Considerable effort has been devoted to the development of streaming algorithms for analyzing massive graphs. Unfortunately, many results have been negative, establishing that a wide variety of problems require $\Omega(n^2)$ space to solve. One of the few bright spots has been the development of semi-streaming algorithms for a handful of ... more >>>

Shpilka and Wigderson (CCC 1999) had posed the problem of proving exponential lower bounds for (nonhomogeneous) depth three arithmetic circuits with bounded bottom fanin over a field $\mathbb{F}$ of characteristic zero. We resolve this problem by proving a $N^{\Omega(\frac{d}{\tau})}$ lower bound for (nonhomogeneous) depth three arithmetic circuits with bottom fanin ... more >>>

We prove that the Fourier dimension of any Boolean function with
Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof
method yields an improved bound of $\widetilde{O}(\sqrt{s})$
assuming a conjecture of Tsang~\etal~\cite{tsang}, that for every
Boolean function of sparsity $s$ there is an affine subspace of
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