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Decidable First-Order Theories of One-Step Rewriting in Trace Monoids

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Abstract

We prove that the first-order theory of the one-step rewriting relation associated with a trace rewriting system is decidable but in general not elementary. This extends known results on semi-Thue systems but our proofs use new methods; these new methods yield the decidability of local properties expressed in first-order logic augmented by modulo-counting quantifiers. Using the main decidability result, we define several subclasses of trace rewriting systems for which the confluence problem is decidable.

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Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, D-01062 Dresden, Germany

    Dietrich Kuske

  2. Institut für Formale Methoden der Informatik (FMI), Universität Stuttgart, Universitätsstrasse 38, D-70569 Stuttgart {lohrey@informatik.uni-stuttgart.de}, Germany

    Markus Lohrey

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  1. Dietrich Kuske
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  2. Markus Lohrey
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Correspondence to Dietrich Kuske or Markus Lohrey.

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Kuske, D., Lohrey, M. Decidable First-Order Theories of One-Step Rewriting in Trace Monoids. Theory Comput Systems 38, 39–81 (2005). https://doi.org/10.1007/s00224-004-1099-9

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  • DOI: https://doi.org/10.1007/s00224-004-1099-9

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