Probabilistic Automaton

Probabilistic Automaton

In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the non-deterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix or stochastic matrix. Thus, the probabilistic automaton generalizes the concept of a Markov chain or subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable.

The concept was introduced by Michael O. Rabin in 1963; a certain special case is sometimes known as the Rabin automaton. In recent years, a variant has been formulated in terms of quantum probabilities, the quantum finite automaton.