Abstract
Satisfiability (SAT) is considered as one of the most important core technologies in formal verification and related areas. Even though there is steady progress in improving practical SAT solving, there are limits on scalability of SAT solvers. We address this issue and present a new approach, called cube-and-conquer, targeted at reducing solving time on hard instances. This two-phase approach partitions a problem into many thousands (or millions) of cubes using lookahead techniques. Afterwards, a conflict-driven solver tackles the problem, using the cubes to guide the search. On several hard competition benchmarks, our hybrid approach outperforms both lookahead and conflict-driven solvers. Moreover, because cube-and-conquer is natural to parallelize, it is a competitive alternative for solving SAT problems in parallel.
The first and the fourth author are supported by the Austrian Science Foundation (FWF) NFN Grant S11408-N23 (RiSE). The third author is supported by Academy of Finland project 139402.
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
Ahmed, T., Kullmann, O., Snevily, H.: On the van der Waerden numbers w(2; 3, t). Tech. Rep. arXiv:1102.5433 [math.CO], arXiv (February 2011)
Bacchus, F.: Enhancing Davis Putnam with extended binary clause reasoning. In: AAAI 2002, pp. 613–619 (2002)
van Beek, P.: Backtracking search algorithms. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 4, pp. 85–134 (2006)
Biere, A.: Bounded model checking. In: Biere, et al. (eds.) [6], ch. 14, pp. 455–481
Biere, A.: Lingeling, Plingeling, Picosat and Precosat at SAT race 2010 (2010)
Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. FAIA, vol. 185. IOS Press (February 2009)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)
Dubois, O., Dequen, G.: A backbone-search heuristic for efficient solving of hard 3-SAT formulae. In: Nebel, B. (ed.) IJCAI, pp. 248–253. Morgan Kaufmann (2001)
Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)
Hamadi, Y.: Conclusion to the special issue on parallel SAT solving. JSAT 6(4), 263 (2009)
Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: a parallel SAT solver. JSAT 6(4), 245–262 (2009)
Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artif. Intell. 14(3), 263–313 (1980)
Harvey, W.D., Ginsberg, M.L.: Limited discrepancy search. In: IJCAI 1995, pp. 607–613 (1995)
Heule, M.J.H., van Maaren, H.: Look-Ahead Based SAT Solvers. In: Biere, et al. (eds.) [6], ch. 5, vol. 185, pp. 155–184 (2009)
Hyvärinen, A.E.J., Junttila, T., Niemelä, I.: Partitioning SAT Instances for Distributed Solving. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 372–386. Springer, Heidelberg (2010)
Hyvärinen, A.E.J., Junttila, T., Niemelä, I.: Grid-Based SAT Solving with Iterative Partitioning and Clause Learning. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 385–399. Springer, Heidelberg (2011)
Kleine Büning, H., Kullmann, O.: Minimal Unsatisfiability and Autarkies. In: Biere, et al. (eds.) [6], ch. 11, vol. 185, pp. 339–401 (February 2009)
Kullmann, O.: Investigating the behaviour of a SAT solver on random formulas. Tech. Rep. CSR 23-2002, University of Wales Swansea, Computer Science Report Series, 119 pages (2002), http://www-compsci.swan.ac.uk/reports/2002.html
Kullmann, O.: Fundaments of Branching Heuristics. In: Biere, et al. (eds.) [6], ch. 7, vol. 185, pp. 205–244 (February 2009)
Kullmann, O.: The OKlibrary: Introducing a ”holistic” research platform for (generalised) SAT solving. Studies in Logic 2(1), 20–53 (2009)
Kullmann, O.: Green-Tao Numbers and SAT. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 352–362. Springer, Heidelberg (2010)
Kullmann, O.: Computing ordinary and palindromic van der Waerden numbers via collaboration between look-ahead and conflict-driven SAT solvers (in preparation, February 2012)
Li, C.M.: Anbulagan: Heuristics based on unit propagation for satisfiability problems. In: IJCAI, vol. (1), pp. 366–371 (1997)
Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-Driven Clause Learning SAT Solvers. In: Biere, et al. (eds.) [6], ch. 4, vol. 185, pp. 131–153 (February 2009)
Mijnders, S., de Wilde, B., Heule, M.J.H.: Symbiosis of search and heuristics for random 3-SAT. In: Mitchell, D., Ternovska, E. (eds.) LaSh 2010 (2010)
Wieringa, S., Niemenmaa, M., Heljanko, K.: Tarmo: A framework for parallelized bounded model checking. In: Brim, L., van de Pol, J. (eds.) PDMC. EPTCS, vol. 14, pp. 62–76 (2009)
Zhang, H.: Combinatorial designs by SAT solvers. In: Biere, et al. (eds.) [6], ch. 17, pp. 533–568
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A. (2012). Cube and Conquer: Guiding CDCL SAT Solvers by Lookaheads. In: Eder, K., Lourenço, J., Shehory, O. (eds) Hardware and Software: Verification and Testing. HVC 2011. Lecture Notes in Computer Science, vol 7261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34188-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-34188-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34187-8
Online ISBN: 978-3-642-34188-5
eBook Packages: Computer ScienceComputer Science (R0)