Modular decomposition of synchronous sequential machines

In this paper we are concerned with the decomposition of synchronous sequential machines into interconnections of component machines. The term interconnection is taken literally; the input terminals of a component machine must be directly connected to either i) a logical constant, ii) an output terminal of a component machine, or iii) an external input line. A fundamental question regarding such decompositions is "Does there exist a finite set of component machines such that any given machine can be realized by an interconnection of copies of the component machines?" The answers to this and related questions comprise the scope of the paper.