Transition Matrices of Sequential Machines

In this paper a matrix technique is introduced for the analysis of state diagrams of synchronous sequential machines. The matrices introduced are closely related to the relation matrices of the calculus of relations and provide a formal tool for discussing state diagrams. It is shown that several of the well-known theorems on state diagrams are consequences of properties of transition matrices, which remain invariant under matrix multiplication. A reduction procedure for state diagrams, based on transition matrices, which is similar to Moore´s technique, is given. A method of extending the results to asynchronous machines is also included.