On the CSP Dichotomy Conjecture

  • Andrei A. Bulatov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6651)

Abstract

We report on the status of the CSP Dichotomy Conjecture and survey recent results and approaches to this problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atserias, A., Bulatov, A., Dawar, A.: Affine systems of equations and counting infinitary logic. In: ICALP, pp. 558–570 (2007)Google Scholar
  2. 2.
    Barto, L.: The dichotomy for conservative constraint satisfaction problems revisited (2011)Google Scholar
  3. 3.
    Barto, L., Kozik, M.: Constraint satisfaction problems of bounded width. In: FOCS, pp. 595–603 (2009)Google Scholar
  4. 4.
    Bulatov, A.: Tractable conservative constraint satisfaction problems. In: Proceedings of the 18th Annual IEEE Simposium on Logic in Computer Science, Ottawa, Canada, pp. 321–330. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  5. 5.
    Bulatov, A.: A graph of a relational structure and constraint satisfaction problems. LICS, pp. 448–457 (2004)Google Scholar
  6. 6.
    Bulatov, A.: A dichotomy theorem for constraint satisfaction problems on a 3-element set. J. ACM 53(1), 66–120 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bulatov, A.: Bounded relational width (2009)Google Scholar
  8. 8.
    Bulatov, A., Dalmau, V.: A simple algorithm for Mal’tsev constraints. SIAM J. Comput. 36(1), 16–27 (2006)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Bulatov, A., Jeavons, P., Krokhin, A.: Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34(3), 720–742 (2005)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Bulatov, A., Krokhin, A., Larose, B.: Dualities for constraint satisfaction problems. In: Complexity of Constraints, pp. 93–124 (2008)Google Scholar
  11. 11.
    Bulatov, A., Valeriote, M.: Recent results on the algebraic approach to the CSP. In: Complexity of Constraints, pp. 68–92 (2008)Google Scholar
  12. 12.
    Dalmau, V., Pearson, J.: Set functions and width 1 problems. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 159–173. Springer, Heidelberg (1999)Google Scholar
  13. 13.
    Dalmau, V.: Generalized majority-minority operations are tractable. Logical Methods in Computer Science 11(1) (2005) (electronic)Google Scholar
  14. 14.
    Fagin, R.: Generalized first order spectra, and polynomial time recognizable sets. In: Complexity of Computations (1974)Google Scholar
  15. 15.
    Feder, T., Vardi, M.Y.: Monotone monadic SNP and constraint satisfaction. In: Proceedings of 25th ACM Symposium on the Theory of Computing (STOC), pp. 612–622 (1993)Google Scholar
  16. 16.
    Feder, T., Vardi, M.Y.: The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM Journal of Computing 28, 57–104 (1998)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Freese, R., Valeriote, M.: On the complexity of some maltsev conditions. IJAC 19(1), 41–77 (2009)MathSciNetMATHGoogle Scholar
  18. 18.
    Freuder, E.C.: Synthesizing constraint expressions. Communications of the ACM 21, 958–966 (1978)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Hell, P., Nešetřil, J.: On the complexity of H-coloring. Journal of Combinatorial Theory, Ser.B 48, 92–110 (1990)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Hobby, D., McKenzie, R.N.: The Structure of Finite Algebras. Contemporary Mathematics, vol. 76. American Mathematical Society, Providence (1988)MATHGoogle Scholar
  21. 21.
    Idziak, P., Markovic, P., McKenzie, R., Valeriote, M., Willard, R.: Tractability and learnability arising from algebras with few subpowers. SIAM J. Comput. 39(7), 3023–3037 (2010)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Jeavons, P., Cohen, D., Cooper, M.: Constraints, consistency and closure. Artificial Intelligence 101(1-2), 251–265 (1998)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Jeavons, P., Cohen, D., Gyssens, M.: Closure properties of constraints. Journal of the ACM 44, 527–548 (1997)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Kolaitis, P., Vardi, M.: A game-theoretic approach to constraint satisfaction. In: Proceedings of the 17th National (US) Conference on Artificial Intelligence, AAAI 2000, pp. 175–181 (2000)Google Scholar
  25. 25.
    Kolaitis, P., Vardi, M.: The decision problem for the probabilities of higher-order properties. In: STOC, pp. 425–435 (1987)Google Scholar
  26. 26.
    Kun, G.: Constraints, MMSNP and expander relational structures. Mathematics, abs/0706.1701 (2007)Google Scholar
  27. 27.
    Kun, G., Nešetřil, J.: NP by means of lifts and shadows. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 171–181. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  28. 28.
    Ladner, R.: On the structure of polynomial time reducibility. Journal of the ACM 22, 155–171 (1975)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Larose, B., Tesson, P.: Universal algebra and hardness results for constraint satisfaction problems. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 267–278. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  30. 30.
    Larose, B., Valeriote, M., Zádori, L.: Omitting types, bounded width and the ability to count. IJAC 19(5), 647–668 (2009)MathSciNetMATHGoogle Scholar
  31. 31.
    Madelaine, F., Stewart, I.: Constraint satisfaction, logic and forbidden patterns. SIAM J. Comput. 37(1), 132–163 (2007)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Reingold, O.: Undirected st-connectivity in log-space. In: STOC, pp. 376–385 (2005)Google Scholar
  33. 33.
    Schaefer, T.: The complexity of satisfiability problems. In: Proceedings of the 10th ACM Symposium on Theory of Computing (STOC 1978), pp. 216–226 (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrei A. Bulatov
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

Personalised recommendations