id	sid	tid	token	lemma	pos
ejpam-4629	1	1	european	european	PROPN
ejpam-4629	1	2	journal	journal	PROPN
ejpam-4629	1	3	of	of	ADP
ejpam-4629	1	4	pure	pure	ADJ
ejpam-4629	1	5	and	and	CCONJ
ejpam-4629	1	6	applied	apply	VERB
ejpam-4629	1	7	mathematics	mathematic	NOUN
ejpam-4629	1	8	vol	vol	NOUN
ejpam-4629	1	9	.	.	PUNCT
ejpam-4629	2	1	16	16	NUM
ejpam-4629	2	2	,	,	PUNCT
ejpam-4629	2	3	no	no	INTJ
ejpam-4629	2	4	.	.	NOUN
ejpam-4629	2	5	1	1	NUM
ejpam-4629	2	6	,	,	PUNCT
ejpam-4629	2	7	2023	2023	NUM
ejpam-4629	2	8	,	,	PUNCT
ejpam-4629	2	9	112	112	NUM
ejpam-4629	2	10	-	-	SYM
ejpam-4629	2	11	120	120	NUM
ejpam-4629	2	12	issn	issn	PROPN
ejpam-4629	2	13	1307	1307	NUM
ejpam-4629	2	14	-	-	SYM
ejpam-4629	2	15	5543	5543	NUM
ejpam-4629	2	16	–	–	PUNCT
ejpam-4629	2	17	ejpam.com	ejpam.com	X
ejpam-4629	2	18	published	publish	VERB
ejpam-4629	2	19	by	by	ADP
ejpam-4629	2	20	new	new	PROPN
ejpam-4629	2	21	york	york	PROPN
ejpam-4629	2	22	business	business	PROPN
ejpam-4629	2	23	global	global	ADJ
ejpam-4629	2	24	graph	graph	NOUN
ejpam-4629	2	25	automata	automata	NOUN
ejpam-4629	2	26	and	and	CCONJ
ejpam-4629	2	27	graph	graph	NOUN
ejpam-4629	2	28	colorability	colorability	NOUN
ejpam-4629	2	29	antonios	antonios	PROPN
ejpam-4629	2	30	kalampakas	kalampakas	PROPN
ejpam-4629	2	31	college	college	PROPN
ejpam-4629	2	32	of	of	ADP
ejpam-4629	2	33	engineering	engineering	NOUN
ejpam-4629	2	34	and	and	CCONJ
ejpam-4629	2	35	technology	technology	NOUN
ejpam-4629	2	36	,	,	PUNCT
ejpam-4629	2	37	american	american	PROPN
ejpam-4629	2	38	university	university	PROPN
ejpam-4629	2	39	of	of	ADP
ejpam-4629	2	40	the	the	DET
ejpam-4629	2	41	middle	middle	PROPN
ejpam-4629	2	42	east	east	PROPN
ejpam-4629	2	43	,	,	PUNCT
ejpam-4629	2	44	kuwait	kuwait	PROPN
ejpam-4629	2	45	abstract	abstract	PROPN
ejpam-4629	2	46	.	.	PUNCT
ejpam-4629	3	1	automata	automata	NOUN
ejpam-4629	3	2	recognizing	recognize	VERB
ejpam-4629	3	3	graphs	graph	NOUN
ejpam-4629	3	4	can	can	AUX
ejpam-4629	3	5	be	be	AUX
ejpam-4629	3	6	constructed	construct	VERB
ejpam-4629	3	7	by	by	ADP
ejpam-4629	3	8	employing	employ	VERB
ejpam-4629	3	9	the	the	DET
ejpam-4629	3	10	algebraic	algebraic	ADJ
ejpam-4629	3	11	structure	structure	NOUN
ejpam-4629	3	12	of	of	ADP
ejpam-4629	3	13	graphoids	graphoid	NOUN
ejpam-4629	3	14	.	.	PUNCT
ejpam-4629	4	1	for	for	ADP
ejpam-4629	4	2	the	the	DET
ejpam-4629	4	3	construction	construction	NOUN
ejpam-4629	4	4	of	of	ADP
ejpam-4629	4	5	a	a	DET
ejpam-4629	4	6	graph	graph	NOUN
ejpam-4629	4	7	automaton	automaton	NOUN
ejpam-4629	4	8	,	,	PUNCT
ejpam-4629	4	9	the	the	DET
ejpam-4629	4	10	relations	relation	NOUN
ejpam-4629	4	11	over	over	ADP
ejpam-4629	4	12	the	the	DET
ejpam-4629	4	13	kleene	kleene	NOUN
ejpam-4629	4	14	star	star	NOUN
ejpam-4629	4	15	of	of	ADP
ejpam-4629	4	16	the	the	DET
ejpam-4629	4	17	state	state	NOUN
ejpam-4629	4	18	set	set	NOUN
ejpam-4629	4	19	must	must	AUX
ejpam-4629	4	20	constitute	constitute	VERB
ejpam-4629	4	21	a	a	DET
ejpam-4629	4	22	graphoid	graphoid	NOUN
ejpam-4629	4	23	.	.	PUNCT
ejpam-4629	5	1	hence	hence	ADV
ejpam-4629	5	2	different	different	ADJ
ejpam-4629	5	3	kinds	kind	NOUN
ejpam-4629	5	4	of	of	ADP
ejpam-4629	5	5	graphoids	graphoid	NOUN
ejpam-4629	5	6	produce	produce	VERB
ejpam-4629	5	7	graph	graph	NOUN
ejpam-4629	5	8	automata	automata	NOUN
ejpam-4629	5	9	with	with	ADP
ejpam-4629	5	10	diverse	diverse	ADJ
ejpam-4629	5	11	operation	operation	NOUN
ejpam-4629	5	12	and	and	CCONJ
ejpam-4629	5	13	recognition	recognition	NOUN
ejpam-4629	5	14	capacity	capacity	NOUN
ejpam-4629	5	15	.	.	PUNCT
ejpam-4629	6	1	in	in	ADP
ejpam-4629	6	2	this	this	DET
ejpam-4629	6	3	paper	paper	NOUN
ejpam-4629	6	4	we	we	PRON
ejpam-4629	6	5	show	show	VERB
ejpam-4629	6	6	that	that	SCONJ
ejpam-4629	6	7	graph	graph	NOUN
ejpam-4629	6	8	colorability	colorability	NOUN
ejpam-4629	6	9	is	be	AUX
ejpam-4629	6	10	recognized	recognize	VERB
ejpam-4629	6	11	by	by	ADP
ejpam-4629	6	12	automata	automata	NOUN
ejpam-4629	6	13	operating	operate	VERB
ejpam-4629	6	14	over	over	ADP
ejpam-4629	6	15	the	the	DET
ejpam-4629	6	16	simplest	simple	ADJ
ejpam-4629	6	17	possible	possible	ADJ
ejpam-4629	6	18	abelian	abelian	ADJ
ejpam-4629	6	19	graphoid	graphoid	NOUN
ejpam-4629	6	20	.	.	PUNCT
ejpam-4629	7	1	2020	2020	NUM
ejpam-4629	7	2	mathematics	mathematic	NOUN
ejpam-4629	7	3	subject	subject	NOUN
ejpam-4629	7	4	classifications	classification	NOUN
ejpam-4629	7	5	:	:	PUNCT
ejpam-4629	7	6	68r10,68q45	68r10,68q45	NOUN
ejpam-4629	7	7	,	,	PUNCT
ejpam-4629	7	8	68q70	68q70	NUM
ejpam-4629	7	9	key	key	ADJ
ejpam-4629	7	10	words	word	NOUN
ejpam-4629	7	11	and	and	CCONJ
ejpam-4629	7	12	phrases	phrase	NOUN
ejpam-4629	7	13	:	:	PUNCT
ejpam-4629	7	14	graph	graph	NOUN
ejpam-4629	7	15	theory	theory	NOUN
ejpam-4629	7	16	,	,	PUNCT
ejpam-4629	7	17	graph	graph	NOUN
ejpam-4629	7	18	automata	automata	NOUN
ejpam-4629	7	19	,	,	PUNCT
ejpam-4629	7	20	graph	graph	NOUN
ejpam-4629	7	21	colorability	colorability	NOUN
ejpam-4629	7	22	1	1	NUM
ejpam-4629	7	23	.	.	PUNCT
ejpam-4629	8	1	introduction	introduction	NOUN
ejpam-4629	8	2	automata	automata	NOUN
ejpam-4629	8	3	on	on	ADP
ejpam-4629	8	4	general	general	ADJ
ejpam-4629	8	5	(	(	PUNCT
ejpam-4629	8	6	hyper)graphs	hyper)graph	NOUN
ejpam-4629	8	7	were	be	AUX
ejpam-4629	8	8	constructed	construct	VERB
ejpam-4629	8	9	for	for	ADP
ejpam-4629	8	10	the	the	DET
ejpam-4629	8	11	first	first	ADJ
ejpam-4629	8	12	time	time	NOUN
ejpam-4629	8	13	in	in	ADP
ejpam-4629	8	14	[	[	X
ejpam-4629	8	15	5	5	NUM
ejpam-4629	8	16	]	]	PUNCT
ejpam-4629	8	17	by	by	ADP
ejpam-4629	8	18	utilizing	utilize	VERB
ejpam-4629	8	19	the	the	DET
ejpam-4629	8	20	algebraic	algebraic	ADJ
ejpam-4629	8	21	properties	property	NOUN
ejpam-4629	8	22	of	of	ADP
ejpam-4629	8	23	graphoids	graphoid	NOUN
ejpam-4629	8	24	,	,	PUNCT
ejpam-4629	8	25	i.e.	i.e.	X
ejpam-4629	8	26	,	,	PUNCT
ejpam-4629	8	27	magmoids	magmoid	NOUN
ejpam-4629	8	28	satisfying	satisfy	VERB
ejpam-4629	8	29	the	the	DET
ejpam-4629	8	30	15	15	NUM
ejpam-4629	8	31	equations	equation	NOUN
ejpam-4629	8	32	of	of	ADP
ejpam-4629	8	33	graphs	graph	NOUN
ejpam-4629	8	34	which	which	PRON
ejpam-4629	8	35	are	be	AUX
ejpam-4629	8	36	specified	specify	VERB
ejpam-4629	8	37	in	in	ADP
ejpam-4629	8	38	[	[	X
ejpam-4629	8	39	2	2	NUM
ejpam-4629	8	40	]	]	PUNCT
ejpam-4629	8	41	.	.	PUNCT
ejpam-4629	9	1	the	the	DET
ejpam-4629	9	2	notion	notion	NOUN
ejpam-4629	9	3	of	of	ADP
ejpam-4629	9	4	magmoids	magmoid	NOUN
ejpam-4629	9	5	,	,	PUNCT
ejpam-4629	9	6	introduced	introduce	VERB
ejpam-4629	9	7	by	by	ADP
ejpam-4629	9	8	arnold	arnold	PROPN
ejpam-4629	9	9	and	and	CCONJ
ejpam-4629	9	10	dauchet	dauchet	VERB
ejpam-4629	9	11	in	in	ADP
ejpam-4629	9	12	[	[	X
ejpam-4629	9	13	1	1	NUM
ejpam-4629	9	14	]	]	PUNCT
ejpam-4629	9	15	,	,	PUNCT
ejpam-4629	9	16	is	be	AUX
ejpam-4629	9	17	the	the	DET
ejpam-4629	9	18	algebraic	algebraic	ADJ
ejpam-4629	9	19	structure	structure	NOUN
ejpam-4629	9	20	employed	employ	VERB
ejpam-4629	9	21	to	to	PART
ejpam-4629	9	22	generate	generate	VERB
ejpam-4629	9	23	graphs	graph	NOUN
ejpam-4629	9	24	from	from	ADP
ejpam-4629	9	25	a	a	DET
ejpam-4629	9	26	finite	finite	NOUN
ejpam-4629	9	27	set	set	VERB
ejpam-4629	9	28	in	in	ADP
ejpam-4629	9	29	a	a	DET
ejpam-4629	9	30	role	role	NOUN
ejpam-4629	9	31	similar	similar	ADJ
ejpam-4629	9	32	to	to	ADP
ejpam-4629	9	33	that	that	PRON
ejpam-4629	9	34	of	of	ADP
ejpam-4629	9	35	monoids	monoid	NOUN
ejpam-4629	9	36	for	for	ADP
ejpam-4629	9	37	the	the	DET
ejpam-4629	9	38	generation	generation	NOUN
ejpam-4629	9	39	of	of	ADP
ejpam-4629	9	40	strings	string	NOUN
ejpam-4629	9	41	.	.	PUNCT
ejpam-4629	10	1	a	a	DET
ejpam-4629	10	2	magmoid	magmoid	NOUN
ejpam-4629	10	3	is	be	AUX
ejpam-4629	10	4	a	a	DET
ejpam-4629	10	5	doubly	doubly	ADV
ejpam-4629	10	6	ranked	rank	VERB
ejpam-4629	10	7	set	set	NOUN
ejpam-4629	10	8	equipped	equip	VERB
ejpam-4629	10	9	with	with	ADP
ejpam-4629	10	10	two	two	NUM
ejpam-4629	10	11	operations	operation	NOUN
ejpam-4629	10	12	which	which	PRON
ejpam-4629	10	13	are	be	AUX
ejpam-4629	10	14	associative	associative	ADJ
ejpam-4629	10	15	,	,	PUNCT
ejpam-4629	10	16	unitary	unitary	ADJ
ejpam-4629	10	17	and	and	CCONJ
ejpam-4629	10	18	mutually	mutually	ADV
ejpam-4629	10	19	coherent	coherent	ADJ
ejpam-4629	10	20	in	in	ADP
ejpam-4629	10	21	a	a	DET
ejpam-4629	10	22	canonical	canonical	ADJ
ejpam-4629	10	23	way	way	NOUN
ejpam-4629	10	24	(	(	PUNCT
ejpam-4629	10	25	cf	cf	NOUN
ejpam-4629	10	26	.	.	PUNCT
ejpam-4629	11	1	[	[	X
ejpam-4629	11	2	4	4	X
ejpam-4629	11	3	]	]	PUNCT
ejpam-4629	11	4	and	and	CCONJ
ejpam-4629	11	5	[	[	X
ejpam-4629	11	6	6	6	NUM
ejpam-4629	11	7	]	]	PUNCT
ejpam-4629	11	8	)	)	PUNCT
ejpam-4629	11	9	.	.	PUNCT
ejpam-4629	12	1	in	in	ADP
ejpam-4629	12	2	[	[	X
ejpam-4629	12	3	7	7	NUM
ejpam-4629	12	4	]	]	X
ejpam-4629	12	5	engelfriet	engelfriet	NOUN
ejpam-4629	12	6	and	and	CCONJ
ejpam-4629	12	7	vereijken	vereijken	VERB
ejpam-4629	12	8	proved	prove	VERB
ejpam-4629	12	9	that	that	SCONJ
ejpam-4629	12	10	every	every	DET
ejpam-4629	12	11	graph	graph	NOUN
ejpam-4629	12	12	with	with	ADP
ejpam-4629	12	13	edges	edge	NOUN
ejpam-4629	12	14	labeled	label	VERB
ejpam-4629	12	15	over	over	ADP
ejpam-4629	12	16	a	a	DET
ejpam-4629	12	17	finite	finite	NOUN
ejpam-4629	12	18	doubly	doubly	ADV
ejpam-4629	12	19	ranked	rank	VERB
ejpam-4629	12	20	set	set	ADJ
ejpam-4629	12	21	σ	σ	NOUN
ejpam-4629	12	22	can	can	AUX
ejpam-4629	12	23	be	be	AUX
ejpam-4629	12	24	built	build	VERB
ejpam-4629	12	25	from	from	ADP
ejpam-4629	12	26	a	a	DET
ejpam-4629	12	27	specific	specific	ADJ
ejpam-4629	12	28	finite	finite	NOUN
ejpam-4629	12	29	set	set	NOUN
ejpam-4629	12	30	of	of	ADP
ejpam-4629	12	31	elementary	elementary	ADJ
ejpam-4629	12	32	graphs	graph	NOUN
ejpam-4629	12	33	d	d	NOUN
ejpam-4629	12	34	,	,	PUNCT
ejpam-4629	12	35	together	together	ADV
ejpam-4629	12	36	with	with	ADP
ejpam-4629	12	37	the	the	DET
ejpam-4629	12	38	elements	element	NOUN
ejpam-4629	12	39	of	of	ADP
ejpam-4629	12	40	σ	σ	PROPN
ejpam-4629	12	41	,	,	PUNCT
ejpam-4629	12	42	by	by	ADP
ejpam-4629	12	43	using	use	VERB
ejpam-4629	12	44	the	the	DET
ejpam-4629	12	45	operations	operation	NOUN
ejpam-4629	12	46	of	of	ADP
ejpam-4629	12	47	graph	graph	NOUN
ejpam-4629	12	48	product	product	NOUN
ejpam-4629	12	49	and	and	CCONJ
ejpam-4629	12	50	graph	graph	NOUN
ejpam-4629	12	51	sum	sum	NOUN
ejpam-4629	12	52	.	.	PUNCT
ejpam-4629	13	1	from	from	ADP
ejpam-4629	13	2	this	this	DET
ejpam-4629	13	3	result	result	NOUN
ejpam-4629	13	4	it	it	PRON
ejpam-4629	13	5	is	be	AUX
ejpam-4629	13	6	derived	derive	VERB
ejpam-4629	13	7	that	that	SCONJ
ejpam-4629	13	8	graphs	graph	NOUN
ejpam-4629	13	9	can	can	AUX
ejpam-4629	13	10	be	be	AUX
ejpam-4629	13	11	organized	organize	VERB
ejpam-4629	13	12	into	into	ADP
ejpam-4629	13	13	a	a	DET
ejpam-4629	13	14	magmoid	magmoid	NOUN
ejpam-4629	13	15	with	with	ADP
ejpam-4629	13	16	operations	operation	NOUN
ejpam-4629	13	17	product	product	NOUN
ejpam-4629	13	18	and	and	CCONJ
ejpam-4629	13	19	sum	sum	NOUN
ejpam-4629	13	20	.	.	PUNCT
ejpam-4629	14	1	although	although	SCONJ
ejpam-4629	14	2	,	,	PUNCT
ejpam-4629	14	3	as	as	SCONJ
ejpam-4629	14	4	it	it	PRON
ejpam-4629	14	5	was	be	AUX
ejpam-4629	14	6	observed	observe	VERB
ejpam-4629	14	7	in	in	ADP
ejpam-4629	14	8	[	[	X
ejpam-4629	14	9	7	7	NUM
ejpam-4629	14	10	]	]	PUNCT
ejpam-4629	14	11	,	,	PUNCT
ejpam-4629	14	12	every	every	DET
ejpam-4629	14	13	hypergraph	hypergraph	NOUN
ejpam-4629	14	14	can	can	AUX
ejpam-4629	14	15	be	be	AUX
ejpam-4629	14	16	constructed	construct	VERB
ejpam-4629	14	17	in	in	ADP
ejpam-4629	14	18	an	an	DET
ejpam-4629	14	19	infinite	infinite	ADJ
ejpam-4629	14	20	number	number	NOUN
ejpam-4629	14	21	of	of	ADP
ejpam-4629	14	22	ways	way	NOUN
ejpam-4629	14	23	,	,	PUNCT
ejpam-4629	14	24	this	this	DET
ejpam-4629	14	25	ambiguity	ambiguity	NOUN
ejpam-4629	14	26	was	be	AUX
ejpam-4629	14	27	settled	settle	VERB
ejpam-4629	14	28	in	in	ADP
ejpam-4629	14	29	[	[	X
ejpam-4629	14	30	2	2	NUM
ejpam-4629	14	31	]	]	PUNCT
ejpam-4629	14	32	(	(	PUNCT
ejpam-4629	14	33	see	see	VERB
ejpam-4629	14	34	also	also	ADV
ejpam-4629	14	35	[	[	X
ejpam-4629	14	36	3	3	NUM
ejpam-4629	14	37	]	]	PUNCT
ejpam-4629	14	38	)	)	PUNCT
ejpam-4629	14	39	by	by	ADP
ejpam-4629	14	40	determining	determine	VERB
ejpam-4629	14	41	a	a	DET
ejpam-4629	14	42	finite	finite	ADJ
ejpam-4629	14	43	set	set	NOUN
ejpam-4629	14	44	of	of	ADP
ejpam-4629	14	45	equations	equation	NOUN
ejpam-4629	14	46	e	e	X
ejpam-4629	14	47	with	with	ADP
ejpam-4629	14	48	the	the	DET
ejpam-4629	14	49	property	property	NOUN
ejpam-4629	14	50	that	that	PRON
ejpam-4629	14	51	two	two	NUM
ejpam-4629	14	52	expressions	expression	NOUN
ejpam-4629	14	53	represent	represent	VERB
ejpam-4629	14	54	the	the	DET
ejpam-4629	14	55	same	same	ADJ
ejpam-4629	14	56	hypergraph	hypergraph	NOUN
ejpam-4629	14	57	,	,	PUNCT
ejpam-4629	14	58	if	if	SCONJ
ejpam-4629	14	59	and	and	CCONJ
ejpam-4629	14	60	only	only	ADV
ejpam-4629	14	61	if	if	SCONJ
ejpam-4629	14	62	,	,	PUNCT
ejpam-4629	14	63	one	one	PRON
ejpam-4629	14	64	can	can	AUX
ejpam-4629	14	65	be	be	AUX
ejpam-4629	14	66	transformed	transform	VERB
ejpam-4629	14	67	into	into	ADP
ejpam-4629	14	68	the	the	DET
ejpam-4629	14	69	other	other	ADJ
ejpam-4629	14	70	through	through	ADP
ejpam-4629	14	71	them	they	PRON
ejpam-4629	14	72	.	.	PUNCT
ejpam-4629	15	1	commencing	commence	VERB
ejpam-4629	15	2	from	from	ADP
ejpam-4629	15	3	this	this	DET
ejpam-4629	15	4	result	result	NOUN
ejpam-4629	15	5	,	,	PUNCT
ejpam-4629	15	6	a	a	DET
ejpam-4629	15	7	graphoid	graphoid	NOUN
ejpam-4629	15	8	m	m	VERB
ejpam-4629	15	9	is	be	AUX
ejpam-4629	15	10	defined	define	VERB
ejpam-4629	15	11	as	as	ADP
ejpam-4629	15	12	a	a	DET
ejpam-4629	15	13	magmoid	magmoid	NOUN
ejpam-4629	15	14	with	with	ADP
ejpam-4629	15	15	a	a	DET
ejpam-4629	15	16	designated	designate	VERB
ejpam-4629	15	17	set	set	NOUN
ejpam-4629	15	18	of	of	ADP
ejpam-4629	15	19	elements	element	NOUN
ejpam-4629	15	20	that	that	PRON
ejpam-4629	15	21	satisfy	satisfy	VERB
ejpam-4629	15	22	the	the	DET
ejpam-4629	15	23	equations	equation	NOUN
ejpam-4629	15	24	e	e	X
ejpam-4629	15	25	.	.	PUNCT
ejpam-4629	16	1	hence	hence	ADV
ejpam-4629	16	2	gr(σ	gr(σ	NOUN
ejpam-4629	16	3	)	)	PUNCT
ejpam-4629	16	4	can	can	AUX
ejpam-4629	16	5	be	be	AUX
ejpam-4629	16	6	structured	structure	VERB
ejpam-4629	16	7	into	into	ADP
ejpam-4629	16	8	a	a	DET
ejpam-4629	16	9	graphoid	graphoid	NOUN
ejpam-4629	16	10	by	by	ADP
ejpam-4629	16	11	virtue	virtue	NOUN
ejpam-4629	16	12	of	of	ADP
ejpam-4629	16	13	the	the	DET
ejpam-4629	16	14	set	set	PROPN
ejpam-4629	16	15	d	d	PROPN
ejpam-4629	16	16	of	of	ADP
ejpam-4629	16	17	elementary	elementary	ADJ
ejpam-4629	16	18	graphs	graph	NOUN
ejpam-4629	16	19	.	.	PUNCT
ejpam-4629	17	1	the	the	DET
ejpam-4629	17	2	relational	relational	ADJ
ejpam-4629	17	3	magmoid	magmoid	NOUN
ejpam-4629	17	4	over	over	ADP
ejpam-4629	17	5	a	a	DET
ejpam-4629	17	6	set	set	NOUN
ejpam-4629	17	7	q	q	NOUN
ejpam-4629	17	8	is	be	AUX
ejpam-4629	17	9	constructed	construct	VERB
ejpam-4629	17	10	by	by	ADP
ejpam-4629	17	11	defining	define	VERB
ejpam-4629	17	12	the	the	DET
ejpam-4629	17	13	operations	operation	NOUN
ejpam-4629	17	14	of	of	ADP
ejpam-4629	17	15	composition	composition	NOUN
ejpam-4629	17	16	and	and	CCONJ
ejpam-4629	17	17	sum	sum	NOUN
ejpam-4629	17	18	on	on	ADP
ejpam-4629	17	19	the	the	DET
ejpam-4629	17	20	set	set	NOUN
ejpam-4629	17	21	of	of	ADP
ejpam-4629	17	22	relations	relation	NOUN
ejpam-4629	17	23	doi	doi	NOUN
ejpam-4629	17	24	:	:	PUNCT
ejpam-4629	17	25	https://doi.org/10.29020/nybg.ejpam.v16i1.4629	https://doi.org/10.29020/nybg.ejpam.v16i1.4629	X
ejpam-4629	17	26	email	email	NOUN
ejpam-4629	17	27	addresses	address	VERB
ejpam-4629	17	28	:	:	PUNCT
ejpam-4629	17	29	antonios.kalampakas@aum.edu.kw	antonios.kalampakas@aum.edu.kw	PRON
ejpam-4629	17	30	(	(	PUNCT
ejpam-4629	17	31	a.	a.	PROPN
ejpam-4629	17	32	kalampakas	kalampakas	PROPN
ejpam-4629	17	33	)	)	PUNCT
ejpam-4629	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4629	18	1	112	112	NUM
ejpam-4629	18	2	©	©	PROPN
ejpam-4629	18	3	2023	2023	NUM
ejpam-4629	18	4	ejpam	ejpam	NOUN
ejpam-4629	18	5	all	all	DET
ejpam-4629	18	6	rights	right	NOUN
ejpam-4629	18	7	reserved	reserve	VERB
ejpam-4629	18	8	.	.	PUNCT
ejpam-4629	19	1	a.	a.	PROPN
ejpam-4629	19	2	kalampakas	kalampakas	PROPN
ejpam-4629	19	3	/	/	SYM
ejpam-4629	19	4	eur	eur	PROPN
ejpam-4629	19	5	.	.	PUNCT
ejpam-4629	20	1	j.	j.	PROPN
ejpam-4629	20	2	pure	pure	PROPN
ejpam-4629	20	3	appl	appl	PROPN
ejpam-4629	20	4	.	.	PROPN
ejpam-4629	20	5	math	math	PROPN
ejpam-4629	20	6	,	,	PUNCT
ejpam-4629	20	7	16	16	NUM
ejpam-4629	20	8	(	(	PUNCT
ejpam-4629	20	9	1	1	NUM
ejpam-4629	20	10	)	)	PUNCT
ejpam-4629	20	11	(	(	PUNCT
ejpam-4629	20	12	2023	2023	NUM
ejpam-4629	20	13	)	)	PUNCT
ejpam-4629	20	14	,	,	PUNCT
ejpam-4629	20	15	112	112	NUM
ejpam-4629	20	16	-	-	SYM
ejpam-4629	20	17	120	120	NUM
ejpam-4629	20	18	113	113	NUM
ejpam-4629	20	19	from	from	ADP
ejpam-4629	20	20	qm	qm	PROPN
ejpam-4629	20	21	to	to	PART
ejpam-4629	20	22	qn	qn	PROPN
ejpam-4629	20	23	.	.	PUNCT
ejpam-4629	21	1	this	this	DET
ejpam-4629	21	2	set	set	NOUN
ejpam-4629	21	3	is	be	AUX
ejpam-4629	21	4	structured	structure	VERB
ejpam-4629	21	5	into	into	ADP
ejpam-4629	21	6	a	a	DET
ejpam-4629	21	7	relational	relational	ADJ
ejpam-4629	21	8	graphoid	graphoid	NOUN
ejpam-4629	21	9	over	over	ADP
ejpam-4629	21	10	q	q	PROPN
ejpam-4629	21	11	,	,	PUNCT
ejpam-4629	21	12	by	by	ADP
ejpam-4629	21	13	specifying	specify	VERB
ejpam-4629	21	14	a	a	DET
ejpam-4629	21	15	set	set	ADJ
ejpam-4629	21	16	d	d	PROPN
ejpam-4629	21	17	of	of	ADP
ejpam-4629	21	18	relations	relation	NOUN
ejpam-4629	21	19	that	that	PRON
ejpam-4629	21	20	satisfy	satisfy	VERB
ejpam-4629	21	21	the	the	DET
ejpam-4629	21	22	equations	equation	NOUN
ejpam-4629	21	23	e	e	X
ejpam-4629	21	24	.	.	PUNCT
ejpam-4629	22	1	a	a	DET
ejpam-4629	22	2	relational	relational	ADJ
ejpam-4629	22	3	graphoid	graphoid	NOUN
ejpam-4629	22	4	is	be	AUX
ejpam-4629	22	5	called	call	VERB
ejpam-4629	22	6	abelian	abelian	ADJ
ejpam-4629	22	7	when	when	SCONJ
ejpam-4629	22	8	a	a	DET
ejpam-4629	22	9	particular	particular	ADJ
ejpam-4629	22	10	relation	relation	NOUN
ejpam-4629	22	11	of	of	ADP
ejpam-4629	22	12	d	d	PROPN
ejpam-4629	22	13	consists	consist	VERB
ejpam-4629	22	14	of	of	ADP
ejpam-4629	22	15	all	all	DET
ejpam-4629	22	16	the	the	DET
ejpam-4629	22	17	transpositions	transposition	NOUN
ejpam-4629	22	18	in	in	ADP
ejpam-4629	22	19	q.	q.	NOUN
ejpam-4629	22	20	in	in	ADP
ejpam-4629	22	21	[	[	X
ejpam-4629	22	22	5	5	NUM
ejpam-4629	22	23	]	]	PUNCT
ejpam-4629	22	24	graph	graph	NOUN
ejpam-4629	22	25	automata	automata	NOUN
ejpam-4629	22	26	,	,	PUNCT
ejpam-4629	22	27	with	with	ADP
ejpam-4629	22	28	state	state	NOUN
ejpam-4629	22	29	set	set	NOUN
ejpam-4629	22	30	q	q	PROPN
ejpam-4629	22	31	,	,	PUNCT
ejpam-4629	22	32	were	be	AUX
ejpam-4629	22	33	introduced	introduce	VERB
ejpam-4629	22	34	by	by	ADP
ejpam-4629	22	35	virtue	virtue	NOUN
ejpam-4629	22	36	of	of	ADP
ejpam-4629	22	37	a	a	DET
ejpam-4629	22	38	specific	specific	ADJ
ejpam-4629	22	39	abelian	abelian	ADJ
ejpam-4629	22	40	relational	relational	ADJ
ejpam-4629	22	41	graphoid	graphoid	NOUN
ejpam-4629	22	42	,	,	PUNCT
ejpam-4629	22	43	denoted	denote	VERB
ejpam-4629	22	44	here	here	ADV
ejpam-4629	22	45	by	by	ADP
ejpam-4629	22	46	tsrel(q	tsrel(q	NOUN
ejpam-4629	22	47	)	)	PUNCT
ejpam-4629	22	48	,	,	PUNCT
ejpam-4629	22	49	and	and	CCONJ
ejpam-4629	22	50	by	by	ADP
ejpam-4629	22	51	exploiting	exploit	VERB
ejpam-4629	22	52	the	the	DET
ejpam-4629	22	53	fact	fact	NOUN
ejpam-4629	22	54	that	that	SCONJ
ejpam-4629	22	55	gr(σ	gr(σ	NOUN
ejpam-4629	22	56	)	)	PUNCT
ejpam-4629	22	57	is	be	AUX
ejpam-4629	22	58	the	the	DET
ejpam-4629	22	59	free	free	ADJ
ejpam-4629	22	60	graphoid	graphoid	NOUN
ejpam-4629	22	61	generated	generate	VERB
ejpam-4629	22	62	by	by	ADP
ejpam-4629	22	63	σ	σ	PROPN
ejpam-4629	22	64	.	.	PROPN
ejpam-4629	23	1	in	in	ADP
ejpam-4629	23	2	the	the	DET
ejpam-4629	23	3	same	same	ADJ
ejpam-4629	23	4	paper	paper	NOUN
ejpam-4629	23	5	it	it	PRON
ejpam-4629	23	6	is	be	AUX
ejpam-4629	23	7	postulated	postulate	VERB
ejpam-4629	23	8	that	that	SCONJ
ejpam-4629	23	9	different	different	ADJ
ejpam-4629	23	10	kinds	kind	NOUN
ejpam-4629	23	11	of	of	ADP
ejpam-4629	23	12	graphoids	graphoid	NOUN
ejpam-4629	23	13	will	will	AUX
ejpam-4629	23	14	produce	produce	VERB
ejpam-4629	23	15	graph	graph	NOUN
ejpam-4629	23	16	automata	automata	NOUN
ejpam-4629	23	17	with	with	ADP
ejpam-4629	23	18	diverse	diverse	ADJ
ejpam-4629	23	19	operation	operation	NOUN
ejpam-4629	23	20	and	and	CCONJ
ejpam-4629	23	21	recognition	recognition	NOUN
ejpam-4629	23	22	capacity	capacity	NOUN
ejpam-4629	23	23	.	.	PUNCT
ejpam-4629	24	1	in	in	ADP
ejpam-4629	24	2	[	[	X
ejpam-4629	24	3	8	8	NUM
ejpam-4629	24	4	]	]	X
ejpam-4629	24	5	it	it	PRON
ejpam-4629	24	6	is	be	AUX
ejpam-4629	24	7	shown	show	VERB
ejpam-4629	24	8	that	that	SCONJ
ejpam-4629	24	9	all	all	DET
ejpam-4629	24	10	abelian	abelian	ADJ
ejpam-4629	24	11	relational	relational	ADJ
ejpam-4629	24	12	graphoids	graphoid	NOUN
ejpam-4629	24	13	are	be	AUX
ejpam-4629	24	14	characterized	characterize	VERB
ejpam-4629	24	15	in	in	ADP
ejpam-4629	24	16	the	the	DET
ejpam-4629	24	17	following	following	ADJ
ejpam-4629	24	18	way	way	NOUN
ejpam-4629	24	19	:	:	PUNCT
ejpam-4629	24	20	a	a	DET
ejpam-4629	24	21	set	set	NOUN
ejpam-4629	24	22	q	q	PUNCT
ejpam-4629	24	23	generates	generate	VERB
ejpam-4629	24	24	an	an	DET
ejpam-4629	24	25	abelian	abelian	ADJ
ejpam-4629	24	26	relational	relational	NOUN
ejpam-4629	24	27	graphoid	graphoid	NOUN
ejpam-4629	24	28	if	if	SCONJ
ejpam-4629	25	1	and	and	CCONJ
ejpam-4629	25	2	only	only	ADV
ejpam-4629	25	3	if	if	SCONJ
ejpam-4629	25	4	q	q	NOUN
ejpam-4629	25	5	is	be	AUX
ejpam-4629	25	6	partitioned	partition	VERB
ejpam-4629	25	7	into	into	ADP
ejpam-4629	25	8	disjoint	disjoint	NOUN
ejpam-4629	25	9	abelian	abelian	ADJ
ejpam-4629	25	10	groups	group	NOUN
ejpam-4629	25	11	with	with	ADP
ejpam-4629	25	12	operations	operation	NOUN
ejpam-4629	25	13	univocally	univocally	ADV
ejpam-4629	25	14	correlated	correlate	VERB
ejpam-4629	25	15	with	with	ADP
ejpam-4629	25	16	d.	d.	PROPN
ejpam-4629	25	17	in	in	ADP
ejpam-4629	25	18	other	other	ADJ
ejpam-4629	25	19	words	word	NOUN
ejpam-4629	25	20	it	it	PRON
ejpam-4629	25	21	is	be	AUX
ejpam-4629	25	22	proved	prove	VERB
ejpam-4629	25	23	that	that	SCONJ
ejpam-4629	25	24	organizing	organize	VERB
ejpam-4629	25	25	rel(q	rel(q	NOUN
ejpam-4629	25	26	)	)	PUNCT
ejpam-4629	25	27	in	in	ADP
ejpam-4629	25	28	a	a	DET
ejpam-4629	25	29	relational	relational	ADJ
ejpam-4629	25	30	graphoid	graphoid	NOUN
ejpam-4629	25	31	is	be	AUX
ejpam-4629	25	32	equivalent	equivalent	ADJ
ejpam-4629	25	33	to	to	ADP
ejpam-4629	25	34	partitioning	partition	VERB
ejpam-4629	25	35	the	the	DET
ejpam-4629	25	36	set	set	NOUN
ejpam-4629	25	37	q	q	NOUN
ejpam-4629	25	38	and	and	CCONJ
ejpam-4629	25	39	structuring	structure	VERB
ejpam-4629	25	40	every	every	DET
ejpam-4629	25	41	class	class	NOUN
ejpam-4629	25	42	in	in	ADP
ejpam-4629	25	43	a	a	DET
ejpam-4629	25	44	group	group	NOUN
ejpam-4629	25	45	.	.	PUNCT
ejpam-4629	26	1	the	the	DET
ejpam-4629	26	2	particular	particular	ADJ
ejpam-4629	26	3	graphoid	graphoid	NOUN
ejpam-4629	26	4	tsrel(q	tsrel(q	NOUN
ejpam-4629	26	5	)	)	PUNCT
ejpam-4629	26	6	employed	employ	VERB
ejpam-4629	26	7	in	in	ADP
ejpam-4629	26	8	[	[	X
ejpam-4629	26	9	5	5	NUM
ejpam-4629	26	10	]	]	PUNCT
ejpam-4629	26	11	corresponds	correspond	VERB
ejpam-4629	26	12	to	to	ADP
ejpam-4629	26	13	the	the	DET
ejpam-4629	26	14	partitioning	partitioning	NOUN
ejpam-4629	26	15	of	of	ADP
ejpam-4629	26	16	q	q	PUNCT
ejpam-4629	26	17	into	into	ADP
ejpam-4629	26	18	singleton	singleton	NOUN
ejpam-4629	26	19	sets	set	VERB
ejpam-4629	26	20	each	each	DET
ejpam-4629	26	21	one	one	NOUN
ejpam-4629	26	22	being	be	AUX
ejpam-4629	26	23	the	the	DET
ejpam-4629	26	24	trivial	trivial	ADJ
ejpam-4629	26	25	group	group	NOUN
ejpam-4629	26	26	.	.	PUNCT
ejpam-4629	27	1	hence	hence	ADV
ejpam-4629	27	2	,	,	PUNCT
ejpam-4629	27	3	due	due	ADP
ejpam-4629	27	4	to	to	ADP
ejpam-4629	27	5	[	[	PUNCT
ejpam-4629	27	6	8	8	NUM
ejpam-4629	27	7	]	]	PUNCT
ejpam-4629	27	8	,	,	PUNCT
ejpam-4629	27	9	it	it	PRON
ejpam-4629	27	10	is	be	AUX
ejpam-4629	27	11	the	the	DET
ejpam-4629	27	12	simplest	simple	ADJ
ejpam-4629	27	13	possible	possible	ADJ
ejpam-4629	27	14	abelian	abelian	ADJ
ejpam-4629	27	15	relational	relational	ADJ
ejpam-4629	27	16	graphoid	graphoid	NOUN
ejpam-4629	27	17	.	.	PUNCT
ejpam-4629	28	1	the	the	DET
ejpam-4629	28	2	smallest	small	ADJ
ejpam-4629	28	3	number	number	NOUN
ejpam-4629	28	4	of	of	ADP
ejpam-4629	28	5	colors	color	NOUN
ejpam-4629	28	6	needed	need	VERB
ejpam-4629	28	7	to	to	PART
ejpam-4629	28	8	color	color	VERB
ejpam-4629	28	9	the	the	DET
ejpam-4629	28	10	vertices	vertex	NOUN
ejpam-4629	28	11	of	of	ADP
ejpam-4629	28	12	the	the	DET
ejpam-4629	28	13	graph	graph	NOUN
ejpam-4629	28	14	so	so	SCONJ
ejpam-4629	28	15	that	that	SCONJ
ejpam-4629	28	16	no	no	DET
ejpam-4629	28	17	two	two	NUM
ejpam-4629	28	18	adjacent	adjacent	ADJ
ejpam-4629	28	19	vertices	vertex	NOUN
ejpam-4629	28	20	share	share	VERB
ejpam-4629	28	21	the	the	DET
ejpam-4629	28	22	same	same	ADJ
ejpam-4629	28	23	color	color	NOUN
ejpam-4629	28	24	is	be	AUX
ejpam-4629	28	25	the	the	DET
ejpam-4629	28	26	chromatic	chromatic	ADJ
ejpam-4629	28	27	number	number	NOUN
ejpam-4629	28	28	of	of	ADP
ejpam-4629	28	29	the	the	DET
ejpam-4629	28	30	graph	graph	NOUN
ejpam-4629	28	31	.	.	PUNCT
ejpam-4629	29	1	a	a	DET
ejpam-4629	29	2	set	set	NOUN
ejpam-4629	29	3	of	of	ADP
ejpam-4629	29	4	graphs	graph	NOUN
ejpam-4629	29	5	is	be	AUX
ejpam-4629	29	6	k	k	ADJ
ejpam-4629	29	7	-	-	ADJ
ejpam-4629	29	8	colorable	colorable	ADJ
ejpam-4629	29	9	if	if	SCONJ
ejpam-4629	29	10	every	every	DET
ejpam-4629	29	11	graph	graph	NOUN
ejpam-4629	29	12	of	of	ADP
ejpam-4629	29	13	the	the	DET
ejpam-4629	29	14	set	set	NOUN
ejpam-4629	29	15	has	have	VERB
ejpam-4629	29	16	chromatic	chromatic	ADJ
ejpam-4629	29	17	number	number	NOUN
ejpam-4629	29	18	at	at	ADP
ejpam-4629	29	19	most	most	ADJ
ejpam-4629	29	20	k.	k.	PROPN
ejpam-4629	29	21	in	in	ADP
ejpam-4629	29	22	this	this	DET
ejpam-4629	29	23	paper	paper	NOUN
ejpam-4629	29	24	we	we	PRON
ejpam-4629	29	25	construct	construct	VERB
ejpam-4629	29	26	for	for	ADP
ejpam-4629	29	27	every	every	DET
ejpam-4629	29	28	k	k	PROPN
ejpam-4629	29	29	,	,	PUNCT
ejpam-4629	29	30	a	a	DET
ejpam-4629	29	31	graph	graph	NOUN
ejpam-4629	29	32	automaton	automaton	NOUN
ejpam-4629	29	33	over	over	ADP
ejpam-4629	29	34	the	the	DET
ejpam-4629	29	35	abelian	abelian	PROPN
ejpam-4629	29	36	graphoid	graphoid	PROPN
ejpam-4629	29	37	tsrel(q	tsrel(q	PROPN
ejpam-4629	29	38	)	)	PUNCT
ejpam-4629	29	39	which	which	PRON
ejpam-4629	29	40	accepts	accept	VERB
ejpam-4629	29	41	all	all	DET
ejpam-4629	29	42	the	the	DET
ejpam-4629	29	43	k	k	ADJ
ejpam-4629	29	44	-	-	ADJ
ejpam-4629	29	45	colorable	colorable	ADJ
ejpam-4629	29	46	graphs	graph	NOUN
ejpam-4629	29	47	.	.	PUNCT
ejpam-4629	30	1	hence	hence	ADV
ejpam-4629	30	2	it	it	PRON
ejpam-4629	30	3	is	be	AUX
ejpam-4629	30	4	manifested	manifest	VERB
ejpam-4629	30	5	that	that	SCONJ
ejpam-4629	30	6	graph	graph	NOUN
ejpam-4629	30	7	automata	automata	NOUN
ejpam-4629	30	8	are	be	AUX
ejpam-4629	30	9	capable	capable	ADJ
ejpam-4629	30	10	of	of	ADP
ejpam-4629	30	11	recognizing	recognize	VERB
ejpam-4629	30	12	important	important	ADJ
ejpam-4629	30	13	classes	class	NOUN
ejpam-4629	30	14	of	of	ADP
ejpam-4629	30	15	graphs	graph	NOUN
ejpam-4629	30	16	even	even	ADV
ejpam-4629	30	17	when	when	SCONJ
ejpam-4629	30	18	operating	operate	VERB
ejpam-4629	30	19	on	on	ADP
ejpam-4629	30	20	the	the	DET
ejpam-4629	30	21	most	most	ADV
ejpam-4629	30	22	trivial	trivial	ADJ
ejpam-4629	30	23	of	of	ADP
ejpam-4629	30	24	the	the	DET
ejpam-4629	30	25	known	know	VERB
ejpam-4629	30	26	graphoids	graphoid	NOUN
ejpam-4629	30	27	.	.	PUNCT
ejpam-4629	31	1	in	in	ADP
ejpam-4629	31	2	the	the	DET
ejpam-4629	31	3	following	follow	VERB
ejpam-4629	31	4	section	section	NOUN
ejpam-4629	31	5	we	we	PRON
ejpam-4629	31	6	recall	recall	VERB
ejpam-4629	31	7	basic	basic	ADJ
ejpam-4629	31	8	definition	definition	NOUN
ejpam-4629	31	9	for	for	ADP
ejpam-4629	31	10	magmoids	magmoid	NOUN
ejpam-4629	31	11	and	and	CCONJ
ejpam-4629	31	12	hypergraphs	hypergraph	NOUN
ejpam-4629	31	13	.	.	PUNCT
ejpam-4629	32	1	graphoids	graphoid	NOUN
ejpam-4629	32	2	are	be	AUX
ejpam-4629	32	3	presented	present	VERB
ejpam-4629	32	4	in	in	ADP
ejpam-4629	32	5	section	section	NOUN
ejpam-4629	32	6	3	3	NUM
ejpam-4629	32	7	and	and	CCONJ
ejpam-4629	32	8	the	the	DET
ejpam-4629	32	9	definition	definition	NOUN
ejpam-4629	32	10	of	of	ADP
ejpam-4629	32	11	a	a	DET
ejpam-4629	32	12	graph	graph	NOUN
ejpam-4629	32	13	automaton	automaton	NOUN
ejpam-4629	32	14	is	be	AUX
ejpam-4629	32	15	given	give	VERB
ejpam-4629	32	16	.	.	PUNCT
ejpam-4629	33	1	in	in	ADP
ejpam-4629	33	2	section	section	NOUN
ejpam-4629	33	3	4	4	NUM
ejpam-4629	33	4	we	we	PRON
ejpam-4629	33	5	construct	construct	VERB
ejpam-4629	33	6	the	the	DET
ejpam-4629	33	7	graph	graph	NOUN
ejpam-4629	33	8	automaton	automaton	NOUN
ejpam-4629	33	9	that	that	PRON
ejpam-4629	33	10	recognizes	recognize	VERB
ejpam-4629	33	11	k	k	ADJ
ejpam-4629	33	12	-	-	ADJ
ejpam-4629	33	13	colorable	colorable	ADJ
ejpam-4629	33	14	graphs	graph	NOUN
ejpam-4629	33	15	and	and	CCONJ
ejpam-4629	33	16	illustrate	illustrate	VERB
ejpam-4629	33	17	its	its	PRON
ejpam-4629	33	18	operation	operation	NOUN
ejpam-4629	33	19	.	.	PUNCT
ejpam-4629	34	1	conclusions	conclusion	NOUN
ejpam-4629	34	2	and	and	CCONJ
ejpam-4629	34	3	future	future	ADJ
ejpam-4629	34	4	work	work	NOUN
ejpam-4629	34	5	are	be	AUX
ejpam-4629	34	6	discussed	discuss	VERB
ejpam-4629	34	7	in	in	ADP
ejpam-4629	34	8	the	the	DET
ejpam-4629	34	9	last	last	ADJ
ejpam-4629	34	10	section	section	NOUN
ejpam-4629	34	11	.	.	PUNCT
ejpam-4629	35	1	2	2	X
ejpam-4629	35	2	.	.	X
ejpam-4629	35	3	magmoids	magmoid	NOUN
ejpam-4629	35	4	and	and	CCONJ
ejpam-4629	35	5	hypergraphs	hypergraph	NOUN
ejpam-4629	35	6	a	a	DET
ejpam-4629	35	7	doubly	doubly	ADV
ejpam-4629	35	8	ranked	rank	VERB
ejpam-4629	35	9	set	set	NOUN
ejpam-4629	35	10	(	(	PUNCT
ejpam-4629	35	11	am	be	AUX
ejpam-4629	35	12	,	,	PUNCT
ejpam-4629	35	13	n)m	n)m	ADV
ejpam-4629	35	14	,	,	PUNCT
ejpam-4629	35	15	n∈n	n∈n	NOUN
ejpam-4629	35	16	is	be	AUX
ejpam-4629	35	17	a	a	DET
ejpam-4629	35	18	set	set	NOUN
ejpam-4629	35	19	a	a	DET
ejpam-4629	35	20	together	together	NOUN
ejpam-4629	35	21	with	with	ADP
ejpam-4629	35	22	a	a	DET
ejpam-4629	35	23	function	function	NOUN
ejpam-4629	35	24	rank	rank	NOUN
ejpam-4629	35	25	:	:	PUNCT
ejpam-4629	35	26	a	a	DET
ejpam-4629	35	27	→	→	SYM
ejpam-4629	35	28	n×	n×	ADP
ejpam-4629	35	29	n	n	PRON
ejpam-4629	35	30	we	we	PRON
ejpam-4629	35	31	set	set	VERB
ejpam-4629	35	32	am	be	AUX
ejpam-4629	35	33	,	,	PUNCT
ejpam-4629	35	34	n	n	X
ejpam-4629	35	35	=	=	PUNCT
ejpam-4629	35	36	{	{	PUNCT
ejpam-4629	35	37	a	a	DET
ejpam-4629	35	38	∈	∈	PROPN
ejpam-4629	35	39	a	a	DET
ejpam-4629	35	40	|	|	NOUN
ejpam-4629	35	41	rank(a	rank(a	NOUN
ejpam-4629	35	42	)	)	PUNCT
ejpam-4629	35	43	=	=	SYM
ejpam-4629	35	44	(	(	PUNCT
ejpam-4629	35	45	m	m	PROPN
ejpam-4629	35	46	,	,	PUNCT
ejpam-4629	35	47	n	n	CCONJ
ejpam-4629	35	48	)	)	PUNCT
ejpam-4629	35	49	}	}	PUNCT
ejpam-4629	35	50	.	.	PUNCT
ejpam-4629	36	1	in	in	ADP
ejpam-4629	36	2	what	what	PRON
ejpam-4629	36	3	follows	follow	VERB
ejpam-4629	36	4	we	we	PRON
ejpam-4629	36	5	will	will	AUX
ejpam-4629	36	6	drop	drop	VERB
ejpam-4629	36	7	the	the	DET
ejpam-4629	36	8	subscript	subscript	NOUN
ejpam-4629	36	9	and	and	CCONJ
ejpam-4629	36	10	denote	denote	VERB
ejpam-4629	36	11	a	a	DET
ejpam-4629	36	12	doubly	doubly	ADV
ejpam-4629	36	13	ranked	rank	VERB
ejpam-4629	36	14	set	set	NOUN
ejpam-4629	36	15	simply	simply	ADV
ejpam-4629	36	16	by	by	ADP
ejpam-4629	36	17	a	a	DET
ejpam-4629	36	18	=	=	X
ejpam-4629	36	19	(	(	PUNCT
ejpam-4629	36	20	am	am	NOUN
ejpam-4629	36	21	,	,	PUNCT
ejpam-4629	36	22	n	n	CCONJ
ejpam-4629	36	23	)	)	PUNCT
ejpam-4629	36	24	.	.	PUNCT
ejpam-4629	37	1	a	a	DET
ejpam-4629	37	2	magmoid	magmoid	NOUN
ejpam-4629	37	3	is	be	AUX
ejpam-4629	37	4	a	a	DET
ejpam-4629	37	5	doubly	doubly	ADV
ejpam-4629	37	6	ranked	rank	VERB
ejpam-4629	37	7	set	set	NOUN
ejpam-4629	37	8	m	m	NOUN
ejpam-4629	37	9	=	=	SYM
ejpam-4629	37	10	(	(	PUNCT
ejpam-4629	37	11	mm	mm	PROPN
ejpam-4629	37	12	,	,	PUNCT
ejpam-4629	37	13	n	n	CCONJ
ejpam-4629	37	14	)	)	PUNCT
ejpam-4629	37	15	equipped	equip	VERB
ejpam-4629	37	16	with	with	ADP
ejpam-4629	37	17	two	two	NUM
ejpam-4629	37	18	operations	operation	NOUN
ejpam-4629	37	19	◦	◦	NOUN
ejpam-4629	37	20	:	:	PUNCT
ejpam-4629	37	21	mm	mm	INTJ
ejpam-4629	37	22	,	,	PUNCT
ejpam-4629	37	23	n	n	PRON
ejpam-4629	37	24	×mn	×mn	NOUN
ejpam-4629	37	25	,	,	PUNCT
ejpam-4629	37	26	k	k	PROPN
ejpam-4629	37	27	→	→	SYM
ejpam-4629	37	28	mm	mm	PROPN
ejpam-4629	37	29	,	,	PUNCT
ejpam-4629	37	30	k	k	PROPN
ejpam-4629	37	31	,	,	PUNCT
ejpam-4629	37	32	□	□	PUNCT
ejpam-4629	37	33	:	:	PUNCT
ejpam-4629	37	34	mm	mm	NUM
ejpam-4629	37	35	,	,	PUNCT
ejpam-4629	37	36	n	n	X
ejpam-4629	37	37	×mm′,n′	×mm′,n′	NOUN
ejpam-4629	37	38	→	→	SYM
ejpam-4629	37	39	mm+m′,n+n′	mm+m′,n+n′	NUM
ejpam-4629	37	40	,	,	PUNCT
ejpam-4629	37	41	which	which	PRON
ejpam-4629	37	42	are	be	AUX
ejpam-4629	37	43	associative	associative	ADJ
ejpam-4629	37	44	in	in	ADP
ejpam-4629	37	45	the	the	DET
ejpam-4629	37	46	obvious	obvious	ADJ
ejpam-4629	37	47	way	way	NOUN
ejpam-4629	37	48	,	,	PUNCT
ejpam-4629	37	49	satisfy	satisfy	VERB
ejpam-4629	37	50	the	the	DET
ejpam-4629	37	51	distributivity	distributivity	NOUN
ejpam-4629	37	52	law	law	NOUN
ejpam-4629	37	53	(	(	PUNCT
ejpam-4629	37	54	f	f	X
ejpam-4629	37	55	◦	◦	VERB
ejpam-4629	37	56	g	g	NOUN
ejpam-4629	37	57	)	)	PUNCT
ejpam-4629	37	58	□	□	PUNCT
ejpam-4629	37	59	(	(	PUNCT
ejpam-4629	37	60	f	f	NOUN
ejpam-4629	37	61	′	′	NUM
ejpam-4629	37	62	◦	◦	NOUN
ejpam-4629	37	63	g′	g′	NOUN
ejpam-4629	37	64	)	)	PUNCT
ejpam-4629	37	65	=	=	PUNCT
ejpam-4629	38	1	(	(	PUNCT
ejpam-4629	38	2	f	f	X
ejpam-4629	38	3	□	□	PUNCT
ejpam-4629	38	4	f	f	PROPN
ejpam-4629	38	5	′	′	NOUN
ejpam-4629	38	6	)	)	PUNCT
ejpam-4629	38	7	◦	◦	NOUN
ejpam-4629	38	8	(	(	PUNCT
ejpam-4629	38	9	g	g	NOUN
ejpam-4629	38	10	□	□	PUNCT
ejpam-4629	38	11	g′	g′	NOUN
ejpam-4629	38	12	)	)	PUNCT
ejpam-4629	38	13	whenever	whenever	SCONJ
ejpam-4629	38	14	all	all	DET
ejpam-4629	38	15	the	the	DET
ejpam-4629	38	16	above	above	ADJ
ejpam-4629	38	17	operations	operation	NOUN
ejpam-4629	38	18	are	be	AUX
ejpam-4629	38	19	defined	define	VERB
ejpam-4629	38	20	and	and	CCONJ
ejpam-4629	38	21	are	be	AUX
ejpam-4629	38	22	equipped	equip	VERB
ejpam-4629	38	23	with	with	ADP
ejpam-4629	38	24	a	a	DET
ejpam-4629	38	25	sequence	sequence	NOUN
ejpam-4629	38	26	of	of	ADP
ejpam-4629	38	27	constants	constant	NOUN
ejpam-4629	38	28	en	en	ADP
ejpam-4629	38	29	∈	∈	PROPN
ejpam-4629	38	30	mn	mn	PROPN
ejpam-4629	38	31	,	,	PUNCT
ejpam-4629	38	32	n	n	CCONJ
ejpam-4629	38	33	,	,	PUNCT
ejpam-4629	38	34	called	call	VERB
ejpam-4629	38	35	units	unit	NOUN
ejpam-4629	38	36	,	,	PUNCT
ejpam-4629	38	37	such	such	ADJ
ejpam-4629	38	38	that	that	SCONJ
ejpam-4629	38	39	em	em	PRON
ejpam-4629	38	40	◦	◦	VERB
ejpam-4629	38	41	f	f	X
ejpam-4629	39	1	=	=	SYM
ejpam-4629	39	2	f	f	PROPN
ejpam-4629	39	3	=	=	SYM
ejpam-4629	39	4	f	f	PROPN
ejpam-4629	39	5	◦	◦	NOUN
ejpam-4629	39	6	en	en	X
ejpam-4629	39	7	,	,	PUNCT
ejpam-4629	39	8	e0	e0	PROPN
ejpam-4629	39	9	□	□	PUNCT
ejpam-4629	39	10	f	f	X
ejpam-4629	39	11	=	=	SYM
ejpam-4629	39	12	f	f	PROPN
ejpam-4629	39	13	=	=	SYM
ejpam-4629	39	14	f	f	PROPN
ejpam-4629	39	15	□	□	PUNCT
ejpam-4629	39	16	e0	e0	PROPN
ejpam-4629	39	17	,	,	PUNCT
ejpam-4629	39	18	em	em	PRON
ejpam-4629	39	19	□	□	PUNCT
ejpam-4629	39	20	en	en	X
ejpam-4629	39	21	=	=	SYM
ejpam-4629	39	22	em+n	em+n	PROPN
ejpam-4629	39	23	a.	a.	NOUN
ejpam-4629	39	24	kalampakas	kalampakas	PROPN
ejpam-4629	39	25	/	/	SYM
ejpam-4629	39	26	eur	eur	PROPN
ejpam-4629	39	27	.	.	PUNCT
ejpam-4629	40	1	j.	j.	PROPN
ejpam-4629	40	2	pure	pure	PROPN
ejpam-4629	40	3	appl	appl	PROPN
ejpam-4629	40	4	.	.	PROPN
ejpam-4629	40	5	math	math	PROPN
ejpam-4629	40	6	,	,	PUNCT
ejpam-4629	40	7	16	16	NUM
ejpam-4629	40	8	(	(	PUNCT
ejpam-4629	40	9	1	1	NUM
ejpam-4629	40	10	)	)	PUNCT
ejpam-4629	40	11	(	(	PUNCT
ejpam-4629	40	12	2023	2023	NUM
ejpam-4629	40	13	)	)	PUNCT
ejpam-4629	40	14	,	,	PUNCT
ejpam-4629	40	15	112	112	NUM
ejpam-4629	40	16	-	-	SYM
ejpam-4629	40	17	120	120	NUM
ejpam-4629	40	18	114	114	NUM
ejpam-4629	40	19	hold	hold	NOUN
ejpam-4629	40	20	for	for	ADP
ejpam-4629	40	21	all	all	DET
ejpam-4629	40	22	f	f	PROPN
ejpam-4629	40	23	∈	∈	PROPN
ejpam-4629	40	24	mm	mm	PROPN
ejpam-4629	40	25	,	,	PUNCT
ejpam-4629	40	26	n	n	PROPN
ejpam-4629	40	27	and	and	CCONJ
ejpam-4629	40	28	all	all	DET
ejpam-4629	40	29	m	m	PROPN
ejpam-4629	40	30	,	,	PUNCT
ejpam-4629	40	31	n	n	PROPN
ejpam-4629	40	32	∈	∈	PROPN
ejpam-4629	40	33	n.	n.	NOUN
ejpam-4629	40	34	notice	notice	VERB
ejpam-4629	40	35	that	that	SCONJ
ejpam-4629	40	36	,	,	PUNCT
ejpam-4629	40	37	due	due	ADP
ejpam-4629	40	38	to	to	ADP
ejpam-4629	40	39	the	the	DET
ejpam-4629	40	40	last	last	ADJ
ejpam-4629	40	41	equation	equation	NOUN
ejpam-4629	40	42	,	,	PUNCT
ejpam-4629	40	43	the	the	DET
ejpam-4629	40	44	elements	element	NOUN
ejpam-4629	40	45	en	en	X
ejpam-4629	40	46	are	be	AUX
ejpam-4629	40	47	uniquely	uniquely	ADV
ejpam-4629	40	48	determined	determine	VERB
ejpam-4629	40	49	by	by	ADP
ejpam-4629	40	50	e1	e1	PROPN
ejpam-4629	40	51	.	.	PUNCT
ejpam-4629	41	1	from	from	ADP
ejpam-4629	41	2	now	now	ADV
ejpam-4629	41	3	on	on	ADP
ejpam-4629	41	4	e1	e1	NOUN
ejpam-4629	41	5	will	will	AUX
ejpam-4629	41	6	be	be	AUX
ejpam-4629	41	7	simply	simply	ADV
ejpam-4629	41	8	denoted	denote	VERB
ejpam-4629	41	9	by	by	ADP
ejpam-4629	41	10	e.	e.	PROPN
ejpam-4629	41	11	the	the	DET
ejpam-4629	41	12	free	free	ADJ
ejpam-4629	41	13	magmoid	magmoid	NOUN
ejpam-4629	41	14	mag(σ	mag(σ	PROPN
ejpam-4629	41	15	)	)	PUNCT
ejpam-4629	41	16	generated	generate	VERB
ejpam-4629	41	17	by	by	ADP
ejpam-4629	41	18	a	a	DET
ejpam-4629	41	19	doubly	doubly	ADV
ejpam-4629	41	20	ranked	rank	VERB
ejpam-4629	41	21	set	set	ADJ
ejpam-4629	41	22	σ	σ	PROPN
ejpam-4629	41	23	is	be	AUX
ejpam-4629	41	24	constructed	construct	VERB
ejpam-4629	41	25	in	in	ADP
ejpam-4629	41	26	[	[	X
ejpam-4629	41	27	2	2	NUM
ejpam-4629	41	28	]	]	PUNCT
ejpam-4629	41	29	.	.	PUNCT
ejpam-4629	42	1	the	the	DET
ejpam-4629	42	2	sets	set	NOUN
ejpam-4629	42	3	relm	relm	NOUN
ejpam-4629	42	4	,	,	PUNCT
ejpam-4629	42	5	n(q	n(q	PROPN
ejpam-4629	42	6	)	)	PUNCT
ejpam-4629	42	7	of	of	ADP
ejpam-4629	42	8	all	all	DET
ejpam-4629	42	9	relations	relation	NOUN
ejpam-4629	42	10	from	from	ADP
ejpam-4629	42	11	qm	qm	PROPN
ejpam-4629	42	12	to	to	ADP
ejpam-4629	42	13	qn	qn	PROPN
ejpam-4629	42	14	relm	relm	PROPN
ejpam-4629	42	15	,	,	PUNCT
ejpam-4629	42	16	n(q	n(q	PROPN
ejpam-4629	42	17	)	)	PUNCT
ejpam-4629	42	18	=	=	PRON
ejpam-4629	43	1	{	{	PUNCT
ejpam-4629	43	2	r	r	NOUN
ejpam-4629	43	3	|	|	ADV
ejpam-4629	43	4	r	r	NOUN
ejpam-4629	43	5	⊆	⊆	NUM
ejpam-4629	43	6	qm	qm	PROPN
ejpam-4629	43	7	×qn	×qn	NOUN
ejpam-4629	43	8	}	}	PUNCT
ejpam-4629	43	9	can	can	AUX
ejpam-4629	43	10	be	be	AUX
ejpam-4629	43	11	structured	structure	VERB
ejpam-4629	43	12	into	into	ADP
ejpam-4629	43	13	a	a	DET
ejpam-4629	43	14	magmoid	magmoid	NOUN
ejpam-4629	43	15	with	with	ADP
ejpam-4629	43	16	◦	◦	NOUN
ejpam-4629	43	17	being	be	AUX
ejpam-4629	43	18	the	the	DET
ejpam-4629	43	19	usual	usual	ADJ
ejpam-4629	43	20	relation	relation	NOUN
ejpam-4629	43	21	composition	composition	NOUN
ejpam-4629	43	22	and	and	CCONJ
ejpam-4629	43	23	□	□	PUNCT
ejpam-4629	43	24	defined	define	VERB
ejpam-4629	43	25	as	as	SCONJ
ejpam-4629	43	26	follows	follow	VERB
ejpam-4629	43	27	:	:	PUNCT
ejpam-4629	43	28	for	for	ADP
ejpam-4629	43	29	r	r	PROPN
ejpam-4629	43	30	∈	∈	PROPN
ejpam-4629	43	31	relm	relm	NOUN
ejpam-4629	43	32	,	,	PUNCT
ejpam-4629	43	33	n(q	n(q	PROPN
ejpam-4629	43	34	)	)	PUNCT
ejpam-4629	43	35	and	and	CCONJ
ejpam-4629	43	36	s	s	PROPN
ejpam-4629	43	37	∈	∈	PROPN
ejpam-4629	43	38	relm′,n′(q	relm′,n′(q	PROPN
ejpam-4629	43	39	)	)	PUNCT
ejpam-4629	44	1	r	r	NOUN
ejpam-4629	44	2	□	□	PUNCT
ejpam-4629	44	3	s	s	PART
ejpam-4629	44	4	=	=	PUNCT
ejpam-4629	44	5	{	{	PUNCT
ejpam-4629	44	6	(	(	PUNCT
ejpam-4629	44	7	u1u2	u1u2	NOUN
ejpam-4629	44	8	,	,	PUNCT
ejpam-4629	44	9	v1v2	v1v2	PUNCT
ejpam-4629	44	10	)	)	PUNCT
ejpam-4629	44	11	|	|	ADV
ejpam-4629	44	12	(	(	PUNCT
ejpam-4629	44	13	u1	u1	NOUN
ejpam-4629	44	14	,	,	PUNCT
ejpam-4629	44	15	v1	v1	NOUN
ejpam-4629	44	16	)	)	PUNCT
ejpam-4629	44	17	∈	∈	PROPN
ejpam-4629	44	18	r	r	NOUN
ejpam-4629	44	19	and	and	CCONJ
ejpam-4629	44	20	(	(	PUNCT
ejpam-4629	44	21	u2	u2	PROPN
ejpam-4629	44	22	,	,	PUNCT
ejpam-4629	44	23	v2	v2	PROPN
ejpam-4629	44	24	)	)	PUNCT
ejpam-4629	44	25	∈	∈	PROPN
ejpam-4629	44	26	s	s	NOUN
ejpam-4629	44	27	)	)	PUNCT
ejpam-4629	44	28	}	}	PUNCT
ejpam-4629	44	29	,	,	PUNCT
ejpam-4629	44	30	where	where	SCONJ
ejpam-4629	44	31	u1	u1	PROPN
ejpam-4629	44	32	∈	∈	PROPN
ejpam-4629	44	33	qm	qm	PROPN
ejpam-4629	44	34	,	,	PUNCT
ejpam-4629	44	35	u2	u2	PROPN
ejpam-4629	44	36	∈	∈	PROPN
ejpam-4629	44	37	qm′	qm′	X
ejpam-4629	44	38	,	,	PUNCT
ejpam-4629	44	39	v1	v1	PROPN
ejpam-4629	44	40	∈	∈	PROPN
ejpam-4629	44	41	qn	qn	NOUN
ejpam-4629	44	42	,	,	PUNCT
ejpam-4629	44	43	v2	v2	PROPN
ejpam-4629	44	44	∈	∈	PROPN
ejpam-4629	44	45	qn′	qn′	NOUN
ejpam-4629	44	46	.	.	PUNCT
ejpam-4629	45	1	notice	notice	VERB
ejpam-4629	45	2	that	that	SCONJ
ejpam-4629	45	3	q0	q0	PROPN
ejpam-4629	45	4	=	=	SYM
ejpam-4629	45	5	{	{	PUNCT
ejpam-4629	45	6	ε	ε	PROPN
ejpam-4629	45	7	}	}	PUNCT
ejpam-4629	45	8	,	,	PUNCT
ejpam-4629	45	9	where	where	SCONJ
ejpam-4629	45	10	ε	ε	PROPN
ejpam-4629	45	11	is	be	AUX
ejpam-4629	45	12	the	the	DET
ejpam-4629	45	13	empty	empty	ADJ
ejpam-4629	45	14	word	word	NOUN
ejpam-4629	45	15	of	of	ADP
ejpam-4629	45	16	q∗.	q∗.	NOUN
ejpam-4629	45	17	the	the	DET
ejpam-4629	45	18	units	unit	NOUN
ejpam-4629	45	19	are	be	AUX
ejpam-4629	45	20	given	give	VERB
ejpam-4629	45	21	by	by	ADP
ejpam-4629	45	22	e0	e0	PROPN
ejpam-4629	45	23	=	=	PUNCT
ejpam-4629	45	24	{	{	PUNCT
ejpam-4629	45	25	(	(	PUNCT
ejpam-4629	45	26	ε	ε	PROPN
ejpam-4629	45	27	,	,	PUNCT
ejpam-4629	45	28	ε	ε	PROPN
ejpam-4629	45	29	)	)	PUNCT
ejpam-4629	45	30	}	}	PUNCT
ejpam-4629	45	31	and	and	CCONJ
ejpam-4629	45	32	e	e	X
ejpam-4629	45	33	=	=	SYM
ejpam-4629	45	34	{	{	PUNCT
ejpam-4629	45	35	(	(	PUNCT
ejpam-4629	45	36	g	g	NOUN
ejpam-4629	45	37	,	,	PUNCT
ejpam-4629	45	38	g	g	NOUN
ejpam-4629	45	39	)	)	PUNCT
ejpam-4629	45	40	|	|	ADV
ejpam-4629	45	41	g	g	PROPN
ejpam-4629	45	42	∈	∈	PROPN
ejpam-4629	45	43	q	q	NOUN
ejpam-4629	45	44	}	}	PUNCT
ejpam-4629	45	45	.	.	PUNCT
ejpam-4629	46	1	we	we	PRON
ejpam-4629	46	2	denote	denote	VERB
ejpam-4629	46	3	by	by	ADP
ejpam-4629	46	4	rel(q	rel(q	PROPN
ejpam-4629	46	5	)	)	PUNCT
ejpam-4629	46	6	=	=	SYM
ejpam-4629	46	7	(	(	PUNCT
ejpam-4629	46	8	relm	relm	NOUN
ejpam-4629	46	9	,	,	PUNCT
ejpam-4629	46	10	n(q	n(q	PROPN
ejpam-4629	46	11	)	)	PUNCT
ejpam-4629	46	12	)	)	PUNCT
ejpam-4629	47	1	the	the	DET
ejpam-4629	47	2	magmoid	magmoid	NOUN
ejpam-4629	47	3	constructed	construct	VERB
ejpam-4629	47	4	in	in	ADP
ejpam-4629	47	5	this	this	DET
ejpam-4629	47	6	way	way	NOUN
ejpam-4629	47	7	and	and	CCONJ
ejpam-4629	47	8	call	call	VERB
ejpam-4629	47	9	it	it	PRON
ejpam-4629	47	10	the	the	DET
ejpam-4629	47	11	relational	relational	ADJ
ejpam-4629	47	12	magmoid	magmoid	NOUN
ejpam-4629	47	13	of	of	ADP
ejpam-4629	47	14	q.	q.	PROPN
ejpam-4629	47	15	an	an	DET
ejpam-4629	47	16	(	(	PUNCT
ejpam-4629	47	17	m	m	PROPN
ejpam-4629	47	18	,	,	PUNCT
ejpam-4629	47	19	n)-(hyper)graph	n)-(hyper)graph	ADP
ejpam-4629	47	20	g	g	NOUN
ejpam-4629	47	21	=	=	SYM
ejpam-4629	47	22	(	(	PUNCT
ejpam-4629	47	23	v	v	NOUN
ejpam-4629	47	24	,	,	PUNCT
ejpam-4629	47	25	e	e	NOUN
ejpam-4629	47	26	,	,	PUNCT
ejpam-4629	47	27	s	s	PROPN
ejpam-4629	47	28	,	,	PUNCT
ejpam-4629	47	29	t	t	PROPN
ejpam-4629	47	30	,	,	PUNCT
ejpam-4629	47	31	l	l	NOUN
ejpam-4629	47	32	,	,	PUNCT
ejpam-4629	47	33	begin	begin	VERB
ejpam-4629	47	34	,	,	PUNCT
ejpam-4629	47	35	end	end	NOUN
ejpam-4629	47	36	)	)	PUNCT
ejpam-4629	47	37	with	with	ADP
ejpam-4629	47	38	edge	edge	NOUN
ejpam-4629	47	39	labels	label	NOUN
ejpam-4629	47	40	from	from	ADP
ejpam-4629	47	41	a	a	DET
ejpam-4629	47	42	doubly	doubly	ADV
ejpam-4629	47	43	ranked	rank	VERB
ejpam-4629	47	44	set	set	VERB
ejpam-4629	47	45	σ	σ	X
ejpam-4629	47	46	=	=	SYM
ejpam-4629	47	47	(	(	PUNCT
ejpam-4629	47	48	σm	σm	NOUN
ejpam-4629	47	49	,	,	PUNCT
ejpam-4629	47	50	n	n	CCONJ
ejpam-4629	47	51	)	)	PUNCT
ejpam-4629	47	52	is	be	AUX
ejpam-4629	47	53	a	a	DET
ejpam-4629	47	54	tuple	tuple	NOUN
ejpam-4629	47	55	consisting	consist	VERB
ejpam-4629	47	56	of	of	ADP
ejpam-4629	47	57	the	the	DET
ejpam-4629	47	58	set	set	NOUN
ejpam-4629	47	59	of	of	ADP
ejpam-4629	47	60	nodes	node	NOUN
ejpam-4629	47	61	or	or	CCONJ
ejpam-4629	47	62	vertices	vertice	VERB
ejpam-4629	47	63	v	v	NUM
ejpam-4629	47	64	,	,	PUNCT
ejpam-4629	47	65	the	the	DET
ejpam-4629	47	66	set	set	NOUN
ejpam-4629	47	67	of	of	ADP
ejpam-4629	47	68	edges	edge	NOUN
ejpam-4629	47	69	e	e	NOUN
ejpam-4629	47	70	,	,	PUNCT
ejpam-4629	47	71	the	the	DET
ejpam-4629	47	72	source	source	NOUN
ejpam-4629	47	73	and	and	CCONJ
ejpam-4629	47	74	target	target	NOUN
ejpam-4629	47	75	functions	function	NOUN
ejpam-4629	47	76	s	s	PART
ejpam-4629	47	77	:	:	PUNCT
ejpam-4629	47	78	e	e	X
ejpam-4629	47	79	→	→	SYM
ejpam-4629	47	80	v	v	PROPN
ejpam-4629	47	81	+	+	CCONJ
ejpam-4629	47	82	and	and	CCONJ
ejpam-4629	47	83	t	t	NOUN
ejpam-4629	47	84	:	:	PUNCT
ejpam-4629	47	85	e	e	X
ejpam-4629	47	86	→	→	SYM
ejpam-4629	47	87	v	v	NOUN
ejpam-4629	47	88	+	+	CCONJ
ejpam-4629	47	89	respectively	respectively	ADV
ejpam-4629	47	90	,	,	PUNCT
ejpam-4629	47	91	the	the	DET
ejpam-4629	47	92	labeling	labeling	NOUN
ejpam-4629	47	93	function	function	NOUN
ejpam-4629	47	94	l	l	NOUN
ejpam-4629	47	95	:	:	PUNCT
ejpam-4629	47	96	e	e	X
ejpam-4629	47	97	→	→	PUNCT
ejpam-4629	47	98	σ	σ	NOUN
ejpam-4629	47	99	such	such	ADJ
ejpam-4629	47	100	that	that	PRON
ejpam-4629	47	101	rank(l(e	rank(l(e	NOUN
ejpam-4629	47	102	)	)	PUNCT
ejpam-4629	47	103	)	)	PUNCT
ejpam-4629	48	1	=	=	SYM
ejpam-4629	48	2	(	(	PUNCT
ejpam-4629	48	3	|s(e)|	|s(e)|	PROPN
ejpam-4629	48	4	,	,	PUNCT
ejpam-4629	48	5	|t(e)|	|t(e)|	NOUN
ejpam-4629	48	6	)	)	PUNCT
ejpam-4629	48	7	,	,	PUNCT
ejpam-4629	48	8	for	for	ADP
ejpam-4629	48	9	all	all	DET
ejpam-4629	48	10	e	e	NOUN
ejpam-4629	48	11	∈	∈	PROPN
ejpam-4629	48	12	e	e	NOUN
ejpam-4629	48	13	,	,	PUNCT
ejpam-4629	48	14	and	and	CCONJ
ejpam-4629	48	15	the	the	DET
ejpam-4629	48	16	sequences	sequence	NOUN
ejpam-4629	48	17	of	of	ADP
ejpam-4629	48	18	begin	begin	NOUN
ejpam-4629	48	19	and	and	CCONJ
ejpam-4629	48	20	end	end	VERB
ejpam-4629	48	21	nodes	node	NOUN
ejpam-4629	48	22	begin	begin	VERB
ejpam-4629	48	23	∈	∈	PROPN
ejpam-4629	48	24	v	v	ADP
ejpam-4629	48	25	∗	∗	NOUN
ejpam-4629	48	26	and	and	CCONJ
ejpam-4629	48	27	end	end	VERB
ejpam-4629	48	28	∈	∈	PROPN
ejpam-4629	48	29	v	v	ADP
ejpam-4629	48	30	∗	∗	NOUN
ejpam-4629	48	31	with	with	ADP
ejpam-4629	48	32	|begin|	|begin|	NOUN
ejpam-4629	48	33	=	=	SYM
ejpam-4629	48	34	m	m	NOUN
ejpam-4629	48	35	and	and	CCONJ
ejpam-4629	48	36	|end|	|end|	PROPN
ejpam-4629	48	37	=	=	PUNCT
ejpam-4629	48	38	n.	n.	PROPN
ejpam-4629	48	39	notice	notice	NOUN
ejpam-4629	48	40	that	that	SCONJ
ejpam-4629	48	41	vertices	vertex	NOUN
ejpam-4629	48	42	can	can	AUX
ejpam-4629	48	43	be	be	AUX
ejpam-4629	48	44	duplicated	duplicate	VERB
ejpam-4629	48	45	in	in	ADP
ejpam-4629	48	46	the	the	DET
ejpam-4629	48	47	begin	begin	NOUN
ejpam-4629	48	48	and	and	CCONJ
ejpam-4629	48	49	end	end	VERB
ejpam-4629	48	50	sequences	sequence	NOUN
ejpam-4629	48	51	of	of	ADP
ejpam-4629	48	52	the	the	DET
ejpam-4629	48	53	graph	graph	NOUN
ejpam-4629	48	54	and	and	CCONJ
ejpam-4629	48	55	also	also	ADV
ejpam-4629	48	56	at	at	ADP
ejpam-4629	48	57	the	the	DET
ejpam-4629	48	58	sources	source	NOUN
ejpam-4629	48	59	and	and	CCONJ
ejpam-4629	48	60	targets	target	NOUN
ejpam-4629	48	61	of	of	ADP
ejpam-4629	48	62	the	the	DET
ejpam-4629	48	63	edges	edge	NOUN
ejpam-4629	48	64	.	.	PUNCT
ejpam-4629	49	1	isomorphism	isomorphism	NOUN
ejpam-4629	49	2	between	between	ADP
ejpam-4629	49	3	two	two	NUM
ejpam-4629	49	4	graphs	graph	NOUN
ejpam-4629	49	5	is	be	AUX
ejpam-4629	49	6	defined	define	VERB
ejpam-4629	49	7	in	in	ADP
ejpam-4629	49	8	the	the	DET
ejpam-4629	49	9	obvious	obvious	ADJ
ejpam-4629	49	10	way	way	NOUN
ejpam-4629	49	11	and	and	CCONJ
ejpam-4629	49	12	we	we	PRON
ejpam-4629	49	13	shall	shall	AUX
ejpam-4629	49	14	not	not	PART
ejpam-4629	49	15	distinguish	distinguish	VERB
ejpam-4629	49	16	between	between	ADP
ejpam-4629	49	17	two	two	NUM
ejpam-4629	49	18	isomorphic	isomorphic	ADJ
ejpam-4629	49	19	graphs	graph	NOUN
ejpam-4629	49	20	.	.	PUNCT
ejpam-4629	50	1	the	the	DET
ejpam-4629	50	2	set	set	NOUN
ejpam-4629	50	3	of	of	ADP
ejpam-4629	50	4	all	all	PRON
ejpam-4629	50	5	(	(	PUNCT
ejpam-4629	50	6	m	m	PROPN
ejpam-4629	50	7	,	,	PUNCT
ejpam-4629	50	8	n)-graphs	n)-graph	NOUN
ejpam-4629	50	9	over	over	ADP
ejpam-4629	50	10	σ	σ	PROPN
ejpam-4629	50	11	is	be	AUX
ejpam-4629	50	12	denoted	denote	VERB
ejpam-4629	50	13	by	by	ADP
ejpam-4629	50	14	grm	grm	PROPN
ejpam-4629	50	15	,	,	PUNCT
ejpam-4629	50	16	n(σ	n(σ	PROPN
ejpam-4629	50	17	)	)	PUNCT
ejpam-4629	50	18	and	and	CCONJ
ejpam-4629	50	19	we	we	PRON
ejpam-4629	50	20	set	set	VERB
ejpam-4629	50	21	gr(σ	gr(σ	NOUN
ejpam-4629	50	22	)	)	PUNCT
ejpam-4629	51	1	=	=	SYM
ejpam-4629	51	2	(	(	PUNCT
ejpam-4629	51	3	grm	grm	PROPN
ejpam-4629	51	4	,	,	PUNCT
ejpam-4629	51	5	n(σ))m	n(σ))m	PROPN
ejpam-4629	51	6	,	,	PUNCT
ejpam-4629	51	7	n∈n	n∈n	NOUN
ejpam-4629	51	8	.	.	PUNCT
ejpam-4629	52	1	ordinary	ordinary	ADJ
ejpam-4629	52	2	unlabeled	unlabele	VERB
ejpam-4629	52	3	directed	direct	VERB
ejpam-4629	52	4	graphs	graph	NOUN
ejpam-4629	52	5	are	be	AUX
ejpam-4629	52	6	obtained	obtain	VERB
ejpam-4629	52	7	as	as	ADP
ejpam-4629	52	8	a	a	DET
ejpam-4629	52	9	special	special	ADJ
ejpam-4629	52	10	case	case	NOUN
ejpam-4629	52	11	of	of	ADP
ejpam-4629	52	12	hypergraphs	hypergraph	NOUN
ejpam-4629	52	13	i.e.	i.e.	X
ejpam-4629	52	14	,	,	PUNCT
ejpam-4629	52	15	in	in	ADP
ejpam-4629	52	16	the	the	DET
ejpam-4629	52	17	case	case	NOUN
ejpam-4629	52	18	that	that	SCONJ
ejpam-4629	52	19	each	each	DET
ejpam-4629	52	20	hyperedge	hyperedge	NOUN
ejpam-4629	52	21	is	be	AUX
ejpam-4629	52	22	binary	binary	ADJ
ejpam-4629	52	23	(	(	PUNCT
ejpam-4629	52	24	has	have	VERB
ejpam-4629	52	25	one	one	NUM
ejpam-4629	52	26	source	source	NOUN
ejpam-4629	52	27	and	and	CCONJ
ejpam-4629	52	28	one	one	NUM
ejpam-4629	52	29	target	target	NOUN
ejpam-4629	52	30	)	)	PUNCT
ejpam-4629	52	31	,	,	PUNCT
ejpam-4629	52	32	every	every	DET
ejpam-4629	52	33	edge	edge	NOUN
ejpam-4629	52	34	has	have	VERB
ejpam-4629	52	35	the	the	DET
ejpam-4629	52	36	same	same	ADJ
ejpam-4629	52	37	label	label	NOUN
ejpam-4629	52	38	and	and	CCONJ
ejpam-4629	52	39	the	the	DET
ejpam-4629	52	40	sequences	sequence	NOUN
ejpam-4629	52	41	begin	begin	VERB
ejpam-4629	52	42	and	and	CCONJ
ejpam-4629	52	43	end	end	NOUN
ejpam-4629	52	44	are	be	AUX
ejpam-4629	52	45	the	the	DET
ejpam-4629	52	46	empty	empty	ADJ
ejpam-4629	52	47	word	word	NOUN
ejpam-4629	52	48	.	.	PUNCT
ejpam-4629	53	1	given	give	VERB
ejpam-4629	53	2	the	the	DET
ejpam-4629	53	3	(	(	PUNCT
ejpam-4629	53	4	m	m	PROPN
ejpam-4629	53	5	,	,	PUNCT
ejpam-4629	53	6	n)-graph	n)-graph	PROPN
ejpam-4629	53	7	g	g	NOUN
ejpam-4629	53	8	=	=	PUNCT
ejpam-4629	53	9	(	(	PUNCT
ejpam-4629	53	10	v	v	NOUN
ejpam-4629	53	11	,	,	PUNCT
ejpam-4629	53	12	e	e	NOUN
ejpam-4629	53	13	,	,	PUNCT
ejpam-4629	53	14	s	s	PROPN
ejpam-4629	53	15	,	,	PUNCT
ejpam-4629	53	16	t	t	PROPN
ejpam-4629	53	17	,	,	PUNCT
ejpam-4629	53	18	l	l	NOUN
ejpam-4629	53	19	,	,	PUNCT
ejpam-4629	53	20	begin	begin	VERB
ejpam-4629	53	21	,	,	PUNCT
ejpam-4629	53	22	end	end	NOUN
ejpam-4629	53	23	)	)	PUNCT
ejpam-4629	53	24	and	and	CCONJ
ejpam-4629	53	25	and	and	CCONJ
ejpam-4629	53	26	the	the	DET
ejpam-4629	53	27	(	(	PUNCT
ejpam-4629	53	28	n	n	CCONJ
ejpam-4629	53	29	,	,	PUNCT
ejpam-4629	53	30	k)-graph	k)-graph	PUNCT
ejpam-4629	53	31	h	h	NOUN
ejpam-4629	53	32	=	=	SYM
ejpam-4629	53	33	(	(	PUNCT
ejpam-4629	53	34	v	v	NOUN
ejpam-4629	53	35	′	′	NUM
ejpam-4629	53	36	,	,	PUNCT
ejpam-4629	53	37	e′	e′	PROPN
ejpam-4629	53	38	,	,	PUNCT
ejpam-4629	53	39	s′	s′	ADJ
ejpam-4629	53	40	,	,	PUNCT
ejpam-4629	53	41	t′	t′	NUM
ejpam-4629	53	42	,	,	PUNCT
ejpam-4629	53	43	l′	l′	PROPN
ejpam-4629	53	44	,	,	PUNCT
ejpam-4629	53	45	begin′	begin′	ADV
ejpam-4629	53	46	,	,	PUNCT
ejpam-4629	53	47	end′	end′	PROPN
ejpam-4629	53	48	)	)	PUNCT
ejpam-4629	53	49	then	then	ADV
ejpam-4629	53	50	their	their	PRON
ejpam-4629	53	51	product	product	NOUN
ejpam-4629	53	52	g	g	PROPN
ejpam-4629	53	53	◦	◦	NOUN
ejpam-4629	53	54	h	h	NOUN
ejpam-4629	53	55	is	be	AUX
ejpam-4629	53	56	the	the	DET
ejpam-4629	53	57	(	(	PUNCT
ejpam-4629	53	58	m	m	PROPN
ejpam-4629	53	59	,	,	PUNCT
ejpam-4629	53	60	k)-graph	k)-graph	PUNCT
ejpam-4629	53	61	that	that	PRON
ejpam-4629	53	62	is	be	AUX
ejpam-4629	53	63	obtained	obtain	VERB
ejpam-4629	53	64	by	by	ADP
ejpam-4629	53	65	taking	take	VERB
ejpam-4629	53	66	the	the	DET
ejpam-4629	53	67	disjoint	disjoint	NOUN
ejpam-4629	53	68	union	union	NOUN
ejpam-4629	53	69	of	of	ADP
ejpam-4629	53	70	g	g	PROPN
ejpam-4629	53	71	and	and	CCONJ
ejpam-4629	53	72	h	h	NOUN
ejpam-4629	53	73	and	and	CCONJ
ejpam-4629	53	74	then	then	ADV
ejpam-4629	53	75	identifying	identify	VERB
ejpam-4629	53	76	the	the	DET
ejpam-4629	53	77	ith	ith	PROPN
ejpam-4629	53	78	end	end	NOUN
ejpam-4629	53	79	node	node	NOUN
ejpam-4629	53	80	of	of	ADP
ejpam-4629	53	81	g	g	PROPN
ejpam-4629	53	82	with	with	ADP
ejpam-4629	53	83	the	the	DET
ejpam-4629	53	84	ith	ith	PROPN
ejpam-4629	53	85	begin	begin	VERB
ejpam-4629	53	86	node	node	NOUN
ejpam-4629	53	87	of	of	ADP
ejpam-4629	53	88	h	h	NOUN
ejpam-4629	53	89	,	,	PUNCT
ejpam-4629	53	90	for	for	ADP
ejpam-4629	53	91	every	every	DET
ejpam-4629	53	92	i	i	PROPN
ejpam-4629	53	93	∈	∈	PROPN
ejpam-4629	53	94	{	{	PUNCT
ejpam-4629	53	95	1	1	NUM
ejpam-4629	53	96	,	,	PUNCT
ejpam-4629	53	97	...	...	PUNCT
ejpam-4629	53	98	,	,	PUNCT
ejpam-4629	53	99	n	n	CCONJ
ejpam-4629	53	100	}	}	PUNCT
ejpam-4629	53	101	;	;	PUNCT
ejpam-4629	53	102	also	also	ADV
ejpam-4629	53	103	,	,	PUNCT
ejpam-4629	53	104	begin(g	begin(g	VERB
ejpam-4629	53	105	◦	◦	NOUN
ejpam-4629	53	106	h	h	NOUN
ejpam-4629	53	107	)	)	PUNCT
ejpam-4629	53	108	=	=	PUNCT
ejpam-4629	53	109	begin(g	begin(g	NOUN
ejpam-4629	53	110	)	)	PUNCT
ejpam-4629	53	111	and	and	CCONJ
ejpam-4629	53	112	end(g	end(g	NUM
ejpam-4629	53	113	◦	◦	NOUN
ejpam-4629	53	114	h	h	NOUN
ejpam-4629	53	115	)	)	PUNCT
ejpam-4629	53	116	=	=	SYM
ejpam-4629	53	117	end(h	end(h	PROPN
ejpam-4629	53	118	)	)	PUNCT
ejpam-4629	53	119	.	.	PUNCT
ejpam-4629	54	1	the	the	DET
ejpam-4629	54	2	sum	sum	NOUN
ejpam-4629	54	3	g	g	PROPN
ejpam-4629	54	4	□	□	PROPN
ejpam-4629	54	5	h	h	NOUN
ejpam-4629	54	6	of	of	ADP
ejpam-4629	54	7	arbitrary	arbitrary	ADJ
ejpam-4629	54	8	graphs	graph	NOUN
ejpam-4629	54	9	g	g	NOUN
ejpam-4629	54	10	andh	andh	NOUN
ejpam-4629	54	11	is	be	AUX
ejpam-4629	54	12	their	their	PRON
ejpam-4629	54	13	disjoint	disjoint	NOUN
ejpam-4629	54	14	union	union	NOUN
ejpam-4629	54	15	with	with	ADP
ejpam-4629	54	16	their	their	PRON
ejpam-4629	54	17	sequences	sequence	NOUN
ejpam-4629	54	18	of	of	ADP
ejpam-4629	54	19	begin	begin	NOUN
ejpam-4629	54	20	nodes	node	NOUN
ejpam-4629	54	21	concatenated	concatenate	VERB
ejpam-4629	54	22	and	and	CCONJ
ejpam-4629	54	23	similarly	similarly	ADV
ejpam-4629	54	24	for	for	ADP
ejpam-4629	54	25	their	their	PRON
ejpam-4629	54	26	end	end	NOUN
ejpam-4629	54	27	nodes	node	NOUN
ejpam-4629	54	28	(	(	PUNCT
ejpam-4629	54	29	see	see	VERB
ejpam-4629	54	30	[	[	X
ejpam-4629	54	31	5	5	NUM
ejpam-4629	54	32	,	,	PUNCT
ejpam-4629	54	33	8	8	NUM
ejpam-4629	54	34	]	]	PUNCT
ejpam-4629	54	35	for	for	ADP
ejpam-4629	54	36	examples	example	NOUN
ejpam-4629	54	37	)	)	PUNCT
ejpam-4629	54	38	.	.	PUNCT
ejpam-4629	55	1	for	for	ADP
ejpam-4629	55	2	every	every	DET
ejpam-4629	55	3	n	n	PRON
ejpam-4629	55	4	∈	∈	NOUN
ejpam-4629	55	5	n	n	CCONJ
ejpam-4629	55	6	we	we	PRON
ejpam-4629	55	7	denote	denote	VERB
ejpam-4629	55	8	by	by	ADP
ejpam-4629	55	9	en	en	INTJ
ejpam-4629	55	10	the	the	DET
ejpam-4629	55	11	discrete	discrete	ADJ
ejpam-4629	55	12	graph	graph	NOUN
ejpam-4629	55	13	of	of	ADP
ejpam-4629	55	14	rank	rank	NOUN
ejpam-4629	55	15	(	(	PUNCT
ejpam-4629	55	16	n	n	CCONJ
ejpam-4629	55	17	,	,	PUNCT
ejpam-4629	55	18	n	n	CCONJ
ejpam-4629	55	19	)	)	PUNCT
ejpam-4629	55	20	with	with	ADP
ejpam-4629	55	21	nodes	node	NOUN
ejpam-4629	55	22	x1	x1	PROPN
ejpam-4629	55	23	,	,	PUNCT
ejpam-4629	55	24	...	...	PUNCT
ejpam-4629	55	25	,	,	PUNCT
ejpam-4629	55	26	xn	xn	PROPN
ejpam-4629	55	27	and	and	CCONJ
ejpam-4629	55	28	begin	begin	VERB
ejpam-4629	55	29	=	=	NOUN
ejpam-4629	55	30	end	end	NOUN
ejpam-4629	56	1	=	=	PUNCT
ejpam-4629	56	2	x1	x1	PROPN
ejpam-4629	56	3	·	·	PUNCT
ejpam-4629	56	4	·	·	PUNCT
ejpam-4629	56	5	·	·	PUNCT
ejpam-4629	56	6	xn	xn	NUM
ejpam-4629	56	7	;	;	PUNCT
ejpam-4629	56	8	we	we	PRON
ejpam-4629	56	9	write	write	VERB
ejpam-4629	56	10	e	e	PROPN
ejpam-4629	56	11	for	for	ADP
ejpam-4629	56	12	e1	e1	NOUN
ejpam-4629	56	13	.	.	PUNCT
ejpam-4629	57	1	it	it	PRON
ejpam-4629	57	2	is	be	AUX
ejpam-4629	57	3	straightforward	straightforward	ADJ
ejpam-4629	57	4	to	to	PART
ejpam-4629	57	5	verify	verify	VERB
ejpam-4629	57	6	that	that	DET
ejpam-4629	57	7	gr(σ	gr(σ	NOUN
ejpam-4629	57	8	)	)	PUNCT
ejpam-4629	57	9	=	=	SYM
ejpam-4629	57	10	(	(	PUNCT
ejpam-4629	57	11	grm	grm	PROPN
ejpam-4629	57	12	,	,	PUNCT
ejpam-4629	57	13	n(σ	n(σ	PROPN
ejpam-4629	57	14	)	)	PUNCT
ejpam-4629	57	15	)	)	PUNCT
ejpam-4629	57	16	with	with	SCONJ
ejpam-4629	57	17	the	the	DET
ejpam-4629	57	18	operations	operation	NOUN
ejpam-4629	57	19	defined	define	VERB
ejpam-4629	57	20	above	above	ADV
ejpam-4629	57	21	is	be	AUX
ejpam-4629	57	22	a	a	DET
ejpam-4629	57	23	magmoid	magmoid	NOUN
ejpam-4629	57	24	,	,	PUNCT
ejpam-4629	57	25	whose	whose	DET
ejpam-4629	57	26	units	unit	NOUN
ejpam-4629	57	27	are	be	AUX
ejpam-4629	57	28	the	the	DET
ejpam-4629	57	29	graphs	graph	NOUN
ejpam-4629	57	30	en	en	X
ejpam-4629	57	31	.	.	PUNCT
ejpam-4629	57	32	a.	a.	PROPN
ejpam-4629	57	33	kalampakas	kalampakas	PROPN
ejpam-4629	57	34	/	/	SYM
ejpam-4629	57	35	eur	eur	PROPN
ejpam-4629	57	36	.	.	PUNCT
ejpam-4629	58	1	j.	j.	PROPN
ejpam-4629	58	2	pure	pure	PROPN
ejpam-4629	58	3	appl	appl	PROPN
ejpam-4629	58	4	.	.	PROPN
ejpam-4629	58	5	math	math	PROPN
ejpam-4629	58	6	,	,	PUNCT
ejpam-4629	58	7	16	16	NUM
ejpam-4629	58	8	(	(	PUNCT
ejpam-4629	58	9	1	1	NUM
ejpam-4629	58	10	)	)	PUNCT
ejpam-4629	58	11	(	(	PUNCT
ejpam-4629	58	12	2023	2023	NUM
ejpam-4629	58	13	)	)	PUNCT
ejpam-4629	58	14	,	,	PUNCT
ejpam-4629	58	15	112	112	NUM
ejpam-4629	58	16	-	-	SYM
ejpam-4629	58	17	120	120	NUM
ejpam-4629	58	18	115	115	NUM
ejpam-4629	58	19	3	3	NUM
ejpam-4629	58	20	.	.	PUNCT
ejpam-4629	59	1	graphoids	graphoid	NOUN
ejpam-4629	59	2	and	and	CCONJ
ejpam-4629	59	3	graph	graph	NOUN
ejpam-4629	59	4	automata	automata	NOUN
ejpam-4629	59	5	in	in	ADP
ejpam-4629	59	6	this	this	DET
ejpam-4629	59	7	section	section	NOUN
ejpam-4629	59	8	we	we	PRON
ejpam-4629	59	9	present	present	VERB
ejpam-4629	59	10	graph	graph	NOUN
ejpam-4629	59	11	automata	automata	NOUN
ejpam-4629	59	12	by	by	ADP
ejpam-4629	59	13	employing	employ	VERB
ejpam-4629	59	14	the	the	DET
ejpam-4629	59	15	algebraic	algebraic	ADJ
ejpam-4629	59	16	structure	structure	NOUN
ejpam-4629	59	17	of	of	ADP
ejpam-4629	59	18	graphoids	graphoid	NOUN
ejpam-4629	59	19	as	as	SCONJ
ejpam-4629	59	20	introduced	introduce	VERB
ejpam-4629	59	21	in	in	ADP
ejpam-4629	59	22	[	[	X
ejpam-4629	59	23	5	5	NUM
ejpam-4629	59	24	]	]	PUNCT
ejpam-4629	59	25	.	.	PUNCT
ejpam-4629	60	1	we	we	PRON
ejpam-4629	60	2	denote	denote	VERB
ejpam-4629	60	3	by	by	ADP
ejpam-4629	60	4	ip	ip	PROPN
ejpam-4629	60	5	,	,	PUNCT
ejpam-4629	60	6	q	q	PUNCT
ejpam-4629	60	7	the	the	DET
ejpam-4629	60	8	discrete	discrete	ADJ
ejpam-4629	60	9	(	(	PUNCT
ejpam-4629	60	10	p	p	NOUN
ejpam-4629	60	11	,	,	PUNCT
ejpam-4629	60	12	q)-graph	q)-graph	NOUN
ejpam-4629	60	13	that	that	PRON
ejpam-4629	60	14	has	have	VERB
ejpam-4629	60	15	a	a	DET
ejpam-4629	60	16	single	single	ADJ
ejpam-4629	60	17	node	node	NOUN
ejpam-4629	60	18	x	x	PUNCT
ejpam-4629	60	19	and	and	CCONJ
ejpam-4629	60	20	whose	whose	DET
ejpam-4629	60	21	begin	begin	NOUN
ejpam-4629	60	22	and	and	CCONJ
ejpam-4629	60	23	end	end	VERB
ejpam-4629	60	24	sequences	sequence	NOUN
ejpam-4629	60	25	are	be	AUX
ejpam-4629	60	26	x	x	X
ejpam-4629	60	27	·	·	PUNCT
ejpam-4629	60	28	·	·	PUNCT
ejpam-4629	60	29	·	·	PUNCT
ejpam-4629	60	30	x	x	X
ejpam-4629	60	31	(	(	PUNCT
ejpam-4629	60	32	p	p	PROPN
ejpam-4629	60	33	times	time	NOUN
ejpam-4629	60	34	)	)	PUNCT
ejpam-4629	60	35	and	and	CCONJ
ejpam-4629	60	36	x	x	X
ejpam-4629	60	37	·	·	PUNCT
ejpam-4629	60	38	·	·	PUNCT
ejpam-4629	60	39	·	·	PUNCT
ejpam-4629	60	40	x	x	X
ejpam-4629	60	41	(	(	PUNCT
ejpam-4629	60	42	q	q	PROPN
ejpam-4629	60	43	times	time	NOUN
ejpam-4629	60	44	)	)	PUNCT
ejpam-4629	60	45	respectively	respectively	ADV
ejpam-4629	60	46	,	,	PUNCT
ejpam-4629	60	47	π	π	PROPN
ejpam-4629	60	48	is	be	AUX
ejpam-4629	60	49	the	the	DET
ejpam-4629	60	50	discrete	discrete	ADJ
ejpam-4629	60	51	(	(	PUNCT
ejpam-4629	60	52	2	2	NUM
ejpam-4629	60	53	,	,	PUNCT
ejpam-4629	60	54	2)-graph	2)-graph	NUM
ejpam-4629	60	55	that	that	PRON
ejpam-4629	60	56	has	have	VERB
ejpam-4629	60	57	two	two	NUM
ejpam-4629	60	58	nodes	node	NOUN
ejpam-4629	60	59	x	x	PUNCT
ejpam-4629	60	60	and	and	CCONJ
ejpam-4629	60	61	y	y	PROPN
ejpam-4629	60	62	and	and	CCONJ
ejpam-4629	60	63	whose	whose	DET
ejpam-4629	60	64	begin	begin	NOUN
ejpam-4629	60	65	and	and	CCONJ
ejpam-4629	60	66	end	end	VERB
ejpam-4629	60	67	sequences	sequence	NOUN
ejpam-4629	60	68	are	be	AUX
ejpam-4629	60	69	xy	xy	PROPN
ejpam-4629	60	70	and	and	CCONJ
ejpam-4629	60	71	yx	yx	NOUN
ejpam-4629	60	72	,	,	PUNCT
ejpam-4629	60	73	respectively	respectively	ADV
ejpam-4629	60	74	,	,	PUNCT
ejpam-4629	60	75	also	also	ADV
ejpam-4629	60	76	for	for	ADP
ejpam-4629	60	77	every	every	DET
ejpam-4629	60	78	σ	σ	NUM
ejpam-4629	60	79	∈	∈	PROPN
ejpam-4629	60	80	σm	σm	NOUN
ejpam-4629	60	81	,	,	PUNCT
ejpam-4629	60	82	n	n	CCONJ
ejpam-4629	60	83	,	,	PUNCT
ejpam-4629	60	84	we	we	PRON
ejpam-4629	60	85	denote	denote	VERB
ejpam-4629	60	86	again	again	ADV
ejpam-4629	60	87	by	by	ADP
ejpam-4629	60	88	σ	σ	PROPN
ejpam-4629	60	89	the	the	DET
ejpam-4629	60	90	(	(	PUNCT
ejpam-4629	60	91	m	m	PROPN
ejpam-4629	60	92	,	,	PUNCT
ejpam-4629	60	93	n)-graph	n)-graph	ADP
ejpam-4629	60	94	having	have	VERB
ejpam-4629	60	95	only	only	ADV
ejpam-4629	60	96	one	one	NUM
ejpam-4629	60	97	edge	edge	NOUN
ejpam-4629	60	98	and	and	CCONJ
ejpam-4629	60	99	m+	m+	NUM
ejpam-4629	60	100	n	n	CCONJ
ejpam-4629	60	101	nodes	node	NOUN
ejpam-4629	60	102	x1	x1	PROPN
ejpam-4629	60	103	,	,	PUNCT
ejpam-4629	60	104	.	.	PUNCT
ejpam-4629	60	105	.	.	PUNCT
ejpam-4629	61	1	.	.	PUNCT
ejpam-4629	62	1	,	,	PUNCT
ejpam-4629	62	2	xm	xm	PROPN
ejpam-4629	62	3	,	,	PUNCT
ejpam-4629	62	4	y1	y1	PROPN
ejpam-4629	62	5	,	,	PUNCT
ejpam-4629	62	6	.	.	PUNCT
ejpam-4629	62	7	.	.	PUNCT
ejpam-4629	63	1	.	.	PUNCT
ejpam-4629	64	1	,	,	PUNCT
ejpam-4629	64	2	yn	yn	PROPN
ejpam-4629	64	3	.	.	PUNCT
ejpam-4629	65	1	the	the	DET
ejpam-4629	65	2	edge	edge	NOUN
ejpam-4629	65	3	is	be	AUX
ejpam-4629	65	4	labeled	label	VERB
ejpam-4629	65	5	by	by	ADP
ejpam-4629	65	6	σ	σ	PROPN
ejpam-4629	65	7	,	,	PUNCT
ejpam-4629	65	8	and	and	CCONJ
ejpam-4629	65	9	the	the	DET
ejpam-4629	65	10	begin	begin	NOUN
ejpam-4629	65	11	(	(	PUNCT
ejpam-4629	65	12	resp	resp	NOUN
ejpam-4629	65	13	.	.	PUNCT
ejpam-4629	66	1	end	end	NOUN
ejpam-4629	66	2	sequence	sequence	NOUN
ejpam-4629	66	3	)	)	PUNCT
ejpam-4629	66	4	of	of	ADP
ejpam-4629	66	5	the	the	DET
ejpam-4629	66	6	graph	graph	NOUN
ejpam-4629	66	7	is	be	AUX
ejpam-4629	66	8	the	the	DET
ejpam-4629	66	9	sequence	sequence	NOUN
ejpam-4629	66	10	of	of	ADP
ejpam-4629	66	11	sources	source	NOUN
ejpam-4629	66	12	(	(	PUNCT
ejpam-4629	66	13	resp	resp	NOUN
ejpam-4629	66	14	.	.	PUNCT
ejpam-4629	66	15	targets	target	NOUN
ejpam-4629	66	16	)	)	PUNCT
ejpam-4629	66	17	of	of	ADP
ejpam-4629	66	18	the	the	DET
ejpam-4629	66	19	edge	edge	NOUN
ejpam-4629	66	20	,	,	PUNCT
ejpam-4629	66	21	viz	viz	PROPN
ejpam-4629	66	22	.	.	PUNCT
ejpam-4629	67	1	x1	x1	PROPN
ejpam-4629	67	2	·	·	PUNCT
ejpam-4629	67	3	·	·	PUNCT
ejpam-4629	68	1	·	·	PUNCT
ejpam-4629	68	2	xm	xm	PROPN
ejpam-4629	68	3	(	(	PUNCT
ejpam-4629	68	4	resp	resp	NOUN
ejpam-4629	68	5	.	.	PUNCT
ejpam-4629	69	1	y1	y1	NOUN
ejpam-4629	69	2	·	·	PUNCT
ejpam-4629	69	3	·	·	PUNCT
ejpam-4629	69	4	·	·	PUNCT
ejpam-4629	69	5	yn	yn	X
ejpam-4629	69	6	)	)	PUNCT
ejpam-4629	69	7	.	.	PUNCT
ejpam-4629	70	1	engelfriet	engelfriet	PROPN
ejpam-4629	70	2	and	and	CCONJ
ejpam-4629	70	3	vereijken	vereijken	ADJ
ejpam-4629	70	4	,	,	PUNCT
ejpam-4629	70	5	in	in	ADP
ejpam-4629	70	6	[	[	PUNCT
ejpam-4629	70	7	7	7	NUM
ejpam-4629	70	8	]	]	PUNCT
ejpam-4629	70	9	,	,	PUNCT
ejpam-4629	70	10	presented	present	VERB
ejpam-4629	70	11	an	an	DET
ejpam-4629	70	12	algorithm	algorithm	NOUN
ejpam-4629	70	13	that	that	PRON
ejpam-4629	70	14	inductively	inductively	ADV
ejpam-4629	70	15	constructs	construct	VERB
ejpam-4629	70	16	every	every	DET
ejpam-4629	70	17	graph	graph	NOUN
ejpam-4629	70	18	g	g	ADP
ejpam-4629	70	19	∈	∈	PROPN
ejpam-4629	70	20	gr(σ	gr(σ	NOUN
ejpam-4629	70	21	)	)	PUNCT
ejpam-4629	70	22	from	from	ADP
ejpam-4629	70	23	the	the	DET
ejpam-4629	70	24	set	set	NOUN
ejpam-4629	70	25	σ	σ	PROPN
ejpam-4629	70	26	∪	∪	X
ejpam-4629	70	27	{	{	PUNCT
ejpam-4629	70	28	π	π	PROPN
ejpam-4629	70	29	,	,	PUNCT
ejpam-4629	70	30	i01	i01	NOUN
ejpam-4629	70	31	,	,	PUNCT
ejpam-4629	70	32	i21	i21	NOUN
ejpam-4629	70	33	,	,	PUNCT
ejpam-4629	70	34	i10	i10	PROPN
ejpam-4629	70	35	,	,	PUNCT
ejpam-4629	70	36	i12	i12	PROPN
ejpam-4629	70	37	,	,	PUNCT
ejpam-4629	70	38	}	}	PUNCT
ejpam-4629	70	39	by	by	ADP
ejpam-4629	70	40	using	use	VERB
ejpam-4629	70	41	graph	graph	NOUN
ejpam-4629	70	42	product	product	NOUN
ejpam-4629	70	43	and	and	CCONJ
ejpam-4629	70	44	graph	graph	NOUN
ejpam-4629	70	45	sum	sum	NOUN
ejpam-4629	70	46	.	.	PUNCT
ejpam-4629	71	1	however	however	ADV
ejpam-4629	71	2	,	,	PUNCT
ejpam-4629	71	3	there	there	PRON
ejpam-4629	71	4	are	be	VERB
ejpam-4629	71	5	infinitely	infinitely	ADV
ejpam-4629	71	6	many	many	ADJ
ejpam-4629	71	7	ways	way	NOUN
ejpam-4629	71	8	to	to	PART
ejpam-4629	71	9	construct	construct	VERB
ejpam-4629	71	10	a	a	DET
ejpam-4629	71	11	given	give	VERB
ejpam-4629	71	12	graph	graph	NOUN
ejpam-4629	71	13	.	.	PUNCT
ejpam-4629	72	1	this	this	PRON
ejpam-4629	72	2	was	be	AUX
ejpam-4629	72	3	overridden	overridden	ADJ
ejpam-4629	72	4	by	by	ADP
ejpam-4629	72	5	identifying	identify	VERB
ejpam-4629	72	6	a	a	DET
ejpam-4629	72	7	finite	finite	ADJ
ejpam-4629	72	8	set	set	VERB
ejpam-4629	72	9	e	e	PROPN
ejpam-4629	72	10	of	of	ADP
ejpam-4629	72	11	equations	equation	NOUN
ejpam-4629	72	12	with	with	ADP
ejpam-4629	72	13	the	the	DET
ejpam-4629	72	14	property	property	NOUN
ejpam-4629	72	15	that	that	PRON
ejpam-4629	72	16	two	two	NUM
ejpam-4629	72	17	expressions	expression	NOUN
ejpam-4629	72	18	represent	represent	VERB
ejpam-4629	72	19	the	the	DET
ejpam-4629	72	20	same	same	ADJ
ejpam-4629	72	21	graph	graph	NOUN
ejpam-4629	72	22	if	if	SCONJ
ejpam-4629	73	1	and	and	CCONJ
ejpam-4629	73	2	only	only	ADV
ejpam-4629	73	3	if	if	SCONJ
ejpam-4629	73	4	one	one	PRON
ejpam-4629	73	5	can	can	AUX
ejpam-4629	73	6	be	be	AUX
ejpam-4629	73	7	transformed	transform	VERB
ejpam-4629	73	8	into	into	ADP
ejpam-4629	73	9	the	the	DET
ejpam-4629	73	10	other	other	ADJ
ejpam-4629	73	11	through	through	ADP
ejpam-4629	73	12	these	these	DET
ejpam-4629	73	13	equations	equation	NOUN
ejpam-4629	74	1	[	[	X
ejpam-4629	74	2	2	2	NUM
ejpam-4629	74	3	]	]	PUNCT
ejpam-4629	74	4	.	.	PUNCT
ejpam-4629	75	1	it	it	PRON
ejpam-4629	75	2	is	be	AUX
ejpam-4629	75	3	evident	evident	ADJ
ejpam-4629	75	4	from	from	ADP
ejpam-4629	75	5	this	this	DET
ejpam-4629	75	6	discussion	discussion	NOUN
ejpam-4629	75	7	that	that	SCONJ
ejpam-4629	75	8	the	the	DET
ejpam-4629	75	9	equations	equation	NOUN
ejpam-4629	75	10	e	e	NOUN
ejpam-4629	75	11	are	be	AUX
ejpam-4629	75	12	satisfied	satisfied	ADJ
ejpam-4629	75	13	in	in	ADP
ejpam-4629	75	14	gr(σ	gr(σ	NOUN
ejpam-4629	75	15	)	)	PUNCT
ejpam-4629	75	16	.	.	PUNCT
ejpam-4629	76	1	magmoids	magmoid	NOUN
ejpam-4629	76	2	with	with	ADP
ejpam-4629	76	3	such	such	DET
ejpam-4629	76	4	a	a	DET
ejpam-4629	76	5	property	property	NOUN
ejpam-4629	76	6	are	be	AUX
ejpam-4629	76	7	called	call	VERB
ejpam-4629	76	8	graphoids	graphoid	NOUN
ejpam-4629	76	9	.	.	PUNCT
ejpam-4629	77	1	formally	formally	ADV
ejpam-4629	77	2	,	,	PUNCT
ejpam-4629	77	3	a	a	DET
ejpam-4629	77	4	graphoid	graphoid	NOUN
ejpam-4629	77	5	m	m	NOUN
ejpam-4629	77	6	=	=	SYM
ejpam-4629	77	7	(	(	PUNCT
ejpam-4629	77	8	m	m	PROPN
ejpam-4629	77	9	,	,	PUNCT
ejpam-4629	77	10	d	d	NOUN
ejpam-4629	77	11	)	)	PUNCT
ejpam-4629	77	12	consists	consist	VERB
ejpam-4629	77	13	of	of	ADP
ejpam-4629	77	14	a	a	DET
ejpam-4629	77	15	magmoid	magmoid	NOUN
ejpam-4629	77	16	m	m	NOUN
ejpam-4629	77	17	and	and	CCONJ
ejpam-4629	77	18	a	a	DET
ejpam-4629	77	19	set	set	NOUN
ejpam-4629	77	20	d	d	NOUN
ejpam-4629	77	21	=	=	PUNCT
ejpam-4629	77	22	{	{	PUNCT
ejpam-4629	77	23	s	s	PROPN
ejpam-4629	77	24	,	,	PUNCT
ejpam-4629	77	25	d01	d01	NOUN
ejpam-4629	77	26	,	,	PUNCT
ejpam-4629	77	27	d21	d21	PROPN
ejpam-4629	77	28	,	,	PUNCT
ejpam-4629	77	29	d10	d10	PROPN
ejpam-4629	77	30	,	,	PUNCT
ejpam-4629	77	31	d12	d12	PROPN
ejpam-4629	77	32	}	}	PUNCT
ejpam-4629	77	33	,	,	PUNCT
ejpam-4629	77	34	with	with	ADP
ejpam-4629	77	35	s	s	PROPN
ejpam-4629	77	36	∈	∈	PROPN
ejpam-4629	77	37	m2,2	m2,2	PROPN
ejpam-4629	77	38	,	,	PUNCT
ejpam-4629	77	39	dκλ	dκλ	NOUN
ejpam-4629	77	40	∈	∈	PROPN
ejpam-4629	77	41	mκ	mκ	PROPN
ejpam-4629	77	42	,	,	PUNCT
ejpam-4629	77	43	λ	λ	PROPN
ejpam-4629	77	44	,	,	PUNCT
ejpam-4629	77	45	such	such	ADJ
ejpam-4629	77	46	that	that	SCONJ
ejpam-4629	77	47	the	the	DET
ejpam-4629	77	48	following	follow	VERB
ejpam-4629	77	49	equations	equation	NOUN
ejpam-4629	77	50	hold	hold	VERB
ejpam-4629	77	51	:	:	PUNCT
ejpam-4629	77	52	s	s	VERB
ejpam-4629	77	53	◦	◦	NOUN
ejpam-4629	77	54	s	s	PART
ejpam-4629	77	55	=	=	PROPN
ejpam-4629	77	56	e2	e2	PROPN
ejpam-4629	77	57	(	(	PUNCT
ejpam-4629	77	58	1	1	NUM
ejpam-4629	77	59	)	)	PUNCT
ejpam-4629	77	60	(	(	PUNCT
ejpam-4629	77	61	s	s	X
ejpam-4629	77	62	□	□	SYM
ejpam-4629	77	63	e	e	ADJ
ejpam-4629	77	64	)	)	PUNCT
ejpam-4629	77	65	◦	◦	NOUN
ejpam-4629	77	66	(	(	PUNCT
ejpam-4629	77	67	e	e	X
ejpam-4629	77	68	□	□	SYM
ejpam-4629	77	69	s	s	PART
ejpam-4629	77	70	)	)	PUNCT
ejpam-4629	77	71	◦	◦	NOUN
ejpam-4629	77	72	(	(	PUNCT
ejpam-4629	77	73	s	s	X
ejpam-4629	77	74	□	□	SYM
ejpam-4629	77	75	e	e	NOUN
ejpam-4629	77	76	)	)	PUNCT
ejpam-4629	77	77	=	=	SYM
ejpam-4629	77	78	(	(	PUNCT
ejpam-4629	77	79	e	e	X
ejpam-4629	77	80	□	□	SYM
ejpam-4629	77	81	s	s	PART
ejpam-4629	77	82	)	)	PUNCT
ejpam-4629	77	83	◦	◦	NOUN
ejpam-4629	77	84	(	(	PUNCT
ejpam-4629	77	85	s	s	X
ejpam-4629	77	86	□	□	SYM
ejpam-4629	77	87	e	e	ADJ
ejpam-4629	77	88	)	)	PUNCT
ejpam-4629	77	89	◦	◦	NOUN
ejpam-4629	77	90	(	(	PUNCT
ejpam-4629	77	91	e	e	X
ejpam-4629	77	92	□	□	SYM
ejpam-4629	77	93	s	s	PART
ejpam-4629	77	94	)	)	PUNCT
ejpam-4629	77	95	(	(	PUNCT
ejpam-4629	77	96	2	2	NUM
ejpam-4629	77	97	)	)	PUNCT
ejpam-4629	77	98	(	(	PUNCT
ejpam-4629	77	99	e	e	NOUN
ejpam-4629	77	100	□	□	SYM
ejpam-4629	77	101	d21	d21	NOUN
ejpam-4629	77	102	)	)	PUNCT
ejpam-4629	77	103	◦	◦	NOUN
ejpam-4629	77	104	d21	d21	NOUN
ejpam-4629	78	1	=	=	SYM
ejpam-4629	78	2	(	(	PUNCT
ejpam-4629	78	3	d21	d21	NOUN
ejpam-4629	78	4	□	□	PUNCT
ejpam-4629	78	5	e	e	NOUN
ejpam-4629	78	6	)	)	PUNCT
ejpam-4629	78	7	◦	◦	NOUN
ejpam-4629	78	8	d21	d21	NOUN
ejpam-4629	78	9	(	(	PUNCT
ejpam-4629	78	10	3	3	NUM
ejpam-4629	78	11	)	)	PUNCT
ejpam-4629	78	12	(	(	PUNCT
ejpam-4629	78	13	e	e	NOUN
ejpam-4629	78	14	□	□	SYM
ejpam-4629	78	15	d01	d01	NOUN
ejpam-4629	78	16	)	)	PUNCT
ejpam-4629	78	17	◦	◦	NOUN
ejpam-4629	78	18	d21	d21	NOUN
ejpam-4629	78	19	=	=	SYM
ejpam-4629	78	20	e	e	X
ejpam-4629	78	21	(	(	PUNCT
ejpam-4629	78	22	4	4	NUM
ejpam-4629	78	23	)	)	PUNCT
ejpam-4629	78	24	s	s	VERB
ejpam-4629	78	25	◦	◦	NOUN
ejpam-4629	78	26	d21	d21	NOUN
ejpam-4629	78	27	=	=	PROPN
ejpam-4629	78	28	d21	d21	NOUN
ejpam-4629	78	29	(	(	PUNCT
ejpam-4629	78	30	5	5	NUM
ejpam-4629	78	31	)	)	PUNCT
ejpam-4629	78	32	(	(	PUNCT
ejpam-4629	78	33	e	e	NOUN
ejpam-4629	78	34	□	□	SYM
ejpam-4629	78	35	d01	d01	NOUN
ejpam-4629	78	36	)	)	PUNCT
ejpam-4629	78	37	◦	◦	NOUN
ejpam-4629	78	38	s	s	PART
ejpam-4629	78	39	=	=	PUNCT
ejpam-4629	78	40	(	(	PUNCT
ejpam-4629	78	41	d01	d01	NOUN
ejpam-4629	78	42	□	□	PUNCT
ejpam-4629	78	43	e	e	NOUN
ejpam-4629	78	44	)	)	PUNCT
ejpam-4629	78	45	(	(	PUNCT
ejpam-4629	78	46	6	6	NUM
ejpam-4629	78	47	)	)	PUNCT
ejpam-4629	78	48	(	(	PUNCT
ejpam-4629	78	49	s	s	X
ejpam-4629	78	50	□	□	SYM
ejpam-4629	78	51	e	e	ADJ
ejpam-4629	78	52	)	)	PUNCT
ejpam-4629	78	53	◦	◦	NOUN
ejpam-4629	78	54	(	(	PUNCT
ejpam-4629	78	55	e	e	X
ejpam-4629	78	56	□	□	SYM
ejpam-4629	78	57	s	s	PART
ejpam-4629	78	58	)	)	PUNCT
ejpam-4629	78	59	◦	◦	NOUN
ejpam-4629	78	60	(	(	PUNCT
ejpam-4629	78	61	d21	d21	NOUN
ejpam-4629	78	62	□	□	PUNCT
ejpam-4629	78	63	e	e	NOUN
ejpam-4629	78	64	)	)	PUNCT
ejpam-4629	78	65	=	=	SYM
ejpam-4629	78	66	(	(	PUNCT
ejpam-4629	78	67	e	e	NOUN
ejpam-4629	78	68	□	□	SYM
ejpam-4629	78	69	d21	d21	NOUN
ejpam-4629	78	70	)	)	PUNCT
ejpam-4629	78	71	◦	◦	NOUN
ejpam-4629	78	72	s	s	PART
ejpam-4629	78	73	(	(	PUNCT
ejpam-4629	78	74	7	7	NUM
ejpam-4629	78	75	)	)	PUNCT
ejpam-4629	78	76	a.	a.	NOUN
ejpam-4629	78	77	kalampakas	kalampakas	PROPN
ejpam-4629	78	78	/	/	SYM
ejpam-4629	78	79	eur	eur	PROPN
ejpam-4629	78	80	.	.	PUNCT
ejpam-4629	79	1	j.	j.	PROPN
ejpam-4629	79	2	pure	pure	PROPN
ejpam-4629	79	3	appl	appl	PROPN
ejpam-4629	79	4	.	.	PROPN
ejpam-4629	79	5	math	math	PROPN
ejpam-4629	79	6	,	,	PUNCT
ejpam-4629	79	7	16	16	NUM
ejpam-4629	79	8	(	(	PUNCT
ejpam-4629	79	9	1	1	NUM
ejpam-4629	79	10	)	)	PUNCT
ejpam-4629	79	11	(	(	PUNCT
ejpam-4629	79	12	2023	2023	NUM
ejpam-4629	79	13	)	)	PUNCT
ejpam-4629	79	14	,	,	PUNCT
ejpam-4629	79	15	112	112	NUM
ejpam-4629	79	16	-	-	SYM
ejpam-4629	79	17	120	120	NUM
ejpam-4629	79	18	116	116	NUM
ejpam-4629	79	19	d12	d12	NOUN
ejpam-4629	79	20	◦	◦	NOUN
ejpam-4629	79	21	(	(	PUNCT
ejpam-4629	79	22	e	e	NOUN
ejpam-4629	79	23	□	□	SYM
ejpam-4629	79	24	d12	d12	NUM
ejpam-4629	79	25	)	)	PUNCT
ejpam-4629	79	26	=	=	SYM
ejpam-4629	80	1	d12	d12	PROPN
ejpam-4629	80	2	◦	◦	NOUN
ejpam-4629	80	3	(	(	PUNCT
ejpam-4629	80	4	d12	d12	NOUN
ejpam-4629	80	5	□	□	PUNCT
ejpam-4629	80	6	e	e	NOUN
ejpam-4629	80	7	)	)	PUNCT
ejpam-4629	80	8	(	(	PUNCT
ejpam-4629	80	9	8)	8)	NUM
ejpam-4629	80	10	d12	d12	NOUN
ejpam-4629	80	11	◦	◦	NOUN
ejpam-4629	80	12	(	(	PUNCT
ejpam-4629	80	13	e	e	NOUN
ejpam-4629	80	14	□	□	SYM
ejpam-4629	80	15	d10	d10	PROPN
ejpam-4629	80	16	)	)	PUNCT
ejpam-4629	80	17	=	=	SYM
ejpam-4629	80	18	e	e	X
ejpam-4629	80	19	(	(	PUNCT
ejpam-4629	80	20	9	9	NUM
ejpam-4629	80	21	)	)	PUNCT
ejpam-4629	80	22	d12	d12	NOUN
ejpam-4629	80	23	◦	◦	PROPN
ejpam-4629	80	24	s	s	PART
ejpam-4629	80	25	=	=	X
ejpam-4629	80	26	d12	d12	X
ejpam-4629	80	27	(	(	PUNCT
ejpam-4629	80	28	10	10	NUM
ejpam-4629	80	29	)	)	PUNCT
ejpam-4629	80	30	s	s	VERB
ejpam-4629	80	31	◦	◦	NOUN
ejpam-4629	80	32	(	(	PUNCT
ejpam-4629	80	33	e	e	NOUN
ejpam-4629	80	34	□	□	SYM
ejpam-4629	80	35	d10	d10	PROPN
ejpam-4629	80	36	)	)	PUNCT
ejpam-4629	80	37	=	=	PUNCT
ejpam-4629	81	1	(	(	PUNCT
ejpam-4629	81	2	d10	d10	PROPN
ejpam-4629	81	3	□	□	PUNCT
ejpam-4629	81	4	e	e	NOUN
ejpam-4629	81	5	)	)	PUNCT
ejpam-4629	81	6	(	(	PUNCT
ejpam-4629	81	7	11	11	NUM
ejpam-4629	81	8	)	)	PUNCT
ejpam-4629	81	9	(	(	PUNCT
ejpam-4629	81	10	d12	d12	NOUN
ejpam-4629	81	11	□	□	PUNCT
ejpam-4629	81	12	e	e	NOUN
ejpam-4629	81	13	)	)	PUNCT
ejpam-4629	81	14	◦	◦	NOUN
ejpam-4629	81	15	(	(	PUNCT
ejpam-4629	81	16	e	e	X
ejpam-4629	81	17	□	□	SYM
ejpam-4629	81	18	s	s	PART
ejpam-4629	81	19	)	)	PUNCT
ejpam-4629	81	20	◦	◦	NOUN
ejpam-4629	81	21	(	(	PUNCT
ejpam-4629	81	22	s	s	X
ejpam-4629	81	23	□	□	SYM
ejpam-4629	81	24	e	e	NOUN
ejpam-4629	81	25	)	)	PUNCT
ejpam-4629	81	26	=	=	SYM
ejpam-4629	81	27	s	s	PART
ejpam-4629	81	28	◦	◦	NOUN
ejpam-4629	81	29	(	(	PUNCT
ejpam-4629	81	30	e	e	NOUN
ejpam-4629	81	31	□	□	SYM
ejpam-4629	81	32	d12	d12	NUM
ejpam-4629	81	33	)	)	PUNCT
ejpam-4629	81	34	(	(	PUNCT
ejpam-4629	81	35	12	12	NUM
ejpam-4629	81	36	)	)	PUNCT
ejpam-4629	81	37	d12	d12	NOUN
ejpam-4629	81	38	◦	◦	PROPN
ejpam-4629	81	39	d21	d21	NOUN
ejpam-4629	81	40	=	=	SYM
ejpam-4629	81	41	e	e	X
ejpam-4629	81	42	(	(	PUNCT
ejpam-4629	81	43	13	13	NUM
ejpam-4629	81	44	)	)	PUNCT
ejpam-4629	81	45	(	(	PUNCT
ejpam-4629	81	46	d12	d12	NOUN
ejpam-4629	81	47	□	□	PUNCT
ejpam-4629	81	48	e	e	NOUN
ejpam-4629	81	49	)	)	PUNCT
ejpam-4629	81	50	◦	◦	NOUN
ejpam-4629	81	51	(	(	PUNCT
ejpam-4629	81	52	e	e	NOUN
ejpam-4629	81	53	□	□	SYM
ejpam-4629	81	54	d21	d21	NOUN
ejpam-4629	81	55	)	)	PUNCT
ejpam-4629	81	56	=	=	SYM
ejpam-4629	81	57	d21	d21	PROPN
ejpam-4629	81	58	◦	◦	PROPN
ejpam-4629	81	59	d12	d12	NUM
ejpam-4629	81	60	(	(	PUNCT
ejpam-4629	81	61	14	14	NUM
ejpam-4629	81	62	)	)	PUNCT
ejpam-4629	81	63	sm,1	sm,1	PROPN
ejpam-4629	81	64	◦	◦	NOUN
ejpam-4629	81	65	(	(	PUNCT
ejpam-4629	81	66	p	p	X
ejpam-4629	81	67	□	□	PUNCT
ejpam-4629	81	68	e	e	NOUN
ejpam-4629	81	69	)	)	PUNCT
ejpam-4629	81	70	=	=	SYM
ejpam-4629	81	71	(	(	PUNCT
ejpam-4629	81	72	e	e	X
ejpam-4629	81	73	□	□	SYM
ejpam-4629	81	74	p	p	ADJ
ejpam-4629	81	75	)	)	PUNCT
ejpam-4629	81	76	◦	◦	NOUN
ejpam-4629	81	77	sn,1	sn,1	PROPN
ejpam-4629	81	78	,	,	PUNCT
ejpam-4629	81	79	for	for	ADP
ejpam-4629	81	80	all	all	DET
ejpam-4629	81	81	p	p	PROPN
ejpam-4629	81	82	∈	∈	PROPN
ejpam-4629	81	83	mm	mm	PROPN
ejpam-4629	81	84	,	,	PUNCT
ejpam-4629	81	85	n	n	CCONJ
ejpam-4629	81	86	(	(	PUNCT
ejpam-4629	81	87	15	15	NUM
ejpam-4629	81	88	)	)	PUNCT
ejpam-4629	81	89	where	where	SCONJ
ejpam-4629	81	90	sm,1	sm,1	PROPN
ejpam-4629	81	91	is	be	AUX
ejpam-4629	81	92	defined	define	VERB
ejpam-4629	81	93	inductively	inductively	ADV
ejpam-4629	81	94	by	by	ADP
ejpam-4629	81	95	s	s	PRON
ejpam-4629	81	96	and	and	CCONJ
ejpam-4629	81	97	represents	represent	VERB
ejpam-4629	81	98	the	the	DET
ejpam-4629	81	99	graph	graph	NOUN
ejpam-4629	81	100	associated	associate	VERB
ejpam-4629	81	101	with	with	ADP
ejpam-4629	81	102	the	the	DET
ejpam-4629	81	103	permutation	permutation	NOUN
ejpam-4629	81	104	that	that	PRON
ejpam-4629	81	105	interchanges	interchange	VERB
ejpam-4629	81	106	the	the	DET
ejpam-4629	81	107	last	last	ADJ
ejpam-4629	81	108	n	n	NOUN
ejpam-4629	81	109	numbers	number	NOUN
ejpam-4629	81	110	with	with	ADP
ejpam-4629	81	111	the	the	DET
ejpam-4629	81	112	first	first	ADJ
ejpam-4629	81	113	one	one	NUM
ejpam-4629	81	114	[	[	X
ejpam-4629	81	115	2	2	NUM
ejpam-4629	81	116	]	]	PUNCT
ejpam-4629	81	117	.	.	PUNCT
ejpam-4629	82	1	we	we	PRON
ejpam-4629	82	2	point	point	VERB
ejpam-4629	82	3	out	out	ADP
ejpam-4629	82	4	that	that	SCONJ
ejpam-4629	82	5	the	the	DET
ejpam-4629	82	6	set	set	NOUN
ejpam-4629	82	7	of	of	ADP
ejpam-4629	82	8	equations	equation	NOUN
ejpam-4629	82	9	(	(	PUNCT
ejpam-4629	82	10	15	15	NUM
ejpam-4629	82	11	)	)	PUNCT
ejpam-4629	82	12	it	it	PRON
ejpam-4629	82	13	only	only	ADV
ejpam-4629	82	14	has	have	VERB
ejpam-4629	82	15	to	to	PART
ejpam-4629	82	16	be	be	AUX
ejpam-4629	82	17	valid	valid	ADJ
ejpam-4629	82	18	for	for	ADP
ejpam-4629	82	19	the	the	DET
ejpam-4629	82	20	elements	element	NOUN
ejpam-4629	82	21	of	of	ADP
ejpam-4629	82	22	σ	σ	PROPN
ejpam-4629	82	23	in	in	ADP
ejpam-4629	82	24	order	order	NOUN
ejpam-4629	82	25	to	to	PART
ejpam-4629	82	26	hold	hold	VERB
ejpam-4629	82	27	for	for	ADP
ejpam-4629	82	28	every	every	DET
ejpam-4629	82	29	element	element	NOUN
ejpam-4629	82	30	of	of	ADP
ejpam-4629	82	31	a	a	DET
ejpam-4629	82	32	magmoid	magmoid	NOUN
ejpam-4629	82	33	generated	generate	VERB
ejpam-4629	82	34	by	by	ADP
ejpam-4629	82	35	σ	σ	PROPN
ejpam-4629	83	1	[	[	X
ejpam-4629	83	2	2	2	NUM
ejpam-4629	83	3	]	]	PUNCT
ejpam-4629	83	4	.	.	PUNCT
ejpam-4629	84	1	thus	thus	ADV
ejpam-4629	84	2	the	the	DET
ejpam-4629	84	3	pair	pair	NOUN
ejpam-4629	84	4	gr(σ	gr(σ	NOUN
ejpam-4629	84	5	)	)	PUNCT
ejpam-4629	84	6	=	=	SYM
ejpam-4629	84	7	(	(	PUNCT
ejpam-4629	84	8	gr(σ	gr(σ	NOUN
ejpam-4629	84	9	)	)	PUNCT
ejpam-4629	84	10	,	,	PUNCT
ejpam-4629	84	11	d	d	NOUN
ejpam-4629	84	12	)	)	PUNCT
ejpam-4629	84	13	,	,	PUNCT
ejpam-4629	84	14	with	with	ADP
ejpam-4629	84	15	d	d	PROPN
ejpam-4629	84	16	=	=	SYM
ejpam-4629	84	17	{	{	PUNCT
ejpam-4629	84	18	π	π	PROPN
ejpam-4629	84	19	,	,	PUNCT
ejpam-4629	84	20	i01	i01	NOUN
ejpam-4629	84	21	,	,	PUNCT
ejpam-4629	84	22	i21	i21	NOUN
ejpam-4629	84	23	,	,	PUNCT
ejpam-4629	84	24	i10	i10	PROPN
ejpam-4629	84	25	,	,	PUNCT
ejpam-4629	84	26	i12	i12	PROPN
ejpam-4629	84	27	}	}	PUNCT
ejpam-4629	84	28	is	be	AUX
ejpam-4629	84	29	a	a	DET
ejpam-4629	84	30	graphoid	graphoid	NOUN
ejpam-4629	84	31	and	and	CCONJ
ejpam-4629	84	32	in	in	ADP
ejpam-4629	84	33	fact	fact	NOUN
ejpam-4629	84	34	it	it	PRON
ejpam-4629	84	35	is	be	AUX
ejpam-4629	84	36	the	the	DET
ejpam-4629	84	37	free	free	ADJ
ejpam-4629	84	38	graphoid	graphoid	NOUN
ejpam-4629	84	39	generated	generate	VERB
ejpam-4629	84	40	by	by	ADP
ejpam-4629	84	41	σ	σ	PROPN
ejpam-4629	84	42	as	as	SCONJ
ejpam-4629	84	43	it	it	PRON
ejpam-4629	84	44	is	be	AUX
ejpam-4629	84	45	illustrated	illustrate	VERB
ejpam-4629	84	46	in	in	ADP
ejpam-4629	84	47	[	[	X
ejpam-4629	84	48	5	5	NUM
ejpam-4629	84	49	]	]	PUNCT
ejpam-4629	84	50	.	.	PUNCT
ejpam-4629	85	1	given	give	VERB
ejpam-4629	85	2	graphoids	graphoid	NOUN
ejpam-4629	85	3	(	(	PUNCT
ejpam-4629	85	4	m	m	PROPN
ejpam-4629	85	5	,	,	PUNCT
ejpam-4629	85	6	d	d	NOUN
ejpam-4629	85	7	)	)	PUNCT
ejpam-4629	85	8	and	and	CCONJ
ejpam-4629	85	9	(	(	PUNCT
ejpam-4629	85	10	m	m	NOUN
ejpam-4629	85	11	′	′	NUM
ejpam-4629	85	12	,	,	PUNCT
ejpam-4629	85	13	d′	d′	NUM
ejpam-4629	85	14	)	)	PUNCT
ejpam-4629	85	15	,	,	PUNCT
ejpam-4629	85	16	a	a	DET
ejpam-4629	85	17	magmoid	magmoid	NOUN
ejpam-4629	85	18	morphism	morphism	NOUN
ejpam-4629	85	19	h	h	NOUN
ejpam-4629	85	20	:	:	PUNCT
ejpam-4629	85	21	m	m	AUX
ejpam-4629	85	22	→	→	SYM
ejpam-4629	85	23	m	m	AUX
ejpam-4629	85	24	′	′	NOUN
ejpam-4629	85	25	preserving	preserve	VERB
ejpam-4629	85	26	d	d	NOUN
ejpam-4629	85	27	-	-	PUNCT
ejpam-4629	85	28	sets	set	NOUN
ejpam-4629	85	29	,	,	PUNCT
ejpam-4629	85	30	i.e.	i.e.	X
ejpam-4629	85	31	,	,	PUNCT
ejpam-4629	85	32	h(s	h(s	NUM
ejpam-4629	85	33	)	)	PUNCT
ejpam-4629	85	34	=	=	SYM
ejpam-4629	85	35	s′	s′	PROPN
ejpam-4629	85	36	and	and	CCONJ
ejpam-4629	85	37	h(dκλ	h(dκλ	PROPN
ejpam-4629	85	38	)	)	PUNCT
ejpam-4629	85	39	=	=	SYM
ejpam-4629	85	40	d′κλ	d′κλ	PROPN
ejpam-4629	85	41	,	,	PUNCT
ejpam-4629	85	42	is	be	AUX
ejpam-4629	85	43	called	call	VERB
ejpam-4629	85	44	a	a	DET
ejpam-4629	85	45	morphism	morphism	NOUN
ejpam-4629	85	46	of	of	ADP
ejpam-4629	85	47	graphoids	graphoid	NOUN
ejpam-4629	85	48	.	.	PUNCT
ejpam-4629	86	1	graphoids	graphoid	NOUN
ejpam-4629	86	2	constructed	construct	VERB
ejpam-4629	86	3	from	from	ADP
ejpam-4629	86	4	the	the	DET
ejpam-4629	86	5	magmoid	magmoid	NOUN
ejpam-4629	86	6	of	of	ADP
ejpam-4629	86	7	relations	relation	NOUN
ejpam-4629	86	8	rel(q	rel(q	PROPN
ejpam-4629	86	9	)	)	PUNCT
ejpam-4629	86	10	over	over	ADP
ejpam-4629	86	11	a	a	DET
ejpam-4629	86	12	given	give	VERB
ejpam-4629	86	13	set	set	NOUN
ejpam-4629	86	14	q	q	PROPN
ejpam-4629	86	15	are	be	AUX
ejpam-4629	86	16	called	call	VERB
ejpam-4629	86	17	relational	relational	ADJ
ejpam-4629	86	18	graphoids	graphoid	NOUN
ejpam-4629	86	19	and	and	CCONJ
ejpam-4629	86	20	a	a	DET
ejpam-4629	86	21	relational	relational	ADJ
ejpam-4629	86	22	graphoid	graphoid	NOUN
ejpam-4629	86	23	is	be	AUX
ejpam-4629	86	24	called	call	VERB
ejpam-4629	86	25	abelian	abelian	ADJ
ejpam-4629	86	26	when	when	SCONJ
ejpam-4629	86	27	s	s	VERB
ejpam-4629	86	28	=	=	PUNCT
ejpam-4629	86	29	{	{	PUNCT
ejpam-4629	86	30	(	(	PUNCT
ejpam-4629	86	31	g1g2	g1g2	X
ejpam-4629	86	32	,	,	PUNCT
ejpam-4629	86	33	g2g1	g2g1	NOUN
ejpam-4629	86	34	)	)	PUNCT
ejpam-4629	86	35	|	|	ADV
ejpam-4629	86	36	g1	g1	NOUN
ejpam-4629	86	37	,	,	PUNCT
ejpam-4629	86	38	g2	g2	PROPN
ejpam-4629	86	39	∈	∈	PROPN
ejpam-4629	86	40	q	q	X
ejpam-4629	86	41	}	}	PUNCT
ejpam-4629	86	42	.	.	PUNCT
ejpam-4629	87	1	the	the	DET
ejpam-4629	87	2	abelian	abelian	PROPN
ejpam-4629	87	3	relational	relational	PROPN
ejpam-4629	87	4	graphoid	graphoid	NOUN
ejpam-4629	87	5	tsrel(q	tsrel(q	NOUN
ejpam-4629	87	6	)	)	PUNCT
ejpam-4629	87	7	=	=	SYM
ejpam-4629	87	8	(	(	PUNCT
ejpam-4629	87	9	rel(q	rel(q	PROPN
ejpam-4629	87	10	)	)	PUNCT
ejpam-4629	87	11	,	,	PUNCT
ejpam-4629	87	12	d	d	X
ejpam-4629	87	13	)	)	PUNCT
ejpam-4629	87	14	that	that	PRON
ejpam-4629	87	15	was	be	AUX
ejpam-4629	87	16	used	use	VERB
ejpam-4629	87	17	for	for	ADP
ejpam-4629	87	18	the	the	DET
ejpam-4629	87	19	introduction	introduction	NOUN
ejpam-4629	87	20	of	of	ADP
ejpam-4629	87	21	graph	graph	NOUN
ejpam-4629	87	22	automata	automata	NOUN
ejpam-4629	87	23	is	be	AUX
ejpam-4629	87	24	constructed	construct	VERB
ejpam-4629	87	25	by	by	ADP
ejpam-4629	87	26	setting	set	VERB
ejpam-4629	87	27	s	s	PRON
ejpam-4629	87	28	as	as	ADV
ejpam-4629	87	29	above	above	ADV
ejpam-4629	87	30	and	and	CCONJ
ejpam-4629	87	31	d01	d01	VERB
ejpam-4629	87	32	=	=	SYM
ejpam-4629	87	33	{	{	PUNCT
ejpam-4629	87	34	(	(	PUNCT
ejpam-4629	87	35	ε	ε	PROPN
ejpam-4629	87	36	,	,	PUNCT
ejpam-4629	87	37	g	g	NOUN
ejpam-4629	87	38	)	)	PUNCT
ejpam-4629	87	39	|	|	ADV
ejpam-4629	87	40	g	g	PROPN
ejpam-4629	87	41	∈	∈	PROPN
ejpam-4629	87	42	q	q	X
ejpam-4629	87	43	}	}	PUNCT
ejpam-4629	87	44	,	,	PUNCT
ejpam-4629	87	45	d21	d21	NOUN
ejpam-4629	87	46	=	=	SYM
ejpam-4629	87	47	{	{	PUNCT
ejpam-4629	87	48	(	(	PUNCT
ejpam-4629	87	49	gg	gg	PROPN
ejpam-4629	87	50	,	,	PUNCT
ejpam-4629	87	51	g	g	NOUN
ejpam-4629	87	52	)	)	PUNCT
ejpam-4629	87	53	|	|	ADV
ejpam-4629	87	54	g	g	PROPN
ejpam-4629	87	55	∈	∈	PROPN
ejpam-4629	87	56	q	q	X
ejpam-4629	87	57	}	}	PUNCT
ejpam-4629	87	58	,	,	PUNCT
ejpam-4629	87	59	d10	d10	PROPN
ejpam-4629	87	60	=	=	SYM
ejpam-4629	87	61	{	{	PUNCT
ejpam-4629	87	62	(	(	PUNCT
ejpam-4629	87	63	g	g	NOUN
ejpam-4629	87	64	,	,	PUNCT
ejpam-4629	87	65	ε	ε	PROPN
ejpam-4629	87	66	)	)	PUNCT
ejpam-4629	87	67	|	|	ADV
ejpam-4629	87	68	g	g	PROPN
ejpam-4629	87	69	∈	∈	PROPN
ejpam-4629	87	70	q	q	X
ejpam-4629	87	71	}	}	PUNCT
ejpam-4629	87	72	,	,	PUNCT
ejpam-4629	87	73	d12	d12	PROPN
ejpam-4629	87	74	=	=	SYM
ejpam-4629	87	75	{	{	PUNCT
ejpam-4629	87	76	(	(	PUNCT
ejpam-4629	87	77	g	g	PROPN
ejpam-4629	87	78	,	,	PUNCT
ejpam-4629	87	79	gg	gg	NOUN
ejpam-4629	87	80	)	)	PUNCT
ejpam-4629	87	81	|	|	ADV
ejpam-4629	87	82	g	g	PROPN
ejpam-4629	87	83	∈	∈	PROPN
ejpam-4629	87	84	q	q	X
ejpam-4629	87	85	}	}	PUNCT
ejpam-4629	87	86	.	.	PUNCT
ejpam-4629	88	1	a	a	DET
ejpam-4629	88	2	nondeterministic	nondeterministic	ADJ
ejpam-4629	88	3	relational	relational	ADJ
ejpam-4629	88	4	graph	graph	NOUN
ejpam-4629	88	5	automaton	automaton	NOUN
ejpam-4629	88	6	is	be	AUX
ejpam-4629	88	7	a	a	DET
ejpam-4629	88	8	structure	structure	NOUN
ejpam-4629	88	9	a	a	PRON
ejpam-4629	88	10	=	=	SYM
ejpam-4629	88	11	(	(	PUNCT
ejpam-4629	88	12	σ	σ	PROPN
ejpam-4629	88	13	,	,	PUNCT
ejpam-4629	88	14	q	q	NOUN
ejpam-4629	88	15	,	,	PUNCT
ejpam-4629	88	16	rel(q	rel(q	PROPN
ejpam-4629	88	17	)	)	PUNCT
ejpam-4629	88	18	,	,	PUNCT
ejpam-4629	88	19	δ	δ	PROPN
ejpam-4629	88	20	,	,	PUNCT
ejpam-4629	88	21	i	i	PRON
ejpam-4629	88	22	,	,	PUNCT
ejpam-4629	88	23	t	t	PROPN
ejpam-4629	88	24	)	)	PUNCT
ejpam-4629	88	25	,	,	PUNCT
ejpam-4629	88	26	a.	a.	PROPN
ejpam-4629	88	27	kalampakas	kalampakas	PROPN
ejpam-4629	88	28	/	/	SYM
ejpam-4629	88	29	eur	eur	PROPN
ejpam-4629	88	30	.	.	PUNCT
ejpam-4629	89	1	j.	j.	PROPN
ejpam-4629	89	2	pure	pure	PROPN
ejpam-4629	89	3	appl	appl	PROPN
ejpam-4629	89	4	.	.	PROPN
ejpam-4629	89	5	math	math	PROPN
ejpam-4629	89	6	,	,	PUNCT
ejpam-4629	89	7	16	16	NUM
ejpam-4629	89	8	(	(	PUNCT
ejpam-4629	89	9	1	1	NUM
ejpam-4629	89	10	)	)	PUNCT
ejpam-4629	89	11	(	(	PUNCT
ejpam-4629	89	12	2023	2023	NUM
ejpam-4629	89	13	)	)	PUNCT
ejpam-4629	89	14	,	,	PUNCT
ejpam-4629	89	15	112	112	NUM
ejpam-4629	89	16	-	-	SYM
ejpam-4629	89	17	120	120	NUM
ejpam-4629	89	18	117	117	NUM
ejpam-4629	89	19	where	where	SCONJ
ejpam-4629	89	20	σ	σ	PROPN
ejpam-4629	89	21	is	be	AUX
ejpam-4629	89	22	the	the	DET
ejpam-4629	89	23	doubly	doubly	ADV
ejpam-4629	89	24	ranked	rank	VERB
ejpam-4629	89	25	set	set	NOUN
ejpam-4629	89	26	of	of	ADP
ejpam-4629	89	27	hyperedge	hyperedge	NOUN
ejpam-4629	89	28	labels	label	NOUN
ejpam-4629	89	29	,	,	PUNCT
ejpam-4629	89	30	q	q	PUNCT
ejpam-4629	89	31	is	be	AUX
ejpam-4629	89	32	the	the	DET
ejpam-4629	89	33	finite	finite	ADJ
ejpam-4629	89	34	set	set	NOUN
ejpam-4629	89	35	of	of	ADP
ejpam-4629	89	36	states	state	NOUN
ejpam-4629	89	37	,	,	PUNCT
ejpam-4629	89	38	rel(q	rel(q	PROPN
ejpam-4629	89	39	)	)	PUNCT
ejpam-4629	89	40	is	be	AUX
ejpam-4629	89	41	a	a	DET
ejpam-4629	89	42	relational	relational	ADJ
ejpam-4629	89	43	graphoid	graphoid	NOUN
ejpam-4629	89	44	over	over	ADP
ejpam-4629	89	45	q	q	PROPN
ejpam-4629	89	46	,	,	PUNCT
ejpam-4629	89	47	δ	δ	PROPN
ejpam-4629	89	48	:	:	PUNCT
ejpam-4629	89	49	σ	σ	PROPN
ejpam-4629	89	50	→	→	SYM
ejpam-4629	89	51	rel(q	rel(q	PROPN
ejpam-4629	89	52	)	)	PUNCT
ejpam-4629	89	53	is	be	AUX
ejpam-4629	89	54	the	the	DET
ejpam-4629	89	55	doubly	doubly	ADV
ejpam-4629	89	56	ranked	rank	VERB
ejpam-4629	89	57	transition	transition	NOUN
ejpam-4629	89	58	function	function	NOUN
ejpam-4629	89	59	and	and	CCONJ
ejpam-4629	89	60	i	i	PRON
ejpam-4629	89	61	,	,	PUNCT
ejpam-4629	89	62	t	t	PROPN
ejpam-4629	89	63	are	be	AUX
ejpam-4629	89	64	initial	initial	ADJ
ejpam-4629	89	65	and	and	CCONJ
ejpam-4629	89	66	final	final	ADJ
ejpam-4629	89	67	rational	rational	ADJ
ejpam-4629	89	68	subsets	subset	NOUN
ejpam-4629	89	69	of	of	ADP
ejpam-4629	89	70	q∗.	q∗.	NOUN
ejpam-4629	89	71	the	the	DET
ejpam-4629	89	72	function	function	NOUN
ejpam-4629	89	73	δ	δ	PROPN
ejpam-4629	89	74	is	be	AUX
ejpam-4629	89	75	uniquely	uniquely	ADV
ejpam-4629	89	76	extended	extend	VERB
ejpam-4629	89	77	into	into	ADP
ejpam-4629	89	78	a	a	DET
ejpam-4629	89	79	morphism	morphism	NOUN
ejpam-4629	89	80	of	of	ADP
ejpam-4629	89	81	graphoids	graphoid	NOUN
ejpam-4629	89	82	δ̄	δ̄	NOUN
ejpam-4629	89	83	:	:	PUNCT
ejpam-4629	89	84	gr(σ	gr(σ	PROPN
ejpam-4629	89	85	)	)	PUNCT
ejpam-4629	89	86	→	→	SYM
ejpam-4629	89	87	rel(q	rel(q	PROPN
ejpam-4629	89	88	)	)	PUNCT
ejpam-4629	89	89	,	,	PUNCT
ejpam-4629	89	90	where	where	SCONJ
ejpam-4629	89	91	δ̄(iκλ	δ̄(iκλ	NOUN
ejpam-4629	89	92	)	)	PUNCT
ejpam-4629	89	93	=	=	SYM
ejpam-4629	89	94	dκλ	dκλ	NOUN
ejpam-4629	89	95	and	and	CCONJ
ejpam-4629	89	96	δ̄(π	δ̄(π	NOUN
ejpam-4629	89	97	)	)	PUNCT
ejpam-4629	89	98	=	=	SYM
ejpam-4629	89	99	s	s	NOUN
ejpam-4629	89	100	,	,	PUNCT
ejpam-4629	89	101	and	and	CCONJ
ejpam-4629	89	102	the	the	DET
ejpam-4629	89	103	behavior	behavior	NOUN
ejpam-4629	89	104	of	of	ADP
ejpam-4629	89	105	a	a	PRON
ejpam-4629	89	106	is	be	AUX
ejpam-4629	89	107	given	give	VERB
ejpam-4629	89	108	by	by	ADP
ejpam-4629	89	109	|a|	|a|	PROPN
ejpam-4629	89	110	=	=	SYM
ejpam-4629	89	111	{	{	PUNCT
ejpam-4629	90	1	f	f	PROPN
ejpam-4629	91	1	|	|	NOUN
ejpam-4629	91	2	f	f	PROPN
ejpam-4629	91	3	∈	∈	PROPN
ejpam-4629	91	4	grm	grm	PROPN
ejpam-4629	91	5	,	,	PUNCT
ejpam-4629	91	6	n(σ	n(σ	PROPN
ejpam-4629	91	7	)	)	PUNCT
ejpam-4629	91	8	,	,	PUNCT
ejpam-4629	91	9	δ̄a(f	δ̄a(f	PROPN
ejpam-4629	91	10	)	)	PUNCT
ejpam-4629	91	11	∩	∩	NOUN
ejpam-4629	91	12	(	(	PUNCT
ejpam-4629	91	13	i	i	PRON
ejpam-4629	91	14	(	(	PUNCT
ejpam-4629	91	15	m	m	PROPN
ejpam-4629	91	16	)	)	PUNCT
ejpam-4629	91	17	a	a	DET
ejpam-4629	91	18	×	×	PROPN
ejpam-4629	91	19	t	t	PROPN
ejpam-4629	91	20	(	(	PUNCT
ejpam-4629	91	21	n	n	CCONJ
ejpam-4629	91	22	)	)	PUNCT
ejpam-4629	91	23	a	a	X
ejpam-4629	91	24	)	)	PUNCT
ejpam-4629	91	25	̸=	̸=	PROPN
ejpam-4629	91	26	∅	∅	NOUN
ejpam-4629	91	27	,	,	PUNCT
ejpam-4629	91	28	m	m	PROPN
ejpam-4629	91	29	,	,	PUNCT
ejpam-4629	91	30	n	n	PROPN
ejpam-4629	91	31	∈	∈	PROPN
ejpam-4629	91	32	n	n	CCONJ
ejpam-4629	91	33	}	}	PUNCT
ejpam-4629	91	34	where	where	SCONJ
ejpam-4629	91	35	i	i	PRON
ejpam-4629	91	36	(	(	PUNCT
ejpam-4629	91	37	m	m	NOUN
ejpam-4629	91	38	)	)	PUNCT
ejpam-4629	91	39	a	a	DET
ejpam-4629	91	40	=	=	X
ejpam-4629	91	41	ia	ia	PROPN
ejpam-4629	91	42	∩qm	∩qm	NOUN
ejpam-4629	91	43	and	and	CCONJ
ejpam-4629	91	44	t	t	PROPN
ejpam-4629	91	45	(	(	PUNCT
ejpam-4629	91	46	n	n	CCONJ
ejpam-4629	91	47	)	)	PUNCT
ejpam-4629	91	48	a	a	PRON
ejpam-4629	91	49	=	=	SYM
ejpam-4629	91	50	ta	ta	X
ejpam-4629	91	51	∩qn	∩qn	ADJ
ejpam-4629	91	52	.	.	PUNCT
ejpam-4629	92	1	from	from	ADP
ejpam-4629	92	2	their	their	PRON
ejpam-4629	92	3	construction	construction	NOUN
ejpam-4629	92	4	,	,	PUNCT
ejpam-4629	92	5	graph	graph	NOUN
ejpam-4629	92	6	automata	automata	NOUN
ejpam-4629	92	7	are	be	AUX
ejpam-4629	92	8	finite	finite	ADJ
ejpam-4629	92	9	machines	machine	NOUN
ejpam-4629	92	10	due	due	ADP
ejpam-4629	92	11	to	to	ADP
ejpam-4629	92	12	the	the	DET
ejpam-4629	92	13	fact	fact	NOUN
ejpam-4629	92	14	that	that	SCONJ
ejpam-4629	92	15	the	the	DET
ejpam-4629	92	16	set	set	NOUN
ejpam-4629	92	17	of	of	ADP
ejpam-4629	92	18	equations	equation	NOUN
ejpam-4629	92	19	(	(	PUNCT
ejpam-4629	92	20	1)-(15	1)-(15	NUM
ejpam-4629	92	21	)	)	PUNCT
ejpam-4629	92	22	is	be	AUX
ejpam-4629	92	23	finite	finite	ADJ
ejpam-4629	92	24	.	.	PUNCT
ejpam-4629	93	1	a	a	DET
ejpam-4629	93	2	graph	graph	NOUN
ejpam-4629	93	3	language	language	NOUN
ejpam-4629	93	4	is	be	AUX
ejpam-4629	93	5	called	call	VERB
ejpam-4629	93	6	recognizable	recognizable	ADJ
ejpam-4629	93	7	whenever	whenever	SCONJ
ejpam-4629	93	8	it	it	PRON
ejpam-4629	93	9	is	be	AUX
ejpam-4629	93	10	obtained	obtain	VERB
ejpam-4629	93	11	as	as	ADP
ejpam-4629	93	12	the	the	DET
ejpam-4629	93	13	behavior	behavior	NOUN
ejpam-4629	93	14	of	of	ADP
ejpam-4629	93	15	a	a	DET
ejpam-4629	93	16	graph	graph	NOUN
ejpam-4629	93	17	automaton	automaton	NOUN
ejpam-4629	93	18	.	.	PUNCT
ejpam-4629	94	1	the	the	DET
ejpam-4629	94	2	class	class	NOUN
ejpam-4629	94	3	of	of	ADP
ejpam-4629	94	4	all	all	DET
ejpam-4629	94	5	such	such	ADJ
ejpam-4629	94	6	languages	language	NOUN
ejpam-4629	94	7	over	over	ADP
ejpam-4629	94	8	the	the	DET
ejpam-4629	94	9	doubly	doubly	ADV
ejpam-4629	94	10	ranked	rank	VERB
ejpam-4629	94	11	set	set	ADJ
ejpam-4629	94	12	σ	σ	PROPN
ejpam-4629	94	13	is	be	AUX
ejpam-4629	94	14	denoted	denote	VERB
ejpam-4629	94	15	by	by	ADP
ejpam-4629	94	16	rec(σ	rec(σ	NOUN
ejpam-4629	94	17	)	)	PUNCT
ejpam-4629	94	18	.	.	PUNCT
ejpam-4629	95	1	4	4	X
ejpam-4629	95	2	.	.	X
ejpam-4629	95	3	a	a	DET
ejpam-4629	95	4	graph	graph	NOUN
ejpam-4629	95	5	automaton	automaton	NOUN
ejpam-4629	95	6	recognizing	recognize	VERB
ejpam-4629	95	7	k	k	ADJ
ejpam-4629	95	8	-	-	ADJ
ejpam-4629	95	9	colorable	colorable	ADJ
ejpam-4629	95	10	graphs	graph	NOUN
ejpam-4629	95	11	in	in	ADP
ejpam-4629	95	12	this	this	DET
ejpam-4629	95	13	section	section	NOUN
ejpam-4629	95	14	we	we	PRON
ejpam-4629	95	15	construct	construct	VERB
ejpam-4629	95	16	a	a	DET
ejpam-4629	95	17	relational	relational	ADJ
ejpam-4629	95	18	graph	graph	NOUN
ejpam-4629	95	19	automaton	automaton	NOUN
ejpam-4629	95	20	over	over	ADP
ejpam-4629	95	21	the	the	DET
ejpam-4629	95	22	abelian	abelian	PROPN
ejpam-4629	95	23	graphoid	graphoid	NOUN
ejpam-4629	95	24	tsrel(q	tsrel(q	NOUN
ejpam-4629	95	25	)	)	PUNCT
ejpam-4629	95	26	recognizing	recognize	VERB
ejpam-4629	95	27	k	k	ADJ
ejpam-4629	95	28	-	-	ADJ
ejpam-4629	95	29	colorable	colorable	ADJ
ejpam-4629	95	30	graphs	graph	NOUN
ejpam-4629	95	31	.	.	PUNCT
ejpam-4629	96	1	for	for	ADP
ejpam-4629	96	2	k	k	PROPN
ejpam-4629	96	3	∈	∈	PROPN
ejpam-4629	96	4	n∗	n∗	PROPN
ejpam-4629	96	5	,	,	PUNCT
ejpam-4629	96	6	we	we	PRON
ejpam-4629	96	7	set	set	VERB
ejpam-4629	96	8	ak	ak	PROPN
ejpam-4629	96	9	clr	clr	NOUN
ejpam-4629	96	10	=	=	SYM
ejpam-4629	96	11	(	(	PUNCT
ejpam-4629	96	12	σ	σ	PROPN
ejpam-4629	96	13	,	,	PUNCT
ejpam-4629	96	14	q	q	NOUN
ejpam-4629	96	15	,	,	PUNCT
ejpam-4629	96	16	tsrel(q	tsrel(q	NOUN
ejpam-4629	96	17	)	)	PUNCT
ejpam-4629	96	18	,	,	PUNCT
ejpam-4629	96	19	δ	δ	PROPN
ejpam-4629	96	20	,	,	PUNCT
ejpam-4629	96	21	i	i	PRON
ejpam-4629	96	22	,	,	PUNCT
ejpam-4629	96	23	t	t	PROPN
ejpam-4629	96	24	)	)	PUNCT
ejpam-4629	96	25	with	with	ADP
ejpam-4629	96	26	•	•	NOUN
ejpam-4629	96	27	σ	σ	NOUN
ejpam-4629	96	28	=	=	PUNCT
ejpam-4629	96	29	{	{	PUNCT
ejpam-4629	96	30	a	a	NOUN
ejpam-4629	96	31	}	}	PUNCT
ejpam-4629	96	32	,	,	PUNCT
ejpam-4629	96	33	rank(a	rank(a	NOUN
ejpam-4629	96	34	)	)	PUNCT
ejpam-4629	96	35	=	=	SYM
ejpam-4629	96	36	(	(	PUNCT
ejpam-4629	96	37	1	1	NUM
ejpam-4629	96	38	,	,	PUNCT
ejpam-4629	96	39	1	1	NUM
ejpam-4629	96	40	)	)	PUNCT
ejpam-4629	96	41	,	,	PUNCT
ejpam-4629	96	42	•	•	NOUN
ejpam-4629	96	43	q	q	NOUN
ejpam-4629	96	44	=	=	PUNCT
ejpam-4629	96	45	{	{	PUNCT
ejpam-4629	96	46	1	1	NUM
ejpam-4629	96	47	,	,	PUNCT
ejpam-4629	96	48	2	2	NUM
ejpam-4629	96	49	,	,	PUNCT
ejpam-4629	96	50	.	.	PUNCT
ejpam-4629	96	51	.	.	PUNCT
ejpam-4629	97	1	.	.	PUNCT
ejpam-4629	98	1	,	,	PUNCT
ejpam-4629	98	2	k	k	X
ejpam-4629	98	3	}	}	PUNCT
ejpam-4629	98	4	,	,	PUNCT
ejpam-4629	98	5	•	•	DET
ejpam-4629	98	6	δ(a	δ(a	PROPN
ejpam-4629	98	7	)	)	PUNCT
ejpam-4629	99	1	=	=	PRON
ejpam-4629	99	2	{	{	PUNCT
ejpam-4629	99	3	(	(	PUNCT
ejpam-4629	99	4	i	i	PROPN
ejpam-4629	99	5	,	,	PUNCT
ejpam-4629	99	6	j	j	PROPN
ejpam-4629	99	7	)	)	PUNCT
ejpam-4629	100	1	|	|	ADV
ejpam-4629	100	2	i	i	PRON
ejpam-4629	100	3	,	,	PUNCT
ejpam-4629	100	4	j	j	PROPN
ejpam-4629	100	5	∈	∈	PROPN
ejpam-4629	101	1	q	q	PROPN
ejpam-4629	101	2	,	,	PUNCT
ejpam-4629	101	3	i	i	PRON
ejpam-4629	101	4	̸=	̸=	PROPN
ejpam-4629	101	5	j	j	PROPN
ejpam-4629	101	6	}	}	PUNCT
ejpam-4629	101	7	,	,	PUNCT
ejpam-4629	101	8	•	•	X
ejpam-4629	101	9	i	i	NOUN
ejpam-4629	101	10	=	=	SYM
ejpam-4629	101	11	t	t	PROPN
ejpam-4629	101	12	=	=	SYM
ejpam-4629	101	13	{	{	PUNCT
ejpam-4629	101	14	ε	ε	PROPN
ejpam-4629	101	15	}	}	PUNCT
ejpam-4629	101	16	.	.	PUNCT
ejpam-4629	102	1	it	it	PRON
ejpam-4629	102	2	is	be	AUX
ejpam-4629	102	3	clear	clear	ADJ
ejpam-4629	102	4	that	that	SCONJ
ejpam-4629	102	5	the	the	DET
ejpam-4629	102	6	automaton	automaton	PROPN
ejpam-4629	102	7	ak	ak	PROPN
ejpam-4629	102	8	clr	clr	PROPN
ejpam-4629	102	9	reads	read	NOUN
ejpam-4629	102	10	unlabeled	unlabele	VERB
ejpam-4629	102	11	(	(	PUNCT
ejpam-4629	102	12	0	0	NUM
ejpam-4629	102	13	,	,	PUNCT
ejpam-4629	102	14	0)-graphs	0)-graphs	NUM
ejpam-4629	102	15	with	with	ADP
ejpam-4629	102	16	binary	binary	ADJ
ejpam-4629	102	17	edges	edge	NOUN
ejpam-4629	102	18	(	(	PUNCT
ejpam-4629	102	19	one	one	NUM
ejpam-4629	102	20	source	source	NOUN
ejpam-4629	102	21	and	and	CCONJ
ejpam-4629	102	22	one	one	NUM
ejpam-4629	102	23	target	target	NOUN
ejpam-4629	102	24	per	per	ADP
ejpam-4629	102	25	edge	edge	NOUN
ejpam-4629	102	26	)	)	PUNCT
ejpam-4629	102	27	,	,	PUNCT
ejpam-4629	102	28	i.e.	i.e.	X
ejpam-4629	102	29	,	,	PUNCT
ejpam-4629	102	30	ordinary	ordinary	ADJ
ejpam-4629	102	31	directed	direct	VERB
ejpam-4629	102	32	graphs	graph	NOUN
ejpam-4629	102	33	.	.	PUNCT
ejpam-4629	103	1	as	as	ADP
ejpam-4629	103	2	an	an	DET
ejpam-4629	103	3	example	example	NOUN
ejpam-4629	103	4	we	we	PRON
ejpam-4629	103	5	shall	shall	AUX
ejpam-4629	103	6	illustrate	illustrate	VERB
ejpam-4629	103	7	the	the	DET
ejpam-4629	103	8	operations	operation	NOUN
ejpam-4629	103	9	of	of	ADP
ejpam-4629	103	10	a2	a2	PROPN
ejpam-4629	103	11	clr	clr	PROPN
ejpam-4629	103	12	,	,	PUNCT
ejpam-4629	103	13	a3	a3	NOUN
ejpam-4629	103	14	clr	clr	NOUN
ejpam-4629	103	15	and	and	CCONJ
ejpam-4629	103	16	a4	a4	NOUN
ejpam-4629	103	17	clr	clr	VERB
ejpam-4629	103	18	on	on	ADP
ejpam-4629	103	19	the	the	DET
ejpam-4629	103	20	following	follow	VERB
ejpam-4629	103	21	graphs	graph	NOUN
ejpam-4629	103	22	,	,	PUNCT
ejpam-4629	103	23	where	where	SCONJ
ejpam-4629	103	24	the	the	DET
ejpam-4629	103	25	label	label	NOUN
ejpam-4629	103	26	in	in	ADP
ejpam-4629	103	27	every	every	DET
ejpam-4629	103	28	edge	edge	NOUN
ejpam-4629	103	29	is	be	AUX
ejpam-4629	103	30	a	a	PRON
ejpam-4629	103	31	and	and	CCONJ
ejpam-4629	103	32	thus	thus	ADV
ejpam-4629	103	33	omitted	omit	VERB
ejpam-4629	103	34	.	.	PUNCT
ejpam-4629	104	1	g	g	PROPN
ejpam-4629	104	2	f	f	PROPN
ejpam-4629	104	3	k3,3	k3,3	PROPN
ejpam-4629	104	4	one	one	NUM
ejpam-4629	104	5	of	of	ADP
ejpam-4629	104	6	the	the	DET
ejpam-4629	104	7	representations	representation	NOUN
ejpam-4629	104	8	of	of	ADP
ejpam-4629	104	9	g	g	PROPN
ejpam-4629	104	10	is	be	AUX
ejpam-4629	104	11	g	g	PROPN
ejpam-4629	104	12	=	=	SYM
ejpam-4629	104	13	i01	i01	PROPN
ejpam-4629	104	14	a	a	DET
ejpam-4629	104	15	i12	i12	PROPN
ejpam-4629	104	16	(	(	PUNCT
ejpam-4629	104	17	a	a	DET
ejpam-4629	104	18	a	a	NOUN
ejpam-4629	104	19	)	)	PUNCT
ejpam-4629	104	20	(	(	PUNCT
ejpam-4629	104	21	a	a	DET
ejpam-4629	104	22	e	e	NOUN
ejpam-4629	104	23	)	)	PUNCT
ejpam-4629	104	24	i21	i21	PROPN
ejpam-4629	104	25	i10	i10	PROPN
ejpam-4629	104	26	a.	a.	PROPN
ejpam-4629	104	27	kalampakas	kalampakas	PROPN
ejpam-4629	104	28	/	/	SYM
ejpam-4629	104	29	eur	eur	PROPN
ejpam-4629	104	30	.	.	PUNCT
ejpam-4629	105	1	j.	j.	PROPN
ejpam-4629	105	2	pure	pure	PROPN
ejpam-4629	105	3	appl	appl	PROPN
ejpam-4629	105	4	.	.	PROPN
ejpam-4629	105	5	math	math	PROPN
ejpam-4629	105	6	,	,	PUNCT
ejpam-4629	105	7	16	16	NUM
ejpam-4629	105	8	(	(	PUNCT
ejpam-4629	105	9	1	1	NUM
ejpam-4629	105	10	)	)	PUNCT
ejpam-4629	105	11	(	(	PUNCT
ejpam-4629	105	12	2023	2023	NUM
ejpam-4629	105	13	)	)	PUNCT
ejpam-4629	105	14	,	,	PUNCT
ejpam-4629	105	15	112	112	NUM
ejpam-4629	105	16	-	-	SYM
ejpam-4629	105	17	120	120	NUM
ejpam-4629	105	18	118	118	NUM
ejpam-4629	105	19	where	where	SCONJ
ejpam-4629	105	20	graph	graph	NOUN
ejpam-4629	105	21	product	product	NOUN
ejpam-4629	105	22	and	and	CCONJ
ejpam-4629	105	23	graph	graph	NOUN
ejpam-4629	105	24	sum	sum	NOUN
ejpam-4629	105	25	are	be	AUX
ejpam-4629	105	26	denoted	denote	VERB
ejpam-4629	105	27	,	,	PUNCT
ejpam-4629	105	28	for	for	ADP
ejpam-4629	105	29	simplicity	simplicity	NOUN
ejpam-4629	105	30	,	,	PUNCT
ejpam-4629	105	31	by	by	ADP
ejpam-4629	105	32	horizontal	horizontal	ADJ
ejpam-4629	105	33	and	and	CCONJ
ejpam-4629	105	34	vertical	vertical	ADJ
ejpam-4629	105	35	concatenation	concatenation	NOUN
ejpam-4629	105	36	.	.	PUNCT
ejpam-4629	106	1	note	note	VERB
ejpam-4629	106	2	that	that	SCONJ
ejpam-4629	106	3	since	since	SCONJ
ejpam-4629	106	4	gr(σ	gr(σ	NOUN
ejpam-4629	106	5	)	)	PUNCT
ejpam-4629	106	6	is	be	AUX
ejpam-4629	106	7	the	the	DET
ejpam-4629	106	8	free	free	ADJ
ejpam-4629	106	9	graphoid	graphoid	NOUN
ejpam-4629	106	10	,	,	PUNCT
ejpam-4629	106	11	the	the	DET
ejpam-4629	106	12	operation	operation	NOUN
ejpam-4629	106	13	of	of	ADP
ejpam-4629	106	14	the	the	DET
ejpam-4629	106	15	automaton	automaton	NOUN
ejpam-4629	106	16	is	be	AUX
ejpam-4629	106	17	the	the	DET
ejpam-4629	106	18	same	same	ADJ
ejpam-4629	106	19	for	for	ADP
ejpam-4629	106	20	every	every	DET
ejpam-4629	106	21	representation	representation	NOUN
ejpam-4629	106	22	of	of	ADP
ejpam-4629	106	23	g.	g.	PROPN
ejpam-4629	106	24	the	the	DET
ejpam-4629	106	25	consumption	consumption	NOUN
ejpam-4629	106	26	of	of	ADP
ejpam-4629	106	27	g	g	NOUN
ejpam-4629	106	28	by	by	ADP
ejpam-4629	106	29	a3	a3	NOUN
ejpam-4629	106	30	clr	clr	NOUN
ejpam-4629	106	31	gives	give	VERB
ejpam-4629	106	32	δ̄(g	δ̄(g	PROPN
ejpam-4629	106	33	)	)	PUNCT
ejpam-4629	107	1	=	=	VERB
ejpam-4629	107	2	d01	d01	PROPN
ejpam-4629	107	3	δ(a	δ(a	PROPN
ejpam-4629	107	4	)	)	PUNCT
ejpam-4629	107	5	d12	d12	NOUN
ejpam-4629	107	6	(	(	PUNCT
ejpam-4629	107	7	δ(a	δ(a	PROPN
ejpam-4629	107	8	)	)	PUNCT
ejpam-4629	107	9	δ(a	δ(a	PROPN
ejpam-4629	107	10	)	)	PUNCT
ejpam-4629	107	11	)	)	PUNCT
ejpam-4629	108	1	(	(	PUNCT
ejpam-4629	108	2	δ(a	δ(a	PROPN
ejpam-4629	108	3	)	)	PUNCT
ejpam-4629	108	4	e	e	NOUN
ejpam-4629	108	5	)	)	PUNCT
ejpam-4629	108	6	d21	d21	PROPN
ejpam-4629	108	7	d10	d10	PROPN
ejpam-4629	108	8	and	and	CCONJ
ejpam-4629	108	9	an	an	DET
ejpam-4629	108	10	accepting	accept	VERB
ejpam-4629	108	11	sequence	sequence	NOUN
ejpam-4629	108	12	of	of	ADP
ejpam-4629	108	13	transitions	transition	NOUN
ejpam-4629	108	14	is	be	AUX
ejpam-4629	108	15	{	{	PUNCT
ejpam-4629	108	16	ε}d01{1}δ(a){2}d12	ε}d01{1}δ(a){2}d12	X
ejpam-4629	108	17	{	{	PUNCT
ejpam-4629	108	18	2	2	NUM
ejpam-4629	108	19	2	2	NUM
ejpam-4629	108	20	}	}	PUNCT
ejpam-4629	108	21	(	(	PUNCT
ejpam-4629	108	22	δ(a	δ(a	PROPN
ejpam-4629	108	23	)	)	PUNCT
ejpam-4629	108	24	δ(a	δ(a	PROPN
ejpam-4629	108	25	)	)	PUNCT
ejpam-4629	108	26	)	)	PUNCT
ejpam-4629	108	27	{	{	PUNCT
ejpam-4629	108	28	3	3	NUM
ejpam-4629	108	29	1	1	NUM
ejpam-4629	108	30	}	}	PUNCT
ejpam-4629	108	31	(	(	PUNCT
ejpam-4629	108	32	δ(a	δ(a	PROPN
ejpam-4629	108	33	)	)	PUNCT
ejpam-4629	108	34	e	e	NOUN
ejpam-4629	108	35	)	)	PUNCT
ejpam-4629	108	36	{	{	PUNCT
ejpam-4629	108	37	1	1	NUM
ejpam-4629	108	38	1	1	NUM
ejpam-4629	108	39	}	}	PUNCT
ejpam-4629	108	40	d21{1	d21{1	PROPN
ejpam-4629	108	41	}	}	PUNCT
ejpam-4629	108	42	d10{ε	d10{ε	ADJ
ejpam-4629	108	43	}	}	PUNCT
ejpam-4629	108	44	where	where	SCONJ
ejpam-4629	108	45	the	the	DET
ejpam-4629	108	46	states	state	NOUN
ejpam-4629	108	47	are	be	AUX
ejpam-4629	108	48	indicated	indicate	VERB
ejpam-4629	108	49	in	in	ADP
ejpam-4629	108	50	brackets	bracket	NOUN
ejpam-4629	108	51	.	.	PUNCT
ejpam-4629	109	1	in	in	ADP
ejpam-4629	109	2	graphical	graphical	ADJ
ejpam-4629	109	3	representation	representation	NOUN
ejpam-4629	109	4	the	the	DET
ejpam-4629	109	5	states	state	NOUN
ejpam-4629	109	6	that	that	SCONJ
ejpam-4629	109	7	the	the	DET
ejpam-4629	109	8	automaton	automaton	NOUN
ejpam-4629	109	9	reaches	reach	VERB
ejpam-4629	109	10	at	at	ADP
ejpam-4629	109	11	each	each	DET
ejpam-4629	109	12	state	state	NOUN
ejpam-4629	109	13	are	be	AUX
ejpam-4629	109	14	1	1	NUM
ejpam-4629	109	15	2	2	NUM
ejpam-4629	109	16	3	3	NUM
ejpam-4629	109	17	1	1	NUM
ejpam-4629	109	18	which	which	PRON
ejpam-4629	109	19	is	be	AUX
ejpam-4629	109	20	actually	actually	ADV
ejpam-4629	109	21	a	a	DET
ejpam-4629	109	22	proper	proper	ADJ
ejpam-4629	109	23	3	3	NUM
ejpam-4629	109	24	-	-	PUNCT
ejpam-4629	109	25	coloring	coloring	NOUN
ejpam-4629	109	26	of	of	ADP
ejpam-4629	109	27	g.	g.	PROPN
ejpam-4629	109	28	similarly	similarly	ADV
ejpam-4629	109	29	,	,	PUNCT
ejpam-4629	109	30	a	a	DET
ejpam-4629	109	31	representation	representation	NOUN
ejpam-4629	109	32	for	for	ADP
ejpam-4629	109	33	f	f	PROPN
ejpam-4629	109	34	is	be	AUX
ejpam-4629	109	35	f	f	PROPN
ejpam-4629	109	36	=	=	PROPN
ejpam-4629	109	37	i01	i01	PROPN
ejpam-4629	109	38	i13	i13	PROPN
ejpam-4629	109	39	a	a	VERB
ejpam-4629	109	40	a	a	DET
ejpam-4629	109	41	a	a	DET
ejpam-4629	109	42			PROPN
ejpam-4629	109	43			PROPN
ejpam-4629	109	44	e	e	PROPN
ejpam-4629	109	45	i12	i12	NOUN
ejpam-4629	109	46	e	e	PROPN
ejpam-4629	109	47			PROPN
ejpam-4629	109	48			PROPN
ejpam-4629	109	49	e	e	NOUN
ejpam-4629	109	50	a	a	DET
ejpam-4629	109	51	a	a	DET
ejpam-4629	109	52	e	e	NOUN
ejpam-4629	109	53			NOUN
ejpam-4629	109	54	(	(	PUNCT
ejpam-4629	109	55	i21	i21	NOUN
ejpam-4629	109	56	i21	i21	NOUN
ejpam-4629	109	57	)	)	PUNCT
ejpam-4629	109	58	(	(	PUNCT
ejpam-4629	109	59	a	a	DET
ejpam-4629	109	60	e	e	NOUN
ejpam-4629	109	61	)	)	PUNCT
ejpam-4629	109	62	i21	i21	NOUN
ejpam-4629	109	63	i10	i10	PROPN
ejpam-4629	109	64	and	and	CCONJ
ejpam-4629	109	65	it	it	PRON
ejpam-4629	109	66	is	be	AUX
ejpam-4629	109	67	clear	clear	ADJ
ejpam-4629	109	68	that	that	SCONJ
ejpam-4629	109	69	there	there	PRON
ejpam-4629	109	70	exists	exist	VERB
ejpam-4629	109	71	no	no	DET
ejpam-4629	109	72	successful	successful	ADJ
ejpam-4629	109	73	transition	transition	NOUN
ejpam-4629	109	74	of	of	ADP
ejpam-4629	109	75	f	f	PROPN
ejpam-4629	109	76	by	by	ADP
ejpam-4629	109	77	a3	a3	PROPN
ejpam-4629	109	78	clr	clr	PROPN
ejpam-4629	109	79	.	.	PUNCT
ejpam-4629	110	1	a	a	DET
ejpam-4629	110	2	successful	successful	ADJ
ejpam-4629	110	3	transition	transition	NOUN
ejpam-4629	110	4	of	of	ADP
ejpam-4629	110	5	f	f	PROPN
ejpam-4629	110	6	by	by	ADP
ejpam-4629	110	7	a4	a4	NOUN
ejpam-4629	110	8	clr	clr	NOUN
ejpam-4629	110	9	is	be	AUX
ejpam-4629	110	10	{	{	PUNCT
ejpam-4629	110	11	ε}d01{1}d13	ε}d01{1}d13	NUM
ejpam-4629	110	12			NOUN
ejpam-4629	110	13	1	1	NUM
ejpam-4629	110	14	1	1	NUM
ejpam-4629	110	15	1	1	NUM
ejpam-4629	110	16			NOUN
ejpam-4629	110	17	δ(a	δ(a	NOUN
ejpam-4629	110	18	)	)	PUNCT
ejpam-4629	110	19	δ(a	δ(a	PROPN
ejpam-4629	110	20	)	)	PUNCT
ejpam-4629	110	21	δ(a	δ(a	PROPN
ejpam-4629	110	22	)	)	PUNCT
ejpam-4629	110	23			VERB
ejpam-4629	110	24	2	2	NUM
ejpam-4629	110	25	3	3	NUM
ejpam-4629	110	26	4	4	NUM
ejpam-4629	110	27			NOUN
ejpam-4629	110	28			PROPN
ejpam-4629	110	29	e	e	PROPN
ejpam-4629	110	30	d12	d12	PROPN
ejpam-4629	110	31	e	e	PROPN
ejpam-4629	110	32			PROPN
ejpam-4629	110	33			NUM
ejpam-4629	110	34	2	2	NUM
ejpam-4629	110	35	3	3	NUM
ejpam-4629	110	36	3	3	NUM
ejpam-4629	110	37	4	4	NUM
ejpam-4629	110	38			PROPN
ejpam-4629	110	39			PROPN
ejpam-4629	110	40	e	e	X
ejpam-4629	110	41	δ(a	δ(a	PROPN
ejpam-4629	110	42	)	)	PUNCT
ejpam-4629	110	43	δ(a	δ(a	PROPN
ejpam-4629	110	44	)	)	PUNCT
ejpam-4629	110	45	e	e	PROPN
ejpam-4629	110	46			X
ejpam-4629	110	47			NUM
ejpam-4629	110	48	2	2	NUM
ejpam-4629	110	49	2	2	NUM
ejpam-4629	110	50	4	4	NUM
ejpam-4629	110	51	4	4	NUM
ejpam-4629	110	52			PROPN
ejpam-4629	110	53	(	(	PUNCT
ejpam-4629	110	54	d21	d21	PROPN
ejpam-4629	110	55	d21	d21	PROPN
ejpam-4629	110	56	)	)	PUNCT
ejpam-4629	110	57	{	{	PUNCT
ejpam-4629	110	58	2	2	NUM
ejpam-4629	110	59	4	4	NUM
ejpam-4629	110	60	}	}	PUNCT
ejpam-4629	110	61	(	(	PUNCT
ejpam-4629	110	62	δ(a	δ(a	PROPN
ejpam-4629	110	63	)	)	PUNCT
ejpam-4629	110	64	e	e	NOUN
ejpam-4629	110	65	)	)	PUNCT
ejpam-4629	110	66	{	{	PUNCT
ejpam-4629	110	67	4	4	NUM
ejpam-4629	110	68	4	4	NUM
ejpam-4629	110	69	}	}	PUNCT
ejpam-4629	110	70	d21{4	d21{4	PROPN
ejpam-4629	110	71	}	}	PUNCT
ejpam-4629	110	72	d10{ε	d10{ε	ADJ
ejpam-4629	110	73	}	}	PUNCT
ejpam-4629	110	74	and	and	CCONJ
ejpam-4629	110	75	the	the	DET
ejpam-4629	110	76	corresponding	correspond	VERB
ejpam-4629	110	77	4	4	NUM
ejpam-4629	110	78	-	-	PUNCT
ejpam-4629	110	79	coloring	coloring	NOUN
ejpam-4629	110	80	that	that	PRON
ejpam-4629	110	81	is	be	AUX
ejpam-4629	110	82	obtained	obtain	VERB
ejpam-4629	110	83	by	by	ADP
ejpam-4629	110	84	the	the	DET
ejpam-4629	110	85	state	state	NOUN
ejpam-4629	110	86	distribution	distribution	NOUN
ejpam-4629	110	87	of	of	ADP
ejpam-4629	110	88	this	this	DET
ejpam-4629	110	89	transition	transition	NOUN
ejpam-4629	110	90	is	be	AUX
ejpam-4629	110	91	1	1	NUM
ejpam-4629	110	92	3	3	NUM
ejpam-4629	110	93	2	2	NUM
ejpam-4629	110	94	4	4	NUM
ejpam-4629	110	95	a.	a.	NOUN
ejpam-4629	110	96	kalampakas	kalampakas	PROPN
ejpam-4629	110	97	/	/	SYM
ejpam-4629	110	98	eur	eur	PROPN
ejpam-4629	110	99	.	.	PUNCT
ejpam-4629	111	1	j.	j.	PROPN
ejpam-4629	111	2	pure	pure	PROPN
ejpam-4629	111	3	appl	appl	PROPN
ejpam-4629	111	4	.	.	PROPN
ejpam-4629	111	5	math	math	PROPN
ejpam-4629	111	6	,	,	PUNCT
ejpam-4629	111	7	16	16	NUM
ejpam-4629	111	8	(	(	PUNCT
ejpam-4629	111	9	1	1	NUM
ejpam-4629	111	10	)	)	PUNCT
ejpam-4629	111	11	(	(	PUNCT
ejpam-4629	111	12	2023	2023	NUM
ejpam-4629	111	13	)	)	PUNCT
ejpam-4629	111	14	,	,	PUNCT
ejpam-4629	111	15	112	112	NUM
ejpam-4629	111	16	-	-	SYM
ejpam-4629	111	17	120	120	NUM
ejpam-4629	111	18	119	119	NUM
ejpam-4629	111	19	note	note	NOUN
ejpam-4629	111	20	that	that	SCONJ
ejpam-4629	111	21	the	the	DET
ejpam-4629	111	22	elementary	elementary	ADJ
ejpam-4629	111	23	graph	graph	NOUN
ejpam-4629	111	24	π	π	PROPN
ejpam-4629	111	25	is	be	AUX
ejpam-4629	111	26	not	not	PART
ejpam-4629	111	27	necessary	necessary	ADJ
ejpam-4629	111	28	for	for	ADP
ejpam-4629	111	29	the	the	DET
ejpam-4629	111	30	representation	representation	NOUN
ejpam-4629	111	31	of	of	ADP
ejpam-4629	111	32	g	g	PROPN
ejpam-4629	111	33	and	and	CCONJ
ejpam-4629	111	34	f	f	PROPN
ejpam-4629	111	35	.	.	PUNCT
ejpam-4629	112	1	more	more	ADV
ejpam-4629	112	2	generally	generally	ADV
ejpam-4629	112	3	,	,	PUNCT
ejpam-4629	112	4	all	all	DET
ejpam-4629	112	5	planar	planar	ADJ
ejpam-4629	112	6	graphs	graph	NOUN
ejpam-4629	112	7	can	can	AUX
ejpam-4629	112	8	be	be	AUX
ejpam-4629	112	9	represented	represent	VERB
ejpam-4629	112	10	without	without	ADP
ejpam-4629	112	11	employing	employ	VERB
ejpam-4629	112	12	π	π	PROPN
ejpam-4629	112	13	.	.	PUNCT
ejpam-4629	113	1	on	on	ADP
ejpam-4629	113	2	the	the	DET
ejpam-4629	113	3	other	other	ADJ
ejpam-4629	113	4	hand	hand	NOUN
ejpam-4629	113	5	,	,	PUNCT
ejpam-4629	113	6	the	the	DET
ejpam-4629	113	7	non	non	ADJ
ejpam-4629	113	8	-	-	ADJ
ejpam-4629	113	9	planar	planar	ADJ
ejpam-4629	113	10	graph	graph	NOUN
ejpam-4629	113	11	k3,3	k3,3	PROPN
ejpam-4629	113	12	is	be	AUX
ejpam-4629	113	13	expressed	express	VERB
ejpam-4629	113	14	as	as	ADP
ejpam-4629	113	15	k3,3	k3,3	PROPN
ejpam-4629	113	16	=	=	PROPN
ejpam-4629	113	17	i01	i01	PROPN
ejpam-4629	113	18	i01	i01	PROPN
ejpam-4629	113	19	i01	i01	PROPN
ejpam-4629	113	20	i13	i13	PROPN
ejpam-4629	113	21	i13	i13	PROPN
ejpam-4629	113	22	i13	i13	PROPN
ejpam-4629	113	23			PROPN
ejpam-4629	114	1	a	a	X
ejpam-4629	114	2	...	...	PUNCT
ejpam-4629	115	1	a	a	DET
ejpam-4629	115	2	πs	πs	NUM
ejpam-4629	115	3	i31	i31	ADJ
ejpam-4629	115	4	i31	i31	NOUN
ejpam-4629	115	5	i31	i31	NOUN
ejpam-4629	115	6	i10	i10	PROPN
ejpam-4629	115	7	i10	i10	PROPN
ejpam-4629	115	8	i10	i10	PROPN
ejpam-4629	115	9			PROPN
ejpam-4629	115	10	where	where	SCONJ
ejpam-4629	115	11	in	in	ADP
ejpam-4629	115	12	the	the	DET
ejpam-4629	115	13	third	third	ADJ
ejpam-4629	115	14	parenthesis	parenthesis	NOUN
ejpam-4629	115	15	there	there	PRON
ejpam-4629	115	16	are	be	VERB
ejpam-4629	115	17	9	9	NUM
ejpam-4629	115	18	a	a	NOUN
ejpam-4629	115	19	and	and	CCONJ
ejpam-4629	115	20	πs	πs	ADV
ejpam-4629	115	21	stands	stand	VERB
ejpam-4629	115	22	for	for	ADP
ejpam-4629	115	23	the	the	DET
ejpam-4629	115	24	graph	graph	NOUN
ejpam-4629	115	25	that	that	PRON
ejpam-4629	115	26	is	be	AUX
ejpam-4629	115	27	associated	associate	VERB
ejpam-4629	115	28	with	with	ADP
ejpam-4629	115	29	the	the	DET
ejpam-4629	115	30	permutation	permutation	NOUN
ejpam-4629	115	31	(	(	PUNCT
ejpam-4629	115	32	1	1	NUM
ejpam-4629	115	33	2	2	NUM
ejpam-4629	115	34	3	3	NUM
ejpam-4629	115	35	4	4	NUM
ejpam-4629	115	36	5	5	NUM
ejpam-4629	115	37	6	6	NUM
ejpam-4629	115	38	7	7	NUM
ejpam-4629	115	39	8	8	NUM
ejpam-4629	115	40	9	9	NUM
ejpam-4629	115	41	1	1	NUM
ejpam-4629	115	42	4	4	NUM
ejpam-4629	115	43	7	7	NUM
ejpam-4629	115	44	2	2	NUM
ejpam-4629	115	45	5	5	NUM
ejpam-4629	115	46	8	8	NUM
ejpam-4629	115	47	3	3	NUM
ejpam-4629	115	48	6	6	NUM
ejpam-4629	115	49	9	9	NUM
ejpam-4629	115	50	)	)	PUNCT
ejpam-4629	115	51	notice	notice	VERB
ejpam-4629	115	52	that	that	SCONJ
ejpam-4629	115	53	as	as	SCONJ
ejpam-4629	115	54	it	it	PRON
ejpam-4629	115	55	is	be	AUX
ejpam-4629	115	56	shown	show	VERB
ejpam-4629	115	57	in	in	ADP
ejpam-4629	115	58	[	[	X
ejpam-4629	115	59	2	2	NUM
ejpam-4629	115	60	]	]	PUNCT
ejpam-4629	115	61	for	for	ADP
ejpam-4629	115	62	every	every	DET
ejpam-4629	115	63	permutation	permutation	NOUN
ejpam-4629	115	64	we	we	PRON
ejpam-4629	115	65	can	can	AUX
ejpam-4629	115	66	construct	construct	VERB
ejpam-4629	115	67	,	,	PUNCT
ejpam-4629	115	68	inductively	inductively	ADV
ejpam-4629	115	69	by	by	ADP
ejpam-4629	115	70	π	π	PROPN
ejpam-4629	115	71	and	and	CCONJ
ejpam-4629	115	72	e	e	X
ejpam-4629	115	73	a	a	DET
ejpam-4629	115	74	graph	graph	NOUN
ejpam-4629	115	75	that	that	PRON
ejpam-4629	115	76	represents	represent	VERB
ejpam-4629	115	77	it	it	PRON
ejpam-4629	115	78	.	.	PUNCT
ejpam-4629	116	1	the	the	DET
ejpam-4629	116	2	graphk3,3	graphk3,3	PROPN
ejpam-4629	116	3	is	be	AUX
ejpam-4629	116	4	2	2	NUM
ejpam-4629	116	5	-	-	PUNCT
ejpam-4629	116	6	colorable	colorable	ADJ
ejpam-4629	116	7	and	and	CCONJ
ejpam-4629	116	8	an	an	DET
ejpam-4629	116	9	accepting	accept	VERB
ejpam-4629	116	10	transition	transition	NOUN
ejpam-4629	116	11	of	of	ADP
ejpam-4629	116	12	a2	a2	PROPN
ejpam-4629	116	13	clr	clr	NOUN
ejpam-4629	116	14	is	be	AUX
ejpam-4629	116	15	{	{	PUNCT
ejpam-4629	116	16	ε	ε	PROPN
ejpam-4629	116	17	}	}	PUNCT
ejpam-4629	116	18	d01	d01	PROPN
ejpam-4629	116	19	d01	d01	NOUN
ejpam-4629	116	20	d01	d01	NOUN
ejpam-4629	116	21			VERB
ejpam-4629	116	22	1	1	NUM
ejpam-4629	116	23	1	1	NUM
ejpam-4629	116	24	1	1	NUM
ejpam-4629	117	1			PROPN
ejpam-4629	117	2	d13	d13	PROPN
ejpam-4629	117	3	d13	d13	NOUN
ejpam-4629	117	4	d13	d13	NOUN
ejpam-4629	117	5			PROPN
ejpam-4629	117	6			NOUN
ejpam-4629	117	7	1	1	NUM
ejpam-4629	117	8	...	...	SYM
ejpam-4629	117	9	1	1	NUM
ejpam-4629	117	10			PRON
ejpam-4629	117	11	δ(a	δ(a	NOUN
ejpam-4629	117	12	)	)	PUNCT
ejpam-4629	117	13	...	...	PUNCT
ejpam-4629	118	1	δ(a	δ(a	X
ejpam-4629	118	2	)	)	PUNCT
ejpam-4629	118	3			PUNCT
ejpam-4629	119	1			NOUN
ejpam-4629	119	2	2	2	NUM
ejpam-4629	119	3	...	...	SYM
ejpam-4629	119	4	2	2	NUM
ejpam-4629	119	5			AUX
ejpam-4629	119	6	ds	ds	VERB
ejpam-4629	119	7			NOUN
ejpam-4629	119	8	2	2	NUM
ejpam-4629	119	9	...	...	SYM
ejpam-4629	119	10	2	2	NUM
ejpam-4629	119	11			ADP
ejpam-4629	119	12	d31	d31	NOUN
ejpam-4629	119	13	d31	d31	NOUN
ejpam-4629	119	14	d31	d31	NOUN
ejpam-4629	119	15			PUNCT
ejpam-4629	119	16	2	2	NUM
ejpam-4629	119	17	2	2	NUM
ejpam-4629	119	18	2	2	NUM
ejpam-4629	119	19			PROPN
ejpam-4629	119	20	d10	d10	PROPN
ejpam-4629	119	21	d10	d10	PROPN
ejpam-4629	119	22	d10	d10	PROPN
ejpam-4629	119	23			PROPN
ejpam-4629	119	24	{	{	PUNCT
ejpam-4629	119	25	ε	ε	PROPN
ejpam-4629	119	26	}	}	PUNCT
ejpam-4629	119	27	hence	hence	ADV
ejpam-4629	119	28	,	,	PUNCT
ejpam-4629	119	29	if	if	SCONJ
ejpam-4629	119	30	we	we	PRON
ejpam-4629	119	31	denote	denote	VERB
ejpam-4629	119	32	by	by	ADP
ejpam-4629	119	33	kcol	kcol	VERB
ejpam-4629	119	34	the	the	DET
ejpam-4629	119	35	set	set	NOUN
ejpam-4629	119	36	of	of	ADP
ejpam-4629	119	37	all	all	DET
ejpam-4629	119	38	k	k	ADJ
ejpam-4629	119	39	-	-	ADJ
ejpam-4629	119	40	colorable	colorable	ADJ
ejpam-4629	119	41	graphs	graph	NOUN
ejpam-4629	119	42	,	,	PUNCT
ejpam-4629	119	43	we	we	PRON
ejpam-4629	119	44	obtain	obtain	VERB
ejpam-4629	119	45	theorem	theorem	ADJ
ejpam-4629	119	46	1	1	NUM
ejpam-4629	119	47	.	.	PUNCT
ejpam-4629	120	1	for	for	ADP
ejpam-4629	120	2	every	every	DET
ejpam-4629	120	3	k	k	PROPN
ejpam-4629	120	4	∈	∈	PROPN
ejpam-4629	120	5	n	n	CCONJ
ejpam-4629	120	6	,	,	PUNCT
ejpam-4629	120	7	the	the	DET
ejpam-4629	120	8	graph	graph	NOUN
ejpam-4629	120	9	language	language	NOUN
ejpam-4629	120	10	kcol	kcol	NOUN
ejpam-4629	120	11	is	be	AUX
ejpam-4629	120	12	recognizable	recognizable	ADJ
ejpam-4629	120	13	.	.	PUNCT
ejpam-4629	121	1	5	5	X
ejpam-4629	121	2	.	.	X
ejpam-4629	121	3	discussion	discussion	NOUN
ejpam-4629	121	4	we	we	PRON
ejpam-4629	121	5	showed	show	VERB
ejpam-4629	121	6	that	that	SCONJ
ejpam-4629	121	7	k	k	ADJ
ejpam-4629	121	8	-	-	PUNCT
ejpam-4629	121	9	colorability	colorability	NOUN
ejpam-4629	121	10	is	be	AUX
ejpam-4629	121	11	graph	graph	NOUN
ejpam-4629	121	12	automaton	automaton	NOUN
ejpam-4629	121	13	recognizable	recognizable	ADJ
ejpam-4629	121	14	even	even	ADV
ejpam-4629	121	15	when	when	SCONJ
ejpam-4629	121	16	the	the	DET
ejpam-4629	121	17	automaton	automaton	NOUN
ejpam-4629	121	18	operates	operate	VERB
ejpam-4629	121	19	over	over	ADP
ejpam-4629	121	20	the	the	DET
ejpam-4629	121	21	most	most	ADV
ejpam-4629	121	22	trivial	trivial	ADJ
ejpam-4629	121	23	abelian	abelian	ADJ
ejpam-4629	121	24	relational	relational	ADJ
ejpam-4629	121	25	graphoid	graphoid	NOUN
ejpam-4629	121	26	.	.	PUNCT
ejpam-4629	122	1	this	this	PRON
ejpam-4629	122	2	indicates	indicate	VERB
ejpam-4629	122	3	that	that	SCONJ
ejpam-4629	122	4	the	the	DET
ejpam-4629	122	5	graph	graph	NOUN
ejpam-4629	122	6	automaton	automaton	NOUN
ejpam-4629	122	7	is	be	AUX
ejpam-4629	122	8	a	a	DET
ejpam-4629	122	9	robust	robust	ADJ
ejpam-4629	122	10	recognition	recognition	NOUN
ejpam-4629	122	11	mechanism	mechanism	NOUN
ejpam-4629	122	12	and	and	CCONJ
ejpam-4629	122	13	evokes	evoke	VERB
ejpam-4629	122	14	numerous	numerous	ADJ
ejpam-4629	122	15	issues	issue	NOUN
ejpam-4629	122	16	regarding	regard	VERB
ejpam-4629	122	17	the	the	DET
ejpam-4629	122	18	class	class	NOUN
ejpam-4629	122	19	of	of	ADP
ejpam-4629	122	20	automaton	automaton	PROPN
ejpam-4629	122	21	recognizable	recognizable	ADJ
ejpam-4629	122	22	graph	graph	NOUN
ejpam-4629	122	23	languages	language	NOUN
ejpam-4629	122	24	.	.	PUNCT
ejpam-4629	123	1	the	the	DET
ejpam-4629	123	2	introduced	introduce	VERB
ejpam-4629	123	3	graph	graph	NOUN
ejpam-4629	123	4	automata	automata	NOUN
ejpam-4629	123	5	are	be	AUX
ejpam-4629	123	6	nondeterministic	nondeterministic	ADJ
ejpam-4629	123	7	in	in	ADP
ejpam-4629	123	8	the	the	DET
ejpam-4629	123	9	sense	sense	NOUN
ejpam-4629	123	10	that	that	SCONJ
ejpam-4629	123	11	if	if	SCONJ
ejpam-4629	123	12	σ	σ	PROPN
ejpam-4629	123	13	∈	∈	PROPN
ejpam-4629	123	14	σm	σm	NOUN
ejpam-4629	123	15	,	,	PUNCT
ejpam-4629	123	16	n	n	PROPN
ejpam-4629	123	17	then	then	ADV
ejpam-4629	123	18	δ(σ	δ(σ	PROPN
ejpam-4629	123	19	)	)	PUNCT
ejpam-4629	123	20	is	be	AUX
ejpam-4629	123	21	a	a	DET
ejpam-4629	123	22	relation	relation	NOUN
ejpam-4629	123	23	in	in	ADP
ejpam-4629	123	24	qm	qm	PROPN
ejpam-4629	123	25	×	×	PROPN
ejpam-4629	123	26	qn	qn	PROPN
ejpam-4629	123	27	.	.	PUNCT
ejpam-4629	124	1	the	the	DET
ejpam-4629	124	2	deterministic	deterministic	ADJ
ejpam-4629	124	3	version	version	NOUN
ejpam-4629	124	4	of	of	ADP
ejpam-4629	124	5	this	this	DET
ejpam-4629	124	6	definition	definition	NOUN
ejpam-4629	124	7	is	be	AUX
ejpam-4629	124	8	obtained	obtain	VERB
ejpam-4629	124	9	by	by	ADP
ejpam-4629	124	10	requiring	require	VERB
ejpam-4629	124	11	that	that	SCONJ
ejpam-4629	124	12	δ(σ	δ(σ	PROPN
ejpam-4629	124	13	)	)	PUNCT
ejpam-4629	124	14	is	be	AUX
ejpam-4629	124	15	a	a	DET
ejpam-4629	124	16	function	function	NOUN
ejpam-4629	124	17	from	from	ADP
ejpam-4629	124	18	qm	qm	PROPN
ejpam-4629	124	19	to	to	ADP
ejpam-4629	124	20	qn	qn	PROPN
ejpam-4629	124	21	,	,	PUNCT
ejpam-4629	124	22	i.e.	i.e.	X
ejpam-4629	124	23	,	,	PUNCT
ejpam-4629	124	24	δ(σ	δ(σ	PROPN
ejpam-4629	124	25	)	)	PUNCT
ejpam-4629	124	26	is	be	AUX
ejpam-4629	124	27	an	an	DET
ejpam-4629	124	28	element	element	NOUN
ejpam-4629	124	29	of	of	ADP
ejpam-4629	124	30	funct(q	funct(q	NOUN
ejpam-4629	124	31	)	)	PUNCT
ejpam-4629	124	32	which	which	PRON
ejpam-4629	124	33	is	be	AUX
ejpam-4629	124	34	a	a	DET
ejpam-4629	124	35	submagmoid	submagmoid	NOUN
ejpam-4629	124	36	of	of	ADP
ejpam-4629	124	37	rel(q	rel(q	PROPN
ejpam-4629	124	38	)	)	PUNCT
ejpam-4629	124	39	called	call	VERB
ejpam-4629	124	40	the	the	DET
ejpam-4629	124	41	magmoid	magmoid	NOUN
ejpam-4629	124	42	of	of	ADP
ejpam-4629	124	43	functions	function	NOUN
ejpam-4629	124	44	[	[	X
ejpam-4629	124	45	5	5	NUM
ejpam-4629	124	46	]	]	PUNCT
ejpam-4629	124	47	.	.	PUNCT
ejpam-4629	125	1	it	it	PRON
ejpam-4629	125	2	is	be	AUX
ejpam-4629	125	3	interesting	interesting	ADJ
ejpam-4629	125	4	to	to	PART
ejpam-4629	125	5	compare	compare	VERB
ejpam-4629	125	6	the	the	DET
ejpam-4629	125	7	two	two	NUM
ejpam-4629	125	8	classes	class	NOUN
ejpam-4629	125	9	and	and	CCONJ
ejpam-4629	125	10	in	in	ADP
ejpam-4629	125	11	particular	particular	ADJ
ejpam-4629	125	12	to	to	PART
ejpam-4629	125	13	investigate	investigate	VERB
ejpam-4629	125	14	the	the	DET
ejpam-4629	125	15	existence	existence	NOUN
ejpam-4629	125	16	of	of	ADP
ejpam-4629	125	17	a	a	DET
ejpam-4629	125	18	deterministic	deterministic	ADJ
ejpam-4629	125	19	graph	graph	NOUN
ejpam-4629	125	20	automaton	automaton	NOUN
ejpam-4629	125	21	recognizing	recognize	VERB
ejpam-4629	125	22	k	k	ADJ
ejpam-4629	125	23	-	-	ADJ
ejpam-4629	125	24	colorable	colorable	ADJ
ejpam-4629	125	25	graphs	graph	NOUN
ejpam-4629	125	26	.	.	PUNCT
ejpam-4629	126	1	as	as	SCONJ
ejpam-4629	126	2	it	it	PRON
ejpam-4629	126	3	has	have	AUX
ejpam-4629	126	4	been	be	AUX
ejpam-4629	126	5	proved	prove	VERB
ejpam-4629	126	6	in	in	ADP
ejpam-4629	126	7	[	[	X
ejpam-4629	126	8	8	8	NUM
ejpam-4629	126	9	]	]	X
ejpam-4629	126	10	an	an	DET
ejpam-4629	126	11	infinite	infinite	ADJ
ejpam-4629	126	12	number	number	NOUN
ejpam-4629	126	13	of	of	ADP
ejpam-4629	126	14	non	non	ADJ
ejpam-4629	126	15	-	-	ADJ
ejpam-4629	126	16	isomorphic	isomorphic	ADJ
ejpam-4629	126	17	abelian	abelian	ADJ
ejpam-4629	126	18	relational	relational	ADJ
ejpam-4629	126	19	graphoids	graphoid	NOUN
ejpam-4629	126	20	exists	exist	VERB
ejpam-4629	126	21	.	.	PUNCT
ejpam-4629	127	1	two	two	NUM
ejpam-4629	127	2	questions	question	NOUN
ejpam-4629	127	3	that	that	PRON
ejpam-4629	127	4	naturally	naturally	ADV
ejpam-4629	127	5	arise	arise	VERB
ejpam-4629	127	6	concern	concern	NOUN
ejpam-4629	127	7	the	the	DET
ejpam-4629	127	8	recognition	recognition	NOUN
ejpam-4629	127	9	capacity	capacity	NOUN
ejpam-4629	127	10	of	of	ADP
ejpam-4629	127	11	the	the	DET
ejpam-4629	127	12	corresponding	corresponding	ADJ
ejpam-4629	127	13	automata	automata	NOUN
ejpam-4629	127	14	as	as	ADV
ejpam-4629	127	15	well	well	ADV
ejpam-4629	127	16	as	as	ADP
ejpam-4629	127	17	the	the	DET
ejpam-4629	127	18	existence	existence	NOUN
ejpam-4629	127	19	of	of	ADP
ejpam-4629	127	20	non	non	ADJ
ejpam-4629	127	21	-	-	ADJ
ejpam-4629	127	22	abelian	abelian	ADJ
ejpam-4629	127	23	or	or	CCONJ
ejpam-4629	127	24	non	non	ADJ
ejpam-4629	127	25	-	-	ADJ
ejpam-4629	127	26	relational	relational	ADJ
ejpam-4629	127	27	graphoids	graphoid	NOUN
ejpam-4629	127	28	.	.	PUNCT
ejpam-4629	128	1	moreover	moreover	ADV
ejpam-4629	128	2	,	,	PUNCT
ejpam-4629	128	3	the	the	DET
ejpam-4629	128	4	time	time	NOUN
ejpam-4629	128	5	complexity	complexity	NOUN
ejpam-4629	128	6	for	for	ADP
ejpam-4629	128	7	checking	check	VERB
ejpam-4629	128	8	if	if	SCONJ
ejpam-4629	128	9	a	a	DET
ejpam-4629	128	10	specific	specific	ADJ
ejpam-4629	128	11	graph	graph	NOUN
ejpam-4629	128	12	belongs	belong	VERB
ejpam-4629	128	13	to	to	ADP
ejpam-4629	128	14	the	the	DET
ejpam-4629	128	15	behavior	behavior	NOUN
ejpam-4629	128	16	of	of	ADP
ejpam-4629	128	17	a	a	DET
ejpam-4629	128	18	graph	graph	NOUN
ejpam-4629	128	19	automaton	automaton	NOUN
ejpam-4629	128	20	grows	grow	VERB
ejpam-4629	128	21	polynomially	polynomially	ADV
ejpam-4629	128	22	as	as	ADP
ejpam-4629	128	23	a	a	DET
ejpam-4629	128	24	function	function	NOUN
ejpam-4629	128	25	of	of	ADP
ejpam-4629	128	26	the	the	DET
ejpam-4629	128	27	number	number	NOUN
ejpam-4629	128	28	of	of	ADP
ejpam-4629	128	29	states	state	NOUN
ejpam-4629	128	30	|q|	|q|	X
ejpam-4629	128	31	(	(	PUNCT
ejpam-4629	128	32	see	see	VERB
ejpam-4629	128	33	[	[	X
ejpam-4629	128	34	5	5	NUM
ejpam-4629	128	35	]	]	NUM
ejpam-4629	128	36	)	)	PUNCT
ejpam-4629	128	37	.	.	PUNCT
ejpam-4629	129	1	on	on	ADP
ejpam-4629	129	2	the	the	DET
ejpam-4629	129	3	other	other	ADJ
ejpam-4629	129	4	hand	hand	NOUN
ejpam-4629	129	5	,	,	PUNCT
ejpam-4629	129	6	the	the	DET
ejpam-4629	129	7	complexity	complexity	NOUN
ejpam-4629	129	8	of	of	ADP
ejpam-4629	129	9	the	the	DET
ejpam-4629	129	10	membership	membership	NOUN
ejpam-4629	129	11	problem	problem	NOUN
ejpam-4629	129	12	for	for	ADP
ejpam-4629	129	13	a	a	DET
ejpam-4629	129	14	given	give	VERB
ejpam-4629	129	15	graph	graph	NOUN
ejpam-4629	129	16	automaton	automaton	NOUN
ejpam-4629	129	17	as	as	ADP
ejpam-4629	129	18	a	a	DET
ejpam-4629	129	19	function	function	NOUN
ejpam-4629	129	20	of	of	ADP
ejpam-4629	129	21	the	the	DET
ejpam-4629	129	22	size	size	NOUN
ejpam-4629	129	23	of	of	ADP
ejpam-4629	129	24	the	the	DET
ejpam-4629	129	25	graph	graph	NOUN
ejpam-4629	129	26	for	for	ADP
ejpam-4629	129	27	both	both	CCONJ
ejpam-4629	129	28	the	the	DET
ejpam-4629	129	29	deterministic	deterministic	NOUN
ejpam-4629	129	30	and	and	CCONJ
ejpam-4629	129	31	the	the	DET
ejpam-4629	129	32	nondeterministic	nondeterministic	ADJ
ejpam-4629	129	33	references	reference	NOUN
ejpam-4629	129	34	120	120	NUM
ejpam-4629	129	35	case	case	NOUN
ejpam-4629	129	36	has	have	AUX
ejpam-4629	129	37	not	not	PART
ejpam-4629	129	38	been	be	AUX
ejpam-4629	129	39	investigated	investigate	VERB
ejpam-4629	129	40	.	.	PUNCT
ejpam-4629	130	1	such	such	DET
ejpam-4629	130	2	a	a	DET
ejpam-4629	130	3	result	result	NOUN
ejpam-4629	130	4	would	would	AUX
ejpam-4629	130	5	classify	classify	VERB
ejpam-4629	130	6	automaton	automaton	NOUN
ejpam-4629	130	7	recognizable	recognizable	ADJ
ejpam-4629	130	8	graph	graph	NOUN
ejpam-4629	130	9	languages	language	NOUN
ejpam-4629	130	10	according	accord	VERB
ejpam-4629	130	11	to	to	ADP
ejpam-4629	130	12	their	their	PRON
ejpam-4629	130	13	computational	computational	ADJ
ejpam-4629	130	14	complexity	complexity	NOUN
ejpam-4629	130	15	.	.	PUNCT
ejpam-4629	131	1	in	in	ADP
ejpam-4629	131	2	a	a	DET
ejpam-4629	131	3	different	different	ADJ
ejpam-4629	131	4	approach	approach	NOUN
ejpam-4629	131	5	,	,	PUNCT
ejpam-4629	131	6	graph	graph	NOUN
ejpam-4629	131	7	colorability	colorability	NOUN
ejpam-4629	131	8	can	can	AUX
ejpam-4629	131	9	be	be	AUX
ejpam-4629	131	10	investigated	investigate	VERB
ejpam-4629	131	11	for	for	ADP
ejpam-4629	131	12	directed	direct	VERB
ejpam-4629	131	13	fuzzy	fuzzy	ADJ
ejpam-4629	131	14	graphs	graph	NOUN
ejpam-4629	131	15	,	,	PUNCT
ejpam-4629	131	16	introduced	introduce	VERB
ejpam-4629	131	17	in	in	ADP
ejpam-4629	131	18	[	[	X
ejpam-4629	131	19	9	9	NUM
ejpam-4629	131	20	,	,	PUNCT
ejpam-4629	131	21	10	10	NUM
ejpam-4629	131	22	]	]	PUNCT
ejpam-4629	131	23	in	in	ADP
ejpam-4629	131	24	relation	relation	NOUN
ejpam-4629	131	25	with	with	ADP
ejpam-4629	131	26	the	the	DET
ejpam-4629	131	27	existing	exist	VERB
ejpam-4629	131	28	concept	concept	NOUN
ejpam-4629	131	29	of	of	ADP
ejpam-4629	131	30	fuzzy	fuzzy	ADJ
ejpam-4629	131	31	graph	graph	NOUN
ejpam-4629	131	32	coloring	coloring	NOUN
ejpam-4629	131	33	as	as	ADP
ejpam-4629	131	34	in	in	ADP
ejpam-4629	131	35	[	[	PUNCT
ejpam-4629	131	36	11	11	NUM
ejpam-4629	131	37	]	]	PUNCT
ejpam-4629	131	38	.	.	PUNCT
ejpam-4629	132	1	additionally	additionally	ADV
ejpam-4629	132	2	,	,	PUNCT
ejpam-4629	132	3	graph	graph	NOUN
ejpam-4629	132	4	recognizability	recognizability	NOUN
ejpam-4629	132	5	via	via	ADP
ejpam-4629	132	6	automata	automata	NOUN
ejpam-4629	132	7	could	could	AUX
ejpam-4629	132	8	also	also	ADV
ejpam-4629	132	9	be	be	AUX
ejpam-4629	132	10	applied	apply	VERB
ejpam-4629	132	11	in	in	ADP
ejpam-4629	132	12	scheduling	scheduling	NOUN
ejpam-4629	132	13	problems	problem	NOUN
ejpam-4629	132	14	using	use	VERB
ejpam-4629	132	15	vertex	vertex	NOUN
ejpam-4629	132	16	colorability	colorability	NOUN
ejpam-4629	132	17	as	as	ADP
ejpam-4629	132	18	in	in	ADP
ejpam-4629	132	19	[	[	X
ejpam-4629	132	20	12	12	NUM
ejpam-4629	132	21	]	]	PUNCT
ejpam-4629	132	22	.	.	PUNCT
ejpam-4629	133	1	references	reference	NOUN
ejpam-4629	133	2	[	[	X
ejpam-4629	133	3	1	1	X
ejpam-4629	133	4	]	]	PUNCT
ejpam-4629	133	5	a	a	DET
ejpam-4629	133	6	arnold	arnold	PROPN
ejpam-4629	133	7	and	and	CCONJ
ejpam-4629	133	8	m	m	PROPN
ejpam-4629	133	9	dauchet	dauchet	NOUN
ejpam-4629	133	10	.	.	PUNCT
ejpam-4629	134	1	théorie	théorie	PROPN
ejpam-4629	134	2	des	des	PROPN
ejpam-4629	134	3	magmoides	magmoides	PROPN
ejpam-4629	134	4	.	.	PUNCT
ejpam-4629	135	1	rairo	rairo	PROPN
ejpam-4629	135	2	theoret	theoret	PROPN
ejpam-4629	135	3	.	.	PUNCT
ejpam-4629	136	1	inform	inform	NOUN
ejpam-4629	136	2	.	.	PUNCT
ejpam-4629	137	1	appl	appl	PROPN
ejpam-4629	137	2	.	.	PROPN
ejpam-4629	137	3	,	,	PUNCT
ejpam-4629	137	4	12:235–257	12:235–257	NUM
ejpam-4629	137	5	,	,	PUNCT
ejpam-4629	137	6	1978	1978	NUM
ejpam-4629	137	7	.	.	PUNCT
ejpam-4629	138	1	[	[	X
ejpam-4629	138	2	2	2	NUM
ejpam-4629	138	3	]	]	SYM
ejpam-4629	138	4	s	s	X
ejpam-4629	138	5	bozapalidis	bozapalidi	NOUN
ejpam-4629	138	6	and	and	CCONJ
ejpam-4629	138	7	a	a	DET
ejpam-4629	138	8	kalampakas	kalampakas	NOUN
ejpam-4629	138	9	.	.	PUNCT
ejpam-4629	139	1	an	an	DET
ejpam-4629	139	2	axiomatization	axiomatization	NOUN
ejpam-4629	139	3	of	of	ADP
ejpam-4629	139	4	graphs	graph	NOUN
ejpam-4629	139	5	.	.	PUNCT
ejpam-4629	140	1	acta	acta	PROPN
ejpam-4629	140	2	inform	inform	PROPN
ejpam-4629	140	3	.	.	PUNCT
ejpam-4629	140	4	,	,	PUNCT
ejpam-4629	140	5	41:19	41:19	NUM
ejpam-4629	140	6	–	–	PUNCT
ejpam-4629	140	7	61	61	NUM
ejpam-4629	140	8	,	,	PUNCT
ejpam-4629	140	9	2004	2004	NUM
ejpam-4629	140	10	.	.	PUNCT
ejpam-4629	141	1	[	[	X
ejpam-4629	141	2	3	3	NUM
ejpam-4629	141	3	]	]	X
ejpam-4629	141	4	s	s	X
ejpam-4629	141	5	bozapalidis	bozapalidi	NOUN
ejpam-4629	141	6	and	and	CCONJ
ejpam-4629	141	7	a	a	DET
ejpam-4629	141	8	kalampakas	kalampakas	NOUN
ejpam-4629	141	9	.	.	PUNCT
ejpam-4629	142	1	automata	automata	PROPN
ejpam-4629	142	2	on	on	ADP
ejpam-4629	142	3	patterns	pattern	NOUN
ejpam-4629	142	4	and	and	CCONJ
ejpam-4629	142	5	graphs	graph	NOUN
ejpam-4629	142	6	.	.	PUNCT
ejpam-4629	143	1	in	in	ADP
ejpam-4629	143	2	proceedings	proceeding	NOUN
ejpam-4629	143	3	of	of	ADP
ejpam-4629	143	4	the	the	DET
ejpam-4629	143	5	1st	1st	ADJ
ejpam-4629	143	6	conference	conference	NOUN
ejpam-4629	143	7	on	on	ADP
ejpam-4629	143	8	algebraic	algebraic	PROPN
ejpam-4629	143	9	informatics	informatic	NOUN
ejpam-4629	143	10	,	,	PUNCT
ejpam-4629	143	11	pages	page	NOUN
ejpam-4629	143	12	31–52	31–52	NUM
ejpam-4629	143	13	,	,	PUNCT
ejpam-4629	143	14	2006	2006	NUM
ejpam-4629	143	15	.	.	PUNCT
ejpam-4629	144	1	[	[	X
ejpam-4629	144	2	4	4	NUM
ejpam-4629	144	3	]	]	SYM
ejpam-4629	144	4	s	s	X
ejpam-4629	144	5	bozapalidis	bozapalidi	NOUN
ejpam-4629	144	6	and	and	CCONJ
ejpam-4629	144	7	a	a	DET
ejpam-4629	144	8	kalampakas	kalampakas	NOUN
ejpam-4629	144	9	.	.	PUNCT
ejpam-4629	145	1	recognizability	recognizability	NOUN
ejpam-4629	145	2	of	of	ADP
ejpam-4629	145	3	graph	graph	NOUN
ejpam-4629	145	4	and	and	CCONJ
ejpam-4629	145	5	pattern	pattern	NOUN
ejpam-4629	145	6	languages	language	NOUN
ejpam-4629	145	7	.	.	PUNCT
ejpam-4629	146	1	acta	acta	PROPN
ejpam-4629	146	2	inform	inform	PROPN
ejpam-4629	146	3	.	.	PUNCT
ejpam-4629	146	4	,	,	PUNCT
ejpam-4629	146	5	42:553–581	42:553–581	PROPN
ejpam-4629	146	6	,	,	PUNCT
ejpam-4629	146	7	2006	2006	NUM
ejpam-4629	146	8	.	.	PUNCT
ejpam-4629	147	1	[	[	X
ejpam-4629	147	2	5	5	NUM
ejpam-4629	147	3	]	]	SYM
ejpam-4629	147	4	s	s	X
ejpam-4629	147	5	bozapalidis	bozapalidi	NOUN
ejpam-4629	147	6	and	and	CCONJ
ejpam-4629	147	7	a	a	DET
ejpam-4629	147	8	kalampakas	kalampakas	NOUN
ejpam-4629	147	9	.	.	PUNCT
ejpam-4629	148	1	graph	graph	NOUN
ejpam-4629	148	2	automata	automata	PROPN
ejpam-4629	148	3	.	.	PUNCT
ejpam-4629	149	1	theoret	theoret	ADJ
ejpam-4629	149	2	.	.	PUNCT
ejpam-4629	150	1	comput	comput	NOUN
ejpam-4629	150	2	.	.	PUNCT
ejpam-4629	151	1	sci	sci	PROPN
ejpam-4629	151	2	.	.	PROPN
ejpam-4629	151	3	,	,	PUNCT
ejpam-4629	151	4	393:147	393:147	NUM
ejpam-4629	151	5	–	–	PUNCT
ejpam-4629	151	6	165	165	NUM
ejpam-4629	151	7	,	,	PUNCT
ejpam-4629	151	8	2008	2008	NUM
ejpam-4629	151	9	.	.	PUNCT
ejpam-4629	152	1	[	[	X
ejpam-4629	152	2	6	6	NUM
ejpam-4629	152	3	]	]	SYM
ejpam-4629	152	4	s	s	X
ejpam-4629	152	5	bozapalidis	bozapalidi	NOUN
ejpam-4629	152	6	and	and	CCONJ
ejpam-4629	152	7	a	a	DET
ejpam-4629	152	8	kalampakas	kalampakas	NOUN
ejpam-4629	152	9	.	.	PUNCT
ejpam-4629	153	1	pattern	pattern	NOUN
ejpam-4629	153	2	language	language	NOUN
ejpam-4629	153	3	recognition	recognition	NOUN
ejpam-4629	153	4	and	and	CCONJ
ejpam-4629	153	5	generation	generation	NOUN
ejpam-4629	153	6	.	.	PUNCT
ejpam-4629	154	1	pure	pure	ADJ
ejpam-4629	154	2	mathematics	mathematic	NOUN
ejpam-4629	154	3	and	and	CCONJ
ejpam-4629	154	4	applications	application	NOUN
ejpam-4629	154	5	,	,	PUNCT
ejpam-4629	154	6	22:1–38	22:1–38	NUM
ejpam-4629	154	7	,	,	PUNCT
ejpam-4629	154	8	2011	2011	NUM
ejpam-4629	154	9	.	.	PUNCT
ejpam-4629	155	1	[	[	X
ejpam-4629	155	2	7	7	X
ejpam-4629	155	3	]	]	X
ejpam-4629	155	4	j	j	PROPN
ejpam-4629	155	5	engelfriet	engelfriet	PROPN
ejpam-4629	155	6	and	and	CCONJ
ejpam-4629	155	7	j	j	PROPN
ejpam-4629	155	8	vereijken	vereijken	PROPN
ejpam-4629	155	9	.	.	PUNCT
ejpam-4629	156	1	context	context	NOUN
ejpam-4629	156	2	-	-	PUNCT
ejpam-4629	156	3	free	free	ADJ
ejpam-4629	156	4	graph	graph	NOUN
ejpam-4629	156	5	grammars	grammar	NOUN
ejpam-4629	156	6	and	and	CCONJ
ejpam-4629	156	7	concatenation	concatenation	NOUN
ejpam-4629	156	8	of	of	ADP
ejpam-4629	156	9	graphs	graph	NOUN
ejpam-4629	156	10	.	.	PUNCT
ejpam-4629	157	1	acta	acta	PROPN
ejpam-4629	157	2	informatica	informatica	PROPN
ejpam-4629	157	3	,	,	PUNCT
ejpam-4629	157	4	34:773–803	34:773–803	NUM
ejpam-4629	157	5	,	,	PUNCT
ejpam-4629	157	6	1997	1997	NUM
ejpam-4629	157	7	.	.	PUNCT
ejpam-4629	158	1	[	[	X
ejpam-4629	158	2	8	8	NUM
ejpam-4629	158	3	]	]	PUNCT
ejpam-4629	158	4	a	a	DET
ejpam-4629	158	5	kalampakas	kalampakas	NOUN
ejpam-4629	158	6	.	.	PUNCT
ejpam-4629	159	1	graph	graph	NOUN
ejpam-4629	159	2	automata	automata	PROPN
ejpam-4629	159	3	:	:	PUNCT
ejpam-4629	159	4	the	the	DET
ejpam-4629	159	5	algebraic	algebraic	ADJ
ejpam-4629	159	6	properties	property	NOUN
ejpam-4629	159	7	of	of	ADP
ejpam-4629	159	8	abelian	abelian	ADJ
ejpam-4629	159	9	relational	relational	ADJ
ejpam-4629	159	10	graphoids	graphoid	NOUN
ejpam-4629	159	11	.	.	PUNCT
ejpam-4629	160	1	lecture	lecture	NOUN
ejpam-4629	160	2	notes	note	NOUN
ejpam-4629	160	3	in	in	ADP
ejpam-4629	160	4	computer	computer	NOUN
ejpam-4629	160	5	science	science	NOUN
ejpam-4629	160	6	,	,	PUNCT
ejpam-4629	160	7	7020:168–182	7020:168–182	NOUN
ejpam-4629	160	8	,	,	PUNCT
ejpam-4629	160	9	2011	2011	NUM
ejpam-4629	160	10	.	.	PUNCT
ejpam-4629	161	1	[	[	X
ejpam-4629	161	2	9	9	NUM
ejpam-4629	161	3	]	]	PUNCT
ejpam-4629	161	4	a	a	DET
ejpam-4629	161	5	kalampakas	kalampakas	NOUN
ejpam-4629	161	6	,	,	PUNCT
ejpam-4629	161	7	s.	s.	PROPN
ejpam-4629	161	8	spartalis	spartalis	PROPN
ejpam-4629	161	9	,	,	PUNCT
ejpam-4629	161	10	and	and	CCONJ
ejpam-4629	161	11	l.	l.	PROPN
ejpam-4629	161	12	iliadis	iliadis	PROPN
ejpam-4629	161	13	.	.	PUNCT
ejpam-4629	162	1	syntactic	syntactic	ADJ
ejpam-4629	162	2	recognizability	recognizability	NOUN
ejpam-4629	162	3	of	of	ADP
ejpam-4629	162	4	graphs	graph	NOUN
ejpam-4629	162	5	with	with	ADP
ejpam-4629	162	6	fuzzy	fuzzy	ADJ
ejpam-4629	162	7	attributes	attribute	NOUN
ejpam-4629	162	8	.	.	PUNCT
ejpam-4629	163	1	fuzzy	fuzzy	ADJ
ejpam-4629	163	2	sets	set	NOUN
ejpam-4629	163	3	and	and	CCONJ
ejpam-4629	163	4	systems	system	NOUN
ejpam-4629	163	5	,	,	PUNCT
ejpam-4629	163	6	229:91–100	229:91–100	NUM
ejpam-4629	163	7	,	,	PUNCT
ejpam-4629	163	8	2013	2013	NUM
ejpam-4629	163	9	.	.	PUNCT
ejpam-4629	164	1	theme	theme	NOUN
ejpam-4629	164	2	:	:	PUNCT
ejpam-4629	164	3	computer	computer	NOUN
ejpam-4629	164	4	science	science	NOUN
ejpam-4629	164	5	.	.	PUNCT
ejpam-4629	165	1	[	[	X
ejpam-4629	165	2	10	10	NUM
ejpam-4629	165	3	]	]	PUNCT
ejpam-4629	165	4	a	a	DET
ejpam-4629	165	5	kalampakas	kalampakas	NOUN
ejpam-4629	165	6	,	,	PUNCT
ejpam-4629	165	7	s	s	NOUN
ejpam-4629	165	8	spartalis	spartalis	PROPN
ejpam-4629	165	9	,	,	PUNCT
ejpam-4629	165	10	l	l	PROPN
ejpam-4629	165	11	iliadis	iliadis	PROPN
ejpam-4629	165	12	,	,	PUNCT
ejpam-4629	165	13	and	and	CCONJ
ejpam-4629	165	14	e	e	PROPN
ejpam-4629	165	15	pimenidis	pimenidis	X
ejpam-4629	165	16	.	.	PUNCT
ejpam-4629	166	1	fuzzy	fuzzy	ADJ
ejpam-4629	166	2	graphs	graph	NOUN
ejpam-4629	166	3	:	:	PUNCT
ejpam-4629	166	4	algebraic	algebraic	ADJ
ejpam-4629	166	5	structure	structure	NOUN
ejpam-4629	166	6	and	and	CCONJ
ejpam-4629	166	7	syntactic	syntactic	ADJ
ejpam-4629	166	8	recognition	recognition	NOUN
ejpam-4629	166	9	.	.	PUNCT
ejpam-4629	167	1	artif	artif	INTJ
ejpam-4629	167	2	.	.	PUNCT
ejpam-4629	168	1	intell	intell	PROPN
ejpam-4629	168	2	.	.	PUNCT
ejpam-4629	169	1	rev	rev	PROPN
ejpam-4629	169	2	.	.	PROPN
ejpam-4629	169	3	,	,	PUNCT
ejpam-4629	169	4	42:479–490	42:479–490	NUM
ejpam-4629	169	5	,	,	PUNCT
ejpam-4629	169	6	2014	2014	NUM
ejpam-4629	169	7	.	.	PUNCT
ejpam-4629	170	1	[	[	X
ejpam-4629	170	2	11	11	NUM
ejpam-4629	170	3	]	]	PUNCT
ejpam-4629	170	4	s.	s.	PROPN
ejpam-4629	170	5	munoz	munoz	PROPN
ejpam-4629	170	6	,	,	PUNCT
ejpam-4629	170	7	m.	m.	NOUN
ejpam-4629	170	8	t.	t.	PROPN
ejpam-4629	170	9	ortuno	ortuno	PROPN
ejpam-4629	170	10	,	,	PUNCT
ejpam-4629	170	11	j.	j.	PROPN
ejpam-4629	170	12	ramirez	ramirez	PROPN
ejpam-4629	170	13	,	,	PUNCT
ejpam-4629	170	14	and	and	CCONJ
ejpam-4629	170	15	j.	j.	PROPN
ejpam-4629	170	16	yanez	yanez	PROPN
ejpam-4629	170	17	.	.	PUNCT
ejpam-4629	171	1	coloring	color	VERB
ejpam-4629	171	2	fuzzy	fuzzy	ADJ
ejpam-4629	171	3	graphs	graph	NOUN
ejpam-4629	171	4	.	.	PUNCT
ejpam-4629	172	1	omega	omega	NOUN
ejpam-4629	172	2	,	,	PUNCT
ejpam-4629	172	3	33(3):211–221	33(3):211–221	PROPN
ejpam-4629	172	4	,	,	PUNCT
ejpam-4629	172	5	2005	2005	NUM
ejpam-4629	172	6	.	.	PUNCT
ejpam-4629	173	1	[	[	X
ejpam-4629	173	2	12	12	NUM
ejpam-4629	173	3	]	]	PUNCT
ejpam-4629	173	4	u	u	NOUN
ejpam-4629	173	5	ufuktepe	ufuktepe	NOUN
ejpam-4629	173	6	and	and	CCONJ
ejpam-4629	173	7	g	g	PROPN
ejpam-4629	173	8	bacak	bacak	NOUN
ejpam-4629	173	9	.	.	PUNCT
ejpam-4629	174	1	applying	apply	VERB
ejpam-4629	174	2	mathematica	mathematica	PROPN
ejpam-4629	174	3	and	and	CCONJ
ejpam-4629	174	4	webmathematica	webmathematica	PROPN
ejpam-4629	174	5	to	to	PART
ejpam-4629	174	6	graph	graph	VERB
ejpam-4629	174	7	coloring	coloring	NOUN
ejpam-4629	174	8	.	.	PUNCT
ejpam-4629	175	1	future	future	ADJ
ejpam-4629	175	2	generation	generation	NOUN
ejpam-4629	175	3	computer	computer	NOUN
ejpam-4629	175	4	systems	system	NOUN
ejpam-4629	175	5	,	,	PUNCT
ejpam-4629	175	6	23(5):716–720	23(5):716–720	PROPN
ejpam-4629	175	7	,	,	PUNCT
ejpam-4629	175	8	2007	2007	NUM
ejpam-4629	175	9	.	.	PUNCT