On finding an estimate of the complexity of discrete k-valued functions

. In this paper the concept of derivative and integral of discrete k-valued functions is introduced, taking into account the properties of the operations of addition and multiplication modulo k. Based on the property of completeness of the integral expansion of k-valued functions, a universal method is proposed for estimating the complexity of k-valued fully defined functions, including not having an analytical representation, but specified only in a tabular way, or representable using other tabular functions. The structure of the “primitive – derivative” relation is studied depending on the properties of the number k. A model in the form of a directed graph of this relationship is proposed. Three main types of introduced relations are identified.