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Conference Papers Year : 2004

An analog Characterization of Elementarily Computable Functions Over the Real Numbers

Abstract

We present an analog and machine-independent algebraic characterizations of elementarily computable functions over the real numbers in the sense of recursive analysis: we prove that they correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema. We generalize this result to all higher levels of the Grzegorczyk Hierarchy. Concerning recursive analysis, our results provide machine-independent characterizations of natural classes of computable functions over the real numbers, allowing to define these classes without usual considerations on higher-order (type 2) Turing machines. Concerning analog models, our results provide a characterization of the power of a natural class of analog models over the real numbers.
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Dates and versions

inria-00099897 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00099897 , version 1

Cite

Olivier Bournez, Emmanuel Hainry. An analog Characterization of Elementarily Computable Functions Over the Real Numbers. 2nd APPSEM II Workshop - APPSEM'2004, 2004, Tallinn, Estonia, 12 p. ⟨inria-00099897⟩
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