On asynchronous stochastic automata

The paper deals with generalized stochastic automata (probabilistic sequential machines) which are able to print not only a single output but an output tape of arbitrary finite length each unit of time. Section 1 contains the basic definitions and some observations concerning the basic probabilities which are associated with each stochastic automaton. In section 2 the equivalence of situations and of automata is investigated. The principal result is the decidability of equivalence of finite situations of finite automata. Section 3, the main portion of the paper, is devoted to an investigation of the input-output relations, i.e., of the externally observable behavior, of stochastic automata. The existence of a so-called state family is shown to be a criterion for the generability of a stochastic operator within a stochastic automaton. The nonuniqueness of state families leads to a consideration of separability of stochastic operators, a property being, for generable stochastic operators, necessary and sufficient for the uniqueness of a state family. This property as well as a somewhat weaker property is characterized then. Some open problems are pointed out