The complexity of testing ground reducibility for linear word rewriting systems with variables

  • Gregory Kucherov
  • Michaël Rusinowitch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 968)


In [9] we proved that for a word rewriting system with variables \(x\mathcal{R}\) and a word with variables Ω, it is undecidable if Ω is ground reducible by \(x\mathcal{R}\), that is if all the instances of Ω obtained by substituting its variables by non-empty words are reducible by \(x\mathcal{R}\). On the other hand, if \(x\mathcal{R}\) is linear, the question is decidable for arbitrary (linear or non-linear) Ω. In this paper we futher study the complexity of the above problem and prove that it is co-NP-complete if both \(x\mathcal{R}\) and Ω are restricted to be linear. The proof is based on the construction of a deterministic finite automaton for the language of words reducible by \(x\mathcal{R}\). The construction generalizes the well-known Aho-Corasick automaton for string matching against a set of keywords.


Regular Expression Pointer Position Regular Language String Match Input String 
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 1995

Authors and Affiliations

  • Gregory Kucherov
    • 1
  • Michaël Rusinowitch
    • 1
  1. 1.INRIA-Lorraine and CRINVandœuvre-lès-NancyFrance

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