In the search for new methods to realize stochastic automata, additive Bernoulli noise linear sequential circuits (ABNLSC) are constructed from linear sequential circuits fed with Bernoulli noise. The characteristics of the subclass of stochastic automata realizable by ABNLSC's are found. These characteristics include: commutativity with respect to input sequences; state minimality; doubly stochastic state transition matrices; and the conditions for the existence of asymptotic distribution of the state.

Using the convex combination of random binary variables, stochastic vectors and stochastic matrices are systematically realized. The techniques are extended to the realization of stochastic automata as randomly fed deterministic automata.