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Research Article | Open Access

Simplification of logical functions with application to circuits

Jun-e Feng1, Rong Zhao1( ), Yanjun Cui2
School of Mathematics, Shandong University, Jinan 250100, China
College of Science and Engineering, University of Minnesota Twin Cities, Minneapolis 55455, USA
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Abstract

The simplification problem of logical functions is investigated via the matrix method. First, necessary and sufficient conditions are put forward for the decomposition of logical matrices. Based on this, several criteria are proposed for the simplification of logical functions. Furthermore, an algorithm, which can derive simpler logical forms, is developed, and illustrative examples are given to verify the effectiveness. Finally, the obtained theoretical results are applied to the simplification of electric circuits.

Keywords

circuitslogical functionssimplificationsemi-tensor product

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Electronic Research Archive
Volume 30 Issue 9,
September 2022
Pages 3320-3336
DOI: 10.3934/era.2022168

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Cite this article:
Feng J-e, Zhao R, Cui Y. Simplification of logical functions with application to circuits. Electronic Research Archive, 2022, 30(9): 3320-3336. https://doi.org/10.3934/era.2022168

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Received: 26 May 2022
Revised: 28 June 2022
Accepted: 01 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)