Real Recursive Functions and Real Extensions of Recursive Functions
Identifieur interne : 003F60 ( Hal/Corpus ); précédent : 003F59; suivant : 003F61Real Recursive Functions and Real Extensions of Recursive Functions
Auteurs : Olivier Bournez ; Emmanuel HainrySource :
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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<front><div type="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.</div>
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<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>
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