, ON THE MEMBERSHIP OF MULTIFUNCTIONS OF RANK TWO IN ES * -PRECOMPLETE SETS // BSU bulletin. Mathematics, Informatics. - 2021. №2. . - С. 3-16.

ON THE MEMBERSHIP OF MULTIFUNCTIONS OF RANK TWO IN ES * -PRECOMPLETE SETS

Multifunctions on a two-element set are considered together with operators of superposition and branching by an equality predicate. In superposition, a special role is assigned to the empty set, which is interpreted as "breakage". In the absence of "breakage", common elements are selected with all possible refinements. The set of common elements is declared as a superposition value. If there are no common elements, then the value of the multifunction is declared to be the set of all elements that occur with all possible refinements. For the introduced superposition and the branching operator by the equality predicate all precomplete sets are described, a completeness criterion is formulated and proved. Multifunctional classification is performed concerning belonging to precomplete sets. Examples of multifunctional classes are given. Precomplete sets are described in the language of predicate preservation by function. When performing the classification of multifunctional functions, a computer search was used.

multioperations; partial operations; hyperoperations; closed classes; E-closure; complete sets; classification; precomplete sets.

Marchenkov S. S. The Closure Operator with the Equality Predicate Branching on the Set of Partial Boolean Functions. Discrete Math. Appl. 2008. 4(18). Pp. 381– 389.

Panteleev V. I., Riabets L. V. The Closure Operator with the Equality Predicate Branching on the Set of Hyperfunctions on Two-Element Set. The Bulletin of Irkutsk State University. Series Mathematics. 2014. (10). Pp. 93–105.

Panteleev V. I. Superpositions of k-valued Logic Functions and Their Generali- zations. Dis. ... Dr. Sci. (Phys. and Math.): 01.01.09. Irkutsk, 2009. 215 p.

Doroslovački R., Pantović J., Vojvodić G. One Interval in the Lattice of Partial Hyperclones. Czechoslovak Mathematical Journal. 2005. 3(55). Pp. 719–724.

Machida H. Hyperclones on a Two-Element Set. Multiple-Valued Logic. An In- ternational Journal. 2002. 4(8). Pp. 495–501.

Marty F. Sur une Generalization de la Notion de Groupe. 8th Congress Math. Scandinaves. Stockholm, 1934. Pp. 45–49.

Panteleev V. I., Riabets L. V. E-closed Sets of Hyperfunctions on Two-Element Set. Journal of Siberian Federal University. Mathematics & Physics. 2020. 2(13). Pp. 231–241.

Pouzet M., Rosenberg I. Small Clones and the Projection Property. Algebra Uni- versalis. 2010. (63). Pp. 37–44.

Panteleev V. I., Riabets L. V. The Closure Operator with the Equality Predicate Branching on the Set of Hyperfunctions on Two-Element Set. The Bulletin of Irkutsk State University. Series Mathematics. 2014. (10). Pp. 93–105.

Panteleev V. I. Superpositions of k-valued Logic Functions and Their Generali- zations. Dis. ... Dr. Sci. (Phys. and Math.): 01.01.09. Irkutsk, 2009. 215 p.

Doroslovački R., Pantović J., Vojvodić G. One Interval in the Lattice of Partial Hyperclones. Czechoslovak Mathematical Journal. 2005. 3(55). Pp. 719–724.

Machida H. Hyperclones on a Two-Element Set. Multiple-Valued Logic. An In- ternational Journal. 2002. 4(8). Pp. 495–501.

Marty F. Sur une Generalization de la Notion de Groupe. 8th Congress Math. Scandinaves. Stockholm, 1934. Pp. 45–49.

Panteleev V. I., Riabets L. V. E-closed Sets of Hyperfunctions on Two-Element Set. Journal of Siberian Federal University. Mathematics & Physics. 2020. 2(13). Pp. 231–241.

Pouzet M., Rosenberg I. Small Clones and the Projection Property. Algebra Uni- versalis. 2010. (63). Pp. 37–44.