Abstract
We exhibit an explicit function f : {0, 1}n →{0, 1} that can be computed by a nondeterministic number-on-forehead protocol communicating O(logn) bits, but that requires nΩ(1) bits of communication for randomized number-on-forehead protocols with k = δ·logn players, for any fixed δ < 1. Recent breakthrough results for the Set-Disjointness function [Lee and Shraibman 2008; Chattopadhyay and Ada 2008] based on the work of Sherstov [2009; 2008a] imply such a separation but only when the number of players is k < loglogn.
We also show that for any k = A ·loglogn the above function f is computable by a small circuit whose depth is constant whenever A is a (possibly large) constant. Recent results again give such functions but only when the number of players is k < loglogn.
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Index Terms
Improved Separations between Nondeterministic and Randomized Multiparty Communication
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