Functions defined on a finite set of cardinality k are considered. For any divisor d of k, values of such functions at points of a mesh with width d are analyzed. The special property of a function called preservation of the first-order d-differences is defined in terms of these values. Functions preserving d-differences and their sets closed with respect to the superposition operations are being studied.

k-valued logics, finite differences, functions superposition, closed classes

Mathematical problems and theory of numerical methods