Abstract
This paper focuses on developing efficient inference techniques for improving conjunctive normal form (CNF) Boolean satisfiability (SAT) solvers. We analyze a variant of hyper binary resolution from various perspectives: We show that it can simulate the circuit-level technique of structural hashing and how it can be realized efficiently using so called tree-based lookahead. Experiments show that our implementation improves the performance of state-of-the-art CNF-level SAT techniques on combinational equivalent checking instances.
The first author is supported by DARPA contract number N66001-10-2-4087. The first and third authors are supported by Austrian Science Foundation (FWF) NFN Grant S11408-N23 (RiSE), and the second author by Academy of Finland (grants 132812 and 251170).
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
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)
Gershman, R., Strichman, O.: Cost-effective hyper-resolution for preprocessing CNF formulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 423–429. Springer, Heidelberg (2005)
Heule, M., Dufour, M., van Zwieten, J., van Maaren, H.: March_eq: Implementing additional reasoning into an efficient look-ahead SAT solver. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 345–359. Springer, Heidelberg (2005)
Heule, M.J.H., van Maaren, H.: Chapter 5: Look-Ahead Based SAT Solvers. In: Handbook of Satisfiability, pp. 155–184. IOS Press (2009)
Van Gelder, A.: Toward leaner binary-clause reasoning in a satisfiability solver. Annals of Mathematics and Artificial Intelligence 43, 239–253 (2005)
Aho, A., Garey, M., Ullman, J.: The transitive reduction of a directed graph. SIAM Journal on Computing 1(2), 131–137 (1972)
Bacchus, F.: Enhancing Davis Putnam with extended binary clause reasoning. In: Proc. AAAI, pp. 613–619. AAAI Press (2002)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35(8), 677–691 (1986)
Kuehlmann, A., Krohm, F.: Equivalence checking using cuts and heaps. In: Proc. DAC, pp. 263–268. ACM (1997)
Williams, P.F., Andersen, H.R., Hulgaard, H.: Satisfiability checking using boolean expression diagrams. STTT 5(1), 4–14 (2003)
Abdulla, P.A., Bjesse, P., Eén, N.: Symbolic reachability analysis based on SAT-solvers. In: Graf, S., Schwartzbach, M. (eds.) TACAS/ETAPS 2000. LNCS, vol. 1785, pp. 411–425. Springer, Heidelberg (2000)
Sheeran, M., Stålmarck, G.: A tutorial on Stålmarck’s proof procedure for propositional logic. Formal Methods in System Design 16(1), 23–58 (2000)
Billionnet, A., Sutter, A.: An efficient algorithm for the 3-satisfiability problem. Operations Research Letters 12(1), 29–36 (1992)
Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 341–355. Springer, Heidelberg (1997)
Anbulagan, Pham, D.N., Slaney, J.K., Sattar, A.: Old resolution meets modern SLS. In: Proc. AAAI, pp. 354–359 (2005)
Heule, M.J.H.: March: Towards a lookahead SAT solver for general purposes, MSc thesis (2004)
Biere, A.: P{re,i}coSAT@SC’09. In: SAT 2009 Competitive Event Booklet (2009)
Boufkhad, Y.: Aspects probabilistes et algorithmiques du problème de satisfaisabilité, PhD thesis, Univertsité de Paris 6 (1996)
Simons, P.: Towards constraint satisfaction through logic programs and the stable model semantics, Report A47, Digital System Laboratory, Helsinki University of Technology (1997)
Mijnders, S., de Wilde, B., Heule, M.J.H.: Symbiosis of search and heuristics for random 3-SAT. In: Proc. LaSh (2010)
Biere, A.: (Q)CompSAT and (Q)PicoSAT at the SAT’06 Race (2006)
Han, H., Jin, H., Somenzi, F.: Clause simplification through dominator analysis. In: Proc. DATE, pp. 143–148. IEEE (2011)
Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. FMV Report Series TR 10/1, JKU, Linz, Austria (2010)
Soos, M.: CryptoMiniSat 2.5.0, SAT Race’10 solver description (2010)
Han, H., Somenzi, F.: On-the-fly clause improvement. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 209–222. Springer, Heidelberg (2009)
Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 355–370. Springer, Heidelberg (2012)
Kunz, W., Pradhan, D.K.: Recursive learning: a new implication technique for efficient solutions to CAD problems-test, verification, and optimization. IEEE T-CAD 13(9) (1994)
Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Chpt. 26: SMT Modulo Theories. In: Handbook of Satisfiability. IOS Press (2009)
Marques-Silva, J., Glass, T.: Combinational equivalence checking using satisfiability and recursive learning. In: Proc. DATE (1999)
Groote, J.F., Warners, J.P.: The propositional formula checker HeerHugo. J. Autom. Reasoning 24(1/2), 101–125 (2000)
Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads. In: Eder, K., Lourenço, J., Shehory, O. (eds.) HVC 2011. LNCS, vol. 7261, pp. 50–65. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heule, M.J.H., Järvisalo, M., Biere, A. (2013). Revisiting Hyper Binary Resolution. In: Gomes, C., Sellmann, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2013. Lecture Notes in Computer Science, vol 7874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38171-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-38171-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38170-6
Online ISBN: 978-3-642-38171-3
eBook Packages: Computer ScienceComputer Science (R0)