Nearly all k-SAT functions are unate

09/11/2022

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by   József Balogh, et al.

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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. 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 Turán problem on partially directed hypergraphs. In this paper we solve this Turán problem.