Advertisement

Abstract

Solvers for propositional logic formulas, so called SAT solvers, are used in many practical applications. As multi-core and multi-processor hardware has become widely available, parallelizations of such solvers are actively researched. Such research typically ignores the incremental problem specification feature that modern SAT solvers possess. This feature is, however, crucial for many of the real-life applications of SAT solvers. Such applications include formal verification, equivalence checking, and typical artificial intelligence tasks such as scheduling, planning and reasoning.

We have developed a multi-core SAT solver called Tarmo, which provides an interface that is compatible with conventional incremental solvers. It enables substantial performance improvements for many applications, without requiring code modifications. We present the asynchronous interface, a natural extension to the conventional solver interface that allows the construction of efficient application specific parallelizations. Through the asynchronous interface multiple problems can be given to the solver simultaneously. This enables conceptually simple but efficient parallelization of the solving process. Moreover, an asynchronous solver is easier to run in parallel with other independent tasks, simplifying the construction of so called coarse grained parallelizations. We provide an extensive experimental evaluation to illustrate the performance of the proposed techniques.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ábrahám, E., Schubert, T., Becker, B., Fränzle, M., Herde, C.: Parallel SAT Solving in Bounded Model Checking. In: Brim, L., Haverkort, B.R., Leucker, M., van de Pol, J. (eds.) FMICS and PDMC 2006. LNCS, vol. 4346, pp. 301–315. Springer, Heidelberg (2007)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.
    Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB standard version 2.0 (2010), http://www.smtlib.org
  4. 4.
    Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS/ETAPS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Böhm, M., Speckenmeyer, E.: A fast parallel SAT-solver - efficient workload balancing. Ann. Math. Artif. Intell. 17(3-4), 381–400 (1996)MATHCrossRefGoogle Scholar
  6. 6.
    Bradley, A.R.: k-step relative inductive generalization. CoRR abs/1003.3649 (2010)Google Scholar
  7. 7.
    Brayton, R., Mishchenko, A.: ABC: An Academic Industrial-Strength Verification Tool. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 24–40. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Bruttomesso, R., Griggio, A.: Broadening the scope of SMT-COMP: the application track. In: COMPARE, pp. 18–27 (2012)Google Scholar
  9. 9.
    Cook, S.A.: The complexity of theorem-proving procedures. In: STOC, pp. 151–158. ACM (1971)Google Scholar
  10. 10.
    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
  11. 11.
    Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electronic Notes in Theoretical Computer Science 89(4), 543–560 (2003)CrossRefGoogle Scholar
  12. 12.
    Gomes, C.P., Selman, B., Crato, N., Kautz, H.A.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. Autom. Reasoning 24(1/2), 67–100 (2000)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Hamadi, Y., Jabbour, S., Sais, L.: Control-based clause sharing in parallel SAT solving. In: Boutilier, C. (ed.) IJCAI, pp. 499–504 (2009)Google Scholar
  14. 14.
    Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: A parallel SAT solver. JSAT 6(4), 245–262 (2009)MATHGoogle Scholar
  15. 15.
    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
  16. 16.
    Hyvärinen, A.E.J., Junttila, T.A., Niemelä, I.: Partitioning Search Spaces of a Randomized Search. In: Serra, R., Cucchiara, R. (eds.) AI*IA 2009. LNCS, vol. 5883, pp. 243–252. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Khasidashvili, Z., Nadel, A., Palti, A., Hanna, Z.: Simultaneous SAT-Based Model Checking of Safety Properties. In: Ur, S., Bin, E., Wolfsthal, Y. (eds.) HVC 2005. LNCS, vol. 3875, pp. 56–75. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Marques-Silva, J., Lynce, I.: On Improving MUS Extraction Algorithms. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 159–173. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: ICCAD, pp. 220–227 (1996)Google Scholar
  22. 22.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: DAC, pp. 530–535 (2001)Google Scholar
  23. 23.
    Rintanen, J., Heljanko, K., Niemelä, I.: Planning as satisfiability: parallel plans and algorithms for plan search. Artif. Intell. 170(12-13), 1031–1080 (2006)MATHCrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Sterin, B., Een, N., Mishchenko, A., Brayton, R.: The benefit of concurrency in model checking. In: IWLS, pp. 176–182 (2011)Google Scholar
  26. 26.
    Whittemore, J., Kim, J., Sakallah, K.A.: SATIRE: A new incremental satisfiability engine. In: DAC, pp. 542–545 (2001)Google Scholar
  27. 27.
    Wieringa, S.: On incremental satisfiability and bounded model checking. In: Ganai, M.K., Biere, A. (eds.) DIFTS, pp. 46–54 (2011)Google Scholar
  28. 28.
    Wieringa, S.: Understanding, Improving and Parallelizing MUS Finding Using Model Rotation. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 672–687. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    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)Google Scholar
  30. 30.
    Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: Portfolio-based algorithm selection for SAT. CoRR abs/1111.2249 (2011)Google Scholar
  31. 31.
    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