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A Galois Connection for Valued Constraint Languages of Infinite Size

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9134))

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Abstract

A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen et al. established a Galois connection between finitely-generated weighted clones and finitely-generated weighted relational clones [SICOMP’13], and asked whether this connection holds in general. We answer this question in the affirmative for weighted (relational) clones with real weights and show that the complexity of the corresponding Valued CSPs is preserved.

The authors were supported by a Royal Society Research Grant. Stanislav Živný was supported by a Royal Society University Research Fellowship.

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References

  1. Barto, L., Kozik, M.: Constraint Satisfaction Problems Solvable by Local Consistency Methods. Journal of the ACM 61(1), article No. 3

    Google Scholar 

  2. Barto, L., Kozik, M., Niven, T.: The CSP dichotomy holds for digraphs with no sources and no sinks. SIAM Journal on Computing 38(5), 1782–1802 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Boyd, S.P., Vandenberghe, L.: Convex Optimization, CUP (2004)

    Google Scholar 

  4. Bulatov, A.: A graph of a relational structure and constraint satisfaction problems. In: Proc. LICS 2004. IEEE Computer Society, pp. 448–457 (2004)

    Google Scholar 

  5. Bulatov, A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. Journal of the ACM 53(1), 66–120 (2006)

    Article  MathSciNet  Google Scholar 

  6. Bulatov, A., Krokhin, A., Jeavons, P.: Classifying the Complexity of Constraints using Finite Algebras. SIAM Journal on Computing 34(3), 720–742 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bulatov, A.A.: Complexity of conservative constraint satisfaction problems. ACM Transactions on Computational Logic 12(4), article 24

    Google Scholar 

  8. Bulatov, A.A., Krokhin, A.A., Jeavons, P.G.: The complexity of maximal constraint languages. In: Proc. STOC 2001, pp. 667–674 (2001)

    Google Scholar 

  9. Cohen, D.A., Cooper, M.C., Creed, P., Jeavons, P., Živný, S.: An algebraic theory of complexity for discrete optimisation. SIAM Journal on Computing 42(5), 915–1939 (2013)

    Article  Google Scholar 

  10. Cohen, D.A., Cooper, M.C., Jeavons, P.G., Krokhin, A.A.: The Complexity of Soft Constraint Satisfaction. Artificial Intelligence 170(11), 983–1016 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feder, T., Vardi, M.Y.: The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory. SIAM Journal on Computing 28(1), 57–104 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hell, P., Nešetřil, J.: On the Complexity of \({H}\)-coloring. Journal of Combinatorial Theory, Series B 48(1), 92–110 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hell, P., Nešetřil, J.: Colouring, constraint satisfaction, and complexity. Computer Science Review 2(3), 143–163 (2008)

    Article  MATH  Google Scholar 

  14. Jeavons, P., Krokhin, A., Živný, S.: The complexity of valued constraint satisfaction. Bulletin of the European Association for Theoretical Computer Science (EATCS) 113, 21–55 (2014)

    Google Scholar 

  15. Jeavons, P.G., Cohen, D.A., Gyssens, M.: Closure Properties of Constraints. Journal of the ACM 44(4), 527–548 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kolmogorov, V., Thapper, J., Živný, S.: The power of linear programming for general-valued CSPs. SIAM Journal on Computing 44(1), 1–36 (2015)

    Article  MathSciNet  Google Scholar 

  17. Kolmogorov, V., Živný, S.: The complexity of conservative valued CSPs. Journal of the ACM 60(2), article No. 10

    Google Scholar 

  18. Kozik, M., Ochremiak, J.: Algebraic properties of valued constraintsatisfaction problem. In: Proc. ICALP 2015. Springer (2015)

    Google Scholar 

  19. Schaefer, T.J.: The complexity of satisfiability problems. In: Proc. STOC 1978, pp. 216–226. ACM (1978)

    Google Scholar 

  20. Thapper, J.: Aspects of a constraint optimisation problem, Ph.D. thesis, Department of Computer Science and Information Science, Linköping University (2010)

    Google Scholar 

  21. Thapper, J., Živný, S.: The power of linear programming for valued CSPs. In: Proc. FOCS 2012, pp. 669–678. IEEE (2012)

    Google Scholar 

  22. Thapper, J., Živný, S.: The complexity of finite-valued CSPs. In: Proc. STOC 2013, pp. 695–704. ACM (2013)

    Google Scholar 

  23. Uppman, H.: The complexity of three-element min-sol and conservative min-cost-hom. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 804–815. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Peter Fulla & Stanislav Živný

Authors
  1. Peter Fulla
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  2. Stanislav Živný
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Corresponding author

Correspondence to Stanislav Živný .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Fulla, P., Živný, S. (2015). A Galois Connection for Valued Constraint Languages of Infinite Size. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_42

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  • DOI: https://doi.org/10.1007/978-3-662-47672-7_42

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  • Print ISBN: 978-3-662-47671-0

  • Online ISBN: 978-3-662-47672-7

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