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The study of seeded randomness extractors is a major line of research in theoretical computer science. The goal is to construct deterministic algorithms which can take a “weak” random source X with min-entropy k and a uniformly random seed Y of length d, and outputs a string of length close to k that is close to uniform and independent of Y.… (More)

Let f be a boolean function on n variables. Its associated XOR function is the two-party function F(x, y) = f(x xor y). We show that, up to polynomial factors, the deterministic communication complexity of F is equal to the parity decision tree complexity of f. This relies on a novel technique of entropy reduction for protocols, combined with existing… (More)

The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemeredi regularity lemma in graph theory. It shows that for any abelian group G and any bounded function f : G → [0, 1], there exists a subgroup H ≤ G of bounded index such that, when restricted to most cosets of H, the function f is pseudorandom in the sense that all… (More)

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