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Some results in church's restricted recursive arithmetic1

Published online by Cambridge University Press:  12 March 2014

Joyce Friedman
Joyce Friedman*
Affiliation:
Washington, D.C.
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Extract

Alonzo Church has proposed a system of “restricted recursive arithmetic” for the analysis of computer circuits which include time delays and feedback. Restricted recursive arithmetic, which will be referred to as rra, was introduced by Church in this Journal, vol. 20 (1955), pp. 286–287, in a review of an article by Edmund C. Berkeley. It is the purpose of this paper to present some results which have been found for the system rra.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 22 , Issue 4 , December 1957 , pp. 337 - 342
Copyright
Copyright © Association for Symbolic Logic 1957

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Footnotes

1

This paper was prepared while I was employed at the Avion Division of ACF Industries, Inc., and was presented at a meeting of the Association for Symbolic Logic, December 29, 1955. I am greatly indebted to Professor Alonzo Church for his help in the development of this material.

References

2 (Added August 5, 1957.) The referee has pointed out that the system rra is equivalent to the earlier formulation of well-formed nets given in Burks, A. W. and Wright, J. B., Theory of logical nets, Proceedings of the Institute of Radio Engineers, vol. 41 (1953), pp. 1357–1365Google Scholar. Through this equivalence the present paper provides a solution to the decision problem for well-formed nets.

3 The symbol “V” is used for disjunction, and juxtaposition is used for conjunction.