@inbook{6d63ee3d2e8641eeb337c50264cabf8a,
title = "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.",
author = "Olivier Bournez and Emmanuel Hainry",
year = "2004",
month = jan,
day = "1",
doi = "10.1007/978-3-540-27836-8\_25",
language = "English",
isbn = "3540228497",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "269--280",
editor = "Josep D{\'i}az and Juhani Karhum{\"a}ki and Arto Lepist{\"o} and Donald Sannella",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
}