Minimization of Boolean functions in the class of orthogonal disjunctive normal forms
The orthogonal disjunctive normal forms (DNFs) of Boolean functions have wide applications in the logical design of discrete devices. The problem of DNF orthogonalization is to get for a given function such a DNF that any two its terms would be orthogonal, i. e. the conjunction of them would be equa...
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The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
2021-07-01
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doaj-3a09ceb9f3204a7193792be027f23a2b2021-07-28T21:07:31ZrusThe United Institute of Informatics Problems of the National Academy of Sciences of Belarus Informatika1816-03012021-07-01182334710.37661/1816-0301-2021-18-2-33-47969Minimization of Boolean functions in the class of orthogonal disjunctive normal formsYu. V. Pottosin0The United Institute of Informatics Problems of the National Academy of Sciences of BelarusThe orthogonal disjunctive normal forms (DNFs) of Boolean functions have wide applications in the logical design of discrete devices. The problem of DNF orthogonalization is to get for a given function such a DNF that any two its terms would be orthogonal, i. e. the conjunction of them would be equal identically to zero. An approach to solve the problem using the means of graph theory is suggested. The approach is proposed by representation of the function as perfect DNF. Obtaining all the intervals of the Boolean space where the given function has value 1 is supposed, and the intersection graph of those intervals is considered. Two methods to obtain a minimum orthogonal DNF are considered. One of them reduces the problem toward finding out the smallest dominating set in the graph by covering its vertices with their closed neighborhoods, the other - to obtain the maximum independent set by lexicographic enumeration. It is shown how the suggested approach can be extended on incompletely specified Boolean functions.https://inf.grid.by/jour/article/view/1131boolean functiondisjunctive normal formorthogonal termsshort cover problemintersection graphdominating setindependent set |
collection |
DOAJ |
language |
Russian |
format |
Article |
sources |
DOAJ |
author |
Yu. V. Pottosin |
spellingShingle |
Yu. V. Pottosin Minimization of Boolean functions in the class of orthogonal disjunctive normal forms Informatika boolean function disjunctive normal form orthogonal terms short cover problem intersection graph dominating set independent set |
author_facet |
Yu. V. Pottosin |
author_sort |
Yu. V. Pottosin |
title |
Minimization of Boolean functions in the class of orthogonal disjunctive normal forms |
title_short |
Minimization of Boolean functions in the class of orthogonal disjunctive normal forms |
title_full |
Minimization of Boolean functions in the class of orthogonal disjunctive normal forms |
title_fullStr |
Minimization of Boolean functions in the class of orthogonal disjunctive normal forms |
title_full_unstemmed |
Minimization of Boolean functions in the class of orthogonal disjunctive normal forms |
title_sort |
minimization of boolean functions in the class of orthogonal disjunctive normal forms |
publisher |
The United Institute of Informatics Problems of the National Academy of Sciences of Belarus |
series |
Informatika |
issn |
1816-0301 |
publishDate |
2021-07-01 |
description |
The orthogonal disjunctive normal forms (DNFs) of Boolean functions have wide applications in the logical design of discrete devices. The problem of DNF orthogonalization is to get for a given function such a DNF that any two its terms would be orthogonal, i. e. the conjunction of them would be equal identically to zero. An approach to solve the problem using the means of graph theory is suggested. The approach is proposed by representation of the function as perfect DNF. Obtaining all the intervals of the Boolean space where the given function has value 1 is supposed, and the intersection graph of those intervals is considered. Two methods to obtain a minimum orthogonal DNF are considered. One of them reduces the problem toward finding out the smallest dominating set in the graph by covering its vertices with their closed neighborhoods, the other - to obtain the maximum independent set by lexicographic enumeration. It is shown how the suggested approach can be extended on incompletely specified Boolean functions. |
topic |
boolean function disjunctive normal form orthogonal terms short cover problem intersection graph dominating set independent set |
url |
https://inf.grid.by/jour/article/view/1131 |
work_keys_str_mv |
AT yuvpottosin minimizationofbooleanfunctionsintheclassoforthogonaldisjunctivenormalforms |
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1721262712356339712 |