This chapter gives an overview of proof complexity and connections to SAT solving, focusing
on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes …

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 …

This note, based on my 4ECM lecture, exposes few basic points of proof complexity in a way
accessible to any mathematician. In many parts of mathematics one finds statements …

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in
width w but require resolution proofs of size n Ω (w). This shows that the simple counting …

We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to
monotone span program size by Pitassi and Robere (2018) so that it works for any gadget …

We show quadratic lower bounds on the total space used in resolution refutations of random
k-CNFs over n variables and of the graph pigeonhole principle and the bit pigeonhole …

We study space complexity and time-space trade-offs with a focus not on peak memory
usage but on overall memory consumption throughout the computation. Such a cumulative …

We investigate the space complexity of refuting 3-CNFs in Resolution and algebraic
systems. We prove that every Polynomial Calculus with Resolution refutation of a random 3 …

Given an unsatisfiable k-CNF formula phi we consider two complexity measures in
Resolution: width and total space. The width is the minimal W such that there exists a …

We show that if a k-CNF requires width w to refute in resolution, then it requires space
square root of√ ω to refute in polynomial calculus, where the space of a polynomial calculus …