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.
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.