Worst-case randomized interactive communication

In the interactive communication model, two distant parties possess correlated inputs such as strings of bits, and the goal is for one party to learn his interlocutor's input while minimizing the communication. Our main contribution is to analyze the power of randomization in this correlated data setting. We show that the deterministic, amortized deterministic, private coin randomized, and public coin randomized models are all equivalent for a large class of problems arising from several practical applications. Furthermore, we conjecture that the private coin randomized model and the deterministic model are equivalent for every problem, and show that a proof of this statement solves the direct-sum problem for interactive communication