On the Efficiency of Solving Boolean Polynomial Systems with the Characteristic Set Method

TL;DR

This paper introduces an improved characteristic set algorithm for solving Boolean polynomial systems, utilizing zero decomposition, variable elimination, and optimized strategies to achieve better efficiency and complexity bounds.

Contribution

The paper presents a novel characteristic set algorithm with techniques that improve efficiency and lower complexity bounds compared to previous methods.

Findings

The new algorithm outperforms previous characteristic set algorithms in efficiency.

Complexity bounds of the proposed algorithm are lower than earlier bounds.

Experimental results confirm the improved performance of the algorithm.

Abstract

An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain pseudo-remainders. Three important techniques are applied in the algorithm. The first one is eliminating variables by new generated linear polynomials. The second one is optimizing the strategy of choosing polynomial for zero decomposition. The third one is to compute add-remainders to eliminate the leading variable of new generated monic polynomials. By analyzing the depth of the zero decomposition tree, we present some complexity bounds of this algorithm, which are lower than the complexity bounds of previous characteristic set algorithms. Extensive experimental results show that this new algorithm is more efficient than previous characteristic set algorithms for solving Boolean polynomial systems.