Investigation of Dense Family of Closure Operations

As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense fami...

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Published inCybernetics and information technologies : CIT Vol. 22; no. 3; pp. 18 - 28
Main Authors Son, Nguyen Hoang, Demetrovics, J., Thi, Vu Duc, Thuy, Nguyen Ngoc
Format Journal Article
LanguageEnglish
Published Sciendo 01.09.2022
Subjects
Closure operation
dense family
hypergraph
minimal key
transversal hypergraph
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Summary:As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense families, including the collection of the whole closed sets and the minimal generator of the closed sets, are also pointed out. More important, a necessary and sufficient condition for an arbitrary family to be dense is provided in our paper. Then we use these dense families to characterize minimal keys of the closure operation under the viewpoint of transversal hypergraphs and construct an algorithm for determining the minimal keys of a closure operation.
ISSN:1314-4081
1314-4081
DOI:10.2478/cait-2022-0025