Abstract
Great progress has been made on DPLL based SAT solvers operating on CNF encoded SAT theories. However, for most problems CNF is not a very natural representation. Typically these problems are more easily expressed using unrestricted propositional formulae and hence must be converted to CNF before modern SAT solvers can be applied. This conversion entails a considerable loss of information about the problem’s structure. In this work we demonstrate that conversion to CNF is both unnecessary and undesirable. In particular, we demonstrate that a SAT solver which operates directly on a propositional formula can achieve the same efficiency as a highly optimized modern CNF solver. Furthermore, since the original formula remains intact, such a solver can exploit the original problem structure to improve over CNF solvers. We present empirical evidence showing that exploiting the original structure can yield considerable benefits.
An extended abstract on this topic was presented at the SAT-2004 conference.
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.
Similar content being viewed by others
References
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 4, 394–397 (1962)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: Proc. of the Design Automation Conference, DAC (2001)
Tseitin, G.: On the complexity of proofs in poropositional logics. In: Siekmann, J., Wrightson, G. (eds.) Automation of Reasoning: Classical Papers in Computational Logic 1967–1970, vol. 2, Springer, Heidelberg (1983); Originally published 1970
Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation 2, 293–304 (1986)
Lang, J., Marquis, P.: Complexity results for independence and definability in propositional logic. In: Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning, pp. 356–367 (1998)
Li, C.M.: Integrating equivalence reasoning into Davis-Putnam procedure. In: Proceedings of the AAAI National Conference (AAAI), pp. 291–296 (2000)
Ostrowski, R., Grégoire, E., Mazure, B., Sais, L.: Recovering and exploiting structural knowledge from CNF formulas. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 185–199. Springer, Heidelberg (2002)
Beame, P., Kautz, H., Sabharwal, A.: Using problem structure for efficient clause learning. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 242–256. Springer, Heidelberg (2004)
Giunchiglia, E., Sebastiani, R.: Applying the Davis-Putnam procedure to non-clausal formulas. In: Lamma, E., Mello, P. (eds.) AI*IA 1999. LNCS (LNAI), vol. 1792, pp. 84–95. Springer, Heidelberg (2000)
Giunchiglia, E., Maratea, M., Tacchella, A.: Dependent and independent variables for propositional satisfiability. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 23–26. Springer, Heidelberg (2002)
Järvisalo, M., Junttila, T., Niemelä, I.: Unrestricted vs restricted cut in a tableau method for Boolean circuits. In: AI&M 2004, 8th International Symposium on Artificial Intelligence and Mathematics (2004), Available on-line at http://rutcor.rutgers.edu/amai/aimath04/
Safarpour, S., Veneris, A., Drechsler, R., Lee, J.: Managing don’t cares in Boolean satisfiability. In: Proceedings of the Design, Automation and Test in Europe Conference and Exhibition (DATE 2004), vol. I, p. 10260. IEEE Computer Society, Los Alamitos (2004)
Gupta, A., Gupta, A., Yang, Z., Ashar, P.: Dynamic detection and removal of inactive clauses in SAT with application in image computation. In: Proceedings of the 38th conference on Design automation, pp. 536–541. ACM Press, New York (2001)
Circuit-based Boolean Reasoning. In: Proceedings of the 38th conference on Design automation, ACM Press, New York (2001)
Ganai, M.K., Ashar, P., Gupta, A., Zhang, L., Malik, S.: Combining strengths of circuitbased and cnf-based algorithms for a high-performance SAT solver. In: Proceedings of the 39th conference on Design automation, pp. 747–750. ACM Press, New York (2002)
Junttila, T., Niemelä, I.: Towards an efficient tableau method for Boolean circuit satisfiability checking. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 553–567. Springer, Heidelberg (2000)
Zhang, L., Madigan, C.F., Moskewicz, M.H., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design, pp. 279–285. IEEE Press, Los Alamitos (2001)
Van Gelder, A., Tsuji, Y.K.: Satisfiability testing with more reasoning and less guessing. In: Johnson, D., Trick, M. (eds.) Cliques, Coloring and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 559–586. American Mathematical Society, Providence (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thiffault, C., Bacchus, F., Walsh, T. (2004). Solving Non-clausal Formulas with DPLL Search. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_48
Download citation
DOI: https://doi.org/10.1007/978-3-540-30201-8_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
Online ISBN: 978-3-540-30201-8
eBook Packages: Springer Book Archive