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Electronic Colloquium on Computational Complexity

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Reports tagged with Affine extractors:
TR10-144 | 20th September 2010
Eli Ben-Sasson, Noga Ron-Zewi

From Affine to Two-Source Extractors via Approximate Duality

Revisions: 1

Two-source and affine extractors and dispersers are fundamental objects studied in the context of derandomization. This paper shows how to construct two-source extractors and dispersers for arbitrarily small min-entropy rate in a black-box manner from affine extractors with sufficiently good parameters. Our analysis relies on the study of approximate duality, ... more >>>

TR11-129 | 22nd September 2011
Eli Ben-Sasson, Ariel Gabizon

Extractors for Polynomials Sources over Constant-Size Fields of Small Characteristic

Let $F$ be the field of $q$ elements, where $q=p^{\ell}$ for prime $p$. Informally speaking, a polynomial source is a distribution over $F^n$ sampled by low degree multivariate polynomials. In this paper, we construct extractors for polynomial sources over fields of constant size $q$ assuming $p \ll q$.

More generally, ... more >>>

TR11-139 | 26th October 2011
Zeev Dvir, Shachar Lovett

Subspace Evasive Sets

In this work we describe an explicit, simple, construction of large subsets of F^n, where F is a finite field, that have small intersection with every k-dimensional affine subspace. Interest in the explicit construction of such sets, termed subspace-evasive sets, started in the work of Pudlak and Rodl (2004) ... more >>>

TR13-145 | 20th October 2013
Gil Cohen, Avishay Tal

Two Structural Results for Low Degree Polynomials and Applications

Revisions: 1

In this paper, two structural results concerning low degree polynomials over the field $\mathbb{F}_2$ are given. The first states that for any degree d polynomial f in n variables, there exists a subspace of $\mathbb{F}_2^n$ with dimension $\Omega(n^{1/(d-1)})$ on which f is constant. This result is shown to be tight. ... more >>>

TR14-099 | 7th August 2014
Gil Cohen, Igor Shinkar

The Complexity of DNF of Parities

We study depth 3 circuits of the form $\mathrm{OR} \circ \mathrm{AND} \circ \mathrm{XOR}$, or equivalently -- DNF of parities. This model was first explicitly studied by Jukna (CPC'06) who obtained a $2^{\Omega(n)}$ lower bound for explicit functions. Several related models have gained attention in the last few years, such as ... more >>>

TR21-075 | 4th June 2021
Eshan Chattopadhyay, Jesse Goodman, Jyun-Jie Liao

Affine Extractors for Almost Logarithmic Entropy

We give an explicit construction of an affine extractor (over $\mathbb{F}_2$) that works for affine sources on $n$ bits with min-entropy $k \ge~ \log n \cdot (\log \log n)^{1 + o(1)}$. This improves prior work of Li (FOCS'16) that requires min-entropy at least $\mathrm{poly}(\log n)$.

Our construction is ... more >>>

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