Nearly All k-SAT Functions Are Unate

被引：0

作者：

Balogh, Jozsef ^{[1
]}

Dong, Dingding ^{[2
]}

Lidicky, Bernard ^{[3
]}

Mani, Nitya ^{[4
]}

Zhao, Yufei ^{[4
]}

机构：

[1] Univ Illinois, Champaign, IL 61820 USA

[2] Harvard Univ, Cambridge, MA USA

[3] Iowa State Univ, Ames, IA USA

[4] MIT, Cambridge, MA USA

来源：

PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023 | 2023年

基金：

美国国家科学基金会;

关键词：

k-SAT function; sum of squares; hypergraph container method; Turan problems; NUMBER;

D O I：

10.1145/3564246.3585123

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that 1 - o (1) fraction of all k-SAT functions on n Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer : and as n -> infinity. This resolves a conjecture by Bollobas, Brightwell, and Leader from 2003. This paper is the second half of a two-part work solving the problem. The first part, by Dong, Mani, and Zhao, reduces the conjecture to a Turan problem on partially directed hypergraphs. In this paper we solve this Turan problem.

引用

页码：958 / 962

页数：5

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