ANALYSIS OF PROBABILISTIC AUTOMATA,

Given a deterministic finite automaton A having M states and N inputs, and its binary realization R with l internal and q input cells, it is required to find a probabilistic finite automaton Apr, the binary realization Rpr of which is obtained from R by replacing the deterministic cells with probabilistic ones. A theorem is presented stating that the elements of the transition matrices of Rpr may be decomposed into conditional probabilities of any of its m internal and n input cells. A second theorem is stated concerning the minimum probability of correct operation of the binary automaton.