On the Theory of One-Step Rewriting in Trace Monoids

  • Dietrich Kuske
  • Markus Lohrey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)


We prove that the first-order theory of the one-step rewriting relation associated with a trace rewriting system is decidable and give a nonelementary lower bound for the complexity. The decidability 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 describe a class of trace rewriting systems for which the confluence problem is decidable. The complete proofs can be found in the Technical Report [14].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dietrich Kuske
    • 1
  • Markus Lohrey
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of LeicesterLeicesterUK
  2. 2.Universität Stuttgart, Institut für InformatikStuttgartGermany

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