Kaave Hosseini

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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 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 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)
Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type(More)
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