Recursive Analysis Characterized as a Class of Real Recursive Functions
Identifieur interne : 004026 ( Hal/Corpus ); précédent : 004025; suivant : 004027Recursive Analysis Characterized as a Class of Real Recursive Functions
Auteurs : Olivier Bournez ; Emmanuel HainrySource :
- Fundamenta Informaticae [ 0169-2968 ] ; 2006.
Abstract
Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimization and limit schema.
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<front><div type="abstract" xml:lang="en">Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimization and limit schema.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Recursive Analysis Characterized as a Class of Real 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">63964</idno>
<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">63965</idno>
<affiliation ref="#struct-2360"></affiliation>
</author>
</analytic>
<monogr><idno type="halJournalId" status="VALID">20891</idno>
<idno type="issn">0169-2968</idno>
<title level="j">Fundamenta Informaticae</title>
<imprint><publisher>Polskie Towarzystwo Matematyczne</publisher>
<biblScope unit="volume">74</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="pp">409-433</biblScope>
<date type="datePub">2006</date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><classCode scheme="halTypology" n="ART">Journal articles</classCode>
</textClass>
<abstract xml:lang="en">Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixing the two approaches we prove that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimization and limit schema.</abstract>
</profileDesc>
</hal>
</record>
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