Improving PPSZ for 3-SAT using Critical Variables

Authors Timon Hertli, Robin A. Moser, Dominik Scheder

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Timon Hertli
Robin A. Moser
Dominik Scheder

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Timon Hertli, Robin A. Moser, and Dominik Scheder. Improving PPSZ for 3-SAT using Critical Variables. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 237-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. Using a simple case distinction on the fraction of critical variables of a CNF formula, we improve the running time for 3-SAT from O(1.32216^n) [Rolf 2006] to O(1.32153^n). Using a different approach, Iwama et al. very recently achieved a running time of O(1.32113^n). Our method nicely combines with theirs, yielding the currently fastest known algorithm with running time O(1.32065^n). We also improve the bound for 4-SAT from O(1.47390^n) [Hofmeister et al. 2002] to O(1.46928^n), where O(1.46981^n) can be obtained using the methods of Hofmeister and Rolf.
  • SAT
  • satisfiability
  • randomized
  • exponential time
  • algorithm
  • 3-SAT
  • 4-SAT


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