419	99	54	definition	definition	NOUN
ijassa-419	99	55	2.5(random	2.5(random	NUM
ijassa-419	99	56	simple	simple	ADJ
ijassa-419	99	57	l	l	NOUN
ijassa-419	99	58	systems	system	NOUN
ijassa-419	99	59	)	)	PUNCT
ijassa-419	99	60	.	.	PUNCT
ijassa-419	100	1	let	let	VERB
ijassa-419	100	2	s	s	PRON
ijassa-419	100	3	and	and	CCONJ
ijassa-419	100	4	s∗	s∗	PROPN
ijassa-419	100	5	be	be	AUX
ijassa-419	100	6	the	the	DET
ijassa-419	100	7	same	same	ADJ
ijassa-419	100	8	as	as	ADP
ijassa-419	100	9	in	in	ADP
ijassa-419	100	10	104	104	NUM
ijassa-419	100	11	xiaojun	xiaojun	PROPN
ijassa-419	100	12	duan	duan	PROPN
ijassa-419	100	13	:	:	PUNCT
ijassa-419	100	14	set	set	VERB
ijassa-419	100	15	-	-	PUNCT
ijassa-419	100	16	theoretic	theoretic	NOUN
ijassa-419	100	17	design	design	NOUN
ijassa-419	100	18	and	and	CCONJ
ijassa-419	100	19	analysis	analysis	NOUN
ijassa-419	100	20	of	of	ADP
ijassa-419	100	21	l	l	NOUN
ijassa-419	100	22	systems	system	NOUN
ijassa-419	100	23	definition	definition	NOUN
ijassa-419	100	24	2.4	2.4	NUM
ijassa-419	100	25	,	,	PUNCT
ijassa-419	100	26	φ	φ	PROPN
ijassa-419	100	27	=	=	SYM
ijassa-419	100	28	{	{	PUNCT
ijassa-419	100	29	φ1	φ1	PROPN
ijassa-419	100	30	,	,	PUNCT
ijassa-419	100	31	φ2	φ2	PROPN
ijassa-419	100	32	,	,	PUNCT
ijassa-419	100	33	...	...	PUNCT
ijassa-419	100	34	,	,	PUNCT
ijassa-419	100	35	φk	φk	ADP
ijassa-419	100	36	}	}	PUNCT
ijassa-419	100	37	a	a	DET
ijassa-419	100	38	set	set	NOUN
ijassa-419	100	39	of	of	ADP
ijassa-419	100	40	k	k	PROPN
ijassa-419	100	41	l	l	NOUN
ijassa-419	100	42	mappings	mapping	NOUN
ijassa-419	100	43	from	from	ADP
ijassa-419	100	44	s∗	s∗	PROPN
ijassa-419	100	45	to	to	ADP
ijassa-419	100	46	s∗	s∗	PROPN
ijassa-419	100	47	,	,	PUNCT
ijassa-419	100	48	and	and	CCONJ
ijassa-419	100	49	ξ	ξ	X
ijassa-419	100	50	the	the	DET
ijassa-419	100	51	l	l	NOUN
ijassa-419	100	52	mapping	mapping	NOUN
ijassa-419	100	53	randomly	randomly	ADV
ijassa-419	100	54	drawn	draw	VERB
ijassa-419	100	55	from	from	ADP
ijassa-419	100	56	φ	φ	PROPN
ijassa-419	100	57	such	such	ADJ
ijassa-419	100	58	that	that	SCONJ
ijassa-419	100	59	the	the	DET
ijassa-419	100	60	probability	probability	NOUN
ijassa-419	100	61	p	p	X
ijassa-419	100	62	(	(	PUNCT
ijassa-419	100	63	ξ	ξ	PROPN
ijassa-419	100	64	=	=	SYM
ijassa-419	100	65	φi	φi	NOUN
ijassa-419	100	66	)	)	PUNCT
ijassa-419	100	67	for	for	ADP
ijassa-419	100	68	ξ	ξ	PROPN
ijassa-419	100	69	to	to	PART
ijassa-419	100	70	be	be	AUX
ijassa-419	100	71	φi	φi	ADV
ijassa-419	100	72	is	be	AUX
ijassa-419	100	73	πi	πi	ADV
ijassa-419	100	74	,	,	PUNCT
ijassa-419	100	75	where	where	SCONJ
ijassa-419	100	76	k∑	k∑	VERB
ijassa-419	100	77	i=1	i=1	PROPN
ijassa-419	100	78	πi	πi	ADV
ijassa-419	100	79	=	=	NOUN
ijassa-419	100	80	1	1	X
ijassa-419	100	81	.	.	X
ijassa-419	100	82	for	for	ADP
ijassa-419	100	83	a	a	DET
ijassa-419	100	84	given	give	VERB
ijassa-419	100	85	initial	initial	ADJ
ijassa-419	100	86	string	string	NOUN
ijassa-419	100	87	of	of	ADP
ijassa-419	100	88	characters	character	NOUN
ijassa-419	101	1	ω	ω	PROPN
ijassa-419	101	2	∈	∈	PROPN
ijassa-419	101	3	s∗	s∗	PROPN
ijassa-419	101	4	,	,	PUNCT
ijassa-419	101	5	the	the	DET
ijassa-419	101	6	system	system	NOUN
ijassa-419	101	7	that	that	PRON
ijassa-419	101	8	is	be	AUX
ijassa-419	101	9	made	make	VERB
ijassa-419	101	10	up	up	ADP
ijassa-419	101	11	of	of	ADP
ijassa-419	101	12	the	the	DET
ijassa-419	101	13	nth	nth	NOUN
ijassa-419	101	14	generalized	generalize	VERB
ijassa-419	101	15	iterations	iteration	NOUN
ijassa-419	101	16	ξnξn−1	ξnξn−1	PROPN
ijassa-419	101	17	...	...	PUNCT
ijassa-419	101	18	ξ1(ω	ξ1(ω	NUM
ijassa-419	101	19	)	)	PUNCT
ijassa-419	101	20	,	,	PUNCT
ijassa-419	101	21	the	the	DET
ijassa-419	101	22	composite	composite	NOUN
ijassa-419	101	23	of	of	ADP
ijassa-419	101	24	the	the	DET
ijassa-419	101	25	mappings	mapping	NOUN
ijassa-419	101	26	ξ1	ξ1	NOUN
ijassa-419	101	27	,	,	PUNCT
ijassa-419	101	28	...	...	PUNCT
ijassa-419	101	29	,	,	PUNCT
ijassa-419	101	30	ξn−1	ξn−1	PROPN
ijassa-419	101	31	,	,	PUNCT
ijassa-419	101	32	ξn	ξn	PROPN
ijassa-419	101	33	,	,	PUNCT
ijassa-419	101	34	n	n	PRON
ijassa-419	101	35	≥	≥	NOUN
ijassa-419	101	36	1	1	NUM
ijassa-419	101	37	,	,	PUNCT
ijassa-419	101	38	is	be	AUX
ijassa-419	101	39	referred	refer	VERB
ijassa-419	101	40	to	to	ADP
ijassa-419	101	41	as	as	ADP
ijassa-419	101	42	a	a	DET
ijassa-419	101	43	random	random	ADJ
ijassa-419	101	44	simple	simple	ADJ
ijassa-419	101	45	l	l	NOUN
ijassa-419	101	46	(	(	PUNCT
ijassa-419	101	47	r0l	r0l	PROPN
ijassa-419	101	48	)	)	PUNCT
ijassa-419	101	49	system	system	NOUN
ijassa-419	101	50	(	(	PUNCT
ijassa-419	101	51	of	of	ADP
ijassa-419	101	52	order	order	NOUN
ijassa-419	101	53	n	n	CCONJ
ijassa-419	101	54	)	)	PUNCT
ijassa-419	101	55	,	,	PUNCT
ijassa-419	101	56	where	where	SCONJ
ijassa-419	101	57	ξ1	ξ1	NOUN
ijassa-419	101	58	,	,	PUNCT
ijassa-419	101	59	ξ2	ξ2	ADJ
ijassa-419	101	60	,	,	PUNCT
ijassa-419	101	61	...	...	PUNCT
ijassa-419	101	62	,	,	PUNCT
ijassa-419	101	63	ξn	ξn	PROPN
ijassa-419	101	64	are	be	AUX
ijassa-419	101	65	independent	independent	ADJ
ijassa-419	101	66	and	and	CCONJ
ijassa-419	101	67	identical	identical	ADJ
ijassa-419	101	68	distributions	distribution	NOUN
ijassa-419	101	69	.	.	PUNCT
ijassa-419	102	1	this	this	DET
ijassa-419	102	2	system	system	NOUN
ijassa-419	102	3	is	be	AUX
ijassa-419	102	4	written	write	VERB
ijassa-419	102	5	as	as	ADP
ijassa-419	102	6	the	the	DET
ijassa-419	102	7	following	following	NOUN
ijassa-419	102	8	ordered	order	VERB
ijassa-419	102	9	quadruple	quadruple	PROPN
ijassa-419	102	10	⟨s	⟨s	PROPN
ijassa-419	102	11	,	,	PUNCT
ijassa-419	102	12	ω	ω	PROPN
ijassa-419	102	13	,	,	PUNCT
ijassa-419	102	14	φ	φ	PROPN
ijassa-419	102	15	,	,	PUNCT
ijassa-419	102	16	π⟩.	π⟩.	NUM
ijassa-419	102	17	3	3	NUM
ijassa-419	102	18	properties	property	NOUN
ijassa-419	102	19	of	of	ADP
ijassa-419	102	20	simple	simple	ADJ
ijassa-419	102	21	l	l	NOUN
ijassa-419	102	22	systems	system	NOUN
ijassa-419	102	23	from	from	ADP
ijassa-419	102	24	the	the	DET
ijassa-419	102	25	definitions	definition	NOUN
ijassa-419	102	26	,	,	PUNCT
ijassa-419	102	27	it	it	PRON
ijassa-419	102	28	follows	follow	VERB
ijassa-419	102	29	that	that	SCONJ
ijassa-419	102	30	each	each	DET
ijassa-419	102	31	simple	simple	ADJ
ijassa-419	102	32	l	l	NOUN
ijassa-419	102	33	system	system	NOUN
ijassa-419	102	34	is	be	AUX
ijassa-419	102	35	produced	produce	VERB
ijassa-419	102	36	by	by	ADP
ijassa-419	102	37	iterations	iteration	NOUN
ijassa-419	102	38	or	or	CCONJ
ijassa-419	102	39	generalized	generalized	ADJ
ijassa-419	102	40	iterations	iteration	NOUN
ijassa-419	102	41	of	of	ADP
ijassa-419	102	42	l	l	NOUN
ijassa-419	102	43	mappings	mapping	NOUN
ijassa-419	102	44	.	.	PUNCT
ijassa-419	103	1	hence	hence	ADV
ijassa-419	103	2	,	,	PUNCT
ijassa-419	103	3	the	the	DET
ijassa-419	103	4	properties	property	NOUN
ijassa-419	103	5	of	of	ADP
ijassa-419	103	6	simple	simple	ADJ
ijassa-419	103	7	l	l	NOUN
ijassa-419	103	8	systems	system	NOUN
ijassa-419	103	9	are	be	AUX
ijassa-419	103	10	determined	determine	VERB
ijassa-419	103	11	by	by	ADP
ijassa-419	103	12	those	those	PRON
ijassa-419	103	13	of	of	ADP
ijassa-419	103	14	l	l	NOUN
ijassa-419	103	15	mappings	mapping	NOUN
ijassa-419	103	16	.	.	PUNCT
ijassa-419	104	1	theorem	theorem	VERB
ijassa-419	104	2	3.1(property	3.1(property	NUM
ijassa-419	104	3	of	of	ADP
ijassa-419	104	4	linearity	linearity	NOUN
ijassa-419	104	5	)	)	PUNCT
ijassa-419	104	6	.	.	PUNCT
ijassa-419	105	1	each	each	DET
ijassa-419	105	2	simple	simple	ADJ
ijassa-419	105	3	l	l	NOUN
ijassa-419	105	4	system	system	NOUN
ijassa-419	105	5	is	be	AUX
ijassa-419	105	6	a	a	DET
ijassa-419	105	7	linear	linear	ADJ
ijassa-419	105	8	system	system	NOUN
ijassa-419	105	9	.	.	PUNCT
ijassa-419	106	1	proof	proof	NOUN
ijassa-419	106	2	.	.	PUNCT
ijassa-419	107	1	assume	assume	VERB
ijassa-419	107	2	that	that	SCONJ
ijassa-419	107	3	the	the	DET
ijassa-419	107	4	deterministic	deterministic	ADJ
ijassa-419	107	5	nth	nth	NOUN
ijassa-419	107	6	order	order	NOUN
ijassa-419	107	7	simple	simple	ADJ
ijassa-419	107	8	l	l	NOUN
ijassa-419	107	9	system	system	NOUN
ijassa-419	107	10	is	be	AUX
ijassa-419	107	11	given	give	VERB
ijassa-419	107	12	as	as	ADP
ijassa-419	107	13	l1	l1	PROPN
ijassa-419	107	14	=	=	SYM
ijassa-419	107	15	⟨s	⟨s	PROPN
ijassa-419	107	16	,	,	PUNCT
ijassa-419	107	17	ω	ω	PROPN
ijassa-419	107	18	,	,	PUNCT
ijassa-419	107	19	φ⟩	φ⟩	NOUN
ijassa-419	107	20	,	,	PUNCT
ijassa-419	107	21	and	and	CCONJ
ijassa-419	107	22	the	the	DET
ijassa-419	107	23	random	random	ADJ
ijassa-419	107	24	nth	nth	NOUN
ijassa-419	107	25	order	order	NOUN
ijassa-419	107	26	simple	simple	ADJ
ijassa-419	107	27	l	l	NOUN
ijassa-419	107	28	system	system	NOUN
ijassa-419	107	29	l2	l2	NOUN
ijassa-419	107	30	=	=	SYM
ijassa-419	107	31	⟨s	⟨s	NOUN
ijassa-419	107	32	,	,	PUNCT
ijassa-419	107	33	ω	ω	PROPN
ijassa-419	107	34	,	,	PUNCT
ijassa-419	107	35	φ	φ	NOUN
ijassa-419	107	36	,	,	PUNCT
ijassa-419	107	37	π⟩	π⟩	NOUN
ijassa-419	107	38	,	,	PUNCT
ijassa-419	107	39	where	where	SCONJ
ijassa-419	107	40	n	n	PRON
ijassa-419	107	41	≥	≥	NOUN
ijassa-419	107	42	1	1	NUM
ijassa-419	107	43	.	.	PUNCT
ijassa-419	107	44	to	to	PART
ijassa-419	107	45	show	show	VERB
ijassa-419	107	46	both	both	DET
ijassa-419	107	47	l1	l1	PROPN
ijassa-419	107	48	and	and	CCONJ
ijassa-419	107	49	l2	l2	NOUN
ijassa-419	107	50	are	be	AUX
ijassa-419	107	51	linear	linear	PROPN
ijassa-419	107	52	systems	system	NOUN
ijassa-419	107	53	,	,	PUNCT
ijassa-419	107	54	it	it	PRON
ijassa-419	107	55	suffices	suffice	VERB
ijassa-419	107	56	to	to	PART
ijassa-419	107	57	show	show	VERB
ijassa-419	107	58	that	that	SCONJ
ijassa-419	107	59	both	both	CCONJ
ijassa-419	107	60	l1	l1	PROPN
ijassa-419	107	61	and	and	CCONJ
ijassa-419	107	62	l2	l2	NOUN
ijassa-419	107	63	systems	system	NOUN
ijassa-419	107	64	respectively	respectively	ADV
ijassa-419	107	65	satisfy	satisfy	VERB
ijassa-419	107	66	the	the	DET
ijassa-419	107	67	superposition	superposition	NOUN
ijassa-419	107	68	principle	principle	NOUN
ijassa-419	107	69	.	.	PUNCT
ijassa-419	108	1	(	(	PUNCT
ijassa-419	108	2	i)we	i)we	NOUN
ijassa-419	108	3	use	use	VERB
ijassa-419	108	4	mathematical	mathematical	ADJ
ijassa-419	108	5	induction	induction	NOUN
ijassa-419	108	6	to	to	PART
ijassa-419	108	7	prove	prove	VERB
ijassa-419	108	8	that	that	SCONJ
ijassa-419	108	9	φn	φn	ADP
ijassa-419	108	10	satisfies	satisfy	VERB
ijassa-419	108	11	the	the	DET
ijassa-419	108	12	superposition	superposition	NOUN
ijassa-419	108	13	principle	principle	NOUN
ijassa-419	108	14	.	.	PUNCT
ijassa-419	109	1	when	when	SCONJ
ijassa-419	109	2	n	n	X
ijassa-419	109	3	=	=	SYM
ijassa-419	109	4	1	1	NUM
ijassa-419	109	5	,	,	PUNCT
ijassa-419	109	6	∀α	∀α	NOUN
ijassa-419	109	7	,	,	PUNCT
ijassa-419	109	8	β	β	X
ijassa-419	109	9	∈	∈	PROPN
ijassa-419	109	10	s∗	s∗	PROPN
ijassa-419	109	11	,	,	PUNCT
ijassa-419	109	12	k1	k1	NOUN
ijassa-419	109	13	,	,	PUNCT
ijassa-419	109	14	k2	k2	PROPN
ijassa-419	109	15	∈	∈	PROPN
ijassa-419	109	16	z+	z+	NUM
ijassa-419	109	17	,	,	PUNCT
ijassa-419	109	18	properties	property	NOUN
ijassa-419	109	19	(	(	PUNCT
ijassa-419	109	20	iv	iv	X
ijassa-419	109	21	)	)	PUNCT
ijassa-419	109	22	and	and	CCONJ
ijassa-419	109	23	(	(	PUNCT
ijassa-419	109	24	v	v	NOUN
ijassa-419	109	25	)	)	PUNCT
ijassa-419	109	26	of	of	ADP
ijassa-419	109	27	l	l	NOUN
ijassa-419	109	28	-	-	PUNCT
ijassa-419	109	29	mappings	mapping	NOUN
ijassa-419	109	30	imply	imply	VERB
ijassa-419	109	31	that	that	SCONJ
ijassa-419	109	32	φ(k1α⊕	φ(k1α⊕	ADP
ijassa-419	109	33	k2β	k2β	NOUN
ijassa-419	109	34	)	)	PUNCT
ijassa-419	109	35	=	=	SYM
ijassa-419	109	36	k1φ(α)⊕	k1φ(α)⊕	PROPN
ijassa-419	109	37	k1φ(β	k1φ(β	PROPN
ijassa-419	109	38	)	)	PUNCT
ijassa-419	109	39	(	(	PUNCT
ijassa-419	109	40	7	7	X
ijassa-419	109	41	)	)	PUNCT
ijassa-419	109	42	so	so	ADV
ijassa-419	109	43	,	,	PUNCT
ijassa-419	109	44	φ	φ	PROPN
ijassa-419	109	45	satisfies	satisfy	VERB
ijassa-419	109	46	the	the	DET
ijassa-419	109	47	superposition	superposition	NOUN
ijassa-419	109	48	principle	principle	NOUN
ijassa-419	109	49	.	.	PUNCT
ijassa-419	110	1	assume	assume	VERB
ijassa-419	110	2	that	that	SCONJ
ijassa-419	110	3	when	when	SCONJ
ijassa-419	110	4	n	n	PROPN
ijassa-419	110	5	=	=	SYM
ijassa-419	110	6	k	k	PROPN
ijassa-419	110	7	,	,	PUNCT
ijassa-419	110	8	k	k	PROPN
ijassa-419	110	9	≥	≥	NUM
ijassa-419	110	10	1,φk	1,φk	NUM
ijassa-419	110	11	satisfies	satisfy	VERB
ijassa-419	110	12	the	the	DET
ijassa-419	110	13	superposition	superposition	NOUN
ijassa-419	110	14	principle	principle	NOUN
ijassa-419	110	15	.	.	PUNCT
ijassa-419	111	1	that	that	PRON
ijassa-419	111	2	is	is	ADV
ijassa-419	111	3	,	,	PUNCT
ijassa-419	111	4	∀α	∀α	NOUN
ijassa-419	111	5	,	,	PUNCT
ijassa-419	111	6	β	β	X
ijassa-419	111	7	∈	∈	PROPN
ijassa-419	111	8	s∗	s∗	PROPN
ijassa-419	111	9	,	,	PUNCT
ijassa-419	111	10	k1	k1	NOUN
ijassa-419	111	11	,	,	PUNCT
ijassa-419	111	12	k2	k2	PROPN
ijassa-419	111	13	∈	∈	PROPN
ijassa-419	111	14	z+	z+	NUM
ijassa-419	111	15	,	,	PUNCT
ijassa-419	111	16	the	the	DET
ijassa-419	111	17	following	follow	VERB
ijassa-419	111	18	holds	hold	VERB
ijassa-419	111	19	true	true	ADJ
ijassa-419	111	20	:	:	PUNCT
ijassa-419	111	21	φk(k1α⊕	φk(k1α⊕	PROPN
ijassa-419	111	22	k2β	k2β	PROPN
ijassa-419	111	23	)	)	PUNCT
ijassa-419	112	1	=	=	PUNCT
ijassa-419	112	2	k1φ	k1φ	NOUN
ijassa-419	112	3	k(α)⊕	k(α)⊕	VERB
ijassa-419	112	4	k2φ	k2φ	PROPN
ijassa-419	112	5	k(β	k(β	PROPN
ijassa-419	112	6	)	)	PUNCT
ijassa-419	112	7	(	(	PUNCT
ijassa-419	112	8	8)	8)	NUM
ijassa-419	112	9	then	then	ADV
ijassa-419	112	10	when	when	SCONJ
ijassa-419	112	11	n	n	PROPN
ijassa-419	112	12	=	=	SYM
ijassa-419	112	13	k	k	PROPN
ijassa-419	113	1	+	+	CCONJ
ijassa-419	113	2	1	1	NUM
ijassa-419	113	3	,	,	PUNCT
ijassa-419	113	4	we	we	PRON
ijassa-419	113	5	have	have	VERB
ijassa-419	113	6	φk+1(k1α⊕	φk+1(k1α⊕	PROPN
ijassa-419	113	7	k2β	k2β	PROPN
ijassa-419	113	8	)	)	PUNCT
ijassa-419	114	1	=	=	NOUN
ijassa-419	114	2	φ(φk(k1α⊕	φ(φk(k1α⊕	PROPN
ijassa-419	114	3	k2β	k2β	PROPN
ijassa-419	114	4	)	)	PUNCT
ijassa-419	114	5	)	)	PUNCT
ijassa-419	115	1	=	=	PUNCT
ijassa-419	115	2	φ(k1φ	φ(k1φ	NOUN
ijassa-419	115	3	k(α)⊕	k(α)⊕	VERB
ijassa-419	115	4	k2φ	k2φ	PROPN
ijassa-419	115	5	k(β	k(β	PROPN
ijassa-419	115	6	)	)	PUNCT
ijassa-419	115	7	)	)	PUNCT
ijassa-419	116	1	=	=	PUNCT
ijassa-419	117	1	k1φ	k1φ	NOUN
ijassa-419	117	2	k+1(α)⊕	k+1(α)⊕	X
ijassa-419	117	3	k2φ	k2φ	PROPN
ijassa-419	117	4	k+1(β	k+1(β	PROPN
ijassa-419	117	5	)	)	PUNCT
ijassa-419	117	6	(	(	PUNCT
ijassa-419	117	7	9	9	X
ijassa-419	117	8	)	)	PUNCT
ijassa-419	117	9	hence	hence	ADV
ijassa-419	117	10	,	,	PUNCT
ijassa-419	117	11	∀n	∀n	NUM
ijassa-419	117	12	≥	≥	NOUN
ijassa-419	117	13	1	1	NUM
ijassa-419	117	14	,	,	PUNCT
ijassa-419	117	15	φn	φn	ADP
ijassa-419	117	16	satisfies	satisfy	VERB
ijassa-419	117	17	the	the	DET
ijassa-419	117	18	superposition	superposition	NOUN
ijassa-419	117	19	principle	principle	NOUN
ijassa-419	117	20	.	.	PUNCT
ijassa-419	118	1	(	(	PUNCT
ijassa-419	118	2	ii)we	ii)we	DET
ijassa-419	118	3	show	show	NOUN
ijassa-419	118	4	that	that	SCONJ
ijassa-419	118	5	ξnξn−1	ξnξn−1	PROPN
ijassa-419	118	6	...	...	PUNCT
ijassa-419	118	7	ξ1	ξ1	NOUN
ijassa-419	118	8	satisfies	satisfy	VERB
ijassa-419	118	9	the	the	DET
ijassa-419	118	10	superposition	superposition	NOUN
ijassa-419	118	11	principle	principle	NOUN
ijassa-419	118	12	.	.	PUNCT
ijassa-419	119	1	from	from	ADP
ijassa-419	119	2	the	the	DET
ijassa-419	119	3	definition	definition	NOUN
ijassa-419	119	4	of	of	ADP
ijassa-419	119	5	random	random	ADJ
ijassa-419	119	6	simple	simple	ADJ
ijassa-419	119	7	l	l	NOUN
ijassa-419	119	8	systems	system	NOUN
ijassa-419	119	9	,	,	PUNCT
ijassa-419	119	10	it	it	PRON
ijassa-419	119	11	follows	follow	VERB
ijassa-419	119	12	that	that	SCONJ
ijassa-419	119	13	ξi	ξi	NOUN
ijassa-419	119	14	,	,	PUNCT
ijassa-419	119	15	1	1	NUM
ijassa-419	119	16	≤	≤	NUM
ijassa-419	119	17	i	i	PRON
ijassa-419	119	18	≤	≤	PROPN
ijassa-419	119	19	n	n	CCONJ
ijassa-419	119	20	,	,	PUNCT
ijassa-419	119	21	stands	stand	VERB
ijassa-419	119	22	for	for	ADP
ijassa-419	119	23	the	the	DET
ijassa-419	119	24	l	l	NOUN
ijassa-419	119	25	mapping	mapping	NOUN
ijassa-419	119	26	φj	φj	NOUN
ijassa-419	119	27	,	,	PUNCT
ijassa-419	119	28	1	1	NUM
ijassa-419	119	29	≤	≤	NUM
ijassa-419	119	30	j	j	PROPN
ijassa-419	119	31	≤	≤	PROPN
ijassa-419	119	32	n	n	CCONJ
ijassa-419	119	33	,	,	PUNCT
ijassa-419	119	34	where	where	SCONJ
ijassa-419	119	35	n	n	PRON
ijassa-419	119	36	is	be	AUX
ijassa-419	119	37	the	the	DET
ijassa-419	119	38	total	total	ADJ
ijassa-419	119	39	number	number	NOUN
ijassa-419	119	40	of	of	ADP
ijassa-419	119	41	elements	element	NOUN
ijassa-419	119	42	in	in	ADP
ijassa-419	119	43	the	the	DET
ijassa-419	119	44	set	set	NOUN
ijassa-419	119	45	φ	φ	PROPN
ijassa-419	119	46	,	,	PUNCT
ijassa-419	119	47	randomly	randomly	ADV
ijassa-419	119	48	selected	select	VERB
ijassa-419	119	49	from	from	ADP
ijassa-419	119	50	φ	φ	PROPN
ijassa-419	119	51	at	at	ADP
ijassa-419	119	52	step	step	NOUN
ijassa-419	119	53	i.	i.	NOUN
ijassa-419	119	54	because	because	SCONJ
ijassa-419	119	55	each	each	DET
ijassa-419	119	56	φi	φi	PROPN
ijassa-419	119	57	∈	∈	PROPN
ijassa-419	119	58	φ	φ	X
ijassa-419	119	59	,	,	PUNCT
ijassa-419	119	60	1	1	NUM
ijassa-419	119	61	≤	≤	NUM
ijassa-419	119	62	i	i	PRON
ijassa-419	119	63	≤	≤	PUNCT
ijassa-419	119	64	n	n	CCONJ
ijassa-419	119	65	,	,	PUNCT
ijassa-419	119	66	satisfies	satisfy	VERB
ijassa-419	119	67	the	the	DET
ijassa-419	119	68	superposition	superposition	NOUN
ijassa-419	119	69	principle	principle	NOUN
ijassa-419	119	70	,	,	PUNCT
ijassa-419	119	71	from	from	ADP
ijassa-419	119	72	advances	advance	NOUN
ijassa-419	119	73	in	in	ADP
ijassa-419	119	74	systems	system	NOUN
ijassa-419	119	75	science	science	NOUN
ijassa-419	119	76	and	and	CCONJ
ijassa-419	119	77	applications	application	NOUN
ijassa-419	119	78	(	(	PUNCT
ijassa-419	119	79	2013	2013	NUM
ijassa-419	119	80	)	)	PUNCT
ijassa-419	119	81	vol.13	vol.13	NOUN
ijassa-419	119	82	no.2	no.2	PROPN
ijassa-419	119	83	105	105	NUM
ijassa-419	119	84	property	property	NOUN
ijassa-419	119	85	(	(	PUNCT
ijassa-419	119	86	vi	vi	NOUN
ijassa-419	119	87	)	)	PUNCT
ijassa-419	119	88	of	of	ADP
ijassa-419	119	89	l	l	NOUN
ijassa-419	119	90	mappings	mapping	NOUN
ijassa-419	119	91	,	,	PUNCT
ijassa-419	119	92	it	it	PRON
ijassa-419	119	93	follows	follow	VERB
ijassa-419	119	94	that	that	SCONJ
ijassa-419	119	95	ξnξn−1	ξnξn−1	PROPN
ijassa-419	119	96	...	...	PUNCT
ijassa-419	119	97	ξ1	ξ1	NOUN
ijassa-419	119	98	satisfies	satisfy	VERB
ijassa-419	119	99	the	the	DET
ijassa-419	119	100	superposition	superposition	NOUN
ijassa-419	119	101	principle	principle	NOUN
ijassa-419	119	102	.	.	PUNCT
ijassa-419	120	1	qed	qed	PROPN
ijassa-419	120	2	.	.	PROPN
ijassa-419	121	1	from	from	ADP
ijassa-419	121	2	theorem	theorem	ADJ
ijassa-419	121	3	3.1	3.1	NUM
ijassa-419	121	4	it	it	PRON
ijassa-419	121	5	follows	follow	VERB
ijassa-419	121	6	that	that	SCONJ
ijassa-419	121	7	in	in	ADP
ijassa-419	121	8	terms	term	NOUN
ijassa-419	121	9	of	of	ADP
ijassa-419	121	10	a	a	DET
ijassa-419	121	11	simple	simple	ADJ
ijassa-419	121	12	l	l	NOUN
ijassa-419	121	13	system	system	NOUN
ijassa-419	121	14	,	,	PUNCT
ijassa-419	121	15	when	when	SCONJ
ijassa-419	121	16	its	its	PRON
ijassa-419	121	17	order	order	NOUN
ijassa-419	121	18	n	n	PRON
ijassa-419	121	19	is	be	AUX
ijassa-419	121	20	relatively	relatively	ADV
ijassa-419	121	21	large	large	ADJ
ijassa-419	121	22	,	,	PUNCT
ijassa-419	121	23	to	to	PART
ijassa-419	121	24	shorten	shorten	VERB
ijassa-419	121	25	the	the	DET
ijassa-419	121	26	computational	computational	ADJ
ijassa-419	121	27	time	time	NOUN
ijassa-419	121	28	,	,	PUNCT
ijassa-419	121	29	one	one	PRON
ijassa-419	121	30	can	can	AUX
ijassa-419	121	31	decompose	decompose	VERB
ijassa-419	121	32	relatively	relatively	ADV
ijassa-419	121	33	long	long	ADJ
ijassa-419	121	34	strings	string	NOUN
ijassa-419	121	35	of	of	ADP
ijassa-419	121	36	characters	character	NOUN
ijassa-419	121	37	into	into	ADP
ijassa-419	121	38	sums	sum	NOUN
ijassa-419	121	39	of	of	ADP
ijassa-419	121	40	several	several	ADJ
ijassa-419	121	41	shorter	short	ADJ
ijassa-419	121	42	strings	string	NOUN
ijassa-419	121	43	,	,	PUNCT
ijassa-419	121	44	which	which	PRON
ijassa-419	121	45	can	can	AUX
ijassa-419	121	46	be	be	AUX
ijassa-419	121	47	handled	handle	VERB
ijassa-419	121	48	using	use	VERB
ijassa-419	121	49	parallel	parallel	ADJ
ijassa-419	121	50	treatments	treatment	NOUN
ijassa-419	121	51	to	to	PART
ijassa-419	121	52	obtain	obtain	VERB
ijassa-419	121	53	the	the	DET
ijassa-419	121	54	state	state	NOUN
ijassa-419	121	55	of	of	ADP
ijassa-419	121	56	the	the	DET
ijassa-419	121	57	next	next	ADJ
ijassa-419	121	58	moment	moment	NOUN
ijassa-419	121	59	.	.	PUNCT
ijassa-419	122	1	theorem	theorem	ADJ
ijassa-419	122	2	3.2	3.2	NUM
ijassa-419	122	3	(	(	PUNCT
ijassa-419	122	4	property	property	NOUN
ijassa-419	122	5	of	of	ADP
ijassa-419	122	6	fixed	fix	VERB
ijassa-419	122	7	points	point	NOUN
ijassa-419	122	8	)	)	PUNCT
ijassa-419	122	9	.	.	PUNCT
ijassa-419	123	1	the	the	DET
ijassa-419	123	2	restriction	restriction	NOUN
ijassa-419	123	3	of	of	ADP
ijassa-419	123	4	the	the	DET
ijassa-419	123	5	l	l	NOUN
ijassa-419	123	6	mapping	mapping	NOUN
ijassa-419	123	7	φ	φ	PROPN
ijassa-419	123	8	in	in	ADP
ijassa-419	123	9	a	a	DET
ijassa-419	123	10	d0l	d0l	NOUN
ijassa-419	123	11	system	system	NOUN
ijassa-419	123	12	on	on	ADP
ijassa-419	123	13	s	s	PROPN
ijassa-419	123	14	is	be	AUX
ijassa-419	123	15	bijective	bijective	ADJ
ijassa-419	123	16	from	from	ADP
ijassa-419	123	17	s	s	PRON
ijassa-419	123	18	to	to	ADP
ijassa-419	123	19	s	s	PRON
ijassa-419	123	20	,	,	PUNCT
ijassa-419	123	21	if	if	SCONJ
ijassa-419	123	22	and	and	CCONJ
ijassa-419	123	23	only	only	ADV
ijassa-419	123	24	if	if	SCONJ
ijassa-419	123	25	for	for	ADP
ijassa-419	123	26	any	any	DET
ijassa-419	123	27	α	α	PROPN
ijassa-419	123	28	∈	∈	PROPN
ijassa-419	123	29	s∗	s∗	NOUN
ijassa-419	123	30	,	,	PUNCT
ijassa-419	123	31	there	there	PRON
ijassa-419	123	32	is	be	VERB
ijassa-419	123	33	a	a	DET
ijassa-419	123	34	natural	natural	ADJ
ijassa-419	123	35	number	number	NOUN
ijassa-419	123	36	k	k	NOUN
ijassa-419	123	37	such	such	ADJ
ijassa-419	123	38	that	that	PRON
ijassa-419	123	39	φk(α	φk(α	NUM
ijassa-419	123	40	)	)	PUNCT
ijassa-419	123	41	=	=	SYM
ijassa-419	124	1	α	α	X
ijassa-419	124	2	.	.	PUNCT
ijassa-419	124	3	before	before	ADP
ijassa-419	124	4	proving	prove	VERB
ijassa-419	124	5	this	this	DET
ijassa-419	124	6	result	result	NOUN
ijassa-419	124	7	,	,	PUNCT
ijassa-419	124	8	let	let	VERB
ijassa-419	124	9	us	we	PRON
ijassa-419	124	10	first	first	ADV
ijassa-419	124	11	look	look	VERB
ijassa-419	124	12	at	at	ADP
ijassa-419	124	13	the	the	DET
ijassa-419	124	14	following	follow	VERB
ijassa-419	124	15	lemma	lemma	PROPN
ijassa-419	124	16	.	.	PUNCT
ijassa-419	125	1	lemma	lemma	PROPN
ijassa-419	125	2	3.1	3.1	NUM
ijassa-419	126	1	if	if	SCONJ
ijassa-419	126	2	the	the	DET
ijassa-419	126	3	restriction	restriction	NOUN
ijassa-419	126	4	of	of	ADP
ijassa-419	126	5	the	the	DET
ijassa-419	126	6	l	l	NOUN
ijassa-419	126	7	mapping	mapping	NOUN
ijassa-419	126	8	φ	φ	PROPN
ijassa-419	126	9	on	on	ADP
ijassa-419	126	10	s	s	PROPN
ijassa-419	126	11	is	be	AUX
ijassa-419	126	12	a	a	DET
ijassa-419	126	13	bijection	bijection	NOUN
ijassa-419	126	14	from	from	ADP
ijassa-419	126	15	s	s	PRON
ijassa-419	126	16	to	to	ADP
ijassa-419	126	17	s	s	PRON
ijassa-419	126	18	,	,	PUNCT
ijassa-419	126	19	then	then	ADV
ijassa-419	126	20	∀si	∀si	PROPN
ijassa-419	126	21	∈	∈	PROPN
ijassa-419	126	22	s	s	PART
ijassa-419	126	23	,	,	PUNCT
ijassa-419	126	24	∃ki	∃ki	ADJ
ijassa-419	126	25	∈	∈	PROPN
ijassa-419	126	26	z+	z+	NUM
ijassa-419	126	27	such	such	ADJ
ijassa-419	126	28	that	that	PRON
ijassa-419	126	29	φki(si	φki(si	PROPN
ijassa-419	126	30	)	)	PUNCT
ijassa-419	127	1	=	=	SYM
ijassa-419	127	2	si	si	X
ijassa-419	127	3	,	,	PUNCT
ijassa-419	127	4	1	1	NUM
ijassa-419	127	5	≤	≤	NUM
ijassa-419	127	6	i	i	PRON
ijassa-419	127	7	≤	≤	ADJ
ijassa-419	127	8	n.	n.	NOUN
ijassa-419	127	9	proof	proof	NOUN
ijassa-419	127	10	.	.	PUNCT
ijassa-419	128	1	by	by	ADP
ijassa-419	128	2	contradiction	contradiction	NOUN
ijassa-419	128	3	,	,	PUNCT
ijassa-419	128	4	assume	assume	VERB
ijassa-419	128	5	that	that	SCONJ
ijassa-419	128	6	∃s	∃s	PROPN
ijassa-419	128	7	∈	∈	PROPN
ijassa-419	128	8	s	s	PROPN
ijassa-419	128	9	,	,	PUNCT
ijassa-419	128	10	∀k	∀k	NOUN
ijassa-419	128	11	∈	∈	PROPN
ijassa-419	128	12	z+	z+	NUM
ijassa-419	128	13	,	,	PUNCT
ijassa-419	128	14	φk(s	φk(	VERB
ijassa-419	128	15	)	)	PUNCT
ijassa-419	128	16	̸=	̸=	PROPN
ijassa-419	128	17	s.	s.	PROPN
ijassa-419	128	18	then	then	ADV
ijassa-419	128	19	let	let	VERB
ijassa-419	128	20	si1	si1	PROPN
ijassa-419	128	21	=	=	SYM
ijassa-419	128	22	φ(s	φ(s	NOUN
ijassa-419	128	23	)	)	PUNCT
ijassa-419	128	24	,	,	PUNCT
ijassa-419	128	25	si2	si2	NOUN
ijassa-419	128	26	=	=	SYM
ijassa-419	128	27	φ2(s	φ2(s	NOUN
ijassa-419	128	28	)	)	PUNCT
ijassa-419	128	29	,	,	PUNCT
ijassa-419	128	30	...	...	PUNCT
ijassa-419	128	31	,	,	PUNCT
ijassa-419	128	32	sin	sin	NOUN
ijassa-419	128	33	=	=	SYM
ijassa-419	128	34	φn(s	φn(	NOUN
ijassa-419	128	35	)	)	PUNCT
ijassa-419	128	36	so	so	SCONJ
ijassa-419	128	37	we	we	PRON
ijassa-419	128	38	have	have	VERB
ijassa-419	128	39	s	s	AUX
ijassa-419	128	40	̸=	̸=	PROPN
ijassa-419	128	41	si1	si1	NUM
ijassa-419	128	42	,	,	PUNCT
ijassa-419	128	43	s	s	PART
ijassa-419	128	44	̸=	̸=	PROPN
ijassa-419	128	45	si2	si2	NOUN
ijassa-419	128	46	,	,	PUNCT
ijassa-419	128	47	...	...	PUNCT
ijassa-419	128	48	,	,	PUNCT
ijassa-419	128	49	s	s	VERB
ijassa-419	128	50	̸=	̸=	PROPN
ijassa-419	128	51	sin	sin	NOUN
ijassa-419	128	52	(	(	PUNCT
ijassa-419	128	53	10	10	NUM
ijassa-419	128	54	)	)	PUNCT
ijassa-419	128	55	step	step	NOUN
ijassa-419	128	56	1	1	NUM
ijassa-419	128	57	:	:	PUNCT
ijassa-419	128	58	from	from	ADP
ijassa-419	128	59	the	the	DET
ijassa-419	128	60	first	first	ADJ
ijassa-419	128	61	(	(	PUNCT
ijassa-419	128	62	n	n	CCONJ
ijassa-419	128	63	−	−	PROPN
ijassa-419	128	64	1	1	NUM
ijassa-419	128	65	)	)	PUNCT
ijassa-419	128	66	inequalities	inequality	NOUN
ijassa-419	128	67	in	in	ADP
ijassa-419	128	68	equ	equ	PROPN
ijassa-419	128	69	.	.	PUNCT
ijassa-419	129	1	(	(	PUNCT
ijassa-419	129	2	10	10	NUM
ijassa-419	129	3	)	)	PUNCT
ijassa-419	129	4	and	and	CCONJ
ijassa-419	129	5	that	that	DET
ijassa-419	129	6	fact	fact	NOUN
ijassa-419	129	7	that	that	SCONJ
ijassa-419	129	8	φ|s	φ|s	PUNCT
ijassa-419	129	9	:	:	PUNCT
ijassa-419	129	10	s	s	AUX
ijassa-419	129	11	→	→	SYM
ijassa-419	129	12	s	s	X
ijassa-419	129	13	is	be	AUX
ijassa-419	129	14	bijective	bijective	ADJ
ijassa-419	129	15	,	,	PUNCT
ijassa-419	129	16	it	it	PRON
ijassa-419	129	17	follows	follow	VERB
ijassa-419	129	18	that	that	SCONJ
ijassa-419	129	19	φ(s	φ(	VERB
ijassa-419	129	20	)	)	PUNCT
ijassa-419	129	21	̸=	̸=	PROPN
ijassa-419	129	22	φ(si1	φ(si1	NUM
ijassa-419	129	23	)	)	PUNCT
ijassa-419	129	24	,	,	PUNCT
ijassa-419	129	25	φ(s	φ(s	NOUN
ijassa-419	129	26	)	)	PUNCT
ijassa-419	129	27	̸=	̸=	PROPN
ijassa-419	129	28	φ(si2	φ(si2	NOUN
ijassa-419	129	29	)	)	PUNCT
ijassa-419	129	30	,	,	PUNCT
ijassa-419	129	31	...	...	PUNCT
ijassa-419	129	32	,	,	PUNCT
ijassa-419	129	33	φ(s	φ(s	NOUN
ijassa-419	129	34	)	)	PUNCT
ijassa-419	129	35	̸=	̸=	PROPN
ijassa-419	129	36	φ(sin−1	φ(sin−1	NUM
ijassa-419	129	37	)	)	PUNCT
ijassa-419	129	38	.	.	PUNCT
ijassa-419	130	1	that	that	PRON
ijassa-419	130	2	is	be	AUX
ijassa-419	130	3	,	,	PUNCT
ijassa-419	130	4	si1	si1	PROPN
ijassa-419	130	5	̸=	̸=	PROPN
ijassa-419	130	6	si2	si2	NOUN
ijassa-419	130	7	,	,	PUNCT
ijassa-419	130	8	si1	si1	PROPN
ijassa-419	130	9	̸=	̸=	PROPN
ijassa-419	130	10	si3	si3	PROPN
ijassa-419	130	11	,	,	PUNCT
ijassa-419	130	12	...	...	PUNCT
ijassa-419	130	13	,	,	PUNCT
ijassa-419	130	14	si1	si1	PROPN
ijassa-419	130	15	̸=	̸=	PROPN
ijassa-419	130	16	sin	sin	NOUN
ijassa-419	130	17	(	(	PUNCT
ijassa-419	130	18	11	11	NUM
ijassa-419	130	19	)	)	PUNCT
ijassa-419	130	20	step	step	NOUN
ijassa-419	130	21	2	2	NUM
ijassa-419	130	22	:	:	PUNCT
ijassa-419	130	23	from	from	ADP
ijassa-419	130	24	the	the	DET
ijassa-419	130	25	first	first	ADJ
ijassa-419	130	26	(	(	PUNCT
ijassa-419	130	27	n	n	CCONJ
ijassa-419	130	28	−	−	PROPN
ijassa-419	130	29	2	2	NUM
ijassa-419	130	30	)	)	PUNCT
ijassa-419	130	31	inequalities	inequality	NOUN
ijassa-419	130	32	in	in	ADP
ijassa-419	130	33	equ	equ	PROPN
ijassa-419	130	34	.	.	PUNCT
ijassa-419	131	1	(	(	PUNCT
ijassa-419	131	2	11	11	NUM
ijassa-419	131	3	)	)	PUNCT
ijassa-419	131	4	and	and	CCONJ
ijassa-419	131	5	that	that	DET
ijassa-419	131	6	fact	fact	NOUN
ijassa-419	131	7	that	that	SCONJ
ijassa-419	131	8	φ|s	φ|s	PUNCT
ijassa-419	131	9	:	:	PUNCT
ijassa-419	131	10	s	s	AUX
ijassa-419	131	11	→	→	SYM
ijassa-419	131	12	s	s	X
ijassa-419	131	13	is	be	AUX
ijassa-419	131	14	bijective	bijective	ADJ
ijassa-419	131	15	,	,	PUNCT
ijassa-419	131	16	it	it	PRON
ijassa-419	131	17	follows	follow	VERB
ijassa-419	131	18	that	that	SCONJ
ijassa-419	131	19	φ(si1	φ(si1	PROPN
ijassa-419	131	20	)	)	PUNCT
ijassa-419	131	21	̸=	̸=	PROPN
ijassa-419	131	22	φ(si2	φ(si2	NOUN
ijassa-419	131	23	)	)	PUNCT
ijassa-419	131	24	,	,	PUNCT
ijassa-419	131	25	φ(si1	φ(si1	PROPN
ijassa-419	131	26	)	)	PUNCT
ijassa-419	131	27	̸=	̸=	PROPN
ijassa-419	131	28	φ(si3	φ(si3	PROPN
ijassa-419	131	29	)	)	PUNCT
ijassa-419	131	30	,	,	PUNCT
ijassa-419	131	31	...	...	PUNCT
ijassa-419	131	32	,	,	PUNCT
ijassa-419	131	33	φ(si1	φ(si1	PROPN
ijassa-419	131	34	)	)	PUNCT
ijassa-419	131	35	̸=	̸=	PROPN
ijassa-419	131	36	φ(sin−1	φ(sin−1	NUM
ijassa-419	131	37	)	)	PUNCT
ijassa-419	131	38	.	.	PUNCT
ijassa-419	132	1	that	that	PRON
ijassa-419	132	2	is	be	AUX
ijassa-419	132	3	,	,	PUNCT
ijassa-419	132	4	si2	si2	ADP
ijassa-419	132	5	̸=	̸=	PROPN
ijassa-419	132	6	si3	si3	PROPN
ijassa-419	132	7	,	,	PUNCT
ijassa-419	132	8	si2	si2	ADP
ijassa-419	132	9	̸=	̸=	PROPN
ijassa-419	132	10	si4	si4	NOUN
ijassa-419	132	11	,	,	PUNCT
ijassa-419	132	12	...	...	PUNCT
ijassa-419	132	13	,	,	PUNCT
ijassa-419	132	14	si2	si2	AUX
ijassa-419	132	15	̸=	̸=	PROPN
ijassa-419	132	16	sin	sin	NOUN
ijassa-419	132	17	(	(	PUNCT
ijassa-419	132	18	12	12	NUM
ijassa-419	132	19	)	)	PUNCT
ijassa-419	132	20	by	by	ADP
ijassa-419	132	21	continuing	continue	VERB
ijassa-419	132	22	this	this	DET
ijassa-419	132	23	procedure	procedure	NOUN
ijassa-419	132	24	,	,	PUNCT
ijassa-419	132	25	we	we	PRON
ijassa-419	132	26	obtain	obtain	VERB
ijassa-419	132	27	at	at	ADP
ijassa-419	132	28	step	step	NOUN
ijassa-419	132	29	(	(	PUNCT
ijassa-419	132	30	n−	n−	NOUN
ijassa-419	132	31	1	1	NUM
ijassa-419	132	32	)	)	PUNCT
ijassa-419	132	33	that	that	SCONJ
ijassa-419	132	34	sin−1	sin−1	PROPN
ijassa-419	132	35	̸=	̸=	PROPN
ijassa-419	132	36	sin	sin	NOUN
ijassa-419	132	37	(	(	PUNCT
ijassa-419	132	38	13	13	NUM
ijassa-419	132	39	)	)	PUNCT
ijassa-419	132	40	therefore	therefore	ADV
ijassa-419	132	41	,	,	PUNCT
ijassa-419	132	42	s	s	VERB
ijassa-419	132	43	̸=	̸=	PROPN
ijassa-419	132	44	si1	si1	VERB
ijassa-419	132	45	̸=	̸=	PROPN
ijassa-419	132	46	si2	si2	NOUN
ijassa-419	132	47	̸=	̸=	PROPN
ijassa-419	132	48	...	...	PUNCT
ijassa-419	133	1	̸=	̸=	PROPN
ijassa-419	133	2	sin	sin	VERB
ijassa-419	133	3	.	.	PUNCT
ijassa-419	134	1	it	it	PRON
ijassa-419	134	2	means	mean	VERB
ijassa-419	134	3	that	that	SCONJ
ijassa-419	134	4	there	there	PRON
ijassa-419	134	5	are	be	VERB
ijassa-419	134	6	n	n	PRON
ijassa-419	134	7	+	+	CCONJ
ijassa-419	134	8	1	1	NUM
ijassa-419	134	9	different	different	ADJ
ijassa-419	134	10	elements	element	NOUN
ijassa-419	134	11	in	in	ADP
ijassa-419	134	12	the	the	DET
ijassa-419	134	13	set	set	NOUN
ijassa-419	134	14	s.	s.	PROPN
ijassa-419	134	15	however	however	ADV
ijassa-419	134	16	,	,	PUNCT
ijassa-419	134	17	s	s	X
ijassa-419	134	18	has	have	VERB
ijassa-419	134	19	only	only	ADV
ijassa-419	134	20	n	n	PRON
ijassa-419	134	21	elements	element	NOUN
ijassa-419	134	22	.	.	PUNCT
ijassa-419	135	1	a	a	DET
ijassa-419	135	2	contradiction	contradiction	NOUN
ijassa-419	135	3	.	.	PUNCT
ijassa-419	136	1	so	so	ADV
ijassa-419	136	2	,	,	PUNCT
ijassa-419	136	3	the	the	DET
ijassa-419	136	4	assumption	assumption	NOUN
ijassa-419	136	5	that	that	SCONJ
ijassa-419	136	6	∃s	∃s	PROPN
ijassa-419	136	7	∈	∈	PROPN
ijassa-419	136	8	s	s	PROPN
ijassa-419	136	9	,	,	PUNCT
ijassa-419	136	10	∀k	∀k	NOUN
ijassa-419	136	11	∈	∈	PROPN
ijassa-419	136	12	z+	z+	X
ijassa-419	136	13	,	,	PUNCT
ijassa-419	136	14	φk(s	φk(s	ADV
ijassa-419	136	15	)	)	PUNCT
ijassa-419	136	16	̸=	̸=	PROPN
ijassa-419	136	17	s	s	AUX
ijassa-419	136	18	does	do	AUX
ijassa-419	136	19	not	not	PART
ijassa-419	136	20	hold	hold	VERB
ijassa-419	136	21	true	true	ADJ
ijassa-419	136	22	.	.	PUNCT
ijassa-419	137	1	in	in	ADP
ijassa-419	137	2	other	other	ADJ
ijassa-419	137	3	words	word	NOUN
ijassa-419	137	4	,	,	PUNCT
ijassa-419	137	5	∀si	∀si	PROPN
ijassa-419	137	6	∈	∈	PROPN
ijassa-419	137	7	s	s	PART
ijassa-419	137	8	,	,	PUNCT
ijassa-419	137	9	∃ki	∃ki	ADJ
ijassa-419	137	10	∈	∈	PROPN
ijassa-419	137	11	z+	z+	NUM
ijassa-419	138	1	such	such	ADJ
ijassa-419	138	2	that	that	PRON
ijassa-419	138	3	φki(si	φki(si	PROPN
ijassa-419	138	4	)	)	PUNCT
ijassa-419	138	5	=	=	SYM
ijassa-419	138	6	si	si	X
ijassa-419	138	7	,	,	PUNCT
ijassa-419	138	8	1	1	NUM
ijassa-419	138	9	≤	≤	NUM
ijassa-419	138	10	i	i	PRON
ijassa-419	138	11	≤	≤	PROPN
ijassa-419	138	12	n.	n.	PROPN
ijassa-419	138	13	qed	qed	PROPN
ijassa-419	138	14	.	.	PUNCT
ijassa-419	139	1	in	in	ADP
ijassa-419	139	2	the	the	DET
ijassa-419	139	3	following	following	NOUN
ijassa-419	139	4	,	,	PUNCT
ijassa-419	139	5	let	let	VERB
ijassa-419	139	6	us	we	PRON
ijassa-419	139	7	prove	prove	VERB
ijassa-419	139	8	theorem	theorem	VERB
ijassa-419	139	9	3.2	3.2	NUM
ijassa-419	139	10	.	.	PUNCT
ijassa-419	140	1	(	(	PUNCT
ijassa-419	140	2	⇒)for	⇒)for	ADP
ijassa-419	140	3	α	α	NOUN
ijassa-419	140	4	=	=	SYM
ijassa-419	140	5	sm1sm2	sm1sm2	NOUN
ijassa-419	140	6	...	...	PUNCT
ijassa-419	140	7	smp	smp	PROPN
ijassa-419	140	8	∈	∈	PROPN
ijassa-419	140	9	s∗	s∗	PROPN
ijassa-419	140	10	,	,	PUNCT
ijassa-419	140	11	from	from	ADP
ijassa-419	140	12	lemma	lemma	PROPN
ijassa-419	140	13	3.1	3.1	NUM
ijassa-419	140	14	,	,	PUNCT
ijassa-419	140	15	it	it	PRON
ijassa-419	140	16	follows	follow	VERB
ijassa-419	140	17	that	that	SCONJ
ijassa-419	140	18	∀smi	∀smi	PROPN
ijassa-419	140	19	∈	∈	PROPN
ijassa-419	140	20	s	s	PROPN
ijassa-419	140	21	,	,	PUNCT
ijassa-419	140	22	∃ki	∃ki	ADJ
ijassa-419	140	23	∈	∈	PROPN
ijassa-419	140	24	z+	z+	NUM
ijassa-419	140	25	,	,	PUNCT
ijassa-419	140	26	φki(smi	φki(smi	NOUN
ijassa-419	140	27	)	)	PUNCT
ijassa-419	140	28	=	=	PROPN
ijassa-419	140	29	smi	smi	PROPN
ijassa-419	140	30	,	,	PUNCT
ijassa-419	140	31	1	1	NUM
ijassa-419	140	32	≤	≤	NUM
ijassa-419	140	33	i	i	NOUN
ijassa-419	140	34	≤	≤	ADJ
ijassa-419	140	35	p	p	NOUN
ijassa-419	140	36	.	.	PUNCT
ijassa-419	141	1	let	let	VERB
ijassa-419	141	2	k	k	NOUN
ijassa-419	141	3	=	=	X
ijassa-419	141	4	<	<	X
ijassa-419	141	5	k1	k1	PROPN
ijassa-419	141	6	,	,	PUNCT
ijassa-419	141	7	k2	k2	NOUN
ijassa-419	141	8	,	,	PUNCT
ijassa-419	141	9	...	...	PUNCT
ijassa-419	141	10	,	,	PUNCT
ijassa-419	141	11	kp	kp	PROPN
ijassa-419	141	12	>	>	PUNCT
ijassa-419	141	13	.	.	PUNCT
ijassa-419	142	1	so	so	ADV
ijassa-419	142	2	,	,	PUNCT
ijassa-419	142	3	φk(α	φk(α	NUM
ijassa-419	142	4	)	)	PUNCT
ijassa-419	143	1	=	=	SYM
ijassa-419	143	2	φk(sm1sm2	φk(sm1sm2	NOUN
ijassa-419	143	3	...	...	PUNCT
ijassa-419	143	4	smp	smp	NOUN
ijassa-419	143	5	)	)	PUNCT
ijassa-419	143	6	=	=	SYM
ijassa-419	143	7	φk(sm1)φ	φk(sm1)φ	PROPN
ijassa-419	143	8	k(sm2)	k(sm2)	PROPN
ijassa-419	143	9	...	...	PUNCT
ijassa-419	143	10	φ	φ	PROPN
ijassa-419	143	11	k(smp	k(smp	PROPN
ijassa-419	143	12	)	)	PUNCT
ijassa-419	143	13	=	=	SYM
ijassa-419	144	1	φk1(sm1)φ	φk1(sm1)φ	PROPN
ijassa-419	144	2	k2(sm2)	k2(sm2)	PROPN
ijassa-419	144	3	...	...	PUNCT
ijassa-419	144	4	φ	φ	PROPN
ijassa-419	144	5	kp(smp	kp(smp	PROPN
ijassa-419	144	6	)	)	PUNCT
ijassa-419	144	7	=	=	SYM
ijassa-419	145	1	α	α	PROPN
ijassa-419	145	2	106	106	NUM
ijassa-419	145	3	xiaojun	xiaojun	PROPN
ijassa-419	145	4	duan	duan	PROPN
ijassa-419	145	5	:	:	PUNCT
ijassa-419	145	6	set	set	VERB
ijassa-419	145	7	-	-	PUNCT
ijassa-419	145	8	theoretic	theoretic	NOUN
ijassa-419	145	9	design	design	NOUN
ijassa-419	145	10	and	and	CCONJ
ijassa-419	145	11	analysis	analysis	NOUN
ijassa-419	145	12	of	of	ADP
ijassa-419	145	13	l	l	NOUN
ijassa-419	145	14	systems	system	NOUN
ijassa-419	145	15	so	so	ADV
ijassa-419	145	16	,	,	PUNCT
ijassa-419	145	17	there	there	PRON
ijassa-419	145	18	is	be	VERB
ijassa-419	145	19	a	a	DET
ijassa-419	145	20	natural	natural	ADJ
ijassa-419	145	21	number	number	NOUN
ijassa-419	145	22	k	k	NOUN
ijassa-419	145	23	such	such	ADJ
ijassa-419	145	24	that	that	PRON
ijassa-419	145	25	φk(α	φk(α	NUM
ijassa-419	145	26	)	)	PUNCT
ijassa-419	145	27	=	=	SYM
ijassa-419	145	28	α	α	PROPN
ijassa-419	145	29	.	.	PUNCT
ijassa-419	146	1	(	(	PUNCT
ijassa-419	146	2	⇐	⇐	NOUN
ijassa-419	146	3	)	)	PUNCT
ijassa-419	146	4	if	if	SCONJ
ijassa-419	146	5	∀α	∀α	X
ijassa-419	146	6	∈	∈	PROPN
ijassa-419	146	7	s∗	s∗	NOUN
ijassa-419	146	8	,	,	PUNCT
ijassa-419	146	9	there	there	PRON
ijassa-419	146	10	is	be	VERB
ijassa-419	146	11	natural	natural	ADJ
ijassa-419	146	12	number	number	NOUN
ijassa-419	146	13	k	k	NOUN
ijassa-419	146	14	such	such	ADJ
ijassa-419	146	15	that	that	PRON
ijassa-419	146	16	φk(α	φk(α	NUM
ijassa-419	146	17	)	)	PUNCT
ijassa-419	147	1	=	=	SYM
ijassa-419	147	2	α	α	NOUN
ijassa-419	147	3	,	,	PUNCT
ijassa-419	147	4	let	let	VERB
ijassa-419	147	5	us	we	PRON
ijassa-419	147	6	take	take	VERB
ijassa-419	147	7	α	α	NOUN
ijassa-419	147	8	=	=	SYM
ijassa-419	147	9	s1	s1	PROPN
ijassa-419	147	10	,	,	PUNCT
ijassa-419	147	11	s2	s2	NOUN
ijassa-419	147	12	,	,	PUNCT
ijassa-419	147	13	.	.	PUNCT
ijassa-419	147	14	.	.	PUNCT
ijassa-419	148	1	.	.	PUNCT
ijassa-419	149	1	,	,	PUNCT
ijassa-419	149	2	sn	sn	PROPN
ijassa-419	149	3	.	.	PUNCT
ijassa-419	150	1	then	then	ADV
ijassa-419	150	2	∃k1	∃k1	NOUN
ijassa-419	150	3	,	,	PUNCT
ijassa-419	150	4	k2	k2	NOUN
ijassa-419	150	5	,	,	PUNCT
ijassa-419	150	6	...	...	PUNCT
ijassa-419	150	7	,	,	PUNCT
ijassa-419	150	8	kn	kn	PROPN
ijassa-419	150	9	such	such	ADJ
ijassa-419	150	10	that	that	SCONJ
ijassa-419	150	11	φk1(s1	φk1(s1	VERB
ijassa-419	150	12	)	)	PUNCT
ijassa-419	150	13	=	=	SYM
ijassa-419	150	14	s1	s1	PROPN
ijassa-419	150	15	,	,	PUNCT
ijassa-419	150	16	φ	φ	PROPN
ijassa-419	150	17	k2(s2	k2(s2	PROPN
ijassa-419	150	18	)	)	PUNCT
ijassa-419	150	19	=	=	SYM
ijassa-419	150	20	s2	s2	PROPN
ijassa-419	150	21	,	,	PUNCT
ijassa-419	150	22	...	...	PUNCT
ijassa-419	150	23	,	,	PUNCT
ijassa-419	150	24	φ	φ	PROPN
ijassa-419	150	25	kn(sn	kn(sn	PROPN
ijassa-419	150	26	)	)	PUNCT
ijassa-419	150	27	=	=	SYM
ijassa-419	150	28	sn	sn	PROPN
ijassa-419	150	29	(	(	PUNCT
ijassa-419	150	30	14	14	NUM
ijassa-419	150	31	)	)	PUNCT
ijassa-419	150	32	according	accord	VERB
ijassa-419	150	33	to	to	ADP
ijassa-419	150	34	property	property	NOUN
ijassa-419	150	35	(	(	PUNCT
ijassa-419	150	36	ii	ii	NOUN
ijassa-419	150	37	)	)	PUNCT
ijassa-419	150	38	of	of	ADP
ijassa-419	150	39	l	l	NOUN
ijassa-419	150	40	mappings	mapping	NOUN
ijassa-419	150	41	,	,	PUNCT
ijassa-419	150	42	to	to	PART
ijassa-419	150	43	show	show	VERB
ijassa-419	150	44	the	the	DET
ijassa-419	150	45	restriction	restriction	NOUN
ijassa-419	150	46	of	of	ADP
ijassa-419	150	47	φ	φ	PROPN
ijassa-419	150	48	on	on	ADP
ijassa-419	150	49	s	s	PROPN
ijassa-419	150	50	is	be	AUX
ijassa-419	150	51	a	a	DET
ijassa-419	150	52	bijection	bijection	NOUN
ijassa-419	150	53	from	from	ADP
ijassa-419	150	54	s	s	PRON
ijassa-419	150	55	to	to	PART
ijassa-419	150	56	s	s	NUM
ijassa-419	150	57	,	,	PUNCT
ijassa-419	150	58	it	it	PRON
ijassa-419	150	59	suffice	suffice	VERB
ijassa-419	150	60	to	to	PART
ijassa-419	150	61	prove	prove	VERB
ijassa-419	150	62	that	that	PRON
ijassa-419	150	63	φ|s	φ|s	PUNCT
ijassa-419	151	1	:	:	PUNCT
ijassa-419	151	2	s	s	AUX
ijassa-419	151	3	→	→	SYM
ijassa-419	151	4	s	s	PART
ijassa-419	151	5	is	be	AUX
ijassa-419	151	6	surjective	surjective	ADJ
ijassa-419	151	7	.	.	PUNCT
ijassa-419	152	1	again	again	ADV
ijassa-419	152	2	,	,	PUNCT
ijassa-419	152	3	we	we	PRON
ijassa-419	152	4	prove	prove	VERB
ijassa-419	152	5	this	this	DET
ijassa-419	152	6	end	end	NOUN
ijassa-419	152	7	by	by	ADP
ijassa-419	152	8	contradiction	contradiction	NOUN
ijassa-419	152	9	.	.	PUNCT
ijassa-419	153	1	assume	assume	VERB
ijassa-419	153	2	that	that	SCONJ
ijassa-419	153	3	∃s	∃s	PROPN
ijassa-419	153	4	∈	∈	PROPN
ijassa-419	153	5	s	s	PART
ijassa-419	153	6	,	,	PUNCT
ijassa-419	153	7	∀si	∀si	PROPN
ijassa-419	153	8	∈	∈	PROPN
ijassa-419	153	9	s	s	NOUN
ijassa-419	153	10	,	,	PUNCT
ijassa-419	153	11	1	1	NUM
ijassa-419	153	12	≤	≤	NUM
ijassa-419	153	13	i	i	PRON
ijassa-419	153	14	≤	≤	ADJ
ijassa-419	153	15	n	n	CCONJ
ijassa-419	153	16	,	,	PUNCT
ijassa-419	153	17	φ(si	φ(si	PROPN
ijassa-419	153	18	)	)	PUNCT
ijassa-419	153	19	̸=	̸=	PROPN
ijassa-419	153	20	s	s	PART
ijassa-419	153	21	.	.	PUNCT
ijassa-419	154	1	then	then	ADV
ijassa-419	154	2	we	we	PRON
ijassa-419	154	3	have	have	VERB
ijassa-419	154	4	that	that	SCONJ
ijassa-419	154	5	∀k	∀k	NOUN
ijassa-419	154	6	≥	≥	NUM
ijassa-419	154	7	1	1	NUM
ijassa-419	154	8	,	,	PUNCT
ijassa-419	154	9	φk(s	φk(	VERB
ijassa-419	154	10	)	)	PUNCT
ijassa-419	154	11	̸=	̸=	PROPN
ijassa-419	154	12	s	s	PART
ijassa-419	154	13	,	,	PUNCT
ijassa-419	154	14	which	which	PRON
ijassa-419	154	15	contradicts	contradict	VERB
ijassa-419	154	16	with	with	ADP
ijassa-419	154	17	equ	equ	PROPN
ijassa-419	154	18	.	.	PUNCT
ijassa-419	155	1	(	(	PUNCT
ijassa-419	155	2	14	14	NUM
ijassa-419	155	3	)	)	PUNCT
ijassa-419	155	4	.	.	PUNCT
ijassa-419	156	1	so	so	ADV
ijassa-419	156	2	,	,	PUNCT
ijassa-419	156	3	φ|s	φ|s	X
ijassa-419	156	4	:	:	PUNCT
ijassa-419	156	5	s	s	AUX
ijassa-419	156	6	→	→	SYM
ijassa-419	156	7	s	s	PART
ijassa-419	156	8	is	be	AUX
ijassa-419	156	9	surjective	surjective	ADJ
ijassa-419	156	10	.	.	PUNCT
ijassa-419	157	1	hence	hence	ADV
ijassa-419	157	2	,	,	PUNCT
ijassa-419	157	3	φ|s	φ|s	PROPN
ijassa-419	157	4	:	:	PUNCT
ijassa-419	157	5	s	s	AUX
ijassa-419	157	6	→	→	SYM
ijassa-419	157	7	s	s	PART
ijassa-419	157	8	is	be	AUX
ijassa-419	157	9	bijective	bijective	ADJ
ijassa-419	157	10	.	.	PUNCT
ijassa-419	158	1	qed	qed	PROPN
ijassa-419	158	2	.	.	PROPN
ijassa-419	159	1	from	from	ADP
ijassa-419	159	2	theorem	theorem	ADJ
ijassa-419	159	3	3.2	3.2	NUM
ijassa-419	159	4	,	,	PUNCT
ijassa-419	159	5	it	it	PRON
ijassa-419	159	6	follows	follow	VERB
ijassa-419	159	7	that	that	SCONJ
ijassa-419	159	8	in	in	ADP
ijassa-419	159	9	terms	term	NOUN
ijassa-419	159	10	of	of	ADP
ijassa-419	159	11	d0l	d0l	PROPN
ijassa-419	159	12	systems	system	NOUN
ijassa-419	159	13	,	,	PUNCT
ijassa-419	159	14	if	if	SCONJ
ijassa-419	159	15	the	the	DET
ijassa-419	159	16	restriction	restriction	NOUN
ijassa-419	159	17	φ|s	φ|s	PUNCT
ijassa-419	160	1	:	:	PUNCT
ijassa-419	160	2	s	s	X
ijassa-419	160	3	→	→	SYM
ijassa-419	160	4	s	s	X
ijassa-419	160	5	of	of	ADP
ijassa-419	160	6	l	l	NOUN
ijassa-419	160	7	-	-	NOUN
ijassa-419	160	8	mapping	mapping	ADJ
ijassa-419	160	9	φ	φ	NOUN
ijassa-419	160	10	is	be	AUX
ijassa-419	160	11	a	a	DET
ijassa-419	160	12	bijection	bijection	NOUN
ijassa-419	160	13	,	,	PUNCT
ijassa-419	160	14	then	then	ADV
ijassa-419	160	15	there	there	PRON
ijassa-419	160	16	are	be	VERB
ijassa-419	160	17	at	at	ADP
ijassa-419	160	18	most	most	ADJ
ijassa-419	160	19	k	k	NOUN
ijassa-419	161	1	=	=	X
ijassa-419	161	2	<	<	X
ijassa-419	161	3	k1	k1	PROPN
ijassa-419	161	4	,	,	PUNCT
ijassa-419	161	5	k2	k2	NOUN
ijassa-419	161	6	,	,	PUNCT
ijassa-419	161	7	...	...	PUNCT
ijassa-419	161	8	,	,	PUNCT
ijassa-419	161	9	kp	kp	PROPN
ijassa-419	161	10	>	>	PUNCT
ijassa-419	161	11	different	different	ADJ
ijassa-419	161	12	states	state	NOUN
ijassa-419	161	13	.	.	PUNCT
ijassa-419	162	1	therefore	therefore	ADV
ijassa-419	162	2	,	,	PUNCT
ijassa-419	162	3	to	to	PART
ijassa-419	162	4	produce	produce	VERB
ijassa-419	162	5	complicated	complicated	ADJ
ijassa-419	162	6	fractal	fractal	ADJ
ijassa-419	162	7	figures	figure	NOUN
ijassa-419	162	8	using	use	VERB
ijassa-419	162	9	d0l	d0l	PROPN
ijassa-419	162	10	systems	system	NOUN
ijassa-419	162	11	,	,	PUNCT
ijassa-419	162	12	one	one	PRON
ijassa-419	162	13	should	should	AUX
ijassa-419	162	14	avoid	avoid	VERB
ijassa-419	162	15	using	use	VERB
ijassa-419	162	16	any	any	DET
ijassa-419	162	17	such	such	ADJ
ijassa-419	162	18	l	l	NOUN
ijassa-419	162	19	mapping	mapping	NOUN
ijassa-419	162	20	whose	whose	DET
ijassa-419	162	21	restriction	restriction	NOUN
ijassa-419	162	22	on	on	ADP
ijassa-419	162	23	s	s	NOUN
ijassa-419	162	24	is	be	AUX
ijassa-419	162	25	a	a	DET
ijassa-419	162	26	bijection	bijection	NOUN
ijassa-419	162	27	from	from	ADP
ijassa-419	162	28	s	s	PRON
ijassa-419	162	29	to	to	ADP
ijassa-419	162	30	s.	s.	PROPN
ijassa-419	162	31	theorem	theorem	VERB
ijassa-419	162	32	3.3(property	3.3(property	NUM
ijassa-419	162	33	of	of	ADP
ijassa-419	162	34	fixed	fix	VERB
ijassa-419	162	35	points	point	NOUN
ijassa-419	162	36	)	)	PUNCT
ijassa-419	162	37	.	.	PUNCT
ijassa-419	163	1	the	the	DET
ijassa-419	163	2	restriction	restriction	NOUN
ijassa-419	163	3	of	of	ADP
ijassa-419	163	4	the	the	DET
ijassa-419	163	5	l	l	NOUN
ijassa-419	163	6	mapping	mapping	NOUN
ijassa-419	163	7	φ	φ	PROPN
ijassa-419	163	8	in	in	ADP
ijassa-419	163	9	a	a	DET
ijassa-419	163	10	r0l	r0l	PROPN
ijassa-419	163	11	system	system	NOUN
ijassa-419	163	12	on	on	ADP
ijassa-419	163	13	s	s	NOUN
ijassa-419	163	14	is	be	AUX
ijassa-419	163	15	a	a	DET
ijassa-419	163	16	bijection	bijection	NOUN
ijassa-419	163	17	from	from	ADP
ijassa-419	163	18	s	s	PRON
ijassa-419	163	19	to	to	ADP
ijassa-419	163	20	s	s	PRON
ijassa-419	163	21	,	,	PUNCT
ijassa-419	163	22	if	if	SCONJ
ijassa-419	163	23	and	and	CCONJ
ijassa-419	163	24	only	only	ADV
ijassa-419	163	25	if	if	SCONJ
ijassa-419	163	26	for	for	ADP
ijassa-419	163	27	any	any	DET
ijassa-419	163	28	α	α	PROPN
ijassa-419	163	29	∈	∈	PROPN
ijassa-419	163	30	s∗	s∗	NOUN
ijassa-419	163	31	,	,	PUNCT
ijassa-419	163	32	there	there	PRON
ijassa-419	163	33	is	be	VERB
ijassa-419	163	34	a	a	DET
ijassa-419	163	35	natural	natural	ADJ
ijassa-419	163	36	number	number	NOUN
ijassa-419	163	37	k	k	NOUN
ijassa-419	163	38	such	such	ADJ
ijassa-419	163	39	that	that	PRON
ijassa-419	163	40	φk(α	φk(α	NUM
ijassa-419	163	41	)	)	PUNCT
ijassa-419	164	1	=	=	SYM
ijassa-419	164	2	α	α	X
ijassa-419	164	3	.	.	PUNCT
ijassa-419	164	4	proof	proof	NOUN
ijassa-419	164	5	.	.	PUNCT
ijassa-419	165	1	although	although	SCONJ
ijassa-419	165	2	as	as	ADP
ijassa-419	165	3	a	a	DET
ijassa-419	165	4	r0l	r0l	PROPN
ijassa-419	165	5	system	system	NOUN
ijassa-419	165	6	,	,	PUNCT
ijassa-419	165	7	the	the	DET
ijassa-419	165	8	probability	probability	NOUN
ijassa-419	165	9	of	of	ADP
ijassa-419	165	10	different	different	ADJ
ijassa-419	165	11	mappings	mapping	NOUN
ijassa-419	165	12	at	at	ADP
ijassa-419	165	13	each	each	DET
ijassa-419	165	14	step	step	NOUN
ijassa-419	165	15	is	be	AUX
ijassa-419	165	16	different	different	ADJ
ijassa-419	165	17	,	,	PUNCT
ijassa-419	165	18	the	the	DET
ijassa-419	165	19	maximum	maximum	ADJ
ijassa-419	165	20	number	number	NOUN
ijassa-419	165	21	n	n	NOUN
ijassa-419	165	22	of	of	ADP
ijassa-419	165	23	total	total	ADJ
ijassa-419	165	24	states	state	NOUN
ijassa-419	165	25	of	of	ADP
ijassa-419	165	26	each	each	DET
ijassa-419	165	27	step	step	NOUN
ijassa-419	165	28	is	be	AUX
ijassa-419	165	29	fixed	fix	VERB
ijassa-419	165	30	.	.	PUNCT
ijassa-419	166	1	since	since	SCONJ
ijassa-419	166	2	the	the	DET
ijassa-419	166	3	length	length	NOUN
ijassa-419	166	4	p	p	NOUN
ijassa-419	166	5	of	of	ADP
ijassa-419	166	6	the	the	DET
ijassa-419	166	7	mapping	mapping	NOUN
ijassa-419	166	8	is	be	AUX
ijassa-419	166	9	finite	finite	ADJ
ijassa-419	166	10	,	,	PUNCT
ijassa-419	166	11	the	the	DET
ijassa-419	166	12	number	number	NOUN
ijassa-419	166	13	of	of	ADP
ijassa-419	166	14	overall	overall	ADJ
ijassa-419	166	15	states	state	NOUN
ijassa-419	166	16	is	be	AUX
ijassa-419	166	17	k	k	NOUN
ijassa-419	166	18	=	=	PUNCT
ijassa-419	166	19	np	np	INTJ
ijassa-419	166	20	at	at	ADV
ijassa-419	166	21	most	most	ADV
ijassa-419	166	22	.	.	PUNCT
ijassa-419	167	1	so	so	ADV
ijassa-419	167	2	there	there	PRON
ijassa-419	167	3	exists	exist	VERB
ijassa-419	167	4	a	a	DET
ijassa-419	167	5	integer	integer	NOUN
ijassa-419	167	6	k	k	PROPN
ijassa-419	167	7	=	=	PUNCT
ijassa-419	167	8	np	np	INTJ
ijassa-419	167	9	to	to	PART
ijassa-419	167	10	satisfy	satisfy	VERB
ijassa-419	167	11	φk(α	φk(α	NOUN
ijassa-419	167	12	)	)	PUNCT
ijassa-419	168	1	=	=	SYM
ijassa-419	168	2	α	α	X
ijassa-419	168	3	.	.	PUNCT
ijassa-419	169	1	other	other	ADJ
ijassa-419	169	2	parts	part	NOUN
ijassa-419	169	3	of	of	ADP
ijassa-419	169	4	the	the	DET
ijassa-419	169	5	proof	proof	NOUN
ijassa-419	169	6	are	be	AUX
ijassa-419	169	7	similar	similar	ADJ
ijassa-419	169	8	to	to	ADP
ijassa-419	169	9	those	those	PRON
ijassa-419	169	10	of	of	ADP
ijassa-419	169	11	theorem	theorem	ADJ
ijassa-419	169	12	3.2	3.2	NUM
ijassa-419	169	13	and	and	CCONJ
ijassa-419	169	14	omitted	omit	VERB
ijassa-419	169	15	.	.	PUNCT
ijassa-419	170	1	qed	qed	PROPN
ijassa-419	170	2	.	.	PROPN
ijassa-419	170	3	remark	remark	PROPN
ijassa-419	170	4	:	:	PUNCT
ijassa-419	170	5	in	in	ADP
ijassa-419	170	6	terms	term	NOUN
ijassa-419	170	7	of	of	ADP
ijassa-419	170	8	numbers	number	NOUN
ijassa-419	170	9	,	,	PUNCT
ijassa-419	170	10	the	the	DET
ijassa-419	170	11	finite	finite	ADJ
ijassa-419	170	12	states	state	NOUN
ijassa-419	170	13	of	of	ADP
ijassa-419	170	14	rol	rol	NOUN
ijassa-419	170	15	are	be	AUX
ijassa-419	170	16	more	more	ADJ
ijassa-419	170	17	than	than	ADP
ijassa-419	170	18	those	those	PRON
ijassa-419	170	19	of	of	ADP
ijassa-419	170	20	dol	dol	NOUN
ijassa-419	170	21	.	.	PUNCT
ijassa-419	171	1	however	however	ADV
ijassa-419	171	2	,	,	PUNCT
ijassa-419	171	3	from	from	ADP
ijassa-419	171	4	theorem	theorem	ADJ
ijassa-419	171	5	3.3	3.3	NUM
ijassa-419	171	6	,	,	PUNCT
ijassa-419	171	7	to	to	PART
ijassa-419	171	8	follows	follow	VERB
ijassa-419	171	9	that	that	SCONJ
ijassa-419	171	10	in	in	ADP
ijassa-419	171	11	order	order	NOUN
ijassa-419	171	12	to	to	PART
ijassa-419	171	13	produce	produce	VERB
ijassa-419	171	14	complicated	complicated	ADJ
ijassa-419	171	15	fractal	fractal	ADJ
ijassa-419	171	16	figures	figure	NOUN
ijassa-419	171	17	using	use	VERB
ijassa-419	171	18	r0l	r0l	PROPN
ijassa-419	171	19	systems	system	NOUN
ijassa-419	171	20	,	,	PUNCT
ijassa-419	171	21	one	one	PRON
ijassa-419	171	22	should	should	AUX
ijassa-419	171	23	still	still	ADV
ijassa-419	171	24	avoid	avoid	VERB
ijassa-419	171	25	using	use	VERB
ijassa-419	171	26	any	any	DET
ijassa-419	171	27	such	such	ADJ
ijassa-419	171	28	l	l	NOUN
ijassa-419	171	29	mapping	mapping	NOUN
ijassa-419	171	30	that	that	SCONJ
ijassa-419	171	31	its	its	PRON
ijassa-419	171	32	restriction	restriction	NOUN
ijassa-419	171	33	on	on	ADP
ijassa-419	171	34	s	s	NOUN
ijassa-419	171	35	is	be	AUX
ijassa-419	171	36	a	a	DET
ijassa-419	171	37	bijection	bijection	NOUN
ijassa-419	171	38	from	from	ADP
ijassa-419	171	39	s	s	PRON
ijassa-419	171	40	to	to	ADP
ijassa-419	171	41	s.	s.	PROPN
ijassa-419	171	42	4	4	NUM
ijassa-419	171	43	an	an	DET
ijassa-419	171	44	explanation	explanation	NOUN
ijassa-419	171	45	of	of	ADP
ijassa-419	171	46	holistic	holistic	ADJ
ijassa-419	171	47	emergence	emergence	NOUN
ijassa-419	171	48	of	of	ADP
ijassa-419	171	49	systems	system	NOUN
ijassa-419	171	50	using	use	VERB
ijassa-419	171	51	dol	dol	NOUN
ijassa-419	171	52	although	although	SCONJ
ijassa-419	171	53	the	the	DET
ijassa-419	171	54	mechanism	mechanism	NOUN
ijassa-419	171	55	for	for	ADP
ijassa-419	171	56	a	a	DET
ijassa-419	171	57	simple	simple	ADJ
ijassa-419	171	58	l	l	NOUN
ijassa-419	171	59	system	system	NOUN
ijassa-419	171	60	appears	appear	VERB
ijassa-419	171	61	is	be	AUX
ijassa-419	171	62	quite	quite	ADV
ijassa-419	171	63	straightforward	straightforward	ADJ
ijassa-419	171	64	,	,	PUNCT
ijassa-419	171	65	it	it	PRON
ijassa-419	171	66	clearly	clearly	ADV
ijassa-419	171	67	shows	show	VERB
ijassa-419	171	68	the	the	DET
ijassa-419	171	69	attribute	attribute	NOUN
ijassa-419	171	70	of	of	ADP
ijassa-419	171	71	holistic	holistic	ADJ
ijassa-419	171	72	emergence	emergence	NOUN
ijassa-419	171	73	of	of	ADP
ijassa-419	171	74	systems	system	NOUN
ijassa-419	171	75	.	.	PUNCT
ijassa-419	172	1	so	so	ADV
ijassa-419	172	2	,	,	PUNCT
ijassa-419	172	3	simple	simple	ADJ
ijassa-419	172	4	l	l	NOUN
ijassa-419	172	5	systems	system	NOUN
ijassa-419	172	6	can	can	AUX
ijassa-419	172	7	be	be	AUX
ijassa-419	172	8	employed	employ	VERB
ijassa-419	172	9	as	as	ADP
ijassa-419	172	10	an	an	DET
ijassa-419	172	11	effective	effective	ADJ
ijassa-419	172	12	tool	tool	NOUN
ijassa-419	172	13	to	to	PART
ijassa-419	172	14	illustrate	illustrate	VERB
ijassa-419	172	15	the	the	DET
ijassa-419	172	16	emergence	emergence	NOUN
ijassa-419	172	17	of	of	ADP
ijassa-419	172	18	systems	system	NOUN
ijassa-419	172	19	’	'	PUNCT
ijassa-419	172	20	wholeness	wholeness	NOUN
ijassa-419	172	21	.	.	PUNCT
ijassa-419	173	1	in	in	ADP
ijassa-419	173	2	the	the	DET
ijassa-419	173	3	following	following	NOUN
ijassa-419	173	4	,	,	PUNCT
ijassa-419	173	5	we	we	PRON
ijassa-419	173	6	will	will	AUX
ijassa-419	173	7	design	design	VERB
ijassa-419	173	8	a	a	DET
ijassa-419	173	9	simple	simple	ADJ
ijassa-419	173	10	binary	binary	ADJ
ijassa-419	173	11	system	system	NOUN
ijassa-419	173	12	to	to	PART
ijassa-419	173	13	explain	explain	VERB
ijassa-419	173	14	the	the	DET
ijassa-419	173	15	emergence	emergence	NOUN
ijassa-419	173	16	of	of	ADP
ijassa-419	173	17	systems	system	NOUN
ijassa-419	173	18	’	'	PUNCT
ijassa-419	173	19	wholeness	wholeness	NOUN
ijassa-419	173	20	.	.	PUNCT
ijassa-419	174	1	in	in	ADP
ijassa-419	174	2	the	the	DET
ijassa-419	174	3	cartesian	cartesian	ADJ
ijassa-419	174	4	coordinate	coordinate	NOUN
ijassa-419	174	5	system	system	NOUN
ijassa-419	174	6	r2	r2	NOUN
ijassa-419	174	7	,	,	PUNCT
ijassa-419	174	8	assume	assume	VERB
ijassa-419	174	9	that	that	SCONJ
ijassa-419	174	10	the	the	DET
ijassa-419	174	11	initial	initial	ADJ
ijassa-419	174	12	location	location	NOUN
ijassa-419	174	13	of	of	ADP
ijassa-419	174	14	particle	particle	NOUN
ijassa-419	174	15	a	a	DET
ijassa-419	174	16	is	be	AUX
ijassa-419	174	17	(	(	PUNCT
ijassa-419	174	18	0,0	0,0	NOUN
ijassa-419	174	19	)	)	PUNCT
ijassa-419	174	20	and	and	CCONJ
ijassa-419	174	21	its	its	PRON
ijassa-419	174	22	initial	initial	ADJ
ijassa-419	174	23	angle	angle	NOUN
ijassa-419	174	24	is	be	AUX
ijassa-419	174	25	0	0	NUM
ijassa-419	174	26	.	.	PUNCT
ijassa-419	175	1	let	let	VERB
ijassa-419	175	2	f	f	PRON
ijassa-419	175	3	stand	stand	VERB
ijassa-419	175	4	for	for	ADP
ijassa-419	175	5	moving	move	VERB
ijassa-419	175	6	forward	forward	ADV
ijassa-419	175	7	one	one	NUM
ijassa-419	175	8	unit	unit	NOUN
ijassa-419	175	9	step	step	NOUN
ijassa-419	175	10	1	1	NUM
ijassa-419	175	11	,	,	PUNCT
ijassa-419	175	12	and	and	CCONJ
ijassa-419	175	13	+	+	PUNCT
ijassa-419	175	14	turning	turn	VERB
ijassa-419	175	15	an	an	DET
ijassa-419	175	16	angle	angle	NOUN
ijassa-419	175	17	of	of	ADP
ijassa-419	175	18	π/3	π/3	X
ijassa-419	175	19	counterclockwise	counterclockwise	NOUN
ijassa-419	175	20	.	.	PUNCT
ijassa-419	176	1	now	now	ADV
ijassa-419	176	2	,	,	PUNCT
ijassa-419	176	3	let	let	VERB
ijassa-419	176	4	us	we	PRON
ijassa-419	176	5	construct	construct	VERB
ijassa-419	176	6	the	the	DET
ijassa-419	176	7	following	follow	VERB
ijassa-419	176	8	d0l	d0l	PROPN
ijassa-419	176	9	system	system	NOUN
ijassa-419	176	10	l2	l2	NOUN
ijassa-419	176	11	=	=	SYM
ijassa-419	176	12	⟨s	⟨s	NOUN
ijassa-419	176	13	,	,	PUNCT
ijassa-419	176	14	ω	ω	PROPN
ijassa-419	176	15	,	,	PUNCT
ijassa-419	176	16	φ⟩	φ⟩	NOUN
ijassa-419	176	17	,	,	PUNCT
ijassa-419	177	1	where	where	SCONJ
ijassa-419	177	2	s	s	VERB
ijassa-419	177	3	=	=	SYM
ijassa-419	177	4	{	{	PUNCT
ijassa-419	177	5	f,+},ω	f,+},ω	NOUN
ijassa-419	177	6	=	=	SYM
ijassa-419	177	7	f	f	PROPN
ijassa-419	177	8	,	,	PUNCT
ijassa-419	177	9	and	and	CCONJ
ijassa-419	177	10	φ	φ	NUM
ijassa-419	177	11	=	=	SYM
ijassa-419	177	12	{	{	PUNCT
ijassa-419	177	13	f	f	PROPN
ijassa-419	177	14	→	→	SYM
ijassa-419	177	15	f	f	PROPN
ijassa-419	178	1	+	+	PROPN
ijassa-419	178	2	+	+	PROPN
ijassa-419	178	3	f	f	X
ijassa-419	178	4	+	+	PROPN
ijassa-419	178	5	+	+	PROPN
ijassa-419	178	6	f	f	X
ijassa-419	178	7	+	+	X
ijassa-419	178	8	→	→	SYM
ijassa-419	178	9	+	+	ADJ
ijassa-419	178	10	advances	advance	NOUN
ijassa-419	178	11	in	in	ADP
ijassa-419	178	12	systems	system	NOUN
ijassa-419	178	13	science	science	NOUN
ijassa-419	178	14	and	and	CCONJ
ijassa-419	178	15	applications	application	NOUN
ijassa-419	178	16	(	(	PUNCT
ijassa-419	178	17	2013	2013	NUM
ijassa-419	178	18	)	)	PUNCT
ijassa-419	178	19	vol.13	vol.13	NOUN
ijassa-419	178	20	no.2	no.2	PROPN
ijassa-419	178	21	107	107	NUM
ijassa-419	178	22	the	the	DET
ijassa-419	178	23	first	first	ADJ
ijassa-419	178	24	iteration	iteration	NOUN
ijassa-419	178	25	φ(ω	φ(ω	PROPN
ijassa-419	178	26	)	)	PUNCT
ijassa-419	178	27	produces	produce	VERB
ijassa-419	178	28	:	:	PUNCT
ijassa-419	178	29	f++f++f	f++f++f	NOUN
ijassa-419	178	30	;	;	PUNCT
ijassa-419	178	31	the	the	DET
ijassa-419	178	32	second	second	ADJ
ijassa-419	178	33	iteration	iteration	NOUN
ijassa-419	178	34	φ2(ω	φ2(ω	NOUN
ijassa-419	178	35	)	)	PUNCT
ijassa-419	178	36	leads	lead	VERB
ijassa-419	178	37	to	to	ADP
ijassa-419	178	38	:	:	PUNCT
ijassa-419	178	39	f++f++f	f++f++f	PROPN
ijassa-419	178	40	+	+	PROPN
ijassa-419	178	41	+	+	CCONJ
ijassa-419	178	42	f++f++f	f++f++f	VERB
ijassa-419	178	43	+	+	PROPN
ijassa-419	178	44	+	+	NUM
ijassa-419	178	45	f++f++f	f++f++f	NUM
ijassa-419	178	46	;	;	PUNCT
ijassa-419	178	47	.	.	PUNCT
ijassa-419	178	48	.	.	PUNCT
ijassa-419	179	1	.	.	PUNCT
ijassa-419	180	1	;	;	PUNCT
ijassa-419	180	2	when	when	SCONJ
ijassa-419	180	3	the	the	DET
ijassa-419	180	4	nth	nth	NOUN
ijassa-419	180	5	order	order	NOUN
ijassa-419	180	6	,	,	PUNCT
ijassa-419	180	7	n	n	PRON
ijassa-419	180	8	≥	≥	NOUN
ijassa-419	180	9	1	1	NUM
ijassa-419	180	10	,	,	PUNCT
ijassa-419	180	11	l	l	NOUN
ijassa-419	180	12	system	system	NOUN
ijassa-419	180	13	l2	l2	NOUN
ijassa-419	180	14	is	be	AUX
ijassa-419	180	15	applied	apply	VERB
ijassa-419	180	16	on	on	ADP
ijassa-419	180	17	the	the	DET
ijassa-419	180	18	particle	particle	NOUN
ijassa-419	180	19	a	a	PRON
ijassa-419	180	20	,	,	PUNCT
ijassa-419	180	21	one	one	PRON
ijassa-419	180	22	can	can	AUX
ijassa-419	180	23	obtain	obtain	VERB
ijassa-419	180	24	the	the	DET
ijassa-419	180	25	output	output	NOUN
ijassa-419	180	26	state	state	NOUN
ijassa-419	180	27	as	as	SCONJ
ijassa-419	180	28	shown	show	VERB
ijassa-419	180	29	in	in	ADP
ijassa-419	180	30	fig.1	fig.1	PROPN
ijassa-419	180	31	.	.	PUNCT
ijassa-419	181	1	as	as	SCONJ
ijassa-419	181	2	shown	show	VERB
ijassa-419	181	3	in	in	ADP
ijassa-419	181	4	fig.1	fig.1	PROPN
ijassa-419	181	5	,	,	PUNCT
ijassa-419	181	6	such	such	DET
ijassa-419	181	7	an	an	DET
ijassa-419	181	8	nth	nth	NOUN
ijassa-419	181	9	order	order	NOUN
ijassa-419	181	10	l	l	NOUN
ijassa-419	181	11	system	system	NOUN
ijassa-419	181	12	,	,	PUNCT
ijassa-419	181	13	a	a	DET
ijassa-419	181	14	binary	binary	ADJ
ijassa-419	181	15	sysfig.1	sysfig.1	PROPN
ijassa-419	181	16	the	the	DET
ijassa-419	181	17	output	output	NOUN
ijassa-419	181	18	state	state	NOUN
ijassa-419	181	19	of	of	ADP
ijassa-419	181	20	the	the	DET
ijassa-419	181	21	l2	l2	NOUN
ijassa-419	181	22	system	system	NOUN
ijassa-419	181	23	tem	tem	PROPN
ijassa-419	181	24	,	,	PUNCT
ijassa-419	181	25	is	be	AUX
ijassa-419	181	26	very	very	ADV
ijassa-419	181	27	simple	simple	ADJ
ijassa-419	181	28	.	.	PUNCT
ijassa-419	182	1	its	its	PRON
ijassa-419	182	2	function	function	NOUN
ijassa-419	182	3	can	can	AUX
ijassa-419	182	4	be	be	AUX
ijassa-419	182	5	comprehended	comprehend	VERB
ijassa-419	182	6	as	as	SCONJ
ijassa-419	182	7	follows	follow	VERB
ijassa-419	182	8	:	:	PUNCT
ijassa-419	182	9	drive	drive	VERB
ijassa-419	182	10	particle	particle	NOUN
ijassa-419	182	11	a	a	PRON
ijassa-419	182	12	from	from	ADP
ijassa-419	182	13	the	the	DET
ijassa-419	182	14	starting	starting	NOUN
ijassa-419	182	15	point	point	NOUN
ijassa-419	182	16	at	at	ADP
ijassa-419	182	17	(	(	PUNCT
ijassa-419	182	18	0,0	0,0	NOUN
ijassa-419	182	19	)	)	PUNCT
ijassa-419	182	20	to	to	PART
ijassa-419	182	21	make	make	VERB
ijassa-419	182	22	3n−1	3n−1	NUM
ijassa-419	182	23	counterclockwise	counterclockwise	NOUN
ijassa-419	182	24	turns	turn	VERB
ijassa-419	182	25	along	along	ADP
ijassa-419	182	26	the	the	DET
ijassa-419	182	27	triangular	triangular	NOUN
ijassa-419	182	28	trajectory	trajectory	NOUN
ijassa-419	182	29	.	.	PUNCT
ijassa-419	183	1	now	now	ADV
ijassa-419	183	2	,	,	PUNCT
ijassa-419	183	3	let	let	VERB
ijassa-419	183	4	us	we	PRON
ijassa-419	183	5	employ	employ	VERB
ijassa-419	183	6	this	this	DET
ijassa-419	183	7	simple	simple	ADJ
ijassa-419	183	8	binary	binary	ADJ
ijassa-419	183	9	system	system	NOUN
ijassa-419	183	10	to	to	PART
ijassa-419	183	11	illustrate	illustrate	VERB
ijassa-419	183	12	the	the	DET
ijassa-419	183	13	emergence	emergence	NOUN
ijassa-419	183	14	of	of	ADP
ijassa-419	183	15	systems	system	NOUN
ijassa-419	183	16	’	'	PUNCT
ijassa-419	183	17	wholeness	wholeness	NOUN
ijassa-419	183	18	:	:	PUNCT
ijassa-419	183	19	(	(	PUNCT
ijassa-419	183	20	1	1	X
ijassa-419	183	21	)	)	PUNCT
ijassa-419	183	22	the	the	DET
ijassa-419	183	23	whole	whole	NOUN
ijassa-419	183	24	is	be	AUX
ijassa-419	183	25	greater	great	ADJ
ijassa-419	183	26	than	than	ADP
ijassa-419	183	27	the	the	DET
ijassa-419	183	28	sum	sum	NOUN
ijassa-419	183	29	of	of	ADP
ijassa-419	183	30	its	its	PRON
ijassa-419	183	31	parts	part	NOUN
ijassa-419	183	32	;	;	PUNCT
ijassa-419	183	33	and	and	CCONJ
ijassa-419	183	34	(	(	PUNCT
ijassa-419	183	35	2	2	X
ijassa-419	183	36	)	)	PUNCT
ijassa-419	183	37	the	the	DET
ijassa-419	183	38	function	function	NOUN
ijassa-419	183	39	of	of	ADP
ijassa-419	183	40	the	the	DET
ijassa-419	183	41	whole	whole	NOUN
ijassa-419	183	42	is	be	AUX
ijassa-419	183	43	more	more	ADJ
ijassa-419	183	44	than	than	ADP
ijassa-419	183	45	the	the	DET
ijassa-419	183	46	sum	sum	NOUN
ijassa-419	183	47	of	of	ADP
ijassa-419	183	48	the	the	DET
ijassa-419	183	49	functions	function	NOUN
ijassa-419	183	50	of	of	ADP
ijassa-419	183	51	the	the	DET
ijassa-419	183	52	parts	part	NOUN
ijassa-419	183	53	.	.	PUNCT
ijassa-419	184	1	for	for	ADP
ijassa-419	184	2	our	our	PRON
ijassa-419	184	3	purpose	purpose	NOUN
ijassa-419	184	4	,	,	PUNCT
ijassa-419	184	5	by	by	ADP
ijassa-419	184	6	the	the	DET
ijassa-419	184	7	word	word	NOUN
ijassa-419	184	8	“	"	PUNCT
ijassa-419	184	9	sum	sum	NOUN
ijassa-419	184	10	”	"	PUNCT
ijassa-419	184	11	,	,	PUNCT
ijassa-419	184	12	it	it	PRON
ijassa-419	184	13	means	mean	VERB
ijassa-419	184	14	the	the	DET
ijassa-419	184	15	collected	collected	ADJ
ijassa-419	184	16	pile	pile	NOUN
ijassa-419	184	17	of	of	ADP
ijassa-419	184	18	parts	part	NOUN
ijassa-419	184	19	without	without	ADP
ijassa-419	184	20	any	any	DET
ijassa-419	184	21	interactions	interaction	NOUN
ijassa-419	184	22	between	between	ADP
ijassa-419	184	23	the	the	DET
ijassa-419	184	24	parts	part	NOUN
ijassa-419	184	25	.	.	PUNCT
ijassa-419	185	1	as	as	ADP
ijassa-419	185	2	for	for	ADP
ijassa-419	185	3	the	the	DET
ijassa-419	185	4	word	word	NOUN
ijassa-419	185	5	“	"	PUNCT
ijassa-419	185	6	function	function	NOUN
ijassa-419	185	7	”	"	PUNCT
ijassa-419	185	8	,	,	PUNCT
ijassa-419	185	9	it	it	PRON
ijassa-419	185	10	is	be	AUX
ijassa-419	185	11	understood	understand	VERB
ijassa-419	185	12	as	as	SCONJ
ijassa-419	185	13	follows	follow	VERB
ijassa-419	185	14	:	:	PUNCT
ijassa-419	185	15	as	as	ADV
ijassa-419	185	16	long	long	ADV
ijassa-419	185	17	as	as	SCONJ
ijassa-419	185	18	a	a	DET
ijassa-419	185	19	system	system	NOUN
ijassa-419	185	20	is	be	AUX
ijassa-419	185	21	identified	identify	VERB
ijassa-419	185	22	,	,	PUNCT
ijassa-419	185	23	its	its	PRON
ijassa-419	185	24	functionality	functionality	NOUN
ijassa-419	185	25	is	be	AUX
ijassa-419	185	26	a	a	DET
ijassa-419	185	27	physical	physical	ADJ
ijassa-419	185	28	existence	existence	NOUN
ijassa-419	185	29	;	;	PUNCT
ijassa-419	185	30	however	however	ADV
ijassa-419	185	31	,	,	PUNCT
ijassa-419	185	32	any	any	DET
ijassa-419	185	33	function	function	NOUN
ijassa-419	185	34	of	of	ADP
ijassa-419	185	35	the	the	DET
ijassa-419	185	36	system	system	NOUN
ijassa-419	185	37	has	have	VERB
ijassa-419	185	38	to	to	PART
ijassa-419	185	39	be	be	AUX
ijassa-419	185	40	manifested	manifest	VERB
ijassa-419	185	41	through	through	ADP
ijassa-419	185	42	the	the	DET
ijassa-419	185	43	system	system	NOUN
ijassa-419	185	44	’s	’s	PART
ijassa-419	185	45	act	act	NOUN
ijassa-419	185	46	on	on	ADP
ijassa-419	185	47	a	a	DET
ijassa-419	185	48	specific	specific	ADJ
ijassa-419	185	49	object	object	NOUN
ijassa-419	185	50	that	that	PRON
ijassa-419	185	51	is	be	AUX
ijassa-419	185	52	external	external	ADJ
ijassa-419	185	53	to	to	ADP
ijassa-419	185	54	the	the	DET
ijassa-419	185	55	system	system	NOUN
ijassa-419	185	56	.	.	PUNCT
ijassa-419	186	1	so	so	ADV
ijassa-419	186	2	,	,	PUNCT
ijassa-419	186	3	to	to	PART
ijassa-419	186	4	investigate	investigate	VERB
ijassa-419	186	5	the	the	DET
ijassa-419	186	6	overall	overall	ADJ
ijassa-419	186	7	function	function	NOUN
ijassa-419	186	8	of	of	ADP
ijassa-419	186	9	a	a	DET
ijassa-419	186	10	system	system	NOUN
ijassa-419	186	11	and	and	CCONJ
ijassa-419	186	12	the	the	DET
ijassa-419	186	13	sum	sum	NOUN
ijassa-419	186	14	of	of	ADP
ijassa-419	186	15	the	the	DET
ijassa-419	186	16	functions	function	NOUN
ijassa-419	186	17	of	of	ADP
ijassa-419	186	18	its	its	PRON
ijassa-419	186	19	parts	part	NOUN
ijassa-419	186	20	,	,	PUNCT
ijassa-419	186	21	one	one	NUM
ijassa-419	186	22	needs	need	VERB
ijassa-419	186	23	to	to	PART
ijassa-419	186	24	consider	consider	VERB
ijassa-419	186	25	the	the	DET
ijassa-419	186	26	respective	respective	ADJ
ijassa-419	186	27	effects	effect	NOUN
ijassa-419	186	28	of	of	ADP
ijassa-419	186	29	the	the	DET
ijassa-419	186	30	system	system	NOUN
ijassa-419	186	31	as	as	ADP
ijassa-419	186	32	a	a	DET
ijassa-419	186	33	whole	whole	NOUN
ijassa-419	186	34	and	and	CCONJ
ijassa-419	186	35	each	each	PRON
ijassa-419	186	36	of	of	ADP
ijassa-419	186	37	its	its	PRON
ijassa-419	186	38	parts	part	NOUN
ijassa-419	186	39	on	on	ADP
ijassa-419	186	40	an	an	DET
ijassa-419	186	41	external	external	ADJ
ijassa-419	186	42	object	object	NOUN
ijassa-419	186	43	.	.	PUNCT
ijassa-419	187	1	through	through	ADP
ijassa-419	187	2	analyzing	analyze	VERB
ijassa-419	187	3	their	their	PRON
ijassa-419	187	4	effects	effect	NOUN
ijassa-419	187	5	on	on	ADP
ijassa-419	187	6	this	this	DET
ijassa-419	187	7	object	object	NOUN
ijassa-419	187	8	,	,	PUNCT
ijassa-419	187	9	one	one	PRON
ijassa-419	187	10	can	can	AUX
ijassa-419	187	11	compare	compare	VERB
ijassa-419	187	12	the	the	DET
ijassa-419	187	13	overall	overall	ADJ
ijassa-419	187	14	effect	effect	NOUN
ijassa-419	187	15	of	of	ADP
ijassa-419	187	16	the	the	DET
ijassa-419	187	17	system	system	NOUN
ijassa-419	187	18	and	and	CCONJ
ijassa-419	187	19	the	the	DET
ijassa-419	187	20	aggregated	aggregated	ADJ
ijassa-419	187	21	effect	effect	NOUN
ijassa-419	187	22	of	of	ADP
ijassa-419	187	23	the	the	DET
ijassa-419	187	24	parts	part	NOUN
ijassa-419	187	25	.	.	PUNCT
ijassa-419	188	1	before	before	SCONJ
ijassa-419	188	2	we	we	PRON
ijassa-419	188	3	illustrate	illustrate	VERB
ijassa-419	188	4	the	the	DET
ijassa-419	188	5	emergence	emergence	NOUN
ijassa-419	188	6	of	of	ADP
ijassa-419	188	7	the	the	DET
ijassa-419	188	8	system	system	NOUN
ijassa-419	188	9	’s	’s	PART
ijassa-419	188	10	wholeness	wholeness	NOUN
ijassa-419	188	11	,	,	PUNCT
ijassa-419	188	12	let	let	VERB
ijassa-419	188	13	us	we	PRON
ijassa-419	188	14	first	first	ADV
ijassa-419	188	15	establish	establish	VERB
ijassa-419	188	16	the	the	DET
ijassa-419	188	17	following	following	ADJ
ijassa-419	188	18	assumptions	assumption	NOUN
ijassa-419	188	19	:	:	PUNCT
ijassa-419	188	20	(	(	PUNCT
ijassa-419	188	21	a	a	X
ijassa-419	188	22	)	)	PUNCT
ijassa-419	188	23	the	the	DET
ijassa-419	188	24	whole	whole	NOUN
ijassa-419	188	25	can	can	AUX
ijassa-419	188	26	always	always	ADV
ijassa-419	188	27	be	be	AUX
ijassa-419	188	28	divided	divide	VERB
ijassa-419	188	29	into	into	ADP
ijassa-419	188	30	several	several	ADJ
ijassa-419	188	31	distinguishable	distinguishable	ADJ
ijassa-419	188	32	parts	part	NOUN
ijassa-419	188	33	in	in	ADP
ijassa-419	188	34	terms	term	NOUN
ijassa-419	188	35	of	of	ADP
ijassa-419	188	36	components	component	NOUN
ijassa-419	188	37	,	,	PUNCT
ijassa-419	188	38	attributes	attribute	VERB
ijassa-419	188	39	,	,	PUNCT
ijassa-419	188	40	or	or	CCONJ
ijassa-419	188	41	functionalities	functionality	NOUN
ijassa-419	188	42	;	;	PUNCT
ijassa-419	188	43	(	(	PUNCT
ijassa-419	188	44	b	b	X
ijassa-419	188	45	)	)	PUNCT
ijassa-419	188	46	similar	similar	ADJ
ijassa-419	188	47	parts	part	NOUN
ijassa-419	188	48	of	of	ADP
ijassa-419	188	49	the	the	DET
ijassa-419	188	50	system	system	NOUN
ijassa-419	188	51	(	(	PUNCT
ijassa-419	188	52	or	or	CCONJ
ijassa-419	188	53	parts	part	NOUN
ijassa-419	188	54	with	with	ADP
ijassa-419	188	55	similar	similar	ADJ
ijassa-419	188	56	attributes	attribute	NOUN
ijassa-419	188	57	)	)	PUNCT
ijassa-419	188	58	satisfy	satisfy	VERB
ijassa-419	188	59	the	the	DET
ijassa-419	188	60	108	108	NUM
ijassa-419	188	61	xiaojun	xiaojun	PROPN
ijassa-419	188	62	duan	duan	PROPN
ijassa-419	188	63	:	:	PUNCT
ijassa-419	188	64	set	set	VERB
ijassa-419	188	65	-	-	PUNCT
ijassa-419	188	66	theoretic	theoretic	NOUN
ijassa-419	188	67	design	design	NOUN
ijassa-419	188	68	and	and	CCONJ
ijassa-419	188	69	analysis	analysis	NOUN
ijassa-419	188	70	of	of	ADP
ijassa-419	188	71	l	l	NOUN
ijassa-419	188	72	systems	system	NOUN
ijassa-419	188	73	additive	additive	ADJ
ijassa-419	188	74	property	property	NOUN
ijassa-419	188	75	,	,	PUNCT
ijassa-419	188	76	while	while	SCONJ
ijassa-419	188	77	different	different	ADJ
ijassa-419	188	78	parts	part	NOUN
ijassa-419	188	79	(	(	PUNCT
ijassa-419	188	80	or	or	CCONJ
ijassa-419	188	81	parts	part	NOUN
ijassa-419	188	82	with	with	ADP
ijassa-419	188	83	different	different	ADJ
ijassa-419	188	84	attributes	attribute	NOUN
ijassa-419	188	85	)	)	PUNCT
ijassa-419	188	86	do	do	AUX
ijassa-419	188	87	not	not	PART
ijassa-419	188	88	comply	comply	VERB
ijassa-419	188	89	with	with	ADP
ijassa-419	188	90	this	this	DET
ijassa-419	188	91	property	property	NOUN
ijassa-419	188	92	.	.	PUNCT
ijassa-419	189	1	here	here	ADV
ijassa-419	189	2	,	,	PUNCT
ijassa-419	189	3	the	the	DET
ijassa-419	189	4	additivity	additivity	NOUN
ijassa-419	189	5	stands	stand	VERB
ijassa-419	189	6	for	for	ADP
ijassa-419	189	7	the	the	DET
ijassa-419	189	8	algebraic	algebraic	ADJ
ijassa-419	189	9	additivity	additivity	NOUN
ijassa-419	189	10	and	and	CCONJ
ijassa-419	189	11	is	be	AUX
ijassa-419	189	12	different	different	ADJ
ijassa-419	189	13	of	of	ADP
ijassa-419	189	14	the	the	DET
ijassa-419	189	15	meaning	meaning	NOUN
ijassa-419	189	16	of	of	ADP
ijassa-419	189	17	the	the	DET
ijassa-419	189	18	“	"	PUNCT
ijassa-419	189	19	sum	sum	NOUN
ijassa-419	189	20	”	"	PUNCT
ijassa-419	189	21	in	in	ADP
ijassa-419	189	22	“	"	PUNCT
ijassa-419	189	23	the	the	DET
ijassa-419	189	24	sum	sum	NOUN
ijassa-419	189	25	of	of	ADP
ijassa-419	189	26	parts	part	NOUN
ijassa-419	189	27	”	"	PUNCT
ijassa-419	189	28	;	;	PUNCT
ijassa-419	189	29	and	and	CCONJ
ijassa-419	189	30	(	(	PUNCT
ijassa-419	189	31	c	c	X
ijassa-419	189	32	)	)	PUNCT
ijassa-419	189	33	when	when	SCONJ
ijassa-419	189	34	studying	study	VERB
ijassa-419	189	35	the	the	DET
ijassa-419	189	36	sum	sum	NOUN
ijassa-419	189	37	of	of	ADP
ijassa-419	189	38	parts	part	NOUN
ijassa-419	189	39	’	'	PUNCT
ijassa-419	189	40	functionalities	functionality	NOUN
ijassa-419	189	41	,	,	PUNCT
ijassa-419	189	42	if	if	SCONJ
ijassa-419	189	43	an	an	DET
ijassa-419	189	44	identified	identify	VERB
ijassa-419	189	45	part	part	NOUN
ijassa-419	189	46	does	do	AUX
ijassa-419	189	47	not	not	PART
ijassa-419	189	48	have	have	VERB
ijassa-419	189	49	any	any	DET
ijassa-419	189	50	function	function	NOUN
ijassa-419	189	51	,	,	PUNCT
ijassa-419	189	52	then	then	ADV
ijassa-419	189	53	the	the	DET
ijassa-419	189	54	functionality	functionality	NOUN
ijassa-419	189	55	of	of	ADP
ijassa-419	189	56	this	this	DET
ijassa-419	189	57	part	part	NOUN
ijassa-419	189	58	is	be	AUX
ijassa-419	189	59	seen	see	VERB
ijassa-419	189	60	as	as	ADP
ijassa-419	189	61	“	"	PUNCT
ijassa-419	189	62	0	0	NUM
ijassa-419	189	63	”	"	PUNCT
ijassa-419	189	64	.	.	PUNCT
ijassa-419	190	1	illustration	illustration	NOUN
ijassa-419	190	2	1	1	NUM
ijassa-419	190	3	:	:	PUNCT
ijassa-419	190	4	the	the	DET
ijassa-419	190	5	whole	whole	NOUN
ijassa-419	190	6	is	be	AUX
ijassa-419	190	7	greater	great	ADJ
ijassa-419	190	8	than	than	ADP
ijassa-419	190	9	the	the	DET
ijassa-419	190	10	sum	sum	NOUN
ijassa-419	190	11	of	of	ADP
ijassa-419	190	12	its	its	PRON
ijassa-419	190	13	parts	part	NOUN
ijassa-419	190	14	let	let	VERB
ijassa-419	190	15	us	we	PRON
ijassa-419	190	16	symbolically	symbolically	ADV
ijassa-419	190	17	denote	denote	VERB
ijassa-419	190	18	the	the	DET
ijassa-419	190	19	constructed	construct	VERB
ijassa-419	190	20	nth	nth	NOUN
ijassa-419	190	21	order	order	NOUN
ijassa-419	190	22	simple	simple	ADJ
ijassa-419	190	23	l	l	NOUN
ijassa-419	190	24	system	system	NOUN
ijassa-419	190	25	l2	l2	NOUN
ijassa-419	190	26	=	=	SYM
ijassa-419	190	27	⟨s	⟨s	NOUN
ijassa-419	190	28	,	,	PUNCT
ijassa-419	190	29	ω	ω	PROPN
ijassa-419	190	30	,	,	PUNCT
ijassa-419	190	31	φ⟩	φ⟩	NOUN
ijassa-419	190	32	,	,	PUNCT
ijassa-419	190	33	n	n	X
ijassa-419	190	34	≥	≥	NOUN
ijassa-419	190	35	1	1	NUM
ijassa-419	190	36	,	,	PUNCT
ijassa-419	190	37	as	as	ADP
ijassa-419	190	38	φn(f	φn(f	NUM
ijassa-419	190	39	)	)	PUNCT
ijassa-419	190	40	,	,	PUNCT
ijassa-419	190	41	and	and	CCONJ
ijassa-419	190	42	sum	sum	NOUN
ijassa-419	190	43	of	of	ADP
ijassa-419	190	44	parts	part	NOUN
ijassa-419	190	45	as	as	ADP
ijassa-419	190	46	∑	∑	ADV
ijassa-419	190	47	i	i	PRON
ijassa-419	190	48	si	si	INTJ
ijassa-419	190	49	,	,	PUNCT
ijassa-419	190	50	where	where	SCONJ
ijassa-419	190	51	si	si	INTJ
ijassa-419	190	52	,	,	PUNCT
ijassa-419	190	53	i	i	PRON
ijassa-419	190	54	=	=	NOUN
ijassa-419	190	55	1	1	NUM
ijassa-419	190	56	,	,	PUNCT
ijassa-419	190	57	2	2	NUM
ijassa-419	190	58	,	,	PUNCT
ijassa-419	190	59	...	...	PUNCT
ijassa-419	190	60	,	,	PUNCT
ijassa-419	190	61	stands	stand	VERB
ijassa-419	190	62	for	for	ADP
ijassa-419	190	63	a	a	DET
ijassa-419	190	64	division	division	NOUN
ijassa-419	190	65	of	of	ADP
ijassa-419	190	66	the	the	DET
ijassa-419	190	67	whole	whole	NOUN
ijassa-419	190	68	φn(f	φn(f	PUNCT
ijassa-419	190	69	)	)	PUNCT
ijassa-419	190	70	,	,	PUNCT
ijassa-419	190	71	including	include	VERB
ijassa-419	190	72	all	all	DET
ijassa-419	190	73	characters	character	NOUN
ijassa-419	190	74	.	.	PUNCT
ijassa-419	191	1	in	in	ADP
ijassa-419	191	2	the	the	DET
ijassa-419	191	3	following	following	NOUN
ijassa-419	191	4	,	,	PUNCT
ijassa-419	191	5	we	we	PRON
ijassa-419	191	6	will	will	AUX
ijassa-419	191	7	discuss	discuss	VERB
ijassa-419	191	8	from	from	ADP
ijassa-419	191	9	two	two	NUM
ijassa-419	191	10	different	different	ADJ
ijassa-419	191	11	angles	angle	NOUN
ijassa-419	191	12	according	accord	VERB
ijassa-419	191	13	to	to	ADP
ijassa-419	191	14	the	the	DET
ijassa-419	191	15	following	follow	VERB
ijassa-419	191	16	different	different	ADJ
ijassa-419	191	17	divisions	division	NOUN
ijassa-419	191	18	of	of	ADP
ijassa-419	191	19	the	the	DET
ijassa-419	191	20	whole	whole	NOUN
ijassa-419	191	21	.	.	PUNCT
ijassa-419	192	1	(	(	PUNCT
ijassa-419	192	2	1	1	X
ijassa-419	192	3	)	)	PUNCT
ijassa-419	192	4	the	the	DET
ijassa-419	192	5	whole	whole	NOUN
ijassa-419	192	6	is	be	AUX
ijassa-419	192	7	greater	great	ADJ
ijassa-419	192	8	than	than	ADP
ijassa-419	192	9	the	the	DET
ijassa-419	192	10	sum	sum	NOUN
ijassa-419	192	11	of	of	ADP
ijassa-419	192	12	all	all	DET
ijassa-419	192	13	the	the	DET
ijassa-419	192	14	elements	element	NOUN
ijassa-419	192	15	(	(	PUNCT
ijassa-419	192	16	the	the	DET
ijassa-419	192	17	whole	whole	NOUN
ijassa-419	192	18	is	be	AUX
ijassa-419	192	19	divided	divide	VERB
ijassa-419	192	20	using	use	VERB
ijassa-419	192	21	components	component	NOUN
ijassa-419	192	22	)	)	PUNCT
ijassa-419	192	23	.	.	PUNCT
ijassa-419	193	1	if	if	SCONJ
ijassa-419	193	2	we	we	PRON
ijassa-419	193	3	treat	treat	VERB
ijassa-419	193	4	the	the	DET
ijassa-419	193	5	system	system	NOUN
ijassa-419	193	6	l2	l2	NOUN
ijassa-419	193	7	as	as	ADP
ijassa-419	193	8	one	one	NUM
ijassa-419	193	9	containing	contain	VERB
ijassa-419	193	10	only	only	ADV
ijassa-419	193	11	two	two	NUM
ijassa-419	193	12	components	component	NOUN
ijassa-419	193	13	(	(	PUNCT
ijassa-419	193	14	operations	operation	NOUN
ijassa-419	193	15	)	)	PUNCT
ijassa-419	193	16	f	f	NOUN
ijassa-419	193	17	and	and	CCONJ
ijassa-419	193	18	+	+	ADP
ijassa-419	193	19	,	,	PUNCT
ijassa-419	193	20	then	then	ADV
ijassa-419	193	21	in	in	ADP
ijassa-419	193	22	the	the	DET
ijassa-419	193	23	nth	nth	NOUN
ijassa-419	193	24	order	order	NOUN
ijassa-419	193	25	l2	l2	NOUN
ijassa-419	193	26	system	system	NOUN
ijassa-419	193	27	,	,	PUNCT
ijassa-419	193	28	there	there	PRON
ijassa-419	193	29	are	be	VERB
ijassa-419	193	30	3n	3n	NUM
ijassa-419	193	31	components	component	NOUN
ijassa-419	193	32	f	f	PROPN
ijassa-419	193	33	and	and	CCONJ
ijassa-419	193	34	2(3n	2(3n	NUM
ijassa-419	193	35	-1	-1	ADJ
ijassa-419	193	36	)	)	PUNCT
ijassa-419	193	37	components	component	NOUN
ijassa-419	194	1	+	+	PROPN
ijassa-419	194	2	.	.	PROPN
ijassa-419	195	1	from	from	ADP
ijassa-419	195	2	the	the	DET
ijassa-419	195	3	basic	basic	ADJ
ijassa-419	195	4	assumptions	assumption	NOUN
ijassa-419	195	5	,	,	PUNCT
ijassa-419	195	6	it	it	PRON
ijassa-419	195	7	follows	follow	VERB
ijassa-419	195	8	that	that	SCONJ
ijassa-419	195	9	f	f	PROPN
ijassa-419	195	10	and	and	CCONJ
ijassa-419	195	11	+	+	CCONJ
ijassa-419	195	12	respectively	respectively	ADV
ijassa-419	195	13	satisfy	satisfy	VERB
ijassa-419	195	14	the	the	DET
ijassa-419	195	15	additive	additive	ADJ
ijassa-419	195	16	property	property	NOUN
ijassa-419	195	17	.	.	PUNCT
ijassa-419	196	1	their	their	PRON
ijassa-419	196	2	algebraic	algebraic	ADJ
ijassa-419	196	3	sums	sum	NOUN
ijassa-419	196	4	are	be	AUX
ijassa-419	196	5	respectively	respectively	ADV
ijassa-419	196	6	written	write	VERB
ijassa-419	196	7	as	as	ADP
ijassa-419	196	8	s1	s1	PROPN
ijassa-419	196	9	=	=	SYM
ijassa-419	196	10	3n(f	3n(f	PROPN
ijassa-419	196	11	)	)	PUNCT
ijassa-419	196	12	and	and	CCONJ
ijassa-419	196	13	s2	s2	NOUN
ijassa-419	196	14	=	=	PUNCT
ijassa-419	196	15	2(3n	2(3n	NUM
ijassa-419	196	16	−	−	NOUN
ijassa-419	196	17	1)(+	1)(+	NUM
ijassa-419	196	18	)	)	PUNCT
ijassa-419	196	19	.	.	PUNCT
ijassa-419	197	1	then	then	ADV
ijassa-419	197	2	,	,	PUNCT
ijassa-419	197	3	the	the	DET
ijassa-419	197	4	sum	sum	NOUN
ijassa-419	197	5	of	of	ADP
ijassa-419	197	6	the	the	DET
ijassa-419	197	7	elements	element	NOUN
ijassa-419	197	8	of	of	ADP
ijassa-419	197	9	the	the	DET
ijassa-419	197	10	l2	l2	NOUN
ijassa-419	197	11	system	system	NOUN
ijassa-419	197	12	can	can	AUX
ijassa-419	197	13	be	be	AUX
ijassa-419	197	14	expressed	express	VERB
ijassa-419	197	15	as	as	ADP
ijassa-419	197	16	2∑	2∑	NUM
ijassa-419	197	17	i=1	i=1	NOUN
ijassa-419	197	18	si	si	X
ijassa-419	197	19	=	=	PUNCT
ijassa-419	197	20	s1s2	s1s2	PROPN
ijassa-419	197	21	or	or	CCONJ
ijassa-419	197	22	2∑	2∑	NUM
ijassa-419	197	23	i=1	i=1	X
ijassa-419	197	24	si	si	X
ijassa-419	198	1	=	=	PUNCT
ijassa-419	198	2	s2s1	s2s1	PROPN
ijassa-419	198	3	.	.	PUNCT
ijassa-419	198	4	applying	apply	VERB
ijassa-419	198	5	the	the	DET
ijassa-419	198	6	output	output	NOUN
ijassa-419	198	7	of	of	ADP
ijassa-419	198	8	the	the	DET
ijassa-419	198	9	elements	element	NOUN
ijassa-419	198	10	’	'	PUNCT
ijassa-419	198	11	sum	sum	NOUN
ijassa-419	198	12	2∑	2∑	NUM
ijassa-419	198	13	i=1	i=1	X
ijassa-419	198	14	si	si	X
ijassa-419	198	15	on	on	ADP
ijassa-419	198	16	the	the	DET
ijassa-419	198	17	particle	particle	NOUN
ijassa-419	198	18	a	a	PRON
ijassa-419	198	19	produces	produce	VERB
ijassa-419	198	20	a	a	DET
ijassa-419	198	21	line	line	NOUN
ijassa-419	198	22	segment	segment	NOUN
ijassa-419	198	23	of	of	ADP
ijassa-419	198	24	length	length	NOUN
ijassa-419	198	25	3n	3n	NOUN
ijassa-419	198	26	,	,	PUNCT
ijassa-419	198	27	while	while	SCONJ
ijassa-419	198	28	applying	apply	VERB
ijassa-419	198	29	the	the	DET
ijassa-419	198	30	output	output	NOUN
ijassa-419	198	31	of	of	ADP
ijassa-419	198	32	the	the	DET
ijassa-419	198	33	whole	whole	NOUN
ijassa-419	198	34	φn(f	φn(f	PUNCT
ijassa-419	198	35	)	)	PUNCT
ijassa-419	198	36	on	on	ADP
ijassa-419	198	37	the	the	DET
ijassa-419	198	38	particle	particle	NOUN
ijassa-419	198	39	a	a	PRON
ijassa-419	198	40	creates	create	VERB
ijassa-419	198	41	a	a	DET
ijassa-419	198	42	regular	regular	ADJ
ijassa-419	198	43	triangle	triangle	NOUN
ijassa-419	198	44	with	with	ADP
ijassa-419	198	45	each	each	DET
ijassa-419	198	46	side	side	NOUN
ijassa-419	198	47	’s	’s	PART
ijassa-419	198	48	length	length	NOUN
ijassa-419	198	49	1	1	NUM
ijassa-419	198	50	.	.	PUNCT
ijassa-419	199	1	the	the	DET
ijassa-419	199	2	whole	whole	NOUN
ijassa-419	199	3	constitutes	constitute	VERB
ijassa-419	199	4	a	a	DET
ijassa-419	199	5	figure	figure	NOUN
ijassa-419	199	6	of	of	ADP
ijassa-419	199	7	the	the	DET
ijassa-419	199	8	2	2	NUM
ijassa-419	199	9	-	-	PUNCT
ijassa-419	199	10	dimensional	dimensional	ADJ
ijassa-419	199	11	space	space	NOUN
ijassa-419	199	12	,	,	PUNCT
ijassa-419	199	13	possessing	possess	VERB
ijassa-419	199	14	a	a	DET
ijassa-419	199	15	special	special	ADJ
ijassa-419	199	16	structure	structure	NOUN
ijassa-419	199	17	,	,	PUNCT
ijassa-419	199	18	while	while	SCONJ
ijassa-419	199	19	the	the	DET
ijassa-419	199	20	sum	sum	NOUN
ijassa-419	199	21	of	of	ADP
ijassa-419	199	22	the	the	DET
ijassa-419	199	23	elements	element	NOUN
ijassa-419	199	24	represents	represent	VERB
ijassa-419	199	25	a	a	DET
ijassa-419	199	26	line	line	NOUN
ijassa-419	199	27	segment	segment	NOUN
ijassa-419	199	28	of	of	ADP
ijassa-419	199	29	the	the	DET
ijassa-419	199	30	1	1	NUM
ijassa-419	199	31	-	-	PUNCT
ijassa-419	199	32	dimensional	dimensional	ADJ
ijassa-419	199	33	space	space	NOUN
ijassa-419	199	34	without	without	ADP
ijassa-419	199	35	any	any	DET
ijassa-419	199	36	qualitative	qualitative	ADJ
ijassa-419	199	37	mutation	mutation	NOUN
ijassa-419	199	38	.	.	PUNCT
ijassa-419	200	1	that	that	PRON
ijassa-419	200	2	is	be	AUX
ijassa-419	200	3	to	to	PART
ijassa-419	200	4	say	say	VERB
ijassa-419	200	5	,	,	PUNCT
ijassa-419	200	6	the	the	DET
ijassa-419	200	7	whole	whole	NOUN
ijassa-419	200	8	has	have	VERB
ijassa-419	200	9	a	a	DET
ijassa-419	200	10	spatial	spatial	ADJ
ijassa-419	200	11	structural	structural	ADJ
ijassa-419	200	12	effect	effect	NOUN
ijassa-419	200	13	that	that	PRON
ijassa-419	200	14	is	be	AUX
ijassa-419	200	15	not	not	PART
ijassa-419	200	16	shared	share	VERB
ijassa-419	200	17	by	by	ADP
ijassa-419	200	18	the	the	DET
ijassa-419	200	19	sum	sum	NOUN
ijassa-419	200	20	of	of	ADP
ijassa-419	200	21	the	the	DET
ijassa-419	200	22	parts	part	NOUN
ijassa-419	200	23	,	,	PUNCT
ijassa-419	200	24	therefore	therefore	ADV
ijassa-419	200	25	,	,	PUNCT
ijassa-419	200	26	φn(f	φn(f	PUNCT
ijassa-419	200	27	)	)	PUNCT
ijassa-419	200	28	>	>	PUNCT
ijassa-419	201	1	2∑	2∑	X
ijassa-419	201	2	i=1	i=1	X
ijassa-419	201	3	si	si	X
ijassa-419	201	4	.	.	PUNCT
ijassa-419	202	1	(	(	PUNCT
ijassa-419	202	2	2	2	X
ijassa-419	202	3	)	)	PUNCT
ijassa-419	202	4	the	the	DET
ijassa-419	202	5	whole	whole	NOUN
ijassa-419	202	6	is	be	AUX
ijassa-419	202	7	greater	great	ADJ
ijassa-419	202	8	than	than	ADP
ijassa-419	202	9	the	the	DET
ijassa-419	202	10	sum	sum	NOUN
ijassa-419	202	11	of	of	ADP
ijassa-419	202	12	its	its	PRON
ijassa-419	202	13	parts	part	NOUN
ijassa-419	202	14	,	,	PUNCT
ijassa-419	202	15	where	where	SCONJ
ijassa-419	202	16	the	the	DET
ijassa-419	202	17	whole	whole	NOUN
ijassa-419	202	18	is	be	AUX
ijassa-419	202	19	divided	divide	VERB
ijassa-419	202	20	using	use	VERB
ijassa-419	202	21	attributes	attribute	NOUN
ijassa-419	202	22	.	.	PUNCT
ijassa-419	203	1	let	let	VERB
ijassa-419	203	2	us	we	PRON
ijassa-419	203	3	treat	treat	VERB
ijassa-419	203	4	the	the	DET
ijassa-419	203	5	l2	l2	NOUN
ijassa-419	203	6	system	system	NOUN
ijassa-419	203	7	as	as	ADP
ijassa-419	203	8	being	be	AUX
ijassa-419	203	9	composed	compose	VERB
ijassa-419	203	10	of	of	ADP
ijassa-419	203	11	3n	3n	NUM
ijassa-419	203	12	unit	unit	NOUN
ijassa-419	203	13	vectors	vector	NOUN
ijassa-419	203	14	of	of	ADP
ijassa-419	203	15	the	the	DET
ijassa-419	203	16	plane	plane	NOUN
ijassa-419	203	17	:	:	PUNCT
ijassa-419	203	18	i⃗1	i⃗1	NOUN
ijassa-419	203	19	,	,	PUNCT
ijassa-419	203	20	i⃗2	i⃗2	ADJ
ijassa-419	203	21	,	,	PUNCT
ijassa-419	203	22	...	...	PUNCT
ijassa-419	203	23	,	,	PUNCT
ijassa-419	203	24	i⃗3n	i⃗3n	PROPN
ijassa-419	203	25	.	.	PUNCT
ijassa-419	204	1	that	that	ADV
ijassa-419	204	2	is	is	ADV
ijassa-419	204	3	,	,	PUNCT
ijassa-419	204	4	we	we	PRON
ijassa-419	204	5	see	see	VERB
ijassa-419	204	6	the	the	DET
ijassa-419	204	7	vectors	vector	NOUN
ijassa-419	204	8	i⃗1	i⃗1	NOUN
ijassa-419	204	9	,	,	PUNCT
ijassa-419	204	10	i⃗2	i⃗2	ADJ
ijassa-419	204	11	,	,	PUNCT
ijassa-419	204	12	...	...	PUNCT
ijassa-419	204	13	,	,	PUNCT
ijassa-419	204	14	i⃗3n	i⃗3n	ADP
ijassa-419	204	15	as	as	ADP
ijassa-419	204	16	having	have	VERB
ijassa-419	204	17	the	the	DET
ijassa-419	204	18	same	same	ADJ
ijassa-419	204	19	attributes	attribute	NOUN
ijassa-419	204	20	.	.	PUNCT
ijassa-419	205	1	then	then	ADV
ijassa-419	205	2	this	this	DET
ijassa-419	205	3	l2	l2	NOUN
ijassa-419	205	4	system	system	NOUN
ijassa-419	205	5	is	be	AUX
ijassa-419	205	6	made	make	VERB
ijassa-419	205	7	up	up	ADP
ijassa-419	205	8	only	only	ADV
ijassa-419	205	9	of	of	ADP
ijassa-419	205	10	these	these	DET
ijassa-419	205	11	3n	3n	NUM
ijassa-419	205	12	components	component	NOUN
ijassa-419	205	13	of	of	ADP
ijassa-419	205	14	the	the	DET
ijassa-419	205	15	same	same	ADJ
ijassa-419	205	16	attributes	attribute	NOUN
ijassa-419	205	17	.	.	PUNCT
ijassa-419	206	1	now	now	ADV
ijassa-419	206	2	,	,	PUNCT
ijassa-419	206	3	we	we	PRON
ijassa-419	206	4	desire	desire	VERB
ijassa-419	206	5	to	to	PART
ijassa-419	206	6	show	show	VERB
ijassa-419	206	7	φn(f	φn(f	PUNCT
ijassa-419	206	8	)	)	PUNCT
ijassa-419	206	9	>	>	PUNCT
ijassa-419	207	1	3n∑	3n∑	NUM
ijassa-419	207	2	k=1	k=1	PUNCT
ijassa-419	208	1	i⃗k	i⃗k	PROPN
ijassa-419	208	2	.	.	PUNCT
ijassa-419	209	1	evidently	evidently	ADV
ijassa-419	209	2	,	,	PUNCT
ijassa-419	209	3	3n∑	3n∑	INTJ
ijassa-419	209	4	k=1	k=1	PUNCT
ijassa-419	210	1	i⃗k	i⃗k	PROPN
ijassa-419	210	2	=	=	PUNCT
ijassa-419	211	1	0	0	X
ijassa-419	211	2	.	.	PUNCT
ijassa-419	212	1	so	so	ADV
ijassa-419	212	2	,	,	PUNCT
ijassa-419	212	3	when	when	SCONJ
ijassa-419	212	4	the	the	DET
ijassa-419	212	5	output	output	NOUN
ijassa-419	212	6	of	of	ADP
ijassa-419	212	7	the	the	DET
ijassa-419	212	8	sum	sum	NOUN
ijassa-419	212	9	3n∑	3n∑	PROPN
ijassa-419	212	10	k=1	k=1	PUNCT
ijassa-419	213	1	i⃗k	i⃗k	PROPN
ijassa-419	213	2	of	of	ADP
ijassa-419	213	3	the	the	DET
ijassa-419	213	4	parts	part	NOUN
ijassa-419	213	5	is	be	AUX
ijassa-419	213	6	advances	advance	NOUN
ijassa-419	213	7	in	in	ADP
ijassa-419	213	8	systems	system	NOUN
ijassa-419	213	9	science	science	NOUN
ijassa-419	213	10	and	and	CCONJ
ijassa-419	213	11	applications	application	NOUN
ijassa-419	213	12	(	(	PUNCT
ijassa-419	213	13	2013	2013	NUM
ijassa-419	213	14	)	)	PUNCT
ijassa-419	214	1	vol.13	vol.13	NOUN
ijassa-419	214	2	no.2	no.2	PROPN
ijassa-419	214	3	109	109	NUM
ijassa-419	214	4	applied	apply	VERB
ijassa-419	214	5	on	on	ADP
ijassa-419	214	6	the	the	DET
ijassa-419	214	7	particle	particle	NOUN
ijassa-419	214	8	a	a	PRON
ijassa-419	214	9	,	,	PUNCT
ijassa-419	214	10	it	it	PRON
ijassa-419	214	11	is	be	AUX
ijassa-419	214	12	like	like	SCONJ
ijassa-419	214	13	that	that	SCONJ
ijassa-419	214	14	no	no	DET
ijassa-419	214	15	operation	operation	NOUN
ijassa-419	214	16	is	be	AUX
ijassa-419	214	17	ever	ever	ADV
ijassa-419	214	18	applied	apply	VERB
ijassa-419	214	19	on	on	ADP
ijassa-419	214	20	a	a	DET
ijassa-419	214	21	so	so	ADV
ijassa-419	214	22	that	that	SCONJ
ijassa-419	214	23	the	the	DET
ijassa-419	214	24	particle	particle	NOUN
ijassa-419	214	25	a	a	PRON
ijassa-419	214	26	is	be	AUX
ijassa-419	214	27	fastened	fasten	VERB
ijassa-419	214	28	at	at	ADP
ijassa-419	214	29	the	the	DET
ijassa-419	214	30	origin	origin	NOUN
ijassa-419	214	31	without	without	ADP
ijassa-419	214	32	moving	move	VERB
ijassa-419	214	33	.	.	PUNCT
ijassa-419	215	1	because	because	SCONJ
ijassa-419	215	2	the	the	DET
ijassa-419	215	3	output	output	NOUN
ijassa-419	215	4	of	of	ADP
ijassa-419	215	5	the	the	DET
ijassa-419	215	6	whole	whole	NOUN
ijassa-419	215	7	φn(f	φn(f	PUNCT
ijassa-419	215	8	)	)	PUNCT
ijassa-419	215	9	is	be	AUX
ijassa-419	215	10	a	a	DET
ijassa-419	215	11	string	string	NOUN
ijassa-419	215	12	of	of	ADP
ijassa-419	215	13	characters	character	NOUN
ijassa-419	215	14	,	,	PUNCT
ijassa-419	215	15	which	which	PRON
ijassa-419	215	16	is	be	AUX
ijassa-419	215	17	equivalent	equivalent	ADJ
ijassa-419	215	18	to	to	ADP
ijassa-419	215	19	a	a	DET
ijassa-419	215	20	sequence	sequence	NOUN
ijassa-419	215	21	of	of	ADP
ijassa-419	215	22	operations	operation	NOUN
ijassa-419	215	23	with	with	ADP
ijassa-419	215	24	a	a	DET
ijassa-419	215	25	before	before	NOUN
ijassa-419	215	26	and	and	CCONJ
ijassa-419	215	27	after	after	ADP
ijassa-419	215	28	order	order	NOUN
ijassa-419	215	29	,	,	PUNCT
ijassa-419	215	30	when	when	SCONJ
ijassa-419	215	31	φn(f	φn(f	PUNCT
ijassa-419	215	32	)	)	PUNCT
ijassa-419	215	33	is	be	AUX
ijassa-419	215	34	applied	apply	VERB
ijassa-419	215	35	on	on	ADP
ijassa-419	215	36	the	the	DET
ijassa-419	215	37	particle	particle	NOUN
ijassa-419	215	38	a	a	PRON
ijassa-419	215	39	,	,	PUNCT
ijassa-419	215	40	this	this	DET
ijassa-419	215	41	particle	particle	NOUN
ijassa-419	215	42	will	will	AUX
ijassa-419	215	43	repeatedly	repeatedly	ADV
ijassa-419	215	44	travel	travel	VERB
ijassa-419	215	45	counterclockwise	counterclockwise	NOUN
ijassa-419	215	46	along	along	ADP
ijassa-419	215	47	the	the	DET
ijassa-419	215	48	triangle	triangle	NOUN
ijassa-419	215	49	and	and	CCONJ
ijassa-419	215	50	eventually	eventually	ADV
ijassa-419	215	51	return	return	VERB
ijassa-419	215	52	to	to	ADP
ijassa-419	215	53	the	the	DET
ijassa-419	215	54	origin	origin	NOUN
ijassa-419	215	55	.	.	PUNCT
ijassa-419	216	1	that	that	PRON
ijassa-419	216	2	is	be	AUX
ijassa-419	216	3	to	to	PART
ijassa-419	216	4	say	say	VERB
ijassa-419	216	5	,	,	PUNCT
ijassa-419	216	6	the	the	DET
ijassa-419	216	7	whole	whole	NOUN
ijassa-419	216	8	possesses	possess	VERB
ijassa-419	216	9	a	a	DET
ijassa-419	216	10	structural	structural	ADJ
ijassa-419	216	11	effect	effect	NOUN
ijassa-419	216	12	of	of	ADP
ijassa-419	216	13	time	time	NOUN
ijassa-419	216	14	that	that	PRON
ijassa-419	216	15	is	be	AUX
ijassa-419	216	16	not	not	PART
ijassa-419	216	17	shared	share	VERB
ijassa-419	216	18	by	by	ADP
ijassa-419	216	19	the	the	DET
ijassa-419	216	20	sum	sum	NOUN
ijassa-419	216	21	of	of	ADP
ijassa-419	216	22	the	the	DET
ijassa-419	216	23	parts	part	NOUN
ijassa-419	216	24	,	,	PUNCT
ijassa-419	216	25	therefore	therefore	ADV
ijassa-419	216	26	,	,	PUNCT
ijassa-419	216	27	we	we	PRON
ijassa-419	216	28	have	have	VERB
ijassa-419	216	29	φn(f	φn(f	PUNCT
ijassa-419	216	30	)	)	PUNCT
ijassa-419	216	31	>	>	PUNCT
ijassa-419	217	1	3n∑	3n∑	NUM
ijassa-419	217	2	k=1	k=1	PUNCT
ijassa-419	218	1	i⃗k	i⃗k	PROPN
ijassa-419	218	2	.	.	PUNCT
ijassa-419	219	1	in	in	ADP
ijassa-419	219	2	fact	fact	NOUN
ijassa-419	219	3	,	,	PUNCT
ijassa-419	219	4	the	the	DET
ijassa-419	219	5	essential	essential	ADJ
ijassa-419	219	6	difference	difference	NOUN
ijassa-419	219	7	between	between	ADP
ijassa-419	219	8	the	the	DET
ijassa-419	219	9	whole	whole	NOUN
ijassa-419	219	10	and	and	CCONJ
ijassa-419	219	11	the	the	DET
ijassa-419	219	12	sum	sum	NOUN
ijassa-419	219	13	of	of	ADP
ijassa-419	219	14	parts	part	NOUN
ijassa-419	219	15	is	be	AUX
ijassa-419	219	16	that	that	SCONJ
ijassa-419	219	17	the	the	DET
ijassa-419	219	18	whole	whole	NOUN
ijassa-419	219	19	has	have	VERB
ijassa-419	219	20	some	some	DET
ijassa-419	219	21	structural	structural	ADJ
ijassa-419	219	22	effect	effect	NOUN
ijassa-419	219	23	in	in	ADP
ijassa-419	219	24	terms	term	NOUN
ijassa-419	219	25	of	of	ADP
ijassa-419	219	26	space	space	NOUN
ijassa-419	219	27	or	or	CCONJ
ijassa-419	219	28	time	time	NOUN
ijassa-419	219	29	,	,	PUNCT
ijassa-419	219	30	while	while	SCONJ
ijassa-419	219	31	the	the	DET
ijassa-419	219	32	sum	sum	NOUN
ijassa-419	219	33	of	of	ADP
ijassa-419	219	34	parts	part	NOUN
ijassa-419	219	35	does	do	AUX
ijassa-419	219	36	not	not	PART
ijassa-419	219	37	have	have	VERB
ijassa-419	219	38	.	.	PUNCT
ijassa-419	220	1	for	for	ADP
ijassa-419	220	2	instance	instance	NOUN
ijassa-419	220	3	,	,	PUNCT
ijassa-419	220	4	when	when	SCONJ
ijassa-419	220	5	n	n	PRON
ijassa-419	220	6	bricks	brick	NOUN
ijassa-419	220	7	are	be	AUX
ijassa-419	220	8	used	use	VERB
ijassa-419	220	9	to	to	PART
ijassa-419	220	10	build	build	VERB
ijassa-419	220	11	a	a	DET
ijassa-419	220	12	house	house	NOUN
ijassa-419	220	13	,	,	PUNCT
ijassa-419	220	14	the	the	DET
ijassa-419	220	15	whole	whole	NOUN
ijassa-419	220	16	stands	stand	VERB
ijassa-419	220	17	for	for	ADP
ijassa-419	220	18	a	a	DET
ijassa-419	220	19	building	building	NOUN
ijassa-419	220	20	along	along	ADP
ijassa-419	220	21	with	with	ADP
ijassa-419	220	22	the	the	DET
ijassa-419	220	23	spatial	spatial	ADJ
ijassa-419	220	24	structure	structure	NOUN
ijassa-419	220	25	of	of	ADP
ijassa-419	220	26	rooms	room	NOUN
ijassa-419	220	27	,	,	PUNCT
ijassa-419	220	28	etc	etc	X
ijassa-419	220	29	.	.	X
ijassa-419	221	1	however	however	ADV
ijassa-419	221	2	,	,	PUNCT
ijassa-419	221	3	when	when	SCONJ
ijassa-419	221	4	the	the	DET
ijassa-419	221	5	components	component	NOUN
ijassa-419	221	6	of	of	ADP
ijassa-419	221	7	this	this	DET
ijassa-419	221	8	building	building	NOUN
ijassa-419	221	9	are	be	AUX
ijassa-419	221	10	divided	divide	VERB
ijassa-419	221	11	,	,	PUNCT
ijassa-419	221	12	because	because	SCONJ
ijassa-419	221	13	there	there	PRON
ijassa-419	221	14	is	be	VERB
ijassa-419	221	15	only	only	ADV
ijassa-419	221	16	one	one	NUM
ijassa-419	221	17	kind	kind	NOUN
ijassa-419	221	18	of	of	ADP
ijassa-419	221	19	component	component	NOUN
ijassa-419	221	20	,	,	PUNCT
ijassa-419	221	21	the	the	DET
ijassa-419	221	22	bricks	brick	NOUN
ijassa-419	221	23	,	,	PUNCT
ijassa-419	221	24	the	the	DET
ijassa-419	221	25	sum	sum	NOUN
ijassa-419	221	26	of	of	ADP
ijassa-419	221	27	the	the	DET
ijassa-419	221	28	parts	part	NOUN
ijassa-419	221	29	satisfies	satisfy	VERB
ijassa-419	221	30	the	the	DET
ijassa-419	221	31	algebraic	algebraic	ADJ
ijassa-419	221	32	additivity	additivity	NOUN
ijassa-419	221	33	and	and	CCONJ
ijassa-419	221	34	is	be	AUX
ijassa-419	221	35	equal	equal	ADJ
ijassa-419	221	36	to	to	ADP
ijassa-419	221	37	the	the	DET
ijassa-419	221	38	n	n	NUM
ijassa-419	221	39	bricks	brick	NOUN
ijassa-419	221	40	,	,	PUNCT
ijassa-419	221	41	which	which	PRON
ijassa-419	221	42	do	do	AUX
ijassa-419	221	43	not	not	PART
ijassa-419	221	44	have	have	VERB
ijassa-419	221	45	the	the	DET
ijassa-419	221	46	spatial	spatial	ADJ
ijassa-419	221	47	structure	structure	NOUN
ijassa-419	221	48	of	of	ADP
ijassa-419	221	49	the	the	DET
ijassa-419	221	50	house	house	NOUN
ijassa-419	221	51	.	.	PUNCT
ijassa-419	222	1	illustration	illustration	NOUN
ijassa-419	222	2	2	2	NUM
ijassa-419	222	3	:	:	PUNCT
ijassa-419	222	4	the	the	DET
ijassa-419	222	5	functionality	functionality	NOUN
ijassa-419	222	6	of	of	ADP
ijassa-419	222	7	the	the	DET
ijassa-419	222	8	whole	whole	NOUN
ijassa-419	222	9	is	be	AUX
ijassa-419	222	10	greater	great	ADJ
ijassa-419	222	11	than	than	ADP
ijassa-419	222	12	the	the	DET
ijassa-419	222	13	sum	sum	NOUN
ijassa-419	222	14	of	of	ADP
ijassa-419	222	15	parts	part	NOUN
ijassa-419	222	16	’	'	PUNCT
ijassa-419	222	17	functionalities	functionality	NOUN
ijassa-419	222	18	.	.	PUNCT
ijassa-419	223	1	let	let	VERB
ijassa-419	223	2	us	we	PRON
ijassa-419	223	3	first	first	ADV
ijassa-419	223	4	introduce	introduce	VERB
ijassa-419	223	5	a	a	DET
ijassa-419	223	6	new	new	ADJ
ijassa-419	223	7	kind	kind	NOUN
ijassa-419	223	8	of	of	ADP
ijassa-419	223	9	set	set	NOUN
ijassa-419	223	10	[	[	X
ijassa-419	223	11	s	s	X
ijassa-419	223	12	]	]	X
ijassa-419	223	13	,	,	PUNCT
ijassa-419	223	14	where	where	SCONJ
ijassa-419	223	15	each	each	DET
ijassa-419	223	16	element	element	NOUN
ijassa-419	223	17	is	be	AUX
ijassa-419	223	18	allowed	allow	VERB
ijassa-419	223	19	to	to	PART
ijassa-419	223	20	appear	appear	VERB
ijassa-419	223	21	more	more	ADV
ijassa-419	223	22	than	than	ADP
ijassa-419	223	23	once	once	ADV
ijassa-419	223	24	.	.	PUNCT
ijassa-419	224	1	to	to	PART
ijassa-419	224	2	avoid	avoid	VERB
ijassa-419	224	3	creating	create	VERB
ijassa-419	224	4	any	any	DET
ijassa-419	224	5	conflict	conflict	NOUN
ijassa-419	224	6	with	with	ADP
ijassa-419	224	7	the	the	DET
ijassa-419	224	8	conventional	conventional	ADJ
ijassa-419	224	9	set	set	NOUN
ijassa-419	224	10	theory	theory	NOUN
ijassa-419	224	11	,	,	PUNCT
ijassa-419	224	12	we	we	PRON
ijassa-419	224	13	will	will	AUX
ijassa-419	224	14	only	only	ADV
ijassa-419	224	15	apply	apply	VERB
ijassa-419	224	16	the	the	DET
ijassa-419	224	17	operation	operation	NOUN
ijassa-419	224	18	of	of	ADP
ijassa-419	224	19	drawing	draw	VERB
ijassa-419	224	20	elements	element	NOUN
ijassa-419	224	21	out	out	ADP
ijassa-419	224	22	of	of	ADP
ijassa-419	224	23	the	the	DET
ijassa-419	224	24	set	set	NOUN
ijassa-419	224	25	[	[	X
ijassa-419	224	26	s	s	X
ijassa-419	224	27	]	]	X
ijassa-419	224	28	with	with	ADP
ijassa-419	224	29	the	the	DET
ijassa-419	224	30	following	follow	VERB
ijassa-419	224	31	convention	convention	NOUN
ijassa-419	224	32	:	:	PUNCT
ijassa-419	224	33	if	if	SCONJ
ijassa-419	224	34	a	a	DET
ijassa-419	224	35	non	non	ADJ
ijassa-419	224	36	-	-	ADJ
ijassa-419	224	37	empty	empty	ADJ
ijassa-419	224	38	set	set	NOUN
ijassa-419	224	39	[	[	X
ijassa-419	224	40	s	s	X
ijassa-419	224	41	]	]	PUNCT
ijassa-419	224	42	contains	contain	VERB
ijassa-419	224	43	element	element	NOUN
ijassa-419	224	44	s	s	PART
ijassa-419	224	45	at	at	ADV
ijassa-419	224	46	least	least	ADJ
ijassa-419	224	47	twice	twice	ADV
ijassa-419	224	48	,	,	PUNCT
ijassa-419	224	49	then	then	ADV
ijassa-419	224	50	drawing	draw	VERB
ijassa-419	224	51	one	one	NUM
ijassa-419	224	52	s	s	NOUN
ijassa-419	224	53	from	from	ADP
ijassa-419	224	54	[	[	X
ijassa-419	224	55	s	s	X
ijassa-419	224	56	]	]	X
ijassa-419	224	57	means	mean	VERB
ijassa-419	224	58	that	that	SCONJ
ijassa-419	224	59	we	we	PRON
ijassa-419	224	60	take	take	VERB
ijassa-419	224	61	any	any	PRON
ijassa-419	224	62	of	of	ADP
ijassa-419	224	63	the	the	DET
ijassa-419	224	64	elements	element	NOUN
ijassa-419	224	65	s	s	VERB
ijassa-419	224	66	’s	’s	NOUN
ijassa-419	224	67	.	.	PUNCT
ijassa-419	225	1	for	for	ADP
ijassa-419	225	2	example	example	NOUN
ijassa-419	225	3	,	,	PUNCT
ijassa-419	225	4	[	[	X
ijassa-419	225	5	s	s	X
ijassa-419	225	6	]	]	X
ijassa-419	225	7	=	=	X
ijassa-419	225	8	{	{	PUNCT
ijassa-419	225	9	a	a	X
ijassa-419	225	10	,	,	PUNCT
ijassa-419	225	11	a	a	DET
ijassa-419	225	12	,	,	PUNCT
ijassa-419	225	13	b	b	NOUN
ijassa-419	225	14	,	,	PUNCT
ijassa-419	225	15	a	a	DET
ijassa-419	225	16	,	,	PUNCT
ijassa-419	225	17	b	b	NOUN
ijassa-419	225	18	}	}	PUNCT
ijassa-419	225	19	.	.	PUNCT
ijassa-419	226	1	then	then	ADV
ijassa-419	226	2	,	,	PUNCT
ijassa-419	226	3	drawing	draw	VERB
ijassa-419	226	4	an	an	DET
ijassa-419	226	5	a	a	NOUN
ijassa-419	226	6	from	from	ADP
ijassa-419	226	7	[	[	X
ijassa-419	226	8	s	s	X
ijassa-419	226	9	]	]	X
ijassa-419	226	10	means	mean	VERB
ijassa-419	226	11	that	that	SCONJ
ijassa-419	226	12	we	we	PRON
ijassa-419	226	13	take	take	VERB
ijassa-419	226	14	any	any	DET
ijassa-419	226	15	one	one	NUM
ijassa-419	226	16	of	of	ADP
ijassa-419	226	17	the	the	DET
ijassa-419	226	18	elements	element	NOUN
ijassa-419	226	19	a	a	DET
ijassa-419	226	20	’s	’s	NOUN
ijassa-419	226	21	.	.	PUNCT
ijassa-419	227	1	for	for	ADP
ijassa-419	227	2	the	the	DET
ijassa-419	227	3	nth	nth	NOUN
ijassa-419	227	4	order	order	NOUN
ijassa-419	227	5	simple	simple	ADJ
ijassa-419	227	6	l2	l2	NOUN
ijassa-419	227	7	system	system	NOUN
ijassa-419	227	8	,	,	PUNCT
ijassa-419	227	9	n	n	X
ijassa-419	227	10	≥	≥	NOUN
ijassa-419	227	11	1	1	NUM
ijassa-419	227	12	,	,	PUNCT
ijassa-419	227	13	the	the	DET
ijassa-419	227	14	individual	individual	ADJ
ijassa-419	227	15	characters	character	NOUN
ijassa-419	227	16	(	(	PUNCT
ijassa-419	227	17	operations	operation	NOUN
ijassa-419	227	18	)	)	PUNCT
ijassa-419	227	19	f	f	NOUN
ijassa-419	227	20	and	and	CCONJ
ijassa-419	227	21	+	+	CCONJ
ijassa-419	227	22	stand	stand	VERB
ijassa-419	227	23	for	for	ADP
ijassa-419	227	24	the	the	DET
ijassa-419	227	25	smallest	small	ADJ
ijassa-419	227	26	units	unit	NOUN
ijassa-419	227	27	of	of	ADP
ijassa-419	227	28	functionalities	functionality	NOUN
ijassa-419	227	29	.	.	PUNCT
ijassa-419	228	1	divide	divide	VERB
ijassa-419	228	2	this	this	DET
ijassa-419	228	3	system	system	NOUN
ijassa-419	228	4	into	into	ADP
ijassa-419	228	5	(	(	PUNCT
ijassa-419	228	6	3n+1−2	3n+1−2	NUM
ijassa-419	228	7	)	)	PUNCT
ijassa-419	228	8	parts	part	NOUN
ijassa-419	228	9	,	,	PUNCT
ijassa-419	228	10	which	which	PRON
ijassa-419	228	11	include	include	VERB
ijassa-419	228	12	3n	3n	NUM
ijassa-419	228	13	functional	functional	ADJ
ijassa-419	228	14	units	unit	NOUN
ijassa-419	228	15	f	f	PROPN
ijassa-419	228	16	and	and	CCONJ
ijassa-419	228	17	2	2	NUM
ijassa-419	228	18	(	(	PUNCT
ijassa-419	228	19	3n-1	3n-1	NUM
ijassa-419	228	20	)	)	PUNCT
ijassa-419	228	21	functional	functional	ADJ
ijassa-419	228	22	units	unit	NOUN
ijassa-419	228	23	+	+	NOUN
ijassa-419	228	24	.	.	PUNCT
ijassa-419	229	1	the	the	DET
ijassa-419	229	2	set	set	NOUN
ijassa-419	229	3	of	of	ADP
ijassa-419	229	4	these	these	PRON
ijassa-419	229	5	(	(	PUNCT
ijassa-419	229	6	3n+1	3n+1	NOUN
ijassa-419	229	7	-	-	PUNCT
ijassa-419	229	8	2	2	NUM
ijassa-419	229	9	)	)	PUNCT
ijassa-419	229	10	functional	functional	ADJ
ijassa-419	229	11	units	unit	NOUN
ijassa-419	229	12	is	be	AUX
ijassa-419	229	13	written	write	VERB
ijassa-419	229	14	as	as	ADP
ijassa-419	229	15	set	set	VERB
ijassa-419	229	16	[	[	X
ijassa-419	229	17	s	s	X
ijassa-419	229	18	]	]	PUNCT
ijassa-419	229	19	.	.	PUNCT
ijassa-419	230	1	we	we	PRON
ijassa-419	230	2	first	first	ADV
ijassa-419	230	3	consider	consider	VERB
ijassa-419	230	4	the	the	DET
ijassa-419	230	5	effect	effect	NOUN
ijassa-419	230	6	of	of	ADP
ijassa-419	230	7	the	the	DET
ijassa-419	230	8	whole	whole	NOUN
ijassa-419	230	9	on	on	ADP
ijassa-419	230	10	the	the	DET
ijassa-419	230	11	particle	particle	NOUN
ijassa-419	230	12	a.	a.	NOUN
ijassa-419	230	13	the	the	DET
ijassa-419	230	14	function	function	NOUN
ijassa-419	230	15	of	of	ADP
ijassa-419	230	16	this	this	DET
ijassa-419	230	17	l2	l2	NOUN
ijassa-419	230	18	system	system	NOUN
ijassa-419	230	19	is	be	AUX
ijassa-419	230	20	to	to	PART
ijassa-419	230	21	order	order	VERB
ijassa-419	230	22	the	the	DET
ijassa-419	230	23	elements	element	NOUN
ijassa-419	230	24	of	of	ADP
ijassa-419	230	25	[	[	X
ijassa-419	230	26	s	s	X
ijassa-419	230	27	]	]	X
ijassa-419	230	28	according	accord	VERB
ijassa-419	230	29	to	to	ADP
ijassa-419	230	30	some	some	DET
ijassa-419	230	31	specific	specific	ADJ
ijassa-419	230	32	rules	rule	NOUN
ijassa-419	230	33	.	.	PUNCT
ijassa-419	231	1	then	then	ADV
ijassa-419	231	2	,	,	PUNCT
ijassa-419	231	3	the	the	DET
ijassa-419	231	4	effect	effect	NOUN
ijassa-419	231	5	of	of	ADP
ijassa-419	231	6	the	the	DET
ijassa-419	231	7	system	system	NOUN
ijassa-419	231	8	on	on	ADP
ijassa-419	231	9	a	a	PRON
ijassa-419	231	10	is	be	AUX
ijassa-419	231	11	force	force	NOUN
ijassa-419	231	12	the	the	DET
ijassa-419	231	13	particle	particle	NOUN
ijassa-419	231	14	a	a	PRON
ijassa-419	231	15	to	to	PART
ijassa-419	231	16	counterclockwisely	counterclockwisely	ADV
ijassa-419	231	17	travel	travel	VERB
ijassa-419	231	18	along	along	ADP
ijassa-419	231	19	the	the	DET
ijassa-419	231	20	triangle	triangle	NOUN
ijassa-419	231	21	3n−1	3n−1	NUM
ijassa-419	231	22	times	time	NOUN
ijassa-419	231	23	.	.	PUNCT
ijassa-419	232	1	now	now	ADV
ijassa-419	232	2	,	,	PUNCT
ijassa-419	232	3	let	let	VERB
ijassa-419	232	4	us	we	PRON
ijassa-419	232	5	look	look	VERB
ijassa-419	232	6	at	at	ADP
ijassa-419	232	7	the	the	DET
ijassa-419	232	8	effect	effect	NOUN
ijassa-419	232	9	on	on	ADP
ijassa-419	232	10	a	a	PRON
ijassa-419	232	11	of	of	ADP
ijassa-419	232	12	each	each	DET
ijassa-419	232	13	part	part	NOUN
ijassa-419	232	14	.	.	PUNCT
ijassa-419	233	1	when	when	SCONJ
ijassa-419	233	2	the	the	DET
ijassa-419	233	3	set	set	NOUN
ijassa-419	233	4	[	[	X
ijassa-419	233	5	s	s	X
ijassa-419	233	6	]	]	X
ijassa-419	233	7	is	be	AUX
ijassa-419	233	8	given	give	VERB
ijassa-419	233	9	,	,	PUNCT
ijassa-419	233	10	the	the	DET
ijassa-419	233	11	sum	sum	NOUN
ijassa-419	233	12	of	of	ADP
ijassa-419	233	13	the	the	DET
ijassa-419	233	14	parts	part	NOUN
ijassa-419	233	15	’	'	PUNCT
ijassa-419	233	16	functions	function	NOUN
ijassa-419	233	17	can	can	AUX
ijassa-419	233	18	be	be	AUX
ijassa-419	233	19	understood	understand	VERB
ijassa-419	233	20	as	as	SCONJ
ijassa-419	233	21	follows	follow	VERB
ijassa-419	233	22	:	:	PUNCT
ijassa-419	233	23	there	there	PRON
ijassa-419	233	24	are	be	VERB
ijassa-419	233	25	a	a	DET
ijassa-419	233	26	total	total	NOUN
ijassa-419	233	27	of	of	ADP
ijassa-419	233	28	m	m	PROPN
ijassa-419	233	29	operations	operation	NOUN
ijassa-419	233	30	,	,	PUNCT
ijassa-419	233	31	each	each	PRON
ijassa-419	233	32	of	of	ADP
ijassa-419	233	33	which	which	PRON
ijassa-419	233	34	takes	take	VERB
ijassa-419	233	35	mi	mi	NOUN
ijassa-419	233	36	arbitrary	arbitrary	ADJ
ijassa-419	233	37	elements	element	NOUN
ijassa-419	233	38	from	from	ADP
ijassa-419	233	39	[	[	X
ijassa-419	233	40	s	s	X
ijassa-419	233	41	]	]	X
ijassa-419	233	42	without	without	ADP
ijassa-419	233	43	replacement	replacement	NOUN
ijassa-419	233	44	to	to	PART
ijassa-419	233	45	act	act	VERB
ijassa-419	233	46	on	on	ADP
ijassa-419	233	47	a	a	PRON
ijassa-419	233	48	,	,	PUNCT
ijassa-419	233	49	until	until	SCONJ
ijassa-419	233	50	all	all	DET
ijassa-419	233	51	the	the	DET
ijassa-419	233	52	elements	element	NOUN
ijassa-419	233	53	in	in	ADP
ijassa-419	233	54	[	[	X
ijassa-419	233	55	s	s	X
ijassa-419	233	56	]	]	X
ijassa-419	233	57	are	be	AUX
ijassa-419	233	58	exhausted	exhaust	VERB
ijassa-419	233	59	.	.	PUNCT
ijassa-419	234	1	evidently	evidently	ADV
ijassa-419	234	2	,	,	PUNCT
ijassa-419	234	3	as	as	ADV
ijassa-419	234	4	long	long	ADV
ijassa-419	234	5	as	as	SCONJ
ijassa-419	234	6	the	the	DET
ijassa-419	234	7	order	order	NOUN
ijassa-419	234	8	of	of	ADP
ijassa-419	234	9	the	the	DET
ijassa-419	234	10	elements	element	NOUN
ijassa-419	234	11	taking	take	VERB
ijassa-419	234	12	out	out	ADP
ijassa-419	234	13	of	of	ADP
ijassa-419	234	14	the	the	DET
ijassa-419	234	15	set	set	NOUN
ijassa-419	234	16	[	[	X
ijassa-419	234	17	s	s	X
ijassa-419	234	18	]	]	X
ijassa-419	234	19	is	be	AUX
ijassa-419	234	20	different	different	ADJ
ijassa-419	234	21	from	from	ADP
ijassa-419	234	22	that	that	PRON
ijassa-419	234	23	of	of	ADP
ijassa-419	234	24	φn(f	φn(f	NUM
ijassa-419	234	25	)	)	PUNCT
ijassa-419	234	26	,	,	PUNCT
ijassa-419	234	27	the	the	DET
ijassa-419	234	28	total	total	ADJ
ijassa-419	234	29	effect	effect	NOUN
ijassa-419	234	30	of	of	ADP
ijassa-419	234	31	these	these	DET
ijassa-419	234	32	elements	element	NOUN
ijassa-419	234	33	that	that	PRON
ijassa-419	234	34	are	be	AUX
ijassa-419	234	35	individually	individually	ADV
ijassa-419	234	36	taken	take	VERB
ijassa-419	234	37	out	out	ADP
ijassa-419	234	38	of	of	ADP
ijassa-419	234	39	[	[	X
ijassa-419	234	40	s	s	X
ijassa-419	234	41	]	]	X
ijassa-419	234	42	will	will	AUX
ijassa-419	234	43	not	not	PART
ijassa-419	234	44	reach	reach	VERB
ijassa-419	234	45	that	that	PRON
ijassa-419	234	46	of	of	ADP
ijassa-419	234	47	the	the	DET
ijassa-419	234	48	l2	l2	NOUN
ijassa-419	234	49	system	system	NOUN
ijassa-419	234	50	.	.	PUNCT
ijassa-419	235	1	therefore	therefore	ADV
ijassa-419	235	2	,	,	PUNCT
ijassa-419	235	3	the	the	DET
ijassa-419	235	4	whole	whole	NOUN
ijassa-419	235	5	possesses	possess	VERB
ijassa-419	235	6	a	a	DET
ijassa-419	235	7	functionality	functionality	NOUN
ijassa-419	235	8	the	the	DET
ijassa-419	235	9	sum	sum	NOUN
ijassa-419	235	10	of	of	ADP
ijassa-419	235	11	the	the	DET
ijassa-419	235	12	parts	part	NOUN
ijassa-419	235	13	does	do	AUX
ijassa-419	235	14	not	not	PART
ijassa-419	235	15	share	share	VERB
ijassa-419	235	16	.	.	PUNCT
ijassa-419	236	1	that	that	PRON
ijassa-419	236	2	is	is	ADV
ijassa-419	236	3	,	,	PUNCT
ijassa-419	236	4	the	the	DET
ijassa-419	236	5	function	function	NOUN
ijassa-419	236	6	of	of	ADP
ijassa-419	236	7	the	the	DET
ijassa-419	236	8	whole	whole	NOUN
ijassa-419	236	9	is	be	AUX
ijassa-419	236	10	greater	great	ADJ
ijassa-419	236	11	110	110	NUM
ijassa-419	236	12	xiaojun	xiaojun	PROPN
ijassa-419	236	13	duan	duan	PROPN
ijassa-419	236	14	:	:	PUNCT
ijassa-419	236	15	set	set	VERB
ijassa-419	236	16	-	-	PUNCT
ijassa-419	236	17	theoretic	theoretic	NOUN
ijassa-419	236	18	design	design	NOUN
ijassa-419	236	19	and	and	CCONJ
ijassa-419	236	20	analysis	analysis	NOUN
ijassa-419	236	21	of	of	ADP
ijassa-419	236	22	l	l	NOUN
ijassa-419	236	23	systems	system	NOUN
ijassa-419	236	24	than	than	ADP
ijassa-419	236	25	the	the	DET
ijassa-419	236	26	sum	sum	NOUN
ijassa-419	236	27	of	of	ADP
ijassa-419	236	28	the	the	DET
ijassa-419	236	29	parts	part	NOUN
ijassa-419	236	30	’	'	PUNCT
ijassa-419	236	31	functions	function	NOUN
ijassa-419	236	32	.	.	PUNCT
ijassa-419	237	1	in	in	ADP
ijassa-419	237	2	fact	fact	NOUN
ijassa-419	237	3	,	,	PUNCT
ijassa-419	237	4	the	the	DET
ijassa-419	237	5	essential	essential	ADJ
ijassa-419	237	6	difference	difference	NOUN
ijassa-419	237	7	between	between	ADP
ijassa-419	237	8	the	the	DET
ijassa-419	237	9	function	function	NOUN
ijassa-419	237	10	of	of	ADP
ijassa-419	237	11	the	the	DET
ijassa-419	237	12	whole	whole	NOUN
ijassa-419	237	13	and	and	CCONJ
ijassa-419	237	14	the	the	DET
ijassa-419	237	15	sum	sum	NOUN
ijassa-419	237	16	of	of	ADP
ijassa-419	237	17	parts	part	NOUN
ijassa-419	237	18	’	'	PUNCT
ijassa-419	237	19	functions	function	NOUN
ijassa-419	237	20	is	be	AUX
ijassa-419	237	21	that	that	SCONJ
ijassa-419	237	22	the	the	DET
ijassa-419	237	23	whole	whole	NOUN
ijassa-419	237	24	has	have	VERB
ijassa-419	237	25	an	an	DET
ijassa-419	237	26	organizational	organizational	ADJ
ijassa-419	237	27	effect	effect	NOUN
ijassa-419	237	28	,	,	PUNCT
ijassa-419	237	29	while	while	SCONJ
ijassa-419	237	30	the	the	DET
ijassa-419	237	31	sum	sum	NOUN
ijassa-419	237	32	of	of	ADP
ijassa-419	237	33	the	the	DET
ijassa-419	237	34	parts	part	NOUN
ijassa-419	237	35	does	do	AUX
ijassa-419	237	36	not	not	PART
ijassa-419	237	37	have	have	VERB
ijassa-419	237	38	.	.	PUNCT
ijassa-419	238	1	5	5	NUM
ijassa-419	238	2	the	the	DET
ijassa-419	238	3	design	design	NOUN
ijassa-419	238	4	of	of	ADP
ijassa-419	238	5	simple	simple	ADJ
ijassa-419	238	6	l	l	NOUN
ijassa-419	238	7	systems	system	NOUN
ijassa-419	238	8	5.1	5.1	NUM
ijassa-419	238	9	the	the	DET
ijassa-419	238	10	basic	basic	ADJ
ijassa-419	238	11	graph	graph	NOUN
ijassa-419	238	12	generation	generation	NOUN
ijassa-419	238	13	principle	principle	NOUN
ijassa-419	238	14	of	of	ADP
ijassa-419	238	15	simple	simple	ADJ
ijassa-419	238	16	l	l	NOUN
ijassa-419	238	17	systems	system	NOUN
ijassa-419	238	18	in	in	ADP
ijassa-419	238	19	essence	essence	NOUN
ijassa-419	238	20	each	each	DET
ijassa-419	238	21	l	l	NOUN
ijassa-419	238	22	system	system	NOUN
ijassa-419	238	23	is	be	AUX
ijassa-419	238	24	a	a	DET
ijassa-419	238	25	system	system	NOUN
ijassa-419	238	26	that	that	PRON
ijassa-419	238	27	rewrites	rewrite	VERB
ijassa-419	238	28	strings	string	NOUN
ijassa-419	238	29	of	of	ADP
ijassa-419	238	30	characters	character	NOUN
ijassa-419	238	31	.	.	PUNCT
ijassa-419	239	1	its	its	PRON
ijassa-419	239	2	working	work	VERB
ijassa-419	239	3	principle	principle	NOUN
ijassa-419	239	4	is	be	AUX
ijassa-419	239	5	quite	quite	ADV
ijassa-419	239	6	simple	simple	ADJ
ijassa-419	239	7	.	.	PUNCT
ijassa-419	240	1	if	if	SCONJ
ijassa-419	240	2	each	each	DET
ijassa-419	240	3	character	character	NOUN
ijassa-419	240	4	is	be	AUX
ijassa-419	240	5	seen	see	VERB
ijassa-419	240	6	as	as	ADP
ijassa-419	240	7	an	an	DET
ijassa-419	240	8	operation	operation	NOUN
ijassa-419	240	9	and	and	CCONJ
ijassa-419	240	10	different	different	ADJ
ijassa-419	240	11	characters	character	NOUN
ijassa-419	240	12	are	be	AUX
ijassa-419	240	13	seen	see	VERB
ijassa-419	240	14	as	as	ADP
ijassa-419	240	15	distinct	distinct	ADJ
ijassa-419	240	16	operations	operation	NOUN
ijassa-419	240	17	,	,	PUNCT
ijassa-419	240	18	then	then	ADV
ijassa-419	240	19	strings	string	NOUN
ijassa-419	240	20	of	of	ADP
ijassa-419	240	21	characters	character	NOUN
ijassa-419	240	22	can	can	AUX
ijassa-419	240	23	be	be	AUX
ijassa-419	240	24	employed	employ	VERB
ijassa-419	240	25	to	to	PART
ijassa-419	240	26	generate	generate	VERB
ijassa-419	240	27	various	various	ADJ
ijassa-419	240	28	fractal	fractal	ADJ
ijassa-419	240	29	figures	figure	NOUN
ijassa-419	240	30	.	.	PUNCT
ijassa-419	241	1	that	that	PRON
ijassa-419	241	2	is	be	AUX
ijassa-419	241	3	,	,	PUNCT
ijassa-419	241	4	as	as	ADV
ijassa-419	241	5	long	long	ADV
ijassa-419	241	6	as	as	SCONJ
ijassa-419	241	7	strings	string	NOUN
ijassa-419	241	8	of	of	ADP
ijassa-419	241	9	characters	character	NOUN
ijassa-419	241	10	can	can	AUX
ijassa-419	241	11	be	be	AUX
ijassa-419	241	12	generated	generate	VERB
ijassa-419	241	13	,	,	PUNCT
ijassa-419	241	14	one	one	PRON
ijassa-419	241	15	is	be	AUX
ijassa-419	241	16	able	able	ADJ
ijassa-419	241	17	to	to	PART
ijassa-419	241	18	produce	produce	VERB
ijassa-419	241	19	figures	figure	NOUN
ijassa-419	241	20	.	.	PUNCT
ijassa-419	242	1	the	the	DET
ijassa-419	242	2	character	character	NOUN
ijassa-419	242	3	strings	string	NOUN
ijassa-419	242	4	of	of	ADP
ijassa-419	242	5	l	l	NOUN
ijassa-419	242	6	systems	system	NOUN
ijassa-419	242	7	that	that	PRON
ijassa-419	242	8	are	be	AUX
ijassa-419	242	9	used	use	VERB
ijassa-419	242	10	to	to	PART
ijassa-419	242	11	generate	generate	VERB
ijassa-419	242	12	figures	figure	NOUN
ijassa-419	242	13	can	can	AUX
ijassa-419	242	14	be	be	AUX
ijassa-419	242	15	made	make	VERB
ijassa-419	242	16	up	up	ADP
ijassa-419	242	17	of	of	ADP
ijassa-419	242	18	any	any	DET
ijassa-419	242	19	recognizable	recognizable	ADJ
ijassa-419	242	20	symbols	symbol	NOUN
ijassa-419	242	21	.	.	PUNCT
ijassa-419	243	1	for	for	ADP
ijassa-419	243	2	example	example	NOUN
ijassa-419	243	3	,	,	PUNCT
ijassa-419	243	4	in	in	ADP
ijassa-419	243	5	the	the	DET
ijassa-419	243	6	design	design	NOUN
ijassa-419	243	7	of	of	ADP
ijassa-419	243	8	programs	program	NOUN
ijassa-419	243	9	,	,	PUNCT
ijassa-419	243	10	the	the	DET
ijassa-419	243	11	symbols	symbol	NOUN
ijassa-419	243	12	f	f	PROPN
ijassa-419	243	13	,	,	PUNCT
ijassa-419	243	14	-	-	PUNCT
ijassa-419	243	15	,	,	PUNCT
ijassa-419	243	16	and	and	CCONJ
ijassa-419	243	17	+	+	CCONJ
ijassa-419	243	18	can	can	AUX
ijassa-419	243	19	be	be	AUX
ijassa-419	243	20	used	use	VERB
ijassa-419	243	21	respectively	respectively	ADV
ijassa-419	243	22	so	so	SCONJ
ijassa-419	243	23	that	that	SCONJ
ijassa-419	243	24	“	"	PUNCT
ijassa-419	243	25	f	f	X
ijassa-419	243	26	”	"	PUNCT
ijassa-419	243	27	means	mean	VERB
ijassa-419	243	28	move	move	VERB
ijassa-419	243	29	one	one	NUM
ijassa-419	243	30	unit	unit	NOUN
ijassa-419	243	31	length	length	VERB
ijassa-419	243	32	forward	forward	ADV
ijassa-419	243	33	from	from	ADP
ijassa-419	243	34	the	the	DET
ijassa-419	243	35	current	current	ADJ
ijassa-419	243	36	location	location	NOUN
ijassa-419	243	37	and	and	CCONJ
ijassa-419	243	38	draw	draw	VERB
ijassa-419	243	39	a	a	DET
ijassa-419	243	40	segment	segment	NOUN
ijassa-419	243	41	,	,	PUNCT
ijassa-419	243	42	“	"	PUNCT
ijassa-419	243	43	-	-	PUNCT
ijassa-419	243	44	”	"	PUNCT
ijassa-419	243	45	stands	stand	VERB
ijassa-419	243	46	for	for	ADP
ijassa-419	243	47	turning	turn	VERB
ijassa-419	243	48	clockwise	clockwise	NOUN
ijassa-419	243	49	from	from	ADP
ijassa-419	243	50	the	the	DET
ijassa-419	243	51	current	current	ADJ
ijassa-419	243	52	direction	direction	NOUN
ijassa-419	243	53	a	a	DET
ijassa-419	243	54	pre	pre	ADJ
ijassa-419	243	55	-	-	ADJ
ijassa-419	243	56	determined	determined	ADJ
ijassa-419	243	57	angle	angle	NOUN
ijassa-419	243	58	,	,	PUNCT
ijassa-419	243	59	and	and	CCONJ
ijassa-419	243	60	“	"	PUNCT
ijassa-419	243	61	+	+	ADJ
ijassa-419	243	62	”	"	PUNCT
ijassa-419	243	63	turning	turn	VERB
ijassa-419	243	64	counterclockwise	counterclockwise	NOUN
ijassa-419	243	65	from	from	ADP
ijassa-419	243	66	the	the	DET
ijassa-419	243	67	current	current	ADJ
ijassa-419	243	68	direction	direction	NOUN
ijassa-419	243	69	another	another	DET
ijassa-419	243	70	pre	pre	ADJ
ijassa-419	243	71	-	-	ADJ
ijassa-419	243	72	determined	determined	ADJ
ijassa-419	243	73	angle	angle	NOUN
ijassa-419	243	74	.	.	PUNCT
ijassa-419	244	1	when	when	SCONJ
ijassa-419	244	2	generating	generate	VERB
ijassa-419	244	3	character	character	NOUN
ijassa-419	244	4	strings	string	NOUN
ijassa-419	244	5	,	,	PUNCT
ijassa-419	244	6	start	start	VERB
ijassa-419	244	7	from	from	ADP
ijassa-419	244	8	an	an	DET
ijassa-419	244	9	initial	initial	ADJ
ijassa-419	244	10	string	string	NOUN
ijassa-419	244	11	and	and	CCONJ
ijassa-419	244	12	replace	replace	VERB
ijassa-419	244	13	the	the	DET
ijassa-419	244	14	characters	character	NOUN
ijassa-419	244	15	of	of	ADP
ijassa-419	244	16	this	this	DET
ijassa-419	244	17	string	string	NOUN
ijassa-419	244	18	by	by	ADP
ijassa-419	244	19	substrings	substring	NOUN
ijassa-419	244	20	of	of	ADP
ijassa-419	244	21	characters	character	NOUN
ijassa-419	244	22	according	accord	VERB
ijassa-419	244	23	to	to	ADP
ijassa-419	244	24	the	the	DET
ijassa-419	244	25	predetermined	predetermine	VERB
ijassa-419	244	26	rules	rule	NOUN
ijassa-419	244	27	.	.	PUNCT
ijassa-419	245	1	that	that	PRON
ijassa-419	245	2	completes	complete	VERB
ijassa-419	245	3	the	the	DET
ijassa-419	245	4	first	first	ADJ
ijassa-419	245	5	iteration	iteration	NOUN
ijassa-419	245	6	.	.	PUNCT
ijassa-419	246	1	then	then	ADV
ijassa-419	246	2	,	,	PUNCT
ijassa-419	246	3	treat	treat	VERB
ijassa-419	246	4	the	the	DET
ijassa-419	246	5	resultant	resultant	NOUN
ijassa-419	246	6	character	character	NOUN
ijassa-419	246	7	string	string	NOUN
ijassa-419	246	8	from	from	ADP
ijassa-419	246	9	the	the	DET
ijassa-419	246	10	first	first	ADJ
ijassa-419	246	11	iteration	iteration	NOUN
ijassa-419	246	12	as	as	ADP
ijassa-419	246	13	the	the	DET
ijassa-419	246	14	mother	mother	NOUN
ijassa-419	246	15	string	string	NOUN
ijassa-419	246	16	and	and	CCONJ
ijassa-419	246	17	replace	replace	VERB
ijassa-419	246	18	each	each	DET
ijassa-419	246	19	character	character	NOUN
ijassa-419	246	20	in	in	ADP
ijassa-419	246	21	this	this	DET
ijassa-419	246	22	string	string	NOUN
ijassa-419	246	23	by	by	ADP
ijassa-419	246	24	strings	string	NOUN
ijassa-419	246	25	determined	determine	VERB
ijassa-419	246	26	by	by	ADP
ijassa-419	246	27	the	the	DET
ijassa-419	246	28	rules	rule	NOUN
ijassa-419	246	29	.	.	PUNCT
ijassa-419	247	1	by	by	ADP
ijassa-419	247	2	continuing	continue	VERB
ijassa-419	247	3	this	this	DET
ijassa-419	247	4	procedure	procedure	NOUN
ijassa-419	247	5	,	,	PUNCT
ijassa-419	247	6	one	one	PRON
ijassa-419	247	7	can	can	AUX
ijassa-419	247	8	finish	finish	VERB
ijassa-419	247	9	the	the	DET
ijassa-419	247	10	required	require	VERB
ijassa-419	247	11	iterations	iteration	NOUN
ijassa-419	247	12	of	of	ADP
ijassa-419	247	13	an	an	DET
ijassa-419	247	14	l	l	NOUN
ijassa-419	247	15	system	system	NOUN
ijassa-419	247	16	,	,	PUNCT
ijassa-419	247	17	where	where	SCONJ
ijassa-419	247	18	the	the	DET
ijassa-419	247	19	length	length	NOUN
ijassa-419	247	20	of	of	ADP
ijassa-419	247	21	the	the	DET
ijassa-419	247	22	resultant	resultant	NOUN
ijassa-419	247	23	string	string	NOUN
ijassa-419	247	24	is	be	AUX
ijassa-419	247	25	controlled	control	VERB
ijassa-419	247	26	by	by	ADP
ijassa-419	247	27	the	the	DET
ijassa-419	247	28	number	number	NOUN
ijassa-419	247	29	of	of	ADP
ijassa-419	247	30	iterations	iteration	NOUN
ijassa-419	247	31	.	.	PUNCT
ijassa-419	248	1	5.2	5.2	NUM
ijassa-419	248	2	a	a	DET
ijassa-419	248	3	fractal	fractal	ADJ
ijassa-419	248	4	structure	structure	NOUN
ijassa-419	248	5	design	design	NOUN
ijassa-419	248	6	based	base	VERB
ijassa-419	248	7	on	on	ADP
ijassa-419	248	8	d0l	d0l	PROPN
ijassa-419	248	9	in	in	ADP
ijassa-419	248	10	terms	term	NOUN
ijassa-419	248	11	of	of	ADP
ijassa-419	248	12	a	a	DET
ijassa-419	248	13	tree	tree	NOUN
ijassa-419	248	14	,	,	PUNCT
ijassa-419	248	15	it	it	PRON
ijassa-419	248	16	stands	stand	VERB
ijassa-419	248	17	for	for	ADP
ijassa-419	248	18	a	a	DET
ijassa-419	248	19	fractal	fractal	ADJ
ijassa-419	248	20	structure	structure	NOUN
ijassa-419	248	21	.	.	PUNCT
ijassa-419	249	1	in	in	ADP
ijassa-419	249	2	particular	particular	ADJ
ijassa-419	249	3	,	,	PUNCT
ijassa-419	249	4	each	each	DET
ijassa-419	249	5	trunk	trunk	NOUN
ijassa-419	249	6	carries	carry	VERB
ijassa-419	249	7	a	a	DET
ijassa-419	249	8	large	large	ADJ
ijassa-419	249	9	amount	amount	NOUN
ijassa-419	249	10	of	of	ADP
ijassa-419	249	11	branches	branch	NOUN
ijassa-419	249	12	,	,	PUNCT
ijassa-419	249	13	and	and	CCONJ
ijassa-419	249	14	each	each	DET
ijassa-419	249	15	branch	branch	NOUN
ijassa-419	249	16	has	have	VERB
ijassa-419	249	17	an	an	DET
ijassa-419	249	18	end	end	NOUN
ijassa-419	249	19	point	point	NOUN
ijassa-419	249	20	,	,	PUNCT
ijassa-419	249	21	representing	represent	VERB
ijassa-419	249	22	a	a	DET
ijassa-419	249	23	figure	figure	NOUN
ijassa-419	249	24	with	with	ADP
ijassa-419	249	25	one	one	NUM
ijassa-419	249	26	staring	stare	VERB
ijassa-419	249	27	point	point	NOUN
ijassa-419	249	28	and	and	CCONJ
ijassa-419	249	29	many	many	ADJ
ijassa-419	249	30	ending	ending	NOUN
ijassa-419	249	31	points	point	NOUN
ijassa-419	249	32	.	.	PUNCT
ijassa-419	250	1	this	this	DET
ijassa-419	250	2	fact	fact	NOUN
ijassa-419	250	3	implies	imply	VERB
ijassa-419	250	4	that	that	SCONJ
ijassa-419	250	5	when	when	SCONJ
ijassa-419	250	6	one	one	PRON
ijassa-419	250	7	draws	draw	VERB
ijassa-419	250	8	a	a	DET
ijassa-419	250	9	branch	branch	NOUN
ijassa-419	250	10	to	to	ADP
ijassa-419	250	11	its	its	PRON
ijassa-419	250	12	end	end	NOUN
ijassa-419	250	13	,	,	PUNCT
ijassa-419	250	14	he	he	PRON
ijassa-419	250	15	has	have	VERB
ijassa-419	250	16	to	to	PART
ijassa-419	250	17	return	return	VERB
ijassa-419	250	18	his	his	PRON
ijassa-419	250	19	drawing	draw	VERB
ijassa-419	250	20	pen	pen	NOUN
ijassa-419	250	21	to	to	PART
ijassa-419	250	22	draw	draw	VERB
ijassa-419	250	23	other	other	ADJ
ijassa-419	250	24	structures	structure	NOUN
ijassa-419	250	25	.	.	PUNCT
ijassa-419	251	1	let	let	VERB
ijassa-419	251	2	us	we	PRON
ijassa-419	251	3	take	take	VERB
ijassa-419	251	4	the	the	DET
ijassa-419	251	5	following	follow	VERB
ijassa-419	251	6	conventions	convention	NOUN
ijassa-419	251	7	:	:	PUNCT
ijassa-419	251	8	“	"	PUNCT
ijassa-419	251	9	f	f	X
ijassa-419	251	10	”	"	PUNCT
ijassa-419	251	11	stands	stand	VERB
ijassa-419	251	12	for	for	ADP
ijassa-419	251	13	moving	move	VERB
ijassa-419	251	14	forward	forward	ADV
ijassa-419	251	15	a	a	DET
ijassa-419	251	16	unit	unit	NOUN
ijassa-419	251	17	length	length	NOUN
ijassa-419	251	18	1	1	NUM
ijassa-419	251	19	,	,	PUNCT
ijassa-419	251	20	and	and	CCONJ
ijassa-419	251	21	“	"	PUNCT
ijassa-419	251	22	+	+	ADJ
ijassa-419	251	23	”	"	PUNCT
ijassa-419	251	24	turning	turn	VERB
ijassa-419	251	25	an	an	DET
ijassa-419	251	26	angle	angle	NOUN
ijassa-419	251	27	of	of	ADP
ijassa-419	251	28	π/8	π/8	NOUN
ijassa-419	251	29	clockwisely	clockwisely	ADV
ijassa-419	251	30	,	,	PUNCT
ijassa-419	251	31	“	"	PUNCT
ijassa-419	251	32	-	-	INTJ
ijassa-419	251	33	”	"	PUNCT
ijassa-419	251	34	turning	turn	VERB
ijassa-419	251	35	an	an	DET
ijassa-419	251	36	angle	angle	NOUN
ijassa-419	251	37	of	of	ADP
ijassa-419	251	38	π/8	π/8	NOUN
ijassa-419	251	39	counterclockwisely	counterclockwisely	ADV
ijassa-419	251	40	,	,	PUNCT
ijassa-419	251	41	and	and	CCONJ
ijassa-419	251	42	the	the	DET
ijassa-419	251	43	characters	character	NOUN
ijassa-419	251	44	within	within	ADP
ijassa-419	251	45	“	"	PUNCT
ijassa-419	251	46	[	[	PUNCT
ijassa-419	251	47	]	]	X
ijassa-419	251	48	”	"	PUNCT
ijassa-419	251	49	represent	represent	VERB
ijassa-419	251	50	a	a	DET
ijassa-419	251	51	branch	branch	NOUN
ijassa-419	251	52	;	;	PUNCT
ijassa-419	251	53	when	when	SCONJ
ijassa-419	251	54	the	the	DET
ijassa-419	251	55	characters	character	NOUN
ijassa-419	251	56	within	within	ADP
ijassa-419	251	57	a	a	DET
ijassa-419	251	58	pair	pair	NOUN
ijassa-419	251	59	of	of	ADP
ijassa-419	251	60	[	[	PUNCT
ijassa-419	251	61	]	]	X
ijassa-419	251	62	are	be	AUX
ijassa-419	251	63	implemented	implement	VERB
ijassa-419	251	64	,	,	PUNCT
ijassa-419	251	65	return	return	VERB
ijassa-419	251	66	to	to	ADP
ijassa-419	251	67	the	the	DET
ijassa-419	251	68	position	position	NOUN
ijassa-419	251	69	right	right	ADV
ijassa-419	251	70	before	before	ADP
ijassa-419	251	71	“	"	PUNCT
ijassa-419	251	72	[	[	X
ijassa-419	251	73	”	"	PUNCT
ijassa-419	251	74	and	and	CCONJ
ijassa-419	251	75	maintain	maintain	VERB
ijassa-419	251	76	the	the	DET
ijassa-419	251	77	original	original	ADJ
ijassa-419	251	78	direction	direction	NOUN
ijassa-419	251	79	,	,	PUNCT
ijassa-419	251	80	and	and	CCONJ
ijassa-419	251	81	then	then	ADV
ijassa-419	251	82	carry	carry	VERB
ijassa-419	251	83	out	out	ADP
ijassa-419	251	84	the	the	DET
ijassa-419	251	85	characters	character	NOUN
ijassa-419	251	86	after	after	ADP
ijassa-419	251	87	“	"	PUNCT
ijassa-419	251	88	]	]	X
ijassa-419	251	89	”	"	PUNCT
ijassa-419	251	90	.	.	PUNCT
ijassa-419	252	1	assume	assume	VERB
ijassa-419	252	2	that	that	SCONJ
ijassa-419	252	3	the	the	DET
ijassa-419	252	4	starting	starting	NOUN
ijassa-419	252	5	point	point	NOUN
ijassa-419	252	6	is	be	AUX
ijassa-419	252	7	at	at	ADP
ijassa-419	252	8	(	(	PUNCT
ijassa-419	252	9	0,0	0,0	NOUN
ijassa-419	252	10	)	)	PUNCT
ijassa-419	252	11	on	on	ADP
ijassa-419	252	12	the	the	DET
ijassa-419	252	13	complex	complex	ADJ
ijassa-419	252	14	plane	plane	NOUN
ijassa-419	252	15	and	and	CCONJ
ijassa-419	252	16	the	the	DET
ijassa-419	252	17	initial	initial	ADJ
ijassa-419	252	18	direction	direction	NOUN
ijassa-419	252	19	at	at	ADP
ijassa-419	252	20	π/2	π/2	PROPN
ijassa-419	252	21	.	.	PUNCT
ijassa-419	253	1	now	now	ADV
ijassa-419	253	2	,	,	PUNCT
ijassa-419	253	3	we	we	PRON
ijassa-419	253	4	design	design	VERB
ijassa-419	253	5	a	a	DET
ijassa-419	253	6	d0l	d0l	NOUN
ijassa-419	253	7	system	system	NOUN
ijassa-419	253	8	g1	g1	NOUN
ijassa-419	253	9	=	=	PUNCT
ijassa-419	253	10	⟨s1	⟨s1	PROPN
ijassa-419	253	11	,	,	PUNCT
ijassa-419	253	12	ω1	ω1	PROPN
ijassa-419	253	13	,	,	PUNCT
ijassa-419	253	14	φ1⟩	φ1⟩	ADV
ijassa-419	253	15	as	as	SCONJ
ijassa-419	253	16	follows	follow	VERB
ijassa-419	253	17	:	:	PUNCT
ijassa-419	254	1	s1	s1	PROPN
ijassa-419	254	2	=	=	PUNCT
ijassa-419	254	3	{	{	PUNCT
ijassa-419	254	4	f,+,−	f,+,−	PROPN
ijassa-419	254	5	,	,	PUNCT
ijassa-419	254	6	[	[	X
ijassa-419	254	7	,	,	PUNCT
ijassa-419	254	8	]	]	X
ijassa-419	254	9	}	}	PUNCT
ijassa-419	254	10	;	;	PUNCT
ijassa-419	254	11	ω1	ω1	PROPN
ijassa-419	254	12	=	=	SYM
ijassa-419	254	13	f	f	PROPN
ijassa-419	254	14	;	;	PUNCT
ijassa-419	254	15	and	and	CCONJ
ijassa-419	254	16	advances	advance	NOUN
ijassa-419	254	17	in	in	ADP
ijassa-419	254	18	systems	system	NOUN
ijassa-419	254	19	science	science	NOUN
ijassa-419	254	20	and	and	CCONJ
ijassa-419	254	21	applications	application	NOUN
ijassa-419	254	22	(	(	PUNCT
ijassa-419	254	23	2013	2013	NUM
ijassa-419	254	24	)	)	PUNCT
ijassa-419	254	25	vol.13	vol.13	NOUN
ijassa-419	254	26	no.2	no.2	PROPN
ijassa-419	254	27	111	111	NUM
ijassa-419	254	28	fig.2	fig.2	PROPN
ijassa-419	254	29	the	the	DET
ijassa-419	254	30	fractal	fractal	ADJ
ijassa-419	254	31	structures	structure	NOUN
ijassa-419	254	32	:	:	PUNCT
ijassa-419	254	33	a	a	DET
ijassa-419	254	34	tree	tree	NOUN
ijassa-419	254	35	dancing	dance	VERB
ijassa-419	254	36	in	in	ADP
ijassa-419	254	37	breeze	breeze	NOUN
ijassa-419	254	38	(	(	PUNCT
ijassa-419	254	39	of	of	ADP
ijassa-419	254	40	different	different	ADJ
ijassa-419	254	41	iteration	iteration	NOUN
ijassa-419	254	42	steps	step	NOUN
ijassa-419	254	43	)	)	PUNCT
ijassa-419	254	44	fig.3	fig.3	PROPN
ijassa-419	254	45	the	the	DET
ijassa-419	254	46	fractal	fractal	ADJ
ijassa-419	254	47	structures	structure	NOUN
ijassa-419	254	48	:	:	PUNCT
ijassa-419	254	49	a	a	DET
ijassa-419	254	50	standing	stand	VERB
ijassa-419	254	51	tree	tree	NOUN
ijassa-419	254	52	(	(	PUNCT
ijassa-419	254	53	n	n	NOUN
ijassa-419	254	54	=	=	SYM
ijassa-419	254	55	5	5	NUM
ijassa-419	254	56	,	,	PUNCT
ijassa-419	254	57	α	α	NOUN
ijassa-419	254	58	=	=	SYM
ijassa-419	254	59	π/8	π/8	NUM
ijassa-419	254	60	,	,	PUNCT
ijassa-419	254	61	with	with	ADP
ijassa-419	254	62	design	design	NOUN
ijassa-419	254	63	form	form	NOUN
ijassa-419	254	64	f→ff+[+f[−ff−]−f]−	f→ff+[+f[−ff−]−f]−	NOUN
ijassa-419	255	1	[	[	X
ijassa-419	255	2	−f[−ff+]f	−f[−ff+]f	NOUN
ijassa-419	255	3	]	]	X
ijassa-419	255	4	)	)	PUNCT
ijassa-419	255	5	112	112	NUM
ijassa-419	255	6	xiaojun	xiaojun	PROPN
ijassa-419	255	7	duan	duan	PROPN
ijassa-419	255	8	:	:	PUNCT
ijassa-419	255	9	set	set	VERB
ijassa-419	255	10	-	-	PUNCT
ijassa-419	255	11	theoretic	theoretic	NOUN
ijassa-419	255	12	design	design	NOUN
ijassa-419	255	13	and	and	CCONJ
ijassa-419	255	14	analysis	analysis	NOUN
ijassa-419	255	15	of	of	ADP
ijassa-419	255	16	l	l	NOUN
ijassa-419	255	17	systems	system	NOUN
ijassa-419	255	18	φ1	φ1	NOUN
ijassa-419	255	19	=	=	PUNCT
ijassa-419	255	20			NOUN
ijassa-419	255	21	f	f	PROPN
ijassa-419	256	1	→	→	PUNCT
ijassa-419	256	2	ff	ff	NOUN
ijassa-419	257	1	+	+	CCONJ
ijassa-419	257	2	[	[	X
ijassa-419	257	3	+	+	ADJ
ijassa-419	257	4	f−	f−	PROPN
ijassa-419	257	5	f−	f−	NOUN
ijassa-419	257	6	f]−	f]−	NOUN
ijassa-419	258	1	[	[	X
ijassa-419	258	2	−	−	X
ijassa-419	258	3	f	f	X
ijassa-419	258	4	+	+	NUM
ijassa-419	258	5	f	f	PROPN
ijassa-419	259	1	+	+	CCONJ
ijassa-419	259	2	f	f	X
ijassa-419	259	3	]	]	X
ijassa-419	259	4	+	+	CCONJ
ijassa-419	259	5	→	→	SYM
ijassa-419	259	6	+	+	NUM
ijassa-419	259	7	−	−	PROPN
ijassa-419	259	8	→	→	SYM
ijassa-419	259	9	−	−	PROPN
ijassa-419	259	10	[	[	PUNCT
ijassa-419	259	11	→	→	X
ijassa-419	259	12	[	[	X
ijassa-419	259	13	]	]	X
ijassa-419	259	14	→	→	X
ijassa-419	259	15	]	]	X
ijassa-419	259	16	then	then	ADV
ijassa-419	259	17	,	,	PUNCT
ijassa-419	259	18	we	we	PRON
ijassa-419	259	19	can	can	AUX
ijassa-419	259	20	produce	produce	VERB
ijassa-419	259	21	the	the	DET
ijassa-419	259	22	fractal	fractal	ADJ
ijassa-419	259	23	structures	structure	NOUN
ijassa-419	259	24	as	as	SCONJ
ijassa-419	259	25	shown	show	VERB
ijassa-419	259	26	in	in	ADP
ijassa-419	259	27	fig.2	fig.2	PROPN
ijassa-419	259	28	.	.	PUNCT
ijassa-419	260	1	we	we	PRON
ijassa-419	260	2	can	can	AUX
ijassa-419	260	3	obtain	obtain	VERB
ijassa-419	260	4	other	other	ADJ
ijassa-419	260	5	illustrations	illustration	NOUN
ijassa-419	260	6	by	by	ADP
ijassa-419	260	7	just	just	ADV
ijassa-419	260	8	changing	change	VERB
ijassa-419	260	9	the	the	DET
ijassa-419	260	10	design	design	NOUN
ijassa-419	260	11	forms	form	NOUN
ijassa-419	260	12	as	as	ADP
ijassa-419	260	13	fig.3	fig.3	PROPN
ijassa-419	260	14	-	-	SYM
ijassa-419	260	15	5	5	NUM
ijassa-419	260	16	.	.	PUNCT
ijassa-419	261	1	fig.4	fig.4	VERB
ijassa-419	261	2	the	the	DET
ijassa-419	261	3	fractal	fractal	ADJ
ijassa-419	261	4	structures	structure	NOUN
ijassa-419	261	5	:	:	PUNCT
ijassa-419	261	6	a	a	DET
ijassa-419	261	7	tree	tree	NOUN
ijassa-419	261	8	towards	towards	ADP
ijassa-419	261	9	sun	sun	NOUN
ijassa-419	261	10	(	(	PUNCT
ijassa-419	261	11	n	n	NOUN
ijassa-419	261	12	=	=	SYM
ijassa-419	261	13	5	5	NUM
ijassa-419	261	14	,	,	PUNCT
ijassa-419	261	15	α	α	NOUN
ijassa-419	261	16	=	=	SYM
ijassa-419	261	17	π/8	π/8	NUM
ijassa-419	261	18	,	,	PUNCT
ijassa-419	261	19	with	with	ADP
ijassa-419	261	20	design	design	NOUN
ijassa-419	261	21	form	form	NOUN
ijassa-419	261	22	f→ff+[+f[−f−f]−f]−	f→ff+[+f[−f−f]−f]−	PUNCT
ijassa-419	262	1	[	[	X
ijassa-419	262	2	−f[f−ff+f]f	−f[f−ff+f]f	NUM
ijassa-419	262	3	]	]	X
ijassa-419	262	4	)	)	PUNCT
ijassa-419	262	5	fig.5	fig.5	VERB
ijassa-419	262	6	the	the	DET
ijassa-419	262	7	fractal	fractal	ADJ
ijassa-419	262	8	structures	structure	NOUN
ijassa-419	262	9	:	:	PUNCT
ijassa-419	262	10	a	a	DET
ijassa-419	262	11	floating	float	VERB
ijassa-419	262	12	grass	grass	NOUN
ijassa-419	262	13	ball	ball	NOUN
ijassa-419	262	14	(	(	PUNCT
ijassa-419	262	15	n	n	NOUN
ijassa-419	262	16	=	=	SYM
ijassa-419	262	17	4	4	NUM
ijassa-419	262	18	,	,	PUNCT
ijassa-419	262	19	α	α	NOUN
ijassa-419	262	20	=	=	SYM
ijassa-419	262	21	π/8	π/8	NUM
ijassa-419	262	22	,	,	PUNCT
ijassa-419	262	23	with	with	ADP
ijassa-419	262	24	design	design	NOUN
ijassa-419	262	25	form	form	NOUN
ijassa-419	262	26	f	f	X
ijassa-419	262	27	→ff+[[+f−ff−f]−	→ff+[[+f−ff−f]−	NOUN
ijassa-419	263	1	[	[	X
ijassa-419	263	2	−f+ff+f	−f+ff+f	NUM
ijassa-419	263	3	]	]	X
ijassa-419	263	4	]	]	PUNCT
ijassa-419	263	5	)	)	PUNCT
ijassa-419	263	6	5.3	5.3	NUM
ijassa-419	263	7	a	a	DET
ijassa-419	263	8	fractal	fractal	ADJ
ijassa-419	263	9	structure	structure	NOUN
ijassa-419	263	10	design	design	NOUN
ijassa-419	263	11	based	base	VERB
ijassa-419	263	12	on	on	ADP
ijassa-419	263	13	r0l	r0l	PROPN
ijassa-419	263	14	systems	system	NOUN
ijassa-419	263	15	in	in	ADP
ijassa-419	263	16	nature	nature	NOUN
ijassa-419	263	17	,	,	PUNCT
ijassa-419	263	18	the	the	DET
ijassa-419	263	19	forms	form	NOUN
ijassa-419	263	20	plants	plant	NOUN
ijassa-419	263	21	take	take	VERB
ijassa-419	263	22	are	be	AUX
ijassa-419	263	23	not	not	PART
ijassa-419	263	24	invariant	invariant	ADJ
ijassa-419	263	25	.	.	PUNCT
ijassa-419	264	1	even	even	ADV
ijassa-419	264	2	for	for	ADP
ijassa-419	264	3	the	the	DET
ijassa-419	264	4	same	same	ADJ
ijassa-419	264	5	kinds	kind	NOUN
ijassa-419	264	6	of	of	ADP
ijassa-419	264	7	plants	plant	NOUN
ijassa-419	264	8	,	,	PUNCT
ijassa-419	264	9	their	their	PRON
ijassa-419	264	10	shapes	shape	NOUN
ijassa-419	264	11	can	can	AUX
ijassa-419	264	12	vary	vary	VERB
ijassa-419	264	13	from	from	ADP
ijassa-419	264	14	one	one	NUM
ijassa-419	264	15	plant	plant	NOUN
ijassa-419	264	16	to	to	ADP
ijassa-419	264	17	another	another	PRON
ijassa-419	264	18	.	.	PUNCT
ijassa-419	265	1	such	such	ADJ
ijassa-419	265	2	varieties	variety	NOUN
ijassa-419	265	3	are	be	AUX
ijassa-419	265	4	caused	cause	VERB
ijassa-419	265	5	advances	advance	NOUN
ijassa-419	265	6	in	in	ADP
ijassa-419	265	7	systems	system	NOUN
ijassa-419	265	8	science	science	NOUN
ijassa-419	265	9	and	and	CCONJ
ijassa-419	265	10	applications	application	NOUN
ijassa-419	265	11	(	(	PUNCT
ijassa-419	265	12	2013	2013	NUM
ijassa-419	265	13	)	)	PUNCT
ijassa-419	265	14	vol.13	vol.13	NOUN
ijassa-419	265	15	no.2	no.2	PROPN
ijassa-419	265	16	113	113	NUM
ijassa-419	265	17	by	by	ADP
ijassa-419	265	18	the	the	DET
ijassa-419	265	19	effects	effect	NOUN
ijassa-419	265	20	of	of	ADP
ijassa-419	265	21	the	the	DET
ijassa-419	265	22	environment	environment	NOUN
ijassa-419	265	23	.	.	PUNCT
ijassa-419	266	1	fig.6	fig.6	VERB
ijassa-419	266	2	the	the	DET
ijassa-419	266	3	different	different	ADJ
ijassa-419	266	4	fractal	fractal	ADJ
ijassa-419	266	5	structures	structure	NOUN
ijassa-419	266	6	for	for	ADP
ijassa-419	266	7	a	a	DET
ijassa-419	266	8	r0l	r0l	PROPN
ijassa-419	266	9	system	system	NOUN
ijassa-419	266	10	with	with	ADP
ijassa-419	266	11	each	each	DET
ijassa-419	266	12	iteration	iteration	NOUN
ijassa-419	266	13	unchanged	unchanged	ADJ
ijassa-419	266	14	(	(	PUNCT
ijassa-419	266	15	n	n	NOUN
ijassa-419	266	16	=	=	SYM
ijassa-419	266	17	4	4	NUM
ijassa-419	266	18	,	,	PUNCT
ijassa-419	266	19	α	α	NOUN
ijassa-419	266	20	=	=	SYM
ijassa-419	266	21	π/16	π/16	NOUN
ijassa-419	266	22	)	)	PUNCT
ijassa-419	266	23	in	in	ADP
ijassa-419	266	24	terms	term	NOUN
ijassa-419	266	25	of	of	ADP
ijassa-419	266	26	the	the	DET
ijassa-419	266	27	simulation	simulation	NOUN
ijassa-419	266	28	effects	effect	NOUN
ijassa-419	266	29	of	of	ADP
ijassa-419	266	30	plants	plant	NOUN
ijassa-419	266	31	,	,	PUNCT
ijassa-419	266	32	the	the	DET
ijassa-419	266	33	figures	figure	NOUN
ijassa-419	266	34	created	create	VERB
ijassa-419	266	35	by	by	ADP
ijassa-419	266	36	using	use	VERB
ijassa-419	266	37	d0l	d0l	PROPN
ijassa-419	266	38	systems	system	NOUN
ijassa-419	266	39	seem	seem	VERB
ijassa-419	266	40	to	to	PART
ijassa-419	266	41	be	be	AUX
ijassa-419	266	42	quite	quite	ADV
ijassa-419	266	43	stiff	stiff	ADJ
ijassa-419	266	44	.	.	PUNCT
ijassa-419	267	1	under	under	ADP
ijassa-419	267	2	the	the	DET
ijassa-419	267	3	prerequisite	prerequisite	NOUN
ijassa-419	267	4	of	of	ADP
ijassa-419	267	5	maintaining	maintain	VERB
ijassa-419	267	6	the	the	DET
ijassa-419	267	7	main	main	ADJ
ijassa-419	267	8	characteristics	characteristic	NOUN
ijassa-419	267	9	of	of	ADP
ijassa-419	267	10	plants	plant	NOUN
ijassa-419	267	11	,	,	PUNCT
ijassa-419	267	12	in	in	ADP
ijassa-419	267	13	order	order	NOUN
ijassa-419	267	14	to	to	PART
ijassa-419	267	15	generate	generate	VERB
ijassa-419	267	16	varieties	variety	NOUN
ijassa-419	267	17	on	on	ADP
ijassa-419	267	18	the	the	DET
ijassa-419	267	19	details	detail	NOUN
ijassa-419	267	20	,	,	PUNCT
ijassa-419	267	21	we	we	PRON
ijassa-419	267	22	can	can	AUX
ijassa-419	267	23	utilize	utilize	VERB
ijassa-419	267	24	the	the	DET
ijassa-419	267	25	plants	plant	NOUN
ijassa-419	267	26	?	?	PUNCT
ijassa-419	268	1	structures	structure	NOUN
ijassa-419	268	2	produced	produce	VERB
ijassa-419	268	3	out	out	ADP
ijassa-419	268	4	of	of	ADP
ijassa-419	268	5	r0l	r0l	PROPN
ijassa-419	268	6	systems	system	NOUN
ijassa-419	268	7	.	.	PUNCT
ijassa-419	269	1	the	the	DET
ijassa-419	269	2	advantage	advantage	NOUN
ijassa-419	269	3	of	of	ADP
ijassa-419	269	4	these	these	DET
ijassa-419	269	5	figures	figure	NOUN
ijassa-419	269	6	is	be	AUX
ijassa-419	269	7	that	that	SCONJ
ijassa-419	269	8	these	these	DET
ijassa-419	269	9	simulated	simulate	VERB
ijassa-419	269	10	plants	plant	NOUN
ijassa-419	269	11	are	be	AUX
ijassa-419	269	12	more	more	ADV
ijassa-419	269	13	real	real	ADJ
ijassa-419	269	14	-	-	PUNCT
ijassa-419	269	15	life	life	NOUN
ijassa-419	269	16	like	like	ADP
ijassa-419	269	17	and	and	CCONJ
ijassa-419	269	18	much	much	ADV
ijassa-419	269	19	closer	close	ADJ
ijassa-419	269	20	to	to	ADP
ijassa-419	269	21	the	the	DET
ijassa-419	269	22	true	true	ADJ
ijassa-419	269	23	forms	form	NOUN
ijassa-419	269	24	of	of	ADP
ijassa-419	269	25	natural	natural	ADJ
ijassa-419	269	26	plants	plant	NOUN
ijassa-419	269	27	.	.	PUNCT
ijassa-419	270	1	to	to	ADP
ijassa-419	270	2	this	this	DET
ijassa-419	270	3	end	end	NOUN
ijassa-419	270	4	,	,	PUNCT
ijassa-419	270	5	let	let	VERB
ijassa-419	270	6	us	we	PRON
ijassa-419	270	7	design	design	VERB
ijassa-419	270	8	a	a	DET
ijassa-419	270	9	r0l	r0l	PROPN
ijassa-419	270	10	system	system	NOUN
ijassa-419	270	11	g2	g2	PROPN
ijassa-419	270	12	=	=	PUNCT
ijassa-419	270	13	⟨s1	⟨s1	PROPN
ijassa-419	270	14	,	,	PUNCT
ijassa-419	270	15	ω1,φ	ω1,φ	PROPN
ijassa-419	270	16	,	,	PUNCT
ijassa-419	270	17	π⟩	π⟩	NOUN
ijassa-419	270	18	as	as	SCONJ
ijassa-419	270	19	follows	follow	VERB
ijassa-419	270	20	:	:	PUNCT
ijassa-419	271	1	s1	s1	NOUN
ijassa-419	271	2	=	=	PUNCT
ijassa-419	271	3	{	{	PUNCT
ijassa-419	271	4	f,+,−	f,+,−	PROPN
ijassa-419	271	5	,	,	PUNCT
ijassa-419	271	6	[	[	X
ijassa-419	271	7	,	,	PUNCT
ijassa-419	271	8	]	]	X
ijassa-419	271	9	}	}	PUNCT
ijassa-419	271	10	;	;	PUNCT
ijassa-419	271	11	ω1	ω1	PROPN
ijassa-419	271	12	=	=	SYM
ijassa-419	271	13	f	f	PROPN
ijassa-419	271	14	;	;	PUNCT
ijassa-419	271	15	φ	φ	PROPN
ijassa-419	271	16	=	=	SYM
ijassa-419	271	17	{	{	PUNCT
ijassa-419	271	18	φ1	φ1	PROPN
ijassa-419	271	19	,	,	PUNCT
ijassa-419	271	20	φ2	φ2	PROPN
ijassa-419	271	21	,	,	PUNCT
ijassa-419	271	22	φ3	φ3	NOUN
ijassa-419	271	23	}	}	PUNCT
ijassa-419	271	24	;	;	PUNCT
ijassa-419	271	25	where	where	SCONJ
ijassa-419	271	26	φ1	φ1	NOUN
ijassa-419	271	27	=	=	PUNCT
ijassa-419	271	28			NOUN
ijassa-419	271	29	f	f	X
ijassa-419	271	30	→	→	SYM
ijassa-419	271	31	f[+f]f[−	f[+f]f[−	ADJ
ijassa-419	271	32	f]f	f]f	NOUN
ijassa-419	271	33	+	+	X
ijassa-419	271	34	→	→	SYM
ijassa-419	271	35	+	+	NUM
ijassa-419	271	36	−	−	PROPN
ijassa-419	271	37	→	→	SYM
ijassa-419	271	38	−	−	PROPN
ijassa-419	271	39	[	[	PUNCT
ijassa-419	271	40	→	→	X
ijassa-419	271	41	[	[	X
ijassa-419	271	42	]	]	X
ijassa-419	271	43	→	→	X
ijassa-419	271	44	]	]	X
ijassa-419	271	45	,	,	PUNCT
ijassa-419	271	46	φ2	φ2	NOUN
ijassa-419	271	47	=	=	PUNCT
ijassa-419	271	48			NOUN
ijassa-419	271	49	f	f	X
ijassa-419	271	50	→	→	SYM
ijassa-419	271	51	f[+f]f[−	f[+f]f[−	ADJ
ijassa-419	271	52	f[+f	f[+f	X
ijassa-419	271	53	]	]	X
ijassa-419	271	54	]	]	PUNCT
ijassa-419	271	55	+	+	CCONJ
ijassa-419	271	56	→	→	SYM
ijassa-419	271	57	+	+	NUM
ijassa-419	271	58	−	−	PROPN
ijassa-419	271	59	→	→	SYM
ijassa-419	271	60	−	−	PROPN
ijassa-419	271	61	[	[	PUNCT
ijassa-419	271	62	→	→	X
ijassa-419	271	63	[	[	X
ijassa-419	271	64	]	]	X
ijassa-419	271	65	→	→	X
ijassa-419	271	66	]	]	X
ijassa-419	271	67	,	,	PUNCT
ijassa-419	271	68	114	114	NUM
ijassa-419	271	69	xiaojun	xiaojun	PROPN
ijassa-419	271	70	duan	duan	PROPN
ijassa-419	271	71	:	:	PUNCT
ijassa-419	271	72	set	set	VERB
ijassa-419	271	73	-	-	PUNCT
ijassa-419	271	74	theoretic	theoretic	NOUN
ijassa-419	271	75	design	design	NOUN
ijassa-419	271	76	and	and	CCONJ
ijassa-419	271	77	analysis	analysis	NOUN
ijassa-419	271	78	of	of	ADP
ijassa-419	271	79	l	l	NOUN
ijassa-419	271	80	systems	system	NOUN
ijassa-419	271	81	φ3	φ3	NOUN
ijassa-419	271	82	=	=	PUNCT
ijassa-419	271	83			NOUN
ijassa-419	271	84	f	f	X
ijassa-419	271	85	→	→	PUNCT
ijassa-419	271	86	ff[−	ff[−	ADJ
ijassa-419	271	87	f	f	NOUN
ijassa-419	271	88	+	+	NUM
ijassa-419	271	89	f	f	PROPN
ijassa-419	272	1	+	+	CCONJ
ijassa-419	273	1	f	f	X
ijassa-419	273	2	]	]	X
ijassa-419	274	1	+	+	CCONJ
ijassa-419	274	2	[	[	X
ijassa-419	274	3	+	+	ADJ
ijassa-419	274	4	f−	f−	PROPN
ijassa-419	274	5	f−	f−	NOUN
ijassa-419	274	6	f	f	X
ijassa-419	274	7	]	]	X
ijassa-419	274	8	+	+	CCONJ
ijassa-419	274	9	→	→	SYM
ijassa-419	274	10	+	+	NUM
ijassa-419	274	11	−	−	PROPN
ijassa-419	274	12	→	→	SYM
ijassa-419	274	13	−	−	PROPN
ijassa-419	274	14	[	[	PUNCT
ijassa-419	274	15	→	→	X
ijassa-419	274	16	[	[	X
ijassa-419	274	17	]	]	X
ijassa-419	274	18	→	→	X
ijassa-419	274	19	]	]	X
ijassa-419	274	20	and	and	CCONJ
ijassa-419	274	21	π	π	X
ijassa-419	274	22	=	=	SYM
ijassa-419	274	23	p	p	X
ijassa-419	274	24	(	(	PUNCT
ijassa-419	274	25	ξ	ξ	PROPN
ijassa-419	274	26	=	=	SYM
ijassa-419	274	27	φi	φi	ADJ
ijassa-419	274	28	)	)	PUNCT
ijassa-419	274	29	=	=	SYM
ijassa-419	274	30	1/3	1/3	NUM
ijassa-419	274	31	,	,	PUNCT
ijassa-419	274	32	i	i	PRON
ijassa-419	274	33	=	=	NOUN
ijassa-419	274	34	1	1	NUM
ijassa-419	274	35	,	,	PUNCT
ijassa-419	274	36	2	2	NUM
ijassa-419	274	37	,	,	PUNCT
ijassa-419	274	38	3	3	NUM
ijassa-419	274	39	.	.	PUNCT
ijassa-419	275	1	then	then	ADV
ijassa-419	275	2	the	the	DET
ijassa-419	275	3	fractal	fractal	ADJ
ijassa-419	275	4	structures	structure	NOUN
ijassa-419	275	5	can	can	AUX
ijassa-419	275	6	be	be	AUX
ijassa-419	275	7	produced	produce	VERB
ijassa-419	275	8	.	.	PUNCT
ijassa-419	276	1	for	for	ADP
ijassa-419	276	2	instance	instance	NOUN
ijassa-419	276	3	,	,	PUNCT
ijassa-419	276	4	fig.6	fig.6	PROPN
ijassa-419	276	5	shows	show	VERB
ijassa-419	276	6	the	the	DET
ijassa-419	276	7	different	different	ADJ
ijassa-419	276	8	fractal	fractal	ADJ
ijassa-419	276	9	structures	structure	NOUN
ijassa-419	276	10	of	of	ADP
ijassa-419	276	11	a	a	DET
ijassa-419	276	12	r0l	r0l	PROPN
ijassa-419	276	13	system	system	NOUN
ijassa-419	276	14	with	with	ADP
ijassa-419	276	15	each	each	DET
ijassa-419	276	16	iteration	iteration	NOUN
ijassa-419	276	17	unchanged	unchanged	ADJ
ijassa-419	276	18	.	.	PUNCT
ijassa-419	277	1	fig.7	fig.7	ADJ
ijassa-419	277	2	shows	show	VERB
ijassa-419	277	3	the	the	DET
ijassa-419	277	4	different	different	ADJ
ijassa-419	277	5	fractal	fractal	ADJ
ijassa-419	277	6	structures	structure	NOUN
ijassa-419	277	7	of	of	ADP
ijassa-419	277	8	a	a	DET
ijassa-419	277	9	r0l	r0l	PROPN
ijassa-419	277	10	system	system	NOUN
ijassa-419	277	11	where	where	SCONJ
ijassa-419	277	12	each	each	DET
ijassa-419	277	13	iteration	iteration	NOUN
ijassa-419	277	14	is	be	AUX
ijassa-419	277	15	different	different	ADJ
ijassa-419	277	16	.	.	PUNCT
ijassa-419	278	1	fig.7	fig.7	ADV
ijassa-419	278	2	the	the	DET
ijassa-419	278	3	different	different	ADJ
ijassa-419	278	4	fractal	fractal	ADJ
ijassa-419	278	5	structures	structure	NOUN
ijassa-419	278	6	of	of	ADP
ijassa-419	278	7	a	a	DET
ijassa-419	278	8	r0l	r0l	PROPN
ijassa-419	278	9	system	system	NOUN
ijassa-419	278	10	with	with	ADP
ijassa-419	278	11	each	each	DET
ijassa-419	278	12	iteration	iteration	NOUN
ijassa-419	278	13	different	different	ADJ
ijassa-419	278	14	(	(	PUNCT
ijassa-419	278	15	n	n	NOUN
ijassa-419	278	16	=	=	SYM
ijassa-419	278	17	5	5	NUM
ijassa-419	278	18	,	,	PUNCT
ijassa-419	278	19	α	α	NOUN
ijassa-419	278	20	=	=	SYM
ijassa-419	278	21	π/16	π/16	NOUN
ijassa-419	278	22	)	)	PUNCT
ijassa-419	278	23	6	6	NUM
ijassa-419	278	24	summary	summary	NOUN
ijassa-419	278	25	although	although	SCONJ
ijassa-419	278	26	the	the	DET
ijassa-419	278	27	design	design	NOUN
ijassa-419	278	28	principle	principle	NOUN
ijassa-419	278	29	underlying	underlie	VERB
ijassa-419	278	30	the	the	DET
ijassa-419	278	31	l	l	NOUN
ijassa-419	278	32	systems	system	NOUN
ijassa-419	278	33	is	be	AUX
ijassa-419	278	34	quite	quite	ADV
ijassa-419	278	35	straightforward	straightforward	ADJ
ijassa-419	278	36	,	,	PUNCT
ijassa-419	278	37	these	these	DET
ijassa-419	278	38	systems	system	NOUN
ijassa-419	278	39	can	can	AUX
ijassa-419	278	40	be	be	AUX
ijassa-419	278	41	employed	employ	VERB
ijassa-419	278	42	to	to	PART
ijassa-419	278	43	produce	produce	VERB
ijassa-419	278	44	many	many	ADJ
ijassa-419	278	45	complicated	complicated	ADJ
ijassa-419	278	46	fractal	fractal	ADJ
ijassa-419	278	47	patterns	pattern	NOUN
ijassa-419	278	48	.	.	PUNCT
ijassa-419	279	1	after	after	ADP
ijassa-419	279	2	many	many	ADJ
ijassa-419	279	3	years	year	NOUN
ijassa-419	279	4	of	of	ADP
ijassa-419	279	5	research	research	NOUN
ijassa-419	279	6	,	,	PUNCT
ijassa-419	279	7	l	l	PROPN
ijassa-419	279	8	systems	system	NOUN
ijassa-419	279	9	have	have	AUX
ijassa-419	279	10	evolved	evolve	VERB
ijassa-419	279	11	from	from	ADP
ijassa-419	279	12	the	the	DET
ijassa-419	279	13	original	original	ADJ
ijassa-419	279	14	rewrite	rewrite	NOUN
ijassa-419	279	15	systems	system	NOUN
ijassa-419	279	16	of	of	ADP
ijassa-419	279	17	characters	character	NOUN
ijassa-419	279	18	to	to	ADP
ijassa-419	279	19	such	such	ADJ
ijassa-419	279	20	capable	capable	ADJ
ijassa-419	279	21	systems	system	NOUN
ijassa-419	279	22	that	that	PRON
ijassa-419	279	23	can	can	AUX
ijassa-419	279	24	describe	describe	VERB
ijassa-419	279	25	complex	complex	ADJ
ijassa-419	279	26	3	3	NUM
ijassa-419	279	27	-	-	PUNCT
ijassa-419	279	28	dimensional	dimensional	ADJ
ijassa-419	279	29	systems	system	NOUN
ijassa-419	279	30	.	.	PUNCT
ijassa-419	280	1	they	they	PRON
ijassa-419	280	2	have	have	AUX
ijassa-419	280	3	evolved	evolve	VERB
ijassa-419	280	4	from	from	ADP
ijassa-419	280	5	the	the	DET
ijassa-419	280	6	simplest	simple	ADJ
ijassa-419	280	7	d0l	d0l	NOUN
ijassa-419	280	8	systems	system	NOUN
ijassa-419	280	9	to	to	ADP
ijassa-419	280	10	random	random	ADJ
ijassa-419	280	11	l	l	NOUN
ijassa-419	280	12	systems	system	NOUN
ijassa-419	280	13	,	,	PUNCT
ijassa-419	280	14	and	and	CCONJ
ijassa-419	280	15	then	then	ADV
ijassa-419	280	16	to	to	PART
ijassa-419	280	17	open	open	VERB
ijassa-419	280	18	l	l	NOUN
ijassa-419	280	19	systems	system	NOUN
ijassa-419	280	20	.	.	PUNCT
ijassa-419	281	1	the	the	DET
ijassa-419	281	2	l	l	PROPN
ijassa-419	281	3	systems	system	NOUN
ijassa-419	281	4	have	have	AUX
ijassa-419	281	5	provided	provide	VERB
ijassa-419	281	6	simulations	simulation	NOUN
ijassa-419	281	7	of	of	ADP
ijassa-419	281	8	fractal	fractal	ADJ
ijassa-419	281	9	structures	structure	NOUN
ijassa-419	281	10	that	that	PRON
ijassa-419	281	11	have	have	AUX
ijassa-419	281	12	become	become	VERB
ijassa-419	281	13	over	over	ADP
ijassa-419	281	14	time	time	NOUN
ijassa-419	281	15	much	much	ADV
ijassa-419	281	16	closer	close	ADJ
ijassa-419	281	17	to	to	ADP
ijassa-419	281	18	real	real	ADJ
ijassa-419	281	19	-	-	PUNCT
ijassa-419	281	20	life	life	NOUN
ijassa-419	281	21	like	like	NOUN
ijassa-419	281	22	,	,	PUNCT
ijassa-419	281	23	and	and	CCONJ
ijassa-419	281	24	have	have	AUX
ijassa-419	281	25	been	be	AUX
ijassa-419	281	26	employed	employ	VERB
ijassa-419	281	27	as	as	ADP
ijassa-419	281	28	an	an	DET
ijassa-419	281	29	important	important	ADJ
ijassa-419	281	30	tool	tool	NOUN
ijassa-419	281	31	for	for	ADP
ijassa-419	281	32	creating	create	VERB
ijassa-419	281	33	virtual	virtual	ADJ
ijassa-419	281	34	plants	plant	NOUN
ijassa-419	281	35	.	.	PUNCT
ijassa-419	282	1	from	from	ADP
ijassa-419	282	2	the	the	DET
ijassa-419	282	3	point	point	NOUN
ijassa-419	282	4	of	of	ADP
ijassa-419	282	5	view	view	NOUN
ijassa-419	282	6	of	of	ADP
ijassa-419	282	7	set	set	NOUN
ijassa-419	282	8	theory	theory	NOUN
ijassa-419	282	9	,	,	PUNCT
ijassa-419	282	10	this	this	DET
ijassa-419	282	11	paper	paper	NOUN
ijassa-419	282	12	first	first	ADV
ijassa-419	282	13	establishes	establish	VERB
ijassa-419	282	14	a	a	DET
ijassa-419	282	15	rigorous	rigorous	ADJ
ijassa-419	282	16	mathematical	mathematical	ADJ
ijassa-419	282	17	definition	definition	NOUN
ijassa-419	282	18	of	of	ADP
ijassa-419	282	19	simple	simple	ADJ
ijassa-419	282	20	l	l	NOUN
ijassa-419	282	21	-	-	NOUN
ijassa-419	282	22	system	system	NOUN
ijassa-419	282	23	,	,	PUNCT
ijassa-419	282	24	and	and	CCONJ
ijassa-419	282	25	then	then	ADV
ijassa-419	282	26	proves	prove	VERB
ijassa-419	282	27	the	the	DET
ijassa-419	282	28	common	common	ADJ
ijassa-419	282	29	characteristics	characteristic	NOUN
ijassa-419	282	30	of	of	ADP
ijassa-419	282	31	simple	simple	ADJ
ijassa-419	282	32	l	l	NOUN
ijassa-419	282	33	-	-	NOUN
ijassa-419	282	34	systems	system	NOUN
ijassa-419	282	35	.	.	PUNCT
ijassa-419	283	1	by	by	ADP
ijassa-419	283	2	doing	do	VERB
ijassa-419	283	3	so	so	ADV
ijassa-419	283	4	,	,	PUNCT
ijassa-419	283	5	this	this	DET
ijassa-419	283	6	paper	paper	NOUN
ijassa-419	283	7	developed	develop	VERB
ijassa-419	283	8	the	the	DET
ijassa-419	283	9	badly	badly	ADV
ijassa-419	283	10	needed	need	VERB
ijassa-419	283	11	fundamental	fundamental	ADJ
ijassa-419	283	12	ground	ground	NOUN
ijassa-419	283	13	for	for	ADP
ijassa-419	283	14	further	further	ADJ
ijassa-419	283	15	investigation	investigation	NOUN
ijassa-419	283	16	of	of	ADP
ijassa-419	283	17	l	l	NOUN
ijassa-419	283	18	systems	system	NOUN
ijassa-419	283	19	.	.	PUNCT
ijassa-419	284	1	it	it	PRON
ijassa-419	284	2	is	be	AUX
ijassa-419	284	3	expected	expect	VERB
ijassa-419	284	4	to	to	PART
ijassa-419	284	5	be	be	AUX
ijassa-419	284	6	applicable	applicable	ADJ
ijassa-419	284	7	to	to	PART
ijassa-419	284	8	form	form	VERB
ijassa-419	284	9	the	the	DET
ijassa-419	284	10	theoretical	theoretical	ADJ
ijassa-419	284	11	framework	framework	NOUN
ijassa-419	284	12	of	of	ADP
ijassa-419	284	13	other	other	ADJ
ijassa-419	284	14	l	l	NOUN
ijassa-419	284	15	systems	system	NOUN
ijassa-419	284	16	.	.	PUNCT
ijassa-419	285	1	acknowledgements	acknowledgement	NOUN
ijassa-419	285	2	advances	advance	NOUN
ijassa-419	285	3	in	in	ADP
ijassa-419	285	4	systems	system	NOUN
ijassa-419	285	5	science	science	NOUN
ijassa-419	285	6	and	and	CCONJ
ijassa-419	285	7	applications	application	NOUN
ijassa-419	285	8	(	(	PUNCT
ijassa-419	285	9	2013	2013	NUM
ijassa-419	285	10	)	)	PUNCT
ijassa-419	286	1	vol.13	vol.13	NOUN
ijassa-419	286	2	no.2	no.2	PROPN
ijassa-419	286	3	115	115	NUM
ijassa-419	287	1	this	this	DET
ijassa-419	287	2	work	work	NOUN
ijassa-419	287	3	is	be	AUX
ijassa-419	287	4	supported	support	VERB
ijassa-419	287	5	by	by	ADP
ijassa-419	287	6	the	the	DET
ijassa-419	287	7	natural	natural	ADJ
ijassa-419	287	8	science	science	PROPN
ijassa-419	287	9	foundation	foundation	PROPN
ijassa-419	287	10	of	of	ADP
ijassa-419	287	11	china	china	PROPN
ijassa-419	287	12	(	(	PUNCT
ijassa-419	287	13	60974124	60974124	NUM
ijassa-419	287	14	)	)	PUNCT
ijassa-419	287	15	,	,	PUNCT
ijassa-419	287	16	the	the	DET
ijassa-419	287	17	program	program	NOUN
ijassa-419	287	18	for	for	ADP
ijassa-419	287	19	new	new	ADJ
ijassa-419	287	20	century	century	NOUN
ijassa-419	287	21	excellent	excellent	ADJ
ijassa-419	287	22	talents	talent	NOUN
ijassa-419	287	23	in	in	ADP
ijassa-419	287	24	university	university	NOUN
ijassa-419	287	25	and	and	CCONJ
ijassa-419	287	26	the	the	DET
ijassa-419	287	27	projectsponsored	projectsponsore	VERB
ijassa-419	287	28	by	by	ADP
ijassa-419	287	29	srf	srf	PROPN
ijassa-419	287	30	for	for	ADP
ijassa-419	287	31	rocs	roc	NOUN
ijassa-419	287	32	,	,	PUNCT
ijassa-419	287	33	sem	sem	NOUN
ijassa-419	287	34	in	in	ADP
ijassa-419	287	35	china	china	PROPN
ijassa-419	287	36	.	.	PUNCT
ijassa-419	288	1	references	reference	NOUN
ijassa-419	288	2	[	[	X
ijassa-419	288	3	1	1	NUM
ijassa-419	288	4	]	]	X
ijassa-419	288	5	lindenmayer	lindenmayer	NOUN
ijassa-419	288	6	,	,	PUNCT
ijassa-419	288	7	a.	a.	NOUN
ijassa-419	288	8	(	(	PUNCT
ijassa-419	288	9	1968	1968	NUM
ijassa-419	288	10	)	)	PUNCT
ijassa-419	288	11	,	,	PUNCT
ijassa-419	288	12	“	"	PUNCT
ijassa-419	288	13	mathematical	mathematical	ADJ
ijassa-419	288	14	models	model	NOUN
ijassa-419	288	15	for	for	ADP
ijassa-419	288	16	cellular	cellular	ADJ
ijassa-419	288	17	interaction	interaction	NOUN
ijassa-419	288	18	in	in	ADP
ijassa-419	288	19	development	development	NOUN
ijassa-419	288	20	”	"	PUNCT
ijassa-419	288	21	,	,	PUNCT
ijassa-419	288	22	journal	journal	NOUN
ijassa-419	288	23	of	of	ADP
ijassa-419	288	24	theoretical	theoretical	ADJ
ijassa-419	288	25	biology	biology	NOUN
ijassa-419	288	26	,	,	PUNCT
ijassa-419	288	27	vol.18	vol.18	NOUN
ijassa-419	288	28	,	,	PUNCT
ijassa-419	288	29	pp.280	pp.280	PROPN
ijassa-419	288	30	-	-	PUNCT
ijassa-419	288	31	289	289	NUM
ijassa-419	288	32	.	.	PUNCT
ijassa-419	289	1	[	[	X
ijassa-419	289	2	2	2	NUM
ijassa-419	289	3	]	]	X
ijassa-419	289	4	prusinkiewicz	prusinkiewicz	NOUN
ijassa-419	289	5	,	,	PUNCT
ijassa-419	289	6	p	p	X
ijassa-419	289	7	,	,	PUNCT
ijassa-419	289	8	lindenmayer	lindenmayer	NOUN
ijassa-419	289	9	,	,	PUNCT
ijassa-419	289	10	a.	a.	NOUN
ijassa-419	289	11	(	(	PUNCT
ijassa-419	289	12	1996	1996	NUM
ijassa-419	289	13	)	)	PUNCT
ijassa-419	289	14	,	,	PUNCT
ijassa-419	289	15	the	the	DET
ijassa-419	289	16	algorithmic	algorithmic	ADJ
ijassa-419	289	17	beauty	beauty	NOUN
ijassa-419	289	18	of	of	ADP
ijassa-419	289	19	plants	plant	NOUN
ijassa-419	289	20	,	,	PUNCT
ijassa-419	289	21	london	london	PROPN
ijassa-419	289	22	:	:	PUNCT
ijassa-419	289	23	springer	springer	NOUN
ijassa-419	289	24	.	.	PUNCT
ijassa-419	290	1	[	[	X
ijassa-419	290	2	3	3	NUM
ijassa-419	290	3	]	]	X
ijassa-419	290	4	eichhorst	eichhorst	NOUN
ijassa-419	290	5	,	,	PUNCT
ijassa-419	290	6	p	p	NOUN
ijassa-419	290	7	,	,	PUNCT
ijassa-419	290	8	savitch	savitch	NOUN
ijassa-419	290	9	,	,	PUNCT
ijassa-419	290	10	w.	w.	PROPN
ijassa-419	290	11	j.	j.	PROPN
ijassa-419	290	12	(	(	PUNCT
ijassa-419	290	13	1980	1980	NUM
ijassa-419	290	14	)	)	PUNCT
ijassa-419	290	15	,	,	PUNCT
ijassa-419	290	16	“	"	PUNCT
ijassa-419	290	17	growth	growth	NOUN
ijassa-419	290	18	functions	function	NOUN
ijassa-419	290	19	of	of	ADP
ijassa-419	290	20	stochastic	stochastic	ADJ
ijassa-419	290	21	lindenmayer	lindenmayer	NOUN
ijassa-419	290	22	systems	system	NOUN
ijassa-419	290	23	”	"	PUNCT
ijassa-419	290	24	,	,	PUNCT
ijassa-419	290	25	information	information	NOUN
ijassa-419	290	26	and	and	CCONJ
ijassa-419	290	27	control	control	NOUN
ijassa-419	290	28	,	,	PUNCT
ijassa-419	290	29	vol.45	vol.45	X
ijassa-419	290	30	,	,	PUNCT
ijassa-419	290	31	pp.217	pp.217	PROPN
ijassa-419	290	32	-	-	SYM
ijassa-419	290	33	228	228	NUM
ijassa-419	290	34	.	.	PUNCT
ijassa-419	291	1	[	[	X
ijassa-419	291	2	4	4	NUM
ijassa-419	291	3	]	]	X
ijassa-419	291	4	herman	herman	PROPN
ijassa-419	291	5	,	,	PUNCT
ijassa-419	291	6	g.t	g.t	PROPN
ijassa-419	291	7	,	,	PUNCT
ijassa-419	291	8	rozenberg	rozenberg	PROPN
ijassa-419	291	9	,	,	PUNCT
ijassa-419	291	10	g.	g.	PROPN
ijassa-419	291	11	(	(	PUNCT
ijassa-419	291	12	1975	1975	NUM
ijassa-419	291	13	)	)	PUNCT
ijassa-419	291	14	,	,	PUNCT
ijassa-419	291	15	developmental	developmental	ADJ
ijassa-419	291	16	systems	system	NOUN
ijassa-419	291	17	and	and	CCONJ
ijassa-419	291	18	languages	language	NOUN
ijassa-419	291	19	,	,	PUNCT
ijassa-419	291	20	amsterdam	amsterdam	PROPN
ijassa-419	291	21	:	:	PUNCT
ijassa-419	291	22	north	north	PROPN
ijassa-419	291	23	-	-	PUNCT
ijassa-419	291	24	holland	holland	PROPN
ijassa-419	291	25	publishing	publishing	NOUN
ijassa-419	291	26	company	company	NOUN
ijassa-419	291	27	.	.	PUNCT
ijassa-419	292	1	[	[	X
ijassa-419	292	2	5	5	NUM
ijassa-419	292	3	]	]	X
ijassa-419	292	4	prusinkiewicz	prusinkiewicz	NOUN
ijassa-419	292	5	,	,	PUNCT
ijassa-419	292	6	p	p	X
ijassa-419	292	7	,	,	PUNCT
ijassa-419	292	8	hammel	hammel	PROPN
ijassa-419	292	9	,	,	PUNCT
ijassa-419	292	10	m	m	PROPN
ijassa-419	292	11	,	,	PUNCT
ijassa-419	292	12	mjolsness	mjolsness	PROPN
ijassa-419	292	13	,	,	PUNCT
ijassa-419	292	14	e.	e.	PROPN
ijassa-419	292	15	(	(	PUNCT
ijassa-419	292	16	1993	1993	NUM
ijassa-419	292	17	)	)	PUNCT
ijassa-419	292	18	,	,	PUNCT
ijassa-419	292	19	“	"	PUNCT
ijassa-419	292	20	animation	animation	NOUN
ijassa-419	292	21	of	of	ADP
ijassa-419	292	22	plant	plant	NOUN
ijassa-419	292	23	developmen	developman	NOUN
ijassa-419	292	24	”	"	PUNCT
ijassa-419	292	25	,	,	PUNCT
ijassa-419	292	26	acm	acm	PROPN
ijassa-419	292	27	siggraph	siggraph	PROPN
ijassa-419	292	28	,	,	PUNCT
ijassa-419	292	29	pp.351	pp.351	NOUN
ijassa-419	292	30	-	-	PUNCT
ijassa-419	292	31	360	360	NUM
ijassa-419	292	32	.	.	PUNCT
ijassa-419	293	1	[	[	X
ijassa-419	293	2	6	6	NUM
ijassa-419	293	3	]	]	X
ijassa-419	293	4	lin	lin	PROPN
ijassa-419	293	5	,	,	PUNCT
ijassa-419	293	6	y.	y.	PROPN
ijassa-419	293	7	(	(	PUNCT
ijassa-419	293	8	1999	1999	NUM
ijassa-419	293	9	)	)	PUNCT
ijassa-419	293	10	,	,	PUNCT
ijassa-419	293	11	“	"	PUNCT
ijassa-419	293	12	general	general	ADJ
ijassa-419	293	13	systems	system	NOUN
ijassa-419	293	14	theory	theory	NOUN
ijassa-419	293	15	:	:	PUNCT
ijassa-419	293	16	a	a	DET
ijassa-419	293	17	mathematical	mathematical	ADJ
ijassa-419	293	18	approach	approach	NOUN
ijassa-419	293	19	”	"	PUNCT
ijassa-419	293	20	,	,	PUNCT
ijassa-419	293	21	new	new	PROPN
ijassa-419	293	22	york	york	PROPN
ijassa-419	293	23	:	:	PUNCT
ijassa-419	293	24	kluwer	kluwer	PROPN
ijassa-419	293	25	academic	academic	NOUN
ijassa-419	293	26	and	and	CCONJ
ijassa-419	293	27	plenum	plenum	NOUN
ijassa-419	293	28	publishers	publisher	NOUN
ijassa-419	293	29	.	.	PUNCT
ijassa-419	294	1	corresponding	correspond	VERB
ijassa-419	294	2	author	author	NOUN
ijassa-419	294	3	xiaojun	xiaojun	PROPN
ijassa-419	294	4	duan	duan	PROPN
ijassa-419	294	5	can	can	AUX
ijassa-419	294	6	be	be	AUX
ijassa-419	294	7	contracted	contract	VERB
ijassa-419	294	8	at	at	ADP
ijassa-419	294	9	:	:	PUNCT
ijassa-419	294	10	xjduan@nudt.edu.cn	xjduan@nudt.edu.cn	NOUN