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.
翻译:我们证明,对于任意固定的正整数 $k$ 且当 $n \to \infty$ 时,在所有 $n$ 个布尔变量上的 $k$-SAT 函数中,有 $1-o(1)$ 的比例是单边的(即:在反转某些变量后具有单调性)。这解决了 Bollobás、Brightwell 和 Leader 于 2003 年提出的一个猜想。