The word problem for inverse monoids presented by one idempotent relator

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)273-289
Number of pages17
JournalTheoretical Computer Science
Volume123
Issue number2
DOIs
StatePublished - 31 Jan 1994
Externally publishedYes

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,

FundersFunder number
N.S.F.

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