Abstract

This paper contains several results regarding the communication complexity model and the 2-prover games model, which are based on interaction between the two models: 1. We show how to improve the rate of exponential decrease in the parallel repetition theorem of [Ra] in terms of the communication complexity of the verifier's predicate. 2. We apply the improved parallel repetition theorem of 2-prover games to derive, for the first time, a direct product theorem for communication complexity. The second derivation uses a common generalization of the two models, which is independently interesting. We initiate a study of its power by considering the GCD problem, and some variations of it, which exhibit a power gap between the new model and the classical communication complexity model. This gap is partly based on the following upper bounds: Given n-bit inputs x and y to Alice and Bob respectively, they can achieve the tasks below with very high probability using only O(n= log n) communica...

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