THRESHOLD FUNCTIONS

Abstract

It is well known, that threshold functions are mathematical models of neurons. They are of interest due to the simplicity of their technical implementation. The work studies the complexity of setting threshold functions of algebra logic by linear forms with integer coefficients and a free member. A number of effects on linear shapes that retain the smallest width and weight are also investigated. By using these operations on elementary linear forms, we can construct an infinite set of linear forms with the smallest width and weight. A subset of this set is a set of linear forms whose weights are Fibonacci numbers.