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International Conference on Theory and Applications of Satisfiability Testing

SAT 2016: Theory and Applications of Satisfiability Testing – SAT 2016 pp 87–103Cite as

Extreme Cases in SAT Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9710))

Abstract

With the increasing performance of SAT solvers, a lot of distinct problems, coming from very disparate fields, are added to the pool of Application problems, regularly used to rank solvers. These problems are also widely used to measure the positive impact of any new idea. We show in this paper that many of them have extreme behaviors that any SAT solvers must cope with. We show that, by adding a few, simple, human-readable, indicators, we can let Glucose choose between four strategies to show important improvements on the set of the hardest problems from all the competitions between 2002 and 2013 included. Moreover, once the SAT solver has been specialized, we show that a new restart polarity policy can improve even more the results. Without the first specialization step mentioned above, this new and effective policy would have been jugged inefficient. Our final Glucose is capable of solving \(20\,\%\) more problems than the original one, while speeding up also UNSAT answers.

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Notes

  1. 1.

    The list of problems with additional informations are available at http://www.labri.fr/perso/lsimon/sat16.

  2. 2.

    This observation was originally pointed out by Lakhdar Saïs (CRIL, Lens) during one of the National ANR-Funded project “UNLOC” in 2010.

  3. 3.

    More informations on this set of problems available at http://www.labri.fr/perso/lsimon/sat16.

References

  1. Amadini, R., Gabbrielli, M., Mauro, J.: Sunny: a lazy portfolio approach for constraint solving. arXiv preprint arXiv:1311.3353 (2013)

  2. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of IJCAI, pp. 399–404 (2009)

    Google Scholar 

  3. Audemard, G., Simon, L.: Glucose 2.1: Aggressive, but reactive, clause database management, dynamic restarts (system description). In: Pragmatics of SAT 2012 (POS 2012), dans le cadre de SAT 2012, June 2012

    Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. Belov, A., Heule, M.J., Diepold, D., Järvisalo, M.: The application and the hard combinatorial benchmarks in sat competition 2014. SAT COMPETITION 2014, p. 81 (2014)

    Google Scholar 

  6. Le Berre, D., Simon, L.: The essentials of the SAT 2003 competition. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 452–467. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Biere, A.: (p)lingeling. http://fmv.jku.at/lingeling

  8. Biere, A.: Lingeling and friends entering the sat race 2015 (2015)

    Google Scholar 

  9. Chen, J.: Minisat bcd and abcdsat: Solvers based on blocked clause decomposition. In: SAT RACE 2015 solvers description (2015)

    Google Scholar 

  10. Dubois, O., Dequen, G.: A backbone-search heuristic for efficient solving of hard 3-sat formulae. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI, pp. 248–253 (2001)

    Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M.T., Ziller, S.: A portfolio solver for answer set programming: preliminary report. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 352–357. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Heule, M., van Maaren, H.: March_dl: Adding adaptive heuristics and a new branching strategy. JSAT 2(1–4), 47–59 (2006)

    MATH  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. In: Proceedings of ISTCS, pp. 128–133 (1993)

    Google Scholar 

  16. Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI) (2013)

    Google Scholar 

  17. Marques-Silva, J., Sakallah, K.: GRASP - a new search algorithm for satisfiability. In: ICCAD 1996, pp. 220–227 (1996)

    Google Scholar 

  18. Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of DAC, pp. 530–535 (2001)

    Google Scholar 

  19. Chanseok, O.: Patching minisat to deliver performance of modern sat solvers (2015)

    Google Scholar 

  20. O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Irish Conference on Artificial Intelligence and Cognitive Science, pp. 210–216 (2008)

    Google Scholar 

  21. 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)

    Chapter  Google Scholar 

  22. Ross Quinlan, J.: C4. 5: programs for machine learning. Elsevier (2014)

    Google Scholar 

  23. Soos, M., Lindauer, M.: The cryptominisat-4.4 set of solvers at the sat race 2015 (2015)

    Google Scholar 

  24. Xu, L., Hutter, F., Hoos, H., Leyton-Brown, K.: Satzilla: Portfolio-based algorithm selection for sat. J. Artif. Intell. Res. 32, 565–606 (2008)

    MATH  Google Scholar 

  25. LeBerre, D.: Exploiting the real power of unit propagation lookahead. In: Proceedings of SAT (2001)

    Google Scholar 

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Acknowledgments

Computer time was provided (1) the MCIA (Mésocentre de Calcul Intensif Aquitain) of the Univ. of Bordeaux and of the Univ. of Pau and des Pays de l’Adour and (2) the CRIL (Univ. d’Artois). The authors were partially supported by the ANR-2016 “SATAS” ANR-15-CE40-0017 National French Project.

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Authors and Affiliations

  1. CRIL, Artois University, Arras, France

    Gilles Audemard

  2. LaBRI, University Bordeaux, Bordeaux, France

    Laurent Simon

Authors
  1. Gilles Audemard
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  2. Laurent Simon
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Correspondence to Laurent Simon .

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Editors and Affiliations

  1. Aix-Marseille Université, Marseille, France

    Nadia Creignou

  2. Université d'Artois, Lens, France

    Daniel Le Berre

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Audemard, G., Simon, L. (2016). Extreme Cases in SAT Problems. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-40970-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40969-6

  • Online ISBN: 978-3-319-40970-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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