A Separation of NP and coNP in Multiparty Communication Complexity

: We prove that coNP MA in the number-on-forehead model of multiparty communication complexity for up to k = (1 - )logn players, where > 0 is any constant. Specifically, we construct an explicit function F : ({0,1}n)k {0,1} with conondeterministic complexity O(logn) and Merlin-Arthur complexity n(1). The problem was open for k 3. As a corollary, we obtain an explicit separation of NP and coNP for up to k = (1-)logn players, complementing an independent result by Beame et al. (2010) who separate these classes nonconstructively for up to k = 2(1-)n players.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Dmitry Gavinsky, Alexander A. Sherstov
• Keywords: Conp Ma, CORR 2010, Education, Multiparty Communication Complexity, Number-on-forehead Model