Recursion Schemata for NC k
Identifieur interne : 004436 ( Main/Merge ); précédent : 004435; suivant : 004437Recursion Schemata for NC k
Auteurs : Guillaume Bonfante [France] ; Reinhard Kahle [Portugal] ; Jean-Yves Marion [France] ; Isabel Oitavem [Portugal]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We give a recursion-theoretic characterization of the complexity classes NC k for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computations (mutual in place recursion). This is, to our knowledge, the first exact characterization of NC k by function algebra over infinite domains in implicit complexity.
Url:
- https://api.istex.fr/ark:/67375/HCB-TLCQ16V6-Q/fulltext.pdf
- https://hal.archives-ouvertes.fr/hal-00342366
DOI: 10.1007/978-3-540-87531-4_6
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000B94
- to stream Istex, to step Curation: 000B87
- to stream Istex, to step Checkpoint: 000D53
- to stream Hal, to step Corpus: 004025
- to stream Hal, to step Curation: 004025
- to stream Hal, to step Checkpoint: 003162
Links to Exploration step
ISTEX:32CA99C052E4886821E24CD15D2C7F25693E27A1Le document en format XML
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CS 25233 - 54052 Nancy cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.univ-lorraine.fr/</ref></desc></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><settlement type="city">Metz</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université de Lorraine</orgName></affiliation></author><author><name sortKey="Oitavem, Isabel" sort="Oitavem, Isabel" uniqKey="Oitavem I" first="Isabel" last="Oitavem">Isabel Oitavem</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-83596" status="INCOMING"><orgName>Departamento de Informática</orgName><desc><address><country key="FR"></country></address><ref type="url">http://di.fct.unl.pt/</ref></desc><listRelation><relation active="#struct-300564" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300564" type="direct"><org type="institution" xml:id="struct-300564" status="VALID"><orgName>Universidade Nova de Lisboa</orgName><desc><address><country key="PT"></country></address><ref type="url">http://www.unl.pt/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author></analytic><idno type="DOI">10.1007/978-3-540-87531-4_6</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We give a recursion-theoretic characterization of the complexity classes NC k for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computations (mutual in place recursion). This is, to our knowledge, the first exact characterization of NC k by function algebra over infinite domains in implicit complexity.</div></front></TEI></HAL><ISTEX><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Recursion Schemata for NC k</title><author><name sortKey="Bonfante, Guillaume" sort="Bonfante, Guillaume" uniqKey="Bonfante G" first="Guillaume" last="Bonfante">Guillaume Bonfante</name></author><author><name sortKey="Kahle, Reinhard" sort="Kahle, Reinhard" uniqKey="Kahle R" first="Reinhard" last="Kahle">Reinhard Kahle</name></author><author><name sortKey="Marion, Jean Yves" sort="Marion, Jean Yves" uniqKey="Marion J" first="Jean-Yves" last="Marion">Jean-Yves Marion</name></author><author><name sortKey="Oitavem, Isabel" sort="Oitavem, Isabel" uniqKey="Oitavem I" first="Isabel" last="Oitavem">Isabel Oitavem</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:32CA99C052E4886821E24CD15D2C7F25693E27A1</idno><date when="2008" year="2008">2008</date><idno type="doi">10.1007/978-3-540-87531-4_6</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-TLCQ16V6-Q/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">000B94</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000B94</idno><idno type="wicri:Area/Istex/Curation">000B87</idno><idno type="wicri:Area/Istex/Checkpoint">000D53</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000D53</idno><idno type="wicri:doubleKey">0302-9743:2008:Bonfante G:recursion:schemata:for</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Recursion Schemata for NC<hi rend="superscript"><hi rend="italic">k</hi></hi></title><author><name sortKey="Bonfante, Guillaume" sort="Bonfante, Guillaume" uniqKey="Bonfante G" first="Guillaume" last="Bonfante">Guillaume Bonfante</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Loria - INPL, 615, rue du Jardin Botanique, BP-101, 54602, Villers-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Kahle, Reinhard" sort="Kahle, Reinhard" uniqKey="Kahle R" first="Reinhard" last="Kahle">Reinhard Kahle</name><affiliation wicri:level="1"><country xml:lang="fr">Portugal</country><wicri:regionArea>CENTRIA and DM, Universidade Nova de Lisboa, 2829-516, Caparica</wicri:regionArea><wicri:noRegion>Caparica</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Portugal</country></affiliation></author><author><name sortKey="Marion, Jean Yves" sort="Marion, Jean Yves" uniqKey="Marion J" first="Jean-Yves" last="Marion">Jean-Yves Marion</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Loria - INPL, 615, rue du Jardin Botanique, BP-101, 54602, Villers-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Oitavem, Isabel" sort="Oitavem, Isabel" uniqKey="Oitavem I" first="Isabel" last="Oitavem">Isabel Oitavem</name><affiliation wicri:level="1"><country xml:lang="fr">Portugal</country><wicri:regionArea>UNL and CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa</wicri:regionArea><wicri:noRegion>Lisboa</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Portugal</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We give a recursion-theoretic characterization of the complexity classes NC k for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computations (mutual in place recursion). This is, to our knowledge, the first exact characterization of NC k by function algebra over infinite domains in implicit complexity.</div></front></TEI></ISTEX></double></record>Pour manipuler ce document sous Unix (Dilib)
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