Complexity reduction in state observation of stochastic automata

Abstract

If an automaton has a set of unobservable states, then the observation result cannot be improved as long as the automaton moves within this set. It is, therefore, reasonable to reduce the automaton and, hence, the complexity of the state observation algorithm by replacing the set of unobservable states by a single state. The paper shows that for stochastic automata it is impossible to perform this reduction in such a way that the observation result for the remaining states remains unchanged. Consequently, the state observation algorithm applied to the reduced automaton does not generate the same probability distribution as for the original automaton. The paper introduces the reduced requirement that the observation results should be complete in the sense that all states in which the complete automaton can reside with positive probability is associated with a positive probability by the reduced state observer. A sufficient condition for satisfying this requirement is given.