Between SAT and UNSAT: The Fundamental Difference in CDCL SAT

  • Chanseok OhEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9340)


The way CDCL SAT solvers find a satisfying assignment is very different from the way they prove unsatisfiability. We propose an explanation to the difference by identifying direct connections to the workings of some of the most important elements in CDCL solvers: the effects of restarts and VSIDS, and the roles of learned clauses. We give a wide range of concrete evidence that highlights the varying effects and roles of these elements. As a result, this paper also sheds a new light on the internal workings of CDCL. Based on our reasoning on the difference in solver behaviors, we present several ideas for optimizing SAT solvers for either SAT or UNSAT instances. We then show that we can achieve improvements on both SAT and UNSAT at the same time by judiciously exploiting the difference. We have implemented a hybrid idea mixing two different restart strategies on top of our new solver COMiniSatPS and observed substantial performance improvement.


Satisfying Assignment Decay Factor Preimage Attack Search Space Exploration Clause Database 
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.
    Aigner, M., Biere, A., Kirsch, C.M., Niemetz, A., Preiner, M.: Analysis of portfolio-style parallel SAT solving on current multi-core architectures. In: POS (2013)Google Scholar
  2. 2.
    Alfonso, E.M., Manthey, N.: Riss 4.27 BlackBox. In: SAT-COMP (2014)Google Scholar
  3. 3.
    Audemard, G., Lagniez, J.-M., Mazure, B., Saïs, L.: On freezing and reactivating learnt clauses. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 188–200. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  4. 4.
    Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: IJCAI (2009)Google Scholar
  5. 5.
    Audemard, G., Simon, L.: Glucose 2.1: aggressive but reactive clause database management, dynamic restarts. In: POS (2012)Google Scholar
  6. 6.
    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) CrossRefGoogle Scholar
  7. 7.
    Biere, A.: Adaptive restart strategies for conflict driven SAT solvers. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 28–33. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  8. 8.
    Biere, A.: Lingeling, plingeling and treengeling entering the SAT competition 2013. In: SAT-COMP (2013)Google Scholar
  9. 9.
    Biere, A.: Yet another local search solver and lingeling and friends entering the SAT competition 2014. In: SAT-COMP (2014)Google Scholar
  10. 10.
    Chen, J.: Solvers with a bit-encoding phase selection policy and a decision-depth-sensitive restart policy. In: SAT-COMP (2013)Google Scholar
  11. 11.
    Chen, J.: Minisat\(\_\)blbd. In: SAT-COMP (2014)Google Scholar
  12. 12.
    Dubois, O., Andre, P., Boufkhad, Y., Carlier, J.: SAT versus UNSAT. In: DIMACS Cliques, Coloring and Satisfiability (1996)Google Scholar
  13. 13.
    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
  14. 14.
    Gelder, A.V.: Contrasat - A contrarian SAT solver. JSAT (2012)Google Scholar
  15. 15.
    Gomes, C.P., Selman, B., Crato, N., Kautz, H.A.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. Autom. Reasoning (2000)Google Scholar
  16. 16.
    van der Grinten, A., Wotzlaw, A., Speckenmeyer, E., Porschen, S.: SATUZK: solver description. In: SAT-COMP (2013)Google Scholar
  17. 17.
    Haim, S., Heule, M.: Towards ultra rapid restarts. CoRR (2014)Google Scholar
  18. 18.
    Haken, A.: The intractability of resolution. Theor. Comput. Sci. (1985)Google Scholar
  19. 19.
    Huang, J.: The effect of restarts on the efficiency of clause learning. In: IJCAI (2007)Google Scholar
  20. 20.
    Hutter, F., Lindauer, M., Balint, A., Bayless, S., Hoos, H., Leyton-Brown, K.: The Configurable SAT Solver Challenge (CSSC). Under review at AIJ; preprint available on arXiv: (2015).
  21. 21.
    Jabbour, S., Lonlac, J., Sais, L., Salhi, Y.: Revisiting the learned clauses database reduction strategies. CoRR (2014)Google Scholar
  22. 22.
    Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of las vegas algorithms. Inf. Process. Lett. (1993)Google Scholar
  23. 23.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: DAC (2001)Google Scholar
  24. 24.
    Nossum, V.: SAT-based preimage attacks on SHA-1. Master’s thesis, University of Oslo (2012)Google Scholar
  25. 25.
    Oh, C.: MiniSat\(\_\)HACK\(\_\)999ED, MiniSat\(\_\)HACK\(\_\)1430ED, and SWDiA5BY. In: SAT-COMP (2014)Google Scholar
  26. 26.
    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
  27. 27.
    Pipatsrisawat, K., Darwiche, A.: On the power of clause-learning SAT solvers as resolution engines. Artif. Intell. (2011)Google Scholar
  28. 28.
    Ryvchin, V., Strichman, O.: Local restarts. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 271–276. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  29. 29.
    Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers (1999)Google Scholar
  30. 30.
    Simon, L.: Post mortem analysis of SAT solver proofs. In: POS (2014)Google Scholar
  31. 31.
    Sonobe, T., Inaba, M.: Counter implication restart for parallel SAT solvers. In: Hamadi, Y., Schoenauer, M. (eds.) LION 2012. LNCS, vol. 7219, pp. 485–490. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  32. 32.
    Yasumoto, T.: SINN. In: SC (2012)Google Scholar
  33. 33.
    Yasumoto, T.: TENN. In: SC (2012)Google Scholar
  34. 34.
    Yasumoto, T.: ZENN. In: SC (2012)Google Scholar
  35. 35.
    Yasumoto, T., Okugawa, T.: SINNminisat. In: SAT-COMP (2013)Google Scholar
  36. 36.
    Yasumoto, T., Okugawa, T.: ROKK. In: SAT-COMP (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.New York UniversityNew YorkUSA

Personalised recommendations