Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity
Computational Complexity
2026-05-12 v1
Abstract
We study the average-case hardness of establishing that a graph does not have a large clique in both proof and communication complexity. We show exponential lower bounds on the length of cutting planes and bounded-depth resolution over parities refutations of the binary encoding of clique formulas on randomly sampled dense graphs. Moreover, we show that the randomized communication complexity of finding a falsified clause in these formulas is polynomial.
Cite
@article{arxiv.2605.10941,
title = {Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity},
author = {Susanna F. de Rezende and David Engström and Yassine Ghannane and Duri Andrea Janett and Artur Riazanov},
journal= {arXiv preprint arXiv:2605.10941},
year = {2026}
}
Comments
Full version of a paper to appear at ICALP 2026