Abstract
In the present paper, an algebraic structure theory of stochastic machines is developed which contains both Bacon's theory [1] and Hartmanis' theory for deterministic machines [5] as special cases. Although the present theory is patterned after both theories, it exhibits many interesting features which are here-to-fore unknown. Among other things, it is shown that the basic concepts involved, e.g., partitions with substitution property, partition pairs, state-behavior realizations, are all equivalent to well-known concepts in linear algebra. Section II introduces the model of stochastic machines to be used in subsequent developments. In Section III, various types of realizations and assignments are introduced. The concepts of partitions with substitution property, partition pairs, etc. are introduced in Section III. The last section gives a formulation of a network of concurrently operating QSMs.
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