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Recursive Analysis Characterized as a Class of Real Recursive Functions

Olivier Bournez 1 Emmanuel Hainry 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimization and limit schema.
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https://hal.inria.fr/inria-00000515
Contributor : Olivier Bournez <>
Submitted on : Wednesday, October 26, 2005 - 6:51:51 PM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM

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Olivier Bournez, Emmanuel Hainry. Recursive Analysis Characterized as a Class of Real Recursive Functions. Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2006, 74 (4), pp.409-433. ⟨inria-00000515⟩

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