Real Recursive Functions and Real Extensions of Recursive Functions
Identifieur interne : 004D26 ( Hal/Checkpoint ); précédent : 004D25; suivant : 004D27Real Recursive Functions and Real Extensions of Recursive Functions
Auteurs : Olivier Bournez [France] ; Emmanuel Hainry [France]Source :
Descripteurs français
Abstract
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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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.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Real Recursive Functions and Real Extensions of Recursive Functions</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@loria.fr</email><idno type="halauthor">130056</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author><author role="aut"><persName><forename type="first">Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@ens-lyon.org</email><idno type="idhal">emmanuel-hainry</idno><idno type="halauthor">130691</idno><orgName ref="#struct-364480"></orgName><affiliation ref="#struct-2360"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-09-26 10:13:44</date><date type="whenModified">2016-05-19 01:09:05</date><date type="whenReleased">2006-09-28 15:22:47</date><date type="whenProduced">2004</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00100053</idno><idno type="halUri">https://hal.inria.fr/inria-00100053</idno><idno type="halBibtex">bournez:inria-00100053</idno><idno type="halRefHtml">Machines and Universal Computations - MCU'2004, 2004, Saint-Petersburg, Russia, 12 p, 2004</idno><idno type="halRef">Machines and Universal Computations - MCU'2004, 2004, Saint-Petersburg, Russia, 12 p, 2004</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="commentary">Colloque avec actes et comité de lecture. internationale.</note><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Real Recursive Functions and Real Extensions of Recursive Functions</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@loria.fr</email><idno type="halAuthorId">130056</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author><author role="aut"><persName><forename type="first">Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@ens-lyon.org</email><idno type="idHal">emmanuel-hainry</idno><idno type="halAuthorId">130691</idno><orgName ref="#struct-364480"></orgName><affiliation ref="#struct-2360"></affiliation></author></analytic><monogr><idno type="localRef">A04-R-290 || bournez04c</idno><meeting><title>Machines and Universal Computations - MCU'2004</title><date type="start">2004</date><settlement>Saint-Petersburg, Russia</settlement></meeting><imprint><biblScope unit="pp">12 p</biblScope><date type="datePub">2004</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">modèles analogiques</term><term xml:lang="fr">computability</term><term xml:lang="fr">analog models</term><term xml:lang="fr">complexity</term><term xml:lang="fr">complexité</term><term xml:lang="fr">calculabilité</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">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.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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