Decidability and complexity in automatic monoids

Authors:
Markus Lohrey
Affiliations:
Lehrstuhl für Informatik I, RWTH Aachen, Germany
Venue:
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Year:
2004

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Abstract

We prove several complexity and decidability results for automatic monoids: (i) there exists an automatic monoid with a P-complete word problem, (ii) there exists an automatic monoid such that the first-order theory of the corresponding Cayley-graph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayley-graph is undecidable. Moreover, we show that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [4].