Nearly All k-SAT Functions Are Unate

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

doi:10.1145/3564246.3585123

STOC2023Top-tier venue

Nearly All k-SAT Functions Are Unate

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

arXiv DOI Publisher

2023Year

4Citations

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 → ∞. This resolves a conjecture by Bollobás, Brightwell, and Leader from 2003.

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