Toward a Theory of Probabilistic Automata with Environments,

The viewpoint is taken that every probabilistic automation is situated within a sequence of environments which affects the initial state distribution and the transition function. There exists a probabilistic automaton within a deterministic environment sequence ADE which defines an event which is not a PCE, yet in certain nontrivial cases the behavior of an ADE can be simulated by a probabilistic automaton. For probabilistic automata within random environment sequences there is a mean equivalent canonical representation which eliminates the randomness due to probabilistic transition. Author