Abstract
Publisher Summary Finite automata can be used as mathematical models for systems with finite number of states that admit at discrete time intervals certain inputs and emit certain outputs. Stochastic automata for which the inputs are constant are called autonomous stochastic automata. An autonomous stochastic automaton can be interpreted as a finite-state Markov chain with the same set state. The formulation of stochastic automata can also be employed to describe the behavior of deterministic automata with random inputs. The state and automata equivalence relations and minimization problems in deterministic finite automata can be extended to the case of stochastic automata. The basic idea used in the synthesis of stochastic automata follows the formulation of deterministic automata with random inputs, that is, autonomous stochastic automata are synthesized as deterministic automata with random inputs. Because of the stochastic nature in state transitions and input-output relations stochastic automata are considered suitable for modeling learning systems. Stochastic automata models find its application in pattern recognition, multimodal search, and learning control.
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