Solution of Boolean equations via atomic decomposition into independent switching equations. Issue 3 (2nd October 2019)

• Record Type: Journal Article
• Authors: Balamesh, Ahmed Said; Rushdi, Ali Muhammad
• Is Part Of: International journal of computer mathematics. Volume 4:Issue 3/4(2019)
• Page Start: 185
• Page End: 203
• Publication Date: 2019-10-02
• Subjects: Big Boolean algebra -- atomic decomposition -- Boolean and switching equations -- particular solutions -- permutative additive form; 03E35 -- 03G05 -- 06E30 -- 94C10; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2019.1700396
• Languages: English
• ISSNs: 2379-9927

Abstract

ABSTRACT: This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one, referred to herein as a 'big' Boolean algebra. The paper suggests the replacement of this system of equations by a single Boolean equation, and then proposes a novel method for solving this equation by using its atomic decomposition into several independent switching equations. This method has many advantages including the efficient derivation of a complete compact listing of all particular solutions in a form similar to the recently developed permutative additive form, but obtained in a more direct fashion without using parameters. Many detailed examples are used to illustrate the proposed new method. The examples demonstrate how the consistency condition might force a collapse of the underlying Boolean algebra into a subalgebra, and also how to list a huge number of particular solutions in a very small space.