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Rectangles Are Nonnegative Juntas

2015
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Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15
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We develop a new method to prove communication lower bounds for composed functions of the form f • g n , where f is any boolean function on n inputs and g is a sufficiently "hard" two-party gadget. Our main structure theorem states that each rectangle in the communication matrix of f •g n can be simulated by a nonnegative combination of juntas. This is a new formalization for the intuition that each low-communication randomized protocol can only "query" a few inputs of f as encoded by the

doi:10.1145/2746539.2746596
dblp:conf/stoc/GoosLM0Z15
fatcat:r4b2hvasyrdz5mtxwuwutisgye