Real recursive functions and real extensions of recursive functions

Olivier Bournez; Emmanuel Hainry

doi:10.1007/978-3-540-31834-7_9

Real recursive functions and real extensions of recursive functions

Olivier Bournez
, Emmanuel Hainry

LORIA Laboratoire Lorrain de Recherche en Informatique et ses Applications

Résultats de recherche: Contribution à un journal › Article de conférence › Revue par des pairs

Résumé

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a very natural unique minimization schema.

langue originale	Anglais
Pages (de - à)	116-127
Nombre de pages	12
journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3354
Les DOIs	https://doi.org/10.1007/978-3-540-31834-7_9
état	Publié - 1 janv. 2005
Modification externe	Oui
Evénement	4th International Conference on Machines, Computations, and Universality, MCU 2004 - Saint Petersburg, Russie Durée: 21 sept. 2004 → 24 sept. 2004

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10.1007/978-3-540-31834-7_9

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Real recursive functions and real extensions of recursive functions. / Bournez, Olivier; Hainry, Emmanuel.
Dans: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol 3354, 01.01.2005, p. 116-127.

Résultats de recherche: Contribution à un journal › Article de conférence › Revue par des pairs

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AU - Bournez, Olivier

AU - Hainry, Emmanuel

PY - 2005/1/1

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AB - Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a very natural unique minimization schema.

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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Real recursive functions and real extensions of recursive functions

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