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Communication Dans Un Congrès Année : 2004

An analog Characterization of Elementarily Computable Functions Over the Real Numbers

Résumé

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.

Domaines

Autre [cs.OH]
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Dates et versions

inria-00100054 , version 1 (26-09-2006)

Identifiants

  • HAL Id : inria-00100054 , version 1

Citer

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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