Advertisement

Automated Generation of Simplification Rules for SAT and MAXSAT

  • Alexander S. Kulikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)

Abstract

Currently best known upper bounds for many NP-hard problems are obtained by using divide-and-conquer (splitting) algorithms. Roughly speaking, there are two ways of splitting algorithm improvement: a more involved case analysis and an introduction of a new simplification rule. It is clear that case analysis can be executed by computer, so it was considered as a machine task. Recently, several programs for automated case analysis were implemented. However, designing a new simplification rule is usually considered as a human task. In this paper we show that designing simplification rules can also be automated. We present several new (previously unknown) automatically generated simplification rules for the SAT and MAXSAT problems. The new approach allows not only to generate simplification rules, but also to find good splittings. To illustrate our technique we present a new algorithm for (n,3)-MAXSAT that uses both splittings and simplification rules based on our approach and has worst-case running time O(1.2721 N L), where N is the number of variables and L is the length of an input formula. This bound improves the previously known bound O(1.3248 N L) of Bansal and Raman.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bansal, N., Raman, V.: Upper bounds for MaxSat: Further improved. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 247–258. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Byskov, J.M., Madsen, B.A., Skjernaa, B.: New algorithms for exact satisfiability. Technical Report RS-03-30, BRICS (2003)Google Scholar
  3. 3.
    Chen, J., Kanj, I.: Improved exact algorithms for MAX-SAT. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 341–355. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Fedin, S.S., Kulikov, A.S.: A 2|E|/4-time algorithm for MAX-CUT. Zapiski nauchnykh seminarov POMI 293, 129–138 (2002)Google Scholar
  5. 5.
    Fedin, S.S., Kulikov, A.S.: Automated proofs of upper bounds on the running time of splitting algorithms. Zapiski nauchnykh seminarov POMI 316, 111–128 (2004)zbMATHGoogle Scholar
  6. 6.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hirsch, E.A.: New worst-case upper bounds for SAT. Journal of Automated Reasoning 24(4), 397–420 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Nikolenko, S.I., Sirotkin, A.V.: Worst-case upper bounds for sat: automated proof. In: Proceedings of the 8th ESSLLI Student Session, pp. 225–232 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alexander S. Kulikov
    • 1
  1. 1.Department of Mathematics and MechanicsSt.Petersburg State UniversitySt.PetersburgRussia

Personalised recommendations