1. This essay embodies research done by the author for the Bell Telephone Laboratories Murray Hill, New Jersey, during the summer of 1958.
2. E. F. Moore, Gedanken-Experiments on Sequential Machines, Automata Studies, Princeton University Press, 1956, pp. 129–153.
3. G. H. Mealy, A Method for Synthesizing Sequential Circuits, Bell System Technical Journal 34 (1955) 1045–1079. The term “merging” is being used below in the sense of Mealy, and not in quite the same sense as is used by such writers as Huffman and Caldwell.
4. For a somewhat different kind of simplification see paragraphs 8.10 and 8.11 of my paper, ‘Representation of Sequential Circuits in Combinatory Logic’, Philosophy of Science 25 (1958) 263–279.
5. Loc. cit.