On the Analysis of Sequential Machines

In this paper we indicate briefly how the methods of the algebraic solution of Markov chains with constant transition probabilities apply to the analysis of sequential machines. Mealy´s model of a sequential machine is assumed. A stochastic matrix is associated with each such machine to provide a starting point for the analysis. ``Closed´´ sets of states are then characterized, for example, by the appropriate theorems about Markov chains. A technique is formulated for reducing the connection matrix of any sequential machine to a canonical form.