Recursion Schemata for NC k
Identifieur interne : 000B94 ( Istex/Corpus ); précédent : 000B93; suivant : 000B95Recursion Schemata for NC k
Auteurs : Guillaume Bonfante ; Reinhard Kahle ; Jean-Yves Marion ; Isabel OitavemSource :
- 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:
DOI: 10.1007/978-3-540-87531-4_6
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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). 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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). 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Robotics)</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="M24005" Priority="4" Type="Secondary">Mathematical Logic and Foundations</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Michael</GivenName><FamilyName>Kaminski</FamilyName></EditorName><Contact><Email>kaminski@cs.technion.ac.il</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Simone</GivenName><FamilyName>Martini</FamilyName></EditorName><Contact><Email>martini@cs.unibo.it</Email></Contact></Editor></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Contributed Papers</PartTitle><PartChapterCount>31</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Computer Science Logic</BookTitle></PartContext></PartInfo><Chapter ID="Chap6" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>6</ChapterID><ChapterDOI>10.1007/978-3-540-87531-4_6</ChapterDOI><ChapterSequenceNumber>6</ChapterSequenceNumber><ChapterTitle Language="En">Recursion Schemata for NC<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript></ChapterTitle><ChapterFirstPage>49</ChapterFirstPage><ChapterLastPage>63</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2008</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>2</PartID><BookID>978-3-540-87531-4</BookID><BookTitle>Computer Science Logic</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Guillaume</GivenName><FamilyName>Bonfante</FamilyName></AuthorName><Contact><Email>Guillaume.Bonfante@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Reinhard</GivenName><FamilyName>Kahle</FamilyName></AuthorName><Contact><Email>kahle@mat.uc.pt</Email></Contact></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Jean-Yves</GivenName><FamilyName>Marion</FamilyName></AuthorName><Contact><Email>Jean-Yves.Marion@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff3"><AuthorName DisplayOrder="Western"><GivenName>Isabel</GivenName><FamilyName>Oitavem</FamilyName></AuthorName><Contact><Email>isarocha@ptmat.fc.ul.pt</Email></Contact></Author><Affiliation ID="Aff1"><OrgName>Loria - INPL</OrgName><OrgAddress><Street>615, rue du Jardin Botanique</Street><Postbox>BP-101</Postbox><Postcode>54602</Postcode><City>Villers-lès-Nancy</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>CENTRIA and DM</OrgDivision><OrgName>Universidade Nova de Lisboa</OrgName><OrgAddress><Postcode>2829-516</Postcode><City>Caparica</City><Country>Portugal</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgDivision>UNL and CMAF</OrgDivision><OrgName>Universidade de Lisboa</OrgName><OrgAddress><Street>Av. Prof. Gama Pinto, 2</Street><Postcode>1649-003</Postcode><City>Lisboa</City><Country>Portugal</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We give a recursion-theoretic characterization of the complexity classes NC<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> for <Emphasis Type="Italic">k</Emphasis> ≥ 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<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> by function algebra over infinite domains in implicit complexity.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Research supported by the project <Emphasis Type="Italic">Teorias e linguagens de programação para computações com recursos limitados</Emphasis> within the <Emphasis Type="Italic">Programa PESSOA 2005/2006</Emphasis> of <Emphasis Type="Italic">GRICES - EGIDE</Emphasis> and partly by the FCT project POCI/MAT/61720/2004 and by DM, FCT-UNL.This work was complete while the first author visited CMAF, Universidade de Lisboa, and the support of the visit is gratefully acknowledged.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Recursion Schemata for NC k</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Recursion Schemata for NC k </title></titleInfo><name type="personal"><namePart type="given">Guillaume</namePart><namePart type="family">Bonfante</namePart><affiliation>Loria - INPL, 615, rue du Jardin Botanique, BP-101, 54602, Villers-lès-Nancy, France</affiliation><affiliation>E-mail: Guillaume.Bonfante@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Reinhard</namePart><namePart type="family">Kahle</namePart><affiliation>CENTRIA and DM, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal</affiliation><affiliation>E-mail: kahle@mat.uc.pt</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jean-Yves</namePart><namePart type="family">Marion</namePart><affiliation>Loria - INPL, 615, rue du Jardin Botanique, BP-101, 54602, Villers-lès-Nancy, France</affiliation><affiliation>E-mail: Jean-Yves.Marion@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Isabel</namePart><namePart type="family">Oitavem</namePart><affiliation>UNL and CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal</affiliation><affiliation>E-mail: isarocha@ptmat.fc.ul.pt</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2008</dateIssued><copyrightDate encoding="w3cdtf">2008</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract 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.</abstract><relatedItem type="host"><titleInfo><title>Computer Science Logic</title><subTitle>22nd International Workshop, CSL 2008, 17th Annual Conference of the EACSL, Bertinoro, Italy, September 16-19, 2008. 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