On the interplay between proof complexity and SAT solving

Abstract

This paper is intended as an informal and accessible survey of proof complexity for non-experts, focusing on some comparatively weak proof systems of particular interest in connection with SAT solving. We review resolution, polynomial calculus, and cutting planes (related to conflict-driven clause learning, Gröbner basis computations, and pseudo-Boolean solving, respectively) and some complexity measures that have been studied for these proof systems. We also discuss briefly to what extent proof complexity could provide insights into SAT solver performance, and how concerns related to applied SAT solving can give rise to interesting complexity-theoretic questions. Along the way, we highlight a number of current research challenges.