Theory of Computing Systems

, Volume 38, Issue 1, pp 39–81 | Cite as

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

Article

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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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institut für Algebra, Technische Universität Dresden, D-01062 DresdenGermany
  2. 2.Institut für Formale Methoden der Informatik (FMI), Universität Stuttgart, Universitätsstrasse 38, D-70569 Stuttgart {lohrey@informatik.uni-stuttgart.de}Germany

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