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Beyond Unit Propagation in SAT Solving

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Experimental Algorithms (SEA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6630))

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Abstract

The tremendous improvement in SAT solving has made SAT solvers a core engine for many real world applications. Though still being a branch-and-bound approach purposive engineering of the original algorithm has enhanced state-of-the-art solvers to tackle huge and difficult SAT instances. The bulk of solving time is spent on iteratively propagating variable assignments that are implied by decisions.

In this paper we present two approaches on how to extend the broadly applied Unit Propagation technique where a variable assignment is implied iff a clause has all but one of its literals assigned to false. We propose efficient ways to utilize more reasoning in the main component of current SAT solvers so as to be less dependent on felicitous branching decisions.

This work was supported by DFG-SPP 1307, project “Structure-based Algorithm Engineering for SAT-Solving”.

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References

  1. The international SAT competition (2002-2009), www.satcompetition.org

  2. Aspvall, B., Plass, M.F., Tarjan, R.E.: A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas. Inf. Proc. Lett. 8, 121–123 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Audemard, G., Bordeaux, L., Hamadi, Y., Jabbour, S.J., Sais, L.: A generalized framework for conflict analysis. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 21–27. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. Bacchus, F.: Enhancing Davis Putnam with Extended Binary Clause Reasoning. In: 18th AAAI Conference on Artificial Intelligence, pp. 613–619 (2002)

    Google Scholar 

  5. Bacchus, F.: Exploring the computational tradeoff of more reasoning and less searching. In: SAT, pp. 7–16 (2002)

    Google Scholar 

  6. Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Beame, P., Kautz, H.A., Sabharwal, A.: Understanding the power of clause learning. IJCAI, 1194–1201 (2003)

    Google Scholar 

  8. Berre, D.L.: Exploiting the real power of unit propagation lookahead. Electronic Notes in Discrete Mathematics 9, 59–80 (2001)

    Article  MATH  Google Scholar 

  9. Biere, A.: Precosat solver description (2009), fmv.jku.at/precosat/preicosat-sc09.pdf

  10. Biere, A.: Picosat essentials. JSAT 4, 75–97 (2008)

    MATH  Google Scholar 

  11. Biere, A.: Lazy hyper binary resolution. In: Algorithms and Applications for Next Generation SAT Solvers, Dagstuhl Seminar 09461, Dagstuhl, Germany (2009)

    Google Scholar 

  12. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  13. Brafman, R.I.: A simplifier for propositional formulas with many binary clauses. IJCAI, 515–522 (2001)

    Google Scholar 

  14. Chu, G., Harwood, A., Stuckey, P.J.: Cache conscious data structures for boolean satisfiability solvers. JSAT 6, 99–120 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Cook, S.A.: The complexity of theorem-proving procedures. In: STOC (1971)

    Google Scholar 

  16. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press and McGraw-Hill Book Company (2001)

    Google Scholar 

  17. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  18. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  19. 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 

  20. Han, H., Somenzi, F.: On-the-fly clause improvement. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 209–222. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Heule, M.: SmArT Solving. PhD thesis, Technische Universiteit Delft (2008)

    Google Scholar 

  22. Heule, M., Maaren, H.V.: Aligning cnf- and equivalence-reasoning. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 174–181. Springer, Heidelberg (2005)

    Google Scholar 

  23. Kautz, H.A., Selman, B.: Planning as satisfiability. In: Proceedings of the Tenth European Conference on Artificial Intelligence, ECAI 1992, pp. 359–363 (1992)

    Google Scholar 

  24. Kottler, S.: Solver descriptions for the SAT competition 2009, satcompetition.org

  25. Kottler, S.: SAT Solving with Reference Points. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 143–157. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  26. Kottler, S., Kaufmann, M., Sinz, C.: Computation of renameable horn backdoors. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 154–160. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Principles and Practice of Constraint Programming (1997)

    Google Scholar 

  28. Marques-Silva, J.P.: Practical Applications of Boolean Satisfiability. In: Workshop on Discrete Event Systems, WODES 2008 (2008)

    Google Scholar 

  29. Marques-Silva, J.P., Sakallah, K.A.: Grasp: A search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  30. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: DAC (2001)

    Google Scholar 

  31. Pipatsrisawat, K., Darwiche, A.: On modern clause-learning satisfiability solvers. J. Autom. Reasoning 44(3), 277–301 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. Selman, B., Kautz, H., Cohen, B.: Local search strategies for satisfiability testing. In: Cliques, Coloring, and Satisfiability: DIMACS Implementation Challenge (1993)

    Google Scholar 

  33. Van Gelder, A., Tsuji, Y.K.: Satisfiability testing with more reasoning and less guessing. In: Johnson, D.S., Trick, M. (eds.) Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge. AMS, Providence (1996)

    Google Scholar 

  34. Velev, M.N.: Using rewriting rules and positive equality to formally verify wide-issue out-of-order microprocessors with a reorder buffer. In: DATE 2002 (2002)

    Google Scholar 

  35. Williams, R., Gomes, C., Selman, B.: Backdoors to typical case complexity. IJCAI (2003)

    Google Scholar 

  36. Zhang, L., Madigan, C.F., Moskewicz, M.H., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: ICCAD 2001 (2001)

    Google Scholar 

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Kaufmann, M., Kottler, S. (2011). Beyond Unit Propagation in SAT Solving. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_23

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  • DOI: https://doi.org/10.1007/978-3-642-20662-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20661-0

  • Online ISBN: 978-3-642-20662-7

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