HordeQBF: A Modular and Massively Parallel QBF Solver

  • Tomáš Balyo
  • Florian LonsingEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)


The recently developed massively parallel satisfiability (SAT) solver HordeSAT was designed in a modular way to allow the integration of any sequential CDCL-based SAT solver in its core. We integrated the QCDCL-based quantified Boolean formula (QBF) solver DepQBF in HordeSAT to obtain a massively parallel QBF solver—HordeQBF. In this paper we describe the details of this integration and report on results of the experimental evaluation of HordeQBF’s performance. HordeQBF achieves superlinear average and median speedup on the hard application instances of the 2014 QBF Gallery.


Message Passing Interface Quantify Boolean Formula Current Assignment Core Solver Shared Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Balabanov, V., Jiang, J.R.: Unified QBF certification and its applications. Formal Meth. Syst. Des. 41(1), 45–65 (2012)CrossRefzbMATHGoogle Scholar
  2. 2.
    Balabanov, V., Widl, M., Jiang, J.H.R.: QBF resolution systems and their proof complexities. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 154–169. Springer, Heidelberg (2014)Google Scholar
  3. 3.
    Balyo, T., Sanders, P., Sinz, C.: HordeSat: A massively parallel portfolio SAT solver. In: Heule, M. (ed.) SAT 2015. LNCS, vol. 9340, pp. 156–172. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  4. 4.
    Biere, A.: PicoSAT essentials. JSAT 4(2–4), 75–97 (2008)zbMATHGoogle Scholar
  5. 5.
    Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified boolean formulae. In: AAAI, pp. 262–267. AAAI Press / The MIT Press (1998)Google Scholar
  6. 6.
    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
  7. 7.
    Feldmann, R., Monien, B., Schamberger, S.: A distributed algorithm to evaluate quantified boolean formulae. In: AAAI, pp. 285–290. AAAI Press / The MIT Press (2000)Google Scholar
  8. 8.
    Giunchiglia, E., Marin, P., Narizzano, M.: QuBE7.0. JSAT 7(2–3), 83–88 (2010)Google Scholar
  9. 9.
    Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term resolution and learning in the evaluation of quantified boolean formulas. JAIR 26, 371–416 (2006)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Gropp, W., Lusk, E., Doss, N., Skjellum, A.: A high-performance, portable implementation of the MPI message passing interface standard. Parallel Comput. 22(6), 789–828 (1996)CrossRefzbMATHGoogle Scholar
  11. 11.
    Heule, M., Järvisalo, M., Lonsing, F., Seidl, M., Biere, A.: Clause elimination for SAT and QSAT. J. Artif. Intell. Res. (JAIR) 53, 127–168 (2015)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Janota, M., Jordan, C., Klieber, W., Lonsing, F., Seidl, M., Van Gelder, A.: The QBF Gallery 2014: The QBF competition at the FLoC olympic games. JSAT 9, 187–206 (2016)Google Scholar
  13. 13.
    Jordan, C., Kaiser, L., Lonsing, F., Seidl, M.: MPIDepQBF: Towards parallel QBF solving without knowledge sharing. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 430–437. Springer, Heidelberg (2014)Google Scholar
  14. 14.
    Kleine Büning, H., Karpinski, M., Flögel, A.: A resolution for quantified boolean formulas. Inf. Comput. 117(1), 12–18 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Letz, R.: Lemma and model caching in decision procedures for quantified boolean formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 160–175. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Lewis, M., Schubert, T., Becker, B.: QMiraXT - a multithreaded QBF solver. In: Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (MBMV) (2009)Google Scholar
  17. 17.
    Lewis, M., Schubert, T., Becker, B., Marin, P., Narizzano, M., Giunchiglia, E.: Parallel QBF solving with advanced knowledge sharing. Fundamenta Informaticae 107(2–3), 139–166 (2011)MathSciNetGoogle Scholar
  18. 18.
    Lonsing, F., Bacchus, F., Biere, A., Egly, U., Seidl, M.: Enhancing search-based QBF solving by dynamic blocked clause elimination. In: Davis, M. (ed.) LPAR-20 2015. LNCS, vol. 9450, pp. 418–433. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  19. 19.
    Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. JSAT 7(2–3), 71–76 (2010)Google Scholar
  20. 20.
    Lonsing, F., Biere, A.: Integrating dependency schemes in search-based QBF solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 158–171. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Mota, B.D., Nicolas, P., Stéphan, I.: A new parallel architecture for QBF tools. In: Proceedings of the International Conferference on High Performance Computing and Simulation (HPCS 2010), pp. 324–330. IEEE (2010)Google Scholar
  22. 22.
    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
  23. 23.
    Pulina, L., Tacchella, A.: AQME’10. JSAT 7(2–3), 65–70 (2010)Google Scholar
  24. 24.
    Vautard, J., Lallouet, A., Hamadi, Y.: A parallel solving algorithm for quantified constraints problems. In: ICTAI, pp. 271–274. IEEE Computer Society (2010)Google Scholar
  25. 25.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zhang, L., Malik, S.: Conflict driven learning in a quantified boolean satisfiability solver. In: ICCAD, pp. 442–449. ACM / IEEE Computer Society (2002)Google Scholar
  27. 27.
    Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 200–215. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Knowledge-Based Systems GroupVienna University of TechnologyViennaAustria

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