Combinatorial rewriting on traces

  • Volker Diekert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)


There are two main problems in working with replacement systems over free partially commutative monoids: For finite noetherian systems confluence is undecidable, in general, and the known algorithm to compute irreducible normal forms need time square in the derivation length instead of linear. We first give a decidable and sufficient condition for finite noetherian systems such that confluence becomes decidable. This condition is weaker than the known ones before. Then we give a decidable and sufficient condition such that irreducible normal forms are computable in time linear to the derivation length. Furthermore, we prove that the first condition is implied by the second. We also present a new uniform algorithm for computing normal forms using Zielonka's theory of asynchronous automata.


Word Problem Turing Machine Replacement System Derivation Step Commutative Monoid 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Volker Diekert
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2

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