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Testing Expressibility Is Hard

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Book cover Principles and Practice of Constraint Programming – CP 2010 (CP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6308))

Abstract

We study the expressibility problem: given a finite constraint language Γ on a finite domain and another relation R, can Γ express R? We prove, by an explicit family of examples, that the standard witnesses to expressibility and inexpressibility (gadgets/formulas/conjunctive queries and polymorphisms respectively) may be required to be exponentially larger than the instances. We also show that the full expressibility problem is co-NEXPTIME-hard. Our proofs hinge on a novel interpretation of a tiling problem into the expressibility problem.

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Authors and Affiliations

  1. Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Ross Willard

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  1. Ross Willard
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, Surrey, United Kingdom

    David Cohen

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Willard, R. (2010). Testing Expressibility Is Hard. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-15396-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15395-2

  • Online ISBN: 978-3-642-15396-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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