Switching function based on hypergraphs with algorithm and python programming

• Published in: Journal of intelligent & fuzzy systems Vol. 39; no. 3; pp. 2845 - 2859
• Main Authors: Hamidi, Mohammad, Rahmati, Marzieh, Rezaei, Akbar
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2020; Sage Publications Ltd
• Subjects: Algorithms; Boolean; Boolean algebra; Boolean functions; Canonical forms; Graph theory; Graphs; Programming languages; Python; Switching; Boolean function–based hypergraph; Boolean functionable hypergraph; T.B.T; Unitor; hypergraphable Boolean function; Switching function
• ISSN: 1064-1246; 1875-8967
• DOI: 10.3233/JIFS-191230

According to Boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions (it can also be described as an OR of AND’s). For each table an arbitrary T.B.T is given (total binary truth table) Boolean expression can be written as a disjunctive normal form. This paper considers a notation of a T.B.T, introduces a new concept of the hypergraphable Boolean functions and the Boolean functionable hypergraphs with respect to any given T.B.T. This study defines a notation of unitors set on switching functions and proves that every T.B.T corresponds to a minimum Boolean expression via unitors set and presents some conditions on a T.B.T to obtain a minimum irreducible Boolean expression from switching functions. Indeed, we generate a switching function in different way via the concept of hypergraphs in terms of Boolean expression in such a way that it has a minimum irreducible Boolean expression, for every given T.B.T. Finally, an algorithm is presented. Therefore, a Python programming(with complete and original codes) such that for any given T.B.T, introduces a minimum irreducible switching expression.