Part 3. Mathematical models

On a minimal Scheffer function in the class of partial-parallel functions defined over binary rational numbers

M. V. Agafonova


Abstract: This article discusses the class of neural partial-parallel functions with binary rational coefficients (BPP-class). It is proven that a minimal Scheffer function exists in this class. By a minimal Scheffer function in the class, we mean a function of this class that generates this class by superposition operations and contains the minimum possible number of variables and threshold functions. It was established that a minimal Scheffer function contains two variables and one threshold function. The article also provides one of the necessary conditions for the Scheffer-type function to be contained in the BPP-class.

Keywords: class, partial-parallel functions, neural functions, binary coefficients, superposition operations, Scheffer function.