Bijective coordinate-forbidden k-valued functions in a problem of synthesis of substitutions

The interest towards the study of transformations in a k-valued logic is driven to a great extent by the development of modern computer technology, particularly by the increase in the amount of information and the increasing speed of information processing. The transition from Boolean operations to k-valued operations is not limited to a quantitative increase in complexity, as it also affects the internal logical framework of the schemes' implementation and functioning.
This article will focus on the study of a specific locally defined problem of k-valued logic, namely, the problem of expansive interpretation of the logical negation operation, which, despite the simplicity of its original definition, has led to the creation of a theory of functions with forbidden signs of subfunctions. Of additional interest are original practical applications of this theory associated with the study of a range of typical information processing nodes using functions of the studied class.