A Separation of NP and coNP in Multiparty Communication Complexity

TL;DR

This paper demonstrates a separation between NP and coNP in the multiparty communication complexity model, showing that NP is not equal to coNP for up to nearly log(n) players, using a new constructed function.

Contribution

It establishes the first separation of NP and coNP in the number-on-forehead model for more than two players, advancing understanding of complexity class distinctions in this setting.

Findings

NP differs from coNP in multiparty communication complexity

Constructed a function with low co-nondeterministic complexity and high Merlin-Arthur complexity

Proved the separation for up to (1-ε)log(n) players

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.