Improving PPSZ for $3$-SAT using Critical Variables

Timon Hertli (1) , Robin Moser (1) , Dominik Scheder (1)

1 Institute for Theoretical Computer Science

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.

Mots clés: SAT; satisfiability; randomized; exponential time; algorithm; 3-SAT; 4-SAT

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Timon Hertli, Robin Moser, Dominik Scheder. Improving PPSZ for $3$-SAT using Critical Variables. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.237-248. ⟨hal-00573628⟩