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Stratified Context Unification Is NP-Complete

  • Jordi Levy
  • Manfred Schmidt-Schauß
  • Mateu Villaret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)

Abstract

Context Unification is the problem to decide for a given set of second-order equations E where all second-order variables are unary, whether there exists a unifier, such that for every second-order variable X, the abstraction λx. r instantiated for X has exactly one occurrence of the bound variable x in r. Stratified Context Unification is a specialization where the nesting of second-order variables in E is restricted.

It is already known that Stratified Context Unification is decidable, NP-hard, and in PSPACE, whereas the decidability and the complexity of Context Unification is unknown. We prove that Stratified Context Unification is in NP by proving that a size-minimal solution can be represented in a singleton tree grammar of polynomial size, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time. This also demonstrates the high potential of singleton tree grammars for optimizing programs maintaining large terms.

A corollary of our result is that solvability of rewrite constraints is NP-complete.

Keywords

Context Variable Function Symbol Decision Algorithm Surface Equation Main Path 
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 Informatik, FB Informatik und MathematikJohann Wolfgang Goethe-UniversitätFrankfurtGermany
  3. 3.IMA, UdGGironaSpain

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