The word problem for inverse monoids presented by one idempotent relator

Jean Camille Birget; Stuart W. Margolis; John C. Meakin

doi:10.1016/0304-3975(92)00063-w

The word problem for inverse monoids presented by one idempotent relator

Jean Camille Birget
, Stuart W. Margolis
, John C. Meakin

University of Nebraska-Lincoln

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We study inverse monoids presented by a finite set of generators and one relation e = 1, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvable by a polynomial-time algorithm; (2) every congruence class (in the free monoid) with respect to such a presentation is a deterministic context-free language. Such congruence classes can be viewed as generalizations of parenthesis languages; and (3) the word problem is solvable by a linear-time algorithm in the more special case where e is a "positively labeled" idempotent.

Original language	English
Pages (from-to)	273-289
Number of pages	17
Journal	Theoretical Computer Science
Volume	123
Issue number	2
DOIs	https://doi.org/10.1016/0304-3975(92)00063-w
State	Published - 31 Jan 1994
Externally published	Yes

Bibliographical note

Funding Information:
Correspondence to: J.-C. Birget, Department Nebraska, Lincoln, NE 68588, USA * Research supported by N.S.F. Grant No. Information Sciences, University of Nebraska,

Funding

Correspondence to: J.-C. Birget, Department Nebraska, Lincoln, NE 68588, USA * Research supported by N.S.F. Grant No. Information Sciences, University of Nebraska,

Funders
N.S.F.

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10.1016/0304-3975(92)00063-w

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abstract = "We study inverse monoids presented by a finite set of generators and one relation e = 1, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvable by a polynomial-time algorithm; (2) every congruence class (in the free monoid) with respect to such a presentation is a deterministic context-free language. Such congruence classes can be viewed as generalizations of parenthesis languages; and (3) the word problem is solvable by a linear-time algorithm in the more special case where e is a {"}positively labeled{"} idempotent.",

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N2 - We study inverse monoids presented by a finite set of generators and one relation e = 1, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvable by a polynomial-time algorithm; (2) every congruence class (in the free monoid) with respect to such a presentation is a deterministic context-free language. Such congruence classes can be viewed as generalizations of parenthesis languages; and (3) the word problem is solvable by a linear-time algorithm in the more special case where e is a "positively labeled" idempotent.

AB - We study inverse monoids presented by a finite set of generators and one relation e = 1, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvable by a polynomial-time algorithm; (2) every congruence class (in the free monoid) with respect to such a presentation is a deterministic context-free language. Such congruence classes can be viewed as generalizations of parenthesis languages; and (3) the word problem is solvable by a linear-time algorithm in the more special case where e is a "positively labeled" idempotent.

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The word problem for inverse monoids presented by one idempotent relator

Abstract

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