Approximately Propagation Complete and Conflict Propagating Constraint Encodings
- 685 Downloads
The effective use of satisfiability (SAT) solvers requires problem encodings that make good use of the reasoning techniques employed in such solvers, such as unit propagation and clause learning. Propagation completeness has been proposed as a useful property for constraint encodings as it maximizes the utility of unit propagation. Experimental results on using encodings with this property in the context of satisfiability modulo theory (SMT) solving have however remained inconclusive, as such encodings are typically very large, which increases the bookkeeping work of solvers.
In this paper, we introduce approximate propagation completeness and approximate conflict propagation as novel SAT encoding property notions. While approximate propagation completeness is a generalization of classical propagation completeness, (approximate) conflict propagation is a new concept for reasoning about how early conflicts can be detected by a SAT solver. Both notions together span a hierarchy of encoding quality choices, with classical propagation completeness as a special case. We show how to compute approximately propagation complete and conflict propagating constraint encodings with a minimal number of clauses using a reduction to MaxSAT. To evaluate the effect of such encodings, we give results on applying them in a case study.
KeywordsConstraint Encoding Propagation Complete Generational Conflict Maximum Satisﬁability (MaxSAT) MaxSAT Instance
This work was supported by DFG grant EH 481/1-1 and the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative. The authors want to thank Armin Biere for early feedback on the propagation quality notions defined in this work and Erika Abraham for proposing MaxSAT solvers as reasoning backend.
- 1.Abío, I., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: A parametric approach for smaller and better encodings of cardinality constraints. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 80–96. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40627-0_9CrossRefGoogle Scholar
- 2.Alviano, M., Dodaro, C., Ricca, F.: A MaxSAT algorithm using cardinality constraints of bounded size. In: Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 2677–2683 (2015). http://ijcai.org/Abstract/15/379
- 6.Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT race 2010. FMV Report Series Technical report 10/1, Johannes Kepler University, Linz, Austria (2010)Google Scholar
- 7.Bjork, M.: Successful SAT encoding techniques. J. Satisfiability Boolean Model. Comput. 7, 189–201 (2009)Google Scholar
- 11.Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press (2001). http://books.google.de/books?id=Nmc4wEaLXFEC
- 13.Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. JSAT 2(1–4), 1–26 (2006). http://jsat.ewi.tudelft.nl/content/volume2/JSAT2_1_Een.pdf
- 14.Franco, J., Martin, J.: A history of satisfiability. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, chap. 1, pp. 3–74. IOS Press (2009)Google Scholar
- 15.Gwynne, M., Kullmann, O.: Towards a theory of good SAT representations. CoRR abs/1302.4421 (2013). http://arxiv.org/abs/1302.4421
- 20.Li, C.M., Manyà, F.: MaxSAT, hard and soft constraints. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, chap. 19, pp. 613–631. IOS Press (2009)Google Scholar
- 24.Roussel, O., Manquinho, V.: Pseudo-boolean and cardinality constraints. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, chap. 22, pp. 695–733. IOS Press (2009)Google Scholar
- 26.Somenzi, F.: CUDD: CU Decision Diagram package release 3.0.0 (2015)Google Scholar