Abstract
SAT Modulo Theories (SMT) consists of deciding the satisfiability of a formula with respect to a decidable background theory, such as linear integer arithmetic, bit-vectors, etc, in first-order logic with equality. SMT has its roots in the field of verification. It is known that the SAT technology offers an interesting, efficient and scalable method for constraint solving, as many experimentations have shown. Although there already exist some results pointing out the adequacy of SMT techniques for constraint solving, there are no available tools to extensively explore such adequacy. In this paper we introduce a tool for translating FlatZinc (MiniZinc intermediate code) instances of constraint satisfaction problems to the standard SMT-LIB language. It can be used for deciding satisfiability as well as for optimization. The tool determines the required logic for solving each instance. The obtained results suggest that SMT can be effectively used to solve CSPs.
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Bofill, M., Palahi, M., Suy, J., Villaret, M.: SIMPLY: a Compiler from a CSP Modeling Language to the SMT-LIB Format. In: Proceedings of the 8th Intl. Workshop on Constraint Modelling and Reformulation, pp. 30–44 (2009)
Cadoli, M., Mancini, T., Patrizi, F.: SAT as an Effective Solving Technology for Constraint Problems. In: Esposito, F., Raś, Z.W., Malerba, D., Semeraro, G. (eds.) ISMIS 2006. LNCS (LNAI), vol. 4203, pp. 540–549. Springer, Heidelberg (2006)
Dutertre, B., de Moura, L.: The Yices SMT solver (August 2006), Tool paper at http://yices.csl.sri.com/tool-paper.pdf
Frisch, A., Harvey, W., Jefferson, C., Martínez-Hernández, B., Miguel, I.: Essence: A Constraint Language for Specifying Combinatorial Problems. Constraints 13(3), 268–306 (2008)
Huang, J.: Universal Booleanization of Constraint Models. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 144–158. Springer, Heidelberg (2008)
Nethercote, N., Stuckey, P., Becket, R., Brand, S., Duck, G., Tack, G.: MiniZinc: Towards a Standard CP Modelling Language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)
Nieuwenhuis, R., Oliveras, A.: On SAT Modulo Theories and Optimization Problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)
Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: Challenges in Satisfiability Modulo Theories. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 2–18. Springer, Heidelberg (2007)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: From an Abstract Davis–Putnam–Logemann–Loveland Procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)
Ranise, S., Tinelli, C.: The SMT-LIB Standard: Version 1.2. Tech. rep., Dept. of Comp. Science, University of Iowa (2006), http://www.SMT-LIB.org
Sebastiani, R.: Lazy Satisfiability Modulo Theories. Journal on Satisfiability, Boolean Modeling and Computation 3(3-4), 141–224 (2007)
Sheini, H., Sakallah, K.: From Propositional Satisfiability to Satisfiability Modulo Theories. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 1–9. Springer, Heidelberg (2006)
Walsh, T.: SAT vs CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
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Bofill, M., Suy, J., Villaret, M. (2010). A System for Solving Constraint Satisfaction Problems with SMT. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_25
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DOI: https://doi.org/10.1007/978-3-642-14186-7_25
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