Algebraic simplification of redundant sequential circuits

The purpose of this essay 1 is to show that if a sequential circuit can be simplified by merging "equivalent states" in the sense of E. F. Moore 2 and G. H. Mealy 3, then the equations defining the original circuit can be transformed algebraically into equations defining the simplified circuit. The transformations are purely algebraic processes occurring in a kind of extended Boolean algebra here called "discrete delay algebra". Furthermore, the procedure for deciding which states, if any, can be thus merged, is shown to be an essentially algebraic procedure, and it is shown that the various states themselves can be viewed as special compound entities of the algebra. This outcome suggests that simplification of the Mealy-Moore sort is primarily algebraic in character and is perhaps a special sort of some more general kind of algebraic simplification that has wider application 4.