On the synthesis of generators of stable probability distributions

Abstract

This research is, in a sense, a generalization of the problems of synthesis of reliable finite automata, beginning from the work of J. von Neumann (1962) . Though the final end of this work is a discussion of the problems of structural synthesis of reliable probabilistic automata, the question here will be just about the generators of probability distributions. The reason is that the synthesis of probabilistic automata can be reduced to synthesis of these generators. The method of solving this problem consists of wide use of the properties of regular bistochastic matrices. A particular case of it was successfully used by Gill (1962) in considering the problem of synthesis of probability transformers. Here, we obtain a generalization by means of some considerations from group theory.