Abstract
This chapter discusses various mathematical models of stochastic sequential machines (SSMs) and provides motivation for these models. The chapter presents methods for synthesizing SSMs from their mathematical models. Various concepts of equivalence and coverings for SSMs are reviewed. Some decision problems and minimization-of-states problems induced by those concepts are discussed, and a procedure is formulated for constructing a minimal state SSM equivalent to a given one. The chapter discusses stochastic input-output relations and their representability by SSMs. An SSM parallel to the Mealy-type deterministic sequential machine is reviewed. The Moore-type machine also has a stochastic version that is discussed in the chapter. It is shown that although every output-independent machine is an SSM, the converse is not always true. Two distributions π and ρ for a given machine are equivalent if and only if they are (n − 1) equivalent, where n is the number of states of the machine.
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