Connecting SAT Algorithms and Complexity Lower Bounds

Abstract

I will describe prior and current work on connecting the art of finding good satisfiability algorithms with the art of proving complexity lower bounds: proofs of limitations on what problems can be solved by good algorithms. Surprisingly, even minor algorithmic progress on solving the circuit satisfiability problem faster than exhaustive search can be applied to prove strong circuit complexity lower bounds. These connections have made it possible to prove new complexity lower bounds that had long been conjectured, and they suggest concrete directions for further progress.