Inprocessing Rules

  • Matti Järvisalo
  • Marijn J. H. Heule
  • Armin Biere
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)

Abstract

Decision procedures for Boolean satisfiability (SAT), especially modern conflict-driven clause learning (CDCL) solvers, act routinely as core solving engines in various real-world applications. Preprocessing, i.e., applying formula rewriting/simplification rules to the input formula before the actual search for satisfiability, has become an essential part of the SAT solving tool chain. Further, some of the strongest SAT solvers today add more reasoning to search by interleaving formula simplification and CDCL search. Such inprocessing SAT solvers witness the fact that implementing additional deduction rules in CDCL solvers leverages the efficiency of state-of-the-art SAT solving further. In this paper we establish formal underpinnings of inprocessing SAT solving via an abstract inprocessing framework that covers a wide range of modern SAT solving techniques.

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References

  1. 1.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Computers 48(5), 506–521 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proc. DAC, pp. 530–535. ACM (2001)Google Scholar
  3. 3.
    Bacchus, F.: Enhancing Davis Putnam with extended binary clause reasoning. In: Proc. AAAI, pp. 613–619. AAAI Press (2002)Google Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Subbarayan, S., Pradhan, D.K.: NiVER: Non-increasing Variable Elimination Resolution for Preprocessing SAT Instances. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 276–291. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Gershman, R., Strichman, O.: Cost-Effective Hyper-Resolution for Preprocessing CNF Formulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 423–429. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Eén, N., Biere, A.: Effective Preprocessing in SAT Through Variable and Clause Elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Jin, H., Somenzi, F.: An incremental algorithm to check satisfiability for bounded model checking. Electronic Notes in Theoretical Computer Science 119(2), 51–65 (2005)CrossRefGoogle Scholar
  9. 9.
    Han, H., Somenzi, F.: Alembic: An efficient algorithm for CNF preprocessing. In: Proc. DAC, pp. 582–587. IEEE (2007)Google Scholar
  10. 10.
    Piette, C., Hamadi, Y., Saïs, L.: Vivifying propositional clausal formulae. In: Proc. ECAI, pp. 525–529. IOS Press (2008)Google Scholar
  11. 11.
    Heule, M.J.H., Järvisalo, M., Biere, A.: Clause Elimination Procedures for CNF Formulas. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 357–371. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Järvisalo, M., Biere, A., Heule, M.J.H.: Simulating circuit-level simplifications on CNF. Journal of Automated Reasoning (2012); OnlineFirst 2011Google Scholar
  13. 13.
    Heule, M.J.H., Järvisalo, M., Biere, A.: Efficient CNF Simplification Based on Binary Implication Graphs. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 201–215. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Heule, M.J.H., Järvisalo, M., Biere, A.: Covered clause elimination. In: LPAR-17 Short Papers (2010), http://arxiv.org/abs/1011.5202
  15. 15.
    Biere, A.: P{re,i}coSAT@SC 2009. In: SAT 2009 Competitive Event Booklet (2009)Google Scholar
  16. 16.
    Soos, M.: CryptoMiniSat 2.5.0, SAT Race 2010 solver description (2010)Google Scholar
  17. 17.
    Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. FMV Technical Report 10/1, Johannes Kepler University, Linz, Austria (2010)Google Scholar
  18. 18.
    Järvisalo, M., Biere, A.: Reconstructing Solutions after Blocked Clause Elimination. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 340–345. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Nieuwenhuis, R., Oliveras, A.: On SAT Modulo Theories and Optimization Problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Larrosa, J., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: A framework for certified boolean branch-and-bound optimization. Journal of Automated Reasoning 46(1) (2011)Google Scholar
  22. 22.
    Andersson, G., Bjesse, P., Cook, B., Hanna, Z.: A proof engine approach to solving combinational design automation problems. In: Proc. DAC, pp. 725–730. ACM (2002)Google Scholar
  23. 23.
    Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Automation of Reasoning 2, pp. 466–483. Springer (1983)Google Scholar
  24. 24.
    Li, C.M.: Integrating equivalency reasoning into Davis-Putnam procedure. In: Proc. AAAI, pp. 291–296. AAAI Press (2000)Google Scholar
  25. 25.
    Beame, P., Kautz, H.A., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. J. Artif. Intell. Res. 22, 319–351 (2004)MathSciNetMATHGoogle Scholar
  26. 26.
    Audemard, G., Katsirelos, G., Simon, L.: A restriction of extended resolution for clause learning SAT solvers. In: Proc. AAAI. AAAI Press (2010)Google Scholar
  27. 27.
    Huang, J.: Extended clause learning. Artificial Intelligence 174(15), 1277–1284 (2010)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Han, H., Somenzi, F.: On-the-Fly Clause Improvement. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 209–222. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  29. 29.
    Hamadi, Y., Jabbour, S., Saïs, L.: Learning for dynamic subsumption. In: Proc. ICTAI, pp. 328–335. IEEE (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Matti Järvisalo
    • 1
  • Marijn J. H. Heule
    • 2
    • 3
  • Armin Biere
    • 3
  1. 1.Department of Computer Science & HIITUniversity of HelsinkiFinland
  2. 2.Department of Software TechnologyDelft University of TechnologyThe Netherlands
  3. 3.Institute for Formal Models and VerificationJohannes Kepler UniversityLinzAustria

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