On the satisfiability of symmetrical constrained satisfaction problems

  • Jean-Francois Puget
Constraint Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 689)


Constraint satisfaction problems (CSP) are a class of combinatorial problems that can be solved efficiently by combining consistency methods such as arc-consistency together with a backtracking search. However these techniques are not adapted to symmetrical CSP. In fact one can exhibit rather small CSP that cannot be solved with consistency techniques. The relevance of this symmetry problem to real world applications is very strong since it can prevent a CSP solver to solve even small instances of real world problems. This paper describes a general solution for this kind of problems. Both a theoretical study and experimental results using the constraint-based library PECOS are provided.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Benhamou B., and Sais L. “Theoretical study of symmetries in propositional calculs and applications”, in proceedings of CADE 92 june 92.Google Scholar
  2. 2.
    Caseau Y, Puget JF, “Constraints on Order Sorted Domains”, submited.Google Scholar
  3. 3.
    Deville, Y., and Van Hentenryck, P, “An Efficient Arc Consistency Algorithm for a Class of CSP Problems”, in proceedings of IJCAI 1991, pp 325–330.Google Scholar
  4. 4.
    Gusgen, Hertzberg “Some fundamental properties of local propagation methods” Art. Int. pp 237–247, 1988.Google Scholar
  5. 5.
    Ilog, PECOS 1.2 reference manual, december 92 1992.Google Scholar
  6. 6.
    Jaffar J., and Lassez J.-L. Constraint Logic Programming, in proceedings of POPL 1987, Munich, January 87.Google Scholar
  7. 7.
    Lauriere J.L., A language and a Program for Stating and Solving Combinatorial Problems, Art. Int. 10(1).Google Scholar
  8. 8.
    Mackworth A.K., “Consistency in networks of relations”, Art. Int 8, pp 99–118, 1977 Google Scholar
  9. 9.
    Mohr, Henderson “Arc and path consistency revisited” Art. Int. 28, pp 128–233, 1986.Google Scholar
  10. 10.
    Mohr, Masini, “Good Old Discrete Relaxation”, in proceedings of ECAI 1988.Google Scholar
  11. 11.
    Puget J.-F., “Pecos: a High Level Constraint programming Language” in proceedings of SPICIS 92, Singapore, Sept 92.Google Scholar
  12. 12.
    Puget J.-F., “Programmation par contraintes oriente'e objet” in proceedings of Tenth international conference on expert systems and applications, Avignon, June 92 (in French).Google Scholar
  13. 13.
    San Miguel Aguire, “HOW to use symmetries in Boolean constraint solving” in A. Colmerauer and F. Benhamou, editors, Selected Papers on Constraint Logic Programming (to appear) MIT Press.Google Scholar
  14. 14.
    Van Hentenryck, P., Constraints Satisfaction in Logic Programming, MIT press, 1989.Google Scholar
  15. 15.
    Van Hentenryck, P., Deville Y., “The cardinal operator; A new logical connective for constraint logic programming” in proceedings of ICLP 91, pp 745–759.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jean-Francois Puget
    • 1
  1. 1.ILOG SAGentilly CedexFrance

Personalised recommendations