Geodesic
On finding an estimate of the complexity of discrete k-valued functions
News of the Kabardin-Balkar scientific center of RAS, no. 6 (2023), pp. 142-151

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. 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.
Keywords: k-valued function, differentiation operator, integration operator, completeness property,integral basis functions, directed graph 
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     author = {D. P. Dimitrichenko},
     title = {On finding an estimate of the complexity of discrete k-valued functions},
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D. P. Dimitrichenko. On finding an estimate of the complexity of discrete k-valued functions. News of the Kabardin-Balkar scientific center of RAS, no. 6 (2023), pp. 142-151. http://geodesic.mathdoc.fr/item/IZKAB_2023_6_a14/