Given two prime monotone boolean functions $f:\{0,1\}^n \to \{0,1\}$ and $g:\{0,1\}^n \to \{0,1\}$ the dualization problem consists in determining if $g$ is the dual of $f$, that is if $f(x_1, \dots, x_n)= \overline{g}(\overline{x_1}, \dots \overline{x_n})$ for all $(x_1, \dots x_n) \in \{0,1\}^n$. Associated to the dualization problem there is the corresponding decision problem: given two monotone prime boolean functions $f$ and $g$ is $g$ the dual of $f$? In this paper we present a quantum computing algorithm that solves the decision version of the dualization problem in polynomial time.

翻译：给定两个素单调布尔函数 $f:\{0,1\}^n \to \{0,1\}$ 和 $g:\{0,1\}^n \to \{0,1\}$，对偶化问题旨在判定 $g$ 是否为 $f$ 的对偶，即对于所有 $(x_1, \dots x_n) \in \{0,1\}^n$ 是否满足 $f(x_1, \dots, x_n)= \overline{g}(\overline{x_1}, \dots \overline{x_n})$。与该对偶化问题相关联的是相应的判定问题：给定两个素单调布尔函数 $f$ 和 $g$，$g$ 是否为 $f$ 的对偶？本文提出了一种量子计算算法，可在多项式时间内解决对偶化问题的判定版本。