布尔多项式方程组的一个公式及其在计算复杂性中的应用
A formula for systems of Boolean polynomial equations and applications to computational complexity
摘要：
已知一种用于将布尔多项式方程组转换成具有较少变量的单个布尔多项式方程的方法。在本文中，我们给出了一个公式的布尔多项式方程组的基础上的方法。该公式具有二叉树结构，符合De Morgan对偶性。利用这个公式，我们证明了一个求解系统的含参数的计算复杂性结果。该参数是矩阵和图论中的带宽：准确地说，定义遵循矩阵中的惯例，值取决于变量的顺序。我们还将结果应用到NP完全问题，SAT和图列表着色，以表明这些问题是固定参数易处理的带宽。
英文摘要：
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.
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