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Стукртура сигнатурного кубу булевих алгебр

Source :
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, Vol 38, Iss 1, Pp 149-156 (2021)
Publication Year :
2021
Publisher :
State University “Uzhhorod National University”, 2021.

Abstract

This paper is a continuation of the research distributed in [1], the theory of Boolean functions is considered from the point of view of universal algebras. This paper describes a class of functionally incomplete algebras, studies the main types of algebras and their location on the tiers of the signature cube. In the data of researches of universal Boolean algebras the 11-dimensional signal cube according to which 2048 algebras enter is created. Codification of these algebras has been offered. The notion of adjacent, boundary, and internal classes of functionally superficial and functionally incomplete algebras is introduced. Boolean algebras of the class are divided into four subclasses: a class of internal functionally incomplete algebras, a class of boundary functionally incomplete algebras, a class of boundary functionally superficial algebras, a class of internal functionally complete algebras. In this paper, an algorithm is proposed for finding boundary functionally complete algebras based on the expansion of signals of functionally incomplete algebras by Boolean operations. Subclasses of boundary algebras have been constructed for each of the eleven operations. The isomorphism of graphs of some classes of boundary algebras has been indicated. -graph of boundary functionally complete algebras was obtained on the basis of combining graphs.

Details

Language :
English
ISSN :
26167700
Volume :
38
Issue :
1
Database :
OpenAIRE
Journal :
Науковий вісник Ужгородського університету. Серія: Математика і інформатика
Accession number :
edsair.doi.dedup.....472d6f6d5641df30be0a9c7eaed251b8