On classes of rank-two hyperfunctions generated by maximal partial ultraclones

The article considers the set of hyperfunctions, which is a subset of the set of multifunctions defined on a two-element set. The closure operator is a specially introduced superposition operation at which the set of all multifunctions makes a full partial two-rank ultraclone. The problem of classification for hyperfunctions, like for other discrete functions, appears to be interesting. One of the variants of classification is based on the belonging of functions to maximal clones. The article is predominantly aimed at classification of all hyperfunctions with respect to their belonging to maximal partial ultraclones. The relation of membership to maximal partial ultraclones is an equivalence relation and generates a corresponding partition into equivalence classes. We have obtained a complete description of all equivalence through computer calculations and identification of the special properties of hyperfunctions, the total number of which is 28.