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A reduction theorem for normal algorithms1

Published online by Cambridge University Press:  12 March 2014

J. W. Swanson
J. W. Swanson*
Affiliation:
University of Massachusetts
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Extract

Markov's [2] notion of Normal Algorithm (NA), with which we assume familiarity, is the simplest of the better known ways of expressing the concept of algorithmicity. An NA consists of an ordered finite list of replacement formulae

The dots in parentheses indicate that a given replacement formula may be either simple (P → Q), or terminal (P → .Q). No restrictions are imposed on the lengths of the Pi and Qi in the replacement formulae, and the only rule of order of application is a priority rule to the effect that of several replacement formulae applicable to a word W at a given step, the earliest one is used.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 1 , March 1966 , pp. 86 - 97
Copyright
Copyright © Association for Symbolic Logic 1996

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Footnotes

1

The author wishes to express his gratitude to Professor Haskell B. Curry for his helpful criticism of an earlier draft of this paper.

References

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