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Representation of Sequential Circuits in Combinatory Logic

Published online by Cambridge University Press:  14 March 2022

Frederic B. Fitch
Frederic B. Fitch*
Affiliation:
Yale University and Bell Telephone Laboratories
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Extract

We will be dealing with “sequential circuits” in the sense of E. F. Moore and G. H. Mealy. Each such circuit is assumed to have a finite number of input wires (possibly none) and a finite number of output wires (but at least one). Each element of such a circuit will be assumed to be an and-circuit, an or-circuit, a not-circuit, or a delay circuit, for some specified temporal delay. Each element has one output wire which, however, may branch in order to serve several purposes simultaneously. (Similarly the inputs of the total circuit may be allowed to branch.) The and-circuits and or-circuits have two input wires each, while the not-circuits and the delay circuits have one input wire each.

Type
Research Article
Information
Philosophy of Science , Volume 25 , Issue 4 , October 1958 , pp. 263 - 280
Copyright
Copyright © 1958, The Williams & Wilkins Company

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References

1 E. F. Moore, “Gedanken-Experiments on Sequential Machines,” Automata Studies, Princeton University Press, 1956, pp. 129-153.

2 G. H. Mealy, “A Method for Synthesizing Sequential Circuits,” Bell System Technical Journal, vol. 34, pp. 1045-1079, September, 1955.

3 See, for example, F. B. Fitch, “A Definition of Negation in Extended Basic Logic,” Journal of Symbolic Logic, vol. 19 (1954), pp. 29-36.

4 See references in Alonzo Church, Calculi of Lambda-Conversion, Princeton University Press, 1941.

5 See Alonzo Church, loc. cit.

6 This paper was read at a colloquim entitled “Constructivity in Mathematics” held at the University of Amsterdam during August 26-31, 1957, and sponsored by the International Union of Logic, Philosophy and Methodology of the Sciences. All papers read at the colloquim are to be published together by the North-Holland Publishing Company under the editorship of Professor A. Heyting.