Second-Order Logic over Finite Structures – Report on a Research Programme
Identifieur interne : 002299 ( Istex/Corpus ); précédent : 002298; suivant : 002300Second-Order Logic over Finite Structures – Report on a Research Programme
Auteurs : Georg GottlobSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: This paper reports about the results achieved so far in the context of a research programme at the cutting point of logic, formal language theory, and complexity theory. The aim of this research programme is to classify the complexity of evaluating formulas from different prefix classes of second-order logic over different types of finite structures, such as strings, graphs, or arbitrary structures. In particular, we report on classifications of second-order logic on strings and of existential second-order logic on graphs.
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DOI: 10.1007/978-3-540-25984-8_16
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ISTEX:959C346C4BEC0856416C1648C45906C5377CB885Le document en format XML
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type="first">Y.</forename><surname>Vardi</surname></persName><affiliation><orgName type="institution">Rice University</orgName><address><settlement>Houston</settlement><region>TX</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation><orgName type="institution">Max-Planck Institute of Computer Science</orgName><address><settlement>Saarbruecken</settlement><country key="DE">GERMANY</country></address></affiliation></editor><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>This paper reports about the results achieved so far in the context of a research programme at the cutting point of logic, formal language theory, and complexity theory. The aim of this research programme is to classify the complexity of evaluating formulas from different prefix classes of second-order logic over different types of finite structures, such as strings, graphs, or arbitrary structures. In particular, we report on classifications of second-order logic on strings and of existential second-order logic on graphs.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I21017</label><item><term type="Secondary" subtype="priority-1">Artificial Intelligence (incl. 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Saarland</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SubSeriesHeader></SubSeries><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-540-25984-8</BookID><BookTitle>Automated Reasoning</BookTitle><BookSubTitle>Second International Joint Conference, IJCAR 2004, Cork, Ireland, July 4-8, 2004. Proceedings</BookSubTitle><BookVolumeNumber>3097</BookVolumeNumber><BookSequenceNumber>3097</BookSequenceNumber><BookDOI>10.1007/b98691</BookDOI><BookTitleID>83243</BookTitleID><BookPrintISBN>978-3-540-22345-0</BookPrintISBN><BookElectronicISBN>978-3-540-25984-8</BookElectronicISBN><BookChapterCount>36</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I21017" Priority="1" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I16048" Priority="2" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I14029" Priority="4" Type="Secondary">Software Engineering</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID><SubSeriesID>1244</SubSeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>David</GivenName><FamilyName>Basin</FamilyName></EditorName><Contact><Email>basin@inf.ethz.ch</Email></Contact></Editor><Editor AffiliationIDS="Aff18"><EditorName DisplayOrder="Western"><GivenName>Michaël</GivenName><FamilyName>Rusinowitch</FamilyName></EditorName><Contact><Email>rusi@loria.fr</Email></Contact></Editor><Affiliation ID="Aff17"><OrgDivision>Information Security Group, Dep. of Computer Science</OrgDivision><OrgName>ETH</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgName>LORIA & INRIA Lorraine UMR 7503</OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part5"><PartInfo TocLevels="0"><PartID>5</PartID><PartSequenceNumber>5</PartSequenceNumber><PartTitle>Reasoning with Finite Structure</PartTitle><PartChapterCount>2</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Automated Reasoning</BookTitle></PartContext></PartInfo><Chapter ID="Chap16" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>16</ChapterID><ChapterDOI>10.1007/978-3-540-25984-8_16</ChapterDOI><ChapterSequenceNumber>16</ChapterSequenceNumber><ChapterTitle Language="En">Second-Order Logic over Finite Structures – Report on a Research Programme</ChapterTitle><ChapterFirstPage>229</ChapterFirstPage><ChapterLastPage>243</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</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>5</PartID><BookID>978-3-540-25984-8</BookID><BookTitle>Automated Reasoning</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Georg</GivenName><FamilyName>Gottlob</FamilyName></AuthorName><Contact><Email>gottlob@dbai.tuwien.ac.at</Email></Contact></Author><Affiliation ID="Aff19"><OrgDivision>Institut für Informationssysteme</OrgDivision><OrgName>Technische Universität Wien</OrgName><OrgAddress><Street>Favoritenstraße 9-11</Street><Postcode>A-1040</Postcode><City>Wien</City><Country>Austria</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>This paper reports about the results achieved so far in the context of a research programme at the cutting point of logic, formal language theory, and complexity theory. The aim of this research programme is to classify the complexity of evaluating formulas from different prefix classes of second-order logic over different types of finite structures, such as strings, graphs, or arbitrary structures. In particular, we report on classifications of second-order logic on strings and of existential second-order logic on graphs.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Most of the material contained in this paper stems, modulo editorial adaptations, from the much longer papers [9, 10, 12].</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Second-Order Logic over Finite Structures – Report on a Research Programme</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Second-Order Logic over Finite Structures – Report on a Research Programme</title></titleInfo><name type="personal"><namePart type="given">Georg</namePart><namePart type="family">Gottlob</namePart><affiliation>Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040, Wien, Austria</affiliation><affiliation>E-mail: gottlob@dbai.tuwien.ac.at</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">2004</dateIssued><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: This paper reports about the results achieved so far in the context of a research programme at the cutting point of logic, formal language theory, and complexity theory. The aim of this research programme is to classify the complexity of evaluating formulas from different prefix classes of second-order logic over different types of finite structures, such as strings, graphs, or arbitrary structures. In particular, we report on classifications of second-order logic on strings and of existential second-order logic on graphs.</abstract><relatedItem type="host"><titleInfo><title>Automated Reasoning</title><subTitle>Second International Joint Conference, IJCAR 2004, Cork, Ireland, July 4-8, 2004. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="family">Basin</namePart><affiliation>Information Security Group, Dep. of Computer Science, ETH, Zurich, Switzerland</affiliation><affiliation>E-mail: basin@inf.ethz.ch</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Michaël</namePart><namePart type="family">Rusinowitch</namePart><affiliation>LORIA & INRIA Lorraine UMR 7503, </affiliation><affiliation>E-mail: rusi@loria.fr</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">2004</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="I21017">Artificial Intelligence (incl. 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type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart 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