A Separation of NP and coNP in Multiparty Communication Complexity

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-ϵ)log(n) players, where ϵ>0 is any constant. Specifically, we construct a function F with co-nondeterministic complexity O(log(n)) and Merlin-Arthur complexity n^Ω(1). The problem was open for k > 2.