Complexity Classes and Rewrite Systems with Polynomial Interpretation
Identifieur interne : 002968 ( Istex/Corpus ); précédent : 002967; suivant : 002969Complexity Classes and Rewrite Systems with Polynomial Interpretation
Auteurs : G. Bonfante ; A. Cichon ; J. Y. Marion ; H. TouzetSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the poly-time, linear exponential-time and doubly linear exponential time computable functions. As a consequence, we also characterize the linear space computable functions.
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DOI: 10.1007/10703163_25
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ISTEX:AFE957BF88B07F168C00C072A9C8D10516D97ED8Le document en format XML
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This leads to the definition of three classes, which turn out to be exactly the poly-time, linear exponential-time and doubly linear exponential time computable functions. As a consequence, we also characterize the linear space computable functions.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>G. Bonfante</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</json:string><json:string>E-mail: bonfante@loria.fr</json:string></affiliations></json:item><json:item><name>A. Cichon</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</json:string><json:string>E-mail: cichon@loria.fr</json:string></affiliations></json:item><json:item><name>J. Y Marion</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</json:string><json:string>E-mail: marionjy@loria.fr</json:string></affiliations></json:item><json:item><name>H. Touzet</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</json:string><json:string>E-mail: touzet@loria.fr</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-369QCZWC-M</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. 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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><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Georg</GivenName><FamilyName>Gottlob</FamilyName></EditorName><Contact><Email>georg.gottlob@comlab.ox.ac.uk</Email></Contact></Editor><Editor AffiliationIDS="Aff5"><EditorName DisplayOrder="Western"><GivenName>Etienne</GivenName><FamilyName>Grandjean</FamilyName></EditorName><Contact><Email>grandjean@info.unicaen.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff6"><EditorName DisplayOrder="Western"><GivenName>Katrin</GivenName><FamilyName>Seyr</FamilyName></EditorName></Editor><Affiliation ID="Aff4"><OrgDivision>Computing Laboratory</OrgDivision><OrgName>Oxford University</OrgName><OrgAddress><Street>Wolfson Building Parks Road Oxford,</Street><Postcode>OX1 3QD</Postcode><Country>United Kingdom</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgDivision>GREYC</OrgDivision><OrgName>Université de Caen, CNRS</OrgName><OrgAddress><Street>Campus 2</Street><Postcode>F-14032</Postcode><City>Caen cedex</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName> </OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Contributed Papers</PartTitle><PartChapterCount>25</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Computer Science Logic</BookTitle></PartContext></PartInfo><Chapter ID="Chap25" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>25</ChapterID><ChapterDOI>10.1007/10703163_25</ChapterDOI><ChapterSequenceNumber>25</ChapterSequenceNumber><ChapterTitle Language="En">Complexity Classes and Rewrite Systems with Polynomial Interpretation</ChapterTitle><ChapterFirstPage>372</ChapterFirstPage><ChapterLastPage>384</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>1999</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>978-3-540-48855-2</BookID><BookTitle>Computer Science Logic</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>G.</GivenName><FamilyName>Bonfante</FamilyName></AuthorName><Contact><Email>bonfante@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><FamilyName>Cichon</FamilyName></AuthorName><Contact><Email>cichon@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>J.</GivenName><GivenName>Y</GivenName><FamilyName>Marion</FamilyName></AuthorName><Contact><Email>marionjy@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>H.</GivenName><FamilyName>Touzet</FamilyName></AuthorName><Contact><Email>touzet@loria.fr</Email></Contact></Author><Affiliation ID="Aff7"><OrgName>Loria, Calligramme project</OrgName><OrgAddress><Postbox>B.P. 239</Postbox><Postcode>54506</Postcode><City>Vandœuvre-lès-Nancy Cedex</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the poly-time, linear exponential-time and doubly linear exponential time computable functions. As a consequence, we also characterize the linear space computable functions.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Complexity Classes and Rewrite Systems with Polynomial Interpretation</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Complexity Classes and Rewrite Systems with Polynomial Interpretation</title></titleInfo><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Bonfante</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: bonfante@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Cichon</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: cichon@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="given">Y</namePart><namePart type="family">Marion</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: marionjy@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">H.</namePart><namePart type="family">Touzet</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: touzet@loria.fr</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">1999</dateIssued><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the poly-time, linear exponential-time and doubly linear exponential time computable functions. As a consequence, we also characterize the linear space computable functions.</abstract><relatedItem type="host"><titleInfo><title>Computer Science Logic</title><subTitle>12th International Workshop, CSL’98, Annual Conference of the EACSL, Brno, Czech Republic, August 24-28, 1998. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Georg</namePart><namePart type="family">Gottlob</namePart><affiliation>Computing Laboratory, Oxford University, Wolfson Building Parks Road Oxford,, OX1 3QD, United Kingdom</affiliation><affiliation>E-mail: georg.gottlob@comlab.ox.ac.uk</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Etienne</namePart><namePart type="family">Grandjean</namePart><affiliation>GREYC, Université de Caen, CNRS, Campus 2, F-14032, Caen cedex, France</affiliation><affiliation>E-mail: grandjean@info.unicaen.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Katrin</namePart><namePart type="family">Seyr</namePart><affiliation> , </affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1999</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="M24005">Mathematical Logic and Foundations</topic></subject><identifier type="DOI">10.1007/10703163</identifier><identifier type="ISBN">978-3-540-65922-8</identifier><identifier type="eISBN">978-3-540-48855-2</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">59608</identifier><identifier type="BookID">978-3-540-48855-2</identifier><identifier type="BookChapterCount">28</identifier><identifier type="BookVolumeNumber">1584</identifier><identifier type="BookSequenceNumber">1584</identifier><identifier type="PartChapterCount">25</identifier><part><date>1999</date><detail type="part"><title>Contributed Papers</title></detail><detail type="volume"><number>1584</number><caption>vol.</caption></detail><extent unit="pages"><start>372</start><end>384</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><affiliation>Karlsruhe University, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><affiliation>Cornell University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><affiliation>Utrecht University, The Netherlands</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1999</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></relatedItem><identifier type="istex">AFE957BF88B07F168C00C072A9C8D10516D97ED8</identifier><identifier type="ark">ark:/67375/HCB-369QCZWC-M</identifier><identifier type="DOI">10.1007/10703163_25</identifier><identifier type="ChapterID">25</identifier><identifier type="ChapterID">Chap25</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 1999</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-RLRX46XW-4">springer</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 1999</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-369QCZWC-M/record.json</uri></json:item></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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