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)

Abstract

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.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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

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