Chapter

Theory and Applications of Satisfiability Testing – SAT 2010

Volume 6175 of the series Lecture Notes in Computer Science pp 99-112

Non Uniform Selection of Solutions for Upper Bounding the 3-SAT Threshold

  • Yacine BoufkhadAffiliated withLIAFA, Université Denis Diderot Paris 7 - CNRS
  • , Thomas HugelAffiliated withLIAFA, Université Denis Diderot Paris 7 - CNRS

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Abstract

We give a new insight into the upper bounding of the 3-SAT threshold by the first moment method. The best criteria developed so far to select the solutions to be counted discriminate among neighboring solutions on the basis of uniform information about each individual free variable. What we mean by uniform information, is information which does not depend on the solution: e.g. the number of positive/negative occurrences of the considered variable. What is new in our approach is that we use non uniform information about variables. Thus we are able to make a more precise tuning, resulting in a slight improvement on upper bounding the 3-SAT threshold for various models of formulas defined by their distributions.