Decidability and Complexity in Automatic Monoids

  • Markus Lohrey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)


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].


Word Problem Regular Language Hyperbolic Group Automatic Structure Combinatorial Group Theory 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Markus Lohrey
    • 1
  1. 1.Lehrstuhl für Informatik IRWTH AachenGermany

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