Lower Bounds for One-way Probabilistic Communication Complexity

We prove three diierent types of complexity lower bounds for the one-way unbounded-error and bounded-error error probabilistic communication protocols for boolean functions. The lower bounds are proved in terms of the deterministic communication complexity of functions and in terms of the notion \probabilistic communication characteristic" that we deene. We present boolean functions with the diierent probabilistic communication characteristics which demonstrates that each of these lower bounds can be more precise than the others depending on the probabilistic communication characteristics of a function. Our lower bounds are good enough for proving proper hierarchy for one-way probabilistic communication complexity classes depends on a measure of bounded error. As the application of lower bounds for probabilistic communication complexity we prove two diierent types of complexity lower bounds for the one-way bounded-error error probabilistic space complexity. Our lower bounds are good enough for proving proper hierarchies for diierent one-way probabilis-tic space communication complexity classes inside SPACE(n) (namely for bounded error probabilistic computation, and for errors of probabilistic computation).