Algorithmic Polynomial Freiman-Ruzsa Theorems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914017370439680 |
|---|---|
| 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 |