A Separation of NP and coNP in Multiparty Communication Complexity
Computational Complexity
2022-03-29 v1
Abstract
We prove that NP differs from coNP and coNP is not a subset of MA in the number-on-forehead model of multiparty communication complexity for up to k = (1-\epsilon)log(n) players, where \epsilon>0 is any constant. Specifically, we construct a function F with co-nondeterministic complexity O(log(n)) and Merlin-Arthur complexity n^{\Omega(1)}. The problem was open for k > 2.
Cite
@article{arxiv.1004.0817,
title = {A Separation of NP and coNP in Multiparty Communication Complexity},
author = {Dmytro Gavinsky and Alexander A. Sherstov},
journal= {arXiv preprint arXiv:1004.0817},
year = {2022}
}