Representing stand-alone automata by characteristic polynomials over a finite field

Abstract

This paper proposes a method of representing a deterministic stand-alone output automaton by a minimal characteristic polynomial over a finite field. It is shown that defining various automaton transition and output functions allows using the algorithm developed to build the sets of minimal polynomials, different in their powers. Estimates of the relevant sets are given here. We have identified the relation between a characteristic minimal polynomial and an ergodic stochastic matrix defining the sequence developed by a stand-alone automaton. It is shown that the minimal degree of a characteristic polynomial depends linearly on the power of the automaton state set and on the accuracy of representing the elements of a given limiting vector of a stochastic matrix.