probabilistic automaton การใช้

• The initial state of a probabilistic automaton is given by a row vector v, whose components add to unity:
• Formally, the definition of a probabilistic automaton does not require the mechanics of the non-deterministic automaton, which may be dispensed with.
• The probabilistic automaton replaces these matrices by a family of stochastic matrices P _ a, for each symbol a in the alphabet \ Sigma so that the probability of a transition is given by
• In particular, the state of a probabilistic automaton is always a stochastic vector, since the product of any two stochastic matrices is a stochastic matrix, and the product of a stochastic vector and a stochastic matrix is again a stochastic vector.