Investigating and Improving the PPSZ Algorithm for SAT Master Thesis

In this thesis, we give a self-contained analysis of the PPSZ algorithm [8], including the combination with Schöning’s algorithm [14] of Iwama and Tamaki [5] and the improvement of Rolf [13]. We also give new bounds for 3-SAT and 4-SAT using the following idea: A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. With a simple case distinction on the fraction of critical variables of a CNF formula, we improve the bound for 3-SAT from O(1.32216n) [13] to O(1.32153n). Using a different approach, Iwama et al. [4] very recently achieved a running time of O(1.32113n). Our method nicely combines with theirs, yielding an even faster algorithm with running time O(1.32065n). We also improve the bound for 4-SAT from O(1.47390n) [5] to O(1.46928n), where O(1.46981n) can be obtained using only the methods of [5] and [13]. This is very close to the bound for unique 4-SAT for PPSZ, O(1.46899n) [8].