Recursive Analysis Characterized as a Class of Real Recursive Functions
Identifieur interne : 005230 ( Main/Exploration ); précédent : 005229; suivant : 005231Recursive Analysis Characterized as a Class of Real Recursive Functions
Auteurs : Olivier Bournez [France] ; Emmanuel Hainry [France]Source :
- 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.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
Links toward previous steps (curation, corpus...)
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Le document en format XML
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type="ISSN">0169-2968</idno><imprint><date type="datePub">2006</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><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></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name></region><name sortKey="Hainry, Emmanuel" sort="Hainry, Emmanuel" uniqKey="Hainry E" first="Emmanuel" last="Hainry">Emmanuel Hainry</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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