InforLorV4, PascalFrancis, Corpus, bibRecord, 000568

Real recursive functions and real extensions of recursive functions

Identifieur interne : 000568 ( PascalFrancis/Corpus ); précédent : 000567; suivant : 000569

Real recursive functions and real extensions of recursive functions

Auteurs : Olivier Bournez ; Emmanuel Hainry

Source :

Lecture notes in computer science [ 0302-9743 ] ; 2005.

RBID : Pascal:05-0283136

Descripteurs français

Pascal (Inist)
- Fonction récursive, Fonction réelle, Minimisation.

English descriptors

KwdEn :
- Minimization, Real function, Recursive function.

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.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

A01	`01`	`1`		`@0 0302-9743`
A05				`@2 3354`
A08	`01`	`1`	`ENG`	`@1 Real recursive functions and real extensions of recursive functions`
A09	`01`	`1`	`ENG`	`@1 MCU : machines, computations, and universality : Saint Petersburg, 21-24 September 2004, revised selected papers`
A11	`01`	`1`		`@1 BOURNEZ (Olivier)`
A11	`02`	`1`		`@1 HAINRY (Emmanuel)`
A12	`01`	`1`		`@1 MARGENSTERN (Maurice) @9 ed.`
A14	`01`			`@1 LORIA/INRIA, 615 Rue du Jardin Botanique @2 54602 Villers-Lès-Nancy @3 FRA @Z 1 aut. @Z 2 aut.`
A20				`@1 116-127`
A21				`@1 2005`
A23	`01`			`@0 ENG`
A26	`01`			`@0 3-540-25261-4`
A43	`01`			`@1 INIST @2 16343 @5 354000124477780090`
A44				`@0 0000 @1 © 2005 INIST-CNRS. All rights reserved.`
A45				`@0 32 ref.`
A47	`01`	`1`		`@0 05-0283136`
A60				`@1 P @2 C`
A61				`@0 A`
A64	`01`	`1`		`@0 Lecture notes in computer science`
A66	`01`			`@0 DEU`
C01	`01`		`ENG`	@0 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.
C02	`01`	`X`		`@0 001D02A05`
C03	`01`	`X`	`FRE`	`@0 Fonction récursive @5 06`
C03	`01`	`X`	`ENG`	`@0 Recursive function @5 06`
C03	`01`	`X`	`SPA`	`@0 Función recursiva @5 06`
C03	`02`	`X`	`FRE`	`@0 Fonction réelle @5 23`
C03	`02`	`X`	`ENG`	`@0 Real function @5 23`
C03	`02`	`X`	`SPA`	`@0 Función real @5 23`
C03	`03`	`X`	`FRE`	`@0 Minimisation @5 24`
C03	`03`	`X`	`ENG`	`@0 Minimization @5 24`
C03	`03`	`X`	`SPA`	`@0 Minimización @5 24`
N21				`@1 199`
N44	`01`			`@1 OTO`
N82				`@1 OTO`

A30	`01`	`1`	`ENG`	`@1 Machines, computations, and universality. International conference @2 4 @3 Saint Petersburg RUS @4 2004-09-21`

Format Inist (serveur)

NO :	PASCAL 05-0283136 INIST
ET :	Real recursive functions and real extensions of recursive functions
AU :	BOURNEZ (Olivier); HAINRY (Emmanuel); MARGENSTERN (Maurice)
AF :	LORIA/INRIA, 615 Rue du Jardin Botanique/54602 Villers-Lès-Nancy/France (1 aut., 2 aut.)
DT :	Publication en série; Congrès; Niveau analytique
SO :	Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2005; Vol. 3354; Pp. 116-127; Bibl. 32 ref.
LA :	Anglais
EA :	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.
CC :	001D02A05
FD :	Fonction récursive; Fonction réelle; Minimisation
ED :	Recursive function; Real function; Minimization
SD :	Función recursiva; Función real; Minimización
LO :	INIST-16343.354000124477780090
ID :	05-0283136

Links to Exploration step

Pascal:05-0283136

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Real recursive functions and real extensions of recursive functions</title>
<author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name>
<affiliation><inist:fA14 i1="01"><s1>LORIA/INRIA, 615 Rue du Jardin Botanique</s1>
<s2>54602 Villers-Lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
<author><name sortKey="Hainry, Emmanuel" sort="Hainry, Emmanuel" uniqKey="Hainry E" first="Emmanuel" last="Hainry">Emmanuel Hainry</name>
<affiliation><inist:fA14 i1="01"><s1>LORIA/INRIA, 615 Rue du Jardin Botanique</s1>
<s2>54602 Villers-Lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">05-0283136</idno>
<date when="2005">2005</date>
<idno type="stanalyst">PASCAL 05-0283136 INIST</idno>
<idno type="RBID">Pascal:05-0283136</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">000568</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Real recursive functions and real extensions of recursive functions</title>
<author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name>
<affiliation><inist:fA14 i1="01"><s1>LORIA/INRIA, 615 Rue du Jardin Botanique</s1>
<s2>54602 Villers-Lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
<author><name sortKey="Hainry, Emmanuel" sort="Hainry, Emmanuel" uniqKey="Hainry E" first="Emmanuel" last="Hainry">Emmanuel Hainry</name>
<affiliation><inist:fA14 i1="01"><s1>LORIA/INRIA, 615 Rue du Jardin Botanique</s1>
<s2>54602 Villers-Lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Lecture notes in computer science</title>
<idno type="ISSN">0302-9743</idno>
<imprint><date when="2005">2005</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Lecture notes in computer science</title>
<idno type="ISSN">0302-9743</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Minimization</term>
<term>Real function</term>
<term>Recursive function</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Fonction récursive</term>
<term>Fonction réelle</term>
<term>Minimisation</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<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>
</front>
</TEI>
<inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0302-9743</s0>
</fA01>
<fA05><s2>3354</s2>
</fA05>
<fA08 i1="01" i2="1" l="ENG"><s1>Real recursive functions and real extensions of recursive functions</s1>
</fA08>
<fA09 i1="01" i2="1" l="ENG"><s1>MCU : machines, computations, and universality : Saint Petersburg, 21-24 September 2004, revised selected papers</s1>
</fA09>
<fA11 i1="01" i2="1"><s1>BOURNEZ (Olivier)</s1>
</fA11>
<fA11 i1="02" i2="1"><s1>HAINRY (Emmanuel)</s1>
</fA11>
<fA12 i1="01" i2="1"><s1>MARGENSTERN (Maurice)</s1>
<s9>ed.</s9>
</fA12>
<fA14 i1="01"><s1>LORIA/INRIA, 615 Rue du Jardin Botanique</s1>
<s2>54602 Villers-Lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</fA14>
<fA20><s1>116-127</s1>
</fA20>
<fA21><s1>2005</s1>
</fA21>
<fA23 i1="01"><s0>ENG</s0>
</fA23>
<fA26 i1="01"><s0>3-540-25261-4</s0>
</fA26>
<fA43 i1="01"><s1>INIST</s1>
<s2>16343</s2>
<s5>354000124477780090</s5>
</fA43>
<fA44><s0>0000</s0>
<s1>© 2005 INIST-CNRS. All rights reserved.</s1>
</fA44>
<fA45><s0>32 ref.</s0>
</fA45>
<fA47 i1="01" i2="1"><s0>05-0283136</s0>
</fA47>
<fA60><s1>P</s1>
<s2>C</s2>
</fA60>
<fA61><s0>A</s0>
</fA61>
<fA64 i1="01" i2="1"><s0>Lecture notes in computer science</s0>
</fA64>
<fA66 i1="01"><s0>DEU</s0>
</fA66>
<fC01 i1="01" l="ENG"><s0>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.</s0>
</fC01>
<fC02 i1="01" i2="X"><s0>001D02A05</s0>
</fC02>
<fC03 i1="01" i2="X" l="FRE"><s0>Fonction récursive</s0>
<s5>06</s5>
</fC03>
<fC03 i1="01" i2="X" l="ENG"><s0>Recursive function</s0>
<s5>06</s5>
</fC03>
<fC03 i1="01" i2="X" l="SPA"><s0>Función recursiva</s0>
<s5>06</s5>
</fC03>
<fC03 i1="02" i2="X" l="FRE"><s0>Fonction réelle</s0>
<s5>23</s5>
</fC03>
<fC03 i1="02" i2="X" l="ENG"><s0>Real function</s0>
<s5>23</s5>
</fC03>
<fC03 i1="02" i2="X" l="SPA"><s0>Función real</s0>
<s5>23</s5>
</fC03>
<fC03 i1="03" i2="X" l="FRE"><s0>Minimisation</s0>
<s5>24</s5>
</fC03>
<fC03 i1="03" i2="X" l="ENG"><s0>Minimization</s0>
<s5>24</s5>
</fC03>
<fC03 i1="03" i2="X" l="SPA"><s0>Minimización</s0>
<s5>24</s5>
</fC03>
<fN21><s1>199</s1>
</fN21>
<fN44 i1="01"><s1>OTO</s1>
</fN44>
<fN82><s1>OTO</s1>
</fN82>
</pA>
<pR><fA30 i1="01" i2="1" l="ENG"><s1>Machines, computations, and universality. International conference</s1>
<s2>4</s2>
<s3>Saint Petersburg RUS</s3>
<s4>2004-09-21</s4>
</fA30>
</pR>
</standard>
<server><NO>PASCAL 05-0283136 INIST</NO>
<ET>Real recursive functions and real extensions of recursive functions</ET>
<AU>BOURNEZ (Olivier); HAINRY (Emmanuel); MARGENSTERN (Maurice)</AU>
<AF>LORIA/INRIA, 615 Rue du Jardin Botanique/54602 Villers-Lès-Nancy/France (1 aut., 2 aut.)</AF>
<DT>Publication en série; Congrès; Niveau analytique</DT>
<SO>Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2005; Vol. 3354; Pp. 116-127; Bibl. 32 ref.</SO>
<LA>Anglais</LA>
<EA>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.</EA>
<CC>001D02A05</CC>
<FD>Fonction récursive; Fonction réelle; Minimisation</FD>
<ED>Recursive function; Real function; Minimization</ED>
<SD>Función recursiva; Función real; Minimización</SD>
<LO>INIST-16343.354000124477780090</LO>
<ID>05-0283136</ID>
</server>
</inist>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/PascalFrancis/Corpus

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000568 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Corpus/biblio.hfd -nk 000568 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    PascalFrancis
   |étape=   Corpus
   |type=    RBID
   |clé=     Pascal:05-0283136
   |texte=   Real recursive functions and real extensions of recursive functions
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

Real recursive functions and real extensions of recursive functions

Real recursive functions and real extensions of recursive functions

Source :

Descripteurs français

English descriptors

Abstract

Notice en format standard (ISO 2709)

Format Inist (serveur)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri