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- Hamed Hatami, Kaave Hosseini, Shachar Lovett
- 2016 IEEE 57th Annual Symposium on Foundations of…
- 2016

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)

- Divesh Aggarwal, Kaave Hosseini, Shachar Lovett
- 2016 IEEE International Symposium on Information…
- 2015

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)

- Kaave Hosseini, Shachar Lovett
- J. Comb. Theory, Ser. A
- 2017

Let G be a finite abelian group and A a subset of G. The spectrum of A is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime |A| = |G| α whenever α ≤ c, where c ≥ 1/2 is some absolute constant. On the other hand, there are statistical results, which apply… (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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