Synthesis of combinational circuits by means of bi-decomposition of Boolean functions
https://doi.org/10.37661/1816-0301-2022-19-1-7-18
Abstract
O b j e c t i v e s . The problem of synthesis of combinational circuits in the basis of two-input gates is considered. Those gates are AND, OR, NAND and NOR. The objective of the paper is to investigate the possibilities of application of bi-decomposition of Boolean functions to the synthesis of combinational circuits.
M e t h o d s . The method for bi-decomposition is reduced to the search in a graph for a weighted two-block cover with complete bipartite subgraphs (bi-cliques).
R e s u l t s . The initial Boolean function is given as two ternary matrices, one of which represents the domain of Boolean space where the function has the value 1, and the other is the domain of Boolean space where the function has the value 0. The orthogonality graph of rows of ternary matrices representing the given function is considered. The method for two-bi-clique covering the orthogonality graph of rows of ternary matrices is described. Every bi-clique in the obtained cover is assigned in a certain way with а set of variables that are the arguments of the function. This set is the weight of the bi-clique. Each of those bi-cliques defines a Boolean function whose arguments are the variables assigned to it. The functions obtained in such a way constitute the required decomposition.
Co n c l u s i o n . The process of synthesis of a combinational circuit consists of a successive application of bi-decomposition to obtained functions. The suggested method allows obtaining the circuits with short delay.
About the Author
Yu. V. Pottosin
The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
Belarus
Belarus
Yuri V. Pottosin - Ph. D. (Phys.-Math.), Leading Researcher, The United Institute of Informatics Problems of the National Academy of Sciences of Belarus.
- Surganova, 6, Minsk, 220012.
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Review
For citations:
Pottosin Yu.V. Synthesis of combinational circuits by means of bi-decomposition of Boolean functions. Informatics. 2022;19(1):7-18. (In Russ.) https://doi.org/10.37661/1816-0301-2022-19-1-7-18
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