Abstract
Ideally, programming propagators as implementations of constraints should be an entirely declarative specification process for a large class of constraints: a high-level declarative specification is automatically translated into an efficient propagator. This paper introduces the use of existential monadic second-order logic as declarative specification language for finite set propagators. The approach taken in the paper is to automatically derive projection propagators (involving a single variable only) implementing constraints described by formulas. By this, the paper transfers the ideas of indexicals to finite set constraints while considerably increasing the level of abstraction available with indexicals. The paper proves soundness and completeness of the derived propagators and presents a run-time analysis, including techniques for efficiently executing projectors for n-ary constraints.
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References
Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)
Ågren, M., Flener, P., Pearson, J.: Incremental algorithms for local search from existential second-order logic. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 47–61. Springer, Heidelberg (2005)
Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace [21], pp. 107–122
Benhamou, F.: Heterogeneous Constraint Solving. In: Hanus, M., Rodríguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 62–76. Springer, Heidelberg (1996)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: The range and roots constraints: Specifying counting and occurrence constraints. In: IJCAI, pp. 60–65 (August 2005)
Carlson, B.: Compiling and Executing Finite Domain Constraints. Ph.D thesis, Uppsala University, Sweden (1995)
Carlson, B., Carlsson, M., Diaz, D.: Entailment of finite domain constraints. In: Proceedings of the Eleventh International Conference on Logic Programming, pp. 339–353. MIT Press, Cambridge (1994)
Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 191–206. Springer, Heidelberg (1997)
Codognet, P., Diaz, D.: Compiling constraints in clp(FD). Journal of Logic Programming 27(3), 185–226 (1996)
Gervet, C.: Interval propagation to reason about sets: Definition and implementation of a practical language. Constraints 1(3), 191–244 (1997)
Hawkins, P., Lagoon, V., Stuckey, P.: Solving set constraint satisfaction problems using ROBDDs. J. Artif. Intell. Res (JAIR) 24, 109–156 (2005)
Hentenryck, P.V., Saraswat, V.A., Deville, Y.: Constraint processing in cc(FD). Technical report, Brown University (1991)
Hentenryck, P.V., Saraswat, V.A., Deville, Y.: Design, implementation, and evaluation of the constraint language cc(FD). Journal of Logic Programming 37(1-3), 293–316 (1998)
Intelligent Systems Laboratory. SICStus Prolog user’s manual, 3.12.1. Technical report, Swedish Institute of Computer Science, Box 1263, 164 29 Kista, Sweden (2006)
Müller, T.: Constraint Propagation in Mozart. Doctoral dissertation, Universität des Saarlandes, Naturwissenschaftlich-Technische Fakultät I, Fachrichtung Informatik, Saarbrücken, Germany (2001)
Puget, J.-F.: PECOS: A high level constraint programming language. In: Proceedings of the first Singapore international conference on Intelligent Systems (SPICIS), pp. 137–142 (1992)
Sadler, A., Gervet, C.: Hybrid set domains to strengthen constraint propagation and reduce symmetries. In: Wallace [21], pp. 604–618
Schulte, C., Stuckey, P.J.: Speeding up constraint propagation. In: Wallace [21], pp. 619–633
Schulte, C., Tack, G.R.: Views and iterators for generic constraint implementations. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS, vol. 3978, pp. 118–132. Springer, Heidelberg (2006)
The Gecode team. Generic constraint development environment (2006), http://www.gecode.org
Wallace, M. (ed.): CP 2004. LNCS, vol. 3258. Springer, Heidelberg (2004)
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Tack, G., Schulte, C., Smolka, G. (2006). Generating Propagators for Finite Set Constraints. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_41
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DOI: https://doi.org/10.1007/11889205_41
Publisher Name: Springer, Berlin, Heidelberg
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