Clause Shortening Combined with Pruning Yields a New Upper Bound for Deterministic SAT Algorithms

  • Evgeny Dantsin
  • Edward A. Hirsch
  • Alexander Wolpert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


We give a deterministic algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its upper bound on the worst-case running time matches the best known upper bound for randomized satisfiability-testing algorithms [6]. In comparison with the randomized algorithm in [6], our deterministic algorithm is simpler and more intuitive.


Steklov Institute Conjunctive Normal Form Deterministic Algorithm Boolean Formula Satisfying 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.
    Bollobás, B.: Random Graphs, 2nd edn. Cambridge University Press, Cambridge (2001)MATHGoogle Scholar
  2. 2.
    Brueggemann, T., Kern, W.: An improved local search algorithm for 3-SAT. Theoretical Computer Science 329(1-3), 303–313 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dantsin, E., Goerdt, A., Hirsch, E.A., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic (2 − 2/(k + 1))n algorithm for k-SAT based on local search. Theoretical Computer Science 289(1), 69–83 (2002)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dantsin, E., Hirsch, E.A., Wolpert, A.: Algorithms for SAT based on search in Hamming balls. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 141–151. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Dantsin, E., Wolpert, A.: Derandomization of Schuler’s algorithm for SAT. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 80–88. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Dantsin, E., Wolpert, A.: A faster clause-shortening algorithm for SAT with no restriction on clause length. Journal on Satisfiability, Boolean Modeling and Computation 1, 49–60 (2005)Google Scholar
  7. 7.
    Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, January 2004, p. 328 (2004)Google Scholar
  8. 8.
    Paturi, R., Pudlák, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. In: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1998, pp. 628–637 (1998)Google Scholar
  9. 9.
    Paturi, R., Pudlák, P., Zane, F.: Satisfiability coding lemma. In: Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1997, pp. 566–574 (1997)Google Scholar
  10. 10.
    Pudlák, P.: Satisfiability – algorithms and logic. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 129–141. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, FOCS 1999, pp. 410–414 (1999)Google Scholar
  12. 12.
    Schuler, R.: An algorithm for the satisfiability problem of formulas in conjunctive normal form. Journal of Algorithms 54(1), 40–44 (2003), A preliminary version appeared as a technical report in 2003Google Scholar
  13. 13.
    Stanley, R.P.: Enumerative Combinatorics, vol. 1. Wadsworth & Brooks/Cole (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Evgeny Dantsin
    • 1
  • Edward A. Hirsch
    • 2
  • Alexander Wolpert
    • 1
  1. 1.Roosevelt UniversityChicagoUSA
  2. 2.Steklov Institute of MathematicsPetersburgRussia

Personalised recommendations