Improving PPSZ for 3-SAT using Critical Variables

Timon Hertli, Robin A. Moser & Dominik Scheder
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...