Advertisement

Arc-Consistency + Unit Propagation = Lookahead

  • Jia-Huai You
  • Guiwen Hou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3132)

Abstract

Arc-consistency has been one of the most popular consistency techniques for space pruning in solving constraint satisfaction problems (CSPs), while lookahead appears to be its counterpart in answer set solvers. In this paper, we perform a theoretical comparison of their pruning powers, based on the translation of Niemelä from CSPs to answer set programs. Especially, we show two results. First, we show that lookahead is strictly stronger than arc-consistency. The extra pruning power comes from the ability to propagate unique values for variables, also called unit propagation in this paper, so that conflicts may be detected. This suggests that arc-consistency can be enhanced with unit propagation for CSPs. We then formalize this technique and show that, under the translation of Niemelä, it has exactly the same pruning power as lookahead.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5(7), 394–397 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)Google Scholar
  3. 3.
    Freeman, J.W.: Improvements to propositional satisfiability search algorithms. PhD thesis, Department of Computer and Information Science, University of Pennsylvania (1995)Google Scholar
  4. 4.
    Freuder, E.C.: Synthesizing constraint expressions. CACM 21(11), 958–966 (1978)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)zbMATHGoogle Scholar
  6. 6.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. 5th ICLP, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  7. 7.
    Gent, I.: Arc consistency in SAT. In: Proc. ECAI 2003, pp. 121–125 (2002)Google Scholar
  8. 8.
    Kasif, S.: On the parallel complexity of discrete relaxation in constraint satisfaction networks. Artificial Intelligence, 275–286 (1990)Google Scholar
  9. 9.
    Leone, N., et al.: DLV: a disjunctive datalog system, release 2000-10-15 (2000), At http://www.dbai.tuwien.ac.at/proj/dlv/
  10. 10.
    Mackworth, A.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Marriott, K., Stucky, P.: Programming with Constraints. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  12. 12.
    Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Math. and Artificial Intelligence 25(3-4), 241–273 (1999)zbMATHCrossRefGoogle Scholar
  13. 13.
    Simons, P.: Extending and Implementing the Stable Model Semantics. PhD thesis, Helsinki University of Technology, Helsinki, Finland (2000)Google Scholar
  14. 14.
    Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1-2) (2002)Google Scholar
  15. 15.
    Walsh, T.: CSP vs. SAT. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jia-Huai You
    • 1
  • Guiwen Hou
    • 1
  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

Personalised recommendations