From DNF compression to sunflower theorems via regularity
Combinatorics
2019-06-10 v2 Discrete Mathematics
Abstract
The sunflower conjecture is one of the most well-known open problems in combinatorics. It has several applications in theoretical computer science, one of which is DNF compression, due to Gopalan, Meka and Reingold [Computational Complexity 2013]. In this paper, we show that improved bounds for DNF compression imply improved bounds for the sunflower conjecture, which is the reverse direction of [Computational Complexity 2013]. The main approach is based on regularity of set systems and a structure-vs-pseudorandomness approach to the sunflower conjecture.
Keywords
Cite
@article{arxiv.1903.00580,
title = {From DNF compression to sunflower theorems via regularity},
author = {Shachar Lovett and Noam Solomon and Jiapeng Zhang},
journal= {arXiv preprint arXiv:1903.00580},
year = {2019}
}