An analog Characterization of Elementarily Computable Functions Over the Real Numbers
Identifieur interne : 006872 ( Main/Exploration ); précédent : 006871; suivant : 006873An analog Characterization of Elementarily Computable Functions Over the Real Numbers
Auteurs : Olivier Bournez ; Emmanuel HainrySource :
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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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