Journal of Siberian Federal University. Mathematics & Physics / E-closed Sets of Hyperfunctions on Two-Element Set

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (2)
Authors
Panteleyev, Vladimir I.; Riabets, Leonid V.
Contact information
Panteleyev, Vladimir I.: Irkutsk State University Irkutsk, Russian Federation; OCRID: 0000-0003-4766-486X; Riabets, Leonid V.: Irkutsk State University Irkutsk, Russian Federation; OCRID: 0000-0003-4047-9573
Keywords
closure; equality predicate; hyperfunction; closed set; composition
Abstract

Hyperfunctions are functions that are defined on a finite set and return all non-empty subsets of the considered set as their values. This paper deals with the classification of hyperfunctions on a two-element set. We consider the composition and the closure operator with the equality predicate branching (E-operator). E-closed sets of hyperfunctions are sets that are obtained using the operations of adding dummy variables, identifying variables, composition, and E-operator. It is shown that the considered classification leads to a finite set of closed classes. The paper presents all 78 E-closed classes of hyperfunctions, among which there are 28 pairs of dual classes and 22 self-dual classes. The inclusion diagram of the E-closed classes is constructed, and for each class, its generating system is obtained

Pages
231-241
DOI
10.17516/1997-1397-2020-13-2-231-241
Paper at repository of SibFU
http://elib.sfu-kras.ru/handle/2311/135140