Average and randomized communication complexity

The communication complexity of a two-variable function f(x,y) is the number of information bits two communicators need to exchange to compute f when, initially, each knows only one of the variables. There are several communication-complexity measures corresponding to whether (1) the worst case or average number of bits is considered, (2) computation errors are allowed and (3) randomization is allowed. Tight bounds are provided for the typical behavior of all bounded-error communication-complexity measures of Boolean functions. In the present work, the authors formally define the deterministic model. They describe randomized protocols and compare them to deterministic ones. They both survey previous work and describe original results