Supercritical Tradeoffs for Monotone Circuits
Computational Complexity
2024-11-22 v1
Abstract
We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size-depth tradeoff result for monotone circuits in the so-called supercritical regime. Our proof is based on an analogous result in proof complexity: We introduce a new family of unsatisfiable 3-CNF formulas (called bracket formulas) that admit resolution refutations of quasipolynomial size while any refutation of polynomial depth requires exponential size.
Cite
@article{arxiv.2411.14268,
title = {Supercritical Tradeoffs for Monotone Circuits},
author = {Mika Göös and Gilbert Maystre and Kilian Risse and Dmitry Sokolov},
journal= {arXiv preprint arXiv:2411.14268},
year = {2024}
}