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ICALP
2004
Springer

An Analog Characterization of Elementarily Computable Functions over the Real Numbers

13 years 8 months ago
An Analog Characterization of Elementarily Computable Functions over the Real Numbers
Abstract We present an analog and machine-independent algebraic characterization 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.
Olivier Bournez, Emmanuel Hainry
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where ICALP
Authors Olivier Bournez, Emmanuel Hainry
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