Open AccessOn the Lattice of -closed Classes of Multifunctions on Two-elements Set
Author(s) -
V. I. Panteleev,
AUTHOR_ID,
E. S. Taglasov,
AUTHOR_ID
Publication year - 2021
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2021.38.96
Subject(s) - mathematics , operator (biology) , predicate (mathematical logic) , lattice (music) , discrete mathematics , combinatorics , pure mathematics , computer science , physics , biochemistry , chemistry , repressor , transcription factor , acoustics , gene , programming language
The paper considers multifunctions on a two-element set with superposition and the equality predicate branching operator. The superposition operator is based on the intersection of sets. The main purpose of the work is to describe all closed classes with respect to the considered operators. The equality predicate branching operator allows the task to be reduced to a description of all closed classes generated by 2-variable multifunctions. Using this, it is shown that the lattice of classes closed with respect to the considered operators contains 237 elements. A generating set is specified for each closed class. The result obtained in the paper extends the known result for all closed classes of partial functions on a two-element set.