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Revision #1 to TR14-022 | 5th May 2014 20:59

Fooling Pairs in Randomized Communication Complexity

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Revision #1
Authors: Shay Moran, Makrand Sinha, Amir Yehudayoff
Accepted on: 5th May 2014 21:00
Downloads: 519
Keywords: 


Abstract:

Fooling pairs are 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 then 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 is tight, for example, for the equality and greater-than functions.



Changes to previous version:

Corrected some minor errors.


Paper:

TR14-022 | 19th February 2014 00:18

Fooling Pairs in Randomized Communication Complexity


Abstract:

Fooling pairs are 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 then 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 is tight, for example, for the equality and greater-than functions.



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