We prove conditional near-quadratic running time lower bounds for approximate
Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically …

The focus of this survey is the question of quantified derandomization, which was introduced
by Goldreich and Wigderson [44]: Does derandomization of probabilistic algorithms become …

We revisit the problem of constructing explicit pseudorandom generators that fool with error
ϵ degree-d polynomials in n variables over the field F q, in the case of large q. Previous …

Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness Page 1
Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness Markus …

This work studies the question of quantified derandomization, which was introduced by
Goldreich and Wigderson (STOC 2014). The generic quantified derandomization problem is …

We introduce the problem of constructing explicit variety evasive subspace families. Given a
family F of subvarieties of a projective or affine space, a collection H of projective or affine k …

We construct explicit pseudorandom generators that fool $ n $-variate polynomials of degree
at most $ d $ over a finite field $\mathbb {F} _q $. The seed length of our generators is $ O …

We give a length-efficient puncturing of Reed-Muller codes which preserves its distance
properties. Formally, for the Reed-Muller code encoding n-variate degree-d polynomials …

The Reed-Muller (RM) code, encoding n-variate degree-d polynomials over F q for d<; q,
with its evaluation on F qn, has a relative distance 1-d/q and can be list decoded from a 1-O …

The problem of constructing pseudorandom generators for polynomials of low degree is
fundamental in complexity theory and has numerous well-known applications. We study the …