Universal two state machines: Characterization theorems and decomposition schemes

In the first part of this paper, an algorithm is derived for testing a given two state machine for the property of being universal. Various characterizations of universality are also obtained, and are stated in the form of necessary and sufficient conditions. The second part of this paper is concerned with the economical realization of sequential machines as networks of identical modules. Bounds are derived for the number of copies of a certain universal modules needed for the realization of an arbitrary machine selected from a given class.