Back to Search
Start Over
Inverse monoids: Decidability and complexity of algebraic questions
- Source :
-
Information & Computation . Aug2007, Vol. 205 Issue 8, p1212-1234. 23p. - Publication Year :
- 2007
-
Abstract
- Abstract: This paper investigates the word problem for inverse monoids generated by a set Γ subject to relations of the form e = f, where e and f are both idempotents in the free inverse monoid generated by Γ. It is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a RAM as well as in deterministic logarithmic space, which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presentation is part of the input, EXPTIME-completeness is shown. For the Cayley-graphs of these monoids, it is shown that the first-order theory with regular path predicates is decidable. Regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language. As a corollary, the decidability of the generalized word problem is deduced. [Copyright &y& Elsevier]
- Subjects :
- *MONOIDS
*SEMIGROUPS (Algebra)
*ALGEBRA
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 08905401
- Volume :
- 205
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Information & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 25558501
- Full Text :
- https://doi.org/10.1016/j.ic.2007.01.002