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Journal Articles Theoretical Computer Science Year : 2005

Elementarily Computable Functions Over the Real Numbers and R-Sub-Recursive Functions

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. This paper improves several previous partial characterizations and has a dual interest: • 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 and provide new insights for understanding the relations between several analog computational models.

Dates and versions

inria-00000518 , version 1 (26-10-2005)

Identifiers

Cite

Olivier Bournez, Emmanuel Hainry. Elementarily Computable Functions Over the Real Numbers and R-Sub-Recursive Functions. Theoretical Computer Science, 2005, 348 (2-3), pp.130--147. ⟨10.1016/j.tcs.2005.09.010⟩. ⟨inria-00000518⟩
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