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Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions

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Abstract

The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set {0, 1, 2} and taking values in the set {0,1} with the property that the restrictions of its functions to the set {0, 1} constitutes a closed class of Boolean functions. We consider all classes whose restriction closure is either the set of all functions of two-valued logic or the set T a of functions preserving \({a, a\in\{0, 1\}}\). In each of these cases, we find a finite total equivalence system, construct a canonical type for formulas, and present a complete algorithm for determining whether any two formulas are equivalent.

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  1. Department of Data Analysis and Artificial Intelligence, National Research University Higher School of Economics, 3 Kochnovskiy Proezd, Moscow, 125319, Russia

    Ilya Makarov

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  1. Ilya Makarov
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Correspondence to Ilya Makarov.

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To my Mother and faithful TA

The research was made under influence of the course “Closed classes of Boolean logic” on Faculty of Mechanics and Mathematics, Lomonosov Moscow State University.

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Makarov, I. Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions. Log. Univers. 9, 1–26 (2015). https://doi.org/10.1007/s11787-015-0117-9

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  • DOI: https://doi.org/10.1007/s11787-015-0117-9

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