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An Improved Deterministic #SAT Algorithm for Small De Morgan Formulas

  • Ruiwen Chen
  • Valentine Kabanets
  • Nitin Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)

Abstract

We give a deterministic #SAT algorithm for de Morgan formulas of size up to n 2.63, which runs in time \(2^{n-n^{\Omega(1)}}\). This improves upon the deterministic #SAT algorithm of [3], which has similar running time but works only for formulas of size less than n 2.5.

Our new algorithm is based on the shrinkage of de Morgan formulas under random restrictions, shown by Paterson and Zwick [12]. We prove a concentrated and constructive version of their shrinkage result. Namely, we give a deterministic polynomial-time algorithm that selects variables in a given de Morgan formula so that, with high probability over the random assignments to the chosen variables, the original formula shrinks in size, when simplified using a deterministic polynomial-time formula-simplification algorithm.

Keywords

de Morgan formulas random restrictions shrinkage SAT algorithms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ruiwen Chen
    • 1
  • Valentine Kabanets
    • 1
  • Nitin Saurabh
    • 2
  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.Institute of Mathematical SciencesChennaiIndia

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