Abstract
Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how we can mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This immediately results in strong nogoods for finite domain propagation. But a naive static translation is impractical except in limited cases. We show how we can convert propagators to lazy clause generators for a SAT solver. The resulting system can solve scheduling problems significantly faster than generating the clauses from scratch, or using Satisfiability Modulo Theories solvers with difference logic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Choi, C.W., Lee, J.H.M., Stuckey, P.J.: Propagation redundancy in redundant modelling. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 229–243. Springer, Heidelberg (2003)
Crawford, J., Baker, A.: Experimental results on the application of satisfiability algorithms to scheduling problems. In: Procs. AAAI 1994, pp. 1092–1097 (1994)
CSP2SAT: (December 2006), http://bach.istc.kobe-u.ac.jp/csp2sat/
Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)
Barcelogic for SMT: (February 2007), http://www.lsi.upc.es/~oliveras/bclt-main.html
GECODE: (February 2007), http://www.gecode.org
Hawkins, P., Stuckey, P.J.: A Hybrid BDD and SAT Finite Domain Constraint Solver. In: Van Hentenryck, P. (ed.) PADL 2006. LNCS, vol. 3819, pp. 103–117. Springer, Heidelberg (2005)
Katsirelos, G., Bacchus, F.: Unrestricted nogood recording in CSP search. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 873–877. Springer, Heidelberg (2003)
Katsirelos, G., Bacchus, F.: Generalized nogoods in CSPs. In: The Twentieth National Conference on Artificial Intelligence (AAAI 2005), pp. 390–396 (2005)
Laborie, P.: Complete MCS-Based Search: Application to Resource Constrained Project Scheduling. In: Proceedings IJCAI 2005, pp. 181–186 (2005)
Marriott, K., Stuckey, P.J.: Programming with Constraints: an Introduction. MIT Press, Cambridge (1998)
MiniSat: (December 2006), http://www.cs.chalmers.se/Cs/Resarch/FormalMethods/MiniSat/
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of DAC 2001 (2001)
Niewenhuis, R., Oliveras, A., Tinelli, C.: Abstract DPLL and abstract DPLL modulo theories. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 36–50. Springer, Heidelberg (2005)
Roussel, O.: Some notes on the implementation of csp2sat+zchaff, a sim- ple translator from CSP to SAT. In: Proceedings of the 2nd International Workshop on Constraint Propagation and Implementation, pp. 83–88 (2005)
Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling finite linear CSP to SAT. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 590–603. Springer, Heidelberg (2006)
Van Hentenryck, P., Saraswat, V., Deville, Y.: Design, implementation and evaluation of the constraint language cc(FD). JLP 37(1–3), 139–164 (1998)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ohrimenko, O., Stuckey, P.J., Codish, M. (2007). Propagation = Lazy Clause Generation. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_39
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)