Dmytro Gavinsky, Alexander A. Sherstov

We prove that NP$\ne$coNP and coNP$\nsubseteq$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 $F:(\zoon)^k\to\zoo$ with co-nondeterministic

complexity $O(\log n)$ and Merlin-Arthur

complexity $n^{\Omega(1)}$.

The problem was open for $k\geq3$.