On the State Assignment Problem for Sequential Machines II

The object of this paper is to find state assignments for the internal states of a sequential machine such that the logical equations representing the machine are relatively simple. This is done by finding assignments for which the computation of a particular state variable depends only on the previous values of a small subset of the variables. The chief tool is the concept of a partition pair, which describes (loosely speaking) the information going into and resulting from the evaluation of a state variable. A necessary and sufficient condition for the existence of assignments with reduced dependence is found in terms of these pairs, and their algebraic properties are worked out so that they can be handled and generated. It is shown that the same methods can also be used to find input and output assignments with reduced dependence. The case of ``don't care'' conditions is considered and the theory is seen to apply, except that the failure of an algebraic property makes it weaker.