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Infinitely Generated Classes of 01-Functions of Three-Valued Logic

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Abstract

Infinitely generated closed classes \(\Pi_{1}{-}\Pi_{4}\) of 01-functions of three-valued logic are investigated. The property of maximality is proved for classes \(\Pi_{3}\) and \(\Pi_{4}\). Each proper extension of classes leads to finitely generated closed classes. It is proved that there is no base in class \(\Pi_{1}\). All of the simplest two- and three-variable functions obtainable by superposition from an arbitrary function not belonging to class \(\Pi_{1}\) are found.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00200.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    S. S. Marchenkov

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  1. S. S. Marchenkov
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Correspondence to S. S. Marchenkov.

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Translated by A. Muravnik

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Marchenkov, S.S. Infinitely Generated Classes of 01-Functions of Three-Valued Logic. MoscowUniv.Comput.Math.Cybern. 45, 103–108 (2021). https://doi.org/10.3103/S027864192103002X

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  • DOI: https://doi.org/10.3103/S027864192103002X

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