A long line of work in the past two decades or so established close connections between
several different pseudorandom objects and applications, including seeded or seedless non …

Can we design efficient algorithms for finding fast algorithms? This question is captured by
various circuit minimization problems, and algorithms for the corresponding tasks have …

We consider the problem of solving systems of multivariate polynomial equations of degree
k over a finite field. For every integer k≤ 2 and finite field q where q= pd for a prime p, we …

We show a number of fine-grained hardness results for the Closest Vector Problem in the ℓp
norm (CVP p), and its approximate and non-uniform variants. First, we show that CVP p …

The Minimum Circuit Size Problem (MCSP) asks for the size of the smallest boolean circuit
that computes a given truth table. It is a prominent problem in NP that is believed to be hard …

In a recent work, Gryaznov, Pudl\'{a} k, and Talebanfard (CCC'22) introduced a stronger
version of affine extractors known as directional affine extractors, together with a …

We study a simple and general template for constructing affine extractors by composing a
linear transformation with resilient functions. Using this we show that good affine extractors …

We prove that for every parity decision tree of depth $ d $ on $ n $ variables, the sum of
absolute values of Fourier coefficients at level $\ell $ is at most $ d^{\ell/2}\cdot O …

We prove that random low-degree polynomials (over $\mathbb {F} _2 $) are unbiased, in an
extremely general sense. That is, we show that random low-degree polynomials are good …

Given a Boolean function f:{-1, 1}^{n}→{-1, 1, define the Fourier distribution to be the
distribution on subsets of [n], where each S⊆[n] is sampled with probability f ˆ (S) 2. The …