NDLI: Improved Separations between Nondeterministic and Randomized Multiparty Communication

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Improved Separations between Nondeterministic and Randomized Multiparty Communication

Content Provider	ACM Digital Library
Author	Viola, Emanuele Pitassi, Toniann David, Matei
Copyright Year	2009
Abstract	We exhibit an explicit function $\textit{f}$ : {0, $1}^{n}$ →{0, 1} that can be computed by a nondeterministic number-on-forehead protocol communicating $\textit{O}(log\textit{n})$ bits, but that requires $n^{Ω(1)}$ bits of communication for randomized number-on-forehead protocols with $\textit{k} = \textit{Δ}·log\textit{n}$ players, for any fixed $\textit{Δ} < 1.$ 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 $\textit{k} < loglog\textit{n}.$ We also show that for any $\textit{k} = \textit{A}$ $·loglog\textit{n}$ the above function $\textit{f}$ is computable by a small circuit whose depth is constant whenever $\textit{A}$ is a (possibly large) constant. Recent results again give such functions but only when the number of players is $\textit{k} < loglog\textit{n}.$
Starting Page	1
Ending Page	20
Page Count	20
File Format	PDF
ISSN	19423454
e-ISSN	19423462
DOI	10.1145/1595391.1595392
Volume Number	1
Issue Number	2
Journal	ACM Transactions on Computation Theory (TOCT)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2009-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Communication complexity Lower bound Nondeterminism Number on forehead Randomization
Content Type	Text
Resource Type	Article
Subject	Computational Theory and Mathematics Theoretical Computer Science

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