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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 05.08.2019
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”, Bulletin of Irkutsk State University. Series Mathematics, 29 (2019), 68–85
Linking options:
https://www.mathnet.ru/eng/iigum385 https://www.mathnet.ru/eng/iigum/v29/p68
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Abstract page: | 136 | Full-text PDF : | 70 | References: | 17 |
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