On Some Classes of Functions and Hypercubes

TL;DR

This paper explores classes of discrete k-valued logic functions, focusing on their construction, representation as hypercubes and Latin hypercubes, and methods for identifying relevant variables, advancing understanding of their structural properties.

Contribution

It introduces new methods for constructing and representing specific classes of k-valued logic functions as hypercubes and Latin hypercubes, including variable identification techniques.

Findings

Functions can be constructed and represented in various forms.

Methods for identifying variables in these functions are developed.

Results facilitate analysis and synthesis of complex discrete functions.

Abstract

In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular, analytical or matrix form, that is, as hypercubes, and in particular Latin hypercubes. Results connected with identifying of variables of some classes of functions are obtained.