We prove that length-space trade-offs in resolution proofs can be optimized for length and space simultaneously, or whether there are trade-off between these two measures.Expand

We propose a new two-player communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be of independent interest.Expand

We present size-space trade-offs for the polynomial calculus (PC and PCR) proof systems, showing that size and space cannot be simultaneously optimized in these models.Expand

We show that if a formula requires large resolution width, then making XOR substitution yields a formula requiring large PCR space, providing some circumstantial evidence that degree might be a lower bound for space.Expand

We show that there are families of 6-CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Omega(n/log n).Expand

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, and some complexity measures that have been studied for these proof systems.Expand

This is an updated and strengthened full-length version of the paper with the same title that appeared in the Proceedings of the 30th Annual Computational Complexity Conference (CCC '15).Expand