Abstract.
We investigate the problem of generalizing acceleration techniques as found in recent satisfiability engines for conjunctive normal forms (CNFs) to linear constraint systems over the Booleans. The rationale behind this research is that rewriting the propositional formulae occurring in e.g. bounded model checking (BMC) [5] to CNF requires a blowup in either the formula size (worst-case exponential) or in the number of propositional variables (linear, thus yielding a worst-case exponential blow-up of the search space). We demonstrate that acceleration techniques like observation lists and lazy clause evaluation [14] as well as the more traditional non-chronological backtracking and learning techniques generalize smoothly to Davis-Putnam-like resolution procedures for the very concise propositional logic of linear constraint systems over the Booleans. Despite the more expressive input language, the performance of our prototype implementation comes surprisingly close to that of state-of-the-art CNF-SAT engines like ZChaff [14]. First experiments with bounded model-construction problems show that the overhead in the satisfiability engine that can be attributed to the richer input language is often amortized by the conciseness gained in the propositional encoding of the BMC problem.
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
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Generic ILP versus specialized 0-1 ILP: An update. In: Proc. ACM/IEEE Intl. Conf. Comp.-Aided Design (ICCAD), November 2002, pp. 450–457 (2002)
Baptista, L., Lynce, I., Marques-Silva, J.: Complete search restart strategies for satisfiability. In: Proc. of the IJCAI 2001 Workshop on Stochastic Search Algorithms (IJCAI-SSA) (August 2001)
Baptista, L., Marques-Silva, J.P.: Using randomization and learning to solve hard real-world instances of satisfiability. In: Proc. of the 6th International Conference on Principles and Practice of Constraint Programming (2000)
Barth, P.: A Davis-Putnam based enumeration algorithm for linear pseudoboolean optimization. Technical Report MPI-I-95-2-003, Max-Planck-Institut für Informatik, Saarbrücken, Germany (1995)
Biere, A., Cimatti, A., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, p. 193. Springer, Heidelberg (1999)
Chai, D., Kuehlmann, A.: A fast pseudo-boolean constraint solver. In: Proc. of the 40th Design Automation Conference (DAC 2003), Anaheim (California, USA), June 2003, pp. 830–835. ACM, New York (2003)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5, 394–397 (1962)
Fränzle, M.: Take it NP-easy: Bounded model construction for duration calculus. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 245–264. Springer, Heidelberg (2002)
Groote, J.F., Warners, J.P.: The propositional formula checker HeerHugo. Technical report SEN-R9905, CWI (1999)
Harel, D., Politi, M.: Modeling Reactive Systems with Statecharts. McGraw-Hill Inc., New York (1998)
Lochmann, R.: Boosting the verification power of the statemate verification engine: on the perfomance benefits of integrating ProverCL (2003) (in preparation)
Marques-Silva, J.P.: The impact of branching heuristics in propositional satisfiability algorithms. In: Barahona, P., Alferes, J.J. (eds.) EPIA 1999. LNCS (LNAI), vol. 1695, pp. 62–74. Springer, Heidelberg (1999)
Marques-Silva, J.P., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the 38th Design Automation Conference (DAC 2001) (June 2001)
Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning. Elsevier Science, B.V. (1999)
Owen, J.H., Mehrotra, S.: On the value of binary expansions for general mixedinteger linear programs. Operations Research 50(5), 810–819 (2002)
Tseitin, G.: On the complexity of derivations in propositional calculus. In: Slisenko, A. (ed.) Studies in Constructive Mathematics and Mathematical Logics (1968)
Warners, J.P.: A linear-time transformation of linear inequalities into conjunctive normal form. Information Processing Letters 68(2), 63–69 (1998)
Whittemore, J., Kim, J., Sakallah, K.: SATIRE: A new incremental satisfiability engine. In: Proc. of the 38th Design Automation Conference (DAC 2001), Las Vegas (Nevada, USA), June 2001, pp. 542–545 (2001)
Zhang, H.: SATO: An efficient propositional prover. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 272–275. Springer, Heidelberg (1997)
Zhang, H., Stickel, M.: An efficient algorithm for unit-propagation. In: Proc. of the International Symposium on Artificial Intelligence and Mathematics (AIMATH 1996), Fort Lauderdale (Florida USA), pp. 166–169 (1996)
Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: Proc. of the International Conference on Computer-Aided Design (ICCAD 2001), November 2001, pp. 279–285 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fränzle, M., Herde, C. (2003). Efficient SAT Engines for Concise Logics: Accelerating Proof Search for Zero-One Linear Constraint Systems. In: Vardi, M.Y., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2003. Lecture Notes in Computer Science(), vol 2850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39813-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-39813-4_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20101-4
Online ISBN: 978-3-540-39813-4
eBook Packages: Springer Book Archive