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Clause Sharing and Partitioning for Cloud-Based SMT Solving

  • Matteo Marescotti
  • Antti E. J. Hyvärinen
  • Natasha Sharygina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9938)

Abstract

Satisfiability modulo theories (SMT) allows the modeling and solving of constraint problems arising from practical domains by combining well-engineered and powerful solvers for propositional satisfiability with expressive, domain-specific background theories in a natural way. The increasing popularity of SMT as a modelling approach means that the SMT solvers need to handle increasingly complex problem instances. This paper studies how SMT solvers can use cloud computing to scale to challenging problems through sharing of learned information in the form of clauses with approaches based on both divide-and-conquer and algorithm portfolios. Our initial experiments, executed on the OpenSMT2 solver, show that parallelization with clause sharing speeds up the solving of instances, on average, by a factor of four or five depending on the problem domain.

Notes

Acknowledgements

This work was financially supported by SNF project number 200021_153402.

References

  1. 1.
    Audemard, G., Hoessen, B., Jabbour, S., Piette, C.: Dolius: A distributed parallel SAT solving framework. In: Berre, D.L. (ed.) POS-14. EPiC Series, vol. 27, pp. 1–11. EasyChair (2014)Google Scholar
  2. 2.
    Balyo, T., Sanders, P., Sinz, C.: HordeSat: a massively parallel portfolio SAT solver. In: Heule, M., et al. (eds.) SAT 2015. LNCS, vol. 9340, pp. 156–172. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24318-4_12 CrossRefGoogle Scholar
  3. 3.
    Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: a theorem prover for program checking. J. ACM 52(3), 365–473 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dutertre, B.: Yices 2.2. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 737–744. Springer, Heidelberg (2014)Google Scholar
  7. 7.
    Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: a parallel SAT solver. J. Satisfiability Boolean Model. Comput. 6(4), 245–262 (2009)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Software verification with BLAST. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 235–239. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Holzmann, G.J.: Cloud-based verification of concurrent software. In: Jobstmann, B., et al. (eds.) VMCAI 2016. LNCS, vol. 9583, pp. 311–327. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49122-5_15 CrossRefGoogle Scholar
  11. 11.
    Huberman, B.A., Lukose, R.M., Hogg, T.: An economics approach to hard computational problems. Science 275(5296), 51–54 (1997)CrossRefGoogle Scholar
  12. 12.
    Hyvärinen, A.E.J., Junttila, T.A., Niemelä, I.: A distribution method for solving SAT in grids. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 430–435. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Hyvärinen, A.E.J., Marescotti, M., Alt, L., Sharygina, N.: OpenSMT2: an SMT solver for multi-core and cloud computing. In: Creignou, N., Le Berre, D., Le Berre, D., Le Berre, D., Le Berre, D., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 547–553. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-40970-2_35 CrossRefGoogle Scholar
  14. 14.
    Hyvärinen, A.E.J., Marescotti, M., Sharygina, N.: Search-space partitioning for parallelizing SMT solvers. In: Heule, M., et al. (eds.) SAT 2015. LNCS, vol. 9340, pp. 369–386. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24318-4_27 CrossRefGoogle Scholar
  15. 15.
    Hyvärinen, A.E.J., Junttila, T.A., Niemelä, I.: Partitioning search spaces of a randomized search. Fundamenta Informaticae 107(2–3), 289–311 (2011)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Martins, R., Manquinho, V.M., Lynce, I.: An overview of parallel SAT solving. Constraints 17(3), 304–347 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    de Moura, L., Bjørner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Nieuwenhuis, R., Oliveras, A.: Proof-producing congruence closure. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 453–468. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53(6), 937–977 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Palikareva, H., Cadar, C.: Multi-solver support in symbolic execution. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 53–68. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  22. 22.
    Rakadjiev, E., Shimosawa, T., Mine, H., Oshima, S.: Parallel SMT solving and concurrent symbolic execution. In: 2015 IEEE TrustCom/BigDataSE/ISPA, Helsinki, Finland, August 20–22, 2015, vol. 3, pp. 17–26 (2015). http://dx.doi.org/10.1109/Trustcom.2015.608
  23. 23.
    Reisenberger, C.: PBoolector: a parallel SMT solver for QF_BV by combining bit-blasting with look-ahead. Master’s thesis, Johannes Kepler Univesität Linz, Linz, Austria (2014)Google Scholar
  24. 24.
    Sebastiani, R., Tomasi, S.: Optimization modulo theories with linear rational costs. ACM Trans. Comput. Logic 16(2), 12:1–12:3 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Wintersteiger, C.M., Hamadi, Y., de Moura, L.: A concurrent portfolio approach to SMT solving. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 715–720. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Yordanov, B., Wintersteiger, C.M., Hamadi, Y., Kugler, H.: SMT-based analysis of biological computation. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 78–92. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Matteo Marescotti
    • 1
  • Antti E. J. Hyvärinen
    • 1
  • Natasha Sharygina
    • 1
  1. 1.Università della Svizzera italianaLuganoSwitzerland

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