Direct Products in Communication Complexity

摘要

We give exponentially small upper bounds on the success probability for computing the direct product of any function over any distribution using a communication protocol. Let suc(μ, f, C) denote the maximum success probability of a 2-party communication protocol for computing the boolean function f(x, sy) with C bits of communication, when the inputs (x, y) are drawn from the distribution μ. Let μn be the product distribution on n inputs and fn denote the function that computes n copies of f on these inputs. We prove that if T log3/2 T