A Synthesis of Constraint Satisfaction and Constraint Solving

  • Michael J. Maher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2833)


This paper offers a critique of the framework of Constraint Satisfaction Problems. While this framework has been successful in studying search techniques, and has inspired some constraint programming languages, it has some weaknesses that leave it not directly applicable to the study of complex constraints (including so-called global constraints) in constraint programming languages. In particular, it deals poorly with semantic relations whose consistency can be determined algorithmically. In this paper the philosophy of the CLP Scheme is applied to extend the CSP framework to a form more suitable for addressing complex constraints, where both constraint satisfaction and constraint solving have a role. Some rough principles for local consistency conditions in the extended framework are developed, and appropriate notions of local consistency are formulated. These can be used as a coarse measure of the degree of constraint propagation achieved by implementations of complex constraints.


Logic Program Semantic Relation Constraint Satisfaction Constraint Programming Global Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aggoun, A., Beldiceanu, N.: Extending CHIP to Solve Complex Scheduling and Packing Problems. In: Journées Francophones De Programmation Logique, Lille, France (1992)Google Scholar
  2. 2.
    Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the Desirability of Acyclic Database Schemes. Journal of the ACM 30(3), 479–513 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Beldiceanu, N.: Global Constraints as Graph Properties on Structured Network of Elementary Constraints of the Same Type, SICS Technical Report T2000/01 (2000)Google Scholar
  4. 4.
    Beldiceanu, N., Contejean, E.: Introducing Global Constraints in CHIP. Mathematical Computer Modelling 20(12), 97–123 (1994)zbMATHCrossRefGoogle Scholar
  5. 5.
    Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising Hull and Box Consistency. In: International Conference on Logic Programming, pp. 230–244 (1999)Google Scholar
  6. 6.
    Benhamou, F., McAllester, D.A., Van Hentenryck, P.: CLP(Intervals) Revisited. In: International Symposium on Logic Programming, pp. 124–138 (1994)Google Scholar
  7. 7.
    Benhamou, F., Older, W.J.: Applying Interval Arithmetic to Real, Integer, and Boolean Constraints. Journal of Logic Programming 32(1), 1–24 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Berlandier, P.: Improving Domain Filtering using Restricted Path Consistency. In: Proc. IEEE International Conference on Artificial Intelligence Applications (CAIA) (1995)Google Scholar
  9. 9.
    Caseau, Y., Josset, F., Laburthe, F.: CLAIRE: Combining sets, search and rules to better express algorithms. Theory and Practice of Logic Programming 2(6), 769–805 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Castro, C.: Building Constraint Satisfaction Problem Solvers Using Rewrite Rules and Strategies. Fundamenta Informaticae 34(3), 263–293 (1998)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Colmerauer, A.: Solving the Multiplication Constraint in Several Approximation Spaces. In: International Conference on Logic Programming 1 (2001)Google Scholar
  12. 12.
    Debruyne, R., Bessière, C.: Some Practicable Filtering Techniques for the Constraint Satisfaction Problem. In: IJCAI, vol. 1, pp. 412–417 (1997)Google Scholar
  13. 13.
    Debruyne, R., Bessière, C.: From Restricted Path Consistency to Max-Restricted Path Consistency. In: Proc. Principles and Practice of Constraint Programming, pp. 312–326 (1997)Google Scholar
  14. 14.
    Dechter, R., van Beek, P.: Local and Global Relational Consistency. Theoretical Computer Science 173(1), 283–308 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Dechter, R., Meiri, I., Pearl, J.: Temporal Constraint Networks. Artificial Intelligence 49, 61–95 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Dincbas, M., Van Hentenryck, P., Simonis, H., Aggoun, A.: The Constraint Logic Programming Language CHIP. In: Proceedings of the 2nd. International Conference on Fifth Generation Computer Systems, pp. 249–264 (1988)Google Scholar
  17. 17.
    Freuder, E.C.: A Sufficient Condition for Backtrack-Bounded Search. Journal of the ACM 32(4), 755–761 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Freuder, E.C., Elfe, C.D.: Neighborhood Inverse Consistency Preprocessing. In: Proc. AAAI/IAAI, vol. 1, pp. 202–208 (1996)Google Scholar
  19. 19.
    Frühwirth, T.W.: Theory and Practice of Constraint Handling Rules. Journal of Logic Programming 37(1-3), 95–138 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Gervet, C.: Interval Propagation to Reason about Sets: Definition and Implementation of a Practical Language. Constraints 1(3), 191–244 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Gyssens, M.: On the Complexity of Join Dependencies. ACM Transactions on Database Systems 11(1), 81–108 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Harvey, W., Stuckey, P.J.: Constraint Representation for Propagation. In: Proc. Conf. on Principles and Practice of Constraint Programming, pp. 235–249 (1998)Google Scholar
  23. 23.
    Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research. McGraw-Hill, New York (2001)Google Scholar
  24. 24.
    ILOG Inc., ILOG Solver 4.2 User’s Manual (1998)Google Scholar
  25. 25.
    Jaffar, J., Lassez, J.-L.: Constraint Logic Programming. In: Proc. 14th ACM Symposium on Principles of Programming Languages, pp. 111–119 (1987)Google Scholar
  26. 26.
    Jaffar, J., Maher, M.J.: Constraint Logic Programming: A Survey. Journal of Logic Programming 19, 20, 503–581 (1994)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Jaffar, J., Michaylov, S., Stuckey, P., Yap, R.H.C.: The CLP(R) Language and System. ACM Transactions on Programming Languages 14(3), 339–395 (1992)CrossRefGoogle Scholar
  28. 28.
    Jaffar, J., Michaylov, S., Yap, R.H.C.: A Methodology for Managing Hard Constraints in CLP Systems. In: Proc. ACM-SIGPLAN Conference on Programming Language Design and Implementation, pp. 306–316 (1991)Google Scholar
  29. 29.
    Jégou, P.: On the Consistency of General Constraint-Satisfaction Problems. In: AAAI, pp. 114–119 (1993)Google Scholar
  30. 30.
    Kanellakis, P.C.: Elements of Relational Database Theory. In: Handbook of Theoretical Computer Science. Formal Models and Sematics, vol. B, pp. 1073–1156. Elsevier, Amsterdam (1990)Google Scholar
  31. 31.
    Maher, M.J.: Adding Constraints to Logic-based Formalisms. In: Apt, K.R., Marek, V., Truszczynski, M., Warren, D.S. (eds.) The Logic Programming Paradigm: a 25 Years Perspective. Artificial Intelligence Series, pp. 313–331. Springer, Heidelberg (1999)Google Scholar
  32. 32.
    Maher, M.J.: Propagation Completeness of Reactive Constraints. In: Proc. International Conference on Logic Programming, pp. 148–162 (2002)Google Scholar
  33. 33.
    Marriott, K., Stuckey, P.J.: Programming with Constraints: An Introduction. MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  34. 34.
    Mohr, R., Masini, G.: Good Old Discrete Relaxation. In: Proc. ECAI, pp. 651–656 (1988)Google Scholar
  35. 35.
    Montanari, U.: Networks of Constraints: Fundamental Properties and Applications to Picture Processing. information Sciences 7, 95–132 (1974)CrossRefMathSciNetGoogle Scholar
  36. 36.
    Pang, W., Goodwin, S.D.: Consistency in General CSPs. In: Mizoguchi, R., Slaney, J.K. (eds.) PRICAI 2000. LNCS, vol. 1886, pp. 469–479. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  37. 37.
    Van Roy, P., Brand, P., Duchier, D., Haridi, S., Henz, M., Schulte, C.: Logic programming in the context of multiparadigm programming: the Oz experience. Theory and Practice of Logic Programming (to appear)Google Scholar
  38. 38.
    Walsh, T.: Relational Consistencies. APES Technical Report, APES-28-2001 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michael J. Maher
    • 1
  1. 1.Department of Computer ScienceLoyola University Chicago 

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