Abstract
Today’s models for propagation-based constraint solvers require propagators as implementations of constraints to be at least contracting and monotonic. These models do not comply with reality: today’s constraint programming systems actually use non-monotonic propagators. This paper introduces the first realistic model of constraint propagation by assuming a propagator to be weakly monotonic (complying with the constraint it implements). Weak monotonicity is shown to be the minimal property that guarantees constraint propagation to be sound and complete. The important insight is that weak monotonicity makes propagation in combination with search well behaved. A case study suggests that non-monotonicity can be seen as an opportunity for more efficient propagation.
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References
Baptiste, P., Le Pape, C.: A theoretical and experimental comparison of constraint propagation techniques for disjunctive scheduling. In: IJCAI, pp. 600–606 (1995)
Menana, J., Demassey, S.: Sequencing and counting with the multicost-regular constraint. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 178–192. Springer, Heidelberg (2009)
Katriel, I.: Expected-case analysis for delayed filtering. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 119–125. Springer, Heidelberg (2006)
Stergiou, K.: Heuristics for dynamically adapting propagation. In: ECAI, pp. 485–489 (2008)
Katriel, I., Van Hentenryck, P.: Randomized filtering algorithms. Technical Report CS-06-09, Brown University, Providence, RI, USA (2006)
Mehta, D., van Dongen, M.R.C.: Probabilistic consistency boosts MAC and SAC. In: IJCAI, pp. 143–148 (2007)
Sellmann, M.: Approximated consistency for Knapsack constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 679–693. Springer, Heidelberg (2003)
Ward, M.: The closure operators of a lattice. Annals of Mathematics 43(2), 191–196 (1942)
Tarski, A.: Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I. Monatshefte für Mathematik 37(1), 361–404 (1930)
Tarski, A.: V. In: Logic, semantics, metamathematics, 2nd edn., pp. 60–109. Hackett Publishing Company (1983)
Saraswat, V.A., Rinard, M.C., Panangaden, P.: Semantic foundations of concurrent constraint programming. In: POPL, pp. 333–352 (1991)
Benhamou, F., McAllester, D.A., Van Hentenryck, P.: CLP(Intervals) revisited. In: ILPS, pp. 124–138. The MIT Press, Cambridge (1994)
Van Hentenryck, P., Saraswat, V.A., Deville, Y.: Constraint processing in cc(FD). Technical report, Brown University (1991)
Apt, K.R.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)
Schulte, C., Stuckey, P.J.: Efficient constraint propagation engines. ACM Trans. Program. Lang. Syst. 31(1), 2:1–2:43 (2008)
Benhamou, F.: Heterogeneous Constraint Solving. In: Hanus, M., Rodríguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 62–76. Springer, Heidelberg (1996)
Müller, T.: Constraint Propagation in Mozart. Doctoral dissertation, Universität des Saarlandes, Saarbrücken, Germany (2001)
Schulte, C.: Programming Constraint Services. LNCS (LNAI), vol. 2302. Springer, Heidelberg (2002)
Perron, L.: Search procedures and parallelism in constraint programming. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 346–361. Springer, Heidelberg (1999)
Choi, C.W., Henz, M., Ng, K.B.: Components for state restoration in tree search. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 240–255. Springer, Heidelberg (2001)
Michel, L., Van Hentenryck, P.: A decomposition-based implementation of search strategies. ACM Trans. Comput. Logic 5(2), 351–383 (2004)
Carlsson, M.: Personal communication (February 2007)
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Schulte, C., Tack, G. (2009). Weakly Monotonic Propagators. In: Gent, I.P. (eds) Principles and Practice of Constraint Programming - CP 2009. CP 2009. Lecture Notes in Computer Science, vol 5732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_56
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DOI: https://doi.org/10.1007/978-3-642-04244-7_56
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