Skip to main content
SpringerLink
Log in

The expressive rate of constraints

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

In reasoning tasks involving logical formulas, high expressiveness is desirable, although it often leads to high computational complexity. We study a simple measure of expressiveness: the number of formulas expressible by a language, up to semantic equivalence. In the context of constraints, we prove a dichotomy theorem on constraint languages regarding this measure.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Böhler, E. Hemaspaandra, S. Reith and H. Vollmer, Playing with Boolean blocks, Part I: Post’s lattice with applications to complexity theory, ACM-SIGACT Newsletter 34(4) (2003) 38–52.

    Article  Google Scholar 

  2. A. Bulatov, H. Chen and V. Dalmau, Learnability of relatively quantified generalized formulas, in: The 15th International Conference on Algorithmic Learning Theory (ALT) (2004).

  3. M. Cadoli and F.M. Donini, A survey on knowledge compilation, AI Communications 10(3/4) (1997) 137–150.

    Google Scholar 

  4. N. Creignou, S. Khanna and M. Sudan, Complexity Classification of Boolean Constraint Satisfaction Problems, SIAM Monographs on Discrete Mathematics and Applications (SIAM, Philadelphia, PA, 2001).

    Google Scholar 

  5. V. Dalmau and P. Jeavons, Learnability of quantifed formulas, Theoretical Computer Science 306(1–3) (2003) 485–511.

    Article  Google Scholar 

  6. P. Jeavons, On the algebraic structure of combinatorial problems, Theoretical Computer Science 200 (1998) 185–204.

    Article  Google Scholar 

  7. P. Jeavons, D. Cohen and M. Cooper, Constraints, consistency, and closure, Articial Intelligence 101(1/2) (1998) 251–265.

    Article  Google Scholar 

  8. P.G. Jeavons, D.A. Cohen and M. Gyssens, Closure properties of constraints, Journal of the ACM 44 (1997) 527–548.

    Article  Google Scholar 

  9. P. Jeavons, D. Cohen and J. Pearson, Constraints and universal algebra, Annals of Mathematics and Artificial Intelligence 24(1–4) (1998) 51–67.

    Article  Google Scholar 

  10. G. Nordh and P. Jonsson, An algebraic approach to the complexity of propositional circumscription, in: Proc. of the 19th IEEE Symposium on Logic in Computer Science (LICS-2004), Turku, Finland (2004), pp. 367–376.

  11. R. Pöschel and L.A. Kalužnin, Funktionen- und Relationenalgebren (DVW, Berlin, 1979).

    Google Scholar 

  12. T.J. Schaefer, The complexity of satisfiability problems, in: Proc. of the ACM Symposium on Theory of Computing (STOC) (1978) pp. 216–226.

  13. A. Szendrei, Clones in Universal Algebra, Séminaires de Mathématiques Supérieures, Vol. 99 (Presses Univ. Montréal, Montreal, PQ, 1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament de Tecnologia, Universitat Pompeu Fabra, Barcelona, Spain

    Hubie Chen

Authors
  1. Hubie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hubie Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, H. The expressive rate of constraints. Ann Math Artif Intell 44, 341–352 (2005). https://doi.org/10.1007/s10472-005-7031-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-005-7031-4

Keywords

Search

Navigation