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 |
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Pages (from-to) | 273-289 |
Number of pages | 17 |
Journal | Theoretical Computer Science |
Volume | 123 |
Issue number | 2 |
DOIs | |
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 | Funder number |
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N.S.F. |