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Conference papers

An analog Characterization of Elementarily Computable Functions Over the Real Numbers

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 : 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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Submitted on : Tuesday, September 26, 2006 - 10:13:44 AM
Last modification on : Thursday, March 5, 2020 - 4:56:39 PM


  • HAL Id : inria-00100054, version 1



Olivier Bournez, Emmanuel Hainry. An analog Characterization of Elementarily Computable Functions Over the Real Numbers. 31st International Colloqiuim on Automata, Languages and Programming - ICALP'2004, 2004, Turku, Finland, pp.269-280. ⟨inria-00100054⟩



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