Exponential lower bounds for the PPSZ k-sat algorithm

In 1998, Paturi, Pudlák, Saks, and Zane presented PPSZ, an elegant randomized algorithm for k-SAT. Fourteen years on, this algorithm is still the fastest known worst-case algorithm. They proved that its expected running time on k-CNF formulas with n variables is at most 2(1−εk)n, where εk ε Ω(1/k). So far, no exponential lower bounds at all have been known. In this paper, we construct hard instances for PPSZ. That is, we construct satisfiable k-CNF formulas over n variables on which the expected running time is at least 2(1--εk)n, for εk ε O(log2 k/k).