Revision #1 Authors: Shay Moran, Makrand Sinha, Amir Yehudayoff

Accepted on: 5th May 2014 21:00

Downloads: 519

Keywords:

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.

Corrected some minor errors.

TR14-022 Authors: Shay Moran, Makrand Sinha, Amir Yehudayoff

Publication: 19th February 2014 03:57

Downloads: 1277

Keywords:

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.