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Stratified Context Unification Is NP-Complete

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Automated Reasoning (IJCAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

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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.

First and third author’s has been partially founded by the CICYT research projects iDEAS (TIN2004-04343) and Mulog (TIN2004-07933-C03-01/03).

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Author information

Authors and Affiliations

  1. IIIA, CSIC, Campus de la UAB, Barcelona, Spain

    Jordi Levy

  2. Institut für Informatik, FB Informatik und Mathematik, Johann Wolfgang Goethe-Universität, Postfach 11 19 32, D-60054, Frankfurt, Germany

    Manfred Schmidt-Schauß

  3. IMA, UdG, Campus de Montilivi, Girona, Spain

    Mateu Villaret

Authors
  1. Jordi Levy
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  2. Manfred Schmidt-Schauß
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  3. Mateu Villaret
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Artificial Intelligence Research Group, University of Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz

    Ulrich Furbach

  2. SRI International, MS EL256,, 333 Ravenswood Avenue, 94025-3493, Menlo Park, CA, USA

    Natarajan Shankar

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Levy, J., Schmidt-Schauß, M., Villaret, M. (2006). Stratified Context Unification Is NP-Complete. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_8

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  • DOI: https://doi.org/10.1007/11814771_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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