A formula for systems of Boolean polynomial equations and applications to computational complexity
Abstract
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the method. The formula has a structure of binary tree, and conforms to De Morgan's duality. Using the formula, we prove a computational complexity result with a parameter for solving systems. The parameter is the bandwidth in matrix and graph theories: to be precise, the definition follows convention in matrix and the value depends on the order of variables. We also apply the result to the NP-complete problems, SAT and graph list-coloring, to show that these problems are fixed parameter tractable by bandwidth.
Cite
@article{arxiv.1907.09686,
title = {A formula for systems of Boolean polynomial equations and applications to computational complexity},
author = {Tomoya Machide},
journal= {arXiv preprint arXiv:1907.09686},
year = {2021}
}
Comments
Ver4: The contents involving rank is removed, but those involving bandwidth (or width in old versions) is improved. An application to graph list-coloring is added