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Decidability and Complexity in Automatic Monoids

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

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].

Keywords

Word Problem Regular Language Hyperbolic Group Automatic Structure Combinatorial Group Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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