Algorithmic Polynomial Freiman-Ruzsa Theorems

Fuente: arXiv
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Main Authors: Arunachalam, Srinivasan, Castro-Silva, Davi, Dutt, Arkopal, Gur, Tom
Format: Preprint
Published: 2025
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author Arunachalam, Srinivasan
Castro-Silva, Davi
Dutt, Arkopal
Gur, Tom
author_facet Arunachalam, Srinivasan
Castro-Silva, Davi
Dutt, Arkopal
Gur, Tom
contents We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for $A \subseteq \mathbb{F}_2^n$ with doubling constant $K$, learn an explicit description of a subspace $V \subseteq \mathbb{F}_2^n$ of size $|V| \leq |A|$ such that $A$ can be covered by $K^C$ translates of $V$, for a universal constant $C>1$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_02338
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Algorithmic Polynomial Freiman-Ruzsa Theorems
Arunachalam, Srinivasan
Castro-Silva, Davi
Dutt, Arkopal
Gur, Tom
Combinatorics
We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for $A \subseteq \mathbb{F}_2^n$ with doubling constant $K$, learn an explicit description of a subspace $V \subseteq \mathbb{F}_2^n$ of size $|V| \leq |A|$ such that $A$ can be covered by $K^C$ translates of $V$, for a universal constant $C>1$.
title Algorithmic Polynomial Freiman-Ruzsa Theorems
topic Combinatorics
url https://arxiv.org/abs/2509.02338