Synthesis of combinational circuits by means of bi-decomposition of Boolean functions
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 co...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
2022-03-01
|
| Series: | Informatika |
| Subjects: | |
| Online Access: | https://inf.grid.by/jour/article/view/1182 |
| _version_ | 1797877152263176192 |
|---|---|
| author | Yu. V. Pottosin |
| author_facet | Yu. V. Pottosin |
| author_sort | Yu. V. Pottosin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T02:13:41Z |
| format | Article |
| id | doaj.art-2e4a1fd495334b7d8ff09bf7afdaff2c |
| institution | Directory Open Access Journal |
| issn | 1816-0301 |
| language | Russian |
| last_indexed | 2024-04-10T02:13:41Z |
| publishDate | 2022-03-01 |
| publisher | The United Institute of Informatics Problems of the National Academy of Sciences of Belarus |
| record_format | Article |
| series | Informatika |
| spelling | doaj.art-2e4a1fd495334b7d8ff09bf7afdaff2c2023-03-13T08:32:25ZrusThe United Institute of Informatics Problems of the National Academy of Sciences of BelarusInformatika1816-03012022-03-0119171810.37661/1816-0301-2022-19-1-7-18994Synthesis of combinational circuits by means of bi-decomposition of Boolean functionsYu. V. Pottosin0The United Institute of Informatics Problems of the National Academy of Sciences of BelarusO 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.https://inf.grid.by/jour/article/view/1182synthesis of combinational circuitsboolean functiondecomposition of boolean functionsternary matrixcomplete bipartite graphbi-cliquetwo-block cover |
| spellingShingle | Yu. V. Pottosin Synthesis of combinational circuits by means of bi-decomposition of Boolean functions Informatika synthesis of combinational circuits boolean function decomposition of boolean functions ternary matrix complete bipartite graph bi-clique two-block cover |
| title | Synthesis of combinational circuits by means of bi-decomposition of Boolean functions |
| title_full | Synthesis of combinational circuits by means of bi-decomposition of Boolean functions |
| title_fullStr | Synthesis of combinational circuits by means of bi-decomposition of Boolean functions |
| title_full_unstemmed | Synthesis of combinational circuits by means of bi-decomposition of Boolean functions |
| title_short | Synthesis of combinational circuits by means of bi-decomposition of Boolean functions |
| title_sort | synthesis of combinational circuits by means of bi decomposition of boolean functions |
| topic | synthesis of combinational circuits boolean function decomposition of boolean functions ternary matrix complete bipartite graph bi-clique two-block cover |
| url | https://inf.grid.by/jour/article/view/1182 |
| work_keys_str_mv | AT yuvpottosin synthesisofcombinationalcircuitsbymeansofbidecompositionofbooleanfunctions |