Inverse Monoids: Decidability and Complexity of Algebraic Questions

12 years 3 months ago
Inverse Monoids: Decidability and Complexity of Algebraic Questions
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.
Markus Lohrey, Nicole Ondrusch
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where MFCS
Authors Markus Lohrey, Nicole Ondrusch
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