期刊名称：Current Journal of Applied Science and Technology
印刷版ISSN：2457-1024
出版年度：2018
卷号：27
期号：3
页码：1-16
DOI：10.9734/CJAST/2018/41481
语种：English
出版社：Sciencedomain International
摘要：This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one. The paper outlines classical and novel direct methods for deriving the general parametric solution of such a system and for listing all its particular solutions. A detailed example over B256 is used to illustrate these two methods as well as a third method that starts by deriving the subsumptive solution first. The example demonstrates how the consistency condition forces a collapse of the underlying Boolean algebra to a subalgebra, and also how to list a huge number of particular solutions in a very compact space. Subsequently, the paper proposes some potential applications for the techniques of Boolean-equation solving. These techniques are very promising as useful extensions of classical techniques based on two-valued Boolean algebra.
关键词：Big Boolean algebra;parametric solution;listing of particular solutions;digital design;direct and inverse arithmetic;integer factorization;Diophantine equations
