Improved Separations between Nondeterministic and Randomized Multiparty Communication

Authors:
Matei David;Toniann Pitassi;Emanuele Viola
Affiliations:
Department of Computer Science, University of Toronto,;Department of Computer Science, University of Toronto,;Computer Science Department, Columbia University,
Venue:
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Year:
2008

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Abstract

We exhibit an explicit function f: {0, 1}n茂戮驴{0,1} that can be computed by a nondeterministic number-on-forehead protocol communicating O(logn) bits, but that requires n茂戮驴(1)bits of communication for randomized number-on-forehead protocols with k= 茂戮驴·lognplayers, for any fixed 茂戮驴kn.We also show that for any k= Aloglognthe above function fis computable by a small circuit whose depth is constant whenever Ais a (possibly large) constant. Recent results again give such functions but only when the number of players is kn.