Fooling Pairs in Randomized Communication Complexity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)

Abstract

The fooling pairs method is one of the standard methods for proving lower bounds for deterministic two-player communication complexity. We study fooling pairs in the context of randomized communication complexity. We show that every fooling pair induces far away distributions on transcripts of private-coin protocols. We use the above to conclude that the private-coin randomized \(\varepsilon \)-error communication complexity of a function f with a fooling set \(\mathcal S\) is at least order \(\log \frac{\log |\mathcal S|}{\varepsilon }\). This relationship was earlier known to hold only for constant values of \(\varepsilon \). The bound we prove is tight, for example, for the equality and greater-than functions.

As an application, we exhibit the following dichotomy: for every boolean function f and integer n, the (1/3)-error public-coin randomized communication complexity of the function \(\bigvee _{i=1}^{n}f(x_i,y_i)\) is either at most c or at least n/c, where \(c>0\) is a universal constant.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Technion, Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of Computer Science and EngineeringUniversity of WashingtonSeattleUSA
  3. 3.Microsoft ResearchHerzliyaIsrael
  4. 4.Max Planck Institute for InformaticsSaarbrückenGermany

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