On the State Assignment Problem for Sequential Machines. I

In this paper, the problem of determining economical state assignments for finite-state sequential machines is studied. The fundamental idea in this study is to find methods for selection of these assignments in which each binary variable describing the new state depends on as few variables of the old state as possible. In general, these variable assignments in which the dependence is reduced yield more economical implementation for the sequential machine than the assignments in which the dependence is not reduced. The main tool used in this study is the partition with the substitution property on the set of states of a sequential machine. It is shown that for a sequential machine the existence of assignments with reduced dependence is very closely connected with the existence of partitions with the substitution property on the set of states of the machine. It is shown how to determine these partitions for a given sequential machine and how they can be used to obtain assignments with reduced dependence.