Simpler Partial Derandomization of PPSZ for $k$-SAT

Abstract

We give a simpler derandomization of the best known $k$-SAT algorithm PPSZ [FOCS'97, JACM'05] for $k$-SAT with \emph{sub-exponential} number of solutions. The existing derandomization uses a complicated construction of small sample space, while we only use \emph{hashing}. Our algorithm and theorem also have a nice byproduct: It outperforms the current fastest deterministic $k$-SAT algorithm when the formula has \emph{moderately exponential} number of solutions.