Theoretical foundation of potential functions method in pattern recognition

Algorithm for teaching automata to pattern recognition is proved. The method Is based on building of so-called potential functions. The main hypothesis on the character of functions which divide ensembles corresponding to different classes is introduced. Basing on the hypothesis, certain theorems on the convergence of the algorithm for the finite number of steps are proved.
The proposed algorithms are shown to be realized by the various classes of circuits. Characteristics of elements the circuits designed of can be chosen practically arbitrary. It is shown that Rozenblatt's perceptron refers to this class of circuits, i. e. it is proved that the perceptron operation can be understood as a realization of the method of potential functions. Therefore the proved theorems concerning the convergence of the algorithm for the potential functions solve the problem of the convergence of the perceptron process as well.