Communication vs. computation

We initiate a study of tradeoffs between communication and computation in well-known communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of communication and the amount of time needed for local computation? Under various standard assumptions, we exhibit boolean functions that show strong tradeoffs in the following computation models: (1) two-party randomized communication complexity; (2) query complexity; (3) property testing. For the model of deterministic communication complexity, we show a similar result relative to a random oracle. Finally, we study a time-degree tradeoff problem that arises in arithmetization of boolean functions, and relate it to time-communication tradeoff questions in multi-party communication complexity and in cryptography