Chapter IV - Applications and Generalizations

Abstract

This chapter discusses some of the most known papers dealing with applications and generalizations of probabilistic automata theory. When a deterministic automaton has some unreliable elements then its external behavior is probabilistic, thus, a motivation for studying probabilistic automata was the reliability problem. Still another motivation for studying stochastic automata was the possibility of using them as models of learning and pattern recognition systems. The model used by Tsetslin consists of a deterministic automaton subject to a probabilistic training process. The input to the deterministic automaton is random and represents the reaction of a medium—“teacher”—to the performance of the automaton. Two inputs are possible, 1—representing a penalty, and 0—representing a non-penalty, and the medium will insert its next input to the automaton in a random way, the probability of a penalty or non-penalty depending on the present state. A connection between stochastic automata and the problem of time sharing in computer programming has been established by Kashiap and the theory of functions of Markov chains has been used by Fox and Rubin for statistical inference—for evaluating the cloud cover estimation of parameters and goodness of fit based on Boston data.