Abstract
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems, to reduce them, and to encode them into ”good” SAT instances. We illustrate our technique on the well-known nqueens problem. Our technique is simpler, more expressive, and less error-prone than direct hand modeling. The SAT instances that we automatically generate are rather small w.r.t. hand-written instances.
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References
Apt, K.: Principles of Constraint Programming. Cambridge University Press (2003)
Bacchus, F.: Gac via unit propagation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 133–147. Springer, Heidelberg (2007)
Bailleux, O., Boufkhad, Y.: Efficient CNF encoding of boolean cardinality constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 108–122. Springer, Heidelberg (2003)
Bessière, C., Hebrard, E., Walsh, T.: Local consistencies in SAT. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 299–314. Springer, Heidelberg (2004)
Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Früwirth, T.: Constraint Handling Rules. Cambridge University Press (2009)
Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman & Company (1979)
Gent, I., Lynce, I.: A sat encoding for the social golfer problem. In: IJCAI 2005 Workshop on Modelling and Solving Problems with Constraints (2005)
Gervet, C.: Conjunto: Constraint propagation over set constraints with finite set domain variables. In: Proc. of ICLP 1994, p. 733. MIT Press (1994)
Lardeux, F., Monfroy, E., Crawford, B., Soto, R.: Set constraint model and automated encoding into sat: Application to the social golfer problem. Submitted to Annals of Operations Research
Lardeux, F., Monfroy, E., Saubion, F., Crawford, B., Castro, C.: SAT encoding and CSP reduction for interconnected alldiff constraints. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds.) MICAI 2009. LNCS, vol. 5845, pp. 360–371. Springer, Heidelberg (2009)
Legeard, B., Legros, E.: Short overview of the CLPS system. In: Małuszyński, J., Wirsing, M. (eds.) PLILP 1991. LNCS, vol. 528, pp. 431–433. Springer, Heidelberg (1991)
Mackworth, A.: Encyclopedia on Artificial Intelligence, chapter Constraint Satisfaction. John Wiley (1987)
Monfroy, E.: A coordination-based chaotic iteration algorithm for constraint propagation. In: Proc of ACM SAC 2000 (1), pp. 262–269. ACM (2000)
Monfroy, E., Saubion, F., Lambert, T.: On hybridization of local search and constraint propagation. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 299–313. Springer, Heidelberg (2004)
Prestwich, S., Roli, A.: Symmetry breaking and local search spaces. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 273–287. Springer, Heidelberg (2005)
Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier (2006)
Triska, M., Musliu, N.: An improved sat formulation for the social golfer problem. Annals of Operations Research 194(1), 427–438 (2012)
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Lardeux, F., Monfroy, E. (2014). From Declarative Set Constraint Models to “Good” SAT Instances. In: Aranda-Corral, G.A., Calmet, J., Martín-Mateos, F.J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2014. Lecture Notes in Computer Science(), vol 8884. Springer, Cham. https://doi.org/10.1007/978-3-319-13770-4_8
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DOI: https://doi.org/10.1007/978-3-319-13770-4_8
Publisher Name: Springer, Cham
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