Improving PPSZ for 3-SAT using Critical Variables

Understand

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 [2006] to O(1.32153^n).
• Using a different approach, Iwama et al.
• [2010] very recently achieved a running time of O(1.32113^n).