Conversion between Logic and Algebraic Expressions of Boolean Control Networks

Abstract

The conversion between logic and algebraic expressions of Boolean control networks plays a worthy role in the analysis and design of digital circuits. In this paper, for a single Boolean function, a direct conversion between the minterm canonical form and the structure matrix is provided. For a Boolean control network consisting of systems of Boolean functions, two algorithms are developed to achieve the mutual conversion between the logic and algebraic expressions. The presented algorithms decrease exponentially the complexity of the semi-tensor product based method. Some numerical examples are given to demonstrate the algorithms and to compare our method with the existing ones.

Keywords

• Boolean control network (BCN)
• logic expression
• algebraic expression
• canonical form
• conversion algorithm
• computational complexity