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During my time as a Ph.D. student in mathematics at the Massachusetts Institute of Technology (MIT), around 1962 or 1963, the authors of a book on control theory [1] introduced me to two researchers at MIT's Lincoln Laboratory, Michael Athanassiades and Peter Falb, who were writing a book on mathematical control theory. They, in turn, provided me with a draft of their book in progress and introduced...
With each state of probabilistic finite automaton, we may associate a function p(u|v), which tells us the probability that, if we apply the input sequence v to the machine started in the state, we should observe output sequence u. We give a necessary and sufficient condition that a function p(u|v) be realizable as such an inputoutput function. We show that a result of Heller on stochastic processes...
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