Improving Ppsz For 3-Sat Using Critical Variables

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)) by Rolf [10] to O(1.32153(n)). Using a different approach, Iwama et al. [5] 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)) [6] to O(1.46928(n)), where O(1.46981(n)) can be obtained using the methods of [6] and [10].