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 The Bulletin of Irkutsk State University. Series Mathematics: Year: Volume: Issue: Page: Find

 The Bulletin of Irkutsk State University. Series Mathematics, 2019, Volume 29, Pages 68–85 (Mi iigum385)

Algebraic and logical methods in computer science and artificial intelligence

The completeness criterion for closure operator with the equality predicate branching on the set of multioperations on two-element set

V. I. Panteleev, L. V. Riabets

Irkutsk State University, Irkutsk, Russian Federation

Abstract: Multioperations are operations from a finite set A to set of all subsets of A. The usual composition operator leads to a continuum of closed sets. Therefore, the research of closure operators, which contain composition and other operations becomes necessary. In the paper, the closure of multioperations that can be obtained using the operations of adding dummy variables, identifying variables, composition operator, and operator with the equality predicate branching is studied. We obtain eleven precomplete closed classes of multioperations of rank 2 and prove the completeness criterion. The diagram of inclusions for one of the precomplete class is presented.

Keywords: closure, equality predicate, multioperation, closed set, composition, completeness criterion.

DOI: https://doi.org/10.26516/1997-7670.2019.29.68

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Bibliographic databases:

UDC: 519.716
MSC: 03B50, 08A99
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Citation: V. I. Panteleev, L. V. Riabets, “The completeness criterion for closure operator with the equality predicate branching on the set of multioperations on two-element set”, The Bulletin of Irkutsk State University. Series Mathematics, 29 (2019), 68–85

Citation in format AMSBIB
\Bibitem{PanRya19} \by V.~I.~Panteleev, L.~V.~Riabets \paper The completeness criterion for closure operator with the equality predicate branching on the set of multioperations on two-element set \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2019 \vol 29 \pages 68--85 \mathnet{http://mi.mathnet.ru/iigum385} \crossref{https://doi.org/10.26516/1997-7670.2019.29.68} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000486448100007}