A polynomial quantum computing algorithm for solving the dualization problem

TL;DR

This paper introduces a polynomial-time quantum algorithm for solving the decision problem of dualization of prime monotone boolean functions, improving computational efficiency in this domain.

Contribution

The paper presents the first polynomial-time quantum algorithm specifically designed for the dualization decision problem involving prime monotone boolean functions.

Findings

Quantum algorithm solves the dualization decision problem in polynomial time

Significantly improves classical computational complexity for this problem

Advances quantum approaches in boolean function analysis

Abstract

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.