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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/20/7180 |
| _version_ | 1797550925473120256 |
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| author | Cailu Wang Yuegang Tao |
| author_facet | Cailu Wang Yuegang Tao |
| author_sort | Cailu Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:36:22Z |
| format | Article |
| id | doaj.art-50fbbecc9bad4313867178ab454e5d07 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T15:36:22Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-50fbbecc9bad4313867178ab454e5d072023-11-20T17:10:03ZengMDPI AGApplied Sciences2076-34172020-10-011020718010.3390/app10207180Conversion between Logic and Algebraic Expressions of Boolean Control NetworksCailu Wang0Yuegang Tao1School of Automation, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, ChinaThe 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.https://www.mdpi.com/2076-3417/10/20/7180Boolean control network (BCN)logic expressionalgebraic expressioncanonical formconversion algorithmcomputational complexity |
| spellingShingle | Cailu Wang Yuegang Tao Conversion between Logic and Algebraic Expressions of Boolean Control Networks Applied Sciences Boolean control network (BCN) logic expression algebraic expression canonical form conversion algorithm computational complexity |
| title | Conversion between Logic and Algebraic Expressions of Boolean Control Networks |
| title_full | Conversion between Logic and Algebraic Expressions of Boolean Control Networks |
| title_fullStr | Conversion between Logic and Algebraic Expressions of Boolean Control Networks |
| title_full_unstemmed | Conversion between Logic and Algebraic Expressions of Boolean Control Networks |
| title_short | Conversion between Logic and Algebraic Expressions of Boolean Control Networks |
| title_sort | conversion between logic and algebraic expressions of boolean control networks |
| topic | Boolean control network (BCN) logic expression algebraic expression canonical form conversion algorithm computational complexity |
| url | https://www.mdpi.com/2076-3417/10/20/7180 |
| work_keys_str_mv | AT cailuwang conversionbetweenlogicandalgebraicexpressionsofbooleancontrolnetworks AT yuegangtao conversionbetweenlogicandalgebraicexpressionsofbooleancontrolnetworks |