Reconsider the state minimization problem for stochastic finite state systems
SWAT '66 Proceedings of the 7th Annual Symposium on Switching and Automata Theory (swat 1966)
Finite automata and their decision problems
IBM Journal of Research and Development
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In an effort to relate various existent schools of thought, this paper describes four models of probabilistic finite-state systems, giving necessary and sufficient conditions for reciprocal describability. An algorithm for the realization (synthesis) of a stochastic sequential machine by a deterministic machine and additive noise is presented. Different definitions of equivalence are listed and related by theorems, the most important of which states that "behavioral equivalence" with the same cutpoints for sequence recognizers is identical to "stochastic equivalence" (indistinguishability) for sequence transducers. Corollaries show the import of these results to the state minimization problem. The paper composes a strong case in favor of the adoption of J. W. Carlyle's model as a unifying one.