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Polynomial Time Operations in Explicit Mathematics

Thomas Strahm
The Journal of Symbolic Logic
Vol. 62, No. 2 (Jun., 1997), pp. 575-594
DOI: 10.2307/2275547
Stable URL: http://www.jstor.org/stable/2275547
Page Count: 20
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Polynomial Time Operations in Explicit Mathematics
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Abstract

In this paper we study (self)-applicative theories of operations and binary words in the context of polynomial time computability. We propose a first order theory PTO which allows full self-application and whose provably total functions on W = {0, 1}* are exactly the polynomial time computable functions. Our treatment of PTO is proof-theoretic and very much in the spirit of reductive proof theory.

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