The paper studies k-valued logic functions for k = 2m, m ≥ 2. Such functions are encoded in the binary number system and a special β-closure operator is defined. The completeness criteria for β-closed classes is obtained and all maximal classes are described for this operator. It is proven that the set of β-closed classes of functions, taking no more than two values, is countably infinite and the description of such classes is provided. A closed class of Boolean functions is associated with every set of the k-valued logic functions and called its boolean closure. For every r = 3, 4 and every Boolean closed class B it is shown that the family of β-closed classes with boolean closure equal to B and containing only functions, taking not more than r values, is finite or continuous. For given r the explicit partition of all Boolean closed classes with respect to this criteria is provided.

functional systems, multivalued logic functions, closed classes, superposition

Mathematical problems and theory of numerical methods