We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map f: F qr→ F qn to an element …
We consider the problem of extracting randomness from sumset sources, a general class of weak sources introduced by Chattopadhyay and Li (STOC, 2016). An (n, k, C)-sumset …
The area of randomness extraction has seen interesting advances in recent years, with rapid progress on many longstanding open problems, along with the introduction of many new …
X Li, Y Zhong - arXiv preprint arXiv:2304.11495, 2023 - arxiv.org
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 …
X Huang, P Ivanov, E Viola - Approximation, Randomization, and …, 2022 - drops.dagstuhl.de
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 …
A Chor–Goldreich (CG) source is a sequence of random variables X= X 1∘…∘ X t, where each X i∼{0, 1} d and X i has δ d min-entropy conditioned on any fixing of X 1∘…∘ X i− 1 …
We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by …
In a recent work, Gryaznov, Pudlák and Talebanfard (CCC'22) introduced a linear variant of read-once branching programs, with motivations from circuit and proof complexity. Such a …
We explicitly construct the first nontrivial extractors for degree d≥ 2 polynomial sources over 𝔽₂. Our extractor requires min-entropy k≥ n-(√{log n})/((log log n/d)^{d/2}). Previously, no …