Technical Report TR-2005-02

BibliographyLohrey, Markus; Ondrusch, Nicole: Inverse monoids: decidability and complexity of algebraic questions.
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Technical Report Computer Science No. 2005/02.
24 pages, english.
CR-SchemaF.4.1 (Mathematical Logic)
F.4.2 (Grammars and Other Rewriting Systems)
Keywordsinverse monoids; word problem; generalized word problem; Cayley-graphs; complexity; decidability
Abstract

This paper investigates the word problem for inverse monoids generated by a set A subject to relations of the form e=f, where e and f are both idempotents in the free inverse monoid generated by A. It is shown that for every fixed monoid of this form the word problem can be solved in polynomial time 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. Finally, it is shown that the Cayley-graph of the free inverse monoid has an undecidable monadic second-order theory.

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Contactlohrey@fmi.uni-stuttgart.de
Department(s)University of Stuttgart, Institute of Formal Methods in Computer Science, Theoretical Computer Science
Entry dateMarch 14, 2005
   Publ. Computer Science