Abstract

This work presents a novel strategy for improving SAT solver performance by using concurrency. Rather than aiming to parallelize search, we use concurrency to aid a conventional CDCL search procedure. More concretely, our work extends a conventional CDCL SAT solver with a second computation thread, which is solely used to strengthen the clauses learned by the solver. This provides a simple and natural way to exploit the availability of multi-core hardware.

We have employed our technique to extend two well established solvers, MiniSAT and Glucose. Despite its conceptual simplicity the technique yields a significant improvement of those solvers’ performances, in particular for unsatisfiable benchmarks. For such benchmarks an extensive empirical evaluation revealed a remarkably consistent reduction of the wall clock time required to determine unsatisfiability, as well as an ability to solve more benchmarks in the same CPU time.

The proposed technique can be applied in combination with existing parallel SAT solving techniques, including both portfolio and search space splitting approaches. The approach presented here can thus be seen as orthogonal to those existing techniques.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.-M., Piette, C.: Revisiting clause exchange in parallel SAT solving. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 200–213. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Boutilier, C. (ed.) IJCAI, pp. 399–404 (2009)Google Scholar
  3. 3.
    Audemard, G., Simon, L.: Refining restarts strategies for SAT and UNSAT. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 118–126. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Balint, A., Belov, A., Diepold, D., Gerber, S., Järvisalo, M., Sinz, C. (eds.): Proceedings of SAT Challenge 2012: Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2012-2. University of Helsinki, Helsinki (2012)Google Scholar
  5. 5.
    Beame, P., Kautz, H.A., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. J. Artif. Intell. Res. (JAIR) 22, 319–351 (2004)MathSciNetMATHGoogle Scholar
  6. 6.
    Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. FMV Technical Report 10/1, Johannes Kepler University, Linz, Austria (2010)Google Scholar
  7. 7.
    Böhm, M., Speckenmeyer, E.: A fast parallel SAT-solver - efficient workload balancing. Ann. Math. Artif. Intell. 17(3-4), 381–400 (1996)MATHCrossRefGoogle Scholar
  8. 8.
    Cook, S.A.: The complexity of theorem-proving procedures. In: STOC, pp. 151–158. ACM (1971)Google Scholar
  9. 9.
    Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Eén, N., Sörensson, N.: MiniSat v1.13 - a SAT solver with conflict-clause minimization. Poster for SAT 2005 (2005), http://www.minisat.se
  12. 12.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)CrossRefGoogle Scholar
  14. 14.
    Van Gelder, A.: Generalized conflict-clause strengthening for satisfiability solvers. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 329–342. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Hamadi, Y., Jabbour, S., Piette, C., Sais, L.: Deterministic parallel DPLL. JSAT 7(4), 127–132 (2011)MathSciNetGoogle Scholar
  16. 16.
    Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: A parallel SAT solver. JSAT 6(4), 245–262 (2009)MATHGoogle Scholar
  17. 17.
    Han, H., Somenzi, F.: Alembic: An efficient algorithm for CNF preprocessing. In: DAC, pp. 582–587. IEEE (2007)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Hyvärinen, A.E.J., Junttila, T.A., Niemelä, I.: Partitioning search spaces of a randomized search. Fundam. Inform. 107(2-3), 289–311 (2011)MATHGoogle Scholar
  20. 20.
    Hyvärinen, A.E.J., Manthey, N.: Designing scalable parallel SAT solvers. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 214–227. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Parallel SAT solver selection and scheduling. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 512–526. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: ICCAD, pp. 220–227 (1996)Google Scholar
  24. 24.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: DAC, pp. 530–535. ACM (2001)Google Scholar
  25. 25.
    Piette, C., Hamadi, Y., Sais, L.: Vivifying propositional clausal formulae. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) ECAI. Frontiers in Artificial Intelligence and Applications, vol. 178, pp. 525–529. IOS Press (2008)Google Scholar
  26. 26.
    Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  27. 27.
    Pipatsrisawat, K., Darwiche, A.: A new clause learning scheme for efficient unsatisfiability proofs. In: Fox, D., Gomes, C.P. (eds.) AAAI, pp. 1481–1484. AAAI Press (2008)Google Scholar
  28. 28.
    Schubert, T., Lewis, M.D.T., Becker, B.: PaMiraXT: Parallel SAT solving with threads and message passing. JSAT 6(4), 203–222 (2009)MATHGoogle Scholar
  29. 29.
    Sörensson, N., Biere, A.: Minimizing learned clauses. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 237–243. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  30. 30.
    Wieringa, S., Heljanko, K.: Asynchronous multi-core incremental SAT solving. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 139–153. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  31. 31.
    Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: Portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. (JAIR) 32, 565–606 (2008)MATHGoogle Scholar
  32. 32.
    Zhang, H., Bonacina, M.P., Hsiang, J.: PSATO: a distributed propositional prover and its application to quasigroup problems. J. Symb. Comput. 21(4), 543–560 (1996)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Siert Wieringa
    • 1
  • Keijo Heljanko
    • 1
  1. 1.School of Science, Department of Information and Computer ScienceAalto UniversityAaltoFinland

Personalised recommendations