BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, ON ONE AGGREGATE OF E-CLOSED CLASSES OF HYPERFUNCTIONS OF K RANK // BSU Bulletin. Mathematics, Informatics. - 2018. №3. . - С. 14-21.
Title:
ON ONE AGGREGATE OF E-CLOSED CLASSES OF HYPERFUNCTIONS OF K RANK
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Hyperfunctions represent functions defined on a finite set and taking as their values all nonempty subsets of the considered set. In the theory of discrete functions the is- sue of classification is interesting and important concerning different closure opera- tors. One such operator is the closure operator with branching by the equality predicate (E-operator). Such operator belongs to a category of strong closure operators.
The article considers the aggregate of the hyperfunctions of the K rank that preserve permutations on a k-element set. It is shown that these classes are E- closed. In case the permutation splits into cycles of the same simple length, then such classes are E-precomplete. Besides, it is shown that a set containing all function-constants and a function that returns on all sets some fixed non-empty subset of the original set is E-complete.
The article considers the aggregate of the hyperfunctions of the K rank that preserve permutations on a k-element set. It is shown that these classes are E- closed. In case the permutation splits into cycles of the same simple length, then such classes are E-precomplete. Besides, it is shown that a set containing all function-constants and a function that returns on all sets some fixed non-empty subset of the original set is E-complete.
Keywords:
closure; equality predicate; hyperfunction; closed set; superposition; precomplete set; clon.
List of references:
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Ryabets L. V., Goncharova M. I. O nekotorykh E-predpolnykh klassah giper- funkcij ranga 3 [On Some E-precomplete Classes of Hyperfunctions on Three-Element Set]. Algebra i teoriya modelej11 - Algebra and Model Theory 11: Works of XII Inter- national Summer School-Conference “Boundary Issues of the Theory of Models and Universal Algebra” (Novosibirsk, June 23-29, 2017) Novosibirsk: NSTU Publ., 2017. Pp. 130–133.
Marchenkov S. S. Operator zamykaniya s razvetvleniem po predikatu ravenstva na mnozhestve chastichnyh bulevyh funkcij [Closure Operator with the Equality Predi- cate Branching on the Set of Partial Boolean Functions]. Diskretnaya matematika - Discrete Math. Appl., 2008, V. 18, No. 4. Pp. 381–389.
Marchenkov S. S. Operator E-zamykaniya na mnozhestve chastichnyh funkcij mnogoznachnoj logiki [The E-closure Operator on the Set of Partial Many-valued Logic Functions]. Matematicheskie voprosy kibernetiki - Mathematical problems in cybernetics, Moscow; Fizmatlit Publ., 2013, V. 19. Pp. 227–238.
Marchenkov S. S. Funkcional'nye sistemy s operaciej superpozicii [Functional Systems with Superposition Operation]. Moscow: Fizmatlit Publ., 2004. 104 p.
Matveev S. A. Postroenie vsekh E-zamknutyh klassov chastichnyh bulevyh funkcij [Construction of All E-closed Classes of Partial Boolean Functions]. Mate- maticheskie voprosy kibernetiki - Mathematical problems in cybernetics. Moscow: Fiz- matlit Publ., 2013. V. 18. Pp. 239–244.
Panteleyev V. I., Ryabets L. V. Operator zamykaniya s razvetvleniem po predi- katu ravenstva na mnozhestve giperfunkcij ranga 2 [The Closure Operator with the Equality Predicate Branching on the Set of Hyperfunctions on Two-Element Set]. Iz- vestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika – Bulletin of the Irkutsk. State University Series. Mathematics. 2014, V. 10. Pp. 93–105.
Ryabets L. V., Goncharova M. I. O nekotorykh E-predpolnykh klassah giper- funkcij ranga 3 [On Some E-precomplete Classes of Hyperfunctions on Three-Element Set]. Algebra i teoriya modelej11 - Algebra and Model Theory 11: Works of XII Inter- national Summer School-Conference “Boundary Issues of the Theory of Models and Universal Algebra” (Novosibirsk, June 23-29, 2017) Novosibirsk: NSTU Publ., 2017. Pp. 130–133.
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