Conversion between Logic and Algebraic Expressions of Boolean Control Networks

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 Bool...

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Bibliographic Details
Published in:Applied sciences Vol. 10; no. 20; p. 7180
Main Authors: Wang, Cailu, Tao, Yuegang
Format: Journal Article
Language:English
Published: Basel MDPI AG 15.10.2020
Subjects:
Algebra
Algebra, Boolean
algebraic expression
Algorithms
Analysis
Boolean
Boolean control network (BCN)
canonical form
Circuits
computational complexity
conversion algorithm
Logic
logic expression
Variables
China
ISSN:2076-3417, 2076-3417
Online Access:Get full text
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Summary: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.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app10207180