Polynomial time operations in explicit mathematics

Journal of Symbolic Logic 62 (2):575-594 (1997)

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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DOI 10.2307/2275547
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References found in this work BETA

The Lambda Calculus. Its Syntax and Semantics.H. P. Barendregt - 1984 - Journal of Symbolic Logic 49 (1):301-303.
Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

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Elementary Explicit Types and Polynomial Time Operations.Daria Spescha & Thomas Strahm - 2009 - Mathematical Logic Quarterly 55 (3):245-258.
Definedness.Solomon Feferman - 1995 - Erkenntnis 43 (3):295 - 320.

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