Boolean expression based on hypergraphs with algorithm

Document Type : Research Paper


1 Department of mathematics, Payame Noor university, Tehran, Iran.

2 Department of mathematics, Payame Noor university, Tehran, Iran.

3 Department of Mathemtics, Payame Noor University, Tehran, Iran



This paper  introduces a novel concept of  Boolean function--based hypergraph  with respect to any given T.B.T(total binary truth table). This study defines a notation of  kernel set   on  switching functions and proves  that every  T.B.T corresponds to a  Minimum   Boolean expression via  kernel set  and presents  some conditions on  T.B.T to obtain  a Minimum irreducible   Boolean expression from switching functions. Finally, we present an algorithm and so Python programming(with complete and original codes) such that for any given T.B.T, introduces a Minimum irreducible   switching expression.


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