Skip to main content

The Complexity of Equality Constraint Languages

  • Conference paper
Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

Included in the following conference series:

Abstract

We apply the algebraic approach to infinite-valued constraint satisfaction to classify the computational complexity of all constraint satisfaction problems with templates that have a highly transitive automorphism group. A relational structure has such an automorphism group if and only if all the constraint types are Boolean combinations of the equality relation, and we call the corresponding constraint languages equality constraint languages. We show that an equality constraint language is tractable if it admits a constant unary or an injective binary polymorphism, and is NP-complete otherwise.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bodirsky, M.: Constraint satisfaction with infinite domains. PhD thesis, Humboldt-Universitat zu Berlin (2004)

    Google Scholar 

  2. Bodirsky, M., Nešetřil, J.: Constraint satisfaction with countable homogeneous templates. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 44–57. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Bodnarčuk, V.G., Kalužnin, L.A., Kotov, V.N., Romov, B.A.: Galois theory for post algebras, part I and II. Cybernetics 5, 243–539 (1969)

    Article  Google Scholar 

  4. Bulatov, A.: Tractable conservative constraint satisfaction problems. In: Proceedings of LICS 2003, pp. 321–330 (2003)

    Google Scholar 

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

    Google Scholar 

  6. Bulatov, A., Krokhin, A., Jeavons, P.G.: Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing 34, 720–742 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cameron, P.J.: Oligomorphic Permutation Groups. Cambridge University Press, Cambridge (1990)

    Book  MATH  Google Scholar 

  8. Dechter, R., van Beek, P.: Local and global relational consistency. TCS 173(1), 283–308 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garey, Johnson: A Guide to NP-completeness. CSLI Press, Stanford (1978)

    MATH  Google Scholar 

  10. Geiger, D.: Closed systems of functions and predicates. Pacific Journal of Mathematics 27, 95–100 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  11. Heindorf, L.: The maximal clones on countable sets that include all permutations. Algebra univers. 48, 209–222 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hodges, W.: A shorter model theory. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  13. Jeavons, P., Cohen, D., Gyssens, M.: Closure properties of constraints. Journal of the ACM 44(4), 527–548 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Krasner, M.: Généralisation et analogues de la théorie de Galois. In: Congrés de la Victoire de l’Ass. France avancement des sciences, pp. 54–58 (1945)

    Google Scholar 

  15. Pinsker, M.: The number of unary clones containing the permutations on an infinite set. Acta Sci. Math, Szeged (to appear, 2005)

    Google Scholar 

  16. Pöschel, R., Kalužnin, L.A.: Funktionen- und Relationenalgebren. Deutscher Verlag der Wissenschaften (1979)

    Google Scholar 

  17. Szendrei, A.: Clones in universal Algebra. Seminaire de mathematiques superieures. Les Presses de L’Universite de Montreal (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bodirsky, M., Kára, J. (2006). The Complexity of Equality Constraint Languages. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_14

Download citation

  • DOI: https://doi.org/10.1007/11753728_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics