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The Complexity of Constraint Satisfaction Problems (Invited Talk)

Author Manuel Bodirsky

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Manuel Bodirsky

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Manuel Bodirsky. The Complexity of Constraint Satisfaction Problems (Invited Talk). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 2-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.STACS.2015.2

Abstract

The tractability conjecture for constraint satisfaction problems (CSPs) 
describes the constraint languages over a finite domain whose CSP can be solved in polynomial-time. The precise formulation of the conjecture 
uses basic notions from universal algebra. In this talk, we give a short introduction to the universal-algebraic approach to the study of the complexity of CSPs. Finally, we discuss attempts to generalise the tractability conjecture to large classes of constraint languages over infinite  domains, in particular for constraint languages that arise in qualitative temporal and spatial reasoning.

Subject Classification

Keywords
  • constraint satisfaction
  • universal algebra
  • model theory
  • clones
  • temporal and spatial reasoning

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References

  1. Libor Barto and Marcin Kozik. Absorbing subalgebras, cyclic terms and the constraint satisfaction problem. Logical Methods in Computer Science, 8/1(07):1-26, 2012. Google Scholar
  2. Manuel Bodirsky and Martin Grohe. Non-dichotomies in constraint satisfaction complexity. In Luca Aceto, Ivan Damgard, Leslie Ann Goldberg, Magnús M. Halldórsson, Anna Ingólfsdóttir, and Igor Walukiewicz, editors, Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, pages 184 -196. Springer Verlag, July 2008. Google Scholar
  3. Manuel Bodirsky, Martin Hils, and Barnaby Martin. On the scope of the universal-algebraic approach to constraint satisfaction. Logical Methods in Computer Science (LMCS), 8(3:13), 2012. An extended abstract that announced some of the results appeared in the proceedings of Logic in Computer Science (LICS'10). Google Scholar
  4. Manuel Bodirsky, Peter Jonsson, and Trung Van Pham. The reducts of the homogeneous binary branching C-relation. Preprint arXiv:1408.2554, 2014. Google Scholar
  5. Manuel Bodirsky, Peter Jonsson, and Timo von Oertzen. Essential convexity and complexity of semi-algebraic constraints. Logical Methods in Computer Science, 8(4), 2012. An extended abstract about a subset of the results has been published under the title Semilinear Program Feasibility at ICALP'10. Google Scholar
  6. Manuel Bodirsky and Jan Kára. The complexity of equality constraint languages. Theory of Computing Systems, 3(2):136-158, 2008. A conference version appeared in the proceedings of Computer Science Russia (CSR'06). Google Scholar
  7. Manuel Bodirsky and Jan Kára. The complexity of temporal constraint satisfaction problems. Journal of the ACM, 57(2):1-41, 2009. An extended abstract appeared in the Proceedings of the Symposium on Theory of Computing (STOC'08). Google Scholar
  8. Manuel Bodirsky and Jaroslav Nešetřil. Constraint satisfaction with countable homogeneous templates. Journal of Logic and Computation, 16(3):359-373, 2006. Google Scholar
  9. Manuel Bodirsky and Michael Pinsker. Reducts of Ramsey structures. AMS Contemporary Mathematics, vol. 558 (Model Theoretic Methods in Finite Combinatorics), pages 489-519, 2011. Google Scholar
  10. Manuel Bodirsky and Michael Pinsker. Schaefer’s theorem for graphs. In Proceedings of the Annual Symposium on Theory of Computing (STOC), pages 655-664, 2011. Preprint of the long version available at arxiv.org/abs/1011.2894. Google Scholar
  11. Manuel Bodirsky and Michael Pinsker. Minimal functions on the random graph. Israel Journal of Mathematics, 200(1):251-296, 2014. Google Scholar
  12. Manuel Bodirsky and Michael Pinsker. Topological Birkhoff. Transactions of the American Mathematical Society, 2014. To appear (electronic version is published). Preprint arxiv.org/abs/1203.1876. Google Scholar
  13. Manuel Bodirsky, Michael Pinsker, and András Pongrácz. The 42 reducts of the random ordered graph. Preprint arXiv:1309.2165, 2013. Google Scholar
  14. Manuel Bodirsky, Michael Pinsker, and Todor Tsankov. Decidability of definability. Journal of Symbolic Logic, 78(4):1036-1054, 2013. A conference version appeared in the Proceedings of LICS 2011, pages 321-328. Google Scholar
  15. Manuel Bodirsky and MichałWrona. Equivalence constraint satisfaction problems. In Proceedings of Computer Science Logic, volume 16 of LIPICS, pages 122-136. Dagstuhl Publishing, September 2012. Google Scholar
  16. V. G. Bodnarčuk, L. A. Kalužnin, V. N. Kotov, and B. A. Romov. Galois theory for Post algebras, part I and II. Cybernetics, 5:243-539, 1969. Google Scholar
  17. Andrei A. Bulatov, Andrei A. Krokhin, and Peter G. Jeavons. Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing, 34:720-742, 2005. Google Scholar
  18. Tomás Feder and Moshe Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM Journal on Computing, 28:57-104, 1999. Google Scholar
  19. David Geiger. Closed systems of functions and predicates. Pacific Journal of Mathematics, 27:95-100, 1968. Google Scholar
  20. C. Ward Henson. Countable homogeneous relational systems and categorical theories. Journal of Symbolic Logic, 37:494-500, 1972. Google Scholar
  21. David Hobby and Ralph McKenzie. The structure of finite algebras, volume 76 of Contemporary Mathematics. American Mathematical Society, 1988. Google Scholar
  22. Wilfrid Hodges. A shorter model theory. Cambridge University Press, Cambridge, 1997. Google Scholar
  23. P. G. Jeavons. On the algebraic structure of combinatorial problems. Theoretical Computer Science, 200:185-204, 1998. Google Scholar
  24. Alexander Kechris, Vladimir Pestov, and Stevo Todorcevic. Fraissé limits, Ramsey theory, and topological dynamics of automorphism groups. Geometric and Functional Analysis, 15(1):106-189, 2005. Google Scholar
  25. Klaus Leeb. Vorlesungen über Pascaltheorie, volume 6 of Arbeitsberichte des Instituts für Mathematische Maschinen und Datenverarbeitung. Friedrich-Alexander-Universität Erlangen-Nürnberg, 1973. Google Scholar
  26. Keith R. Milliken. A Ramsey theorem for trees. Journal of Combinatorial Theory, Series A, 26(3):215 - 237, 1979. Google Scholar
  27. Jaroslav Nešetřil and Vojtěch Rödl. The partite construction and Ramsey set systems. Discrete Mathematics, 75(1-3):327-334, 1989. Google Scholar
  28. Walter Taylor. Varieties obeying homotopy laws. Canadian Journal of Mathematics, 29:498-527, 1977. Google Scholar
  29. Lionel Nguyen Van Thé. A survey on structural ramsey theory and topological dynamics with the Kechris-Pestov-Todorcevic correspondence in mind. Accepted for publication in Zb. Rad. (Beogr.), 2014. Preprint arXiv:1412.3254v2. Google Scholar
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