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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 theoryOther Versions
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Citations of this work
Elementary explicit types and polynomial time operations.Daria Spescha & Thomas Strahm - 2009 - Mathematical Logic Quarterly 55 (3):245-258.
Weak Theories of Truth and Explicit Mathematics.Sebastian Eberhard & Thomas Strahm - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger, Logic, Construction, Computation. Berlin, Boston: De Gruyter. pp. 157-184.
Weak Theories of Operations and Types.Thomas Strahm - 2010 - In Ralf Schindler, Ways of Proof Theory. Berlin, Boston: De Gruyter. pp. 441-468.
Applicative theories for the polynomial hierarchy of time and its levels.Reinhard Kahle & Isabel Oitavem - 2013 - Annals of Pure and Applied Logic 164 (6):663-675.
References found in this work
Barendregt H. P.. The lambda calculus. Its syntax and semantics. Studies in logic and foundations of mathematics, vol. 103. North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1981, xiv + 615 pp.E. Engeler - 1984 - Journal of Symbolic Logic 49 (1):301-303.
Functional interpretations of feasibly constructive arithmetic.Stephen Cook & Alasdair Urquhart - 1993 - Annals of Pure and Applied Logic 63 (2):103-200.
Systems of explicit mathematics with non-constructive μ-operator. Part II.Solomon Feferman & Gerhard Jäger - 1996 - Annals of Pure and Applied Logic 79 (1):37-52.
Systems of explicit mathematics with non-constructive μ-operator. Part I.Solomon Feferman & Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 65 (3):243-263.
Totality in applicative theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.
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