Switching Systems Synthesis Method Using Permuted Gray Code Tables (PGC Method)

César David Troya Sherdek, Valentin Salgado-Fuentes, Jaime Molina, Gustavo Moreno

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    Abstract

    Finding the shortest function on switching systems is a necessity for the development of efficient automatic systems. Currently, several methodologies aim to solve this need with different techniques. This article proposes a new methodology to find a propositional formula that describes a switching system problem using several truth tables which are based on an original one; these tables are generated using Gray Code principles and permutations. As it will be shown, the used
    code has a direct relation to the Hamiltonian paths, where each permutation is a different connection in a hypervolume, and each node is represented as a bit combination. An algorithm was developed using MATLAB and compared with the solutions from the software Boole- Deusto to verify and validate the applicability and implementation of the method. Finally, examples of execution, computational cost comparison and future work proposals are presented.
    Original languageEnglish
    JournalLatin American Journal of Computing
    Volume8
    Issue number1
    Pages (from-to)119-129
    ISSN1390-9266
    Publication statusPublished - 2021

    Bibliographical note

    This work is under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Ecuador License

    Keywords

    • Boolean functions
    • Discrete problems
    • Gray Code
    • Hamiltonian Paths
    • Hypercube
    • Switching systems

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