id	sid	tid	token	lemma	pos
ejpam-5850	1	1	european	european	PROPN
ejpam-5850	1	2	journal	journal	PROPN
ejpam-5850	1	3	of	of	ADP
ejpam-5850	1	4	pure	pure	ADJ
ejpam-5850	1	5	and	and	CCONJ
ejpam-5850	1	6	applied	applied	ADJ
ejpam-5850	1	7	mathematics	mathematic	NOUN
ejpam-5850	1	8	2025	2025	NUM
ejpam-5850	1	9	,	,	PUNCT
ejpam-5850	1	10	vol	vol	NOUN
ejpam-5850	1	11	.	.	PROPN
ejpam-5850	1	12	18	18	NUM
ejpam-5850	1	13	,	,	PUNCT
ejpam-5850	1	14	issue	issue	NOUN
ejpam-5850	1	15	1	1	NUM
ejpam-5850	1	16	,	,	PUNCT
ejpam-5850	1	17	article	article	NOUN
ejpam-5850	1	18	number	number	NOUN
ejpam-5850	1	19	5850	5850	NUM
ejpam-5850	1	20	issn	issn	VERB
ejpam-5850	1	21	1307	1307	NUM
ejpam-5850	1	22	-	-	SYM
ejpam-5850	1	23	5543	5543	NUM
ejpam-5850	1	24	–	–	PUNCT
ejpam-5850	1	25	ejpam.com	ejpam.com	X
ejpam-5850	1	26	published	publish	VERB
ejpam-5850	1	27	by	by	ADP
ejpam-5850	1	28	new	new	PROPN
ejpam-5850	1	29	york	york	PROPN
ejpam-5850	1	30	business	business	PROPN
ejpam-5850	1	31	global	global	PROPN
ejpam-5850	1	32	on	on	ADP
ejpam-5850	1	33	the	the	DET
ejpam-5850	1	34	recognition	recognition	NOUN
ejpam-5850	1	35	capacity	capacity	NOUN
ejpam-5850	1	36	of	of	ADP
ejpam-5850	1	37	abelian	abelian	ADJ
ejpam-5850	1	38	graph	graph	NOUN
ejpam-5850	1	39	automata	automata	PROPN
ejpam-5850	1	40	kyriakos	kyriakos	PROPN
ejpam-5850	1	41	papadopoulos	papadopoulos	PROPN
ejpam-5850	1	42	department	department	PROPN
ejpam-5850	1	43	of	of	ADP
ejpam-5850	1	44	mathematics	mathematics	PROPN
ejpam-5850	1	45	,	,	PUNCT
ejpam-5850	1	46	kuwait	kuwait	PROPN
ejpam-5850	1	47	university	university	PROPN
ejpam-5850	1	48	,	,	PUNCT
ejpam-5850	1	49	safat	safat	PROPN
ejpam-5850	1	50	13060	13060	NUM
ejpam-5850	1	51	,	,	PUNCT
ejpam-5850	1	52	kuwait	kuwait	PROPN
ejpam-5850	1	53	abstract	abstract	NOUN
ejpam-5850	1	54	.	.	PUNCT
ejpam-5850	2	1	this	this	DET
ejpam-5850	2	2	paper	paper	NOUN
ejpam-5850	2	3	explores	explore	VERB
ejpam-5850	2	4	the	the	DET
ejpam-5850	2	5	recognition	recognition	NOUN
ejpam-5850	2	6	capacity	capacity	NOUN
ejpam-5850	2	7	of	of	ADP
ejpam-5850	2	8	both	both	CCONJ
ejpam-5850	2	9	unitary	unitary	ADJ
ejpam-5850	2	10	and	and	CCONJ
ejpam-5850	2	11	non	non	ADJ
ejpam-5850	2	12	-	-	ADJ
ejpam-5850	2	13	unitary	unitary	ADJ
ejpam-5850	2	14	abelian	abelian	ADJ
ejpam-5850	2	15	graph	graph	NOUN
ejpam-5850	2	16	automata	automata	VERB
ejpam-5850	2	17	through	through	ADP
ejpam-5850	2	18	the	the	DET
ejpam-5850	2	19	algebraic	algebraic	ADJ
ejpam-5850	2	20	structure	structure	NOUN
ejpam-5850	2	21	of	of	ADP
ejpam-5850	2	22	graphoids	graphoid	NOUN
ejpam-5850	2	23	.	.	PUNCT
ejpam-5850	3	1	we	we	PRON
ejpam-5850	3	2	investigate	investigate	VERB
ejpam-5850	3	3	for	for	ADP
ejpam-5850	3	4	the	the	DET
ejpam-5850	3	5	first	first	ADJ
ejpam-5850	3	6	time	time	NOUN
ejpam-5850	3	7	in	in	ADP
ejpam-5850	3	8	the	the	DET
ejpam-5850	3	9	literature	literature	NOUN
ejpam-5850	3	10	the	the	DET
ejpam-5850	3	11	recognition	recognition	NOUN
ejpam-5850	3	12	mechanism	mechanism	NOUN
ejpam-5850	3	13	of	of	ADP
ejpam-5850	3	14	non	non	ADJ
ejpam-5850	3	15	-	-	ADJ
ejpam-5850	3	16	unitary	unitary	ADJ
ejpam-5850	3	17	abelian	abelian	ADJ
ejpam-5850	3	18	graph	graph	NOUN
ejpam-5850	3	19	automata	automata	NOUN
ejpam-5850	3	20	and	and	CCONJ
ejpam-5850	3	21	prove	prove	VERB
ejpam-5850	3	22	that	that	SCONJ
ejpam-5850	3	23	they	they	PRON
ejpam-5850	3	24	can	can	AUX
ejpam-5850	3	25	recognize	recognize	VERB
ejpam-5850	3	26	graph	graph	NOUN
ejpam-5850	3	27	languages	language	NOUN
ejpam-5850	3	28	which	which	PRON
ejpam-5850	3	29	are	be	AUX
ejpam-5850	3	30	beyond	beyond	ADP
ejpam-5850	3	31	the	the	DET
ejpam-5850	3	32	recognition	recognition	NOUN
ejpam-5850	3	33	power	power	NOUN
ejpam-5850	3	34	of	of	ADP
ejpam-5850	3	35	unitary	unitary	ADJ
ejpam-5850	3	36	graph	graph	NOUN
ejpam-5850	3	37	automata	automata	NOUN
ejpam-5850	3	38	.	.	PUNCT
ejpam-5850	4	1	consequently	consequently	ADV
ejpam-5850	4	2	,	,	PUNCT
ejpam-5850	4	3	we	we	PRON
ejpam-5850	4	4	establish	establish	VERB
ejpam-5850	4	5	that	that	SCONJ
ejpam-5850	4	6	the	the	DET
ejpam-5850	4	7	class	class	NOUN
ejpam-5850	4	8	of	of	ADP
ejpam-5850	4	9	graph	graph	NOUN
ejpam-5850	4	10	languages	language	NOUN
ejpam-5850	4	11	recognized	recognize	VERB
ejpam-5850	4	12	by	by	ADP
ejpam-5850	4	13	unitary	unitary	ADJ
ejpam-5850	4	14	automata	automata	NOUN
ejpam-5850	4	15	is	be	AUX
ejpam-5850	4	16	strictly	strictly	ADV
ejpam-5850	4	17	contained	contain	VERB
ejpam-5850	4	18	within	within	ADP
ejpam-5850	4	19	the	the	DET
ejpam-5850	4	20	class	class	NOUN
ejpam-5850	4	21	of	of	ADP
ejpam-5850	4	22	those	those	PRON
ejpam-5850	4	23	recognized	recognize	VERB
ejpam-5850	4	24	by	by	ADP
ejpam-5850	4	25	abelian	abelian	ADJ
ejpam-5850	4	26	graph	graph	NOUN
ejpam-5850	4	27	automata	automata	NOUN
ejpam-5850	4	28	.	.	PUNCT
ejpam-5850	5	1	these	these	DET
ejpam-5850	5	2	results	result	NOUN
ejpam-5850	5	3	manifest	manifest	VERB
ejpam-5850	5	4	a	a	DET
ejpam-5850	5	5	proper	proper	ADJ
ejpam-5850	5	6	hierarchy	hierarchy	NOUN
ejpam-5850	5	7	among	among	ADP
ejpam-5850	5	8	graph	graph	NOUN
ejpam-5850	5	9	automata	automata	NOUN
ejpam-5850	5	10	classes	class	NOUN
ejpam-5850	5	11	and	and	CCONJ
ejpam-5850	5	12	provide	provide	VERB
ejpam-5850	5	13	new	new	ADJ
ejpam-5850	5	14	insights	insight	NOUN
ejpam-5850	5	15	into	into	ADP
ejpam-5850	5	16	the	the	DET
ejpam-5850	5	17	recognition	recognition	NOUN
ejpam-5850	5	18	capabilities	capability	NOUN
ejpam-5850	5	19	of	of	ADP
ejpam-5850	5	20	graph	graph	NOUN
ejpam-5850	5	21	automata	automata	NOUN
ejpam-5850	5	22	.	.	PUNCT
ejpam-5850	6	1	2020	2020	NUM
ejpam-5850	6	2	mathematics	mathematics	PROPN
ejpam-5850	6	3	subject	subject	NOUN
ejpam-5850	6	4	classifications	classification	NOUN
ejpam-5850	6	5	:	:	PUNCT
ejpam-5850	6	6	05c20,05c85,68t10,68r10	05c20,05c85,68t10,68r10	NUM
ejpam-5850	6	7	key	key	ADJ
ejpam-5850	6	8	words	word	NOUN
ejpam-5850	6	9	and	and	CCONJ
ejpam-5850	6	10	phrases	phrase	NOUN
ejpam-5850	6	11	:	:	PUNCT
ejpam-5850	6	12	graph	graph	NOUN
ejpam-5850	6	13	automata	automata	NOUN
ejpam-5850	6	14	,	,	PUNCT
ejpam-5850	6	15	pattern	pattern	NOUN
ejpam-5850	6	16	recognition	recognition	NOUN
ejpam-5850	6	17	,	,	PUNCT
ejpam-5850	6	18	graph	graph	NOUN
ejpam-5850	6	19	theory	theory	NOUN
ejpam-5850	6	20	1	1	NUM
ejpam-5850	6	21	.	.	PUNCT
ejpam-5850	7	1	introduction	introduction	NOUN
ejpam-5850	7	2	graphs	graph	NOUN
ejpam-5850	7	3	serve	serve	VERB
ejpam-5850	7	4	as	as	ADP
ejpam-5850	7	5	powerful	powerful	ADJ
ejpam-5850	7	6	tools	tool	NOUN
ejpam-5850	7	7	for	for	ADP
ejpam-5850	7	8	modeling	model	VERB
ejpam-5850	7	9	relationships	relationship	NOUN
ejpam-5850	7	10	and	and	CCONJ
ejpam-5850	7	11	dependencies	dependency	NOUN
ejpam-5850	7	12	across	across	ADP
ejpam-5850	7	13	various	various	ADJ
ejpam-5850	7	14	fields	field	NOUN
ejpam-5850	7	15	from	from	ADP
ejpam-5850	7	16	network	network	NOUN
ejpam-5850	7	17	analysis	analysis	NOUN
ejpam-5850	7	18	to	to	ADP
ejpam-5850	7	19	artificial	artificial	ADJ
ejpam-5850	7	20	intelligence	intelligence	NOUN
ejpam-5850	7	21	[	[	X
ejpam-5850	7	22	21	21	NUM
ejpam-5850	7	23	]	]	PUNCT
ejpam-5850	7	24	,	,	PUNCT
ejpam-5850	7	25	[	[	X
ejpam-5850	7	26	25	25	NUM
ejpam-5850	7	27	]	]	PUNCT
ejpam-5850	7	28	,	,	PUNCT
ejpam-5850	7	29	[	[	X
ejpam-5850	7	30	26	26	NUM
ejpam-5850	7	31	]	]	PUNCT
ejpam-5850	7	32	,	,	PUNCT
ejpam-5850	7	33	[	[	X
ejpam-5850	7	34	1	1	NUM
ejpam-5850	7	35	]	]	PUNCT
ejpam-5850	7	36	.	.	PUNCT
ejpam-5850	8	1	automata	automata	PROPN
ejpam-5850	8	2	theory	theory	NOUN
ejpam-5850	8	3	,	,	PUNCT
ejpam-5850	8	4	with	with	ADP
ejpam-5850	8	5	its	its	PRON
ejpam-5850	8	6	robust	robust	ADJ
ejpam-5850	8	7	framework	framework	NOUN
ejpam-5850	8	8	for	for	ADP
ejpam-5850	8	9	recognizing	recognize	VERB
ejpam-5850	8	10	structured	structured	ADJ
ejpam-5850	8	11	data	datum	NOUN
ejpam-5850	8	12	(	(	PUNCT
ejpam-5850	8	13	see	see	VERB
ejpam-5850	8	14	[	[	X
ejpam-5850	8	15	11–14	11–14	NUM
ejpam-5850	8	16	]	]	PUNCT
ejpam-5850	8	17	)	)	PUNCT
ejpam-5850	8	18	,	,	PUNCT
ejpam-5850	8	19	can	can	AUX
ejpam-5850	8	20	be	be	AUX
ejpam-5850	8	21	naturally	naturally	ADV
ejpam-5850	8	22	extended	extend	VERB
ejpam-5850	8	23	into	into	ADP
ejpam-5850	8	24	graph	graph	NOUN
ejpam-5850	8	25	theory	theory	NOUN
ejpam-5850	8	26	,	,	PUNCT
ejpam-5850	8	27	enabling	enable	VERB
ejpam-5850	8	28	a	a	DET
ejpam-5850	8	29	systematic	systematic	ADJ
ejpam-5850	8	30	verification	verification	NOUN
ejpam-5850	8	31	of	of	ADP
ejpam-5850	8	32	graph	graph	NOUN
ejpam-5850	8	33	characteristics	characteristic	NOUN
ejpam-5850	9	1	[	[	X
ejpam-5850	10	1	18],[8	18],[8	NOUN
ejpam-5850	10	2	]	]	X
ejpam-5850	10	3	.	.	PUNCT
ejpam-5850	11	1	central	central	ADJ
ejpam-5850	11	2	to	to	ADP
ejpam-5850	11	3	this	this	DET
ejpam-5850	11	4	approach	approach	NOUN
ejpam-5850	11	5	is	be	AUX
ejpam-5850	11	6	the	the	DET
ejpam-5850	11	7	algebraic	algebraic	ADJ
ejpam-5850	11	8	representation	representation	NOUN
ejpam-5850	11	9	of	of	ADP
ejpam-5850	11	10	graphs	graph	NOUN
ejpam-5850	11	11	through	through	ADP
ejpam-5850	11	12	magmoids	magmoid	NOUN
ejpam-5850	11	13	,	,	PUNCT
ejpam-5850	11	14	where	where	SCONJ
ejpam-5850	11	15	the	the	DET
ejpam-5850	11	16	operations	operation	NOUN
ejpam-5850	11	17	of	of	ADP
ejpam-5850	11	18	graph	graph	NOUN
ejpam-5850	11	19	product	product	NOUN
ejpam-5850	11	20	and	and	CCONJ
ejpam-5850	11	21	graph	graph	NOUN
ejpam-5850	11	22	sum	sum	NOUN
ejpam-5850	11	23	are	be	AUX
ejpam-5850	11	24	employed	employ	VERB
ejpam-5850	11	25	to	to	PART
ejpam-5850	11	26	represent	represent	VERB
ejpam-5850	11	27	graph	graph	NOUN
ejpam-5850	11	28	structures	structure	NOUN
ejpam-5850	11	29	(	(	PUNCT
ejpam-5850	11	30	see	see	VERB
ejpam-5850	11	31	[	[	X
ejpam-5850	11	32	7	7	NUM
ejpam-5850	11	33	]	]	PUNCT
ejpam-5850	11	34	,	,	PUNCT
ejpam-5850	11	35	[	[	X
ejpam-5850	11	36	9	9	NUM
ejpam-5850	11	37	]	]	PUNCT
ejpam-5850	11	38	)	)	PUNCT
ejpam-5850	11	39	playing	play	VERB
ejpam-5850	11	40	a	a	DET
ejpam-5850	11	41	role	role	NOUN
ejpam-5850	11	42	similar	similar	ADJ
ejpam-5850	11	43	to	to	ADP
ejpam-5850	11	44	monoids	monoid	NOUN
ejpam-5850	11	45	in	in	ADP
ejpam-5850	11	46	string	string	NOUN
ejpam-5850	11	47	generation	generation	NOUN
ejpam-5850	11	48	.	.	PUNCT
ejpam-5850	12	1	a	a	DET
ejpam-5850	12	2	magmoid	magmoid	NOUN
ejpam-5850	12	3	is	be	AUX
ejpam-5850	12	4	defined	define	VERB
ejpam-5850	12	5	as	as	ADP
ejpam-5850	12	6	a	a	DET
ejpam-5850	12	7	doubly	doubly	ADV
ejpam-5850	12	8	ranked	rank	VERB
ejpam-5850	12	9	set	set	NOUN
ejpam-5850	12	10	equipped	equip	VERB
ejpam-5850	12	11	with	with	ADP
ejpam-5850	12	12	two	two	NUM
ejpam-5850	12	13	operations	operation	NOUN
ejpam-5850	12	14	that	that	PRON
ejpam-5850	12	15	are	be	AUX
ejpam-5850	12	16	associative	associative	ADJ
ejpam-5850	12	17	,	,	PUNCT
ejpam-5850	12	18	unitary	unitary	ADJ
ejpam-5850	12	19	,	,	PUNCT
ejpam-5850	12	20	and	and	CCONJ
ejpam-5850	12	21	canonically	canonically	ADV
ejpam-5850	12	22	distributed	distribute	VERB
ejpam-5850	12	23	[	[	X
ejpam-5850	12	24	5	5	NUM
ejpam-5850	12	25	]	]	PUNCT
ejpam-5850	12	26	.	.	PUNCT
ejpam-5850	13	1	as	as	SCONJ
ejpam-5850	13	2	engelfriet	engelfriet	PROPN
ejpam-5850	13	3	and	and	CCONJ
ejpam-5850	13	4	vereijken	vereijken	PROPN
ejpam-5850	13	5	showed	show	VERB
ejpam-5850	13	6	in	in	ADP
ejpam-5850	13	7	[	[	X
ejpam-5850	13	8	15	15	NUM
ejpam-5850	13	9	]	]	PUNCT
ejpam-5850	13	10	,	,	PUNCT
ejpam-5850	13	11	every	every	DET
ejpam-5850	13	12	graph	graph	NOUN
ejpam-5850	13	13	can	can	AUX
ejpam-5850	13	14	be	be	AUX
ejpam-5850	13	15	represented	represent	VERB
ejpam-5850	13	16	in	in	ADP
ejpam-5850	13	17	an	an	DET
ejpam-5850	13	18	infinite	infinite	ADJ
ejpam-5850	13	19	number	number	NOUN
ejpam-5850	13	20	of	of	ADP
ejpam-5850	13	21	different	different	ADJ
ejpam-5850	13	22	ways	way	NOUN
ejpam-5850	13	23	inside	inside	ADP
ejpam-5850	13	24	a	a	DET
ejpam-5850	13	25	magmoid	magmoid	NOUN
ejpam-5850	13	26	.	.	PUNCT
ejpam-5850	14	1	to	to	PART
ejpam-5850	14	2	overcome	overcome	VERB
ejpam-5850	14	3	this	this	DET
ejpam-5850	14	4	ambiguity	ambiguity	NOUN
ejpam-5850	14	5	,	,	PUNCT
ejpam-5850	14	6	the	the	DET
ejpam-5850	14	7	algebraic	algebraic	ADJ
ejpam-5850	14	8	structure	structure	NOUN
ejpam-5850	14	9	of	of	ADP
ejpam-5850	14	10	graphoids	graphoid	NOUN
ejpam-5850	14	11	was	be	AUX
ejpam-5850	14	12	introduced	introduce	VERB
ejpam-5850	14	13	in	in	ADP
ejpam-5850	14	14	[	[	X
ejpam-5850	14	15	10	10	NUM
ejpam-5850	14	16	]	]	PUNCT
ejpam-5850	14	17	by	by	ADP
ejpam-5850	14	18	considering	consider	VERB
ejpam-5850	14	19	the	the	DET
ejpam-5850	14	20	quotient	quotient	NOUN
ejpam-5850	14	21	magmoid	magmoid	NOUN
ejpam-5850	14	22	obtained	obtain	VERB
ejpam-5850	14	23	via	via	ADP
ejpam-5850	14	24	a	a	DET
ejpam-5850	14	25	finite	finite	ADJ
ejpam-5850	14	26	set	set	NOUN
ejpam-5850	14	27	equivalences	equivalence	NOUN
ejpam-5850	14	28	.	.	PUNCT
ejpam-5850	15	1	by	by	ADP
ejpam-5850	15	2	employing	employ	VERB
ejpam-5850	15	3	a	a	DET
ejpam-5850	15	4	special	special	ADJ
ejpam-5850	15	5	type	type	NOUN
ejpam-5850	15	6	of	of	ADP
ejpam-5850	15	7	graphoid	graphoid	NOUN
ejpam-5850	15	8	,	,	PUNCT
ejpam-5850	15	9	called	call	VERB
ejpam-5850	15	10	here	here	ADV
ejpam-5850	15	11	unitary	unitary	ADJ
ejpam-5850	15	12	graphoid	graphoid	NOUN
ejpam-5850	15	13	,	,	PUNCT
ejpam-5850	15	14	automata	automata	NOUN
ejpam-5850	15	15	operating	operate	VERB
ejpam-5850	15	16	on	on	ADP
ejpam-5850	15	17	graphs	graph	NOUN
ejpam-5850	15	18	were	be	AUX
ejpam-5850	15	19	defined	define	VERB
ejpam-5850	15	20	for	for	ADP
ejpam-5850	15	21	the	the	DET
ejpam-5850	15	22	first	first	ADJ
ejpam-5850	15	23	time	time	NOUN
ejpam-5850	15	24	in	in	ADP
ejpam-5850	15	25	[	[	X
ejpam-5850	15	26	10	10	NUM
ejpam-5850	15	27	]	]	PUNCT
ejpam-5850	15	28	.	.	PUNCT
ejpam-5850	16	1	as	as	SCONJ
ejpam-5850	16	2	it	it	PRON
ejpam-5850	16	3	was	be	AUX
ejpam-5850	16	4	shown	show	VERB
ejpam-5850	16	5	in	in	ADP
ejpam-5850	16	6	[	[	X
ejpam-5850	16	7	19	19	NUM
ejpam-5850	16	8	]	]	PUNCT
ejpam-5850	16	9	,	,	PUNCT
ejpam-5850	16	10	unitary	unitary	ADJ
ejpam-5850	16	11	graphoids	graphoid	NOUN
ejpam-5850	16	12	are	be	AUX
ejpam-5850	16	13	the	the	DET
ejpam-5850	16	14	simplest	simple	ADJ
ejpam-5850	16	15	kind	kind	NOUN
ejpam-5850	16	16	of	of	ADP
ejpam-5850	16	17	abelian	abelian	ADJ
ejpam-5850	16	18	relational	relational	ADJ
ejpam-5850	16	19	graphoids	graphoid	NOUN
ejpam-5850	16	20	.	.	PUNCT
ejpam-5850	17	1	the	the	DET
ejpam-5850	17	2	class	class	NOUN
ejpam-5850	17	3	of	of	ADP
ejpam-5850	17	4	abelian	abelian	PROPN
ejpam-5850	17	5	doi	doi	PROPN
ejpam-5850	17	6	:	:	PUNCT
ejpam-5850	17	7	https://doi.org/10.29020/nybg.ejpam.v18i1.5850	https://doi.org/10.29020/nybg.ejpam.v18i1.5850	NUM
ejpam-5850	17	8	email	email	NOUN
ejpam-5850	17	9	address	address	NOUN
ejpam-5850	17	10	:	:	PUNCT
ejpam-5850	17	11	kyriakos.papadopoulos@ku.edu.kw	kyriakos.papadopoulos@ku.edu.kw	PROPN
ejpam-5850	17	12	(	(	PUNCT
ejpam-5850	17	13	k.	k.	PROPN
ejpam-5850	17	14	papadopoulos	papadopoulos	PROPN
ejpam-5850	17	15	)	)	PUNCT
ejpam-5850	17	16	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5850	17	17	1	1	NUM
ejpam-5850	17	18	copyright	copyright	NOUN
ejpam-5850	17	19	:	:	PUNCT
ejpam-5850	17	20	©	©	PROPN
ejpam-5850	17	21	2025	2025	NUM
ejpam-5850	17	22	the	the	DET
ejpam-5850	17	23	author(s	author(s	NOUN
ejpam-5850	17	24	)	)	PUNCT
ejpam-5850	17	25	.	.	PUNCT
ejpam-5850	18	1	(	(	PUNCT
ejpam-5850	18	2	cc	cc	NOUN
ejpam-5850	18	3	by	by	ADP
ejpam-5850	18	4	-	-	PUNCT
ejpam-5850	18	5	nc	nc	PROPN
ejpam-5850	18	6	4.0	4.0	NUM
ejpam-5850	18	7	)	)	PUNCT
ejpam-5850	18	8	k.	k.	PROPN
ejpam-5850	18	9	papadopoulos	papadopoulos	PROPN
ejpam-5850	18	10	/	/	SYM
ejpam-5850	18	11	eur	eur	PROPN
ejpam-5850	18	12	.	.	PUNCT
ejpam-5850	19	1	j.	j.	PROPN
ejpam-5850	19	2	pure	pure	PROPN
ejpam-5850	19	3	appl	appl	PROPN
ejpam-5850	19	4	.	.	PROPN
ejpam-5850	19	5	math	math	PROPN
ejpam-5850	19	6	,	,	PUNCT
ejpam-5850	19	7	18	18	NUM
ejpam-5850	19	8	(	(	PUNCT
ejpam-5850	19	9	1	1	NUM
ejpam-5850	19	10	)	)	PUNCT
ejpam-5850	19	11	(	(	PUNCT
ejpam-5850	19	12	2025	2025	NUM
ejpam-5850	19	13	)	)	PUNCT
ejpam-5850	19	14	,	,	PUNCT
ejpam-5850	19	15	5850	5850	NUM
ejpam-5850	19	16	2	2	NUM
ejpam-5850	19	17	of	of	ADP
ejpam-5850	19	18	13	13	NUM
ejpam-5850	19	19	graphoids	graphoid	NOUN
ejpam-5850	19	20	is	be	AUX
ejpam-5850	19	21	in	in	ADP
ejpam-5850	19	22	turn	turn	NOUN
ejpam-5850	19	23	included	include	VERB
ejpam-5850	19	24	in	in	ADP
ejpam-5850	19	25	a	a	DET
ejpam-5850	19	26	larger	large	ADJ
ejpam-5850	19	27	class	class	NOUN
ejpam-5850	19	28	of	of	ADP
ejpam-5850	19	29	graphoids	graphoid	NOUN
ejpam-5850	19	30	called	call	VERB
ejpam-5850	19	31	relational	relational	ADJ
ejpam-5850	19	32	graphoids	graphoid	NOUN
ejpam-5850	19	33	which	which	PRON
ejpam-5850	19	34	are	be	AUX
ejpam-5850	19	35	obtained	obtain	VERB
ejpam-5850	19	36	by	by	ADP
ejpam-5850	19	37	appropriately	appropriately	ADV
ejpam-5850	19	38	structuring	structure	VERB
ejpam-5850	19	39	the	the	DET
ejpam-5850	19	40	set	set	NOUN
ejpam-5850	19	41	of	of	ADP
ejpam-5850	19	42	all	all	DET
ejpam-5850	19	43	relations	relation	NOUN
ejpam-5850	19	44	on	on	ADP
ejpam-5850	19	45	the	the	DET
ejpam-5850	19	46	state	state	NOUN
ejpam-5850	19	47	set	set	NOUN
ejpam-5850	19	48	of	of	ADP
ejpam-5850	19	49	the	the	DET
ejpam-5850	19	50	graph	graph	NOUN
ejpam-5850	19	51	automaton	automaton	NOUN
ejpam-5850	19	52	into	into	ADP
ejpam-5850	19	53	a	a	DET
ejpam-5850	19	54	graphoid	graphoid	NOUN
ejpam-5850	19	55	[	[	X
ejpam-5850	19	56	19	19	NUM
ejpam-5850	19	57	]	]	PUNCT
ejpam-5850	19	58	.	.	PUNCT
ejpam-5850	20	1	the	the	DET
ejpam-5850	20	2	definition	definition	NOUN
ejpam-5850	20	3	of	of	ADP
ejpam-5850	20	4	graph	graph	NOUN
ejpam-5850	20	5	automata	automata	NOUN
ejpam-5850	20	6	given	give	VERB
ejpam-5850	20	7	in	in	ADP
ejpam-5850	20	8	[	[	X
ejpam-5850	20	9	10	10	NUM
ejpam-5850	20	10	]	]	PUNCT
ejpam-5850	20	11	,	,	PUNCT
ejpam-5850	20	12	implies	imply	VERB
ejpam-5850	20	13	that	that	SCONJ
ejpam-5850	20	14	the	the	DET
ejpam-5850	20	15	recognition	recognition	NOUN
ejpam-5850	20	16	capacity	capacity	NOUN
ejpam-5850	20	17	of	of	ADP
ejpam-5850	20	18	graph	graph	NOUN
ejpam-5850	20	19	automata	automata	NOUN
ejpam-5850	20	20	may	may	AUX
ejpam-5850	20	21	vary	vary	VERB
ejpam-5850	20	22	with	with	ADP
ejpam-5850	20	23	respect	respect	NOUN
ejpam-5850	20	24	to	to	ADP
ejpam-5850	20	25	the	the	DET
ejpam-5850	20	26	specific	specific	ADJ
ejpam-5850	20	27	graphoid	graphoid	NOUN
ejpam-5850	20	28	employed	employ	VERB
ejpam-5850	20	29	in	in	ADP
ejpam-5850	20	30	their	their	PRON
ejpam-5850	20	31	construction	construction	NOUN
ejpam-5850	20	32	.	.	PUNCT
ejpam-5850	21	1	however	however	ADV
ejpam-5850	21	2	,	,	PUNCT
ejpam-5850	21	3	this	this	PRON
ejpam-5850	21	4	remains	remain	VERB
ejpam-5850	21	5	an	an	DET
ejpam-5850	21	6	open	open	ADJ
ejpam-5850	21	7	question	question	NOUN
ejpam-5850	21	8	,	,	PUNCT
ejpam-5850	21	9	since	since	SCONJ
ejpam-5850	21	10	the	the	DET
ejpam-5850	21	11	recognition	recognition	NOUN
ejpam-5850	21	12	mechanism	mechanism	NOUN
ejpam-5850	21	13	of	of	ADP
ejpam-5850	21	14	the	the	DET
ejpam-5850	21	15	various	various	ADJ
ejpam-5850	21	16	types	type	NOUN
ejpam-5850	21	17	of	of	ADP
ejpam-5850	21	18	graph	graph	NOUN
ejpam-5850	21	19	automata	automata	NOUN
ejpam-5850	21	20	with	with	ADP
ejpam-5850	21	21	respect	respect	NOUN
ejpam-5850	21	22	to	to	ADP
ejpam-5850	21	23	their	their	PRON
ejpam-5850	21	24	underlying	underlie	VERB
ejpam-5850	21	25	graphoid	graphoid	NOUN
ejpam-5850	21	26	has	have	AUX
ejpam-5850	21	27	not	not	PART
ejpam-5850	21	28	been	be	AUX
ejpam-5850	21	29	further	far	ADV
ejpam-5850	21	30	investigated	investigate	VERB
ejpam-5850	21	31	besides	besides	SCONJ
ejpam-5850	21	32	unitary	unitary	ADJ
ejpam-5850	21	33	graphoids	graphoid	NOUN
ejpam-5850	21	34	.	.	PUNCT
ejpam-5850	22	1	regarding	regard	VERB
ejpam-5850	22	2	the	the	DET
ejpam-5850	22	3	recognition	recognition	NOUN
ejpam-5850	22	4	ability	ability	NOUN
ejpam-5850	22	5	of	of	ADP
ejpam-5850	22	6	unitary	unitary	ADJ
ejpam-5850	22	7	graph	graph	NOUN
ejpam-5850	22	8	automata	automata	NOUN
ejpam-5850	22	9	,	,	PUNCT
ejpam-5850	22	10	i.e.	i.e.	X
ejpam-5850	22	11	,	,	PUNCT
ejpam-5850	22	12	graph	graph	NOUN
ejpam-5850	22	13	automata	automata	NOUN
ejpam-5850	22	14	employing	employ	VERB
ejpam-5850	22	15	unitary	unitary	ADJ
ejpam-5850	22	16	graphoids	graphoid	NOUN
ejpam-5850	22	17	,	,	PUNCT
ejpam-5850	22	18	we	we	PRON
ejpam-5850	22	19	know	know	VERB
ejpam-5850	22	20	that	that	SCONJ
ejpam-5850	22	21	they	they	PRON
ejpam-5850	22	22	recognize	recognize	VERB
ejpam-5850	22	23	for	for	ADP
ejpam-5850	22	24	every	every	DET
ejpam-5850	22	25	positive	positive	ADJ
ejpam-5850	22	26	integer	integer	NOUN
ejpam-5850	22	27	k	k	PROPN
ejpam-5850	22	28	,	,	PUNCT
ejpam-5850	22	29	the	the	DET
ejpam-5850	22	30	set	set	NOUN
ejpam-5850	22	31	of	of	ADP
ejpam-5850	22	32	all	all	DET
ejpam-5850	22	33	directed	direct	VERB
ejpam-5850	22	34	k	k	ADJ
ejpam-5850	22	35	-	-	ADJ
ejpam-5850	22	36	colorable	colorable	ADJ
ejpam-5850	22	37	graphs	graph	NOUN
ejpam-5850	22	38	without	without	ADP
ejpam-5850	22	39	inputs	input	NOUN
ejpam-5850	22	40	and	and	CCONJ
ejpam-5850	22	41	outputs	output	NOUN
ejpam-5850	22	42	[	[	X
ejpam-5850	22	43	20	20	NUM
ejpam-5850	22	44	]	]	PUNCT
ejpam-5850	22	45	.	.	PUNCT
ejpam-5850	23	1	graph	graph	NOUN
ejpam-5850	23	2	colorability	colorability	NOUN
ejpam-5850	23	3	and	and	CCONJ
ejpam-5850	23	4	the	the	DET
ejpam-5850	23	5	associated	associated	ADJ
ejpam-5850	23	6	chromatic	chromatic	ADJ
ejpam-5850	23	7	number	number	NOUN
ejpam-5850	23	8	of	of	ADP
ejpam-5850	23	9	a	a	DET
ejpam-5850	23	10	graph	graph	NOUN
ejpam-5850	23	11	is	be	AUX
ejpam-5850	23	12	a	a	DET
ejpam-5850	23	13	fundamental	fundamental	ADJ
ejpam-5850	23	14	concept	concept	NOUN
ejpam-5850	23	15	in	in	ADP
ejpam-5850	23	16	graph	graph	NOUN
ejpam-5850	23	17	theory	theory	NOUN
ejpam-5850	23	18	,	,	PUNCT
ejpam-5850	23	19	representing	represent	VERB
ejpam-5850	23	20	the	the	DET
ejpam-5850	23	21	minimum	minimum	ADJ
ejpam-5850	23	22	number	number	NOUN
ejpam-5850	23	23	of	of	ADP
ejpam-5850	23	24	colors	color	NOUN
ejpam-5850	23	25	required	require	VERB
ejpam-5850	23	26	to	to	PART
ejpam-5850	23	27	color	color	VERB
ejpam-5850	23	28	the	the	DET
ejpam-5850	23	29	vertices	vertex	NOUN
ejpam-5850	23	30	of	of	ADP
ejpam-5850	23	31	a	a	DET
ejpam-5850	23	32	graph	graph	NOUN
ejpam-5850	23	33	such	such	ADJ
ejpam-5850	23	34	that	that	SCONJ
ejpam-5850	23	35	no	no	DET
ejpam-5850	23	36	two	two	NUM
ejpam-5850	23	37	adjacent	adjacent	ADJ
ejpam-5850	23	38	vertices	vertex	NOUN
ejpam-5850	23	39	share	share	VERB
ejpam-5850	23	40	the	the	DET
ejpam-5850	23	41	same	same	ADJ
ejpam-5850	23	42	color	color	NOUN
ejpam-5850	23	43	(	(	PUNCT
ejpam-5850	23	44	see	see	VERB
ejpam-5850	23	45	[	[	X
ejpam-5850	23	46	2–4	2–4	NUM
ejpam-5850	23	47	,	,	PUNCT
ejpam-5850	23	48	6	6	NUM
ejpam-5850	23	49	,	,	PUNCT
ejpam-5850	23	50	16	16	NUM
ejpam-5850	23	51	]	]	PUNCT
ejpam-5850	23	52	)	)	PUNCT
ejpam-5850	23	53	.	.	PUNCT
ejpam-5850	24	1	in	in	ADP
ejpam-5850	24	2	this	this	DET
ejpam-5850	24	3	respect	respect	NOUN
ejpam-5850	24	4	,	,	PUNCT
ejpam-5850	24	5	it	it	PRON
ejpam-5850	24	6	is	be	AUX
ejpam-5850	24	7	manifested	manifest	VERB
ejpam-5850	24	8	that	that	SCONJ
ejpam-5850	24	9	graph	graph	NOUN
ejpam-5850	24	10	automata	automata	NOUN
ejpam-5850	24	11	can	can	AUX
ejpam-5850	24	12	recognize	recognize	VERB
ejpam-5850	24	13	complex	complex	ADJ
ejpam-5850	24	14	algebraic	algebraic	ADJ
ejpam-5850	24	15	structures	structure	NOUN
ejpam-5850	24	16	even	even	ADV
ejpam-5850	24	17	when	when	SCONJ
ejpam-5850	24	18	operating	operate	VERB
ejpam-5850	24	19	on	on	ADP
ejpam-5850	24	20	the	the	DET
ejpam-5850	24	21	simplest	simple	ADJ
ejpam-5850	24	22	type	type	NOUN
ejpam-5850	24	23	of	of	ADP
ejpam-5850	24	24	graphoid	graphoid	NOUN
ejpam-5850	24	25	.	.	PUNCT
ejpam-5850	25	1	in	in	ADP
ejpam-5850	25	2	this	this	DET
ejpam-5850	25	3	paper	paper	NOUN
ejpam-5850	25	4	,	,	PUNCT
ejpam-5850	25	5	we	we	PRON
ejpam-5850	25	6	investigate	investigate	VERB
ejpam-5850	25	7	further	further	ADJ
ejpam-5850	25	8	unitary	unitary	ADJ
ejpam-5850	25	9	graph	graph	NOUN
ejpam-5850	25	10	automata	automata	NOUN
ejpam-5850	25	11	and	and	CCONJ
ejpam-5850	25	12	we	we	PRON
ejpam-5850	25	13	prove	prove	VERB
ejpam-5850	25	14	that	that	SCONJ
ejpam-5850	25	15	the	the	DET
ejpam-5850	25	16	set	set	NOUN
ejpam-5850	25	17	of	of	ADP
ejpam-5850	25	18	directed	direct	VERB
ejpam-5850	25	19	graphs	graph	NOUN
ejpam-5850	25	20	of	of	ADP
ejpam-5850	25	21	length	length	NOUN
ejpam-5850	25	22	at	at	ADP
ejpam-5850	25	23	most	most	ADV
ejpam-5850	25	24	k	k	PROPN
ejpam-5850	25	25	is	be	AUX
ejpam-5850	25	26	recognized	recognize	VERB
ejpam-5850	25	27	automata	automata	NOUN
ejpam-5850	25	28	of	of	ADP
ejpam-5850	25	29	this	this	DET
ejpam-5850	25	30	type	type	NOUN
ejpam-5850	25	31	and	and	CCONJ
ejpam-5850	25	32	hence	hence	ADV
ejpam-5850	25	33	belongs	belong	VERB
ejpam-5850	25	34	to	to	ADP
ejpam-5850	25	35	the	the	DET
ejpam-5850	25	36	associate	associate	ADJ
ejpam-5850	25	37	class	class	NOUN
ejpam-5850	25	38	of	of	ADP
ejpam-5850	25	39	graph	graph	NOUN
ejpam-5850	25	40	languages	language	NOUN
ejpam-5850	25	41	denoted	denote	VERB
ejpam-5850	25	42	here	here	ADV
ejpam-5850	25	43	by	by	ADP
ejpam-5850	25	44	urec(σ	urec(σ	NOUN
ejpam-5850	25	45	)	)	PUNCT
ejpam-5850	25	46	.	.	PUNCT
ejpam-5850	26	1	using	use	VERB
ejpam-5850	26	2	a	a	DET
ejpam-5850	26	3	similar	similar	ADJ
ejpam-5850	26	4	construction	construction	NOUN
ejpam-5850	26	5	,	,	PUNCT
ejpam-5850	26	6	we	we	PRON
ejpam-5850	26	7	also	also	ADV
ejpam-5850	26	8	generalize	generalize	VERB
ejpam-5850	26	9	the	the	DET
ejpam-5850	26	10	result	result	NOUN
ejpam-5850	26	11	of	of	ADP
ejpam-5850	26	12	[	[	X
ejpam-5850	26	13	20	20	NUM
ejpam-5850	26	14	]	]	PUNCT
ejpam-5850	26	15	by	by	ADP
ejpam-5850	26	16	showing	show	VERB
ejpam-5850	26	17	that	that	SCONJ
ejpam-5850	26	18	,	,	PUNCT
ejpam-5850	26	19	for	for	ADP
ejpam-5850	26	20	every	every	DET
ejpam-5850	26	21	k	k	PROPN
ejpam-5850	26	22	,	,	PUNCT
ejpam-5850	26	23	the	the	DET
ejpam-5850	26	24	set	set	NOUN
ejpam-5850	26	25	of	of	ADP
ejpam-5850	26	26	all	all	DET
ejpam-5850	26	27	directed	direct	VERB
ejpam-5850	26	28	graphs	graph	NOUN
ejpam-5850	26	29	with	with	ADP
ejpam-5850	26	30	chromatic	chromatic	ADJ
ejpam-5850	26	31	number	number	NOUN
ejpam-5850	26	32	at	at	ADP
ejpam-5850	26	33	most	most	ADJ
ejpam-5850	26	34	k	k	PROPN
ejpam-5850	26	35	belongs	belong	VERB
ejpam-5850	26	36	to	to	ADP
ejpam-5850	26	37	urec(σ	urec(σ	NOUN
ejpam-5850	26	38	)	)	PUNCT
ejpam-5850	26	39	.	.	PUNCT
ejpam-5850	27	1	moreover	moreover	ADV
ejpam-5850	27	2	,	,	PUNCT
ejpam-5850	27	3	in	in	ADP
ejpam-5850	27	4	this	this	DET
ejpam-5850	27	5	paper	paper	NOUN
ejpam-5850	27	6	,	,	PUNCT
ejpam-5850	27	7	we	we	PRON
ejpam-5850	27	8	examine	examine	VERB
ejpam-5850	27	9	,	,	PUNCT
ejpam-5850	27	10	for	for	ADP
ejpam-5850	27	11	the	the	DET
ejpam-5850	27	12	first	first	ADJ
ejpam-5850	27	13	time	time	NOUN
ejpam-5850	27	14	in	in	ADP
ejpam-5850	27	15	the	the	DET
ejpam-5850	27	16	literature	literature	NOUN
ejpam-5850	27	17	,	,	PUNCT
ejpam-5850	27	18	abelian	abelian	ADJ
ejpam-5850	27	19	nonunitary	nonunitary	ADJ
ejpam-5850	27	20	graph	graph	NOUN
ejpam-5850	27	21	automata	automata	NOUN
ejpam-5850	27	22	.	.	PUNCT
ejpam-5850	28	1	we	we	PRON
ejpam-5850	28	2	show	show	VERB
ejpam-5850	28	3	that	that	SCONJ
ejpam-5850	28	4	the	the	DET
ejpam-5850	28	5	set	set	NOUN
ejpam-5850	28	6	of	of	ADP
ejpam-5850	28	7	all	all	DET
ejpam-5850	28	8	graphs	graph	NOUN
ejpam-5850	28	9	with	with	ADP
ejpam-5850	28	10	an	an	DET
ejpam-5850	28	11	odd	odd	ADJ
ejpam-5850	28	12	number	number	NOUN
ejpam-5850	28	13	of	of	ADP
ejpam-5850	28	14	edges	edge	NOUN
ejpam-5850	28	15	belongs	belong	VERB
ejpam-5850	28	16	to	to	ADP
ejpam-5850	28	17	the	the	DET
ejpam-5850	28	18	class	class	NOUN
ejpam-5850	28	19	arec(σ	arec(σ	NOUN
ejpam-5850	28	20	)	)	PUNCT
ejpam-5850	28	21	of	of	ADP
ejpam-5850	28	22	all	all	DET
ejpam-5850	28	23	graph	graph	NOUN
ejpam-5850	28	24	languages	language	NOUN
ejpam-5850	28	25	recognized	recognize	VERB
ejpam-5850	28	26	by	by	ADP
ejpam-5850	28	27	abelian	abelian	ADJ
ejpam-5850	28	28	relational	relational	ADJ
ejpam-5850	28	29	graph	graph	NOUN
ejpam-5850	28	30	automata	automata	NOUN
ejpam-5850	28	31	.	.	PUNCT
ejpam-5850	29	1	this	this	PRON
ejpam-5850	29	2	is	be	AUX
ejpam-5850	29	3	proved	prove	VERB
ejpam-5850	29	4	by	by	ADP
ejpam-5850	29	5	constructing	construct	VERB
ejpam-5850	29	6	an	an	DET
ejpam-5850	29	7	abelian	abelian	ADJ
ejpam-5850	29	8	non	non	ADJ
ejpam-5850	29	9	-	-	ADJ
ejpam-5850	29	10	unitary	unitary	ADJ
ejpam-5850	29	11	graph	graph	NOUN
ejpam-5850	29	12	automaton	automaton	NOUN
ejpam-5850	29	13	with	with	ADP
ejpam-5850	29	14	two	two	NUM
ejpam-5850	29	15	states	state	NOUN
ejpam-5850	29	16	that	that	PRON
ejpam-5850	29	17	can	can	AUX
ejpam-5850	29	18	be	be	AUX
ejpam-5850	29	19	structured	structure	VERB
ejpam-5850	29	20	into	into	ADP
ejpam-5850	29	21	a	a	DET
ejpam-5850	29	22	group	group	NOUN
ejpam-5850	29	23	via	via	ADP
ejpam-5850	29	24	the	the	DET
ejpam-5850	29	25	operation	operation	NOUN
ejpam-5850	29	26	of	of	ADP
ejpam-5850	29	27	modulo	modulo	NOUN
ejpam-5850	29	28	2	2	NUM
ejpam-5850	29	29	addition	addition	NOUN
ejpam-5850	29	30	,	,	PUNCT
ejpam-5850	29	31	as	as	SCONJ
ejpam-5850	29	32	dictated	dictate	VERB
ejpam-5850	29	33	by	by	ADP
ejpam-5850	29	34	the	the	DET
ejpam-5850	29	35	classification	classification	NOUN
ejpam-5850	29	36	theorem	theorem	NOUN
ejpam-5850	29	37	of	of	ADP
ejpam-5850	29	38	[	[	X
ejpam-5850	29	39	19	19	NUM
ejpam-5850	29	40	]	]	PUNCT
ejpam-5850	29	41	.	.	PUNCT
ejpam-5850	30	1	in	in	ADP
ejpam-5850	30	2	addition	addition	NOUN
ejpam-5850	30	3	to	to	ADP
ejpam-5850	30	4	that	that	PRON
ejpam-5850	30	5	,	,	PUNCT
ejpam-5850	30	6	we	we	PRON
ejpam-5850	30	7	prove	prove	VERB
ejpam-5850	30	8	that	that	SCONJ
ejpam-5850	30	9	unitary	unitary	ADJ
ejpam-5850	30	10	graph	graph	NOUN
ejpam-5850	30	11	automata	automata	NOUN
ejpam-5850	30	12	can	can	AUX
ejpam-5850	30	13	not	not	PART
ejpam-5850	30	14	recognize	recognize	VERB
ejpam-5850	30	15	this	this	DET
ejpam-5850	30	16	graph	graph	NOUN
ejpam-5850	30	17	language	language	NOUN
ejpam-5850	30	18	.	.	PUNCT
ejpam-5850	31	1	as	as	ADP
ejpam-5850	31	2	a	a	DET
ejpam-5850	31	3	consequence	consequence	NOUN
ejpam-5850	31	4	it	it	PRON
ejpam-5850	31	5	is	be	AUX
ejpam-5850	31	6	proved	prove	VERB
ejpam-5850	31	7	that	that	SCONJ
ejpam-5850	31	8	urec(σ	urec(σ	NOUN
ejpam-5850	31	9	)	)	PUNCT
ejpam-5850	31	10	is	be	AUX
ejpam-5850	31	11	properly	properly	ADV
ejpam-5850	31	12	contained	contain	VERB
ejpam-5850	31	13	in	in	ADP
ejpam-5850	31	14	arec(σ	arec(σ	NOUN
ejpam-5850	31	15	)	)	PUNCT
ejpam-5850	31	16	.	.	PUNCT
ejpam-5850	32	1	in	in	ADP
ejpam-5850	32	2	the	the	DET
ejpam-5850	32	3	next	next	ADJ
ejpam-5850	32	4	section	section	NOUN
ejpam-5850	32	5	,	,	PUNCT
ejpam-5850	32	6	we	we	PRON
ejpam-5850	32	7	review	review	VERB
ejpam-5850	32	8	the	the	DET
ejpam-5850	32	9	fundamental	fundamental	ADJ
ejpam-5850	32	10	definitions	definition	NOUN
ejpam-5850	32	11	of	of	ADP
ejpam-5850	32	12	magmoids	magmoid	NOUN
ejpam-5850	32	13	and	and	CCONJ
ejpam-5850	32	14	hypergraphs	hypergraph	NOUN
ejpam-5850	32	15	.	.	PUNCT
ejpam-5850	33	1	section	section	NOUN
ejpam-5850	33	2	3	3	NUM
ejpam-5850	33	3	presents	present	VERB
ejpam-5850	33	4	the	the	DET
ejpam-5850	33	5	basic	basic	ADJ
ejpam-5850	33	6	algebraic	algebraic	ADJ
ejpam-5850	33	7	structures	structure	NOUN
ejpam-5850	33	8	employed	employ	VERB
ejpam-5850	33	9	for	for	ADP
ejpam-5850	33	10	the	the	DET
ejpam-5850	33	11	construction	construction	NOUN
ejpam-5850	33	12	of	of	ADP
ejpam-5850	33	13	graph	graph	NOUN
ejpam-5850	33	14	automata	automata	NOUN
ejpam-5850	33	15	and	and	CCONJ
ejpam-5850	33	16	introduces	introduce	VERB
ejpam-5850	33	17	the	the	DET
ejpam-5850	33	18	notions	notion	NOUN
ejpam-5850	33	19	of	of	ADP
ejpam-5850	33	20	relational	relational	NOUN
ejpam-5850	33	21	,	,	PUNCT
ejpam-5850	33	22	abelian	abelian	NOUN
ejpam-5850	33	23	and	and	CCONJ
ejpam-5850	33	24	unitary	unitary	ADJ
ejpam-5850	33	25	graphoids	graphoid	NOUN
ejpam-5850	33	26	.	.	PUNCT
ejpam-5850	34	1	in	in	ADP
ejpam-5850	34	2	the	the	DET
ejpam-5850	34	3	next	next	ADJ
ejpam-5850	34	4	section	section	NOUN
ejpam-5850	34	5	,	,	PUNCT
ejpam-5850	34	6	we	we	PRON
ejpam-5850	34	7	provide	provide	VERB
ejpam-5850	34	8	the	the	DET
ejpam-5850	34	9	formal	formal	ADJ
ejpam-5850	34	10	definition	definition	NOUN
ejpam-5850	34	11	of	of	ADP
ejpam-5850	34	12	a	a	DET
ejpam-5850	34	13	graph	graph	NOUN
ejpam-5850	34	14	automaton	automaton	NOUN
ejpam-5850	34	15	and	and	CCONJ
ejpam-5850	34	16	the	the	DET
ejpam-5850	34	17	different	different	ADJ
ejpam-5850	34	18	types	type	NOUN
ejpam-5850	34	19	of	of	ADP
ejpam-5850	34	20	graph	graph	NOUN
ejpam-5850	34	21	automata	automata	NOUN
ejpam-5850	34	22	corresponding	correspond	VERB
ejpam-5850	34	23	to	to	ADP
ejpam-5850	34	24	the	the	DET
ejpam-5850	34	25	introduced	introduce	VERB
ejpam-5850	34	26	graphoids	graphoid	NOUN
ejpam-5850	34	27	.	.	PUNCT
ejpam-5850	35	1	moreover	moreover	ADV
ejpam-5850	35	2	,	,	PUNCT
ejpam-5850	35	3	in	in	ADP
ejpam-5850	35	4	this	this	DET
ejpam-5850	35	5	section	section	NOUN
ejpam-5850	35	6	we	we	PRON
ejpam-5850	35	7	construct	construct	VERB
ejpam-5850	35	8	a	a	DET
ejpam-5850	35	9	unitary	unitary	ADJ
ejpam-5850	35	10	graph	graph	NOUN
ejpam-5850	35	11	automaton	automaton	NOUN
ejpam-5850	35	12	recognizing	recognize	VERB
ejpam-5850	35	13	the	the	DET
ejpam-5850	35	14	set	set	NOUN
ejpam-5850	35	15	of	of	ADP
ejpam-5850	35	16	all	all	DET
ejpam-5850	35	17	directed	direct	VERB
ejpam-5850	35	18	graphs	graph	NOUN
ejpam-5850	35	19	with	with	ADP
ejpam-5850	35	20	a	a	DET
ejpam-5850	35	21	given	give	VERB
ejpam-5850	35	22	chromatic	chromatic	ADJ
ejpam-5850	35	23	number	number	NOUN
ejpam-5850	35	24	.	.	PUNCT
ejpam-5850	36	1	in	in	ADP
ejpam-5850	36	2	section	section	NOUN
ejpam-5850	36	3	5	5	NUM
ejpam-5850	36	4	we	we	PRON
ejpam-5850	36	5	introduce	introduce	VERB
ejpam-5850	36	6	a	a	DET
ejpam-5850	36	7	type	type	NOUN
ejpam-5850	36	8	of	of	ADP
ejpam-5850	36	9	abelian	abelian	ADJ
ejpam-5850	36	10	non	non	ADJ
ejpam-5850	36	11	-	-	ADJ
ejpam-5850	36	12	unitary	unitary	ADJ
ejpam-5850	36	13	graph	graph	NOUN
ejpam-5850	36	14	automaton	automaton	NOUN
ejpam-5850	36	15	which	which	PRON
ejpam-5850	36	16	recognizes	recognize	VERB
ejpam-5850	36	17	all	all	DET
ejpam-5850	36	18	graphs	graph	NOUN
ejpam-5850	36	19	with	with	ADP
ejpam-5850	36	20	an	an	DET
ejpam-5850	36	21	odd	odd	ADJ
ejpam-5850	36	22	number	number	NOUN
ejpam-5850	36	23	of	of	ADP
ejpam-5850	36	24	edges	edge	NOUN
ejpam-5850	36	25	.	.	PUNCT
ejpam-5850	37	1	it	it	PRON
ejpam-5850	37	2	is	be	AUX
ejpam-5850	37	3	then	then	ADV
ejpam-5850	37	4	proved	prove	VERB
ejpam-5850	37	5	that	that	SCONJ
ejpam-5850	37	6	this	this	DET
ejpam-5850	37	7	graph	graph	NOUN
ejpam-5850	37	8	language	language	NOUN
ejpam-5850	37	9	can	can	AUX
ejpam-5850	37	10	not	not	PART
ejpam-5850	37	11	be	be	AUX
ejpam-5850	37	12	recognized	recognize	VERB
ejpam-5850	37	13	by	by	ADP
ejpam-5850	37	14	a	a	DET
ejpam-5850	37	15	unitary	unitary	ADJ
ejpam-5850	37	16	graph	graph	NOUN
ejpam-5850	37	17	automaton	automaton	NOUN
ejpam-5850	37	18	establishing	establish	VERB
ejpam-5850	37	19	the	the	DET
ejpam-5850	37	20	proper	proper	ADJ
ejpam-5850	37	21	hierarchy	hierarchy	NOUN
ejpam-5850	37	22	of	of	ADP
ejpam-5850	37	23	the	the	DET
ejpam-5850	37	24	corresponding	correspond	VERB
ejpam-5850	37	25	classes	class	NOUN
ejpam-5850	37	26	.	.	PUNCT
ejpam-5850	38	1	k.	k.	PROPN
ejpam-5850	38	2	papadopoulos	papadopoulos	PROPN
ejpam-5850	38	3	/	/	SYM
ejpam-5850	38	4	eur	eur	PROPN
ejpam-5850	38	5	.	.	PUNCT
ejpam-5850	39	1	j.	j.	PROPN
ejpam-5850	39	2	pure	pure	PROPN
ejpam-5850	39	3	appl	appl	PROPN
ejpam-5850	39	4	.	.	PROPN
ejpam-5850	39	5	math	math	PROPN
ejpam-5850	39	6	,	,	PUNCT
ejpam-5850	39	7	18	18	NUM
ejpam-5850	39	8	(	(	PUNCT
ejpam-5850	39	9	1	1	NUM
ejpam-5850	39	10	)	)	PUNCT
ejpam-5850	39	11	(	(	PUNCT
ejpam-5850	39	12	2025	2025	NUM
ejpam-5850	39	13	)	)	PUNCT
ejpam-5850	39	14	,	,	PUNCT
ejpam-5850	39	15	5850	5850	NUM
ejpam-5850	39	16	3	3	NUM
ejpam-5850	39	17	of	of	ADP
ejpam-5850	39	18	13	13	NUM
ejpam-5850	39	19	2	2	NUM
ejpam-5850	39	20	.	.	PUNCT
ejpam-5850	39	21	magmoids	magmoid	NOUN
ejpam-5850	39	22	and	and	CCONJ
ejpam-5850	39	23	hypergraphs	hypergraph	NOUN
ejpam-5850	39	24	in	in	ADP
ejpam-5850	39	25	this	this	DET
ejpam-5850	39	26	section	section	NOUN
ejpam-5850	39	27	we	we	PRON
ejpam-5850	39	28	first	first	ADV
ejpam-5850	39	29	introduce	introduce	VERB
ejpam-5850	39	30	the	the	DET
ejpam-5850	39	31	algebraic	algebraic	ADJ
ejpam-5850	39	32	structure	structure	NOUN
ejpam-5850	39	33	of	of	ADP
ejpam-5850	39	34	magmoids	magmoid	NOUN
ejpam-5850	39	35	and	and	CCONJ
ejpam-5850	39	36	then	then	ADV
ejpam-5850	39	37	we	we	PRON
ejpam-5850	39	38	define	define	VERB
ejpam-5850	39	39	directed	directed	ADJ
ejpam-5850	39	40	graphs	graph	NOUN
ejpam-5850	39	41	with	with	ADP
ejpam-5850	39	42	specified	specified	ADJ
ejpam-5850	39	43	inputs	input	NOUN
ejpam-5850	39	44	and	and	CCONJ
ejpam-5850	39	45	outputs	output	NOUN
ejpam-5850	39	46	.	.	PUNCT
ejpam-5850	40	1	we	we	PRON
ejpam-5850	40	2	also	also	ADV
ejpam-5850	40	3	present	present	VERB
ejpam-5850	40	4	two	two	NUM
ejpam-5850	40	5	graph	graph	NOUN
ejpam-5850	40	6	operations	operation	NOUN
ejpam-5850	40	7	,	,	PUNCT
ejpam-5850	40	8	called	call	VERB
ejpam-5850	40	9	graph	graph	NOUN
ejpam-5850	40	10	sum	sum	NOUN
ejpam-5850	40	11	and	and	CCONJ
ejpam-5850	40	12	graph	graph	NOUN
ejpam-5850	40	13	product	product	NOUN
ejpam-5850	40	14	.	.	PUNCT
ejpam-5850	41	1	it	it	PRON
ejpam-5850	41	2	turns	turn	VERB
ejpam-5850	41	3	out	out	ADP
ejpam-5850	41	4	that	that	SCONJ
ejpam-5850	41	5	these	these	DET
ejpam-5850	41	6	two	two	NUM
ejpam-5850	41	7	operations	operation	NOUN
ejpam-5850	41	8	organize	organize	VERB
ejpam-5850	41	9	the	the	DET
ejpam-5850	41	10	set	set	NOUN
ejpam-5850	41	11	of	of	ADP
ejpam-5850	41	12	graphs	graph	NOUN
ejpam-5850	41	13	can	can	AUX
ejpam-5850	41	14	into	into	ADP
ejpam-5850	41	15	a	a	DET
ejpam-5850	41	16	magmoid	magmoid	NOUN
ejpam-5850	41	17	.	.	PUNCT
ejpam-5850	42	1	given	give	VERB
ejpam-5850	42	2	a	a	DET
ejpam-5850	42	3	set	set	NOUN
ejpam-5850	42	4	s	s	X
ejpam-5850	42	5	we	we	PRON
ejpam-5850	42	6	denote	denote	VERB
ejpam-5850	42	7	by	by	ADP
ejpam-5850	42	8	s∗	s∗	PROPN
ejpam-5850	42	9	the	the	DET
ejpam-5850	42	10	set	set	NOUN
ejpam-5850	42	11	of	of	ADP
ejpam-5850	42	12	all	all	DET
ejpam-5850	42	13	strings	string	NOUN
ejpam-5850	42	14	constructed	construct	VERB
ejpam-5850	42	15	from	from	ADP
ejpam-5850	42	16	the	the	DET
ejpam-5850	42	17	elements	element	NOUN
ejpam-5850	42	18	of	of	ADP
ejpam-5850	42	19	s	s	PROPN
ejpam-5850	42	20	,	,	PUNCT
ejpam-5850	42	21	we	we	PRON
ejpam-5850	42	22	denote	denote	VERB
ejpam-5850	42	23	by	by	ADP
ejpam-5850	42	24	ε	ε	PROPN
ejpam-5850	42	25	the	the	DET
ejpam-5850	42	26	empty	empty	ADJ
ejpam-5850	42	27	string	string	NOUN
ejpam-5850	42	28	,	,	PUNCT
ejpam-5850	42	29	and	and	CCONJ
ejpam-5850	42	30	we	we	PRON
ejpam-5850	42	31	set	set	VERB
ejpam-5850	42	32	s+	s+	ADV
ejpam-5850	42	33	=	=	PUNCT
ejpam-5850	42	34	s∗	s∗	PROPN
ejpam-5850	42	35	−	−	PROPN
ejpam-5850	42	36	{	{	PUNCT
ejpam-5850	42	37	ε	ε	PROPN
ejpam-5850	42	38	}	}	PUNCT
ejpam-5850	42	39	.	.	PUNCT
ejpam-5850	43	1	a	a	DET
ejpam-5850	43	2	doubly	doubly	ADV
ejpam-5850	43	3	ranked	rank	VERB
ejpam-5850	43	4	set	set	NOUN
ejpam-5850	43	5	a	a	PRON
ejpam-5850	43	6	=	=	X
ejpam-5850	43	7	(	(	PUNCT
ejpam-5850	43	8	am	am	NOUN
ejpam-5850	43	9	,	,	PUNCT
ejpam-5850	43	10	n)m	n)m	ADV
ejpam-5850	43	11	,	,	PUNCT
ejpam-5850	43	12	n∈n	n∈n	PROPN
ejpam-5850	43	13	,	,	PUNCT
ejpam-5850	43	14	consists	consist	VERB
ejpam-5850	43	15	of	of	ADP
ejpam-5850	43	16	a	a	DET
ejpam-5850	43	17	set	set	NOUN
ejpam-5850	43	18	a	a	DET
ejpam-5850	43	19	along	along	NOUN
ejpam-5850	43	20	with	with	ADP
ejpam-5850	43	21	a	a	DET
ejpam-5850	43	22	function	function	NOUN
ejpam-5850	43	23	rank	rank	NOUN
ejpam-5850	43	24	:	:	PUNCT
ejpam-5850	43	25	a	a	DET
ejpam-5850	43	26	→	→	SYM
ejpam-5850	43	27	n×	n×	NOUN
ejpam-5850	43	28	n	n	NOUN
ejpam-5850	43	29	and	and	CCONJ
ejpam-5850	43	30	is	be	AUX
ejpam-5850	43	31	defined	define	VERB
ejpam-5850	43	32	as	as	ADP
ejpam-5850	43	33	am	am	NOUN
ejpam-5850	43	34	,	,	PUNCT
ejpam-5850	43	35	n	n	X
ejpam-5850	43	36	=	=	PRON
ejpam-5850	43	37	{	{	PUNCT
ejpam-5850	43	38	a	a	DET
ejpam-5850	43	39	∈	∈	PROPN
ejpam-5850	43	40	a	a	DET
ejpam-5850	43	41	|	|	NOUN
ejpam-5850	43	42	rank(a	rank(a	NOUN
ejpam-5850	43	43	)	)	PUNCT
ejpam-5850	43	44	=	=	SYM
ejpam-5850	43	45	(	(	PUNCT
ejpam-5850	43	46	m	m	PROPN
ejpam-5850	43	47	,	,	PUNCT
ejpam-5850	43	48	n	n	CCONJ
ejpam-5850	43	49	)	)	PUNCT
ejpam-5850	43	50	}	}	PUNCT
ejpam-5850	43	51	.	.	PUNCT
ejpam-5850	44	1	for	for	ADP
ejpam-5850	44	2	simplicity	simplicity	NOUN
ejpam-5850	44	3	,	,	PUNCT
ejpam-5850	44	4	we	we	PRON
ejpam-5850	44	5	will	will	AUX
ejpam-5850	44	6	omit	omit	VERB
ejpam-5850	44	7	the	the	DET
ejpam-5850	44	8	subscript	subscript	NOUN
ejpam-5850	44	9	and	and	CCONJ
ejpam-5850	44	10	denote	denote	VERB
ejpam-5850	44	11	a	a	DET
ejpam-5850	44	12	doubly	doubly	ADV
ejpam-5850	44	13	ranked	rank	VERB
ejpam-5850	44	14	set	set	VERB
ejpam-5850	44	15	by	by	ADP
ejpam-5850	44	16	a	a	DET
ejpam-5850	44	17	=	=	X
ejpam-5850	44	18	(	(	PUNCT
ejpam-5850	44	19	am	am	NOUN
ejpam-5850	44	20	,	,	PUNCT
ejpam-5850	44	21	n	n	CCONJ
ejpam-5850	44	22	)	)	PUNCT
ejpam-5850	44	23	.	.	PUNCT
ejpam-5850	45	1	a	a	DET
ejpam-5850	45	2	magmoid	magmoid	NOUN
ejpam-5850	45	3	is	be	AUX
ejpam-5850	45	4	a	a	DET
ejpam-5850	45	5	doubly	doubly	ADV
ejpam-5850	45	6	ranked	rank	VERB
ejpam-5850	45	7	set	set	NOUN
ejpam-5850	45	8	m	m	NOUN
ejpam-5850	45	9	=	=	SYM
ejpam-5850	45	10	(	(	PUNCT
ejpam-5850	45	11	mm	mm	PROPN
ejpam-5850	45	12	,	,	PUNCT
ejpam-5850	45	13	n	n	CCONJ
ejpam-5850	45	14	)	)	PUNCT
ejpam-5850	45	15	equipped	equip	VERB
ejpam-5850	45	16	with	with	ADP
ejpam-5850	45	17	two	two	NUM
ejpam-5850	45	18	operations	operation	NOUN
ejpam-5850	45	19	◦	◦	NOUN
ejpam-5850	45	20	:	:	PUNCT
ejpam-5850	45	21	mm	mm	INTJ
ejpam-5850	45	22	,	,	PUNCT
ejpam-5850	45	23	n	n	PRON
ejpam-5850	45	24	×mn	×mn	NOUN
ejpam-5850	45	25	,	,	PUNCT
ejpam-5850	45	26	k	k	PROPN
ejpam-5850	45	27	→	→	SYM
ejpam-5850	45	28	mm	mm	PROPN
ejpam-5850	45	29	,	,	PUNCT
ejpam-5850	45	30	k	k	PROPN
ejpam-5850	45	31	,	,	PUNCT
ejpam-5850	45	32	□	□	PUNCT
ejpam-5850	45	33	:	:	PUNCT
ejpam-5850	45	34	mm	mm	NUM
ejpam-5850	45	35	,	,	PUNCT
ejpam-5850	45	36	n	n	X
ejpam-5850	45	37	×mm′,n′	×mm′,n′	NOUN
ejpam-5850	45	38	→	→	SYM
ejpam-5850	45	39	mm+m′,n+n′	mm+m′,n+n′	NUM
ejpam-5850	45	40	that	that	PRON
ejpam-5850	45	41	are	be	AUX
ejpam-5850	45	42	associative	associative	ADJ
ejpam-5850	45	43	in	in	ADP
ejpam-5850	45	44	the	the	DET
ejpam-5850	45	45	usual	usual	ADJ
ejpam-5850	45	46	way	way	NOUN
ejpam-5850	45	47	and	and	CCONJ
ejpam-5850	45	48	satisfy	satisfy	VERB
ejpam-5850	45	49	the	the	DET
ejpam-5850	45	50	distributive	distributive	ADJ
ejpam-5850	45	51	law	law	NOUN
ejpam-5850	45	52	(	(	PUNCT
ejpam-5850	45	53	f	f	X
ejpam-5850	45	54	◦	◦	VERB
ejpam-5850	45	55	g	g	NOUN
ejpam-5850	45	56	)	)	PUNCT
ejpam-5850	45	57	□	□	PUNCT
ejpam-5850	45	58	(	(	PUNCT
ejpam-5850	45	59	f	f	NOUN
ejpam-5850	45	60	′	′	NUM
ejpam-5850	45	61	◦	◦	NOUN
ejpam-5850	45	62	g′	g′	NOUN
ejpam-5850	45	63	)	)	PUNCT
ejpam-5850	45	64	=	=	PUNCT
ejpam-5850	46	1	(	(	PUNCT
ejpam-5850	46	2	f	f	X
ejpam-5850	46	3	□	□	PUNCT
ejpam-5850	46	4	f	f	PROPN
ejpam-5850	46	5	′	′	NOUN
ejpam-5850	46	6	)	)	PUNCT
ejpam-5850	46	7	◦	◦	NOUN
ejpam-5850	46	8	(	(	PUNCT
ejpam-5850	46	9	g	g	NOUN
ejpam-5850	46	10	□	□	PUNCT
ejpam-5850	46	11	g′	g′	NOUN
ejpam-5850	46	12	)	)	PUNCT
ejpam-5850	46	13	whenever	whenever	SCONJ
ejpam-5850	46	14	the	the	DET
ejpam-5850	46	15	operations	operation	NOUN
ejpam-5850	46	16	are	be	AUX
ejpam-5850	46	17	defined	define	VERB
ejpam-5850	46	18	.	.	PUNCT
ejpam-5850	47	1	additionally	additionally	ADV
ejpam-5850	47	2	,	,	PUNCT
ejpam-5850	47	3	there	there	PRON
ejpam-5850	47	4	exists	exist	VERB
ejpam-5850	47	5	a	a	DET
ejpam-5850	47	6	sequence	sequence	NOUN
ejpam-5850	47	7	of	of	ADP
ejpam-5850	47	8	constants	constant	NOUN
ejpam-5850	47	9	en	en	ADP
ejpam-5850	47	10	∈	∈	PROPN
ejpam-5850	47	11	mn	mn	PROPN
ejpam-5850	47	12	,	,	PUNCT
ejpam-5850	47	13	n	n	CCONJ
ejpam-5850	47	14	,	,	PUNCT
ejpam-5850	47	15	called	call	VERB
ejpam-5850	47	16	units	unit	NOUN
ejpam-5850	47	17	,	,	PUNCT
ejpam-5850	47	18	such	such	ADJ
ejpam-5850	47	19	that	that	SCONJ
ejpam-5850	47	20	em	em	PRON
ejpam-5850	47	21	◦	◦	VERB
ejpam-5850	47	22	f	f	X
ejpam-5850	48	1	=	=	SYM
ejpam-5850	48	2	f	f	PROPN
ejpam-5850	48	3	=	=	SYM
ejpam-5850	48	4	f	f	PROPN
ejpam-5850	48	5	◦	◦	NOUN
ejpam-5850	48	6	en	en	X
ejpam-5850	48	7	,	,	PUNCT
ejpam-5850	48	8	e0	e0	PROPN
ejpam-5850	48	9	□	□	PUNCT
ejpam-5850	48	10	f	f	X
ejpam-5850	48	11	=	=	SYM
ejpam-5850	48	12	f	f	PROPN
ejpam-5850	48	13	=	=	SYM
ejpam-5850	48	14	f	f	PROPN
ejpam-5850	48	15	□	□	PUNCT
ejpam-5850	48	16	e0	e0	PROPN
ejpam-5850	48	17	,	,	PUNCT
ejpam-5850	48	18	em	em	PRON
ejpam-5850	48	19	□	□	PUNCT
ejpam-5850	48	20	en	en	X
ejpam-5850	48	21	=	=	SYM
ejpam-5850	48	22	em+n	em+n	PROPN
ejpam-5850	48	23	for	for	ADP
ejpam-5850	48	24	all	all	DET
ejpam-5850	48	25	f	f	PROPN
ejpam-5850	48	26	∈	∈	PROPN
ejpam-5850	48	27	mm	mm	PROPN
ejpam-5850	48	28	,	,	PUNCT
ejpam-5850	48	29	n	n	PROPN
ejpam-5850	48	30	and	and	CCONJ
ejpam-5850	48	31	all	all	DET
ejpam-5850	48	32	m	m	PROPN
ejpam-5850	48	33	,	,	PUNCT
ejpam-5850	48	34	n	n	PROPN
ejpam-5850	48	35	∈	∈	PROPN
ejpam-5850	48	36	n.	n.	NOUN
ejpam-5850	48	37	the	the	DET
ejpam-5850	48	38	final	final	ADJ
ejpam-5850	48	39	equation	equation	NOUN
ejpam-5850	48	40	implies	imply	VERB
ejpam-5850	48	41	that	that	SCONJ
ejpam-5850	48	42	the	the	DET
ejpam-5850	48	43	elements	element	NOUN
ejpam-5850	48	44	en	en	ADV
ejpam-5850	48	45	are	be	AUX
ejpam-5850	48	46	uniquely	uniquely	ADV
ejpam-5850	48	47	determined	determine	VERB
ejpam-5850	48	48	by	by	ADP
ejpam-5850	48	49	e1	e1	NOUN
ejpam-5850	48	50	,	,	PUNCT
ejpam-5850	48	51	which	which	PRON
ejpam-5850	48	52	we	we	PRON
ejpam-5850	48	53	shall	shall	AUX
ejpam-5850	48	54	denote	denote	VERB
ejpam-5850	48	55	simply	simply	ADV
ejpam-5850	48	56	by	by	ADP
ejpam-5850	48	57	e.	e.	PROPN
ejpam-5850	48	58	the	the	DET
ejpam-5850	48	59	free	free	ADJ
ejpam-5850	48	60	magmoid	magmoid	NOUN
ejpam-5850	48	61	mag(σ	mag(σ	PROPN
ejpam-5850	48	62	)	)	PUNCT
ejpam-5850	48	63	generated	generate	VERB
ejpam-5850	48	64	by	by	ADP
ejpam-5850	48	65	a	a	DET
ejpam-5850	48	66	doubly	doubly	ADV
ejpam-5850	48	67	ranked	rank	VERB
ejpam-5850	48	68	set	set	ADJ
ejpam-5850	48	69	σ	σ	PROPN
ejpam-5850	48	70	is	be	AUX
ejpam-5850	48	71	constructed	construct	VERB
ejpam-5850	48	72	in	in	ADP
ejpam-5850	48	73	[	[	X
ejpam-5850	48	74	7	7	NUM
ejpam-5850	48	75	]	]	PUNCT
ejpam-5850	48	76	.	.	PUNCT
ejpam-5850	49	1	the	the	DET
ejpam-5850	49	2	sets	set	NOUN
ejpam-5850	49	3	relm	relm	NOUN
ejpam-5850	49	4	,	,	PUNCT
ejpam-5850	49	5	n(q	n(q	PROPN
ejpam-5850	49	6	)	)	PUNCT
ejpam-5850	49	7	of	of	ADP
ejpam-5850	49	8	all	all	DET
ejpam-5850	49	9	relations	relation	NOUN
ejpam-5850	49	10	from	from	ADP
ejpam-5850	49	11	qm	qm	PROPN
ejpam-5850	49	12	to	to	ADP
ejpam-5850	49	13	qn	qn	PROPN
ejpam-5850	49	14	are	be	AUX
ejpam-5850	49	15	defined	define	VERB
ejpam-5850	49	16	as	as	ADP
ejpam-5850	49	17	relm	relm	NOUN
ejpam-5850	49	18	,	,	PUNCT
ejpam-5850	49	19	n(q	n(q	PROPN
ejpam-5850	49	20	)	)	PUNCT
ejpam-5850	49	21	=	=	PRON
ejpam-5850	50	1	{	{	PUNCT
ejpam-5850	50	2	r	r	NOUN
ejpam-5850	50	3	|	|	ADV
ejpam-5850	50	4	r	r	NOUN
ejpam-5850	50	5	⊆	⊆	NUM
ejpam-5850	50	6	qm	qm	PROPN
ejpam-5850	50	7	×qn	×qn	PROPN
ejpam-5850	50	8	}	}	PUNCT
ejpam-5850	50	9	and	and	CCONJ
ejpam-5850	50	10	can	can	AUX
ejpam-5850	50	11	be	be	AUX
ejpam-5850	50	12	structured	structure	VERB
ejpam-5850	50	13	into	into	ADP
ejpam-5850	50	14	a	a	DET
ejpam-5850	50	15	magmoid	magmoid	NOUN
ejpam-5850	50	16	with	with	ADP
ejpam-5850	50	17	◦	◦	NOUN
ejpam-5850	50	18	as	as	ADP
ejpam-5850	50	19	the	the	DET
ejpam-5850	50	20	usual	usual	ADJ
ejpam-5850	50	21	relational	relational	ADJ
ejpam-5850	50	22	composition	composition	NOUN
ejpam-5850	50	23	and	and	CCONJ
ejpam-5850	50	24	□	□	PUNCT
ejpam-5850	50	25	defined	define	VERB
ejpam-5850	50	26	as	as	SCONJ
ejpam-5850	50	27	follows	follow	VERB
ejpam-5850	50	28	:	:	PUNCT
ejpam-5850	50	29	for	for	ADP
ejpam-5850	50	30	r	r	PROPN
ejpam-5850	50	31	∈	∈	PROPN
ejpam-5850	50	32	relm	relm	NOUN
ejpam-5850	50	33	,	,	PUNCT
ejpam-5850	50	34	n(q	n(q	PROPN
ejpam-5850	50	35	)	)	PUNCT
ejpam-5850	50	36	and	and	CCONJ
ejpam-5850	50	37	s	s	PROPN
ejpam-5850	50	38	∈	∈	PROPN
ejpam-5850	50	39	relm′,n′(q	relm′,n′(q	PROPN
ejpam-5850	50	40	)	)	PUNCT
ejpam-5850	50	41	,	,	PUNCT
ejpam-5850	50	42	r	r	X
ejpam-5850	50	43	□	□	PUNCT
ejpam-5850	50	44	s	s	PART
ejpam-5850	50	45	=	=	PUNCT
ejpam-5850	50	46	{	{	PUNCT
ejpam-5850	50	47	(	(	PUNCT
ejpam-5850	50	48	u1u2	u1u2	NOUN
ejpam-5850	50	49	,	,	PUNCT
ejpam-5850	50	50	v1v2	v1v2	PUNCT
ejpam-5850	50	51	)	)	PUNCT
ejpam-5850	50	52	|	|	ADV
ejpam-5850	50	53	(	(	PUNCT
ejpam-5850	50	54	u1	u1	NOUN
ejpam-5850	50	55	,	,	PUNCT
ejpam-5850	50	56	v1	v1	NOUN
ejpam-5850	50	57	)	)	PUNCT
ejpam-5850	50	58	∈	∈	PROPN
ejpam-5850	50	59	r	r	NOUN
ejpam-5850	50	60	and	and	CCONJ
ejpam-5850	50	61	(	(	PUNCT
ejpam-5850	50	62	u2	u2	PROPN
ejpam-5850	50	63	,	,	PUNCT
ejpam-5850	50	64	v2	v2	PROPN
ejpam-5850	50	65	)	)	PUNCT
ejpam-5850	50	66	∈	∈	PROPN
ejpam-5850	50	67	s	s	PART
ejpam-5850	50	68	}	}	PUNCT
ejpam-5850	50	69	,	,	PUNCT
ejpam-5850	50	70	where	where	SCONJ
ejpam-5850	50	71	u1	u1	PROPN
ejpam-5850	50	72	∈	∈	PROPN
ejpam-5850	50	73	qm	qm	PROPN
ejpam-5850	50	74	,	,	PUNCT
ejpam-5850	50	75	u2	u2	PROPN
ejpam-5850	50	76	∈	∈	PROPN
ejpam-5850	50	77	qm′	qm′	X
ejpam-5850	50	78	,	,	PUNCT
ejpam-5850	50	79	v1	v1	PROPN
ejpam-5850	50	80	∈	∈	PROPN
ejpam-5850	50	81	qn	qn	NOUN
ejpam-5850	50	82	,	,	PUNCT
ejpam-5850	50	83	v2	v2	PROPN
ejpam-5850	50	84	∈	∈	PROPN
ejpam-5850	50	85	qn′	qn′	NOUN
ejpam-5850	50	86	.	.	PUNCT
ejpam-5850	51	1	here	here	ADV
ejpam-5850	51	2	,	,	PUNCT
ejpam-5850	51	3	q0	q0	PROPN
ejpam-5850	51	4	=	=	SYM
ejpam-5850	51	5	{	{	PUNCT
ejpam-5850	51	6	ε	ε	PROPN
ejpam-5850	51	7	}	}	PUNCT
ejpam-5850	51	8	,	,	PUNCT
ejpam-5850	51	9	with	with	ADP
ejpam-5850	51	10	ε	ε	PROPN
ejpam-5850	51	11	as	as	ADP
ejpam-5850	51	12	the	the	DET
ejpam-5850	51	13	empty	empty	ADJ
ejpam-5850	51	14	word	word	NOUN
ejpam-5850	51	15	of	of	ADP
ejpam-5850	51	16	q∗.	q∗.	NOUN
ejpam-5850	51	17	the	the	DET
ejpam-5850	51	18	units	unit	NOUN
ejpam-5850	51	19	are	be	AUX
ejpam-5850	51	20	defined	define	VERB
ejpam-5850	51	21	as	as	ADP
ejpam-5850	51	22	e0	e0	PROPN
ejpam-5850	51	23	=	=	SYM
ejpam-5850	51	24	{	{	PUNCT
ejpam-5850	51	25	(	(	PUNCT
ejpam-5850	51	26	ε	ε	PROPN
ejpam-5850	51	27	,	,	PUNCT
ejpam-5850	51	28	ε	ε	PROPN
ejpam-5850	51	29	)	)	PUNCT
ejpam-5850	51	30	}	}	PUNCT
ejpam-5850	51	31	and	and	CCONJ
ejpam-5850	51	32	e	e	X
ejpam-5850	51	33	=	=	SYM
ejpam-5850	51	34	{	{	PUNCT
ejpam-5850	51	35	(	(	PUNCT
ejpam-5850	51	36	g	g	NOUN
ejpam-5850	51	37	,	,	PUNCT
ejpam-5850	51	38	g	g	NOUN
ejpam-5850	51	39	)	)	PUNCT
ejpam-5850	51	40	|	|	ADV
ejpam-5850	51	41	g	g	PROPN
ejpam-5850	51	42	∈	∈	PROPN
ejpam-5850	51	43	q	q	NOUN
ejpam-5850	51	44	}	}	PUNCT
ejpam-5850	51	45	.	.	PUNCT
ejpam-5850	52	1	we	we	PRON
ejpam-5850	52	2	denote	denote	VERB
ejpam-5850	52	3	by	by	ADP
ejpam-5850	52	4	rel(q	rel(q	PROPN
ejpam-5850	52	5	)	)	PUNCT
ejpam-5850	52	6	=	=	SYM
ejpam-5850	52	7	(	(	PUNCT
ejpam-5850	52	8	relm	relm	NOUN
ejpam-5850	52	9	,	,	PUNCT
ejpam-5850	52	10	n(q	n(q	PROPN
ejpam-5850	52	11	)	)	PUNCT
ejpam-5850	52	12	)	)	PUNCT
ejpam-5850	53	1	the	the	DET
ejpam-5850	53	2	magmoid	magmoid	NOUN
ejpam-5850	53	3	constructed	construct	VERB
ejpam-5850	53	4	in	in	ADP
ejpam-5850	53	5	this	this	DET
ejpam-5850	53	6	manner	manner	NOUN
ejpam-5850	53	7	,	,	PUNCT
ejpam-5850	53	8	referred	refer	VERB
ejpam-5850	53	9	to	to	ADP
ejpam-5850	53	10	as	as	ADP
ejpam-5850	53	11	the	the	DET
ejpam-5850	53	12	relational	relational	ADJ
ejpam-5850	53	13	magmoid	magmoid	NOUN
ejpam-5850	53	14	of	of	ADP
ejpam-5850	53	15	q.	q.	PROPN
ejpam-5850	53	16	k.	k.	PROPN
ejpam-5850	53	17	papadopoulos	papadopoulos	PROPN
ejpam-5850	53	18	/	/	SYM
ejpam-5850	53	19	eur	eur	PROPN
ejpam-5850	53	20	.	.	PUNCT
ejpam-5850	54	1	j.	j.	PROPN
ejpam-5850	54	2	pure	pure	PROPN
ejpam-5850	54	3	appl	appl	PROPN
ejpam-5850	54	4	.	.	PROPN
ejpam-5850	54	5	math	math	PROPN
ejpam-5850	54	6	,	,	PUNCT
ejpam-5850	54	7	18	18	NUM
ejpam-5850	54	8	(	(	PUNCT
ejpam-5850	54	9	1	1	NUM
ejpam-5850	54	10	)	)	PUNCT
ejpam-5850	54	11	(	(	PUNCT
ejpam-5850	54	12	2025	2025	NUM
ejpam-5850	54	13	)	)	PUNCT
ejpam-5850	54	14	,	,	PUNCT
ejpam-5850	54	15	5850	5850	NUM
ejpam-5850	54	16	4	4	NUM
ejpam-5850	54	17	of	of	ADP
ejpam-5850	54	18	13	13	NUM
ejpam-5850	54	19	an	an	DET
ejpam-5850	54	20	(	(	PUNCT
ejpam-5850	54	21	m	m	PROPN
ejpam-5850	54	22	,	,	PUNCT
ejpam-5850	54	23	n)-(hyper)graph	n)-(hyper)graph	ADP
ejpam-5850	54	24	g	g	NOUN
ejpam-5850	54	25	=	=	SYM
ejpam-5850	54	26	(	(	PUNCT
ejpam-5850	54	27	v	v	NOUN
ejpam-5850	54	28	,	,	PUNCT
ejpam-5850	54	29	e	e	NOUN
ejpam-5850	54	30	,	,	PUNCT
ejpam-5850	54	31	s	s	PROPN
ejpam-5850	54	32	,	,	PUNCT
ejpam-5850	54	33	t	t	PROPN
ejpam-5850	54	34	,	,	PUNCT
ejpam-5850	54	35	l	l	NOUN
ejpam-5850	54	36	,	,	PUNCT
ejpam-5850	54	37	begin	begin	VERB
ejpam-5850	54	38	,	,	PUNCT
ejpam-5850	54	39	end	end	NOUN
ejpam-5850	54	40	)	)	PUNCT
ejpam-5850	54	41	with	with	ADP
ejpam-5850	54	42	edge	edge	NOUN
ejpam-5850	54	43	labels	label	NOUN
ejpam-5850	54	44	from	from	ADP
ejpam-5850	54	45	a	a	DET
ejpam-5850	54	46	doubly	doubly	ADV
ejpam-5850	54	47	ranked	rank	VERB
ejpam-5850	54	48	set	set	VERB
ejpam-5850	54	49	σ	σ	X
ejpam-5850	54	50	=	=	SYM
ejpam-5850	54	51	(	(	PUNCT
ejpam-5850	54	52	σm	σm	NOUN
ejpam-5850	54	53	,	,	PUNCT
ejpam-5850	54	54	n	n	CCONJ
ejpam-5850	54	55	)	)	PUNCT
ejpam-5850	54	56	is	be	AUX
ejpam-5850	54	57	a	a	DET
ejpam-5850	54	58	structure	structure	NOUN
ejpam-5850	54	59	consisting	consist	VERB
ejpam-5850	54	60	of	of	ADP
ejpam-5850	54	61	a	a	DET
ejpam-5850	54	62	finite	finite	ADJ
ejpam-5850	54	63	set	set	NOUN
ejpam-5850	54	64	of	of	ADP
ejpam-5850	54	65	vertices	vertex	NOUN
ejpam-5850	54	66	v	v	NUM
ejpam-5850	54	67	,	,	PUNCT
ejpam-5850	54	68	a	a	DET
ejpam-5850	54	69	finite	finite	ADJ
ejpam-5850	54	70	set	set	NOUN
ejpam-5850	54	71	of	of	ADP
ejpam-5850	54	72	edges	edge	NOUN
ejpam-5850	54	73	e	e	NOUN
ejpam-5850	54	74	,	,	PUNCT
ejpam-5850	54	75	the	the	DET
ejpam-5850	54	76	source	source	NOUN
ejpam-5850	54	77	and	and	CCONJ
ejpam-5850	54	78	target	target	NOUN
ejpam-5850	54	79	functions	function	NOUN
ejpam-5850	54	80	s	s	PART
ejpam-5850	54	81	:	:	PUNCT
ejpam-5850	54	82	e	e	X
ejpam-5850	54	83	→	→	SYM
ejpam-5850	54	84	v	v	PROPN
ejpam-5850	54	85	+	+	CCONJ
ejpam-5850	54	86	and	and	CCONJ
ejpam-5850	54	87	t	t	NOUN
ejpam-5850	54	88	:	:	PUNCT
ejpam-5850	55	1	e	e	X
ejpam-5850	55	2	→	→	SYM
ejpam-5850	55	3	v	v	X
ejpam-5850	55	4	+	+	PROPN
ejpam-5850	55	5	,	,	PUNCT
ejpam-5850	55	6	the	the	DET
ejpam-5850	55	7	labeling	labeling	NOUN
ejpam-5850	55	8	function	function	NOUN
ejpam-5850	55	9	l	l	NOUN
ejpam-5850	55	10	:	:	PUNCT
ejpam-5850	55	11	e	e	X
ejpam-5850	55	12	→	→	PUNCT
ejpam-5850	55	13	σ	σ	NOUN
ejpam-5850	55	14	such	such	ADJ
ejpam-5850	55	15	that	that	PRON
ejpam-5850	55	16	rank(l(e	rank(l(e	NOUN
ejpam-5850	55	17	)	)	PUNCT
ejpam-5850	55	18	)	)	PUNCT
ejpam-5850	56	1	=	=	SYM
ejpam-5850	56	2	(	(	PUNCT
ejpam-5850	56	3	|s(e)|	|s(e)|	PROPN
ejpam-5850	56	4	,	,	PUNCT
ejpam-5850	56	5	|t(e)|	|t(e)|	NOUN
ejpam-5850	56	6	)	)	PUNCT
ejpam-5850	56	7	and	and	CCONJ
ejpam-5850	56	8	sequences	sequence	NOUN
ejpam-5850	56	9	of	of	ADP
ejpam-5850	56	10	begin	begin	NOUN
ejpam-5850	56	11	and	and	CCONJ
ejpam-5850	56	12	end	end	VERB
ejpam-5850	56	13	nodes	node	NOUN
ejpam-5850	56	14	,	,	PUNCT
ejpam-5850	56	15	begin	begin	VERB
ejpam-5850	56	16	∈	∈	PROPN
ejpam-5850	56	17	v	v	ADP
ejpam-5850	56	18	∗	∗	NOUN
ejpam-5850	56	19	and	and	CCONJ
ejpam-5850	56	20	end	end	VERB
ejpam-5850	56	21	∈	∈	PROPN
ejpam-5850	56	22	v	v	ADP
ejpam-5850	56	23	∗	∗	NOUN
ejpam-5850	56	24	,	,	PUNCT
ejpam-5850	56	25	with	with	ADP
ejpam-5850	56	26	|begin|	|begin|	ADJ
ejpam-5850	56	27	=	=	SYM
ejpam-5850	56	28	m	m	NOUN
ejpam-5850	56	29	and	and	CCONJ
ejpam-5850	56	30	|end|	|end|	PROPN
ejpam-5850	56	31	=	=	SYM
ejpam-5850	56	32	n.	n.	PROPN
ejpam-5850	56	33	note	note	NOUN
ejpam-5850	56	34	that	that	SCONJ
ejpam-5850	56	35	vertices	vertex	NOUN
ejpam-5850	56	36	may	may	AUX
ejpam-5850	56	37	repeat	repeat	VERB
ejpam-5850	56	38	in	in	ADP
ejpam-5850	56	39	the	the	DET
ejpam-5850	56	40	begin	begin	NOUN
ejpam-5850	56	41	and	and	CCONJ
ejpam-5850	56	42	end	end	VERB
ejpam-5850	56	43	sequences	sequence	NOUN
ejpam-5850	56	44	,	,	PUNCT
ejpam-5850	56	45	as	as	ADV
ejpam-5850	56	46	well	well	ADV
ejpam-5850	56	47	as	as	ADP
ejpam-5850	56	48	in	in	ADP
ejpam-5850	56	49	edge	edge	NOUN
ejpam-5850	56	50	sources	source	NOUN
ejpam-5850	56	51	and	and	CCONJ
ejpam-5850	56	52	targets	target	NOUN
ejpam-5850	56	53	.	.	PUNCT
ejpam-5850	57	1	the	the	DET
ejpam-5850	57	2	set	set	NOUN
ejpam-5850	57	3	of	of	ADP
ejpam-5850	57	4	all	all	PRON
ejpam-5850	57	5	(	(	PUNCT
ejpam-5850	57	6	m	m	PROPN
ejpam-5850	57	7	,	,	PUNCT
ejpam-5850	57	8	n)-graphs	n)-graph	NOUN
ejpam-5850	57	9	over	over	ADP
ejpam-5850	57	10	σ	σ	PROPN
ejpam-5850	57	11	is	be	AUX
ejpam-5850	57	12	denoted	denote	VERB
ejpam-5850	57	13	by	by	ADP
ejpam-5850	57	14	grm	grm	PROPN
ejpam-5850	57	15	,	,	PUNCT
ejpam-5850	57	16	n(σ	n(σ	PROPN
ejpam-5850	57	17	)	)	PUNCT
ejpam-5850	57	18	,	,	PUNCT
ejpam-5850	57	19	and	and	CCONJ
ejpam-5850	57	20	we	we	PRON
ejpam-5850	57	21	define	define	VERB
ejpam-5850	57	22	gr(σ	gr(σ	NOUN
ejpam-5850	57	23	)	)	PUNCT
ejpam-5850	58	1	=	=	SYM
ejpam-5850	58	2	(	(	PUNCT
ejpam-5850	58	3	grm	grm	PROPN
ejpam-5850	58	4	,	,	PUNCT
ejpam-5850	58	5	n(σ))m	n(σ))m	PROPN
ejpam-5850	58	6	,	,	PUNCT
ejpam-5850	58	7	n∈n	n∈n	NOUN
ejpam-5850	58	8	.	.	PUNCT
ejpam-5850	59	1	a	a	DET
ejpam-5850	59	2	path	path	NOUN
ejpam-5850	59	3	of	of	ADP
ejpam-5850	59	4	length	length	NOUN
ejpam-5850	59	5	n	n	PROPN
ejpam-5850	59	6	inside	inside	ADP
ejpam-5850	59	7	a	a	DET
ejpam-5850	59	8	graph	graph	NOUN
ejpam-5850	59	9	g	g	NOUN
ejpam-5850	59	10	is	be	AUX
ejpam-5850	59	11	a	a	DET
ejpam-5850	59	12	sequence	sequence	NOUN
ejpam-5850	59	13	of	of	ADP
ejpam-5850	59	14	edges	edge	NOUN
ejpam-5850	59	15	e1	e1	NOUN
ejpam-5850	59	16	,	,	PUNCT
ejpam-5850	59	17	.	.	PUNCT
ejpam-5850	59	18	.	.	PUNCT
ejpam-5850	60	1	.	.	PUNCT
ejpam-5850	61	1	,	,	PUNCT
ejpam-5850	61	2	en	en	X
ejpam-5850	61	3	,	,	PUNCT
ejpam-5850	61	4	such	such	ADJ
ejpam-5850	61	5	that	that	SCONJ
ejpam-5850	61	6	,	,	PUNCT
ejpam-5850	61	7	for	for	ADP
ejpam-5850	61	8	every	every	DET
ejpam-5850	61	9	i	i	PRON
ejpam-5850	61	10	<	<	X
ejpam-5850	61	11	n	n	CCONJ
ejpam-5850	61	12	−	−	PROPN
ejpam-5850	61	13	1	1	NUM
ejpam-5850	61	14	,	,	PUNCT
ejpam-5850	61	15	there	there	PRON
ejpam-5850	61	16	exists	exist	VERB
ejpam-5850	61	17	a	a	DET
ejpam-5850	61	18	node	node	PROPN
ejpam-5850	61	19	vi	vi	NOUN
ejpam-5850	61	20	of	of	ADP
ejpam-5850	61	21	g	g	PROPN
ejpam-5850	61	22	,	,	PUNCT
ejpam-5850	61	23	that	that	PRON
ejpam-5850	61	24	appears	appear	VERB
ejpam-5850	61	25	in	in	ADP
ejpam-5850	61	26	both	both	CCONJ
ejpam-5850	61	27	the	the	DET
ejpam-5850	61	28	strings	string	NOUN
ejpam-5850	61	29	t(ei	t(ei	PROPN
ejpam-5850	61	30	)	)	PUNCT
ejpam-5850	61	31	and	and	CCONJ
ejpam-5850	61	32	s(ei+1	s(ei+1	ADJ
ejpam-5850	61	33	)	)	PUNCT
ejpam-5850	61	34	.	.	PUNCT
ejpam-5850	62	1	we	we	PRON
ejpam-5850	62	2	say	say	VERB
ejpam-5850	62	3	that	that	SCONJ
ejpam-5850	62	4	a	a	DET
ejpam-5850	62	5	path	path	NOUN
ejpam-5850	62	6	e1	e1	NOUN
ejpam-5850	62	7	,	,	PUNCT
ejpam-5850	62	8	.	.	PUNCT
ejpam-5850	62	9	.	.	PUNCT
ejpam-5850	62	10	.	.	PUNCT
ejpam-5850	63	1	,	,	PUNCT
ejpam-5850	63	2	en	en	ADV
ejpam-5850	63	3	inside	inside	ADP
ejpam-5850	63	4	g	g	PROPN
ejpam-5850	63	5	is	be	AUX
ejpam-5850	63	6	a	a	DET
ejpam-5850	63	7	cycle	cycle	NOUN
ejpam-5850	63	8	,	,	PUNCT
ejpam-5850	63	9	if	if	SCONJ
ejpam-5850	63	10	there	there	PRON
ejpam-5850	63	11	exists	exist	VERB
ejpam-5850	63	12	a	a	DET
ejpam-5850	63	13	node	node	NOUN
ejpam-5850	63	14	v	v	NOUN
ejpam-5850	63	15	of	of	ADP
ejpam-5850	63	16	g	g	NOUN
ejpam-5850	63	17	,	,	PUNCT
ejpam-5850	63	18	that	that	PRON
ejpam-5850	63	19	appears	appear	VERB
ejpam-5850	63	20	in	in	ADP
ejpam-5850	63	21	both	both	CCONJ
ejpam-5850	63	22	the	the	DET
ejpam-5850	63	23	strings	string	NOUN
ejpam-5850	63	24	s(e1	s(e1	NOUN
ejpam-5850	63	25	)	)	PUNCT
ejpam-5850	63	26	and	and	CCONJ
ejpam-5850	63	27	t(en	t(en	NOUN
ejpam-5850	63	28	)	)	PUNCT
ejpam-5850	63	29	.	.	PUNCT
ejpam-5850	64	1	the	the	DET
ejpam-5850	64	2	length	length	NOUN
ejpam-5850	64	3	of	of	ADP
ejpam-5850	64	4	a	a	DET
ejpam-5850	64	5	graph	graph	NOUN
ejpam-5850	64	6	g	g	NOUN
ejpam-5850	64	7	is	be	AUX
ejpam-5850	64	8	defined	define	VERB
ejpam-5850	64	9	as	as	ADP
ejpam-5850	64	10	the	the	DET
ejpam-5850	64	11	length	length	NOUN
ejpam-5850	64	12	of	of	ADP
ejpam-5850	64	13	the	the	DET
ejpam-5850	64	14	longest	long	ADJ
ejpam-5850	64	15	path	path	NOUN
ejpam-5850	64	16	inside	inside	ADP
ejpam-5850	64	17	g	g	NOUN
ejpam-5850	64	18	,	,	PUNCT
ejpam-5850	64	19	see	see	VERB
ejpam-5850	64	20	[	[	X
ejpam-5850	64	21	17	17	NUM
ejpam-5850	64	22	,	,	PUNCT
ejpam-5850	64	23	24	24	NUM
ejpam-5850	64	24	,	,	PUNCT
ejpam-5850	64	25	27	27	NUM
ejpam-5850	64	26	,	,	PUNCT
ejpam-5850	64	27	28	28	NUM
ejpam-5850	64	28	]	]	PUNCT
ejpam-5850	64	29	.	.	PUNCT
ejpam-5850	65	1	note	note	VERB
ejpam-5850	65	2	that	that	SCONJ
ejpam-5850	65	3	if	if	SCONJ
ejpam-5850	65	4	a	a	DET
ejpam-5850	65	5	graph	graph	NOUN
ejpam-5850	65	6	g	g	NOUN
ejpam-5850	65	7	has	have	VERB
ejpam-5850	65	8	a	a	DET
ejpam-5850	65	9	cycle	cycle	NOUN
ejpam-5850	65	10	then	then	ADV
ejpam-5850	65	11	there	there	PRON
ejpam-5850	65	12	will	will	AUX
ejpam-5850	65	13	be	be	AUX
ejpam-5850	65	14	a	a	DET
ejpam-5850	65	15	path	path	NOUN
ejpam-5850	65	16	of	of	ADP
ejpam-5850	65	17	length	length	NOUN
ejpam-5850	65	18	n	n	CCONJ
ejpam-5850	65	19	inside	inside	ADP
ejpam-5850	65	20	g	g	NOUN
ejpam-5850	65	21	for	for	ADP
ejpam-5850	65	22	any	any	DET
ejpam-5850	65	23	n	n	PRON
ejpam-5850	65	24	∈	∈	NOUN
ejpam-5850	65	25	n.	n.	NOUN
ejpam-5850	65	26	hence	hence	ADV
ejpam-5850	65	27	the	the	DET
ejpam-5850	65	28	length	length	NOUN
ejpam-5850	65	29	of	of	ADP
ejpam-5850	65	30	a	a	DET
ejpam-5850	65	31	graph	graph	NOUN
ejpam-5850	65	32	is	be	AUX
ejpam-5850	65	33	finite	finite	ADJ
ejpam-5850	65	34	if	if	SCONJ
ejpam-5850	65	35	and	and	CCONJ
ejpam-5850	65	36	only	only	ADV
ejpam-5850	65	37	if	if	SCONJ
ejpam-5850	65	38	the	the	DET
ejpam-5850	65	39	graph	graph	NOUN
ejpam-5850	65	40	is	be	AUX
ejpam-5850	65	41	acyclic	acyclic	ADJ
ejpam-5850	65	42	.	.	PUNCT
ejpam-5850	66	1	ordinary	ordinary	ADJ
ejpam-5850	66	2	graphs	graph	NOUN
ejpam-5850	66	3	are	be	AUX
ejpam-5850	66	4	obtained	obtain	VERB
ejpam-5850	66	5	as	as	ADP
ejpam-5850	66	6	a	a	DET
ejpam-5850	66	7	special	special	ADJ
ejpam-5850	66	8	case	case	NOUN
ejpam-5850	66	9	of	of	ADP
ejpam-5850	66	10	hypergraphs	hypergraph	NOUN
ejpam-5850	66	11	,	,	PUNCT
ejpam-5850	66	12	where	where	SCONJ
ejpam-5850	66	13	each	each	DET
ejpam-5850	66	14	hyperedge	hyperedge	NOUN
ejpam-5850	66	15	is	be	AUX
ejpam-5850	66	16	binary	binary	ADJ
ejpam-5850	66	17	,	,	PUNCT
ejpam-5850	66	18	i.e.	i.e.	X
ejpam-5850	66	19	for	for	ADP
ejpam-5850	66	20	every	every	DET
ejpam-5850	66	21	edge	edge	NOUN
ejpam-5850	66	22	e	e	NOUN
ejpam-5850	66	23	of	of	ADP
ejpam-5850	66	24	the	the	DET
ejpam-5850	66	25	graph	graph	NOUN
ejpam-5850	66	26	it	it	PRON
ejpam-5850	66	27	holds	hold	VERB
ejpam-5850	66	28	|s(e)|	|s(e)|	PROPN
ejpam-5850	66	29	=	=	SYM
ejpam-5850	66	30	|t(e)|	|t(e)|	NOUN
ejpam-5850	66	31	=	=	NOUN
ejpam-5850	66	32	1	1	X
ejpam-5850	66	33	.	.	PUNCT
ejpam-5850	67	1	a	a	DET
ejpam-5850	67	2	graph	graph	NOUN
ejpam-5850	67	3	is	be	AUX
ejpam-5850	67	4	called	call	VERB
ejpam-5850	67	5	unlabeled	unlabeled	ADJ
ejpam-5850	67	6	if	if	SCONJ
ejpam-5850	67	7	every	every	DET
ejpam-5850	67	8	edge	edge	NOUN
ejpam-5850	67	9	has	have	VERB
ejpam-5850	67	10	the	the	DET
ejpam-5850	67	11	same	same	ADJ
ejpam-5850	67	12	label	label	NOUN
ejpam-5850	67	13	.	.	PUNCT
ejpam-5850	68	1	an	an	DET
ejpam-5850	68	2	ordinary	ordinary	ADJ
ejpam-5850	68	3	,	,	PUNCT
ejpam-5850	68	4	unlabeled	unlabeled	ADJ
ejpam-5850	68	5	graph	graph	NOUN
ejpam-5850	68	6	is	be	AUX
ejpam-5850	68	7	called	call	VERB
ejpam-5850	68	8	conventional	conventional	ADJ
ejpam-5850	68	9	graph	graph	NOUN
ejpam-5850	68	10	.	.	PUNCT
ejpam-5850	69	1	a	a	DET
ejpam-5850	69	2	graph	graph	NOUN
ejpam-5850	69	3	has	have	VERB
ejpam-5850	69	4	no	no	DET
ejpam-5850	69	5	input	input	NOUN
ejpam-5850	69	6	(	(	PUNCT
ejpam-5850	69	7	resp	resp	NOUN
ejpam-5850	69	8	.	.	PUNCT
ejpam-5850	70	1	output	output	NOUN
ejpam-5850	70	2	)	)	PUNCT
ejpam-5850	71	1	if	if	SCONJ
ejpam-5850	71	2	the	the	DET
ejpam-5850	71	3	begin	begin	NOUN
ejpam-5850	71	4	(	(	PUNCT
ejpam-5850	71	5	resp	resp	NOUN
ejpam-5850	71	6	.	.	PUNCT
ejpam-5850	71	7	end	end	NOUN
ejpam-5850	71	8	)	)	PUNCT
ejpam-5850	71	9	sequence	sequence	NOUN
ejpam-5850	71	10	is	be	AUX
ejpam-5850	71	11	ε	ε	PROPN
ejpam-5850	71	12	.	.	PUNCT
ejpam-5850	72	1	a	a	DET
ejpam-5850	72	2	graph	graph	NOUN
ejpam-5850	72	3	without	without	ADP
ejpam-5850	72	4	input	input	NOUN
ejpam-5850	72	5	and	and	CCONJ
ejpam-5850	72	6	output	output	NOUN
ejpam-5850	72	7	is	be	AUX
ejpam-5850	72	8	by	by	ADP
ejpam-5850	72	9	definition	definition	NOUN
ejpam-5850	72	10	a	a	DET
ejpam-5850	72	11	(	(	PUNCT
ejpam-5850	72	12	0	0	NUM
ejpam-5850	72	13	,	,	PUNCT
ejpam-5850	72	14	0)-graph	0)-graph	PROPN
ejpam-5850	72	15	.	.	PROPN
ejpam-5850	73	1	conventional	conventional	ADJ
ejpam-5850	73	2	(	(	PUNCT
ejpam-5850	73	3	0	0	NUM
ejpam-5850	73	4	,	,	PUNCT
ejpam-5850	73	5	0)-graphs	0)-graphs	PRON
ejpam-5850	73	6	is	be	AUX
ejpam-5850	73	7	the	the	DET
ejpam-5850	73	8	most	most	ADV
ejpam-5850	73	9	commonly	commonly	ADV
ejpam-5850	73	10	examined	examine	VERB
ejpam-5850	73	11	type	type	NOUN
ejpam-5850	73	12	of	of	ADP
ejpam-5850	73	13	directed	direct	VERB
ejpam-5850	73	14	graphs	graph	NOUN
ejpam-5850	73	15	in	in	ADP
ejpam-5850	73	16	the	the	DET
ejpam-5850	73	17	literature	literature	NOUN
ejpam-5850	73	18	.	.	PUNCT
ejpam-5850	74	1	the	the	DET
ejpam-5850	74	2	product	product	NOUN
ejpam-5850	74	3	and	and	CCONJ
ejpam-5850	74	4	the	the	DET
ejpam-5850	74	5	sum	sum	NOUN
ejpam-5850	74	6	of	of	ADP
ejpam-5850	74	7	two	two	NUM
ejpam-5850	74	8	graphs	graph	NOUN
ejpam-5850	74	9	where	where	SCONJ
ejpam-5850	74	10	introduced	introduce	VERB
ejpam-5850	74	11	by	by	ADP
ejpam-5850	74	12	engelfriet	engelfriet	PROPN
ejpam-5850	74	13	and	and	CCONJ
ejpam-5850	74	14	vereijken	vereijken	VERB
ejpam-5850	74	15	in	in	ADP
ejpam-5850	74	16	[	[	X
ejpam-5850	74	17	15	15	NUM
ejpam-5850	74	18	]	]	PUNCT
ejpam-5850	74	19	,	,	PUNCT
ejpam-5850	74	20	see	see	VERB
ejpam-5850	74	21	also	also	ADV
ejpam-5850	74	22	[	[	X
ejpam-5850	74	23	7	7	NUM
ejpam-5850	74	24	,	,	PUNCT
ejpam-5850	74	25	10	10	NUM
ejpam-5850	74	26	,	,	PUNCT
ejpam-5850	74	27	19	19	NUM
ejpam-5850	74	28	]	]	PUNCT
ejpam-5850	74	29	.	.	PUNCT
ejpam-5850	75	1	for	for	ADP
ejpam-5850	75	2	an	an	DET
ejpam-5850	75	3	(	(	PUNCT
ejpam-5850	75	4	m	m	PROPN
ejpam-5850	75	5	,	,	PUNCT
ejpam-5850	75	6	n)-graph	n)-graph	PROPN
ejpam-5850	75	7	g	g	NOUN
ejpam-5850	75	8	and	and	CCONJ
ejpam-5850	75	9	an	an	DET
ejpam-5850	75	10	(	(	PUNCT
ejpam-5850	75	11	n	n	NOUN
ejpam-5850	75	12	,	,	PUNCT
ejpam-5850	75	13	k)-graph	k)-graph	PROPN
ejpam-5850	75	14	h	h	NOUN
ejpam-5850	75	15	,	,	PUNCT
ejpam-5850	75	16	the	the	DET
ejpam-5850	75	17	product	product	NOUN
ejpam-5850	75	18	g	g	NOUN
ejpam-5850	75	19	◦	◦	NOUN
ejpam-5850	75	20	h	h	NOUN
ejpam-5850	75	21	is	be	AUX
ejpam-5850	75	22	the	the	DET
ejpam-5850	75	23	(	(	PUNCT
ejpam-5850	75	24	m	m	PROPN
ejpam-5850	75	25	,	,	PUNCT
ejpam-5850	75	26	k)-graph	k)-graph	PUNCT
ejpam-5850	75	27	obtained	obtain	VERB
ejpam-5850	75	28	by	by	ADP
ejpam-5850	75	29	taking	take	VERB
ejpam-5850	75	30	the	the	DET
ejpam-5850	75	31	disjoint	disjoint	NOUN
ejpam-5850	75	32	union	union	NOUN
ejpam-5850	75	33	of	of	ADP
ejpam-5850	75	34	the	the	DET
ejpam-5850	75	35	two	two	NUM
ejpam-5850	75	36	graphs	graph	NOUN
ejpam-5850	75	37	and	and	CCONJ
ejpam-5850	75	38	identifying	identify	VERB
ejpam-5850	75	39	the	the	DET
ejpam-5850	75	40	ith	ith	PROPN
ejpam-5850	75	41	end	end	NOUN
ejpam-5850	75	42	node	node	NOUN
ejpam-5850	75	43	of	of	ADP
ejpam-5850	75	44	g	g	PROPN
ejpam-5850	75	45	with	with	ADP
ejpam-5850	75	46	the	the	DET
ejpam-5850	75	47	ith	ith	PROPN
ejpam-5850	75	48	begin	begin	VERB
ejpam-5850	75	49	node	node	NOUN
ejpam-5850	75	50	of	of	ADP
ejpam-5850	75	51	h	h	NOUN
ejpam-5850	75	52	for	for	ADP
ejpam-5850	75	53	all	all	DET
ejpam-5850	75	54	i.	i.	NOUN
ejpam-5850	75	55	the	the	DET
ejpam-5850	75	56	begin	begin	NOUN
ejpam-5850	75	57	and	and	CCONJ
ejpam-5850	75	58	end	end	VERB
ejpam-5850	75	59	sequences	sequence	NOUN
ejpam-5850	75	60	of	of	ADP
ejpam-5850	75	61	the	the	DET
ejpam-5850	75	62	product	product	NOUN
ejpam-5850	75	63	are	be	AUX
ejpam-5850	75	64	respectively	respectively	ADV
ejpam-5850	75	65	the	the	DET
ejpam-5850	75	66	begin	begin	NOUN
ejpam-5850	75	67	sequence	sequence	NOUN
ejpam-5850	75	68	of	of	ADP
ejpam-5850	75	69	g	g	PROPN
ejpam-5850	75	70	and	and	CCONJ
ejpam-5850	75	71	the	the	DET
ejpam-5850	75	72	end	end	NOUN
ejpam-5850	75	73	sequence	sequence	NOUN
ejpam-5850	75	74	of	of	ADP
ejpam-5850	75	75	h.	h.	PROPN
ejpam-5850	75	76	the	the	DET
ejpam-5850	75	77	sum	sum	NOUN
ejpam-5850	75	78	g	g	PROPN
ejpam-5850	75	79	□	□	PUNCT
ejpam-5850	75	80	h	h	NOUN
ejpam-5850	75	81	of	of	ADP
ejpam-5850	75	82	two	two	NUM
ejpam-5850	75	83	arbitrary	arbitrary	ADJ
ejpam-5850	75	84	graphs	graph	NOUN
ejpam-5850	75	85	g	g	NOUN
ejpam-5850	75	86	and	and	CCONJ
ejpam-5850	75	87	h	h	NOUN
ejpam-5850	75	88	is	be	AUX
ejpam-5850	75	89	obtained	obtain	VERB
ejpam-5850	75	90	by	by	ADP
ejpam-5850	75	91	taking	take	VERB
ejpam-5850	75	92	their	their	PRON
ejpam-5850	75	93	disjoint	disjoint	NOUN
ejpam-5850	75	94	union	union	NOUN
ejpam-5850	75	95	and	and	CCONJ
ejpam-5850	75	96	concatenating	concatenate	VERB
ejpam-5850	75	97	their	their	PRON
ejpam-5850	75	98	begin	begin	NOUN
ejpam-5850	75	99	and	and	CCONJ
ejpam-5850	75	100	end	end	VERB
ejpam-5850	75	101	node	node	ADJ
ejpam-5850	75	102	sequences	sequence	NOUN
ejpam-5850	75	103	.	.	PUNCT
ejpam-5850	76	1	for	for	ADP
ejpam-5850	76	2	each	each	DET
ejpam-5850	76	3	n	n	PRON
ejpam-5850	76	4	∈	∈	PROPN
ejpam-5850	76	5	n	n	CCONJ
ejpam-5850	76	6	,	,	PUNCT
ejpam-5850	76	7	let	let	VERB
ejpam-5850	76	8	en	en	INTJ
ejpam-5850	76	9	represent	represent	VERB
ejpam-5850	76	10	the	the	DET
ejpam-5850	76	11	discrete	discrete	ADJ
ejpam-5850	76	12	graph	graph	NOUN
ejpam-5850	76	13	of	of	ADP
ejpam-5850	76	14	rank	rank	NOUN
ejpam-5850	76	15	(	(	PUNCT
ejpam-5850	76	16	n	n	CCONJ
ejpam-5850	76	17	,	,	PUNCT
ejpam-5850	76	18	n	n	CCONJ
ejpam-5850	76	19	)	)	PUNCT
ejpam-5850	76	20	with	with	ADP
ejpam-5850	76	21	nodes	node	NOUN
ejpam-5850	76	22	x1	x1	PROPN
ejpam-5850	76	23	,	,	PUNCT
ejpam-5850	76	24	.	.	PUNCT
ejpam-5850	76	25	.	.	PUNCT
ejpam-5850	77	1	.	.	PUNCT
ejpam-5850	78	1	,	,	PUNCT
ejpam-5850	78	2	xn	xn	PROPN
ejpam-5850	78	3	and	and	CCONJ
ejpam-5850	78	4	begin	begin	VERB
ejpam-5850	78	5	=	=	NOUN
ejpam-5850	78	6	end	end	NOUN
ejpam-5850	79	1	=	=	PUNCT
ejpam-5850	79	2	x1	x1	PROPN
ejpam-5850	79	3	·	·	PUNCT
ejpam-5850	79	4	·	·	PUNCT
ejpam-5850	79	5	·	·	PUNCT
ejpam-5850	79	6	xn	xn	NUM
ejpam-5850	79	7	;	;	PUNCT
ejpam-5850	79	8	we	we	PRON
ejpam-5850	79	9	denote	denote	VERB
ejpam-5850	79	10	e1	e1	PROPN
ejpam-5850	79	11	simply	simply	ADV
ejpam-5850	79	12	by	by	ADP
ejpam-5850	79	13	e.	e.	PROPN
ejpam-5850	79	14	it	it	PRON
ejpam-5850	79	15	is	be	AUX
ejpam-5850	79	16	straightforward	straightforward	ADJ
ejpam-5850	79	17	to	to	PART
ejpam-5850	79	18	verify	verify	VERB
ejpam-5850	79	19	that	that	DET
ejpam-5850	79	20	gr(σ	gr(σ	NOUN
ejpam-5850	79	21	)	)	PUNCT
ejpam-5850	79	22	=	=	SYM
ejpam-5850	79	23	(	(	PUNCT
ejpam-5850	79	24	grm	grm	PROPN
ejpam-5850	79	25	,	,	PUNCT
ejpam-5850	79	26	n(σ	n(σ	PROPN
ejpam-5850	79	27	)	)	PUNCT
ejpam-5850	79	28	)	)	PUNCT
ejpam-5850	79	29	forms	form	VERB
ejpam-5850	79	30	a	a	DET
ejpam-5850	79	31	magmoid	magmoid	NOUN
ejpam-5850	79	32	with	with	ADP
ejpam-5850	79	33	operations	operation	NOUN
ejpam-5850	79	34	product	product	NOUN
ejpam-5850	79	35	and	and	CCONJ
ejpam-5850	79	36	sum	sum	NOUN
ejpam-5850	79	37	,	,	PUNCT
ejpam-5850	79	38	the	the	DET
ejpam-5850	79	39	units	unit	NOUN
ejpam-5850	79	40	are	be	AUX
ejpam-5850	79	41	the	the	DET
ejpam-5850	79	42	graphs	graph	NOUN
ejpam-5850	79	43	en	en	ADP
ejpam-5850	79	44	.	.	PROPN
ejpam-5850	79	45	3	3	X
ejpam-5850	79	46	.	.	X
ejpam-5850	80	1	graphoids	graphoid	NOUN
ejpam-5850	80	2	in	in	ADP
ejpam-5850	80	3	this	this	DET
ejpam-5850	80	4	section	section	NOUN
ejpam-5850	80	5	,	,	PUNCT
ejpam-5850	80	6	we	we	PRON
ejpam-5850	80	7	explore	explore	VERB
ejpam-5850	80	8	graph	graph	NOUN
ejpam-5850	80	9	automata	automata	NOUN
ejpam-5850	80	10	by	by	ADP
ejpam-5850	80	11	utilizing	utilize	VERB
ejpam-5850	80	12	the	the	DET
ejpam-5850	80	13	algebraic	algebraic	ADJ
ejpam-5850	80	14	structure	structure	NOUN
ejpam-5850	80	15	of	of	ADP
ejpam-5850	80	16	graphoids	graphoid	NOUN
ejpam-5850	80	17	as	as	SCONJ
ejpam-5850	80	18	defined	define	VERB
ejpam-5850	80	19	in	in	ADP
ejpam-5850	80	20	[	[	X
ejpam-5850	80	21	10	10	NUM
ejpam-5850	80	22	]	]	PUNCT
ejpam-5850	80	23	.	.	PUNCT
ejpam-5850	81	1	let	let	VERB
ejpam-5850	81	2	ip	ip	ADP
ejpam-5850	81	3	,	,	PUNCT
ejpam-5850	81	4	q	q	PUNCT
ejpam-5850	81	5	denote	denote	VERB
ejpam-5850	81	6	the	the	DET
ejpam-5850	81	7	discrete	discrete	ADJ
ejpam-5850	81	8	(	(	PUNCT
ejpam-5850	81	9	p	p	NOUN
ejpam-5850	81	10	,	,	PUNCT
ejpam-5850	81	11	q)-graph	q)-graph	NOUN
ejpam-5850	81	12	that	that	PRON
ejpam-5850	81	13	has	have	VERB
ejpam-5850	81	14	a	a	DET
ejpam-5850	81	15	single	single	ADJ
ejpam-5850	81	16	node	node	NOUN
ejpam-5850	81	17	x	x	PUNCT
ejpam-5850	81	18	with	with	ADP
ejpam-5850	81	19	begin	begin	NOUN
ejpam-5850	81	20	and	and	CCONJ
ejpam-5850	81	21	end	end	VERB
ejpam-5850	81	22	sequences	sequence	NOUN
ejpam-5850	81	23	both	both	PRON
ejpam-5850	81	24	formed	form	VERB
ejpam-5850	81	25	by	by	ADP
ejpam-5850	81	26	x	x	SYM
ejpam-5850	81	27	repeated	repeat	VERB
ejpam-5850	81	28	p	p	NOUN
ejpam-5850	81	29	and	and	CCONJ
ejpam-5850	81	30	q	q	PROPN
ejpam-5850	81	31	times	time	NOUN
ejpam-5850	81	32	,	,	PUNCT
ejpam-5850	81	33	respectively	respectively	ADV
ejpam-5850	81	34	.	.	PUNCT
ejpam-5850	82	1	we	we	PRON
ejpam-5850	82	2	also	also	ADV
ejpam-5850	82	3	let	let	VERB
ejpam-5850	82	4	π	π	NOUN
ejpam-5850	82	5	be	be	AUX
ejpam-5850	82	6	the	the	DET
ejpam-5850	82	7	discrete	discrete	ADJ
ejpam-5850	82	8	(	(	PUNCT
ejpam-5850	82	9	2	2	NUM
ejpam-5850	82	10	,	,	PUNCT
ejpam-5850	82	11	2)-graph	2)-graph	NUM
ejpam-5850	82	12	with	with	ADP
ejpam-5850	82	13	two	two	NUM
ejpam-5850	82	14	nodes	node	NOUN
ejpam-5850	82	15	,	,	PUNCT
ejpam-5850	82	16	x	x	SYM
ejpam-5850	82	17	and	and	CCONJ
ejpam-5850	82	18	y	y	PROPN
ejpam-5850	82	19	,	,	PUNCT
ejpam-5850	82	20	whose	whose	DET
ejpam-5850	82	21	begin	begin	VERB
ejpam-5850	82	22	sequence	sequence	NOUN
ejpam-5850	82	23	is	be	AUX
ejpam-5850	82	24	xy	xy	PROPN
ejpam-5850	82	25	and	and	CCONJ
ejpam-5850	82	26	end	end	VERB
ejpam-5850	82	27	sequence	sequence	NOUN
ejpam-5850	82	28	is	be	AUX
ejpam-5850	82	29	yx	yx	NOUN
ejpam-5850	82	30	.	.	PUNCT
ejpam-5850	83	1	for	for	ADP
ejpam-5850	83	2	each	each	DET
ejpam-5850	83	3	σ	σ	PROPN
ejpam-5850	83	4	∈	∈	PROPN
ejpam-5850	83	5	σm	σm	NOUN
ejpam-5850	83	6	,	,	PUNCT
ejpam-5850	83	7	n	n	CCONJ
ejpam-5850	83	8	,	,	PUNCT
ejpam-5850	83	9	we	we	PRON
ejpam-5850	83	10	denote	denote	VERB
ejpam-5850	83	11	by	by	ADP
ejpam-5850	83	12	σ	σ	PROPN
ejpam-5850	83	13	the	the	DET
ejpam-5850	83	14	(	(	PUNCT
ejpam-5850	83	15	m	m	PROPN
ejpam-5850	83	16	,	,	PUNCT
ejpam-5850	83	17	n)-graph	n)-graph	PUNCT
ejpam-5850	83	18	with	with	ADP
ejpam-5850	83	19	a	a	DET
ejpam-5850	83	20	single	single	ADJ
ejpam-5850	83	21	edge	edge	NOUN
ejpam-5850	83	22	and	and	CCONJ
ejpam-5850	83	23	m+	m+	NOUN
ejpam-5850	83	24	n	n	PRON
ejpam-5850	83	25	nodes	node	NOUN
ejpam-5850	83	26	labeled	label	VERB
ejpam-5850	83	27	x1	x1	PROPN
ejpam-5850	83	28	,	,	PUNCT
ejpam-5850	83	29	.	.	PUNCT
ejpam-5850	83	30	.	.	PUNCT
ejpam-5850	84	1	.	.	PUNCT
ejpam-5850	85	1	,	,	PUNCT
ejpam-5850	85	2	xm	xm	PROPN
ejpam-5850	85	3	,	,	PUNCT
ejpam-5850	85	4	y1	y1	PROPN
ejpam-5850	85	5	,	,	PUNCT
ejpam-5850	85	6	.	.	PUNCT
ejpam-5850	85	7	.	.	PUNCT
ejpam-5850	86	1	.	.	PUNCT
ejpam-5850	87	1	,	,	PUNCT
ejpam-5850	87	2	yn	yn	PROPN
ejpam-5850	87	3	.	.	PUNCT
ejpam-5850	88	1	the	the	DET
ejpam-5850	88	2	edge	edge	NOUN
ejpam-5850	88	3	is	be	AUX
ejpam-5850	88	4	labeled	label	VERB
ejpam-5850	88	5	σ	σ	PROPN
ejpam-5850	88	6	,	,	PUNCT
ejpam-5850	88	7	with	with	ADP
ejpam-5850	88	8	the	the	DET
ejpam-5850	88	9	begin	begin	NOUN
ejpam-5850	88	10	(	(	PUNCT
ejpam-5850	88	11	resp	resp	NOUN
ejpam-5850	88	12	.	.	PUNCT
ejpam-5850	89	1	end	end	NOUN
ejpam-5850	89	2	)	)	PUNCT
ejpam-5850	89	3	sequence	sequence	NOUN
ejpam-5850	89	4	of	of	ADP
ejpam-5850	89	5	the	the	DET
ejpam-5850	89	6	graph	graph	NOUN
ejpam-5850	89	7	as	as	ADP
ejpam-5850	89	8	the	the	DET
ejpam-5850	89	9	sequence	sequence	NOUN
ejpam-5850	89	10	of	of	ADP
ejpam-5850	89	11	sources	source	NOUN
ejpam-5850	89	12	(	(	PUNCT
ejpam-5850	89	13	resp	resp	NOUN
ejpam-5850	89	14	.	.	PUNCT
ejpam-5850	89	15	targets	target	NOUN
ejpam-5850	89	16	)	)	PUNCT
ejpam-5850	89	17	of	of	ADP
ejpam-5850	89	18	the	the	DET
ejpam-5850	89	19	edge	edge	NOUN
ejpam-5850	89	20	:	:	PUNCT
ejpam-5850	89	21	x1	x1	PROPN
ejpam-5850	89	22	·	·	PUNCT
ejpam-5850	89	23	·	·	PUNCT
ejpam-5850	90	1	·	·	PUNCT
ejpam-5850	90	2	xm	xm	PROPN
ejpam-5850	90	3	(	(	PUNCT
ejpam-5850	90	4	resp	resp	NOUN
ejpam-5850	90	5	.	.	PUNCT
ejpam-5850	91	1	y1	y1	NOUN
ejpam-5850	91	2	·	·	PUNCT
ejpam-5850	91	3	·	·	PUNCT
ejpam-5850	91	4	·	·	PUNCT
ejpam-5850	91	5	yn	yn	X
ejpam-5850	91	6	)	)	PUNCT
ejpam-5850	91	7	.	.	PUNCT
ejpam-5850	92	1	engelfriet	engelfriet	PROPN
ejpam-5850	92	2	and	and	CCONJ
ejpam-5850	92	3	vereijken	vereijken	ADJ
ejpam-5850	92	4	,	,	PUNCT
ejpam-5850	92	5	in	in	ADP
ejpam-5850	92	6	[	[	PUNCT
ejpam-5850	92	7	15	15	NUM
ejpam-5850	92	8	]	]	PUNCT
ejpam-5850	92	9	,	,	PUNCT
ejpam-5850	92	10	proposed	propose	VERB
ejpam-5850	92	11	an	an	DET
ejpam-5850	92	12	algorithm	algorithm	NOUN
ejpam-5850	92	13	that	that	PRON
ejpam-5850	92	14	inductively	inductively	ADV
ejpam-5850	92	15	constructs	construct	VERB
ejpam-5850	92	16	any	any	DET
ejpam-5850	92	17	graph	graph	NOUN
ejpam-5850	92	18	g	g	ADP
ejpam-5850	92	19	∈	∈	PROPN
ejpam-5850	92	20	gr(σ	gr(σ	NOUN
ejpam-5850	92	21	)	)	PUNCT
ejpam-5850	92	22	from	from	ADP
ejpam-5850	92	23	the	the	DET
ejpam-5850	92	24	set	set	NOUN
ejpam-5850	92	25	σ∪{π	σ∪{π	PROPN
ejpam-5850	92	26	,	,	PUNCT
ejpam-5850	92	27	i01	i01	NOUN
ejpam-5850	92	28	,	,	PUNCT
ejpam-5850	92	29	i21	i21	NOUN
ejpam-5850	92	30	,	,	PUNCT
ejpam-5850	92	31	i10	i10	PROPN
ejpam-5850	92	32	,	,	PUNCT
ejpam-5850	92	33	i12	i12	PROPN
ejpam-5850	92	34	}	}	PUNCT
ejpam-5850	92	35	by	by	ADP
ejpam-5850	92	36	using	use	VERB
ejpam-5850	92	37	graph	graph	NOUN
ejpam-5850	92	38	product	product	NOUN
ejpam-5850	92	39	and	and	CCONJ
ejpam-5850	92	40	graph	graph	NOUN
ejpam-5850	92	41	k.	k.	PROPN
ejpam-5850	92	42	papadopoulos	papadopoulos	PROPN
ejpam-5850	92	43	/	/	SYM
ejpam-5850	92	44	eur	eur	PROPN
ejpam-5850	92	45	.	.	PUNCT
ejpam-5850	93	1	j.	j.	PROPN
ejpam-5850	93	2	pure	pure	PROPN
ejpam-5850	93	3	appl	appl	PROPN
ejpam-5850	93	4	.	.	PROPN
ejpam-5850	93	5	math	math	PROPN
ejpam-5850	93	6	,	,	PUNCT
ejpam-5850	93	7	18	18	NUM
ejpam-5850	93	8	(	(	PUNCT
ejpam-5850	93	9	1	1	NUM
ejpam-5850	93	10	)	)	PUNCT
ejpam-5850	93	11	(	(	PUNCT
ejpam-5850	93	12	2025	2025	NUM
ejpam-5850	93	13	)	)	PUNCT
ejpam-5850	93	14	,	,	PUNCT
ejpam-5850	93	15	5850	5850	NUM
ejpam-5850	93	16	5	5	NUM
ejpam-5850	93	17	of	of	ADP
ejpam-5850	93	18	13	13	NUM
ejpam-5850	93	19	sum	sum	NOUN
ejpam-5850	93	20	.	.	PUNCT
ejpam-5850	94	1	however	however	ADV
ejpam-5850	94	2	,	,	PUNCT
ejpam-5850	94	3	a	a	DET
ejpam-5850	94	4	given	give	VERB
ejpam-5850	94	5	graph	graph	NOUN
ejpam-5850	94	6	can	can	AUX
ejpam-5850	94	7	be	be	AUX
ejpam-5850	94	8	constructed	construct	VERB
ejpam-5850	94	9	in	in	ADP
ejpam-5850	94	10	infinitely	infinitely	ADV
ejpam-5850	94	11	many	many	ADJ
ejpam-5850	94	12	ways	way	NOUN
ejpam-5850	94	13	.	.	PUNCT
ejpam-5850	95	1	this	this	DET
ejpam-5850	95	2	issue	issue	NOUN
ejpam-5850	95	3	was	be	AUX
ejpam-5850	95	4	addressed	address	VERB
ejpam-5850	95	5	by	by	ADP
ejpam-5850	95	6	identifying	identify	VERB
ejpam-5850	95	7	a	a	DET
ejpam-5850	95	8	finite	finite	ADJ
ejpam-5850	95	9	set	set	VERB
ejpam-5850	95	10	e	e	PROPN
ejpam-5850	95	11	of	of	ADP
ejpam-5850	95	12	equations	equation	NOUN
ejpam-5850	95	13	with	with	ADP
ejpam-5850	95	14	the	the	DET
ejpam-5850	95	15	property	property	NOUN
ejpam-5850	95	16	that	that	PRON
ejpam-5850	95	17	two	two	NUM
ejpam-5850	95	18	expressions	expression	NOUN
ejpam-5850	95	19	represent	represent	VERB
ejpam-5850	95	20	the	the	DET
ejpam-5850	95	21	same	same	ADJ
ejpam-5850	95	22	graph	graph	NOUN
ejpam-5850	95	23	if	if	SCONJ
ejpam-5850	96	1	and	and	CCONJ
ejpam-5850	96	2	only	only	ADV
ejpam-5850	96	3	if	if	SCONJ
ejpam-5850	96	4	one	one	PRON
ejpam-5850	96	5	can	can	AUX
ejpam-5850	96	6	be	be	AUX
ejpam-5850	96	7	transformed	transform	VERB
ejpam-5850	96	8	into	into	ADP
ejpam-5850	96	9	the	the	DET
ejpam-5850	96	10	other	other	ADJ
ejpam-5850	96	11	using	use	VERB
ejpam-5850	96	12	these	these	DET
ejpam-5850	96	13	equations	equation	NOUN
ejpam-5850	97	1	[	[	X
ejpam-5850	97	2	7	7	NUM
ejpam-5850	97	3	]	]	PUNCT
ejpam-5850	97	4	.	.	PUNCT
ejpam-5850	98	1	thus	thus	ADV
ejpam-5850	98	2	,	,	PUNCT
ejpam-5850	98	3	the	the	DET
ejpam-5850	98	4	equations	equation	NOUN
ejpam-5850	98	5	in	in	ADP
ejpam-5850	98	6	e	e	PROPN
ejpam-5850	98	7	are	be	AUX
ejpam-5850	98	8	valid	valid	ADJ
ejpam-5850	98	9	in	in	ADP
ejpam-5850	98	10	gr(σ	gr(σ	NOUN
ejpam-5850	98	11	)	)	PUNCT
ejpam-5850	98	12	,	,	PUNCT
ejpam-5850	98	13	and	and	CCONJ
ejpam-5850	98	14	magmoids	magmoid	NOUN
ejpam-5850	98	15	satisfying	satisfy	VERB
ejpam-5850	98	16	this	this	DET
ejpam-5850	98	17	property	property	NOUN
ejpam-5850	98	18	are	be	AUX
ejpam-5850	98	19	referred	refer	VERB
ejpam-5850	98	20	to	to	ADP
ejpam-5850	98	21	as	as	ADP
ejpam-5850	98	22	graphoids	graphoid	NOUN
ejpam-5850	98	23	.	.	PUNCT
ejpam-5850	99	1	formally	formally	ADV
ejpam-5850	99	2	,	,	PUNCT
ejpam-5850	99	3	a	a	DET
ejpam-5850	99	4	graphoid	graphoid	NOUN
ejpam-5850	99	5	m	m	NOUN
ejpam-5850	99	6	=	=	SYM
ejpam-5850	99	7	(	(	PUNCT
ejpam-5850	99	8	m	m	PROPN
ejpam-5850	99	9	,	,	PUNCT
ejpam-5850	99	10	dm	dm	NOUN
ejpam-5850	99	11	)	)	PUNCT
ejpam-5850	99	12	consists	consist	VERB
ejpam-5850	99	13	of	of	ADP
ejpam-5850	99	14	a	a	DET
ejpam-5850	99	15	magmoid	magmoid	NOUN
ejpam-5850	99	16	m	m	NOUN
ejpam-5850	99	17	and	and	CCONJ
ejpam-5850	99	18	a	a	DET
ejpam-5850	99	19	set	set	NOUN
ejpam-5850	99	20	dm	dm	NOUN
ejpam-5850	99	21	=	=	SYM
ejpam-5850	99	22	{	{	PUNCT
ejpam-5850	99	23	s	s	PROPN
ejpam-5850	99	24	,	,	PUNCT
ejpam-5850	99	25	d01	d01	NOUN
ejpam-5850	99	26	,	,	PUNCT
ejpam-5850	99	27	d21	d21	PROPN
ejpam-5850	99	28	,	,	PUNCT
ejpam-5850	99	29	d10	d10	PROPN
ejpam-5850	99	30	,	,	PUNCT
ejpam-5850	99	31	d12	d12	PROPN
ejpam-5850	99	32	}	}	PUNCT
ejpam-5850	99	33	,	,	PUNCT
ejpam-5850	99	34	where	where	SCONJ
ejpam-5850	99	35	s	s	VERB
ejpam-5850	99	36	∈	∈	PROPN
ejpam-5850	99	37	m2,2	m2,2	PROPN
ejpam-5850	99	38	and	and	CCONJ
ejpam-5850	99	39	dκλ	dκλ	PROPN
ejpam-5850	99	40	∈	∈	PROPN
ejpam-5850	99	41	mκ	mκ	PROPN
ejpam-5850	99	42	,	,	PUNCT
ejpam-5850	99	43	λ	λ	PROPN
ejpam-5850	99	44	,	,	PUNCT
ejpam-5850	99	45	such	such	ADJ
ejpam-5850	99	46	that	that	SCONJ
ejpam-5850	99	47	the	the	DET
ejpam-5850	99	48	following	follow	VERB
ejpam-5850	99	49	equations	equation	NOUN
ejpam-5850	99	50	hold	hold	VERB
ejpam-5850	99	51	:	:	PUNCT
ejpam-5850	99	52	s	s	VERB
ejpam-5850	99	53	◦	◦	NOUN
ejpam-5850	99	54	s	s	PART
ejpam-5850	99	55	=	=	PROPN
ejpam-5850	99	56	e2	e2	PROPN
ejpam-5850	99	57	,	,	PUNCT
ejpam-5850	99	58	(	(	PUNCT
ejpam-5850	99	59	1	1	NUM
ejpam-5850	99	60	)	)	PUNCT
ejpam-5850	99	61	(	(	PUNCT
ejpam-5850	99	62	s	s	X
ejpam-5850	99	63	□	□	SYM
ejpam-5850	99	64	e	e	ADJ
ejpam-5850	99	65	)	)	PUNCT
ejpam-5850	99	66	◦	◦	NOUN
ejpam-5850	99	67	(	(	PUNCT
ejpam-5850	99	68	e	e	X
ejpam-5850	99	69	□	□	SYM
ejpam-5850	99	70	s	s	PART
ejpam-5850	99	71	)	)	PUNCT
ejpam-5850	99	72	◦	◦	NOUN
ejpam-5850	99	73	(	(	PUNCT
ejpam-5850	99	74	s	s	X
ejpam-5850	99	75	□	□	SYM
ejpam-5850	99	76	e	e	NOUN
ejpam-5850	99	77	)	)	PUNCT
ejpam-5850	99	78	=	=	SYM
ejpam-5850	99	79	(	(	PUNCT
ejpam-5850	99	80	e	e	X
ejpam-5850	99	81	□	□	SYM
ejpam-5850	99	82	s	s	PART
ejpam-5850	99	83	)	)	PUNCT
ejpam-5850	99	84	◦	◦	NOUN
ejpam-5850	99	85	(	(	PUNCT
ejpam-5850	99	86	s	s	X
ejpam-5850	99	87	□	□	SYM
ejpam-5850	99	88	e	e	ADJ
ejpam-5850	99	89	)	)	PUNCT
ejpam-5850	99	90	◦	◦	NOUN
ejpam-5850	99	91	(	(	PUNCT
ejpam-5850	99	92	e	e	X
ejpam-5850	99	93	□	□	PUNCT
ejpam-5850	99	94	s	s	PART
ejpam-5850	99	95	)	)	PUNCT
ejpam-5850	99	96	,	,	PUNCT
ejpam-5850	99	97	(	(	PUNCT
ejpam-5850	99	98	2	2	X
ejpam-5850	99	99	)	)	PUNCT
ejpam-5850	99	100	(	(	PUNCT
ejpam-5850	99	101	e	e	NOUN
ejpam-5850	99	102	□	□	SYM
ejpam-5850	99	103	d21	d21	NOUN
ejpam-5850	99	104	)	)	PUNCT
ejpam-5850	99	105	◦	◦	NOUN
ejpam-5850	99	106	d21	d21	NOUN
ejpam-5850	100	1	=	=	SYM
ejpam-5850	100	2	(	(	PUNCT
ejpam-5850	100	3	d21	d21	NOUN
ejpam-5850	100	4	□	□	PUNCT
ejpam-5850	100	5	e	e	NOUN
ejpam-5850	100	6	)	)	PUNCT
ejpam-5850	100	7	◦	◦	PROPN
ejpam-5850	100	8	d21	d21	NOUN
ejpam-5850	100	9	,	,	PUNCT
ejpam-5850	100	10	(	(	PUNCT
ejpam-5850	100	11	3	3	NUM
ejpam-5850	100	12	)	)	PUNCT
ejpam-5850	100	13	(	(	PUNCT
ejpam-5850	100	14	e	e	NOUN
ejpam-5850	100	15	□	□	SYM
ejpam-5850	100	16	d01	d01	NOUN
ejpam-5850	100	17	)	)	PUNCT
ejpam-5850	100	18	◦	◦	NOUN
ejpam-5850	100	19	d21	d21	NOUN
ejpam-5850	100	20	=	=	SYM
ejpam-5850	100	21	e	e	NOUN
ejpam-5850	100	22	,	,	PUNCT
ejpam-5850	100	23	(	(	PUNCT
ejpam-5850	100	24	4	4	NUM
ejpam-5850	100	25	)	)	PUNCT
ejpam-5850	100	26	s	s	VERB
ejpam-5850	100	27	◦	◦	NOUN
ejpam-5850	100	28	d21	d21	NOUN
ejpam-5850	100	29	=	=	PROPN
ejpam-5850	100	30	d21	d21	PROPN
ejpam-5850	100	31	,	,	PUNCT
ejpam-5850	100	32	(	(	PUNCT
ejpam-5850	100	33	5	5	NUM
ejpam-5850	100	34	)	)	PUNCT
ejpam-5850	100	35	(	(	PUNCT
ejpam-5850	100	36	e	e	NOUN
ejpam-5850	100	37	□	□	SYM
ejpam-5850	100	38	d01	d01	NOUN
ejpam-5850	100	39	)	)	PUNCT
ejpam-5850	100	40	◦	◦	NOUN
ejpam-5850	100	41	s	s	PART
ejpam-5850	100	42	=	=	PUNCT
ejpam-5850	100	43	(	(	PUNCT
ejpam-5850	100	44	d01	d01	NOUN
ejpam-5850	100	45	□	□	PUNCT
ejpam-5850	100	46	e	e	NOUN
ejpam-5850	100	47	)	)	PUNCT
ejpam-5850	100	48	,	,	PUNCT
ejpam-5850	100	49	(	(	PUNCT
ejpam-5850	100	50	6	6	NUM
ejpam-5850	100	51	)	)	PUNCT
ejpam-5850	100	52	(	(	PUNCT
ejpam-5850	100	53	s	s	X
ejpam-5850	100	54	□	□	SYM
ejpam-5850	100	55	e	e	ADJ
ejpam-5850	100	56	)	)	PUNCT
ejpam-5850	100	57	◦	◦	NOUN
ejpam-5850	100	58	(	(	PUNCT
ejpam-5850	100	59	e	e	X
ejpam-5850	100	60	□	□	SYM
ejpam-5850	100	61	s	s	PART
ejpam-5850	100	62	)	)	PUNCT
ejpam-5850	100	63	◦	◦	NOUN
ejpam-5850	100	64	(	(	PUNCT
ejpam-5850	100	65	d21	d21	NOUN
ejpam-5850	100	66	□	□	PUNCT
ejpam-5850	100	67	e	e	NOUN
ejpam-5850	100	68	)	)	PUNCT
ejpam-5850	100	69	=	=	SYM
ejpam-5850	100	70	(	(	PUNCT
ejpam-5850	100	71	e	e	NOUN
ejpam-5850	100	72	□	□	SYM
ejpam-5850	100	73	d21	d21	NOUN
ejpam-5850	100	74	)	)	PUNCT
ejpam-5850	100	75	◦	◦	NOUN
ejpam-5850	100	76	s	s	NUM
ejpam-5850	100	77	,	,	PUNCT
ejpam-5850	100	78	(	(	PUNCT
ejpam-5850	100	79	7	7	X
ejpam-5850	100	80	)	)	PUNCT
ejpam-5850	100	81	d12	d12	NOUN
ejpam-5850	100	82	◦	◦	NOUN
ejpam-5850	100	83	(	(	PUNCT
ejpam-5850	100	84	e	e	NOUN
ejpam-5850	100	85	□	□	SYM
ejpam-5850	100	86	d12	d12	NUM
ejpam-5850	100	87	)	)	PUNCT
ejpam-5850	100	88	=	=	SYM
ejpam-5850	100	89	d12	d12	PROPN
ejpam-5850	100	90	◦	◦	NOUN
ejpam-5850	100	91	(	(	PUNCT
ejpam-5850	100	92	d12	d12	NOUN
ejpam-5850	100	93	□	□	PUNCT
ejpam-5850	100	94	e	e	NOUN
ejpam-5850	100	95	)	)	PUNCT
ejpam-5850	100	96	,	,	PUNCT
ejpam-5850	100	97	(	(	PUNCT
ejpam-5850	100	98	8)	8)	NUM
ejpam-5850	100	99	d12	d12	NOUN
ejpam-5850	100	100	◦	◦	NOUN
ejpam-5850	100	101	(	(	PUNCT
ejpam-5850	100	102	e	e	NOUN
ejpam-5850	100	103	□	□	PUNCT
ejpam-5850	100	104	d10	d10	PROPN
ejpam-5850	100	105	)	)	PUNCT
ejpam-5850	100	106	=	=	SYM
ejpam-5850	101	1	e	e	NOUN
ejpam-5850	101	2	,	,	PUNCT
ejpam-5850	101	3	(	(	PUNCT
ejpam-5850	101	4	9	9	X
ejpam-5850	101	5	)	)	PUNCT
ejpam-5850	101	6	d12	d12	NOUN
ejpam-5850	101	7	◦	◦	PROPN
ejpam-5850	101	8	s	s	PART
ejpam-5850	101	9	=	=	X
ejpam-5850	101	10	d12	d12	PROPN
ejpam-5850	101	11	,	,	PUNCT
ejpam-5850	101	12	(	(	PUNCT
ejpam-5850	101	13	10	10	NUM
ejpam-5850	101	14	)	)	PUNCT
ejpam-5850	101	15	s	s	VERB
ejpam-5850	101	16	◦	◦	NOUN
ejpam-5850	101	17	(	(	PUNCT
ejpam-5850	101	18	e	e	NOUN
ejpam-5850	101	19	□	□	SYM
ejpam-5850	101	20	d10	d10	PROPN
ejpam-5850	101	21	)	)	PUNCT
ejpam-5850	101	22	=	=	PUNCT
ejpam-5850	101	23	(	(	PUNCT
ejpam-5850	101	24	d10	d10	PROPN
ejpam-5850	101	25	□	□	PUNCT
ejpam-5850	101	26	e	e	NOUN
ejpam-5850	101	27	)	)	PUNCT
ejpam-5850	101	28	,	,	PUNCT
ejpam-5850	101	29	(	(	PUNCT
ejpam-5850	101	30	11	11	NUM
ejpam-5850	101	31	)	)	PUNCT
ejpam-5850	101	32	(	(	PUNCT
ejpam-5850	101	33	d12	d12	NOUN
ejpam-5850	101	34	□	□	PUNCT
ejpam-5850	101	35	e	e	NOUN
ejpam-5850	101	36	)	)	PUNCT
ejpam-5850	101	37	◦	◦	NOUN
ejpam-5850	101	38	(	(	PUNCT
ejpam-5850	101	39	e	e	X
ejpam-5850	101	40	□	□	SYM
ejpam-5850	101	41	s	s	PART
ejpam-5850	101	42	)	)	PUNCT
ejpam-5850	101	43	◦	◦	NOUN
ejpam-5850	101	44	(	(	PUNCT
ejpam-5850	101	45	s	s	X
ejpam-5850	101	46	□	□	SYM
ejpam-5850	101	47	e	e	NOUN
ejpam-5850	101	48	)	)	PUNCT
ejpam-5850	101	49	=	=	SYM
ejpam-5850	101	50	s	s	PART
ejpam-5850	101	51	◦	◦	NOUN
ejpam-5850	101	52	(	(	PUNCT
ejpam-5850	101	53	e	e	NOUN
ejpam-5850	101	54	□	□	SYM
ejpam-5850	101	55	d12	d12	NUM
ejpam-5850	101	56	)	)	PUNCT
ejpam-5850	101	57	,	,	PUNCT
ejpam-5850	101	58	(	(	PUNCT
ejpam-5850	101	59	12	12	NUM
ejpam-5850	101	60	)	)	PUNCT
ejpam-5850	101	61	d12	d12	NOUN
ejpam-5850	101	62	◦	◦	PROPN
ejpam-5850	101	63	d21	d21	NOUN
ejpam-5850	101	64	=	=	SYM
ejpam-5850	101	65	e	e	NOUN
ejpam-5850	101	66	,	,	PUNCT
ejpam-5850	101	67	(	(	PUNCT
ejpam-5850	101	68	13	13	NUM
ejpam-5850	101	69	)	)	PUNCT
ejpam-5850	101	70	(	(	PUNCT
ejpam-5850	101	71	d12	d12	NOUN
ejpam-5850	101	72	□	□	PUNCT
ejpam-5850	101	73	e	e	NOUN
ejpam-5850	101	74	)	)	PUNCT
ejpam-5850	101	75	◦	◦	NOUN
ejpam-5850	101	76	(	(	PUNCT
ejpam-5850	101	77	e	e	NOUN
ejpam-5850	101	78	□	□	SYM
ejpam-5850	101	79	d21	d21	NOUN
ejpam-5850	101	80	)	)	PUNCT
ejpam-5850	101	81	=	=	SYM
ejpam-5850	101	82	d21	d21	PROPN
ejpam-5850	101	83	◦	◦	PROPN
ejpam-5850	101	84	d12	d12	PROPN
ejpam-5850	101	85	,	,	PUNCT
ejpam-5850	101	86	(	(	PUNCT
ejpam-5850	101	87	14	14	NUM
ejpam-5850	101	88	)	)	PUNCT
ejpam-5850	101	89	sm,1	sm,1	PROPN
ejpam-5850	101	90	◦	◦	NOUN
ejpam-5850	101	91	(	(	PUNCT
ejpam-5850	101	92	p	p	X
ejpam-5850	101	93	□	□	PUNCT
ejpam-5850	101	94	e	e	NOUN
ejpam-5850	101	95	)	)	PUNCT
ejpam-5850	101	96	=	=	SYM
ejpam-5850	101	97	(	(	PUNCT
ejpam-5850	101	98	e	e	X
ejpam-5850	101	99	□	□	SYM
ejpam-5850	101	100	p	p	ADJ
ejpam-5850	101	101	)	)	PUNCT
ejpam-5850	101	102	◦	◦	NOUN
ejpam-5850	101	103	sn,1	sn,1	PROPN
ejpam-5850	101	104	,	,	PUNCT
ejpam-5850	101	105	for	for	ADP
ejpam-5850	101	106	all	all	DET
ejpam-5850	101	107	p	p	PROPN
ejpam-5850	101	108	∈	∈	PROPN
ejpam-5850	101	109	mm	mm	PROPN
ejpam-5850	101	110	,	,	PUNCT
ejpam-5850	101	111	n.	n.	NOUN
ejpam-5850	101	112	(	(	PUNCT
ejpam-5850	101	113	15	15	NUM
ejpam-5850	101	114	)	)	PUNCT
ejpam-5850	101	115	where	where	SCONJ
ejpam-5850	101	116	sm,1	sm,1	PROPN
ejpam-5850	101	117	is	be	AUX
ejpam-5850	101	118	defined	define	VERB
ejpam-5850	101	119	inductively	inductively	ADV
ejpam-5850	101	120	by	by	ADP
ejpam-5850	101	121	s	s	PRON
ejpam-5850	101	122	and	and	CCONJ
ejpam-5850	101	123	represents	represent	VERB
ejpam-5850	101	124	the	the	DET
ejpam-5850	101	125	graph	graph	NOUN
ejpam-5850	101	126	associated	associate	VERB
ejpam-5850	101	127	with	with	ADP
ejpam-5850	101	128	the	the	DET
ejpam-5850	101	129	permutation	permutation	NOUN
ejpam-5850	101	130	that	that	PRON
ejpam-5850	101	131	interchanges	interchange	VERB
ejpam-5850	101	132	the	the	DET
ejpam-5850	101	133	last	last	ADJ
ejpam-5850	101	134	n	n	NOUN
ejpam-5850	101	135	numbers	number	NOUN
ejpam-5850	101	136	with	with	ADP
ejpam-5850	101	137	the	the	DET
ejpam-5850	101	138	first	first	ADJ
ejpam-5850	101	139	one	one	NUM
ejpam-5850	101	140	[	[	X
ejpam-5850	101	141	7	7	NUM
ejpam-5850	101	142	]	]	PUNCT
ejpam-5850	101	143	.	.	PUNCT
ejpam-5850	102	1	notably	notably	ADV
ejpam-5850	102	2	,	,	PUNCT
ejpam-5850	102	3	equation	equation	NOUN
ejpam-5850	102	4	(	(	PUNCT
ejpam-5850	102	5	15	15	NUM
ejpam-5850	102	6	)	)	PUNCT
ejpam-5850	102	7	only	only	ADV
ejpam-5850	102	8	needs	need	VERB
ejpam-5850	102	9	to	to	PART
ejpam-5850	102	10	hold	hold	VERB
ejpam-5850	102	11	for	for	ADP
ejpam-5850	102	12	elements	element	NOUN
ejpam-5850	102	13	of	of	ADP
ejpam-5850	102	14	σ	σ	NOUN
ejpam-5850	102	15	to	to	PART
ejpam-5850	102	16	be	be	AUX
ejpam-5850	102	17	valid	valid	ADJ
ejpam-5850	102	18	for	for	ADP
ejpam-5850	102	19	every	every	DET
ejpam-5850	102	20	element	element	NOUN
ejpam-5850	102	21	of	of	ADP
ejpam-5850	102	22	a	a	DET
ejpam-5850	102	23	magmoid	magmoid	NOUN
ejpam-5850	102	24	generated	generate	VERB
ejpam-5850	102	25	by	by	ADP
ejpam-5850	102	26	σ	σ	PROPN
ejpam-5850	102	27	(	(	PUNCT
ejpam-5850	102	28	see	see	VERB
ejpam-5850	102	29	[	[	X
ejpam-5850	102	30	7	7	NUM
ejpam-5850	102	31	]	]	NUM
ejpam-5850	102	32	)	)	PUNCT
ejpam-5850	102	33	.	.	PUNCT
ejpam-5850	103	1	hence	hence	ADV
ejpam-5850	103	2	,	,	PUNCT
ejpam-5850	103	3	the	the	DET
ejpam-5850	103	4	pair	pair	NOUN
ejpam-5850	103	5	(	(	PUNCT
ejpam-5850	103	6	gr(σ	gr(σ	NOUN
ejpam-5850	103	7	)	)	PUNCT
ejpam-5850	103	8	,	,	PUNCT
ejpam-5850	103	9	dgr(σ	dgr(σ	PROPN
ejpam-5850	103	10	)	)	PUNCT
ejpam-5850	103	11	)	)	PUNCT
ejpam-5850	103	12	with	with	ADP
ejpam-5850	103	13	d	d	PROPN
ejpam-5850	103	14	=	=	SYM
ejpam-5850	103	15	{	{	PUNCT
ejpam-5850	103	16	π	π	PROPN
ejpam-5850	103	17	,	,	PUNCT
ejpam-5850	103	18	i01	i01	NOUN
ejpam-5850	103	19	,	,	PUNCT
ejpam-5850	103	20	i21	i21	NOUN
ejpam-5850	103	21	,	,	PUNCT
ejpam-5850	103	22	i10	i10	PROPN
ejpam-5850	103	23	,	,	PUNCT
ejpam-5850	103	24	i12	i12	PROPN
ejpam-5850	103	25	}	}	PUNCT
ejpam-5850	103	26	,	,	PUNCT
ejpam-5850	103	27	is	be	AUX
ejpam-5850	103	28	a	a	DET
ejpam-5850	103	29	graphoid	graphoid	NOUN
ejpam-5850	103	30	and	and	CCONJ
ejpam-5850	103	31	is	be	AUX
ejpam-5850	103	32	,	,	PUNCT
ejpam-5850	103	33	in	in	ADP
ejpam-5850	103	34	fact	fact	NOUN
ejpam-5850	103	35	,	,	PUNCT
ejpam-5850	103	36	the	the	DET
ejpam-5850	103	37	free	free	ADJ
ejpam-5850	103	38	graphoid	graphoid	NOUN
ejpam-5850	103	39	generated	generate	VERB
ejpam-5850	103	40	by	by	ADP
ejpam-5850	103	41	σ	σ	PROPN
ejpam-5850	103	42	as	as	SCONJ
ejpam-5850	103	43	illustrated	illustrate	VERB
ejpam-5850	103	44	in	in	ADP
ejpam-5850	103	45	[	[	X
ejpam-5850	103	46	10	10	NUM
ejpam-5850	103	47	]	]	PUNCT
ejpam-5850	103	48	.	.	PUNCT
ejpam-5850	104	1	for	for	ADP
ejpam-5850	104	2	graphoids	graphoids	PROPN
ejpam-5850	104	3	(	(	PUNCT
ejpam-5850	104	4	m	m	PROPN
ejpam-5850	104	5	,	,	PUNCT
ejpam-5850	104	6	dm	dm	PROPN
ejpam-5850	104	7	)	)	PUNCT
ejpam-5850	104	8	and	and	CCONJ
ejpam-5850	104	9	(	(	PUNCT
ejpam-5850	104	10	m	m	NOUN
ejpam-5850	104	11	′	′	NOUN
ejpam-5850	104	12	,	,	PUNCT
ejpam-5850	104	13	dm	dm	PROPN
ejpam-5850	104	14	′	′	NUM
ejpam-5850	104	15	)	)	PUNCT
ejpam-5850	104	16	,	,	PUNCT
ejpam-5850	104	17	a	a	DET
ejpam-5850	104	18	magmoid	magmoid	NOUN
ejpam-5850	104	19	morphism	morphism	NOUN
ejpam-5850	104	20	h	h	NOUN
ejpam-5850	104	21	:	:	PUNCT
ejpam-5850	104	22	m	m	VERB
ejpam-5850	104	23	→	→	SYM
ejpam-5850	104	24	m	m	VERB
ejpam-5850	104	25	′	′	NOUN
ejpam-5850	104	26	that	that	PRON
ejpam-5850	104	27	preserves	preserve	VERB
ejpam-5850	104	28	d	d	NOUN
ejpam-5850	104	29	-	-	PUNCT
ejpam-5850	104	30	sets	set	NOUN
ejpam-5850	104	31	,	,	PUNCT
ejpam-5850	104	32	i.e.	i.e.	X
ejpam-5850	104	33	,	,	PUNCT
ejpam-5850	104	34	h(s	h(s	NUM
ejpam-5850	104	35	)	)	PUNCT
ejpam-5850	104	36	=	=	SYM
ejpam-5850	104	37	s′	s′	PROPN
ejpam-5850	104	38	and	and	CCONJ
ejpam-5850	104	39	h(dκλ	h(dκλ	PROPN
ejpam-5850	104	40	)	)	PUNCT
ejpam-5850	104	41	=	=	SYM
ejpam-5850	105	1	d′κλ	d′κλ	PROPN
ejpam-5850	105	2	,	,	PUNCT
ejpam-5850	105	3	is	be	AUX
ejpam-5850	105	4	called	call	VERB
ejpam-5850	105	5	a	a	DET
ejpam-5850	105	6	morphism	morphism	NOUN
ejpam-5850	105	7	of	of	ADP
ejpam-5850	105	8	graphoids	graphoid	NOUN
ejpam-5850	105	9	.	.	PUNCT
ejpam-5850	106	1	a	a	DET
ejpam-5850	106	2	graphoid	graphoid	NOUN
ejpam-5850	106	3	(	(	PUNCT
ejpam-5850	106	4	rel(q	rel(q	PROPN
ejpam-5850	106	5	)	)	PUNCT
ejpam-5850	106	6	,	,	PUNCT
ejpam-5850	106	7	drel(q	drel(q	PROPN
ejpam-5850	106	8	)	)	PUNCT
ejpam-5850	106	9	)	)	PUNCT
ejpam-5850	106	10	formed	form	VERB
ejpam-5850	106	11	from	from	ADP
ejpam-5850	106	12	the	the	DET
ejpam-5850	106	13	magmoid	magmoid	NOUN
ejpam-5850	106	14	of	of	ADP
ejpam-5850	106	15	relations	relation	NOUN
ejpam-5850	106	16	rel(q	rel(q	PROPN
ejpam-5850	106	17	)	)	PUNCT
ejpam-5850	106	18	is	be	AUX
ejpam-5850	106	19	called	call	VERB
ejpam-5850	106	20	relational	relational	ADJ
ejpam-5850	106	21	graphoid	graphoid	NOUN
ejpam-5850	106	22	.	.	PUNCT
ejpam-5850	107	1	if	if	SCONJ
ejpam-5850	107	2	the	the	DET
ejpam-5850	107	3	element	element	NOUN
ejpam-5850	107	4	s	s	PART
ejpam-5850	107	5	∈	∈	NOUN
ejpam-5850	107	6	drel(q	drel(q	NOUN
ejpam-5850	107	7	)	)	PUNCT
ejpam-5850	107	8	of	of	ADP
ejpam-5850	107	9	a	a	DET
ejpam-5850	107	10	relational	relational	ADJ
ejpam-5850	107	11	graphoid	graphoid	NOUN
ejpam-5850	107	12	is	be	AUX
ejpam-5850	107	13	s	s	NOUN
ejpam-5850	107	14	=	=	PUNCT
ejpam-5850	107	15	{	{	PUNCT
ejpam-5850	107	16	(	(	PUNCT
ejpam-5850	107	17	g1g2	g1g2	X
ejpam-5850	107	18	,	,	PUNCT
ejpam-5850	107	19	g2g1	g2g1	NOUN
ejpam-5850	107	20	)	)	PUNCT
ejpam-5850	107	21	|	|	ADV
ejpam-5850	107	22	g1	g1	NOUN
ejpam-5850	107	23	,	,	PUNCT
ejpam-5850	107	24	g2	g2	PROPN
ejpam-5850	107	25	∈	∈	PROPN
ejpam-5850	107	26	q	q	X
ejpam-5850	107	27	}	}	PUNCT
ejpam-5850	107	28	,	,	PUNCT
ejpam-5850	107	29	(	(	PUNCT
ejpam-5850	107	30	16	16	NUM
ejpam-5850	107	31	)	)	PUNCT
ejpam-5850	107	32	then	then	ADV
ejpam-5850	107	33	the	the	DET
ejpam-5850	107	34	pair	pair	NOUN
ejpam-5850	107	35	(	(	PUNCT
ejpam-5850	107	36	rel(q	rel(q	PROPN
ejpam-5850	107	37	)	)	PUNCT
ejpam-5850	107	38	,	,	PUNCT
ejpam-5850	107	39	drel(q	drel(q	PROPN
ejpam-5850	107	40	)	)	PUNCT
ejpam-5850	107	41	)	)	PUNCT
ejpam-5850	107	42	is	be	AUX
ejpam-5850	107	43	called	call	VERB
ejpam-5850	107	44	abelian	abelian	ADJ
ejpam-5850	107	45	graphoid	graphoid	NOUN
ejpam-5850	107	46	(	(	PUNCT
ejpam-5850	107	47	see	see	VERB
ejpam-5850	107	48	[	[	X
ejpam-5850	107	49	19	19	NUM
ejpam-5850	107	50	]	]	NUM
ejpam-5850	107	51	)	)	PUNCT
ejpam-5850	107	52	.	.	PUNCT
ejpam-5850	108	1	k.	k.	PROPN
ejpam-5850	108	2	papadopoulos	papadopoulos	PROPN
ejpam-5850	108	3	/	/	SYM
ejpam-5850	108	4	eur	eur	PROPN
ejpam-5850	108	5	.	.	PUNCT
ejpam-5850	109	1	j.	j.	PROPN
ejpam-5850	109	2	pure	pure	PROPN
ejpam-5850	109	3	appl	appl	PROPN
ejpam-5850	109	4	.	.	PROPN
ejpam-5850	109	5	math	math	PROPN
ejpam-5850	109	6	,	,	PUNCT
ejpam-5850	109	7	18	18	NUM
ejpam-5850	109	8	(	(	PUNCT
ejpam-5850	109	9	1	1	NUM
ejpam-5850	109	10	)	)	PUNCT
ejpam-5850	109	11	(	(	PUNCT
ejpam-5850	109	12	2025	2025	NUM
ejpam-5850	109	13	)	)	PUNCT
ejpam-5850	109	14	,	,	PUNCT
ejpam-5850	109	15	5850	5850	NUM
ejpam-5850	109	16	6	6	NUM
ejpam-5850	109	17	of	of	ADP
ejpam-5850	109	18	13	13	NUM
ejpam-5850	109	19	the	the	DET
ejpam-5850	109	20	unitary	unitary	ADJ
ejpam-5850	109	21	graphoid	graphoid	NOUN
ejpam-5850	109	22	u(q	u(q	ADP
ejpam-5850	109	23	)	)	PUNCT
ejpam-5850	109	24	=	=	SYM
ejpam-5850	109	25	(	(	PUNCT
ejpam-5850	109	26	rel(q	rel(q	PROPN
ejpam-5850	109	27	)	)	PUNCT
ejpam-5850	109	28	,	,	PUNCT
ejpam-5850	109	29	du	du	PROPN
ejpam-5850	109	30	rel(q	rel(q	PROPN
ejpam-5850	109	31	)	)	PUNCT
ejpam-5850	109	32	)	)	PUNCT
ejpam-5850	109	33	,	,	PUNCT
ejpam-5850	109	34	which	which	PRON
ejpam-5850	109	35	was	be	AUX
ejpam-5850	109	36	used	use	VERB
ejpam-5850	109	37	for	for	ADP
ejpam-5850	109	38	introducing	introduce	VERB
ejpam-5850	109	39	graph	graph	NOUN
ejpam-5850	109	40	automata	automata	NOUN
ejpam-5850	109	41	in	in	ADP
ejpam-5850	109	42	[	[	X
ejpam-5850	109	43	10	10	NUM
ejpam-5850	109	44	]	]	PUNCT
ejpam-5850	109	45	,	,	PUNCT
ejpam-5850	109	46	is	be	AUX
ejpam-5850	109	47	an	an	DET
ejpam-5850	109	48	abelian	abelian	ADJ
ejpam-5850	109	49	graphoid	graphoid	NOUN
ejpam-5850	109	50	constructed	construct	VERB
ejpam-5850	109	51	by	by	ADP
ejpam-5850	109	52	defining	define	VERB
ejpam-5850	109	53	,	,	PUNCT
ejpam-5850	109	54	in	in	ADP
ejpam-5850	109	55	addition	addition	NOUN
ejpam-5850	109	56	to	to	ADP
ejpam-5850	109	57	s	s	PRON
ejpam-5850	109	58	as	as	ADP
ejpam-5850	109	59	above	above	ADV
ejpam-5850	109	60	,	,	PUNCT
ejpam-5850	109	61	the	the	DET
ejpam-5850	109	62	elements	element	NOUN
ejpam-5850	109	63	d01	d01	NOUN
ejpam-5850	109	64	,	,	PUNCT
ejpam-5850	109	65	d21	d21	PROPN
ejpam-5850	109	66	,	,	PUNCT
ejpam-5850	109	67	d10	d10	PROPN
ejpam-5850	109	68	,	,	PUNCT
ejpam-5850	109	69	d12	d12	PROPN
ejpam-5850	109	70	as	as	SCONJ
ejpam-5850	109	71	follows	follow	VERB
ejpam-5850	109	72	d01	d01	NOUN
ejpam-5850	109	73	=	=	SYM
ejpam-5850	109	74	{	{	PUNCT
ejpam-5850	109	75	(	(	PUNCT
ejpam-5850	109	76	ε	ε	PROPN
ejpam-5850	109	77	,	,	PUNCT
ejpam-5850	109	78	g	g	NOUN
ejpam-5850	109	79	)	)	PUNCT
ejpam-5850	109	80	|	|	ADV
ejpam-5850	109	81	g	g	PROPN
ejpam-5850	109	82	∈	∈	PROPN
ejpam-5850	109	83	q	q	X
ejpam-5850	109	84	}	}	PUNCT
ejpam-5850	109	85	,	,	PUNCT
ejpam-5850	109	86	(	(	PUNCT
ejpam-5850	109	87	17	17	NUM
ejpam-5850	109	88	)	)	PUNCT
ejpam-5850	109	89	d21	d21	NOUN
ejpam-5850	109	90	=	=	SYM
ejpam-5850	109	91	{	{	PUNCT
ejpam-5850	109	92	(	(	PUNCT
ejpam-5850	109	93	gg	gg	PROPN
ejpam-5850	109	94	,	,	PUNCT
ejpam-5850	109	95	g	g	NOUN
ejpam-5850	109	96	)	)	PUNCT
ejpam-5850	110	1	|	|	ADV
ejpam-5850	110	2	g	g	PROPN
ejpam-5850	110	3	∈	∈	PROPN
ejpam-5850	110	4	q	q	X
ejpam-5850	110	5	}	}	PUNCT
ejpam-5850	110	6	,	,	PUNCT
ejpam-5850	110	7	(	(	PUNCT
ejpam-5850	110	8	18	18	NUM
ejpam-5850	110	9	)	)	PUNCT
ejpam-5850	110	10	d10	d10	PROPN
ejpam-5850	110	11	=	=	SYM
ejpam-5850	110	12	{	{	PUNCT
ejpam-5850	110	13	(	(	PUNCT
ejpam-5850	110	14	g	g	NOUN
ejpam-5850	110	15	,	,	PUNCT
ejpam-5850	110	16	ε	ε	PROPN
ejpam-5850	110	17	)	)	PUNCT
ejpam-5850	111	1	|	|	ADV
ejpam-5850	111	2	g	g	PROPN
ejpam-5850	111	3	∈	∈	PROPN
ejpam-5850	111	4	q	q	X
ejpam-5850	111	5	}	}	PUNCT
ejpam-5850	111	6	,	,	PUNCT
ejpam-5850	111	7	(	(	PUNCT
ejpam-5850	111	8	19	19	NUM
ejpam-5850	111	9	)	)	PUNCT
ejpam-5850	111	10	d12	d12	NOUN
ejpam-5850	111	11	=	=	SYM
ejpam-5850	111	12	{	{	PUNCT
ejpam-5850	111	13	(	(	PUNCT
ejpam-5850	111	14	g	g	PROPN
ejpam-5850	111	15	,	,	PUNCT
ejpam-5850	111	16	gg	gg	NOUN
ejpam-5850	111	17	)	)	PUNCT
ejpam-5850	111	18	|	|	ADV
ejpam-5850	111	19	g	g	PROPN
ejpam-5850	111	20	∈	∈	PROPN
ejpam-5850	111	21	q	q	X
ejpam-5850	111	22	}	}	PUNCT
ejpam-5850	111	23	.	.	PUNCT
ejpam-5850	112	1	(	(	PUNCT
ejpam-5850	112	2	20	20	NUM
ejpam-5850	112	3	)	)	PUNCT
ejpam-5850	112	4	in	in	ADP
ejpam-5850	112	5	[	[	X
ejpam-5850	112	6	19	19	NUM
ejpam-5850	112	7	]	]	X
ejpam-5850	112	8	it	it	PRON
ejpam-5850	112	9	is	be	AUX
ejpam-5850	112	10	proved	prove	VERB
ejpam-5850	112	11	that	that	SCONJ
ejpam-5850	112	12	a	a	DET
ejpam-5850	112	13	set	set	NOUN
ejpam-5850	112	14	of	of	ADP
ejpam-5850	112	15	states	state	NOUN
ejpam-5850	112	16	q	q	NOUN
ejpam-5850	112	17	can	can	AUX
ejpam-5850	112	18	be	be	AUX
ejpam-5850	112	19	structured	structure	VERB
ejpam-5850	112	20	into	into	ADP
ejpam-5850	112	21	an	an	DET
ejpam-5850	112	22	abelian	abelian	ADJ
ejpam-5850	112	23	graphoid	graphoid	NOUN
ejpam-5850	113	1	if	if	SCONJ
ejpam-5850	113	2	and	and	CCONJ
ejpam-5850	113	3	only	only	ADV
ejpam-5850	113	4	if	if	SCONJ
ejpam-5850	113	5	it	it	PRON
ejpam-5850	113	6	can	can	AUX
ejpam-5850	113	7	be	be	AUX
ejpam-5850	113	8	partitioned	partition	VERB
ejpam-5850	113	9	into	into	ADP
ejpam-5850	113	10	disjoint	disjoint	NOUN
ejpam-5850	113	11	abelian	abelian	ADJ
ejpam-5850	113	12	groups	group	NOUN
ejpam-5850	113	13	with	with	ADP
ejpam-5850	113	14	operations	operation	NOUN
ejpam-5850	113	15	derived	derive	VERB
ejpam-5850	113	16	from	from	ADP
ejpam-5850	113	17	d21	d21	NOUN
ejpam-5850	113	18	and	and	CCONJ
ejpam-5850	113	19	unit	unit	NOUN
ejpam-5850	113	20	derived	derive	VERB
ejpam-5850	113	21	from	from	ADP
ejpam-5850	113	22	d10	d10	PROPN
ejpam-5850	113	23	(	(	PUNCT
ejpam-5850	113	24	or	or	CCONJ
ejpam-5850	113	25	equivalently	equivalently	ADV
ejpam-5850	113	26	from	from	ADP
ejpam-5850	113	27	d12	d12	NUM
ejpam-5850	113	28	and	and	CCONJ
ejpam-5850	113	29	d01	d01	NOUN
ejpam-5850	113	30	)	)	PUNCT
ejpam-5850	113	31	.	.	PUNCT
ejpam-5850	114	1	in	in	ADP
ejpam-5850	114	2	this	this	DET
ejpam-5850	114	3	setup	setup	NOUN
ejpam-5850	114	4	the	the	DET
ejpam-5850	114	5	unitary	unitary	ADJ
ejpam-5850	114	6	graphoid	graphoid	NOUN
ejpam-5850	114	7	u(q	u(q	ADP
ejpam-5850	114	8	)	)	PUNCT
ejpam-5850	114	9	,	,	PUNCT
ejpam-5850	114	10	introduced	introduce	VERB
ejpam-5850	114	11	above	above	ADV
ejpam-5850	114	12	,	,	PUNCT
ejpam-5850	114	13	corresponds	correspond	VERB
ejpam-5850	114	14	to	to	ADP
ejpam-5850	114	15	the	the	DET
ejpam-5850	114	16	partition	partition	NOUN
ejpam-5850	114	17	of	of	ADP
ejpam-5850	114	18	the	the	DET
ejpam-5850	114	19	state	state	NOUN
ejpam-5850	114	20	set	set	VERB
ejpam-5850	114	21	q	q	PROPN
ejpam-5850	114	22	=	=	SYM
ejpam-5850	114	23	{	{	PUNCT
ejpam-5850	114	24	q1	q1	PROPN
ejpam-5850	114	25	,	,	PUNCT
ejpam-5850	114	26	q2	q2	NOUN
ejpam-5850	114	27	,	,	PUNCT
ejpam-5850	114	28	.	.	PUNCT
ejpam-5850	114	29	.	.	PUNCT
ejpam-5850	115	1	.	.	PUNCT
ejpam-5850	116	1	,	,	PUNCT
ejpam-5850	116	2	qk	qk	AUX
ejpam-5850	116	3	}	}	PUNCT
ejpam-5850	116	4	into	into	ADP
ejpam-5850	116	5	k	k	PROPN
ejpam-5850	116	6	singleton	singleton	PROPN
ejpam-5850	116	7	sets	set	VERB
ejpam-5850	116	8	q	q	NOUN
ejpam-5850	116	9	=	=	PUNCT
ejpam-5850	116	10	{	{	PUNCT
ejpam-5850	116	11	qi	qi	NOUN
ejpam-5850	116	12	}	}	PUNCT
ejpam-5850	116	13	which	which	PRON
ejpam-5850	116	14	can	can	AUX
ejpam-5850	116	15	then	then	ADV
ejpam-5850	116	16	be	be	AUX
ejpam-5850	116	17	structured	structure	VERB
ejpam-5850	116	18	into	into	ADP
ejpam-5850	116	19	k	k	ADJ
ejpam-5850	116	20	trivial	trivial	ADJ
ejpam-5850	116	21	groups	group	NOUN
ejpam-5850	116	22	.	.	PUNCT
ejpam-5850	117	1	4	4	X
ejpam-5850	117	2	.	.	X
ejpam-5850	117	3	graph	graph	NOUN
ejpam-5850	117	4	automata	automata	NOUN
ejpam-5850	117	5	in	in	ADP
ejpam-5850	117	6	this	this	DET
ejpam-5850	117	7	section	section	NOUN
ejpam-5850	117	8	we	we	PRON
ejpam-5850	117	9	introduce	introduce	VERB
ejpam-5850	117	10	different	different	ADJ
ejpam-5850	117	11	types	type	NOUN
ejpam-5850	117	12	of	of	ADP
ejpam-5850	117	13	relational	relational	ADJ
ejpam-5850	117	14	automata	automata	NOUN
ejpam-5850	117	15	operating	operate	VERB
ejpam-5850	117	16	on	on	ADP
ejpam-5850	117	17	graphs	graph	NOUN
ejpam-5850	117	18	,	,	PUNCT
ejpam-5850	117	19	corresponding	correspond	VERB
ejpam-5850	117	20	to	to	ADP
ejpam-5850	117	21	different	different	ADJ
ejpam-5850	117	22	types	type	NOUN
ejpam-5850	117	23	of	of	ADP
ejpam-5850	117	24	relational	relational	ADJ
ejpam-5850	117	25	graphoids	graphoid	NOUN
ejpam-5850	117	26	.	.	PUNCT
ejpam-5850	118	1	a	a	DET
ejpam-5850	118	2	relational	relational	ADJ
ejpam-5850	118	3	graph	graph	NOUN
ejpam-5850	118	4	automaton	automaton	NOUN
ejpam-5850	118	5	,	,	PUNCT
ejpam-5850	118	6	as	as	SCONJ
ejpam-5850	118	7	introduced	introduce	VERB
ejpam-5850	118	8	in	in	ADP
ejpam-5850	118	9	[	[	X
ejpam-5850	118	10	10	10	NUM
ejpam-5850	118	11	]	]	PUNCT
ejpam-5850	118	12	,	,	PUNCT
ejpam-5850	118	13	is	be	AUX
ejpam-5850	118	14	a	a	DET
ejpam-5850	118	15	structure	structure	NOUN
ejpam-5850	118	16	a	a	PRON
ejpam-5850	118	17	=	=	SYM
ejpam-5850	118	18	(	(	PUNCT
ejpam-5850	118	19	σ	σ	PROPN
ejpam-5850	118	20	,	,	PUNCT
ejpam-5850	118	21	q	q	NOUN
ejpam-5850	118	22	,	,	PUNCT
ejpam-5850	118	23	(	(	PUNCT
ejpam-5850	118	24	rel(q	rel(q	PROPN
ejpam-5850	118	25	)	)	PUNCT
ejpam-5850	118	26	,	,	PUNCT
ejpam-5850	118	27	drel(q	drel(q	PROPN
ejpam-5850	118	28	)	)	PUNCT
ejpam-5850	118	29	)	)	PUNCT
ejpam-5850	118	30	,	,	PUNCT
ejpam-5850	118	31	δa	δa	PROPN
ejpam-5850	118	32	,	,	PUNCT
ejpam-5850	118	33	ia	ia	PROPN
ejpam-5850	118	34	,	,	PUNCT
ejpam-5850	118	35	ta	ta	PROPN
ejpam-5850	118	36	)	)	PUNCT
ejpam-5850	118	37	,	,	PUNCT
ejpam-5850	118	38	where	where	SCONJ
ejpam-5850	118	39	σ	σ	PROPN
ejpam-5850	118	40	is	be	AUX
ejpam-5850	118	41	the	the	DET
ejpam-5850	118	42	doubly	doubly	ADV
ejpam-5850	118	43	ranked	rank	VERB
ejpam-5850	118	44	set	set	NOUN
ejpam-5850	118	45	of	of	ADP
ejpam-5850	118	46	hyperedge	hyperedge	NOUN
ejpam-5850	118	47	labels	label	NOUN
ejpam-5850	118	48	,	,	PUNCT
ejpam-5850	118	49	q	q	PUNCT
ejpam-5850	118	50	is	be	AUX
ejpam-5850	118	51	a	a	DET
ejpam-5850	118	52	finite	finite	ADJ
ejpam-5850	118	53	set	set	NOUN
ejpam-5850	118	54	of	of	ADP
ejpam-5850	118	55	states	state	NOUN
ejpam-5850	118	56	,	,	PUNCT
ejpam-5850	118	57	δa	δa	PROPN
ejpam-5850	118	58	:	:	PUNCT
ejpam-5850	118	59	σ	σ	PROPN
ejpam-5850	118	60	→	→	SYM
ejpam-5850	118	61	rel(q	rel(q	PROPN
ejpam-5850	118	62	)	)	PUNCT
ejpam-5850	118	63	is	be	AUX
ejpam-5850	118	64	the	the	DET
ejpam-5850	118	65	doubly	doubly	ADV
ejpam-5850	118	66	ranked	rank	VERB
ejpam-5850	118	67	transition	transition	NOUN
ejpam-5850	118	68	function	function	NOUN
ejpam-5850	118	69	,	,	PUNCT
ejpam-5850	118	70	and	and	CCONJ
ejpam-5850	118	71	ia	ia	PROPN
ejpam-5850	118	72	,	,	PUNCT
ejpam-5850	118	73	ta	ta	X
ejpam-5850	118	74	are	be	AUX
ejpam-5850	118	75	initial	initial	ADJ
ejpam-5850	118	76	and	and	CCONJ
ejpam-5850	118	77	final	final	ADJ
ejpam-5850	118	78	rational	rational	ADJ
ejpam-5850	118	79	subsets	subset	NOUN
ejpam-5850	118	80	of	of	ADP
ejpam-5850	118	81	q∗.	q∗.	NOUN
ejpam-5850	118	82	according	accord	VERB
ejpam-5850	118	83	to	to	ADP
ejpam-5850	118	84	theorem	theorem	NOUN
ejpam-5850	118	85	3	3	NUM
ejpam-5850	118	86	of	of	ADP
ejpam-5850	118	87	[	[	X
ejpam-5850	118	88	10	10	NUM
ejpam-5850	118	89	]	]	PUNCT
ejpam-5850	118	90	,	,	PUNCT
ejpam-5850	118	91	the	the	DET
ejpam-5850	118	92	function	function	NOUN
ejpam-5850	118	93	δa	δa	PROPN
ejpam-5850	118	94	is	be	AUX
ejpam-5850	118	95	uniquely	uniquely	ADV
ejpam-5850	118	96	extended	extended	ADJ
ejpam-5850	118	97	to	to	ADP
ejpam-5850	118	98	a	a	DET
ejpam-5850	118	99	morphism	morphism	NOUN
ejpam-5850	118	100	of	of	ADP
ejpam-5850	118	101	graphoids	graphoid	NOUN
ejpam-5850	118	102	δ̄a	δ̄a	PROPN
ejpam-5850	118	103	:	:	PUNCT
ejpam-5850	118	104	gr(σ	gr(σ	NUM
ejpam-5850	118	105	)	)	PUNCT
ejpam-5850	118	106	→	→	SYM
ejpam-5850	118	107	(	(	PUNCT
ejpam-5850	118	108	rel(q	rel(q	PROPN
ejpam-5850	118	109	)	)	PUNCT
ejpam-5850	118	110	,	,	PUNCT
ejpam-5850	118	111	drel(q	drel(q	PROPN
ejpam-5850	118	112	)	)	PUNCT
ejpam-5850	118	113	)	)	PUNCT
ejpam-5850	118	114	,	,	PUNCT
ejpam-5850	118	115	where	where	SCONJ
ejpam-5850	118	116	δ̄a(iij	δ̄a(iij	ADJ
ejpam-5850	118	117	)	)	PUNCT
ejpam-5850	118	118	=	=	SYM
ejpam-5850	118	119	dij	dij	NOUN
ejpam-5850	118	120	and	and	CCONJ
ejpam-5850	118	121	δ̄a(π	δ̄a(π	PROPN
ejpam-5850	118	122	)	)	PUNCT
ejpam-5850	118	123	=	=	VERB
ejpam-5850	119	1	s.	s.	PROPN
ejpam-5850	119	2	the	the	DET
ejpam-5850	119	3	behavior	behavior	NOUN
ejpam-5850	119	4	of	of	ADP
ejpam-5850	119	5	a	a	PRON
ejpam-5850	119	6	is	be	AUX
ejpam-5850	119	7	defined	define	VERB
ejpam-5850	119	8	by	by	ADP
ejpam-5850	119	9	|a|	|a|	PROPN
ejpam-5850	119	10	=	=	SYM
ejpam-5850	119	11	{	{	PUNCT
ejpam-5850	119	12	f	f	PROPN
ejpam-5850	119	13	|	|	NOUN
ejpam-5850	119	14	f	f	PROPN
ejpam-5850	119	15	∈	∈	PROPN
ejpam-5850	119	16	grm	grm	PROPN
ejpam-5850	119	17	,	,	PUNCT
ejpam-5850	119	18	n(σ	n(σ	PROPN
ejpam-5850	119	19	)	)	PUNCT
ejpam-5850	119	20	,	,	PUNCT
ejpam-5850	119	21	δ̄a(f	δ̄a(f	PROPN
ejpam-5850	119	22	)	)	PUNCT
ejpam-5850	119	23	∩	∩	NOUN
ejpam-5850	119	24	(	(	PUNCT
ejpam-5850	119	25	i	i	PRON
ejpam-5850	119	26	(	(	PUNCT
ejpam-5850	119	27	m	m	PROPN
ejpam-5850	119	28	)	)	PUNCT
ejpam-5850	119	29	a	a	DET
ejpam-5850	119	30	×	×	PROPN
ejpam-5850	119	31	t	t	PROPN
ejpam-5850	119	32	(	(	PUNCT
ejpam-5850	119	33	n	n	CCONJ
ejpam-5850	119	34	)	)	PUNCT
ejpam-5850	119	35	a	a	X
ejpam-5850	119	36	)	)	PUNCT
ejpam-5850	119	37	̸=	̸=	PROPN
ejpam-5850	119	38	∅	∅	NOUN
ejpam-5850	119	39	,	,	PUNCT
ejpam-5850	119	40	m	m	PROPN
ejpam-5850	119	41	,	,	PUNCT
ejpam-5850	119	42	n	n	PROPN
ejpam-5850	119	43	∈	∈	PROPN
ejpam-5850	119	44	n	n	CCONJ
ejpam-5850	119	45	}	}	PUNCT
ejpam-5850	119	46	,	,	PUNCT
ejpam-5850	119	47	where	where	SCONJ
ejpam-5850	119	48	i	i	PRON
ejpam-5850	119	49	(	(	PUNCT
ejpam-5850	119	50	m	m	NOUN
ejpam-5850	119	51	)	)	PUNCT
ejpam-5850	119	52	a	a	DET
ejpam-5850	119	53	=	=	X
ejpam-5850	119	54	ia	ia	PROPN
ejpam-5850	119	55	∩qm	∩qm	NOUN
ejpam-5850	119	56	and	and	CCONJ
ejpam-5850	119	57	t	t	PROPN
ejpam-5850	119	58	(	(	PUNCT
ejpam-5850	119	59	n	n	CCONJ
ejpam-5850	119	60	)	)	PUNCT
ejpam-5850	119	61	a	a	PRON
ejpam-5850	119	62	=	=	SYM
ejpam-5850	119	63	ta	ta	AUX
ejpam-5850	119	64	∩qn	∩qn	ADJ
ejpam-5850	119	65	.	.	PUNCT
ejpam-5850	120	1	notice	notice	VERB
ejpam-5850	120	2	that	that	SCONJ
ejpam-5850	120	3	,	,	PUNCT
ejpam-5850	120	4	due	due	ADP
ejpam-5850	120	5	to	to	ADP
ejpam-5850	120	6	the	the	DET
ejpam-5850	120	7	use	use	NOUN
ejpam-5850	120	8	of	of	ADP
ejpam-5850	120	9	the	the	DET
ejpam-5850	120	10	relational	relational	ADJ
ejpam-5850	120	11	graphoid	graphoid	NOUN
ejpam-5850	120	12	,	,	PUNCT
ejpam-5850	120	13	the	the	DET
ejpam-5850	120	14	resulting	result	VERB
ejpam-5850	120	15	graph	graph	NOUN
ejpam-5850	120	16	automata	automata	NOUN
ejpam-5850	120	17	are	be	AUX
ejpam-5850	120	18	non	non	ADJ
ejpam-5850	120	19	-	-	ADJ
ejpam-5850	120	20	deterministic	deterministic	ADJ
ejpam-5850	120	21	.	.	PUNCT
ejpam-5850	121	1	graph	graph	NOUN
ejpam-5850	121	2	automata	automata	NOUN
ejpam-5850	121	3	can	can	AUX
ejpam-5850	121	4	be	be	AUX
ejpam-5850	121	5	obtained	obtain	VERB
ejpam-5850	121	6	similarly	similarly	ADV
ejpam-5850	121	7	to	to	ADP
ejpam-5850	121	8	the	the	DET
ejpam-5850	121	9	above	above	ADJ
ejpam-5850	121	10	definition	definition	NOUN
ejpam-5850	121	11	using	use	VERB
ejpam-5850	121	12	non	non	ADJ
ejpam-5850	121	13	-	-	ADJ
ejpam-5850	121	14	relational	relational	ADJ
ejpam-5850	121	15	graphoids	graphoid	NOUN
ejpam-5850	121	16	,	,	PUNCT
ejpam-5850	121	17	although	although	SCONJ
ejpam-5850	121	18	this	this	PRON
ejpam-5850	121	19	has	have	AUX
ejpam-5850	121	20	never	never	ADV
ejpam-5850	121	21	been	be	AUX
ejpam-5850	121	22	examined	examine	VERB
ejpam-5850	121	23	in	in	ADP
ejpam-5850	121	24	the	the	DET
ejpam-5850	121	25	literature	literature	NOUN
ejpam-5850	121	26	.	.	PUNCT
ejpam-5850	122	1	in	in	ADP
ejpam-5850	122	2	the	the	DET
ejpam-5850	122	3	particular	particular	ADJ
ejpam-5850	122	4	case	case	NOUN
ejpam-5850	122	5	that	that	SCONJ
ejpam-5850	122	6	the	the	DET
ejpam-5850	122	7	relational	relational	ADJ
ejpam-5850	122	8	graphoid	graphoid	NOUN
ejpam-5850	122	9	satisfies	satisfie	NOUN
ejpam-5850	122	10	eq	eq	ADP
ejpam-5850	122	11	.	.	PROPN
ejpam-5850	122	12	16	16	NUM
ejpam-5850	122	13	,	,	PUNCT
ejpam-5850	122	14	then	then	ADV
ejpam-5850	122	15	the	the	DET
ejpam-5850	122	16	corresponding	corresponding	ADJ
ejpam-5850	122	17	relational	relational	ADJ
ejpam-5850	122	18	graph	graph	NOUN
ejpam-5850	122	19	automaton	automaton	NOUN
ejpam-5850	122	20	is	be	AUX
ejpam-5850	122	21	called	call	VERB
ejpam-5850	122	22	abelian	abelian	ADJ
ejpam-5850	122	23	graph	graph	NOUN
ejpam-5850	122	24	automaton	automaton	NOUN
ejpam-5850	122	25	.	.	PUNCT
ejpam-5850	123	1	in	in	ADP
ejpam-5850	123	2	addition	addition	NOUN
ejpam-5850	123	3	,	,	PUNCT
ejpam-5850	123	4	if	if	SCONJ
ejpam-5850	123	5	it	it	PRON
ejpam-5850	123	6	satisfies	satisfy	VERB
ejpam-5850	123	7	eq	eq	ADP
ejpam-5850	123	8	.	.	PROPN
ejpam-5850	123	9	16	16	NUM
ejpam-5850	123	10	and	and	CCONJ
ejpam-5850	123	11	eqs.1720	eqs.1720	PROPN
ejpam-5850	123	12	,	,	PUNCT
ejpam-5850	123	13	it	it	PRON
ejpam-5850	123	14	is	be	AUX
ejpam-5850	123	15	called	call	VERB
ejpam-5850	123	16	unitary	unitary	ADJ
ejpam-5850	123	17	graph	graph	NOUN
ejpam-5850	123	18	automaton	automaton	NOUN
ejpam-5850	123	19	.	.	PUNCT
ejpam-5850	124	1	the	the	DET
ejpam-5850	124	2	set	set	NOUN
ejpam-5850	124	3	of	of	ADP
ejpam-5850	124	4	all	all	DET
ejpam-5850	124	5	graph	graph	NOUN
ejpam-5850	124	6	languages	language	NOUN
ejpam-5850	124	7	over	over	ADP
ejpam-5850	124	8	the	the	DET
ejpam-5850	124	9	doubly	doubly	ADV
ejpam-5850	124	10	ranked	rank	VERB
ejpam-5850	124	11	set	set	PROPN
ejpam-5850	124	12	σ	σ	PROPN
ejpam-5850	124	13	,	,	PUNCT
ejpam-5850	124	14	recognized	recognize	VERB
ejpam-5850	124	15	by	by	ADP
ejpam-5850	124	16	a	a	DET
ejpam-5850	124	17	relational	relational	ADJ
ejpam-5850	124	18	graph	graph	NOUN
ejpam-5850	124	19	automaton	automaton	NOUN
ejpam-5850	124	20	is	be	AUX
ejpam-5850	124	21	denoted	denote	VERB
ejpam-5850	124	22	by	by	ADP
ejpam-5850	124	23	rrec(σ	rrec(σ	ADJ
ejpam-5850	124	24	)	)	PUNCT
ejpam-5850	124	25	.	.	PUNCT
ejpam-5850	125	1	analogously	analogously	ADV
ejpam-5850	125	2	,	,	PUNCT
ejpam-5850	125	3	we	we	PRON
ejpam-5850	125	4	denote	denote	VERB
ejpam-5850	125	5	by	by	ADP
ejpam-5850	125	6	arec(σ	arec(σ	PROPN
ejpam-5850	125	7	)	)	PUNCT
ejpam-5850	125	8	the	the	DET
ejpam-5850	125	9	set	set	NOUN
ejpam-5850	125	10	of	of	ADP
ejpam-5850	125	11	k.	k.	PROPN
ejpam-5850	125	12	papadopoulos	papadopoulos	PROPN
ejpam-5850	125	13	/	/	SYM
ejpam-5850	125	14	eur	eur	PROPN
ejpam-5850	125	15	.	.	PUNCT
ejpam-5850	126	1	j.	j.	PROPN
ejpam-5850	126	2	pure	pure	PROPN
ejpam-5850	126	3	appl	appl	PROPN
ejpam-5850	126	4	.	.	PROPN
ejpam-5850	126	5	math	math	PROPN
ejpam-5850	126	6	,	,	PUNCT
ejpam-5850	126	7	18	18	NUM
ejpam-5850	126	8	(	(	PUNCT
ejpam-5850	126	9	1	1	NUM
ejpam-5850	126	10	)	)	PUNCT
ejpam-5850	126	11	(	(	PUNCT
ejpam-5850	126	12	2025	2025	NUM
ejpam-5850	126	13	)	)	PUNCT
ejpam-5850	126	14	,	,	PUNCT
ejpam-5850	126	15	5850	5850	NUM
ejpam-5850	126	16	7	7	NUM
ejpam-5850	126	17	of	of	ADP
ejpam-5850	126	18	13	13	NUM
ejpam-5850	126	19	figure	figure	NOUN
ejpam-5850	126	20	1	1	NUM
ejpam-5850	126	21	:	:	PUNCT
ejpam-5850	126	22	the	the	DET
ejpam-5850	126	23	class	class	NOUN
ejpam-5850	126	24	hierarchy	hierarchy	NOUN
ejpam-5850	126	25	of	of	ADP
ejpam-5850	126	26	graph	graph	NOUN
ejpam-5850	126	27	automata	automata	NOUN
ejpam-5850	126	28	graph	graph	NOUN
ejpam-5850	126	29	languages	language	NOUN
ejpam-5850	126	30	recognized	recognize	VERB
ejpam-5850	126	31	by	by	ADP
ejpam-5850	126	32	abelian	abelian	ADJ
ejpam-5850	126	33	graph	graph	NOUN
ejpam-5850	126	34	automata	automata	NOUN
ejpam-5850	126	35	and	and	CCONJ
ejpam-5850	126	36	by	by	ADP
ejpam-5850	126	37	urec(σ	urec(σ	NOUN
ejpam-5850	126	38	)	)	PUNCT
ejpam-5850	126	39	the	the	DET
ejpam-5850	126	40	set	set	NOUN
ejpam-5850	126	41	of	of	ADP
ejpam-5850	126	42	graph	graph	NOUN
ejpam-5850	126	43	languages	language	NOUN
ejpam-5850	126	44	recognized	recognize	VERB
ejpam-5850	126	45	by	by	ADP
ejpam-5850	126	46	unitary	unitary	ADJ
ejpam-5850	126	47	graph	graph	NOUN
ejpam-5850	126	48	automata	automata	NOUN
ejpam-5850	126	49	.	.	PUNCT
ejpam-5850	127	1	in	in	ADP
ejpam-5850	127	2	[	[	X
ejpam-5850	127	3	20	20	NUM
ejpam-5850	127	4	]	]	PUNCT
ejpam-5850	127	5	it	it	PRON
ejpam-5850	127	6	was	be	AUX
ejpam-5850	127	7	shown	show	VERB
ejpam-5850	127	8	that	that	SCONJ
ejpam-5850	127	9	the	the	DET
ejpam-5850	127	10	set	set	NOUN
ejpam-5850	127	11	of	of	ADP
ejpam-5850	127	12	conventional	conventional	ADJ
ejpam-5850	127	13	k	k	ADJ
ejpam-5850	127	14	-	-	ADJ
ejpam-5850	127	15	colorable	colorable	ADJ
ejpam-5850	127	16	graphs	graph	NOUN
ejpam-5850	127	17	without	without	ADP
ejpam-5850	127	18	inputs	input	NOUN
ejpam-5850	127	19	and	and	CCONJ
ejpam-5850	127	20	outputs	output	NOUN
ejpam-5850	127	21	belongs	belong	VERB
ejpam-5850	127	22	to	to	ADP
ejpam-5850	127	23	urec(σ	urec(σ	NOUN
ejpam-5850	127	24	)	)	PUNCT
ejpam-5850	127	25	for	for	ADP
ejpam-5850	127	26	every	every	DET
ejpam-5850	127	27	positive	positive	ADJ
ejpam-5850	127	28	integer	integer	NOUN
ejpam-5850	128	1	k.	k.	PROPN
ejpam-5850	129	1	this	this	PRON
ejpam-5850	129	2	was	be	AUX
ejpam-5850	129	3	achieved	achieve	VERB
ejpam-5850	129	4	by	by	ADP
ejpam-5850	129	5	constructing	construct	VERB
ejpam-5850	129	6	a	a	DET
ejpam-5850	129	7	unitary	unitary	ADJ
ejpam-5850	129	8	graph	graph	NOUN
ejpam-5850	129	9	automaton	automaton	NOUN
ejpam-5850	129	10	able	able	ADJ
ejpam-5850	129	11	to	to	PART
ejpam-5850	129	12	read	read	VERB
ejpam-5850	129	13	all	all	PRON
ejpam-5850	129	14	ordinary	ordinary	ADJ
ejpam-5850	129	15	(	(	PUNCT
ejpam-5850	129	16	0	0	NUM
ejpam-5850	129	17	,	,	PUNCT
ejpam-5850	129	18	0)-graphs	0)-graphs	NUM
ejpam-5850	129	19	with	with	ADP
ejpam-5850	129	20	identical	identical	ADJ
ejpam-5850	129	21	edge	edge	NOUN
ejpam-5850	129	22	labels	label	NOUN
ejpam-5850	129	23	,	,	PUNCT
ejpam-5850	129	24	and	and	CCONJ
ejpam-5850	129	25	recognize	recognize	VERB
ejpam-5850	129	26	those	those	PRON
ejpam-5850	129	27	that	that	PRON
ejpam-5850	129	28	can	can	AUX
ejpam-5850	129	29	be	be	AUX
ejpam-5850	129	30	assigned	assign	VERB
ejpam-5850	129	31	a	a	DET
ejpam-5850	129	32	proper	proper	ADJ
ejpam-5850	129	33	k	k	NOUN
ejpam-5850	129	34	-	-	NOUN
ejpam-5850	129	35	coloring	coloring	NOUN
ejpam-5850	129	36	.	.	PUNCT
ejpam-5850	130	1	next	next	ADV
ejpam-5850	130	2	we	we	PRON
ejpam-5850	130	3	will	will	AUX
ejpam-5850	130	4	construct	construct	VERB
ejpam-5850	130	5	a	a	DET
ejpam-5850	130	6	unitary	unitary	ADJ
ejpam-5850	130	7	graph	graph	NOUN
ejpam-5850	130	8	automaton	automaton	NOUN
ejpam-5850	130	9	recognizing	recognize	VERB
ejpam-5850	130	10	all	all	DET
ejpam-5850	130	11	conventional	conventional	ADJ
ejpam-5850	130	12	graphs	graph	NOUN
ejpam-5850	130	13	of	of	ADP
ejpam-5850	130	14	length	length	NOUN
ejpam-5850	130	15	at	at	ADP
ejpam-5850	130	16	most	most	ADJ
ejpam-5850	130	17	k.	k.	NOUN
ejpam-5850	130	18	proposition	proposition	PROPN
ejpam-5850	130	19	1	1	NUM
ejpam-5850	130	20	.	.	PUNCT
ejpam-5850	131	1	given	give	VERB
ejpam-5850	131	2	k	k	PROPN
ejpam-5850	131	3	∈	∈	PROPN
ejpam-5850	131	4	n	n	CCONJ
ejpam-5850	131	5	,	,	PUNCT
ejpam-5850	131	6	the	the	DET
ejpam-5850	131	7	set	set	NOUN
ejpam-5850	131	8	of	of	ADP
ejpam-5850	131	9	conventional	conventional	ADJ
ejpam-5850	131	10	graphs	graph	NOUN
ejpam-5850	131	11	of	of	ADP
ejpam-5850	131	12	length	length	NOUN
ejpam-5850	131	13	at	at	ADP
ejpam-5850	131	14	most	most	ADV
ejpam-5850	131	15	k	k	PROPN
ejpam-5850	131	16	belongs	belong	VERB
ejpam-5850	131	17	to	to	ADP
ejpam-5850	131	18	urec(σ	urec(σ	NOUN
ejpam-5850	131	19	)	)	PUNCT
ejpam-5850	131	20	.	.	PUNCT
ejpam-5850	132	1	proof	proof	NOUN
ejpam-5850	132	2	.	.	PUNCT
ejpam-5850	133	1	we	we	PRON
ejpam-5850	133	2	are	be	AUX
ejpam-5850	133	3	first	first	ADV
ejpam-5850	133	4	going	go	VERB
ejpam-5850	133	5	to	to	PART
ejpam-5850	133	6	construct	construct	VERB
ejpam-5850	133	7	a	a	DET
ejpam-5850	133	8	graph	graph	NOUN
ejpam-5850	133	9	automaton	automaton	NOUN
ejpam-5850	133	10	recognizing	recognize	VERB
ejpam-5850	133	11	all	all	DET
ejpam-5850	133	12	ordinary	ordinary	ADJ
ejpam-5850	133	13	unlabeled	unlabele	VERB
ejpam-5850	133	14	(	(	PUNCT
ejpam-5850	133	15	0	0	NUM
ejpam-5850	133	16	,	,	PUNCT
ejpam-5850	133	17	0)-graphs	0)-graphs	NUM
ejpam-5850	133	18	of	of	ADP
ejpam-5850	133	19	length	length	NOUN
ejpam-5850	133	20	at	at	ADP
ejpam-5850	133	21	most	most	ADJ
ejpam-5850	133	22	k.	k.	PROPN
ejpam-5850	133	23	consider	consider	VERB
ejpam-5850	133	24	the	the	DET
ejpam-5850	133	25	unitary	unitary	ADJ
ejpam-5850	133	26	graph	graph	NOUN
ejpam-5850	133	27	automaton	automaton	PROPN
ejpam-5850	133	28	ak	ak	PROPN
ejpam-5850	133	29	len	len	PROPN
ejpam-5850	133	30	=	=	SYM
ejpam-5850	133	31	(	(	PUNCT
ejpam-5850	133	32	σ	σ	PROPN
ejpam-5850	133	33	,	,	PUNCT
ejpam-5850	133	34	q	q	X
ejpam-5850	133	35	,	,	PUNCT
ejpam-5850	133	36	u(q	u(q	ADV
ejpam-5850	133	37	)	)	PUNCT
ejpam-5850	133	38	,	,	PUNCT
ejpam-5850	133	39	δak	δak	NOUN
ejpam-5850	133	40	len	len	NOUN
ejpam-5850	133	41	,	,	PUNCT
ejpam-5850	133	42	iak	iak	PROPN
ejpam-5850	133	43	len	len	NOUN
ejpam-5850	133	44	,	,	PUNCT
ejpam-5850	133	45	tak	tak	NOUN
ejpam-5850	133	46	len	len	NOUN
ejpam-5850	133	47	)	)	PUNCT
ejpam-5850	133	48	with	with	ADP
ejpam-5850	133	49	σ	σ	PROPN
ejpam-5850	133	50	=	=	SYM
ejpam-5850	133	51	σ1,1	σ1,1	PROPN
ejpam-5850	133	52	=	=	PUNCT
ejpam-5850	133	53	{	{	PUNCT
ejpam-5850	133	54	a	a	NOUN
ejpam-5850	133	55	}	}	PUNCT
ejpam-5850	133	56	,	,	PUNCT
ejpam-5850	133	57	state	state	NOUN
ejpam-5850	133	58	set	set	VERB
ejpam-5850	133	59	q	q	NOUN
ejpam-5850	133	60	=	=	PUNCT
ejpam-5850	133	61	{	{	PUNCT
ejpam-5850	133	62	1	1	NUM
ejpam-5850	133	63	,	,	PUNCT
ejpam-5850	133	64	2	2	NUM
ejpam-5850	133	65	,	,	PUNCT
ejpam-5850	133	66	...	...	PUNCT
ejpam-5850	133	67	,	,	PUNCT
ejpam-5850	133	68	k	k	PROPN
ejpam-5850	134	1	+	+	PROPN
ejpam-5850	134	2	1	1	NUM
ejpam-5850	134	3	}	}	PUNCT
ejpam-5850	134	4	,	,	PUNCT
ejpam-5850	134	5	transition	transition	NOUN
ejpam-5850	134	6	function	function	NOUN
ejpam-5850	134	7	given	give	VERB
ejpam-5850	134	8	by	by	ADP
ejpam-5850	134	9	δak	δak	NOUN
ejpam-5850	134	10	len	len	NOUN
ejpam-5850	134	11	(	(	PUNCT
ejpam-5850	134	12	a	a	X
ejpam-5850	134	13	)	)	PUNCT
ejpam-5850	134	14	=	=	SYM
ejpam-5850	134	15	{	{	PUNCT
ejpam-5850	134	16	(	(	PUNCT
ejpam-5850	134	17	i	i	PROPN
ejpam-5850	134	18	,	,	PUNCT
ejpam-5850	134	19	j	j	PROPN
ejpam-5850	134	20	)	)	PUNCT
ejpam-5850	135	1	|	|	ADV
ejpam-5850	135	2	i	i	PRON
ejpam-5850	135	3	,	,	PUNCT
ejpam-5850	135	4	j	j	PROPN
ejpam-5850	135	5	∈	∈	PROPN
ejpam-5850	136	1	q	q	PROPN
ejpam-5850	136	2	,	,	PUNCT
ejpam-5850	136	3	i	i	PRON
ejpam-5850	136	4	<	<	X
ejpam-5850	136	5	j	j	X
ejpam-5850	136	6	}	}	PUNCT
ejpam-5850	136	7	,	,	PUNCT
ejpam-5850	136	8	and	and	CCONJ
ejpam-5850	136	9	iak	iak	X
ejpam-5850	136	10	len	len	PROPN
ejpam-5850	136	11	=	=	PROPN
ejpam-5850	136	12	tak	tak	NOUN
ejpam-5850	136	13	len	len	NOUN
ejpam-5850	136	14	=	=	SYM
ejpam-5850	136	15	{	{	PUNCT
ejpam-5850	136	16	ε	ε	PROPN
ejpam-5850	136	17	}	}	PUNCT
ejpam-5850	136	18	.	.	PUNCT
ejpam-5850	137	1	from	from	ADP
ejpam-5850	137	2	this	this	DET
ejpam-5850	137	3	construction	construction	NOUN
ejpam-5850	137	4	we	we	PRON
ejpam-5850	137	5	see	see	VERB
ejpam-5850	137	6	that	that	SCONJ
ejpam-5850	137	7	any	any	DET
ejpam-5850	137	8	successful	successful	ADJ
ejpam-5850	137	9	transition	transition	NOUN
ejpam-5850	137	10	inside	inside	ADP
ejpam-5850	137	11	this	this	DET
ejpam-5850	137	12	automaton	automaton	NOUN
ejpam-5850	137	13	will	will	AUX
ejpam-5850	137	14	increase	increase	VERB
ejpam-5850	137	15	the	the	DET
ejpam-5850	137	16	state	state	NOUN
ejpam-5850	137	17	index	index	NOUN
ejpam-5850	137	18	for	for	ADP
ejpam-5850	137	19	each	each	DET
ejpam-5850	137	20	edge	edge	NOUN
ejpam-5850	137	21	of	of	ADP
ejpam-5850	137	22	the	the	DET
ejpam-5850	137	23	graph	graph	NOUN
ejpam-5850	137	24	it	it	PRON
ejpam-5850	137	25	reads	read	VERB
ejpam-5850	137	26	.	.	PUNCT
ejpam-5850	138	1	as	as	ADP
ejpam-5850	138	2	a	a	DET
ejpam-5850	138	3	result	result	NOUN
ejpam-5850	138	4	,	,	PUNCT
ejpam-5850	138	5	by	by	ADP
ejpam-5850	138	6	taking	take	VERB
ejpam-5850	138	7	into	into	ADP
ejpam-5850	138	8	account	account	NOUN
ejpam-5850	138	9	the	the	DET
ejpam-5850	138	10	path	path	NOUN
ejpam-5850	138	11	length	length	NOUN
ejpam-5850	138	12	definition	definition	NOUN
ejpam-5850	138	13	,	,	PUNCT
ejpam-5850	138	14	there	there	PRON
ejpam-5850	138	15	will	will	AUX
ejpam-5850	138	16	be	be	AUX
ejpam-5850	138	17	not	not	PART
ejpam-5850	138	18	successful	successful	ADJ
ejpam-5850	138	19	transition	transition	NOUN
ejpam-5850	138	20	for	for	ADP
ejpam-5850	138	21	any	any	DET
ejpam-5850	138	22	graph	graph	NOUN
ejpam-5850	138	23	that	that	PRON
ejpam-5850	138	24	has	have	VERB
ejpam-5850	138	25	a	a	DET
ejpam-5850	138	26	path	path	NOUN
ejpam-5850	138	27	of	of	ADP
ejpam-5850	138	28	length	length	NOUN
ejpam-5850	138	29	larger	large	ADJ
ejpam-5850	138	30	than	than	ADP
ejpam-5850	138	31	k	k	PROPN
ejpam-5850	138	32	but	but	CCONJ
ejpam-5850	138	33	every	every	DET
ejpam-5850	138	34	graph	graph	NOUN
ejpam-5850	138	35	of	of	ADP
ejpam-5850	138	36	smaller	small	ADJ
ejpam-5850	138	37	length	length	NOUN
ejpam-5850	138	38	will	will	AUX
ejpam-5850	138	39	be	be	AUX
ejpam-5850	138	40	recognized	recognize	VERB
ejpam-5850	138	41	.	.	PUNCT
ejpam-5850	139	1	h1	h1	VERB
ejpam-5850	139	2	h2	h2	PROPN
ejpam-5850	139	3	h3	h3	NOUN
ejpam-5850	139	4	figure	figure	NOUN
ejpam-5850	139	5	2	2	NUM
ejpam-5850	139	6	:	:	PUNCT
ejpam-5850	139	7	three	three	NUM
ejpam-5850	139	8	unlabeled	unlabeled	ADJ
ejpam-5850	139	9	(	(	PUNCT
ejpam-5850	139	10	0	0	NUM
ejpam-5850	139	11	,	,	PUNCT
ejpam-5850	139	12	0)graphs	0)graphs	NUM
ejpam-5850	139	13	with	with	ADP
ejpam-5850	139	14	binary	binary	ADJ
ejpam-5850	139	15	edges	edge	NOUN
ejpam-5850	139	16	k.	k.	PROPN
ejpam-5850	139	17	papadopoulos	papadopoulos	PROPN
ejpam-5850	139	18	/	/	SYM
ejpam-5850	139	19	eur	eur	PROPN
ejpam-5850	139	20	.	.	PUNCT
ejpam-5850	140	1	j.	j.	PROPN
ejpam-5850	140	2	pure	pure	PROPN
ejpam-5850	140	3	appl	appl	PROPN
ejpam-5850	140	4	.	.	PROPN
ejpam-5850	140	5	math	math	PROPN
ejpam-5850	140	6	,	,	PUNCT
ejpam-5850	140	7	18	18	NUM
ejpam-5850	140	8	(	(	PUNCT
ejpam-5850	140	9	1	1	NUM
ejpam-5850	140	10	)	)	PUNCT
ejpam-5850	140	11	(	(	PUNCT
ejpam-5850	140	12	2025	2025	NUM
ejpam-5850	140	13	)	)	PUNCT
ejpam-5850	140	14	,	,	PUNCT
ejpam-5850	140	15	5850	5850	NUM
ejpam-5850	140	16	8	8	NUM
ejpam-5850	140	17	of	of	ADP
ejpam-5850	140	18	13	13	NUM
ejpam-5850	140	19	we	we	PRON
ejpam-5850	140	20	will	will	AUX
ejpam-5850	140	21	illustrate	illustrate	VERB
ejpam-5850	140	22	this	this	PRON
ejpam-5850	140	23	by	by	ADP
ejpam-5850	140	24	examining	examine	VERB
ejpam-5850	140	25	the	the	DET
ejpam-5850	140	26	three	three	NUM
ejpam-5850	140	27	ordinary	ordinary	ADJ
ejpam-5850	140	28	graphs	graph	NOUN
ejpam-5850	140	29	shown	show	VERB
ejpam-5850	140	30	in	in	ADP
ejpam-5850	140	31	figure	figure	NOUN
ejpam-5850	140	32	2	2	NUM
ejpam-5850	140	33	,	,	PUNCT
ejpam-5850	140	34	starting	start	VERB
ejpam-5850	140	35	with	with	ADP
ejpam-5850	140	36	h1	h1	PROPN
ejpam-5850	140	37	,	,	PUNCT
ejpam-5850	140	38	a	a	DET
ejpam-5850	140	39	graph	graph	NOUN
ejpam-5850	140	40	of	of	ADP
ejpam-5850	140	41	length	length	NOUN
ejpam-5850	140	42	3	3	NUM
ejpam-5850	140	43	.	.	PUNCT
ejpam-5850	141	1	we	we	PRON
ejpam-5850	141	2	know	know	VERB
ejpam-5850	141	3	that	that	DET
ejpam-5850	141	4	gr(σ	gr(σ	NOUN
ejpam-5850	141	5	)	)	PUNCT
ejpam-5850	141	6	is	be	AUX
ejpam-5850	141	7	the	the	DET
ejpam-5850	141	8	free	free	ADJ
ejpam-5850	141	9	graphoid	graphoid	NOUN
ejpam-5850	141	10	,	,	PUNCT
ejpam-5850	141	11	hence	hence	ADV
ejpam-5850	141	12	the	the	DET
ejpam-5850	141	13	operation	operation	NOUN
ejpam-5850	141	14	of	of	ADP
ejpam-5850	141	15	any	any	DET
ejpam-5850	141	16	automaton	automaton	NOUN
ejpam-5850	141	17	does	do	AUX
ejpam-5850	141	18	not	not	PART
ejpam-5850	141	19	depend	depend	VERB
ejpam-5850	141	20	to	to	ADP
ejpam-5850	141	21	the	the	DET
ejpam-5850	141	22	specific	specific	ADJ
ejpam-5850	141	23	representation	representation	NOUN
ejpam-5850	141	24	of	of	ADP
ejpam-5850	141	25	h1	h1	PROPN
ejpam-5850	141	26	we	we	PRON
ejpam-5850	141	27	will	will	AUX
ejpam-5850	141	28	employ	employ	VERB
ejpam-5850	141	29	.	.	PUNCT
ejpam-5850	142	1	below	below	ADP
ejpam-5850	142	2	is	be	AUX
ejpam-5850	142	3	a	a	DET
ejpam-5850	142	4	representation	representation	NOUN
ejpam-5850	142	5	of	of	ADP
ejpam-5850	142	6	h1	h1	NOUN
ejpam-5850	142	7	where	where	SCONJ
ejpam-5850	142	8	graph	graph	NOUN
ejpam-5850	142	9	product	product	NOUN
ejpam-5850	142	10	and	and	CCONJ
ejpam-5850	142	11	graph	graph	NOUN
ejpam-5850	142	12	sum	sum	NOUN
ejpam-5850	142	13	are	be	AUX
ejpam-5850	142	14	denoted	denote	VERB
ejpam-5850	142	15	,	,	PUNCT
ejpam-5850	142	16	for	for	ADP
ejpam-5850	142	17	simplicity	simplicity	NOUN
ejpam-5850	142	18	,	,	PUNCT
ejpam-5850	142	19	by	by	ADP
ejpam-5850	142	20	horizontal	horizontal	ADJ
ejpam-5850	142	21	and	and	CCONJ
ejpam-5850	142	22	vertical	vertical	ADJ
ejpam-5850	142	23	concatenation	concatenation	NOUN
ejpam-5850	142	24	.	.	PUNCT
ejpam-5850	143	1	h1	h1	PROPN
ejpam-5850	143	2	=	=	SYM
ejpam-5850	143	3	i01	i01	PROPN
ejpam-5850	143	4	a	a	DET
ejpam-5850	143	5	i12	i12	PROPN
ejpam-5850	144	1	(	(	PUNCT
ejpam-5850	144	2	a	a	DET
ejpam-5850	144	3	a	a	NOUN
ejpam-5850	144	4	)	)	PUNCT
ejpam-5850	144	5	(	(	PUNCT
ejpam-5850	144	6	a	a	DET
ejpam-5850	144	7	e	e	NOUN
ejpam-5850	144	8	)	)	PUNCT
ejpam-5850	144	9	i21	i21	NOUN
ejpam-5850	144	10	i10	i10	PROPN
ejpam-5850	144	11	the	the	DET
ejpam-5850	144	12	image	image	NOUN
ejpam-5850	144	13	of	of	ADP
ejpam-5850	144	14	h1	h1	NOUN
ejpam-5850	144	15	by	by	ADP
ejpam-5850	144	16	the	the	DET
ejpam-5850	144	17	transition	transition	NOUN
ejpam-5850	144	18	function	function	NOUN
ejpam-5850	144	19	of	of	ADP
ejpam-5850	144	20	a3	a3	NOUN
ejpam-5850	144	21	len	len	PROPN
ejpam-5850	144	22	is	be	AUX
ejpam-5850	144	23	δa3	δa3	NOUN
ejpam-5850	144	24	len	len	ADJ
ejpam-5850	144	25	(	(	PUNCT
ejpam-5850	144	26	h1	h1	PROPN
ejpam-5850	144	27	)	)	PUNCT
ejpam-5850	144	28	=	=	SYM
ejpam-5850	145	1	d01	d01	PROPN
ejpam-5850	145	2	δa3	δa3	PROPN
ejpam-5850	145	3	len	len	PROPN
ejpam-5850	145	4	(	(	PUNCT
ejpam-5850	145	5	a	a	X
ejpam-5850	145	6	)	)	PUNCT
ejpam-5850	145	7	d12	d12	NOUN
ejpam-5850	145	8	(	(	PUNCT
ejpam-5850	145	9	δa3	δa3	NOUN
ejpam-5850	145	10	len	len	PROPN
ejpam-5850	145	11	(	(	PUNCT
ejpam-5850	145	12	a	a	X
ejpam-5850	145	13	)	)	PUNCT
ejpam-5850	145	14	δa3	δa3	NOUN
ejpam-5850	145	15	len	len	NOUN
ejpam-5850	145	16	(	(	PUNCT
ejpam-5850	145	17	a	a	NOUN
ejpam-5850	145	18	)	)	PUNCT
ejpam-5850	145	19	)	)	PUNCT
ejpam-5850	145	20	(	(	PUNCT
ejpam-5850	145	21	δa3	δa3	NOUN
ejpam-5850	145	22	len	len	X
ejpam-5850	145	23	(	(	PUNCT
ejpam-5850	145	24	a	a	NOUN
ejpam-5850	145	25	)	)	PUNCT
ejpam-5850	145	26	e	e	NOUN
ejpam-5850	145	27	)	)	PUNCT
ejpam-5850	145	28	d21	d21	PROPN
ejpam-5850	145	29	d10	d10	PROPN
ejpam-5850	145	30	and	and	CCONJ
ejpam-5850	145	31	an	an	DET
ejpam-5850	145	32	accepting	accept	VERB
ejpam-5850	145	33	state	state	NOUN
ejpam-5850	145	34	map	map	NOUN
ejpam-5850	145	35	for	for	ADP
ejpam-5850	145	36	it	it	PRON
ejpam-5850	145	37	will	will	AUX
ejpam-5850	145	38	be	be	AUX
ejpam-5850	145	39	{	{	PUNCT
ejpam-5850	145	40	ε}d01{1}δa3	ε}d01{1}δa3	VERB
ejpam-5850	145	41	len	len	PROPN
ejpam-5850	145	42	(	(	PUNCT
ejpam-5850	145	43	a){2}d12	a){2}d12	PROPN
ejpam-5850	145	44	{	{	PUNCT
ejpam-5850	145	45	2	2	NUM
ejpam-5850	145	46	2	2	NUM
ejpam-5850	145	47	}	}	PUNCT
ejpam-5850	145	48	(	(	PUNCT
ejpam-5850	145	49	δa3	δa3	PROPN
ejpam-5850	145	50	len	len	X
ejpam-5850	145	51	(	(	PUNCT
ejpam-5850	145	52	a	a	X
ejpam-5850	145	53	)	)	PUNCT
ejpam-5850	145	54	δa3	δa3	NOUN
ejpam-5850	145	55	len	len	NOUN
ejpam-5850	145	56	(	(	PUNCT
ejpam-5850	145	57	a	a	NOUN
ejpam-5850	145	58	)	)	PUNCT
ejpam-5850	145	59	)	)	PUNCT
ejpam-5850	145	60	{	{	PUNCT
ejpam-5850	145	61	3	3	NUM
ejpam-5850	145	62	4	4	NUM
ejpam-5850	145	63	}	}	PUNCT
ejpam-5850	145	64	(	(	PUNCT
ejpam-5850	145	65	δa3	δa3	PROPN
ejpam-5850	145	66	len	len	X
ejpam-5850	145	67	(	(	PUNCT
ejpam-5850	145	68	a	a	NOUN
ejpam-5850	145	69	)	)	PUNCT
ejpam-5850	145	70	e	e	NOUN
ejpam-5850	145	71	)	)	PUNCT
ejpam-5850	145	72	{	{	PUNCT
ejpam-5850	145	73	4	4	NUM
ejpam-5850	145	74	4	4	NUM
ejpam-5850	145	75	}	}	PUNCT
ejpam-5850	145	76	d21{4	d21{4	PROPN
ejpam-5850	145	77	}	}	PUNCT
ejpam-5850	145	78	d10{ε	d10{ε	PROPN
ejpam-5850	145	79	}	}	PUNCT
ejpam-5850	145	80	where	where	SCONJ
ejpam-5850	145	81	the	the	DET
ejpam-5850	145	82	states	state	NOUN
ejpam-5850	145	83	are	be	AUX
ejpam-5850	145	84	indicated	indicate	VERB
ejpam-5850	145	85	in	in	ADP
ejpam-5850	145	86	brackets	bracket	NOUN
ejpam-5850	145	87	.	.	PUNCT
ejpam-5850	146	1	hence	hence	ADV
ejpam-5850	146	2	the	the	DET
ejpam-5850	146	3	graph	graph	NOUN
ejpam-5850	146	4	is	be	AUX
ejpam-5850	146	5	recognized	recognize	VERB
ejpam-5850	146	6	by	by	ADP
ejpam-5850	146	7	a3	a3	PROPN
ejpam-5850	146	8	len	len	PROPN
ejpam-5850	146	9	.	.	PUNCT
ejpam-5850	147	1	represented	represent	VERB
ejpam-5850	147	2	on	on	ADP
ejpam-5850	147	3	the	the	DET
ejpam-5850	147	4	graph	graph	NOUN
ejpam-5850	147	5	,	,	PUNCT
ejpam-5850	147	6	the	the	DET
ejpam-5850	147	7	states	state	NOUN
ejpam-5850	147	8	that	that	SCONJ
ejpam-5850	147	9	the	the	DET
ejpam-5850	147	10	automaton	automaton	NOUN
ejpam-5850	147	11	reaches	reach	VERB
ejpam-5850	147	12	at	at	ADP
ejpam-5850	147	13	each	each	DET
ejpam-5850	147	14	vertex	vertex	NOUN
ejpam-5850	147	15	are	be	AUX
ejpam-5850	147	16	1	1	NUM
ejpam-5850	147	17	2	2	NUM
ejpam-5850	147	18	3	3	NUM
ejpam-5850	147	19	4	4	NUM
ejpam-5850	147	20	the	the	DET
ejpam-5850	147	21	graph	graph	NOUN
ejpam-5850	147	22	h2	h2	NOUN
ejpam-5850	147	23	of	of	ADP
ejpam-5850	147	24	figure	figure	NOUN
ejpam-5850	147	25	2	2	NUM
ejpam-5850	147	26	has	have	VERB
ejpam-5850	147	27	length	length	NOUN
ejpam-5850	147	28	4	4	NUM
ejpam-5850	147	29	.	.	PUNCT
ejpam-5850	148	1	we	we	PRON
ejpam-5850	148	2	can	can	AUX
ejpam-5850	148	3	employ	employ	VERB
ejpam-5850	148	4	the	the	DET
ejpam-5850	148	5	below	below	ADJ
ejpam-5850	148	6	representation	representation	NOUN
ejpam-5850	148	7	h2	h2	NOUN
ejpam-5850	148	8	=	=	SYM
ejpam-5850	148	9	i01	i01	PROPN
ejpam-5850	148	10	a	a	DET
ejpam-5850	148	11	i12	i12	PROPN
ejpam-5850	148	12	(	(	PUNCT
ejpam-5850	148	13	a	a	DET
ejpam-5850	148	14	a	a	NOUN
ejpam-5850	148	15	)	)	PUNCT
ejpam-5850	148	16	(	(	PUNCT
ejpam-5850	148	17	a	a	DET
ejpam-5850	148	18	a	a	NOUN
ejpam-5850	148	19	)	)	PUNCT
ejpam-5850	148	20	i21	i21	NOUN
ejpam-5850	148	21	a	a	DET
ejpam-5850	148	22	i10	i10	NOUN
ejpam-5850	148	23	and	and	CCONJ
ejpam-5850	148	24	observe	observe	VERB
ejpam-5850	148	25	that	that	SCONJ
ejpam-5850	148	26	this	this	DET
ejpam-5850	148	27	graph	graph	NOUN
ejpam-5850	148	28	can	can	AUX
ejpam-5850	148	29	not	not	PART
ejpam-5850	148	30	be	be	AUX
ejpam-5850	148	31	accepted	accept	VERB
ejpam-5850	148	32	by	by	ADP
ejpam-5850	148	33	a3	a3	NOUN
ejpam-5850	148	34	len	len	PROPN
ejpam-5850	148	35	since	since	SCONJ
ejpam-5850	148	36	any	any	DET
ejpam-5850	148	37	possible	possible	ADJ
ejpam-5850	148	38	transition	transition	NOUN
ejpam-5850	148	39	can	can	AUX
ejpam-5850	148	40	reach	reach	VERB
ejpam-5850	148	41	at	at	ADV
ejpam-5850	148	42	most	most	ADJ
ejpam-5850	148	43	to	to	ADP
ejpam-5850	148	44	the	the	DET
ejpam-5850	148	45	last	last	ADJ
ejpam-5850	148	46	δa3	δa3	NOUN
ejpam-5850	149	1	len	len	PROPN
ejpam-5850	149	2	(	(	PUNCT
ejpam-5850	149	3	a	a	NOUN
ejpam-5850	149	4	)	)	PUNCT
ejpam-5850	149	5	before	before	ADP
ejpam-5850	149	6	halting	halt	VERB
ejpam-5850	149	7	as	as	ADV
ejpam-5850	149	8	seen	see	VERB
ejpam-5850	149	9	below	below	ADV
ejpam-5850	149	10	.	.	PUNCT
ejpam-5850	150	1	{	{	PUNCT
ejpam-5850	150	2	ε}d01{1}δa3	ε}d01{1}δa3	VERB
ejpam-5850	150	3	len	len	PROPN
ejpam-5850	150	4	(	(	PUNCT
ejpam-5850	150	5	a){2}d12	a){2}d12	PROPN
ejpam-5850	150	6	{	{	PUNCT
ejpam-5850	150	7	2	2	NUM
ejpam-5850	150	8	2	2	NUM
ejpam-5850	150	9	}	}	PUNCT
ejpam-5850	150	10	(	(	PUNCT
ejpam-5850	150	11	δa3	δa3	PROPN
ejpam-5850	150	12	len	len	X
ejpam-5850	150	13	(	(	PUNCT
ejpam-5850	150	14	a	a	X
ejpam-5850	150	15	)	)	PUNCT
ejpam-5850	150	16	δa3	δa3	NOUN
ejpam-5850	150	17	len	len	NOUN
ejpam-5850	150	18	(	(	PUNCT
ejpam-5850	150	19	a	a	NOUN
ejpam-5850	150	20	)	)	PUNCT
ejpam-5850	150	21	)	)	PUNCT
ejpam-5850	150	22	{	{	PUNCT
ejpam-5850	150	23	3	3	NUM
ejpam-5850	150	24	3	3	NUM
ejpam-5850	150	25	}	}	PUNCT
ejpam-5850	150	26	(	(	PUNCT
ejpam-5850	150	27	δa3	δa3	PROPN
ejpam-5850	150	28	len	len	X
ejpam-5850	150	29	(	(	PUNCT
ejpam-5850	150	30	a	a	X
ejpam-5850	150	31	)	)	PUNCT
ejpam-5850	150	32	δa3	δa3	NOUN
ejpam-5850	150	33	len	len	NOUN
ejpam-5850	150	34	(	(	PUNCT
ejpam-5850	150	35	a	a	NOUN
ejpam-5850	150	36	)	)	PUNCT
ejpam-5850	150	37	)	)	PUNCT
ejpam-5850	150	38	{	{	PUNCT
ejpam-5850	150	39	4	4	NUM
ejpam-5850	150	40	4	4	NUM
ejpam-5850	150	41	}	}	PUNCT
ejpam-5850	150	42	d21{4	d21{4	PROPN
ejpam-5850	150	43	}	}	PUNCT
ejpam-5850	150	44	δa3	δa3	NOUN
ejpam-5850	150	45	len	len	PROPN
ejpam-5850	150	46	(	(	PUNCT
ejpam-5850	150	47	a	a	X
ejpam-5850	150	48	)	)	PUNCT
ejpam-5850	150	49	the	the	DET
ejpam-5850	150	50	third	third	ADJ
ejpam-5850	150	51	graph	graph	NOUN
ejpam-5850	150	52	of	of	ADP
ejpam-5850	150	53	figure	figure	NOUN
ejpam-5850	150	54	2	2	NUM
ejpam-5850	150	55	has	have	VERB
ejpam-5850	150	56	a	a	DET
ejpam-5850	150	57	cycle	cycle	NOUN
ejpam-5850	150	58	and	and	CCONJ
ejpam-5850	150	59	hence	hence	ADV
ejpam-5850	150	60	its	its	PRON
ejpam-5850	150	61	length	length	NOUN
ejpam-5850	150	62	is	be	AUX
ejpam-5850	150	63	infinite	infinite	ADJ
ejpam-5850	150	64	.	.	PUNCT
ejpam-5850	151	1	a	a	DET
ejpam-5850	151	2	possible	possible	ADJ
ejpam-5850	151	3	representation	representation	NOUN
ejpam-5850	151	4	of	of	ADP
ejpam-5850	151	5	h3	h3	NOUN
ejpam-5850	151	6	is	be	AUX
ejpam-5850	151	7	given	give	VERB
ejpam-5850	151	8	below	below	ADV
ejpam-5850	151	9	.	.	PUNCT
ejpam-5850	152	1	h3	h3	NOUN
ejpam-5850	152	2	=	=	SYM
ejpam-5850	152	3	i01	i01	PROPN
ejpam-5850	152	4	a	a	DET
ejpam-5850	152	5	i12	i12	PROPN
ejpam-5850	152	6	(	(	PUNCT
ejpam-5850	152	7	a	a	DET
ejpam-5850	152	8	e	e	NOUN
ejpam-5850	152	9	)	)	PUNCT
ejpam-5850	152	10	(	(	PUNCT
ejpam-5850	152	11	a	a	DET
ejpam-5850	152	12	e	e	NOUN
ejpam-5850	152	13	)	)	PUNCT
ejpam-5850	152	14	(	(	PUNCT
ejpam-5850	152	15	a	a	DET
ejpam-5850	152	16	e	e	NOUN
ejpam-5850	152	17	)	)	PUNCT
ejpam-5850	152	18	i21	i21	PROPN
ejpam-5850	152	19	i10	i10	PROPN
ejpam-5850	152	20	k.	k.	PROPN
ejpam-5850	152	21	papadopoulos	papadopoulos	PROPN
ejpam-5850	152	22	/	/	SYM
ejpam-5850	152	23	eur	eur	PROPN
ejpam-5850	152	24	.	.	PUNCT
ejpam-5850	153	1	j.	j.	PROPN
ejpam-5850	153	2	pure	pure	PROPN
ejpam-5850	153	3	appl	appl	PROPN
ejpam-5850	153	4	.	.	PROPN
ejpam-5850	153	5	math	math	PROPN
ejpam-5850	153	6	,	,	PUNCT
ejpam-5850	153	7	18	18	NUM
ejpam-5850	153	8	(	(	PUNCT
ejpam-5850	153	9	1	1	NUM
ejpam-5850	153	10	)	)	PUNCT
ejpam-5850	153	11	(	(	PUNCT
ejpam-5850	153	12	2025	2025	NUM
ejpam-5850	153	13	)	)	PUNCT
ejpam-5850	153	14	,	,	PUNCT
ejpam-5850	153	15	5850	5850	NUM
ejpam-5850	153	16	9	9	NUM
ejpam-5850	153	17	of	of	ADP
ejpam-5850	153	18	13	13	NUM
ejpam-5850	153	19	from	from	ADP
ejpam-5850	153	20	this	this	DET
ejpam-5850	153	21	representation	representation	NOUN
ejpam-5850	153	22	,	,	PUNCT
ejpam-5850	153	23	we	we	PRON
ejpam-5850	153	24	see	see	VERB
ejpam-5850	153	25	that	that	SCONJ
ejpam-5850	153	26	h3	h3	NOUN
ejpam-5850	153	27	can	can	AUX
ejpam-5850	153	28	not	not	PART
ejpam-5850	153	29	be	be	AUX
ejpam-5850	153	30	accepted	accept	VERB
ejpam-5850	153	31	by	by	ADP
ejpam-5850	153	32	a3	a3	NOUN
ejpam-5850	153	33	len	len	NOUN
ejpam-5850	153	34	since	since	SCONJ
ejpam-5850	153	35	any	any	DET
ejpam-5850	153	36	transition	transition	NOUN
ejpam-5850	153	37	will	will	AUX
ejpam-5850	153	38	halt	halt	VERB
ejpam-5850	153	39	when	when	SCONJ
ejpam-5850	153	40	reaching	reach	VERB
ejpam-5850	153	41	d21	d21	NOUN
ejpam-5850	153	42	as	as	ADP
ejpam-5850	153	43	illustrated	illustrate	VERB
ejpam-5850	153	44	below	below	ADV
ejpam-5850	153	45	.	.	PUNCT
ejpam-5850	154	1	{	{	PUNCT
ejpam-5850	154	2	ε}d01{1}δa3	ε}d01{1}δa3	VERB
ejpam-5850	154	3	len	len	PROPN
ejpam-5850	154	4	(	(	PUNCT
ejpam-5850	154	5	a){2}d12	a){2}d12	PROPN
ejpam-5850	154	6	{	{	PUNCT
ejpam-5850	154	7	2	2	NUM
ejpam-5850	154	8	2	2	NUM
ejpam-5850	154	9	}	}	PUNCT
ejpam-5850	154	10	(	(	PUNCT
ejpam-5850	154	11	δa3	δa3	PROPN
ejpam-5850	154	12	len	len	X
ejpam-5850	154	13	(	(	PUNCT
ejpam-5850	154	14	a	a	NOUN
ejpam-5850	154	15	)	)	PUNCT
ejpam-5850	154	16	e	e	NOUN
ejpam-5850	154	17	)	)	PUNCT
ejpam-5850	154	18	{	{	PUNCT
ejpam-5850	154	19	3	3	NUM
ejpam-5850	154	20	2	2	NUM
ejpam-5850	154	21	}	}	PUNCT
ejpam-5850	154	22	(	(	PUNCT
ejpam-5850	154	23	δa3	δa3	PROPN
ejpam-5850	154	24	len	len	X
ejpam-5850	154	25	(	(	PUNCT
ejpam-5850	154	26	a	a	NOUN
ejpam-5850	154	27	)	)	PUNCT
ejpam-5850	154	28	e	e	NOUN
ejpam-5850	154	29	)	)	PUNCT
ejpam-5850	154	30	{	{	PUNCT
ejpam-5850	154	31	4	4	NUM
ejpam-5850	154	32	2	2	NUM
ejpam-5850	154	33	}	}	PUNCT
ejpam-5850	154	34	(	(	PUNCT
ejpam-5850	154	35	δa3	δa3	PROPN
ejpam-5850	154	36	len	len	X
ejpam-5850	154	37	(	(	PUNCT
ejpam-5850	154	38	a	a	NOUN
ejpam-5850	154	39	)	)	PUNCT
ejpam-5850	154	40	e	e	NOUN
ejpam-5850	154	41	)	)	PUNCT
ejpam-5850	154	42	{	{	PUNCT
ejpam-5850	154	43	5	5	NUM
ejpam-5850	154	44	2	2	NUM
ejpam-5850	154	45	}	}	PUNCT
ejpam-5850	154	46	d21	d21	NOUN
ejpam-5850	154	47	the	the	DET
ejpam-5850	154	48	graph	graph	NOUN
ejpam-5850	154	49	automaton	automaton	PROPN
ejpam-5850	154	50	a3	a3	NOUN
ejpam-5850	154	51	len	len	NOUN
ejpam-5850	154	52	can	can	AUX
ejpam-5850	154	53	be	be	AUX
ejpam-5850	154	54	generalized	generalize	VERB
ejpam-5850	154	55	to	to	PART
ejpam-5850	154	56	consider	consider	VERB
ejpam-5850	154	57	every	every	DET
ejpam-5850	154	58	(	(	PUNCT
ejpam-5850	154	59	m	m	PROPN
ejpam-5850	154	60	,	,	PUNCT
ejpam-5850	154	61	n)-graph	n)-graph	ADP
ejpam-5850	154	62	if	if	SCONJ
ejpam-5850	154	63	we	we	PRON
ejpam-5850	154	64	modify	modify	VERB
ejpam-5850	154	65	the	the	DET
ejpam-5850	154	66	initial	initial	ADJ
ejpam-5850	154	67	and	and	CCONJ
ejpam-5850	154	68	final	final	ADJ
ejpam-5850	154	69	sequences	sequence	NOUN
ejpam-5850	154	70	by	by	ADP
ejpam-5850	154	71	setting	set	VERB
ejpam-5850	154	72	iak	iak	NOUN
ejpam-5850	154	73	len	len	PROPN
ejpam-5850	154	74	=	=	PUNCT
ejpam-5850	154	75	qm	qm	PROPN
ejpam-5850	154	76	and	and	CCONJ
ejpam-5850	154	77	tak	tak	NOUN
ejpam-5850	154	78	len	len	NOUN
ejpam-5850	155	1	=	=	PUNCT
ejpam-5850	155	2	qn	qn	NOUN
ejpam-5850	155	3	.	.	PUNCT
ejpam-5850	156	1	this	this	PRON
ejpam-5850	156	2	will	will	AUX
ejpam-5850	156	3	not	not	PART
ejpam-5850	156	4	affect	affect	VERB
ejpam-5850	156	5	the	the	DET
ejpam-5850	156	6	behavior	behavior	NOUN
ejpam-5850	156	7	of	of	ADP
ejpam-5850	156	8	the	the	DET
ejpam-5850	156	9	automaton	automaton	NOUN
ejpam-5850	156	10	as	as	SCONJ
ejpam-5850	156	11	it	it	PRON
ejpam-5850	156	12	is	be	AUX
ejpam-5850	156	13	evident	evident	ADJ
ejpam-5850	156	14	from	from	ADP
ejpam-5850	156	15	the	the	DET
ejpam-5850	156	16	equations	equation	NOUN
ejpam-5850	156	17	17	17	NUM
ejpam-5850	156	18	-	-	SYM
ejpam-5850	156	19	20	20	NUM
ejpam-5850	156	20	which	which	PRON
ejpam-5850	156	21	hold	hold	VERB
ejpam-5850	156	22	for	for	ADP
ejpam-5850	156	23	every	every	DET
ejpam-5850	156	24	unitary	unitary	ADJ
ejpam-5850	156	25	automaton	automaton	NOUN
ejpam-5850	156	26	.	.	PUNCT
ejpam-5850	157	1	from	from	ADP
ejpam-5850	157	2	the	the	DET
ejpam-5850	157	3	above	above	ADJ
ejpam-5850	157	4	proposition	proposition	NOUN
ejpam-5850	157	5	we	we	PRON
ejpam-5850	157	6	get	get	VERB
ejpam-5850	157	7	that	that	SCONJ
ejpam-5850	157	8	the	the	DET
ejpam-5850	157	9	graph	graph	NOUN
ejpam-5850	157	10	language	language	NOUN
ejpam-5850	157	11	lenk	lenk	PROPN
ejpam-5850	157	12	that	that	PRON
ejpam-5850	157	13	consists	consist	VERB
ejpam-5850	157	14	of	of	ADP
ejpam-5850	157	15	all	all	DET
ejpam-5850	157	16	conventional	conventional	ADJ
ejpam-5850	157	17	graphs	graph	NOUN
ejpam-5850	157	18	with	with	ADP
ejpam-5850	157	19	length	length	NOUN
ejpam-5850	157	20	at	at	ADP
ejpam-5850	157	21	most	most	ADV
ejpam-5850	157	22	k	k	PROPN
ejpam-5850	157	23	lies	lie	VERB
ejpam-5850	157	24	in	in	ADP
ejpam-5850	157	25	the	the	DET
ejpam-5850	157	26	class	class	NOUN
ejpam-5850	157	27	urec(σ	urec(σ	NOUN
ejpam-5850	157	28	)	)	PUNCT
ejpam-5850	157	29	,	,	PUNCT
ejpam-5850	157	30	for	for	ADP
ejpam-5850	157	31	every	every	DET
ejpam-5850	157	32	positive	positive	ADJ
ejpam-5850	157	33	integer	integer	NOUN
ejpam-5850	157	34	k.	k.	NOUN
ejpam-5850	157	35	using	use	VERB
ejpam-5850	157	36	the	the	DET
ejpam-5850	157	37	same	same	ADJ
ejpam-5850	157	38	argument	argument	NOUN
ejpam-5850	157	39	as	as	ADP
ejpam-5850	157	40	in	in	ADP
ejpam-5850	157	41	the	the	DET
ejpam-5850	157	42	end	end	NOUN
ejpam-5850	157	43	of	of	ADP
ejpam-5850	157	44	the	the	DET
ejpam-5850	157	45	above	above	ADJ
ejpam-5850	157	46	proof	proof	NOUN
ejpam-5850	157	47	we	we	PRON
ejpam-5850	157	48	can	can	AUX
ejpam-5850	157	49	generalize	generalize	VERB
ejpam-5850	157	50	the	the	DET
ejpam-5850	157	51	result	result	NOUN
ejpam-5850	157	52	of	of	ADP
ejpam-5850	157	53	[	[	X
ejpam-5850	157	54	20	20	NUM
ejpam-5850	157	55	]	]	PUNCT
ejpam-5850	157	56	to	to	PART
ejpam-5850	157	57	obtain	obtain	VERB
ejpam-5850	157	58	the	the	DET
ejpam-5850	157	59	following	following	NOUN
ejpam-5850	157	60	.	.	PUNCT
ejpam-5850	158	1	proposition	proposition	NOUN
ejpam-5850	158	2	2	2	NUM
ejpam-5850	158	3	.	.	PUNCT
ejpam-5850	158	4	given	give	VERB
ejpam-5850	158	5	k	k	PROPN
ejpam-5850	158	6	∈	∈	PROPN
ejpam-5850	158	7	n	n	CCONJ
ejpam-5850	158	8	,	,	PUNCT
ejpam-5850	158	9	the	the	DET
ejpam-5850	158	10	set	set	NOUN
ejpam-5850	158	11	of	of	ADP
ejpam-5850	158	12	all	all	DET
ejpam-5850	158	13	conventional	conventional	ADJ
ejpam-5850	158	14	graphs	graph	NOUN
ejpam-5850	158	15	with	with	ADP
ejpam-5850	158	16	chromatic	chromatic	ADJ
ejpam-5850	158	17	number	number	NOUN
ejpam-5850	158	18	at	at	ADP
ejpam-5850	158	19	most	most	ADJ
ejpam-5850	158	20	k	k	NOUN
ejpam-5850	158	21	,	,	PUNCT
ejpam-5850	158	22	belongs	belong	VERB
ejpam-5850	158	23	to	to	ADP
ejpam-5850	158	24	urec(σ	urec(σ	NOUN
ejpam-5850	158	25	)	)	PUNCT
ejpam-5850	158	26	.	.	PUNCT
ejpam-5850	159	1	5	5	X
ejpam-5850	159	2	.	.	X
ejpam-5850	159	3	non	non	ADJ
ejpam-5850	159	4	-	-	ADJ
ejpam-5850	159	5	unitary	unitary	ADJ
ejpam-5850	159	6	abelian	abelian	ADJ
ejpam-5850	159	7	graph	graph	NOUN
ejpam-5850	159	8	automata	automata	NOUN
ejpam-5850	159	9	non	non	ADJ
ejpam-5850	159	10	-	-	ADJ
ejpam-5850	159	11	unitary	unitary	ADJ
ejpam-5850	159	12	graph	graph	NOUN
ejpam-5850	159	13	automata	automata	NOUN
ejpam-5850	159	14	have	have	AUX
ejpam-5850	159	15	never	never	ADV
ejpam-5850	159	16	been	be	AUX
ejpam-5850	159	17	examined	examine	VERB
ejpam-5850	159	18	in	in	ADP
ejpam-5850	159	19	the	the	DET
ejpam-5850	159	20	literature	literature	NOUN
ejpam-5850	159	21	and	and	CCONJ
ejpam-5850	159	22	their	their	PRON
ejpam-5850	159	23	recognition	recognition	NOUN
ejpam-5850	159	24	capacity	capacity	NOUN
ejpam-5850	159	25	remains	remain	VERB
ejpam-5850	159	26	unknown	unknown	ADJ
ejpam-5850	159	27	.	.	PUNCT
ejpam-5850	160	1	as	as	ADP
ejpam-5850	160	2	a	a	DET
ejpam-5850	160	3	result	result	NOUN
ejpam-5850	160	4	,	,	PUNCT
ejpam-5850	160	5	we	we	PRON
ejpam-5850	160	6	do	do	AUX
ejpam-5850	160	7	n’t	not	PART
ejpam-5850	160	8	know	know	VERB
ejpam-5850	160	9	if	if	SCONJ
ejpam-5850	160	10	the	the	DET
ejpam-5850	160	11	class	class	NOUN
ejpam-5850	160	12	hierarchy	hierarchy	NOUN
ejpam-5850	160	13	depicted	depict	VERB
ejpam-5850	160	14	in	in	ADP
ejpam-5850	160	15	figure	figure	NOUN
ejpam-5850	160	16	1	1	NUM
ejpam-5850	160	17	is	be	AUX
ejpam-5850	160	18	proper	proper	ADJ
ejpam-5850	160	19	.	.	PUNCT
ejpam-5850	161	1	in	in	ADP
ejpam-5850	161	2	this	this	DET
ejpam-5850	161	3	section	section	NOUN
ejpam-5850	161	4	,	,	PUNCT
ejpam-5850	161	5	we	we	PRON
ejpam-5850	161	6	will	will	AUX
ejpam-5850	161	7	introduce	introduce	VERB
ejpam-5850	161	8	non	non	ADJ
ejpam-5850	161	9	-	-	ADJ
ejpam-5850	161	10	unitary	unitary	ADJ
ejpam-5850	161	11	abelian	abelian	ADJ
ejpam-5850	161	12	graph	graph	NOUN
ejpam-5850	161	13	automata	automata	NOUN
ejpam-5850	161	14	operating	operate	VERB
ejpam-5850	161	15	by	by	ADP
ejpam-5850	161	16	virtue	virtue	NOUN
ejpam-5850	161	17	of	of	ADP
ejpam-5850	161	18	graphoids	graphoid	NOUN
ejpam-5850	161	19	associated	associate	VERB
ejpam-5850	161	20	to	to	ADP
ejpam-5850	161	21	non	non	ADJ
ejpam-5850	161	22	-	-	ADJ
ejpam-5850	161	23	trivial	trivial	ADJ
ejpam-5850	161	24	groups	group	NOUN
ejpam-5850	161	25	.	.	PUNCT
ejpam-5850	162	1	we	we	PRON
ejpam-5850	162	2	will	will	AUX
ejpam-5850	162	3	identify	identify	VERB
ejpam-5850	162	4	a	a	DET
ejpam-5850	162	5	graph	graph	NOUN
ejpam-5850	162	6	language	language	NOUN
ejpam-5850	162	7	recognized	recognize	VERB
ejpam-5850	162	8	by	by	ADP
ejpam-5850	162	9	such	such	DET
ejpam-5850	162	10	a	a	DET
ejpam-5850	162	11	graph	graph	NOUN
ejpam-5850	162	12	automaton	automaton	NOUN
ejpam-5850	162	13	and	and	CCONJ
ejpam-5850	162	14	show	show	VERB
ejpam-5850	162	15	that	that	SCONJ
ejpam-5850	162	16	it	it	PRON
ejpam-5850	162	17	does	do	AUX
ejpam-5850	162	18	n’t	not	PART
ejpam-5850	162	19	belong	belong	VERB
ejpam-5850	162	20	to	to	ADP
ejpam-5850	162	21	urec(σ	urec(σ	NOUN
ejpam-5850	162	22	)	)	PUNCT
ejpam-5850	162	23	,	,	PUNCT
ejpam-5850	162	24	demonstrating	demonstrate	VERB
ejpam-5850	162	25	that	that	SCONJ
ejpam-5850	162	26	urec(σ	urec(σ	NOUN
ejpam-5850	162	27	)	)	PUNCT
ejpam-5850	162	28	is	be	AUX
ejpam-5850	162	29	properly	properly	ADV
ejpam-5850	162	30	included	include	VERB
ejpam-5850	162	31	in	in	ADP
ejpam-5850	162	32	arec(σ	arec(σ	NOUN
ejpam-5850	162	33	)	)	PUNCT
ejpam-5850	162	34	.	.	PUNCT
ejpam-5850	163	1	for	for	ADP
ejpam-5850	163	2	this	this	PRON
ejpam-5850	163	3	we	we	PRON
ejpam-5850	163	4	define	define	VERB
ejpam-5850	163	5	the	the	DET
ejpam-5850	163	6	abelian	abelian	PROPN
ejpam-5850	163	7	graphoid	graphoid	NOUN
ejpam-5850	163	8	g2(0,1	g2(0,1	NOUN
ejpam-5850	163	9	)	)	PUNCT
ejpam-5850	163	10	that	that	PRON
ejpam-5850	163	11	is	be	AUX
ejpam-5850	163	12	obtained	obtain	VERB
ejpam-5850	163	13	by	by	ADP
ejpam-5850	163	14	the	the	DET
ejpam-5850	163	15	trivial	trivial	ADJ
ejpam-5850	163	16	partition	partition	NOUN
ejpam-5850	163	17	of	of	ADP
ejpam-5850	163	18	the	the	DET
ejpam-5850	163	19	set	set	NOUN
ejpam-5850	163	20	{	{	PUNCT
ejpam-5850	163	21	0	0	NUM
ejpam-5850	163	22	,	,	PUNCT
ejpam-5850	163	23	1	1	NUM
ejpam-5850	163	24	}	}	PUNCT
ejpam-5850	163	25	to	to	ADP
ejpam-5850	163	26	a	a	DET
ejpam-5850	163	27	single	single	ADJ
ejpam-5850	163	28	set	set	NOUN
ejpam-5850	163	29	that	that	PRON
ejpam-5850	163	30	is	be	AUX
ejpam-5850	163	31	structured	structure	VERB
ejpam-5850	163	32	into	into	ADP
ejpam-5850	163	33	a	a	DET
ejpam-5850	163	34	group	group	NOUN
ejpam-5850	163	35	via	via	ADP
ejpam-5850	163	36	the	the	DET
ejpam-5850	163	37	operation	operation	NOUN
ejpam-5850	163	38	of	of	ADP
ejpam-5850	163	39	addition	addition	NOUN
ejpam-5850	163	40	mod	mod	NOUN
ejpam-5850	163	41	2	2	X
ejpam-5850	163	42	.	.	PUNCT
ejpam-5850	164	1	+	+	CCONJ
ejpam-5850	164	2	0	0	NUM
ejpam-5850	164	3	1	1	NUM
ejpam-5850	164	4	0	0	NUM
ejpam-5850	164	5	0	0	NUM
ejpam-5850	164	6	1	1	NUM
ejpam-5850	164	7	1	1	NUM
ejpam-5850	164	8	1	1	NUM
ejpam-5850	164	9	0	0	NUM
ejpam-5850	164	10	from	from	ADP
ejpam-5850	164	11	theorem	theorem	ADJ
ejpam-5850	164	12	3	3	NUM
ejpam-5850	164	13	of	of	ADP
ejpam-5850	164	14	[	[	X
ejpam-5850	164	15	19	19	NUM
ejpam-5850	164	16	]	]	PUNCT
ejpam-5850	164	17	,	,	PUNCT
ejpam-5850	164	18	we	we	PRON
ejpam-5850	164	19	get	get	VERB
ejpam-5850	164	20	that	that	SCONJ
ejpam-5850	164	21	the	the	DET
ejpam-5850	164	22	elements	element	NOUN
ejpam-5850	164	23	of	of	ADP
ejpam-5850	164	24	dg2(0,1	dg2(0,1	NOUN
ejpam-5850	164	25	)	)	PUNCT
ejpam-5850	164	26	,	,	PUNCT
ejpam-5850	164	27	besides	besides	SCONJ
ejpam-5850	164	28	s	s	PRON
ejpam-5850	164	29	will	will	AUX
ejpam-5850	164	30	be	be	AUX
ejpam-5850	164	31	as	as	SCONJ
ejpam-5850	164	32	follows	follow	VERB
ejpam-5850	164	33	d21	d21	PROPN
ejpam-5850	164	34	=	=	SYM
ejpam-5850	164	35	{	{	PUNCT
ejpam-5850	164	36	(	(	PUNCT
ejpam-5850	164	37	01	01	NUM
ejpam-5850	164	38	,	,	PUNCT
ejpam-5850	164	39	1	1	NUM
ejpam-5850	164	40	)	)	PUNCT
ejpam-5850	164	41	,	,	PUNCT
ejpam-5850	164	42	(	(	PUNCT
ejpam-5850	164	43	10	10	NUM
ejpam-5850	164	44	,	,	PUNCT
ejpam-5850	164	45	1	1	NUM
ejpam-5850	164	46	)	)	PUNCT
ejpam-5850	164	47	}	}	PUNCT
ejpam-5850	164	48	,	,	PUNCT
ejpam-5850	164	49	d10	d10	PROPN
ejpam-5850	164	50	=	=	SYM
ejpam-5850	164	51	{	{	PUNCT
ejpam-5850	164	52	(	(	PUNCT
ejpam-5850	164	53	0	0	NUM
ejpam-5850	164	54	,	,	PUNCT
ejpam-5850	164	55	ε	ε	PROPN
ejpam-5850	164	56	)	)	PUNCT
ejpam-5850	164	57	}	}	PUNCT
ejpam-5850	164	58	,	,	PUNCT
ejpam-5850	164	59	d12	d12	PROPN
ejpam-5850	164	60	=	=	SYM
ejpam-5850	164	61	{	{	PUNCT
ejpam-5850	164	62	(	(	PUNCT
ejpam-5850	164	63	1	1	NUM
ejpam-5850	164	64	,	,	PUNCT
ejpam-5850	164	65	01	01	NUM
ejpam-5850	164	66	)	)	PUNCT
ejpam-5850	164	67	,	,	PUNCT
ejpam-5850	164	68	(	(	PUNCT
ejpam-5850	164	69	1	1	NUM
ejpam-5850	164	70	,	,	PUNCT
ejpam-5850	164	71	10	10	NUM
ejpam-5850	164	72	)	)	PUNCT
ejpam-5850	164	73	}	}	PUNCT
ejpam-5850	164	74	,	,	PUNCT
ejpam-5850	164	75	d01	d01	NOUN
ejpam-5850	164	76	=	=	SYM
ejpam-5850	164	77	{	{	PUNCT
ejpam-5850	164	78	(	(	PUNCT
ejpam-5850	164	79	ε	ε	PROPN
ejpam-5850	164	80	,	,	PUNCT
ejpam-5850	164	81	0	0	NUM
ejpam-5850	164	82	)	)	PUNCT
ejpam-5850	164	83	}	}	PUNCT
ejpam-5850	164	84	.	.	PUNCT
ejpam-5850	165	1	clearly	clearly	ADV
ejpam-5850	165	2	,	,	PUNCT
ejpam-5850	165	3	graph	graph	NOUN
ejpam-5850	165	4	automata	automata	NOUN
ejpam-5850	165	5	operating	operate	VERB
ejpam-5850	165	6	on	on	ADP
ejpam-5850	165	7	g2(0,1	g2(0,1	NOUN
ejpam-5850	165	8	)	)	PUNCT
ejpam-5850	165	9	are	be	AUX
ejpam-5850	165	10	abelian	abelian	ADJ
ejpam-5850	165	11	but	but	CCONJ
ejpam-5850	165	12	non	non	ADJ
ejpam-5850	165	13	-	-	ADJ
ejpam-5850	165	14	unitary	unitary	ADJ
ejpam-5850	165	15	.	.	PUNCT
ejpam-5850	166	1	hence	hence	ADV
ejpam-5850	166	2	the	the	DET
ejpam-5850	166	3	graph	graph	NOUN
ejpam-5850	166	4	languages	language	NOUN
ejpam-5850	166	5	they	they	PRON
ejpam-5850	166	6	recognize	recognize	VERB
ejpam-5850	166	7	belong	belong	VERB
ejpam-5850	166	8	to	to	ADP
ejpam-5850	166	9	arec(σ	arec(σ	PROPN
ejpam-5850	166	10	)	)	PUNCT
ejpam-5850	166	11	but	but	CCONJ
ejpam-5850	166	12	necessarily	necessarily	ADV
ejpam-5850	166	13	to	to	ADP
ejpam-5850	166	14	urec(σ	urec(σ	NOUN
ejpam-5850	166	15	)	)	PUNCT
ejpam-5850	166	16	.	.	PUNCT
ejpam-5850	167	1	now	now	ADV
ejpam-5850	167	2	we	we	PRON
ejpam-5850	167	3	consider	consider	VERB
ejpam-5850	167	4	the	the	DET
ejpam-5850	167	5	graph	graph	NOUN
ejpam-5850	167	6	language	language	NOUN
ejpam-5850	167	7	l	l	NOUN
ejpam-5850	167	8	(	(	PUNCT
ejpam-5850	167	9	1,1	1,1	NUM
ejpam-5850	167	10	)	)	PUNCT
ejpam-5850	167	11	od	od	ADV
ejpam-5850	167	12	of	of	ADP
ejpam-5850	167	13	all	all	DET
ejpam-5850	167	14	conventional	conventional	ADJ
ejpam-5850	167	15	(	(	PUNCT
ejpam-5850	167	16	1	1	NUM
ejpam-5850	167	17	,	,	PUNCT
ejpam-5850	167	18	1)-graphs	1)-graphs	NUM
ejpam-5850	167	19	with	with	ADP
ejpam-5850	167	20	an	an	DET
ejpam-5850	167	21	odd	odd	ADJ
ejpam-5850	167	22	number	number	NOUN
ejpam-5850	167	23	of	of	ADP
ejpam-5850	167	24	edges	edge	NOUN
ejpam-5850	167	25	.	.	PUNCT
ejpam-5850	168	1	we	we	PRON
ejpam-5850	168	2	prove	prove	VERB
ejpam-5850	168	3	the	the	DET
ejpam-5850	168	4	following	follow	VERB
ejpam-5850	168	5	proposition	proposition	NOUN
ejpam-5850	168	6	.	.	PUNCT
ejpam-5850	169	1	k.	k.	PROPN
ejpam-5850	169	2	papadopoulos	papadopoulos	PROPN
ejpam-5850	169	3	/	/	SYM
ejpam-5850	169	4	eur	eur	PROPN
ejpam-5850	169	5	.	.	PUNCT
ejpam-5850	170	1	j.	j.	PROPN
ejpam-5850	170	2	pure	pure	PROPN
ejpam-5850	170	3	appl	appl	PROPN
ejpam-5850	170	4	.	.	PROPN
ejpam-5850	170	5	math	math	PROPN
ejpam-5850	170	6	,	,	PUNCT
ejpam-5850	170	7	18	18	NUM
ejpam-5850	170	8	(	(	PUNCT
ejpam-5850	170	9	1	1	NUM
ejpam-5850	170	10	)	)	PUNCT
ejpam-5850	170	11	(	(	PUNCT
ejpam-5850	170	12	2025	2025	NUM
ejpam-5850	170	13	)	)	PUNCT
ejpam-5850	170	14	,	,	PUNCT
ejpam-5850	170	15	5850	5850	NUM
ejpam-5850	170	16	10	10	NUM
ejpam-5850	170	17	of	of	ADP
ejpam-5850	170	18	13	13	NUM
ejpam-5850	170	19	proposition	proposition	NOUN
ejpam-5850	170	20	3	3	NUM
ejpam-5850	170	21	.	.	PUNCT
ejpam-5850	171	1	the	the	DET
ejpam-5850	171	2	graph	graph	NOUN
ejpam-5850	171	3	language	language	NOUN
ejpam-5850	171	4	l	l	NOUN
ejpam-5850	171	5	(	(	PUNCT
ejpam-5850	171	6	1,1	1,1	NUM
ejpam-5850	171	7	)	)	PUNCT
ejpam-5850	171	8	od	od	NOUN
ejpam-5850	171	9	belongs	belong	VERB
ejpam-5850	171	10	to	to	ADP
ejpam-5850	171	11	arec(σ	arec(σ	PROPN
ejpam-5850	171	12	)	)	PUNCT
ejpam-5850	171	13	.	.	PUNCT
ejpam-5850	172	1	proof	proof	NOUN
ejpam-5850	172	2	.	.	PUNCT
ejpam-5850	173	1	we	we	PRON
ejpam-5850	173	2	use	use	VERB
ejpam-5850	173	3	this	this	DET
ejpam-5850	173	4	g2(0,1	g2(0,1	NOUN
ejpam-5850	173	5	)	)	PUNCT
ejpam-5850	173	6	to	to	PART
ejpam-5850	173	7	construct	construct	VERB
ejpam-5850	173	8	the	the	DET
ejpam-5850	173	9	following	follow	VERB
ejpam-5850	173	10	graph	graph	NOUN
ejpam-5850	173	11	automaton	automaton	PROPN
ejpam-5850	173	12	aod	aod	PROPN
ejpam-5850	173	13	=	=	SYM
ejpam-5850	173	14	(	(	PUNCT
ejpam-5850	173	15	σ	σ	PROPN
ejpam-5850	173	16	,	,	PUNCT
ejpam-5850	173	17	{	{	PUNCT
ejpam-5850	173	18	0	0	NUM
ejpam-5850	173	19	,	,	PUNCT
ejpam-5850	173	20	1},g2(0,1	1},g2(0,1	NUM
ejpam-5850	173	21	)	)	PUNCT
ejpam-5850	173	22	,	,	PUNCT
ejpam-5850	173	23	δaod	δaod	NOUN
ejpam-5850	173	24	,	,	PUNCT
ejpam-5850	173	25	iaod	iaod	NOUN
ejpam-5850	173	26	,	,	PUNCT
ejpam-5850	173	27	taod	taod	X
ejpam-5850	173	28	)	)	PUNCT
ejpam-5850	173	29	with	with	ADP
ejpam-5850	173	30	σ	σ	PROPN
ejpam-5850	173	31	=	=	SYM
ejpam-5850	173	32	σ1,1	σ1,1	PROPN
ejpam-5850	173	33	=	=	PUNCT
ejpam-5850	173	34	{	{	PUNCT
ejpam-5850	173	35	a	a	NOUN
ejpam-5850	173	36	}	}	PUNCT
ejpam-5850	173	37	,	,	PUNCT
ejpam-5850	173	38	state	state	NOUN
ejpam-5850	173	39	set	set	VERB
ejpam-5850	173	40	q	q	NOUN
ejpam-5850	173	41	=	=	PUNCT
ejpam-5850	173	42	{	{	PUNCT
ejpam-5850	173	43	0	0	NUM
ejpam-5850	173	44	,	,	PUNCT
ejpam-5850	173	45	1	1	NUM
ejpam-5850	173	46	}	}	PUNCT
ejpam-5850	173	47	,	,	PUNCT
ejpam-5850	173	48	iaod	iaod	NOUN
ejpam-5850	173	49	=	=	PUNCT
ejpam-5850	173	50	{	{	PUNCT
ejpam-5850	173	51	0	0	NUM
ejpam-5850	173	52	}	}	PUNCT
ejpam-5850	173	53	,	,	PUNCT
ejpam-5850	173	54	taod	taod	X
ejpam-5850	173	55	=	=	SYM
ejpam-5850	173	56	{	{	PUNCT
ejpam-5850	173	57	1	1	NUM
ejpam-5850	173	58	}	}	PUNCT
ejpam-5850	173	59	and	and	CCONJ
ejpam-5850	173	60	the	the	DET
ejpam-5850	173	61	transition	transition	NOUN
ejpam-5850	173	62	function	function	NOUN
ejpam-5850	173	63	given	give	VERB
ejpam-5850	173	64	by	by	ADP
ejpam-5850	173	65	δaod	δaod	NOUN
ejpam-5850	173	66	(	(	PUNCT
ejpam-5850	173	67	a	a	NOUN
ejpam-5850	173	68	)	)	PUNCT
ejpam-5850	173	69	=	=	SYM
ejpam-5850	173	70	{	{	PUNCT
ejpam-5850	173	71	(	(	PUNCT
ejpam-5850	173	72	0	0	NUM
ejpam-5850	173	73	,	,	PUNCT
ejpam-5850	173	74	1	1	NUM
ejpam-5850	173	75	)	)	PUNCT
ejpam-5850	173	76	,	,	PUNCT
ejpam-5850	173	77	(	(	PUNCT
ejpam-5850	173	78	1	1	NUM
ejpam-5850	173	79	,	,	PUNCT
ejpam-5850	173	80	0	0	NUM
ejpam-5850	173	81	)	)	PUNCT
ejpam-5850	173	82	}	}	PUNCT
ejpam-5850	173	83	.	.	PUNCT
ejpam-5850	174	1	this	this	DET
ejpam-5850	174	2	graph	graph	NOUN
ejpam-5850	174	3	automaton	automaton	NOUN
ejpam-5850	174	4	recognizes	recognize	VERB
ejpam-5850	174	5	the	the	DET
ejpam-5850	174	6	graph	graph	NOUN
ejpam-5850	174	7	language	language	NOUN
ejpam-5850	174	8	l	l	NOUN
ejpam-5850	174	9	(	(	PUNCT
ejpam-5850	174	10	1,1	1,1	NUM
ejpam-5850	174	11	)	)	PUNCT
ejpam-5850	174	12	od	od	ADV
ejpam-5850	174	13	of	of	ADP
ejpam-5850	174	14	all	all	DET
ejpam-5850	174	15	conventional	conventional	ADJ
ejpam-5850	174	16	(	(	PUNCT
ejpam-5850	174	17	1	1	NUM
ejpam-5850	174	18	,	,	PUNCT
ejpam-5850	174	19	1)graphs	1)graphs	NUM
ejpam-5850	174	20	with	with	ADP
ejpam-5850	174	21	an	an	DET
ejpam-5850	174	22	odd	odd	ADJ
ejpam-5850	174	23	number	number	NOUN
ejpam-5850	174	24	of	of	ADP
ejpam-5850	174	25	edges	edge	NOUN
ejpam-5850	174	26	.	.	PUNCT
ejpam-5850	175	1	to	to	PART
ejpam-5850	175	2	illustrate	illustrate	VERB
ejpam-5850	175	3	this	this	PRON
ejpam-5850	175	4	,	,	PUNCT
ejpam-5850	175	5	we	we	PRON
ejpam-5850	175	6	consider	consider	VERB
ejpam-5850	175	7	the	the	DET
ejpam-5850	175	8	following	follow	VERB
ejpam-5850	175	9	graphs	graph	NOUN
ejpam-5850	175	10	,	,	PUNCT
ejpam-5850	175	11	where	where	SCONJ
ejpam-5850	175	12	the	the	DET
ejpam-5850	175	13	nodes	node	NOUN
ejpam-5850	175	14	of	of	ADP
ejpam-5850	175	15	the	the	DET
ejpam-5850	175	16	begin	begin	NOUN
ejpam-5850	175	17	and	and	CCONJ
ejpam-5850	175	18	end	end	VERB
ejpam-5850	175	19	sequences	sequence	NOUN
ejpam-5850	175	20	are	be	AUX
ejpam-5850	175	21	designated	designate	VERB
ejpam-5850	175	22	by	by	ADP
ejpam-5850	175	23	b1	b1	NOUN
ejpam-5850	175	24	and	and	CCONJ
ejpam-5850	175	25	e1	e1	NOUN
ejpam-5850	175	26	respectively	respectively	ADV
ejpam-5850	175	27	.	.	PUNCT
ejpam-5850	176	1	b1	b1	NOUN
ejpam-5850	176	2	e1	e1	PROPN
ejpam-5850	176	3	h4	h4	PROPN
ejpam-5850	176	4	b1	b1	PROPN
ejpam-5850	176	5	e1	e1	PROPN
ejpam-5850	176	6	h5	h5	PROPN
ejpam-5850	176	7	b1	b1	PROPN
ejpam-5850	176	8	e1	e1	PROPN
ejpam-5850	176	9	h6	h6	PROPN
ejpam-5850	176	10	figure	figure	VERB
ejpam-5850	176	11	3	3	NUM
ejpam-5850	176	12	:	:	SYM
ejpam-5850	176	13	three	three	NUM
ejpam-5850	176	14	unlabeled	unlabeled	ADJ
ejpam-5850	176	15	(	(	PUNCT
ejpam-5850	176	16	1	1	NUM
ejpam-5850	176	17	,	,	PUNCT
ejpam-5850	176	18	1)-graphs	1)-graphs	NUM
ejpam-5850	176	19	with	with	ADP
ejpam-5850	176	20	binary	binary	ADJ
ejpam-5850	176	21	edges	edge	NOUN
ejpam-5850	176	22	the	the	DET
ejpam-5850	176	23	image	image	NOUN
ejpam-5850	176	24	of	of	ADP
ejpam-5850	176	25	a	a	DET
ejpam-5850	176	26	representation	representation	NOUN
ejpam-5850	176	27	of	of	ADP
ejpam-5850	176	28	h4	h4	NOUN
ejpam-5850	176	29	by	by	ADP
ejpam-5850	176	30	the	the	DET
ejpam-5850	176	31	transition	transition	NOUN
ejpam-5850	176	32	function	function	NOUN
ejpam-5850	176	33	of	of	ADP
ejpam-5850	176	34	aod	aod	PROPN
ejpam-5850	176	35	gives	give	VERB
ejpam-5850	176	36	δ̄aod	δ̄aod	PROPN
ejpam-5850	176	37	(	(	PUNCT
ejpam-5850	176	38	h4	h4	PROPN
ejpam-5850	176	39	)	)	PUNCT
ejpam-5850	177	1	=	=	PRON
ejpam-5850	177	2	δaod	δaod	NOUN
ejpam-5850	177	3	(	(	PUNCT
ejpam-5850	177	4	a	a	X
ejpam-5850	177	5	)	)	PUNCT
ejpam-5850	177	6	d12	d12	NOUN
ejpam-5850	177	7	(	(	PUNCT
ejpam-5850	177	8	δaod	δaod	PROPN
ejpam-5850	177	9	(	(	PUNCT
ejpam-5850	177	10	a	a	NOUN
ejpam-5850	177	11	)	)	PUNCT
ejpam-5850	177	12	δaod	δaod	NOUN
ejpam-5850	177	13	(	(	PUNCT
ejpam-5850	177	14	a	a	NOUN
ejpam-5850	177	15	)	)	PUNCT
ejpam-5850	177	16	)	)	PUNCT
ejpam-5850	177	17	d21	d21	NOUN
ejpam-5850	177	18	and	and	CCONJ
ejpam-5850	177	19	an	an	DET
ejpam-5850	177	20	accepting	accept	VERB
ejpam-5850	177	21	sequence	sequence	NOUN
ejpam-5850	177	22	of	of	ADP
ejpam-5850	177	23	states	state	NOUN
ejpam-5850	177	24	is	be	AUX
ejpam-5850	177	25	{	{	PUNCT
ejpam-5850	177	26	0}δaod	0}δaod	PROPN
ejpam-5850	177	27	(	(	PUNCT
ejpam-5850	177	28	a){1}d12	a){1}d12	X
ejpam-5850	177	29	{	{	PUNCT
ejpam-5850	177	30	1	1	NUM
ejpam-5850	177	31	0	0	NUM
ejpam-5850	177	32	}	}	PUNCT
ejpam-5850	177	33	(	(	PUNCT
ejpam-5850	177	34	δaod	δaod	PROPN
ejpam-5850	177	35	(	(	PUNCT
ejpam-5850	177	36	a	a	NOUN
ejpam-5850	177	37	)	)	PUNCT
ejpam-5850	177	38	δaod	δaod	NOUN
ejpam-5850	177	39	(	(	PUNCT
ejpam-5850	177	40	a	a	NOUN
ejpam-5850	177	41	)	)	PUNCT
ejpam-5850	177	42	)	)	PUNCT
ejpam-5850	177	43	{	{	PUNCT
ejpam-5850	177	44	0	0	NUM
ejpam-5850	177	45	1	1	NUM
ejpam-5850	177	46	}	}	PUNCT
ejpam-5850	177	47	d21{1	d21{1	PROPN
ejpam-5850	177	48	}	}	PUNCT
ejpam-5850	177	49	which	which	PRON
ejpam-5850	177	50	shows	show	VERB
ejpam-5850	177	51	that	that	SCONJ
ejpam-5850	177	52	h4	h4	PROPN
ejpam-5850	177	53	is	be	AUX
ejpam-5850	177	54	recognized	recognize	VERB
ejpam-5850	177	55	by	by	ADP
ejpam-5850	177	56	aod	aod	PROPN
ejpam-5850	177	57	.	.	PROPN
ejpam-5850	177	58	similarly	similarly	ADV
ejpam-5850	177	59	,	,	PUNCT
ejpam-5850	177	60	we	we	PRON
ejpam-5850	177	61	can	can	AUX
ejpam-5850	177	62	see	see	VERB
ejpam-5850	177	63	that	that	PRON
ejpam-5850	177	64	for	for	ADP
ejpam-5850	177	65	h5	h5	NOUN
ejpam-5850	177	66	and	and	CCONJ
ejpam-5850	177	67	h6	h6	PROPN
ejpam-5850	177	68	the	the	DET
ejpam-5850	177	69	following	follow	VERB
ejpam-5850	177	70	sequences	sequence	NOUN
ejpam-5850	177	71	of	of	ADP
ejpam-5850	177	72	states	state	NOUN
ejpam-5850	177	73	can	can	AUX
ejpam-5850	177	74	be	be	AUX
ejpam-5850	177	75	respectively	respectively	ADV
ejpam-5850	177	76	obtained	obtain	VERB
ejpam-5850	177	77	{	{	PUNCT
ejpam-5850	177	78	0}δaod	0}δaod	PROPN
ejpam-5850	177	79	(	(	PUNCT
ejpam-5850	177	80	a){1}d12	a){1}d12	X
ejpam-5850	177	81	{	{	PUNCT
ejpam-5850	177	82	1	1	NUM
ejpam-5850	177	83	0	0	NUM
ejpam-5850	177	84	}	}	PUNCT
ejpam-5850	177	85	(	(	PUNCT
ejpam-5850	177	86	δaod	δaod	PROPN
ejpam-5850	177	87	(	(	PUNCT
ejpam-5850	177	88	a	a	NOUN
ejpam-5850	177	89	)	)	PUNCT
ejpam-5850	177	90	δaod	δaod	NOUN
ejpam-5850	177	91	(	(	PUNCT
ejpam-5850	177	92	a	a	NOUN
ejpam-5850	177	93	)	)	PUNCT
ejpam-5850	177	94	)	)	PUNCT
ejpam-5850	177	95	{	{	PUNCT
ejpam-5850	177	96	0	0	NUM
ejpam-5850	177	97	1	1	NUM
ejpam-5850	177	98	}	}	PUNCT
ejpam-5850	177	99	d21{1}δaod	d21{1}δaod	PROPN
ejpam-5850	177	100	(	(	PUNCT
ejpam-5850	177	101	a){0	a){0	PROPN
ejpam-5850	177	102	}	}	PUNCT
ejpam-5850	177	103	and	and	CCONJ
ejpam-5850	177	104	{	{	PUNCT
ejpam-5850	177	105	0}d12	0}d12	NOUN
ejpam-5850	177	106	{	{	PUNCT
ejpam-5850	177	107	1	1	NUM
ejpam-5850	177	108	0	0	NUM
ejpam-5850	177	109	}	}	PUNCT
ejpam-5850	177	110	(	(	PUNCT
ejpam-5850	177	111	δaod	δaod	PROPN
ejpam-5850	177	112	(	(	PUNCT
ejpam-5850	177	113	a	a	NOUN
ejpam-5850	177	114	)	)	PUNCT
ejpam-5850	177	115	e	e	NOUN
ejpam-5850	177	116	)	)	PUNCT
ejpam-5850	177	117	{	{	PUNCT
ejpam-5850	177	118	0	0	NUM
ejpam-5850	177	119	0	0	NUM
ejpam-5850	177	120	}	}	PUNCT
ejpam-5850	177	121	d21{0	d21{0	PROPN
ejpam-5850	177	122	}	}	PUNCT
ejpam-5850	177	123	,	,	PUNCT
ejpam-5850	177	124	which	which	PRON
ejpam-5850	177	125	shows	show	VERB
ejpam-5850	177	126	that	that	SCONJ
ejpam-5850	177	127	h6	h6	PROPN
ejpam-5850	177	128	is	be	AUX
ejpam-5850	177	129	accepted	accept	VERB
ejpam-5850	177	130	but	but	CCONJ
ejpam-5850	177	131	not	not	PART
ejpam-5850	177	132	h5	h5	NOUN
ejpam-5850	177	133	.	.	PUNCT
ejpam-5850	178	1	notice	notice	VERB
ejpam-5850	178	2	that	that	SCONJ
ejpam-5850	178	3	,	,	PUNCT
ejpam-5850	178	4	according	accord	VERB
ejpam-5850	178	5	to	to	ADP
ejpam-5850	178	6	[	[	X
ejpam-5850	178	7	10	10	NUM
ejpam-5850	178	8	]	]	PUNCT
ejpam-5850	178	9	,	,	PUNCT
ejpam-5850	178	10	the	the	DET
ejpam-5850	178	11	behavior	behavior	NOUN
ejpam-5850	178	12	of	of	ADP
ejpam-5850	178	13	the	the	DET
ejpam-5850	178	14	graph	graph	NOUN
ejpam-5850	178	15	automaton	automaton	NOUN
ejpam-5850	178	16	will	will	AUX
ejpam-5850	178	17	be	be	AUX
ejpam-5850	178	18	the	the	DET
ejpam-5850	178	19	same	same	ADJ
ejpam-5850	178	20	regardless	regardless	ADV
ejpam-5850	178	21	of	of	ADP
ejpam-5850	178	22	which	which	DET
ejpam-5850	178	23	representation	representation	NOUN
ejpam-5850	178	24	we	we	PRON
ejpam-5850	178	25	select	select	VERB
ejpam-5850	178	26	.	.	PUNCT
ejpam-5850	179	1	next	next	ADV
ejpam-5850	179	2	we	we	PRON
ejpam-5850	179	3	are	be	AUX
ejpam-5850	179	4	going	go	VERB
ejpam-5850	179	5	to	to	PART
ejpam-5850	179	6	prove	prove	VERB
ejpam-5850	179	7	that	that	SCONJ
ejpam-5850	179	8	l(1,1	l(1,1	NOUN
ejpam-5850	179	9	)	)	PUNCT
ejpam-5850	179	10	od	od	NOUN
ejpam-5850	179	11	does	do	AUX
ejpam-5850	179	12	not	not	PART
ejpam-5850	179	13	belong	belong	VERB
ejpam-5850	179	14	to	to	ADP
ejpam-5850	179	15	urec(σ	urec(σ	NOUN
ejpam-5850	179	16	)	)	PUNCT
ejpam-5850	179	17	,	,	PUNCT
ejpam-5850	179	18	thus	thus	ADV
ejpam-5850	179	19	obtaining	obtain	VERB
ejpam-5850	179	20	the	the	DET
ejpam-5850	179	21	following	follow	VERB
ejpam-5850	179	22	proposition	proposition	NOUN
ejpam-5850	179	23	4	4	NUM
ejpam-5850	179	24	.	.	PUNCT
ejpam-5850	180	1	the	the	DET
ejpam-5850	180	2	class	class	NOUN
ejpam-5850	180	3	urec(σ	urec(σ	NOUN
ejpam-5850	180	4	)	)	PUNCT
ejpam-5850	180	5	is	be	AUX
ejpam-5850	180	6	properly	properly	ADV
ejpam-5850	180	7	contained	contain	VERB
ejpam-5850	180	8	in	in	ADP
ejpam-5850	180	9	arec(σ	arec(σ	NOUN
ejpam-5850	180	10	)	)	PUNCT
ejpam-5850	180	11	.	.	PUNCT
ejpam-5850	181	1	k.	k.	PROPN
ejpam-5850	181	2	papadopoulos	papadopoulos	PROPN
ejpam-5850	181	3	/	/	SYM
ejpam-5850	181	4	eur	eur	PROPN
ejpam-5850	181	5	.	.	PUNCT
ejpam-5850	182	1	j.	j.	PROPN
ejpam-5850	182	2	pure	pure	PROPN
ejpam-5850	182	3	appl	appl	PROPN
ejpam-5850	182	4	.	.	PROPN
ejpam-5850	182	5	math	math	PROPN
ejpam-5850	182	6	,	,	PUNCT
ejpam-5850	182	7	18	18	NUM
ejpam-5850	182	8	(	(	PUNCT
ejpam-5850	182	9	1	1	NUM
ejpam-5850	182	10	)	)	PUNCT
ejpam-5850	182	11	(	(	PUNCT
ejpam-5850	182	12	2025	2025	NUM
ejpam-5850	182	13	)	)	PUNCT
ejpam-5850	182	14	,	,	PUNCT
ejpam-5850	182	15	5850	5850	NUM
ejpam-5850	182	16	11	11	NUM
ejpam-5850	182	17	of	of	ADP
ejpam-5850	182	18	13	13	NUM
ejpam-5850	182	19	proof	proof	NOUN
ejpam-5850	182	20	.	.	PUNCT
ejpam-5850	183	1	assume	assume	VERB
ejpam-5850	183	2	that	that	SCONJ
ejpam-5850	183	3	there	there	PRON
ejpam-5850	183	4	is	be	VERB
ejpam-5850	183	5	a	a	DET
ejpam-5850	183	6	unitary	unitary	ADJ
ejpam-5850	183	7	automaton	automaton	NOUN
ejpam-5850	183	8	au	au	NOUN
ejpam-5850	183	9	od	od	X
ejpam-5850	183	10	recognizing	recognize	VERB
ejpam-5850	183	11	l	l	PROPN
ejpam-5850	183	12	(	(	PUNCT
ejpam-5850	183	13	1,1	1,1	NUM
ejpam-5850	183	14	)	)	PUNCT
ejpam-5850	183	15	od	od	NOUN
ejpam-5850	183	16	and	and	CCONJ
ejpam-5850	183	17	a	a	DET
ejpam-5850	183	18	graph	graph	NOUN
ejpam-5850	183	19	g	g	ADP
ejpam-5850	183	20	∈	∈	PROPN
ejpam-5850	183	21	l	l	NOUN
ejpam-5850	183	22	(	(	PUNCT
ejpam-5850	183	23	1,1	1,1	NUM
ejpam-5850	183	24	)	)	PUNCT
ejpam-5850	183	25	od	od	NOUN
ejpam-5850	183	26	.	.	PUNCT
ejpam-5850	184	1	then	then	ADV
ejpam-5850	184	2	there	there	PRON
ejpam-5850	184	3	will	will	AUX
ejpam-5850	184	4	be	be	AUX
ejpam-5850	184	5	states	state	NOUN
ejpam-5850	184	6	a	a	DET
ejpam-5850	184	7	∈	∈	PROPN
ejpam-5850	184	8	iau	iau	PROPN
ejpam-5850	184	9	od	od	PROPN
ejpam-5850	184	10	and	and	CCONJ
ejpam-5850	184	11	b	b	PROPN
ejpam-5850	184	12	∈	∈	PROPN
ejpam-5850	184	13	tau	tau	PROPN
ejpam-5850	184	14	od	od	INTJ
ejpam-5850	184	15	,	,	PUNCT
ejpam-5850	184	16	and	and	CCONJ
ejpam-5850	184	17	the	the	DET
ejpam-5850	184	18	following	follow	VERB
ejpam-5850	184	19	accepting	accept	VERB
ejpam-5850	184	20	transition	transition	NOUN
ejpam-5850	184	21	.	.	PUNCT
ejpam-5850	185	1	{	{	PUNCT
ejpam-5850	185	2	a}δau	a}δau	PROPN
ejpam-5850	185	3	od	od	PROPN
ejpam-5850	185	4	(	(	PUNCT
ejpam-5850	185	5	g){b	g){b	PROPN
ejpam-5850	185	6	}	}	PUNCT
ejpam-5850	185	7	we	we	PRON
ejpam-5850	185	8	consider	consider	VERB
ejpam-5850	185	9	now	now	ADV
ejpam-5850	185	10	the	the	DET
ejpam-5850	185	11	graph	graph	NOUN
ejpam-5850	185	12	gp	gp	NOUN
ejpam-5850	185	13	=	=	PUNCT
ejpam-5850	185	14	i12	i12	PROPN
ejpam-5850	185	15	◦	◦	NOUN
ejpam-5850	185	16	(	(	PUNCT
ejpam-5850	185	17	g	g	NOUN
ejpam-5850	185	18	□	□	SYM
ejpam-5850	185	19	g	g	NOUN
ejpam-5850	185	20	)	)	PUNCT
ejpam-5850	185	21	◦	◦	NOUN
ejpam-5850	185	22	i21	i21	NOUN
ejpam-5850	185	23	,	,	PUNCT
ejpam-5850	185	24	which	which	PRON
ejpam-5850	185	25	is	be	AUX
ejpam-5850	185	26	accepted	accept	VERB
ejpam-5850	185	27	by	by	ADP
ejpam-5850	185	28	the	the	DET
ejpam-5850	185	29	graph	graph	NOUN
ejpam-5850	185	30	automaton	automaton	NOUN
ejpam-5850	185	31	au	au	NOUN
ejpam-5850	185	32	od	od	ADV
ejpam-5850	185	33	with	with	ADP
ejpam-5850	185	34	accepting	accept	VERB
ejpam-5850	185	35	transition	transition	NOUN
ejpam-5850	185	36	as	as	SCONJ
ejpam-5850	185	37	shown	show	VERB
ejpam-5850	185	38	below	below	ADV
ejpam-5850	185	39	.	.	PUNCT
ejpam-5850	186	1	{	{	PUNCT
ejpam-5850	186	2	a}d12	a}d12	PROPN
ejpam-5850	186	3	{	{	PUNCT
ejpam-5850	186	4	a	a	DET
ejpam-5850	186	5	a	a	NOUN
ejpam-5850	186	6	}	}	PUNCT
ejpam-5850	186	7	(	(	PUNCT
ejpam-5850	186	8	δau	δau	PROPN
ejpam-5850	186	9	od	od	PROPN
ejpam-5850	186	10	(	(	PUNCT
ejpam-5850	186	11	g	g	NOUN
ejpam-5850	186	12	)	)	PUNCT
ejpam-5850	186	13	δau	δau	NOUN
ejpam-5850	186	14	od	od	PROPN
ejpam-5850	186	15	(	(	PUNCT
ejpam-5850	186	16	g	g	NOUN
ejpam-5850	186	17	)	)	PUNCT
ejpam-5850	186	18	)	)	PUNCT
ejpam-5850	186	19	{	{	PUNCT
ejpam-5850	186	20	b	b	X
ejpam-5850	186	21	b	b	PROPN
ejpam-5850	186	22	}	}	PUNCT
ejpam-5850	186	23	d21{b	d21{b	PROPN
ejpam-5850	186	24	}	}	PUNCT
ejpam-5850	186	25	this	this	PRON
ejpam-5850	186	26	is	be	AUX
ejpam-5850	186	27	a	a	DET
ejpam-5850	186	28	contradiction	contradiction	NOUN
ejpam-5850	186	29	since	since	SCONJ
ejpam-5850	186	30	gp	gp	NOUN
ejpam-5850	186	31	has	have	VERB
ejpam-5850	186	32	an	an	DET
ejpam-5850	186	33	even	even	ADJ
ejpam-5850	186	34	number	number	NOUN
ejpam-5850	186	35	of	of	ADP
ejpam-5850	186	36	edges	edge	NOUN
ejpam-5850	186	37	.	.	PUNCT
ejpam-5850	187	1	hence	hence	ADV
ejpam-5850	187	2	l	l	NOUN
ejpam-5850	187	3	(	(	PUNCT
ejpam-5850	187	4	1,1	1,1	NUM
ejpam-5850	187	5	)	)	PUNCT
ejpam-5850	187	6	od	od	NOUN
ejpam-5850	187	7	does	do	AUX
ejpam-5850	187	8	not	not	PART
ejpam-5850	187	9	belong	belong	VERB
ejpam-5850	187	10	to	to	ADP
ejpam-5850	187	11	urec(σ	urec(σ	NOUN
ejpam-5850	187	12	)	)	PUNCT
ejpam-5850	187	13	and	and	CCONJ
ejpam-5850	187	14	from	from	ADP
ejpam-5850	187	15	proposition	proposition	NOUN
ejpam-5850	187	16	3	3	NUM
ejpam-5850	187	17	we	we	PRON
ejpam-5850	187	18	obtain	obtain	VERB
ejpam-5850	187	19	the	the	DET
ejpam-5850	187	20	result	result	NOUN
ejpam-5850	187	21	.	.	PUNCT
ejpam-5850	188	1	6	6	X
ejpam-5850	188	2	.	.	X
ejpam-5850	188	3	conclusion	conclusion	NOUN
ejpam-5850	188	4	we	we	PRON
ejpam-5850	188	5	investigated	investigate	VERB
ejpam-5850	188	6	unitary	unitary	ADJ
ejpam-5850	188	7	and	and	CCONJ
ejpam-5850	188	8	non	non	ADJ
ejpam-5850	188	9	-	-	ADJ
ejpam-5850	188	10	unitary	unitary	ADJ
ejpam-5850	188	11	abelian	abelian	ADJ
ejpam-5850	188	12	graph	graph	NOUN
ejpam-5850	188	13	automata	automata	NOUN
ejpam-5850	188	14	by	by	ADP
ejpam-5850	188	15	leveraging	leverage	VERB
ejpam-5850	188	16	the	the	DET
ejpam-5850	188	17	algebraic	algebraic	ADJ
ejpam-5850	188	18	structure	structure	NOUN
ejpam-5850	188	19	of	of	ADP
ejpam-5850	188	20	graphoids	graphoid	NOUN
ejpam-5850	188	21	and	and	CCONJ
ejpam-5850	188	22	demonstrated	demonstrate	VERB
ejpam-5850	188	23	that	that	SCONJ
ejpam-5850	188	24	unitary	unitary	ADJ
ejpam-5850	188	25	graph	graph	NOUN
ejpam-5850	188	26	automata	automata	NOUN
ejpam-5850	188	27	effectively	effectively	ADV
ejpam-5850	188	28	recognize	recognize	VERB
ejpam-5850	188	29	sets	set	NOUN
ejpam-5850	188	30	of	of	ADP
ejpam-5850	188	31	directed	direct	VERB
ejpam-5850	188	32	graphs	graph	NOUN
ejpam-5850	188	33	with	with	ADP
ejpam-5850	188	34	chromatic	chromatic	ADJ
ejpam-5850	188	35	numbers	number	NOUN
ejpam-5850	188	36	bounded	bound	VERB
ejpam-5850	188	37	by	by	ADP
ejpam-5850	188	38	any	any	DET
ejpam-5850	188	39	given	give	VERB
ejpam-5850	188	40	integer	integer	NOUN
ejpam-5850	188	41	,	,	PUNCT
ejpam-5850	188	42	thereby	thereby	ADV
ejpam-5850	188	43	extending	extend	VERB
ejpam-5850	188	44	existing	exist	VERB
ejpam-5850	188	45	results	result	NOUN
ejpam-5850	188	46	in	in	ADP
ejpam-5850	188	47	the	the	DET
ejpam-5850	188	48	literature	literature	NOUN
ejpam-5850	188	49	.	.	PUNCT
ejpam-5850	189	1	in	in	ADP
ejpam-5850	189	2	addition	addition	NOUN
ejpam-5850	189	3	,	,	PUNCT
ejpam-5850	189	4	we	we	PRON
ejpam-5850	189	5	introduced	introduce	VERB
ejpam-5850	189	6	and	and	CCONJ
ejpam-5850	189	7	examined	examine	VERB
ejpam-5850	189	8	non	non	ADJ
ejpam-5850	189	9	-	-	ADJ
ejpam-5850	189	10	unitary	unitary	ADJ
ejpam-5850	189	11	abelian	abelian	ADJ
ejpam-5850	189	12	graph	graph	NOUN
ejpam-5850	189	13	automata	automata	NOUN
ejpam-5850	189	14	,	,	PUNCT
ejpam-5850	189	15	showing	show	VERB
ejpam-5850	189	16	that	that	SCONJ
ejpam-5850	189	17	they	they	PRON
ejpam-5850	189	18	can	can	AUX
ejpam-5850	189	19	recognize	recognize	VERB
ejpam-5850	189	20	graph	graph	NOUN
ejpam-5850	189	21	languages	language	NOUN
ejpam-5850	189	22	—	—	PUNCT
ejpam-5850	189	23	such	such	ADJ
ejpam-5850	189	24	as	as	ADP
ejpam-5850	189	25	graphs	graph	NOUN
ejpam-5850	189	26	the	the	DET
ejpam-5850	189	27	set	set	NOUN
ejpam-5850	189	28	of	of	ADP
ejpam-5850	189	29	conventionawith	conventionawith	NOUN
ejpam-5850	189	30	an	an	DET
ejpam-5850	189	31	odd	odd	ADJ
ejpam-5850	189	32	number	number	NOUN
ejpam-5850	189	33	of	of	ADP
ejpam-5850	189	34	edges	edge	NOUN
ejpam-5850	189	35	—	—	PUNCT
ejpam-5850	189	36	that	that	PRON
ejpam-5850	189	37	lie	lie	VERB
ejpam-5850	189	38	beyond	beyond	ADP
ejpam-5850	189	39	the	the	DET
ejpam-5850	189	40	recognition	recognition	NOUN
ejpam-5850	189	41	capabilities	capability	NOUN
ejpam-5850	189	42	of	of	ADP
ejpam-5850	189	43	unitary	unitary	ADJ
ejpam-5850	189	44	graph	graph	NOUN
ejpam-5850	189	45	automata	automata	NOUN
ejpam-5850	189	46	.	.	PUNCT
ejpam-5850	190	1	this	this	PRON
ejpam-5850	190	2	establishes	establish	VERB
ejpam-5850	190	3	a	a	DET
ejpam-5850	190	4	strict	strict	ADJ
ejpam-5850	190	5	hierarchy	hierarchy	NOUN
ejpam-5850	190	6	between	between	ADP
ejpam-5850	190	7	the	the	DET
ejpam-5850	190	8	graph	graph	NOUN
ejpam-5850	190	9	languages	language	NOUN
ejpam-5850	190	10	recognized	recognize	VERB
ejpam-5850	190	11	by	by	ADP
ejpam-5850	190	12	these	these	DET
ejpam-5850	190	13	two	two	NUM
ejpam-5850	190	14	classes	class	NOUN
ejpam-5850	190	15	of	of	ADP
ejpam-5850	190	16	automata	automata	NOUN
ejpam-5850	190	17	namely	namely	ADV
ejpam-5850	190	18	,	,	PUNCT
ejpam-5850	190	19	urec(σ	urec(σ	NOUN
ejpam-5850	190	20	)	)	PUNCT
ejpam-5850	190	21	⊂	⊂	PROPN
ejpam-5850	190	22	arec(σ	arec(σ	PROPN
ejpam-5850	190	23	)	)	PUNCT
ejpam-5850	190	24	.	.	PUNCT
ejpam-5850	191	1	the	the	DET
ejpam-5850	191	2	presented	present	VERB
ejpam-5850	191	3	results	result	NOUN
ejpam-5850	191	4	demonstrate	demonstrate	VERB
ejpam-5850	191	5	the	the	DET
ejpam-5850	191	6	robust	robust	ADJ
ejpam-5850	191	7	expressive	expressive	ADJ
ejpam-5850	191	8	power	power	NOUN
ejpam-5850	191	9	of	of	ADP
ejpam-5850	191	10	non	non	ADJ
ejpam-5850	191	11	-	-	ADJ
ejpam-5850	191	12	unitary	unitary	ADJ
ejpam-5850	191	13	automata	automata	NOUN
ejpam-5850	191	14	and	and	CCONJ
ejpam-5850	191	15	provide	provide	VERB
ejpam-5850	191	16	new	new	ADJ
ejpam-5850	191	17	insights	insight	NOUN
ejpam-5850	191	18	into	into	ADP
ejpam-5850	191	19	the	the	DET
ejpam-5850	191	20	interplay	interplay	NOUN
ejpam-5850	191	21	between	between	ADP
ejpam-5850	191	22	graph	graph	NOUN
ejpam-5850	191	23	automata	automata	NOUN
ejpam-5850	191	24	and	and	CCONJ
ejpam-5850	191	25	their	their	PRON
ejpam-5850	191	26	corresponding	corresponding	ADJ
ejpam-5850	191	27	algebraic	algebraic	ADJ
ejpam-5850	191	28	structures	structure	NOUN
ejpam-5850	191	29	.	.	PUNCT
ejpam-5850	192	1	by	by	ADP
ejpam-5850	192	2	showing	show	VERB
ejpam-5850	192	3	how	how	SCONJ
ejpam-5850	192	4	variations	variation	NOUN
ejpam-5850	192	5	in	in	ADP
ejpam-5850	192	6	the	the	DET
ejpam-5850	192	7	underlying	underlie	VERB
ejpam-5850	192	8	graphoid	graphoid	NOUN
ejpam-5850	192	9	influence	influence	NOUN
ejpam-5850	192	10	recognition	recognition	NOUN
ejpam-5850	192	11	capability	capability	NOUN
ejpam-5850	192	12	,	,	PUNCT
ejpam-5850	192	13	this	this	DET
ejpam-5850	192	14	work	work	NOUN
ejpam-5850	192	15	paves	pave	VERB
ejpam-5850	192	16	the	the	DET
ejpam-5850	192	17	way	way	NOUN
ejpam-5850	192	18	for	for	ADP
ejpam-5850	192	19	further	further	ADJ
ejpam-5850	192	20	exploration	exploration	NOUN
ejpam-5850	192	21	of	of	ADP
ejpam-5850	192	22	the	the	DET
ejpam-5850	192	23	theoretical	theoretical	ADJ
ejpam-5850	192	24	and	and	CCONJ
ejpam-5850	192	25	practical	practical	ADJ
ejpam-5850	192	26	implications	implication	NOUN
ejpam-5850	192	27	of	of	ADP
ejpam-5850	192	28	graph	graph	NOUN
ejpam-5850	192	29	automata	automata	NOUN
ejpam-5850	192	30	.	.	PUNCT
ejpam-5850	193	1	as	as	ADP
ejpam-5850	193	2	a	a	DET
ejpam-5850	193	3	continuation	continuation	NOUN
ejpam-5850	193	4	of	of	ADP
ejpam-5850	193	5	this	this	DET
ejpam-5850	193	6	study	study	NOUN
ejpam-5850	193	7	,	,	PUNCT
ejpam-5850	193	8	the	the	DET
ejpam-5850	193	9	recognition	recognition	NOUN
ejpam-5850	193	10	mechanisms	mechanism	NOUN
ejpam-5850	193	11	of	of	ADP
ejpam-5850	193	12	non	non	ADJ
ejpam-5850	193	13	-	-	ADJ
ejpam-5850	193	14	unitary	unitary	ADJ
ejpam-5850	193	15	graph	graph	NOUN
ejpam-5850	193	16	automata	automata	NOUN
ejpam-5850	193	17	derived	derive	VERB
ejpam-5850	193	18	from	from	ADP
ejpam-5850	193	19	graphoids	graphoid	NOUN
ejpam-5850	193	20	based	base	VERB
ejpam-5850	193	21	on	on	ADP
ejpam-5850	193	22	non	non	ADJ
ejpam-5850	193	23	-	-	ADJ
ejpam-5850	193	24	abelian	abelian	ADJ
ejpam-5850	193	25	groups	group	NOUN
ejpam-5850	193	26	with	with	ADP
ejpam-5850	193	27	more	more	ADJ
ejpam-5850	193	28	than	than	ADP
ejpam-5850	193	29	two	two	NUM
ejpam-5850	193	30	elements	element	NOUN
ejpam-5850	193	31	need	need	VERB
ejpam-5850	193	32	to	to	PART
ejpam-5850	193	33	be	be	AUX
ejpam-5850	193	34	investigated	investigate	VERB
ejpam-5850	193	35	.	.	PUNCT
ejpam-5850	194	1	such	such	DET
ejpam-5850	194	2	an	an	DET
ejpam-5850	194	3	exploration	exploration	NOUN
ejpam-5850	194	4	could	could	AUX
ejpam-5850	194	5	further	far	ADV
ejpam-5850	194	6	expand	expand	VERB
ejpam-5850	194	7	the	the	DET
ejpam-5850	194	8	hierarchy	hierarchy	NOUN
ejpam-5850	194	9	of	of	ADP
ejpam-5850	194	10	graph	graph	NOUN
ejpam-5850	194	11	language	language	NOUN
ejpam-5850	194	12	recognition	recognition	NOUN
ejpam-5850	194	13	within	within	ADP
ejpam-5850	194	14	the	the	DET
ejpam-5850	194	15	class	class	NOUN
ejpam-5850	194	16	of	of	ADP
ejpam-5850	194	17	abelian	abelian	ADJ
ejpam-5850	194	18	graph	graph	NOUN
ejpam-5850	194	19	automata	automata	NOUN
ejpam-5850	194	20	.	.	PUNCT
ejpam-5850	195	1	additionally	additionally	ADV
ejpam-5850	195	2	,	,	PUNCT
ejpam-5850	195	3	while	while	SCONJ
ejpam-5850	195	4	constructing	construct	VERB
ejpam-5850	195	5	non	non	ADJ
ejpam-5850	195	6	-	-	ADJ
ejpam-5850	195	7	abelian	abelian	ADJ
ejpam-5850	195	8	and	and	CCONJ
ejpam-5850	195	9	non	non	ADJ
ejpam-5850	195	10	-	-	ADJ
ejpam-5850	195	11	relational	relational	ADJ
ejpam-5850	195	12	graphoids	graphoid	NOUN
ejpam-5850	195	13	is	be	AUX
ejpam-5850	195	14	theoretically	theoretically	ADV
ejpam-5850	195	15	feasible	feasible	ADJ
ejpam-5850	195	16	,	,	PUNCT
ejpam-5850	195	17	it	it	PRON
ejpam-5850	195	18	remains	remain	VERB
ejpam-5850	195	19	an	an	DET
ejpam-5850	195	20	open	open	ADJ
ejpam-5850	195	21	problem	problem	NOUN
ejpam-5850	195	22	.	.	PUNCT
ejpam-5850	196	1	the	the	DET
ejpam-5850	196	2	successful	successful	ADJ
ejpam-5850	196	3	development	development	NOUN
ejpam-5850	196	4	of	of	ADP
ejpam-5850	196	5	such	such	ADJ
ejpam-5850	196	6	machines	machine	NOUN
ejpam-5850	196	7	would	would	AUX
ejpam-5850	196	8	enable	enable	VERB
ejpam-5850	196	9	comparisons	comparison	NOUN
ejpam-5850	196	10	with	with	ADP
ejpam-5850	196	11	existing	exist	VERB
ejpam-5850	196	12	unitary	unitary	ADJ
ejpam-5850	196	13	and	and	CCONJ
ejpam-5850	196	14	abelian	abelian	ADJ
ejpam-5850	196	15	graph	graph	NOUN
ejpam-5850	196	16	automata	automata	NOUN
ejpam-5850	196	17	,	,	PUNCT
ejpam-5850	196	18	thereby	thereby	ADV
ejpam-5850	196	19	broadening	broaden	VERB
ejpam-5850	196	20	our	our	PRON
ejpam-5850	196	21	understanding	understanding	NOUN
ejpam-5850	196	22	of	of	ADP
ejpam-5850	196	23	the	the	DET
ejpam-5850	196	24	recognition	recognition	NOUN
ejpam-5850	196	25	capabilities	capability	NOUN
ejpam-5850	196	26	of	of	ADP
ejpam-5850	196	27	graph	graph	NOUN
ejpam-5850	196	28	automata	automata	NOUN
ejpam-5850	196	29	.	.	PUNCT
ejpam-5850	197	1	moreover	moreover	ADV
ejpam-5850	197	2	,	,	PUNCT
ejpam-5850	197	3	drawing	draw	VERB
ejpam-5850	197	4	parallels	parallel	NOUN
ejpam-5850	197	5	to	to	ADP
ejpam-5850	197	6	the	the	DET
ejpam-5850	197	7	string	string	NOUN
ejpam-5850	197	8	case	case	NOUN
ejpam-5850	197	9	,	,	PUNCT
ejpam-5850	197	10	we	we	PRON
ejpam-5850	197	11	can	can	AUX
ejpam-5850	197	12	compare	compare	VERB
ejpam-5850	197	13	the	the	DET
ejpam-5850	197	14	recognition	recognition	NOUN
ejpam-5850	197	15	power	power	NOUN
ejpam-5850	197	16	of	of	ADP
ejpam-5850	197	17	graph	graph	NOUN
ejpam-5850	197	18	automata	automata	NOUN
ejpam-5850	197	19	to	to	ADP
ejpam-5850	197	20	the	the	DET
ejpam-5850	197	21	syntactic	syntactic	ADJ
ejpam-5850	197	22	recognizability	recognizability	NOUN
ejpam-5850	197	23	of	of	ADP
ejpam-5850	197	24	graphs	graph	NOUN
ejpam-5850	197	25	,	,	PUNCT
ejpam-5850	197	26	as	as	SCONJ
ejpam-5850	197	27	introduced	introduce	VERB
ejpam-5850	197	28	in	in	ADP
ejpam-5850	197	29	[	[	X
ejpam-5850	197	30	9	9	NUM
ejpam-5850	197	31	]	]	PUNCT
ejpam-5850	197	32	.	.	PUNCT
ejpam-5850	198	1	we	we	PRON
ejpam-5850	198	2	can	can	AUX
ejpam-5850	198	3	also	also	ADV
ejpam-5850	198	4	investigate	investigate	VERB
ejpam-5850	198	5	the	the	DET
ejpam-5850	198	6	possible	possible	ADJ
ejpam-5850	198	7	construction	construction	NOUN
ejpam-5850	198	8	of	of	ADP
ejpam-5850	198	9	fuzzy	fuzzy	ADJ
ejpam-5850	198	10	graph	graph	NOUN
ejpam-5850	198	11	automata	automata	NOUN
ejpam-5850	198	12	,	,	PUNCT
ejpam-5850	198	13	similarly	similarly	ADV
ejpam-5850	198	14	to	to	ADP
ejpam-5850	198	15	syntactic	syntactic	ADJ
ejpam-5850	198	16	fuzzy	fuzzy	ADJ
ejpam-5850	198	17	recognition	recognition	NOUN
ejpam-5850	198	18	,	,	PUNCT
ejpam-5850	198	19	as	as	SCONJ
ejpam-5850	198	20	described	describe	VERB
ejpam-5850	198	21	in	in	ADP
ejpam-5850	198	22	[	[	X
ejpam-5850	198	23	22	22	NUM
ejpam-5850	198	24	,	,	PUNCT
ejpam-5850	198	25	23	23	NUM
ejpam-5850	198	26	]	]	PUNCT
ejpam-5850	198	27	.	.	PUNCT
ejpam-5850	199	1	k.	k.	PROPN
ejpam-5850	199	2	papadopoulos	papadopoulos	PROPN
ejpam-5850	199	3	/	/	SYM
ejpam-5850	199	4	eur	eur	PROPN
ejpam-5850	199	5	.	.	PUNCT
ejpam-5850	200	1	j.	j.	PROPN
ejpam-5850	200	2	pure	pure	PROPN
ejpam-5850	200	3	appl	appl	PROPN
ejpam-5850	200	4	.	.	PROPN
ejpam-5850	200	5	math	math	PROPN
ejpam-5850	200	6	,	,	PUNCT
ejpam-5850	200	7	18	18	NUM
ejpam-5850	200	8	(	(	PUNCT
ejpam-5850	200	9	1	1	NUM
ejpam-5850	200	10	)	)	PUNCT
ejpam-5850	200	11	(	(	PUNCT
ejpam-5850	200	12	2025	2025	NUM
ejpam-5850	200	13	)	)	PUNCT
ejpam-5850	200	14	,	,	PUNCT
ejpam-5850	200	15	5850	5850	NUM
ejpam-5850	200	16	12	12	NUM
ejpam-5850	200	17	of	of	ADP
ejpam-5850	200	18	13	13	NUM
ejpam-5850	200	19	references	reference	NOUN
ejpam-5850	200	20	[	[	X
ejpam-5850	200	21	1	1	NUM
ejpam-5850	200	22	]	]	PUNCT
ejpam-5850	200	23	shaikh	shaikh	PROPN
ejpam-5850	200	24	ibrahim	ibrahim	PROPN
ejpam-5850	200	25	abdullah	abdullah	PROPN
ejpam-5850	200	26	,	,	PUNCT
ejpam-5850	200	27	sovan	sovan	PROPN
ejpam-5850	200	28	samanta	samanta	PROPN
ejpam-5850	200	29	,	,	PUNCT
ejpam-5850	200	30	kajal	kajal	PROPN
ejpam-5850	200	31	de	de	PROPN
ejpam-5850	200	32	,	,	PUNCT
ejpam-5850	200	33	et	et	PROPN
ejpam-5850	200	34	al	al	PROPN
ejpam-5850	200	35	.	.	PUNCT
ejpam-5850	201	1	properties	property	NOUN
ejpam-5850	201	2	of	of	ADP
ejpam-5850	201	3	the	the	DET
ejpam-5850	201	4	forgotten	forget	VERB
ejpam-5850	201	5	index	index	NOUN
ejpam-5850	201	6	in	in	ADP
ejpam-5850	201	7	bipolar	bipolar	ADJ
ejpam-5850	201	8	fuzzy	fuzzy	ADJ
ejpam-5850	201	9	graphs	graph	NOUN
ejpam-5850	201	10	and	and	CCONJ
ejpam-5850	201	11	applications	application	NOUN
ejpam-5850	201	12	.	.	PUNCT
ejpam-5850	202	1	scientific	scientific	ADJ
ejpam-5850	202	2	reports	report	NOUN
ejpam-5850	202	3	,	,	PUNCT
ejpam-5850	202	4	14:28264	14:28264	NUM
ejpam-5850	202	5	,	,	PUNCT
ejpam-5850	202	6	2024	2024	NUM
ejpam-5850	202	7	.	.	PUNCT
ejpam-5850	203	1	[	[	X
ejpam-5850	203	2	2	2	NUM
ejpam-5850	203	3	]	]	PUNCT
ejpam-5850	203	4	noga	noga	PROPN
ejpam-5850	203	5	alon	alon	PROPN
ejpam-5850	203	6	,	,	PUNCT
ejpam-5850	203	7	janos	janos	PROPN
ejpam-5850	203	8	pach	pach	PROPN
ejpam-5850	203	9	,	,	PUNCT
ejpam-5850	203	10	and	and	CCONJ
ejpam-5850	203	11	josef	josef	PROPN
ejpam-5850	203	12	solymosi	solymosi	PROPN
ejpam-5850	203	13	.	.	PUNCT
ejpam-5850	204	1	ramsey	ramsey	ADJ
ejpam-5850	204	2	-	-	PUNCT
ejpam-5850	204	3	type	type	NOUN
ejpam-5850	204	4	theorems	theorem	NOUN
ejpam-5850	204	5	with	with	ADP
ejpam-5850	204	6	forbidden	forbid	VERB
ejpam-5850	204	7	subgraphs	subgraph	NOUN
ejpam-5850	204	8	.	.	PUNCT
ejpam-5850	205	1	combinatorica	combinatorica	PROPN
ejpam-5850	205	2	,	,	PUNCT
ejpam-5850	205	3	21:155–170	21:155–170	PROPN
ejpam-5850	205	4	,	,	PUNCT
ejpam-5850	205	5	2001	2001	NUM
ejpam-5850	205	6	.	.	PUNCT
ejpam-5850	206	1	[	[	X
ejpam-5850	206	2	3	3	NUM
ejpam-5850	206	3	]	]	X
ejpam-5850	206	4	kenneth	kenneth	PROPN
ejpam-5850	206	5	appel	appel	PROPN
ejpam-5850	206	6	and	and	CCONJ
ejpam-5850	206	7	wolfgang	wolfgang	PROPN
ejpam-5850	206	8	haken	haken	PROPN
ejpam-5850	206	9	.	.	PUNCT
ejpam-5850	207	1	every	every	DET
ejpam-5850	207	2	planar	planar	ADJ
ejpam-5850	207	3	map	map	NOUN
ejpam-5850	207	4	is	be	AUX
ejpam-5850	207	5	four	four	NUM
ejpam-5850	207	6	colorable	colorable	ADJ
ejpam-5850	207	7	.	.	PUNCT
ejpam-5850	208	1	i.	i.	PROPN
ejpam-5850	208	2	discharging	discharging	PROPN
ejpam-5850	208	3	.	.	PUNCT
ejpam-5850	209	1	illinois	illinois	PROPN
ejpam-5850	209	2	journal	journal	PROPN
ejpam-5850	209	3	of	of	ADP
ejpam-5850	209	4	mathematics	mathematic	NOUN
ejpam-5850	209	5	,	,	PUNCT
ejpam-5850	209	6	21:429–490	21:429–490	NUM
ejpam-5850	209	7	,	,	PUNCT
ejpam-5850	209	8	1977	1977	NUM
ejpam-5850	209	9	.	.	PUNCT
ejpam-5850	210	1	[	[	X
ejpam-5850	210	2	4	4	NUM
ejpam-5850	210	3	]	]	X
ejpam-5850	210	4	kenneth	kenneth	PROPN
ejpam-5850	210	5	appel	appel	PROPN
ejpam-5850	210	6	,	,	PUNCT
ejpam-5850	210	7	wolfgang	wolfgang	PROPN
ejpam-5850	210	8	haken	haken	PROPN
ejpam-5850	210	9	,	,	PUNCT
ejpam-5850	210	10	and	and	CCONJ
ejpam-5850	210	11	john	john	PROPN
ejpam-5850	210	12	koch	koch	PROPN
ejpam-5850	210	13	.	.	PUNCT
ejpam-5850	211	1	every	every	DET
ejpam-5850	211	2	planar	planar	ADJ
ejpam-5850	211	3	map	map	NOUN
ejpam-5850	211	4	is	be	AUX
ejpam-5850	211	5	four	four	NUM
ejpam-5850	211	6	colorable	colorable	ADJ
ejpam-5850	211	7	.	.	PUNCT
ejpam-5850	212	1	ii	ii	PROPN
ejpam-5850	212	2	.	.	PUNCT
ejpam-5850	213	1	reducibility	reducibility	PROPN
ejpam-5850	213	2	.	.	PUNCT
ejpam-5850	214	1	illinois	illinois	PROPN
ejpam-5850	214	2	journal	journal	PROPN
ejpam-5850	214	3	of	of	ADP
ejpam-5850	214	4	mathematics	mathematic	NOUN
ejpam-5850	214	5	,	,	PUNCT
ejpam-5850	214	6	21:491–567	21:491–567	NUM
ejpam-5850	214	7	,	,	PUNCT
ejpam-5850	214	8	1977	1977	NUM
ejpam-5850	214	9	.	.	PUNCT
ejpam-5850	215	1	[	[	X
ejpam-5850	215	2	5	5	X
ejpam-5850	215	3	]	]	PUNCT
ejpam-5850	215	4	andre	andre	PROPN
ejpam-5850	215	5	arnold	arnold	PROPN
ejpam-5850	215	6	and	and	CCONJ
ejpam-5850	215	7	max	max	PROPN
ejpam-5850	215	8	dauchet	dauchet	PROPN
ejpam-5850	215	9	.	.	PUNCT
ejpam-5850	216	1	théorie	théorie	PROPN
ejpam-5850	216	2	des	des	PROPN
ejpam-5850	216	3	magmoides	magmoides	PROPN
ejpam-5850	216	4	.	.	PUNCT
ejpam-5850	217	1	rairo	rairo	PROPN
ejpam-5850	217	2	theoret	theoret	PROPN
ejpam-5850	217	3	.	.	PUNCT
ejpam-5850	218	1	inform	inform	NOUN
ejpam-5850	218	2	.	.	PUNCT
ejpam-5850	219	1	appl	appl	PROPN
ejpam-5850	219	2	.	.	PROPN
ejpam-5850	219	3	,	,	PUNCT
ejpam-5850	219	4	12:235–257	12:235–257	NUM
ejpam-5850	219	5	,	,	PUNCT
ejpam-5850	219	6	1978	1978	NUM
ejpam-5850	219	7	.	.	PUNCT
ejpam-5850	220	1	[	[	X
ejpam-5850	220	2	6	6	NUM
ejpam-5850	220	3	]	]	X
ejpam-5850	220	4	edgar	edgar	NOUN
ejpam-5850	220	5	asplund	asplund	ADP
ejpam-5850	220	6	and	and	CCONJ
ejpam-5850	220	7	branko	branko	PROPN
ejpam-5850	220	8	grünbaum	grünbaum	PROPN
ejpam-5850	220	9	.	.	PUNCT
ejpam-5850	221	1	on	on	ADP
ejpam-5850	221	2	a	a	DET
ejpam-5850	221	3	coloring	coloring	NOUN
ejpam-5850	221	4	problem	problem	NOUN
ejpam-5850	221	5	.	.	PUNCT
ejpam-5850	222	1	mathematica	mathematica	PROPN
ejpam-5850	222	2	scandinavica	scandinavica	PROPN
ejpam-5850	222	3	,	,	PUNCT
ejpam-5850	222	4	8:181–188	8:181–188	NUM
ejpam-5850	222	5	,	,	PUNCT
ejpam-5850	222	6	1960	1960	NUM
ejpam-5850	222	7	.	.	PUNCT
ejpam-5850	223	1	[	[	X
ejpam-5850	223	2	7	7	NUM
ejpam-5850	223	3	]	]	X
ejpam-5850	223	4	symeon	symeon	NOUN
ejpam-5850	223	5	bozapalidis	bozapalidi	NOUN
ejpam-5850	223	6	and	and	CCONJ
ejpam-5850	223	7	antonios	antonios	PROPN
ejpam-5850	223	8	kalampakas	kalampakas	PROPN
ejpam-5850	223	9	.	.	PUNCT
ejpam-5850	224	1	an	an	DET
ejpam-5850	224	2	axiomatization	axiomatization	NOUN
ejpam-5850	224	3	of	of	ADP
ejpam-5850	224	4	graphs	graph	NOUN
ejpam-5850	224	5	.	.	PUNCT
ejpam-5850	225	1	acta	acta	PROPN
ejpam-5850	225	2	inform	inform	PROPN
ejpam-5850	225	3	.	.	PUNCT
ejpam-5850	225	4	,	,	PUNCT
ejpam-5850	225	5	41:19–61	41:19–61	PROPN
ejpam-5850	225	6	,	,	PUNCT
ejpam-5850	225	7	2004	2004	NUM
ejpam-5850	225	8	.	.	PUNCT
ejpam-5850	226	1	[	[	X
ejpam-5850	226	2	8	8	NUM
ejpam-5850	226	3	]	]	X
ejpam-5850	226	4	symeon	symeon	NOUN
ejpam-5850	226	5	bozapalidis	bozapalidi	NOUN
ejpam-5850	226	6	and	and	CCONJ
ejpam-5850	226	7	antonios	antonios	PROPN
ejpam-5850	226	8	kalampakas	kalampakas	PROPN
ejpam-5850	226	9	.	.	PUNCT
ejpam-5850	227	1	automata	automata	PROPN
ejpam-5850	227	2	on	on	ADP
ejpam-5850	227	3	patterns	pattern	NOUN
ejpam-5850	227	4	and	and	CCONJ
ejpam-5850	227	5	graphs	graph	NOUN
ejpam-5850	227	6	.	.	PUNCT
ejpam-5850	228	1	in	in	ADP
ejpam-5850	228	2	proceedings	proceeding	NOUN
ejpam-5850	228	3	of	of	ADP
ejpam-5850	228	4	the	the	DET
ejpam-5850	228	5	1st	1st	ADJ
ejpam-5850	228	6	conference	conference	NOUN
ejpam-5850	228	7	on	on	ADP
ejpam-5850	228	8	algebraic	algebraic	PROPN
ejpam-5850	228	9	informatics	informatic	NOUN
ejpam-5850	228	10	,	,	PUNCT
ejpam-5850	228	11	pages	page	NOUN
ejpam-5850	228	12	31–52	31–52	NUM
ejpam-5850	228	13	,	,	PUNCT
ejpam-5850	228	14	2006	2006	NUM
ejpam-5850	228	15	.	.	PUNCT
ejpam-5850	229	1	[	[	X
ejpam-5850	229	2	9	9	NUM
ejpam-5850	229	3	]	]	PUNCT
ejpam-5850	229	4	symeon	symeon	NOUN
ejpam-5850	229	5	bozapalidis	bozapalidi	NOUN
ejpam-5850	229	6	and	and	CCONJ
ejpam-5850	229	7	antonios	antonios	PROPN
ejpam-5850	229	8	kalampakas	kalampakas	PROPN
ejpam-5850	229	9	.	.	PUNCT
ejpam-5850	230	1	recognizability	recognizability	NOUN
ejpam-5850	230	2	of	of	ADP
ejpam-5850	230	3	graph	graph	NOUN
ejpam-5850	230	4	and	and	CCONJ
ejpam-5850	230	5	pattern	pattern	NOUN
ejpam-5850	230	6	languages	language	NOUN
ejpam-5850	230	7	.	.	PUNCT
ejpam-5850	231	1	acta	acta	PROPN
ejpam-5850	231	2	inform	inform	PROPN
ejpam-5850	231	3	.	.	PUNCT
ejpam-5850	231	4	,	,	PUNCT
ejpam-5850	231	5	42:553–581	42:553–581	PROPN
ejpam-5850	231	6	,	,	PUNCT
ejpam-5850	231	7	2006	2006	NUM
ejpam-5850	231	8	.	.	PUNCT
ejpam-5850	232	1	[	[	X
ejpam-5850	232	2	10	10	NUM
ejpam-5850	232	3	]	]	X
ejpam-5850	232	4	symeon	symeon	NOUN
ejpam-5850	232	5	bozapalidis	bozapalidi	NOUN
ejpam-5850	232	6	and	and	CCONJ
ejpam-5850	232	7	antonios	antonios	PROPN
ejpam-5850	232	8	kalampakas	kalampakas	PROPN
ejpam-5850	232	9	.	.	PUNCT
ejpam-5850	233	1	graph	graph	NOUN
ejpam-5850	233	2	automata	automata	PROPN
ejpam-5850	233	3	.	.	PUNCT
ejpam-5850	234	1	theoret	theoret	ADJ
ejpam-5850	234	2	.	.	PUNCT
ejpam-5850	235	1	comput	comput	NOUN
ejpam-5850	235	2	.	.	PUNCT
ejpam-5850	236	1	sci	sci	PROPN
ejpam-5850	236	2	.	.	PROPN
ejpam-5850	236	3	,	,	PUNCT
ejpam-5850	236	4	393:147–165	393:147–165	NUM
ejpam-5850	236	5	,	,	PUNCT
ejpam-5850	236	6	2008	2008	NUM
ejpam-5850	236	7	.	.	PUNCT
ejpam-5850	237	1	[	[	X
ejpam-5850	237	2	11	11	NUM
ejpam-5850	237	3	]	]	X
ejpam-5850	237	4	sander	sander	PROPN
ejpam-5850	237	5	bruggink	bruggink	PROPN
ejpam-5850	237	6	and	and	CCONJ
ejpam-5850	237	7	barbara	barbara	PROPN
ejpam-5850	237	8	könig	könig	PROPN
ejpam-5850	237	9	.	.	PUNCT
ejpam-5850	238	1	recognizable	recognizable	ADJ
ejpam-5850	238	2	languages	language	NOUN
ejpam-5850	238	3	of	of	ADP
ejpam-5850	238	4	arrows	arrow	NOUN
ejpam-5850	238	5	and	and	CCONJ
ejpam-5850	238	6	cospans	cospan	NOUN
ejpam-5850	238	7	.	.	PUNCT
ejpam-5850	239	1	mathematical	mathematical	ADJ
ejpam-5850	239	2	structures	structure	NOUN
ejpam-5850	239	3	in	in	ADP
ejpam-5850	239	4	computer	computer	NOUN
ejpam-5850	239	5	science	science	NOUN
ejpam-5850	239	6	,	,	PUNCT
ejpam-5850	239	7	28(8):1290	28(8):1290	PROPN
ejpam-5850	239	8	–	–	PUNCT
ejpam-5850	239	9	1332	1332	NUM
ejpam-5850	239	10	,	,	PUNCT
ejpam-5850	239	11	2018	2018	NUM
ejpam-5850	239	12	.	.	PUNCT
ejpam-5850	240	1	[	[	X
ejpam-5850	240	2	12	12	NUM
ejpam-5850	240	3	]	]	PUNCT
ejpam-5850	240	4	bruno	bruno	PROPN
ejpam-5850	240	5	courcelle	courcelle	NOUN
ejpam-5850	240	6	.	.	PUNCT
ejpam-5850	241	1	on	on	ADP
ejpam-5850	241	2	recognizable	recognizable	ADJ
ejpam-5850	241	3	sets	set	NOUN
ejpam-5850	241	4	and	and	CCONJ
ejpam-5850	241	5	tree	tree	NOUN
ejpam-5850	241	6	automata	automata	NOUN
ejpam-5850	241	7	.	.	PUNCT
ejpam-5850	242	1	in	in	ADP
ejpam-5850	242	2	algebraic	algebraic	PROPN
ejpam-5850	242	3	techniques	technique	NOUN
ejpam-5850	242	4	,	,	PUNCT
ejpam-5850	242	5	pages	page	NOUN
ejpam-5850	242	6	93–126	93–126	PROPN
ejpam-5850	242	7	.	.	PUNCT
ejpam-5850	243	1	academic	academic	ADJ
ejpam-5850	243	2	press	press	NOUN
ejpam-5850	243	3	,	,	PUNCT
ejpam-5850	243	4	1989	1989	NUM
ejpam-5850	243	5	.	.	PUNCT
ejpam-5850	244	1	[	[	X
ejpam-5850	244	2	13	13	NUM
ejpam-5850	244	3	]	]	SYM
ejpam-5850	244	4	alexsander	alexsander	NOUN
ejpam-5850	244	5	andrade	andrade	PROPN
ejpam-5850	244	6	de	de	PROPN
ejpam-5850	244	7	melo	melo	PROPN
ejpam-5850	244	8	and	and	CCONJ
ejpam-5850	244	9	mateus	mateus	PROPN
ejpam-5850	244	10	de	de	PROPN
ejpam-5850	244	11	oliveira	oliveira	PROPN
ejpam-5850	244	12	oliveira	oliveira	PROPN
ejpam-5850	244	13	.	.	PUNCT
ejpam-5850	245	1	second	second	ADJ
ejpam-5850	245	2	-	-	PUNCT
ejpam-5850	245	3	order	order	NOUN
ejpam-5850	245	4	finite	finite	ADJ
ejpam-5850	245	5	automata	automata	NOUN
ejpam-5850	245	6	.	.	PUNCT
ejpam-5850	246	1	theory	theory	NOUN
ejpam-5850	246	2	of	of	ADP
ejpam-5850	246	3	computing	computing	NOUN
ejpam-5850	246	4	systems	system	NOUN
ejpam-5850	246	5	,	,	PUNCT
ejpam-5850	246	6	66(4):861	66(4):861	NUM
ejpam-5850	246	7	–	–	PUNCT
ejpam-5850	246	8	909	909	NUM
ejpam-5850	246	9	,	,	PUNCT
ejpam-5850	246	10	2022	2022	NUM
ejpam-5850	246	11	.	.	PUNCT
ejpam-5850	247	1	[	[	X
ejpam-5850	247	2	14	14	NUM
ejpam-5850	247	3	]	]	X
ejpam-5850	247	4	heinz	heinz	ADJ
ejpam-5850	247	5	-	-	PUNCT
ejpam-5850	247	6	dieter	dieter	NOUN
ejpam-5850	247	7	ebbinghaus	ebbinghaus	NOUN
ejpam-5850	247	8	and	and	CCONJ
ejpam-5850	247	9	jörg	jörg	PROPN
ejpam-5850	247	10	flum	flum	PROPN
ejpam-5850	247	11	.	.	PROPN
ejpam-5850	248	1	finite	finite	PROPN
ejpam-5850	248	2	automata	automata	NOUN
ejpam-5850	248	3	and	and	CCONJ
ejpam-5850	248	4	logic	logic	NOUN
ejpam-5850	248	5	:	:	PUNCT
ejpam-5850	248	6	a	a	DET
ejpam-5850	248	7	microcosm	microcosm	NOUN
ejpam-5850	248	8	of	of	ADP
ejpam-5850	248	9	finite	finite	PROPN
ejpam-5850	248	10	model	model	PROPN
ejpam-5850	248	11	theory	theory	NOUN
ejpam-5850	248	12	,	,	PUNCT
ejpam-5850	248	13	pages	page	NOUN
ejpam-5850	248	14	107–118	107–118	NUM
ejpam-5850	248	15	.	.	PUNCT
ejpam-5850	249	1	springer	springer	PROPN
ejpam-5850	249	2	berlin	berlin	PROPN
ejpam-5850	249	3	heidelberg	heidelberg	PROPN
ejpam-5850	249	4	,	,	PUNCT
ejpam-5850	249	5	1995	1995	NUM
ejpam-5850	249	6	.	.	PUNCT
ejpam-5850	250	1	[	[	X
ejpam-5850	250	2	15	15	NUM
ejpam-5850	250	3	]	]	X
ejpam-5850	250	4	joost	joost	PROPN
ejpam-5850	250	5	engelfriet	engelfriet	PROPN
ejpam-5850	250	6	and	and	CCONJ
ejpam-5850	250	7	jan	jan	PROPN
ejpam-5850	250	8	joris	joris	PROPN
ejpam-5850	250	9	vereijken	vereijken	PROPN
ejpam-5850	250	10	.	.	PUNCT
ejpam-5850	251	1	context	context	NOUN
ejpam-5850	251	2	-	-	PUNCT
ejpam-5850	251	3	free	free	ADJ
ejpam-5850	251	4	graph	graph	NOUN
ejpam-5850	251	5	grammars	grammar	NOUN
ejpam-5850	251	6	and	and	CCONJ
ejpam-5850	251	7	concatenation	concatenation	NOUN
ejpam-5850	251	8	of	of	ADP
ejpam-5850	251	9	graphs	graph	NOUN
ejpam-5850	251	10	.	.	PUNCT
ejpam-5850	252	1	acta	acta	PROPN
ejpam-5850	252	2	informatica	informatica	PROPN
ejpam-5850	252	3	,	,	PUNCT
ejpam-5850	252	4	34:773–803	34:773–803	NUM
ejpam-5850	252	5	,	,	PUNCT
ejpam-5850	252	6	1997	1997	NUM
ejpam-5850	252	7	.	.	PUNCT
ejpam-5850	253	1	[	[	X
ejpam-5850	253	2	16	16	NUM
ejpam-5850	253	3	]	]	X
ejpam-5850	253	4	paul	paul	PROPN
ejpam-5850	253	5	erdős	erdős	PROPN
ejpam-5850	253	6	.	.	PUNCT
ejpam-5850	254	1	graph	graph	NOUN
ejpam-5850	254	2	theory	theory	NOUN
ejpam-5850	254	3	and	and	CCONJ
ejpam-5850	254	4	probability	probability	NOUN
ejpam-5850	254	5	.	.	PUNCT
ejpam-5850	255	1	canadian	canadian	ADJ
ejpam-5850	255	2	journal	journal	PROPN
ejpam-5850	255	3	of	of	ADP
ejpam-5850	255	4	mathematics	mathematic	NOUN
ejpam-5850	255	5	,	,	PUNCT
ejpam-5850	255	6	11:34	11:34	NUM
ejpam-5850	255	7	–	–	PUNCT
ejpam-5850	255	8	38	38	NUM
ejpam-5850	255	9	,	,	PUNCT
ejpam-5850	255	10	1959	1959	NUM
ejpam-5850	255	11	.	.	PUNCT
ejpam-5850	256	1	[	[	X
ejpam-5850	256	2	17	17	NUM
ejpam-5850	256	3	]	]	PUNCT
ejpam-5850	256	4	tibor	tibor	NOUN
ejpam-5850	256	5	gallai	gallai	NOUN
ejpam-5850	256	6	.	.	PUNCT
ejpam-5850	257	1	on	on	ADP
ejpam-5850	257	2	directed	direct	VERB
ejpam-5850	257	3	paths	path	NOUN
ejpam-5850	257	4	and	and	CCONJ
ejpam-5850	257	5	circuits	circuit	NOUN
ejpam-5850	257	6	.	.	PUNCT
ejpam-5850	258	1	in	in	ADP
ejpam-5850	258	2	p.	p.	PROPN
ejpam-5850	258	3	erdös	erdös	PROPN
ejpam-5850	258	4	and	and	CCONJ
ejpam-5850	258	5	g.	g.	PROPN
ejpam-5850	258	6	katona	katona	PROPN
ejpam-5850	258	7	,	,	PUNCT
ejpam-5850	258	8	editors	editor	NOUN
ejpam-5850	258	9	,	,	PUNCT
ejpam-5850	258	10	theory	theory	NOUN
ejpam-5850	258	11	of	of	ADP
ejpam-5850	258	12	graphs	graph	NOUN
ejpam-5850	258	13	,	,	PUNCT
ejpam-5850	258	14	pages	page	NOUN
ejpam-5850	258	15	115–118	115–118	NUM
ejpam-5850	258	16	.	.	PUNCT
ejpam-5850	259	1	academic	academic	ADJ
ejpam-5850	259	2	press	press	NOUN
ejpam-5850	259	3	,	,	PUNCT
ejpam-5850	259	4	new	new	PROPN
ejpam-5850	259	5	york	york	PROPN
ejpam-5850	259	6	,	,	PUNCT
ejpam-5850	259	7	1968	1968	NUM
ejpam-5850	259	8	.	.	PUNCT
ejpam-5850	260	1	[	[	X
ejpam-5850	260	2	18	18	NUM
ejpam-5850	260	3	]	]	X
ejpam-5850	260	4	antonios	antonios	PROPN
ejpam-5850	260	5	kalampakas	kalampakas	PROPN
ejpam-5850	260	6	.	.	PUNCT
ejpam-5850	261	1	the	the	DET
ejpam-5850	261	2	syntactic	syntactic	ADJ
ejpam-5850	261	3	complexity	complexity	NOUN
ejpam-5850	261	4	of	of	ADP
ejpam-5850	261	5	eulerian	eulerian	ADJ
ejpam-5850	261	6	graphs	graph	NOUN
ejpam-5850	261	7	.	.	PUNCT
ejpam-5850	262	1	lecture	lecture	NOUN
ejpam-5850	262	2	notes	note	NOUN
ejpam-5850	262	3	in	in	ADP
ejpam-5850	262	4	computer	computer	NOUN
ejpam-5850	262	5	science	science	NOUN
ejpam-5850	262	6	,	,	PUNCT
ejpam-5850	262	7	4728:208	4728:208	NOUN
ejpam-5850	262	8	–	–	PUNCT
ejpam-5850	262	9	217	217	NUM
ejpam-5850	262	10	,	,	PUNCT
ejpam-5850	262	11	2007	2007	NUM
ejpam-5850	262	12	.	.	PUNCT
ejpam-5850	263	1	[	[	X
ejpam-5850	263	2	19	19	NUM
ejpam-5850	263	3	]	]	X
ejpam-5850	263	4	antonios	antonios	PROPN
ejpam-5850	263	5	kalampakas	kalampakas	PROPN
ejpam-5850	263	6	.	.	PUNCT
ejpam-5850	264	1	graph	graph	NOUN
ejpam-5850	264	2	automata	automata	PROPN
ejpam-5850	264	3	:	:	PUNCT
ejpam-5850	264	4	the	the	DET
ejpam-5850	264	5	algebraic	algebraic	ADJ
ejpam-5850	264	6	properties	property	NOUN
ejpam-5850	264	7	of	of	ADP
ejpam-5850	264	8	abelian	abelian	ADJ
ejpam-5850	264	9	relational	relational	ADJ
ejpam-5850	264	10	graphoids	graphoid	NOUN
ejpam-5850	264	11	.	.	PUNCT
ejpam-5850	265	1	lecture	lecture	NOUN
ejpam-5850	265	2	notes	note	NOUN
ejpam-5850	265	3	in	in	ADP
ejpam-5850	265	4	computer	computer	NOUN
ejpam-5850	265	5	science	science	NOUN
ejpam-5850	265	6	,	,	PUNCT
ejpam-5850	265	7	7020:168–182	7020:168–182	NOUN
ejpam-5850	265	8	,	,	PUNCT
ejpam-5850	265	9	2011	2011	NUM
ejpam-5850	265	10	.	.	PUNCT
ejpam-5850	266	1	[	[	X
ejpam-5850	266	2	20	20	NUM
ejpam-5850	266	3	]	]	X
ejpam-5850	266	4	antonios	antonios	PROPN
ejpam-5850	266	5	kalampakas	kalampakas	PROPN
ejpam-5850	266	6	.	.	PUNCT
ejpam-5850	267	1	graph	graph	NOUN
ejpam-5850	267	2	automata	automata	NOUN
ejpam-5850	267	3	and	and	CCONJ
ejpam-5850	267	4	graph	graph	NOUN
ejpam-5850	267	5	colorability	colorability	NOUN
ejpam-5850	267	6	.	.	PUNCT
ejpam-5850	268	1	european	european	PROPN
ejpam-5850	268	2	journal	journal	PROPN
ejpam-5850	268	3	of	of	ADP
ejpam-5850	268	4	pure	pure	ADJ
ejpam-5850	268	5	and	and	CCONJ
ejpam-5850	268	6	applied	applied	ADJ
ejpam-5850	268	7	mathematics	mathematic	NOUN
ejpam-5850	268	8	,	,	PUNCT
ejpam-5850	268	9	16(1):112–120	16(1):112–120	NUM
ejpam-5850	268	10	,	,	PUNCT
ejpam-5850	268	11	2023	2023	NUM
ejpam-5850	268	12	.	.	PUNCT
ejpam-5850	269	1	[	[	X
ejpam-5850	269	2	21	21	NUM
ejpam-5850	269	3	]	]	X
ejpam-5850	269	4	antonios	antonios	PROPN
ejpam-5850	269	5	kalampakas	kalampakas	PROPN
ejpam-5850	269	6	.	.	PUNCT
ejpam-5850	270	1	wardrop	wardrop	VERB
ejpam-5850	270	2	optimal	optimal	ADJ
ejpam-5850	270	3	networks	network	NOUN
ejpam-5850	270	4	.	.	PUNCT
ejpam-5850	271	1	eur	eur	PROPN
ejpam-5850	271	2	.	.	PUNCT
ejpam-5850	272	1	j.	j.	PROPN
ejpam-5850	272	2	pure	pure	PROPN
ejpam-5850	272	3	appl	appl	PROPN
ejpam-5850	272	4	.	.	PUNCT
ejpam-5850	272	5	math	math	PROPN
ejpam-5850	272	6	.	.	PUNCT
ejpam-5850	273	1	,	,	PUNCT
ejpam-5850	273	2	k.	k.	PROPN
ejpam-5850	273	3	papadopoulos	papadopoulos	PROPN
ejpam-5850	273	4	/	/	SYM
ejpam-5850	273	5	eur	eur	PROPN
ejpam-5850	273	6	.	.	PUNCT
ejpam-5850	274	1	j.	j.	PROPN
ejpam-5850	274	2	pure	pure	PROPN
ejpam-5850	274	3	appl	appl	PROPN
ejpam-5850	274	4	.	.	PROPN
ejpam-5850	274	5	math	math	PROPN
ejpam-5850	274	6	,	,	PUNCT
ejpam-5850	274	7	18	18	NUM
ejpam-5850	274	8	(	(	PUNCT
ejpam-5850	274	9	1	1	NUM
ejpam-5850	274	10	)	)	PUNCT
ejpam-5850	274	11	(	(	PUNCT
ejpam-5850	274	12	2025	2025	NUM
ejpam-5850	274	13	)	)	PUNCT
ejpam-5850	274	14	,	,	PUNCT
ejpam-5850	274	15	5850	5850	NUM
ejpam-5850	274	16	13	13	NUM
ejpam-5850	274	17	of	of	ADP
ejpam-5850	274	18	13	13	NUM
ejpam-5850	274	19	17(4):2448–2466	17(4):2448–2466	NUM
ejpam-5850	274	20	,	,	PUNCT
ejpam-5850	274	21	2024	2024	NUM
ejpam-5850	274	22	.	.	PUNCT
ejpam-5850	275	1	[	[	X
ejpam-5850	275	2	22	22	NUM
ejpam-5850	275	3	]	]	X
ejpam-5850	275	4	antonios	antonios	PROPN
ejpam-5850	275	5	kalampakas	kalampakas	PROPN
ejpam-5850	275	6	,	,	PUNCT
ejpam-5850	275	7	stefanos	stefanos	PROPN
ejpam-5850	275	8	spartalis	spartali	VERB
ejpam-5850	275	9	,	,	PUNCT
ejpam-5850	275	10	and	and	CCONJ
ejpam-5850	275	11	lazaros	lazaro	VERB
ejpam-5850	275	12	iliadis	iliadi	NOUN
ejpam-5850	275	13	.	.	PUNCT
ejpam-5850	276	1	syntactic	syntactic	ADJ
ejpam-5850	276	2	recognizability	recognizability	NOUN
ejpam-5850	276	3	of	of	ADP
ejpam-5850	276	4	graphs	graph	NOUN
ejpam-5850	276	5	with	with	ADP
ejpam-5850	276	6	fuzzy	fuzzy	ADJ
ejpam-5850	276	7	attributes	attribute	NOUN
ejpam-5850	276	8	.	.	PUNCT
ejpam-5850	277	1	fuzzy	fuzzy	ADJ
ejpam-5850	277	2	sets	set	NOUN
ejpam-5850	277	3	and	and	CCONJ
ejpam-5850	277	4	systems	system	NOUN
ejpam-5850	277	5	,	,	PUNCT
ejpam-5850	277	6	229:91–100	229:91–100	NUM
ejpam-5850	277	7	,	,	PUNCT
ejpam-5850	277	8	2013	2013	NUM
ejpam-5850	277	9	.	.	PUNCT
ejpam-5850	278	1	[	[	X
ejpam-5850	278	2	23	23	NUM
ejpam-5850	278	3	]	]	X
ejpam-5850	278	4	antonios	antonios	PROPN
ejpam-5850	278	5	kalampakas	kalampakas	PROPN
ejpam-5850	278	6	,	,	PUNCT
ejpam-5850	278	7	stefanos	stefanos	PROPN
ejpam-5850	278	8	spartalis	spartalis	PROPN
ejpam-5850	278	9	,	,	PUNCT
ejpam-5850	278	10	lazaros	lazaro	VERB
ejpam-5850	278	11	iliadis	iliadi	NOUN
ejpam-5850	278	12	,	,	PUNCT
ejpam-5850	278	13	and	and	CCONJ
ejpam-5850	278	14	elias	elias	PROPN
ejpam-5850	278	15	pimenidis	pimenidi	VERB
ejpam-5850	278	16	.	.	PUNCT
ejpam-5850	279	1	fuzzy	fuzzy	ADJ
ejpam-5850	279	2	graphs	graph	NOUN
ejpam-5850	279	3	:	:	PUNCT
ejpam-5850	279	4	algebraic	algebraic	ADJ
ejpam-5850	279	5	structure	structure	NOUN
ejpam-5850	279	6	and	and	CCONJ
ejpam-5850	279	7	syntactic	syntactic	ADJ
ejpam-5850	279	8	recognition	recognition	NOUN
ejpam-5850	279	9	.	.	PUNCT
ejpam-5850	280	1	artif	artif	INTJ
ejpam-5850	280	2	.	.	PUNCT
ejpam-5850	281	1	intell	intell	PROPN
ejpam-5850	281	2	.	.	PUNCT
ejpam-5850	282	1	rev	rev	PROPN
ejpam-5850	282	2	.	.	PROPN
ejpam-5850	282	3	,	,	PUNCT
ejpam-5850	282	4	42:479–490	42:479–490	NUM
ejpam-5850	282	5	,	,	PUNCT
ejpam-5850	282	6	2014	2014	NUM
ejpam-5850	282	7	.	.	PUNCT
ejpam-5850	283	1	[	[	X
ejpam-5850	283	2	24	24	NUM
ejpam-5850	283	3	]	]	X
ejpam-5850	283	4	chen	chen	PROPN
ejpam-5850	283	5	-	-	PUNCT
ejpam-5850	283	6	yu	yu	PROPN
ejpam-5850	283	7	lin	lin	PROPN
ejpam-5850	283	8	.	.	PUNCT
ejpam-5850	284	1	simple	simple	ADJ
ejpam-5850	284	2	proofs	proof	NOUN
ejpam-5850	284	3	of	of	ADP
ejpam-5850	284	4	results	result	NOUN
ejpam-5850	284	5	on	on	ADP
ejpam-5850	284	6	paths	path	NOUN
ejpam-5850	284	7	representing	represent	VERB
ejpam-5850	284	8	all	all	DET
ejpam-5850	284	9	colors	color	NOUN
ejpam-5850	284	10	in	in	ADP
ejpam-5850	284	11	proper	proper	ADJ
ejpam-5850	284	12	vertex	vertex	NOUN
ejpam-5850	284	13	-	-	PUNCT
ejpam-5850	284	14	colorings	coloring	NOUN
ejpam-5850	284	15	.	.	PUNCT
ejpam-5850	285	1	graphs	graph	NOUN
ejpam-5850	285	2	and	and	CCONJ
ejpam-5850	285	3	combinatorics	combinatoric	NOUN
ejpam-5850	285	4	,	,	PUNCT
ejpam-5850	285	5	23:201–203	23:201–203	NUM
ejpam-5850	285	6	,	,	PUNCT
ejpam-5850	285	7	2007	2007	NUM
ejpam-5850	285	8	.	.	PUNCT
ejpam-5850	286	1	[	[	X
ejpam-5850	286	2	25	25	NUM
ejpam-5850	286	3	]	]	PUNCT
ejpam-5850	286	4	rupkumar	rupkumar	NOUN
ejpam-5850	286	5	mahapatra	mahapatra	PROPN
ejpam-5850	286	6	,	,	PUNCT
ejpam-5850	286	7	sovan	sovan	PROPN
ejpam-5850	286	8	samanta	samanta	PROPN
ejpam-5850	286	9	,	,	PUNCT
ejpam-5850	286	10	madhumangal	madhumangal	ADJ
ejpam-5850	286	11	pal	pal	NOUN
ejpam-5850	286	12	,	,	PUNCT
ejpam-5850	286	13	et	et	PROPN
ejpam-5850	286	14	al	al	PROPN
ejpam-5850	286	15	.	.	PUNCT
ejpam-5850	287	1	a	a	DET
ejpam-5850	287	2	study	study	NOUN
ejpam-5850	287	3	on	on	ADP
ejpam-5850	287	4	linguistic	linguistic	ADJ
ejpam-5850	287	5	z	z	NOUN
ejpam-5850	287	6	-	-	PUNCT
ejpam-5850	287	7	graph	graph	NOUN
ejpam-5850	287	8	and	and	CCONJ
ejpam-5850	287	9	its	its	PRON
ejpam-5850	287	10	application	application	NOUN
ejpam-5850	287	11	in	in	ADP
ejpam-5850	287	12	social	social	ADJ
ejpam-5850	287	13	networks	network	NOUN
ejpam-5850	287	14	.	.	PUNCT
ejpam-5850	288	1	mathematics	mathematic	NOUN
ejpam-5850	288	2	,	,	PUNCT
ejpam-5850	288	3	12(18):2898	12(18):2898	NUM
ejpam-5850	288	4	,	,	PUNCT
ejpam-5850	288	5	2024	2024	NUM
ejpam-5850	288	6	.	.	PUNCT
ejpam-5850	289	1	[	[	X
ejpam-5850	289	2	26	26	NUM
ejpam-5850	289	3	]	]	X
ejpam-5850	289	4	jambi	jambi	PROPN
ejpam-5850	289	5	ratna	ratna	PROPN
ejpam-5850	289	6	raja	raja	PROPN
ejpam-5850	289	7	,	,	PUNCT
ejpam-5850	289	8	jeong	jeong	PROPN
ejpam-5850	289	9	gon	gon	PROPN
ejpam-5850	289	10	lee	lee	PROPN
ejpam-5850	289	11	,	,	PUNCT
ejpam-5850	289	12	dhanraj	dhanraj	ADJ
ejpam-5850	289	13	dhotre	dhotre	NOUN
ejpam-5850	289	14	,	,	PUNCT
ejpam-5850	289	15	et	et	PROPN
ejpam-5850	289	16	al	al	PROPN
ejpam-5850	289	17	.	.	PROPN
ejpam-5850	289	18	fuzzy	fuzzy	ADJ
ejpam-5850	289	19	graphs	graph	NOUN
ejpam-5850	289	20	and	and	CCONJ
ejpam-5850	289	21	their	their	PRON
ejpam-5850	289	22	applications	application	NOUN
ejpam-5850	289	23	in	in	ADP
ejpam-5850	289	24	finding	find	VERB
ejpam-5850	289	25	the	the	DET
ejpam-5850	289	26	best	good	ADJ
ejpam-5850	289	27	route	route	NOUN
ejpam-5850	289	28	,	,	PUNCT
ejpam-5850	289	29	dominant	dominant	ADJ
ejpam-5850	289	30	node	node	NOUN
ejpam-5850	289	31	and	and	CCONJ
ejpam-5850	289	32	influence	influence	NOUN
ejpam-5850	289	33	index	index	NOUN
ejpam-5850	289	34	in	in	ADP
ejpam-5850	289	35	a	a	DET
ejpam-5850	289	36	network	network	NOUN
ejpam-5850	289	37	under	under	ADP
ejpam-5850	289	38	the	the	DET
ejpam-5850	289	39	hesitant	hesitant	ADJ
ejpam-5850	289	40	bipolar	bipolar	ADV
ejpam-5850	289	41	-	-	PUNCT
ejpam-5850	289	42	valued	value	VERB
ejpam-5850	289	43	fuzzy	fuzzy	ADJ
ejpam-5850	289	44	environment	environment	NOUN
ejpam-5850	289	45	.	.	PUNCT
ejpam-5850	290	1	complex	complex	ADJ
ejpam-5850	290	2	&	&	CCONJ
ejpam-5850	290	3	intelligent	intelligent	ADJ
ejpam-5850	290	4	systems	system	NOUN
ejpam-5850	290	5	,	,	PUNCT
ejpam-5850	290	6	10(4):5195–5211	10(4):5195–5211	NUM
ejpam-5850	290	7	,	,	PUNCT
ejpam-5850	290	8	2024	2024	NUM
ejpam-5850	290	9	.	.	PUNCT
ejpam-5850	291	1	[	[	X
ejpam-5850	291	2	27	27	NUM
ejpam-5850	291	3	]	]	X
ejpam-5850	291	4	bernard	bernard	PROPN
ejpam-5850	291	5	roy	roy	PROPN
ejpam-5850	291	6	.	.	PROPN
ejpam-5850	292	1	nombre	nombre	PROPN
ejpam-5850	292	2	chromatique	chromatique	PROPN
ejpam-5850	292	3	et	et	PROPN
ejpam-5850	292	4	plus	plus	CCONJ
ejpam-5850	292	5	longs	long	NOUN
ejpam-5850	292	6	chemins	chemin	VERB
ejpam-5850	292	7	d’un	d’un	NOUN
ejpam-5850	292	8	graph	graph	NOUN
ejpam-5850	292	9	.	.	PUNCT
ejpam-5850	293	1	rev	rev	PROPN
ejpam-5850	293	2	.	.	PROPN
ejpam-5850	293	3	afiro	afiro	PROPN
ejpam-5850	293	4	,	,	PUNCT
ejpam-5850	293	5	1:127–132	1:127–132	PROPN
ejpam-5850	293	6	,	,	PUNCT
ejpam-5850	293	7	1967	1967	NUM
ejpam-5850	293	8	.	.	PUNCT
ejpam-5850	294	1	[	[	X
ejpam-5850	294	2	28	28	NUM
ejpam-5850	294	3	]	]	X
ejpam-5850	294	4	douglas	douglas	PROPN
ejpam-5850	294	5	west	west	PROPN
ejpam-5850	294	6	.	.	PUNCT
ejpam-5850	295	1	introduction	introduction	NOUN
ejpam-5850	295	2	to	to	AUX
ejpam-5850	295	3	graph	graph	NOUN
ejpam-5850	295	4	theory	theory	NOUN
ejpam-5850	295	5	.	.	PUNCT
ejpam-5850	296	1	prentice	prentice	NOUN
ejpam-5850	296	2	-	-	PUNCT
ejpam-5850	296	3	hall	hall	NOUN
ejpam-5850	296	4	,	,	PUNCT
ejpam-5850	296	5	new	new	PROPN
ejpam-5850	296	6	jersey	jersey	PROPN
ejpam-5850	296	7	,	,	PUNCT
ejpam-5850	296	8	1996	1996	NUM
ejpam-5850	296	9	.	.	PUNCT
ejpam-5850	297	1	introduction	introduction	NOUN
ejpam-5850	297	2	magmoids	magmoid	NOUN
ejpam-5850	297	3	and	and	CCONJ
ejpam-5850	297	4	hypergraphs	hypergraph	NOUN
ejpam-5850	297	5	graphoids	graphoid	NOUN
ejpam-5850	297	6	graph	graph	NOUN
ejpam-5850	297	7	automata	automata	NOUN
ejpam-5850	297	8	non	non	ADJ
ejpam-5850	297	9	-	-	ADJ
ejpam-5850	297	10	unitary	unitary	ADJ
ejpam-5850	297	11	abelian	abelian	ADJ
ejpam-5850	297	12	graph	graph	NOUN
ejpam-5850	297	13	automata	automata	NOUN
ejpam-5850	297	14	conclusion	conclusion	NOUN