Beyond Unit Propagation in SAT Solving

  • Michael Kaufmann
  • Stephan Kottler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


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.


Unit Propagation Extended Propagation Conjunctive Normal Form Variable Assignment Partial Assignment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    The international SAT competition (2002-2009),
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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. 5.
    Bacchus, F.: Exploring the computational tradeoff of more reasoning and less searching. In: SAT, pp. 7–16 (2002)Google Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    Beame, P., Kautz, H.A., Sabharwal, A.: Understanding the power of clause learning. IJCAI, 1194–1201 (2003)Google Scholar
  8. 8.
    Berre, D.L.: Exploiting the real power of unit propagation lookahead. Electronic Notes in Discrete Mathematics 9, 59–80 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Biere, A.: Precosat solver description (2009),
  10. 10.
    Biere, A.: Picosat essentials. JSAT 4, 75–97 (2008)zbMATHGoogle Scholar
  11. 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. 12.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications. IOS Press, Amsterdam (2009)zbMATHGoogle Scholar
  13. 13.
    Brafman, R.I.: A simplifier for propositional formulas with many binary clauses. IJCAI, 515–522 (2001)Google Scholar
  14. 14.
    Chu, G., Harwood, A., Stuckey, P.J.: Cache conscious data structures for boolean satisfiability solvers. JSAT 6, 99–120 (2009)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Cook, S.A.: The complexity of theorem-proving procedures. In: STOC (1971)Google Scholar
  16. 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. 17.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 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)CrossRefGoogle Scholar
  20. 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)CrossRefGoogle Scholar
  21. 21.
    Heule, M.: SmArT Solving. PhD thesis, Technische Universiteit Delft (2008)Google Scholar
  22. 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. 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. 24.
    Kottler, S.: Solver descriptions for the SAT competition 2009,
  25. 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)CrossRefGoogle Scholar
  26. 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)CrossRefGoogle Scholar
  27. 27.
    Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Principles and Practice of Constraint Programming (1997)Google Scholar
  28. 28.
    Marques-Silva, J.P.: Practical Applications of Boolean Satisfiability. In: Workshop on Discrete Event Systems, WODES 2008 (2008)Google Scholar
  29. 29.
    Marques-Silva, J.P., Sakallah, K.A.: Grasp: A search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)MathSciNetCrossRefGoogle Scholar
  30. 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. 31.
    Pipatsrisawat, K., Darwiche, A.: On modern clause-learning satisfiability solvers. J. Autom. Reasoning 44(3), 277–301 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 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. 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. 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. 35.
    Williams, R., Gomes, C., Selman, B.: Backdoors to typical case complexity. IJCAI (2003)Google Scholar
  36. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michael Kaufmann
    • 1
  • Stephan Kottler
    • 1
  1. 1.Wilhelm–Schickard–Institut für InformatikUniversity of TübingenGermany

Personalised recommendations