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Bounded Second-Order Unification Is NP-Complete

  • Jordi Levy
  • Manfred Schmidt-Schauß
  • Mateu Villaret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)

Abstract

Bounded Second-Order Unification is the problem of deciding, for a given second-order equation \({t {\stackrel{_?}=} u}\) and a positive integer m, whether there exists a unifier σ such that, for every second-order variable F, the terms instantiated for F have at most m occurrences of every bound variable.

It is already known that Bounded Second-Order Unification is decidable and NP-hard, whereas general Second-Order Unification is undecidable. We prove that Bounded Second-Order Unification is NP-complete, provided that m is given in unary encoding, by proving that a size-minimal solution can be represented in polynomial space, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time.

Keywords

Equivalence Class Main Path Surface Position Tree Automaton Tree Grammar 
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 2006

Authors and Affiliations

  • Jordi Levy
    • 1
  • Manfred Schmidt-Schauß
    • 2
  • Mateu Villaret
    • 3
  1. 1.IIIA, CSICBarcelonaSpain
  2. 2.Institut für InformatikJohann Wolfgang Goethe-UniversitätFrankfurtGermany
  3. 3.IMA, UdGGironaSpain

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