Nearly all $k$-SAT functions are unate

József Balogh; Dingding Dong; Bernard Lidický; Nitya Mani; Yufei Zhao

Nearly all $k$-SAT functions are unate

Combinatorics 2023-10-04 v2 Computational Complexity

Authors: József Balogh , Dingding Dong , Bernard Lidický , Nitya Mani , Yufei Zhao

Abstract

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 $k$ and as $n \to \infty$ . This resolves a conjecture by Bollob\'as, Brightwell, and Leader from 2003.

Keywords

monotone functions function theory

Cite

@article{arxiv.2209.04894,
  title  = {Nearly all $k$-SAT functions are unate},
  author = {József Balogh and Dingding Dong and Bernard Lidický and Nitya Mani and Yufei Zhao},
  journal= {arXiv preprint arXiv:2209.04894},
  year   = {2023}
}

Comments

43 pages. v2 merges arXiv:2107.09233 (SODA22) and arXiv:2209.04894v1 (STOC23) along with expository improvements. This combined version is intended for journal submission

Nearly all $k$-SAT functions are unate

Abstract

Keywords

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