Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi
Identifieur interne : 001454 ( Istex/Corpus ); précédent : 001453; suivant : 001455Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi
Auteurs : Flemming Nielson ; Hanne Riis Nielson ; Helmut SeidlSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2002.
Abstract
Abstract: We exhibit a rich class of Horn clauses, which we call $$ \mathcal{H}_{\text{1}} $$ , whose least models, though possibly infinite, can be computed effectively. We show that the least model of an $$ \mathcal{H}_{\text{1}} $$ clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of $$ \mathcal{H}_{\text{1}} $$ clauses, which we call $$ \mathcal{H}_{\text{2}} $$ , where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside $$ \mathcal{H}_{\text{2}} $$ , we exhibit a fragment $$ \mathcal{H}_{\text{3}} $$ where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].
Url:
DOI: 10.1007/3-540-45789-5_5
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We show that the least model of an $$ \mathcal{H}_{\text{1}} $$ clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of $$ \mathcal{H}_{\text{1}} $$ clauses, which we call $$ \mathcal{H}_{\text{2}} $$ , where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside $$ \mathcal{H}_{\text{2}} $$ , we exhibit a fragment $$ \mathcal{H}_{\text{3}} $$ where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Flemming Nielson</name><affiliations><json:string>Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark</json:string><json:string>E-mail: nielson@imm.dtu.dk</json:string></affiliations></json:item><json:item><name>Hanne Riis Nielson</name><affiliations><json:string>Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark</json:string><json:string>E-mail: riis@imm.dtu.dk</json:string></affiliations></json:item><json:item><name>Helmut Seidl</name><affiliations><json:string>Universität Trier, FB IV - Informatik, D-54286, Trier, Germany</json:string><json:string>E-mail: seidl@uni-trier.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We exhibit a rich class of Horn clauses, which we call $$ \mathcal{H}_{\text{1}} $$ , whose least models, though possibly infinite, can be computed effectively. 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We show that the least model of an $$ \mathcal{H}_{\text{1}} $$ clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of $$ \mathcal{H}_{\text{1}} $$ clauses, which we call $$ \mathcal{H}_{\text{2}} $$ , where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside $$ \mathcal{H}_{\text{2}} $$ , we exhibit a fragment $$ \mathcal{H}_{\text{3}} $$ where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>I</label><label>I14037</label><label>I1603X</label><label>I14029</label><label>I16048</label><label>I14010</label><item><term>Computer Science</term></item><item><term>Programming Languages, Compilers, Interpreters</term></item><item><term>Logics and Meanings of Programs</term></item><item><term>Software Engineering</term></item><item><term>Mathematical Logic and Formal Languages</term></item><item><term>Programming Techniques</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2002-09-05">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References 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Language="En">Lecture Notes in Computer Science</SeriesTitle></SeriesInfo><SeriesHeader><EditorGroup><Editor AffiliationIDS="Aff1"><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Goos</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff2"><EditorName DisplayOrder="Western"><GivenName>Juris</GivenName><FamilyName>Hartmanis</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff3"><EditorName DisplayOrder="Western"><GivenName>Jan</GivenName><Particle>van</Particle><FamilyName>Leeuwen</FamilyName></EditorName></Editor><Affiliation ID="Aff1"><OrgName>Karlsruhe University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Cornell University</OrgName><OrgAddress><City>NY</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>Utrecht University</OrgName><OrgAddress><Country>The Netherlands</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="Unnumbered" TocLevels="0"><BookID>3-540-45789-5</BookID><BookTitle>Static Analysis</BookTitle><BookSubTitle>9th International Symposium, SAS 2002 Madrid, Spain, September 17–20, 2002 Proceedings</BookSubTitle><BookVolumeNumber>2477</BookVolumeNumber><BookSequenceNumber>2477</BookSequenceNumber><BookDOI>10.1007/3-540-45789-5</BookDOI><BookTitleID>72502</BookTitleID><BookPrintISBN>978-3-540-44235-6</BookPrintISBN><BookElectronicISBN>978-3-540-45789-3</BookElectronicISBN><BookChapterCount>35</BookChapterCount><BookHistory><OnlineDate><Year>2002</Year><Month>9</Month><Day>5</Day></OnlineDate></BookHistory><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2002</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I14037" Priority="1" Type="Secondary">Programming Languages, Compilers, Interpreters</BookSubject><BookSubject Code="I1603X" Priority="2" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I14029" Priority="3" Type="Secondary">Software Engineering</BookSubject><BookSubject Code="I16048" Priority="4" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I14010" Priority="5" Type="Secondary">Programming Techniques</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Manuel</GivenName><GivenName>V.</GivenName><FamilyName>Hermenegildo</FamilyName></EditorName><Contact><Email>herme@fi.upm.es</Email></Contact></Editor><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Germán</GivenName><FamilyName>Puebla</FamilyName></EditorName><Contact><Email>german@fi.upm.es</Email></Contact></Editor><Affiliation ID="Aff4"><OrgDivision>Department of Computer Science Facultad de Informática</OrgDivision><OrgName>Technical University of Madrid</OrgName><OrgAddress><Street>Campus de Montegancedo</Street><Postcode>28660</Postcode><City>Boadilla del Monte, Madrid</City><Country>Spain</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap5" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" Language="En" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>5</ChapterID><ChapterDOI>10.1007/3-540-45789-5_5</ChapterDOI><ChapterSequenceNumber>5</ChapterSequenceNumber><ChapterTitle Language="En">Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi</ChapterTitle><ChapterFirstPage>20</ChapterFirstPage><ChapterLastPage>35</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2002</CopyrightYear></ChapterCopyright><ChapterHistory><RegistrationDate><Year>2002</Year><Month>9</Month><Day>4</Day></RegistrationDate><OnlineDate><Year>2002</Year><Month>9</Month><Day>5</Day></OnlineDate></ChapterHistory><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><BookID>3-540-45789-5</BookID><BookTitle>Static Analysis</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff5"><AuthorName DisplayOrder="Western"><GivenName>Flemming</GivenName><FamilyName>Nielson</FamilyName></AuthorName><Contact><Email>nielson@imm.dtu.dk</Email></Contact></Author><Author AffiliationIDS="Aff5"><AuthorName DisplayOrder="Western"><GivenName>Hanne</GivenName><GivenName>Riis</GivenName><FamilyName>Nielson</FamilyName></AuthorName><Contact><Email>riis@imm.dtu.dk</Email></Contact></Author><Author AffiliationIDS="Aff6"><AuthorName DisplayOrder="Western"><GivenName>Helmut</GivenName><FamilyName>Seidl</FamilyName></AuthorName><Contact><Email>seidl@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff5"><OrgDivision>Informatics and Mathematical Modelling</OrgDivision><OrgName>Technical University of Denmark</OrgName><OrgAddress><Postcode>DK-2800</Postcode><City>Kongens Lyngby</City><Country>Denmark</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Universität Trier, FB IV - Informatik</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We exhibit a rich class of Horn clauses, which we call <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{1}} $$</EquationSource></InlineEquation>, whose least models, though possibly infinite, can be computed effectively. We show that the least model of an <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq2.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{1}} $$</EquationSource></InlineEquation> clause consists of so-called <Emphasis Type="Italic">strongly</Emphasis> recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of <InlineEquation ID="IEq3"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq3.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{1}} $$</EquationSource></InlineEquation> clauses, which we call <InlineEquation ID="IEq4"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq4.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{2}} $$</EquationSource></InlineEquation>, where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside <InlineEquation ID="IEq5"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq5.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{2}} $$</EquationSource></InlineEquation>, we exhibit a fragment <InlineEquation ID="IEq6"><InlineMediaObject><ImageObject FileRef="3-540-45789-5_5_Chapter_TeX2GIFIEq6.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$$ \mathcal{H}_{\text{3}} $$</EquationSource></InlineEquation> where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Program analysis</Keyword><Keyword>uniform Horn clauses</Keyword><Keyword>strongly recognizable relations</Keyword><Keyword>Spi calculus</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi</title></titleInfo><name type="personal"><namePart type="given">Flemming</namePart><namePart type="family">Nielson</namePart><affiliation>Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark</affiliation><affiliation>E-mail: nielson@imm.dtu.dk</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Hanne</namePart><namePart type="given">Riis</namePart><namePart type="family">Nielson</namePart><affiliation>Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark</affiliation><affiliation>E-mail: riis@imm.dtu.dk</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Helmut</namePart><namePart type="family">Seidl</namePart><affiliation>Universität Trier, FB IV - Informatik, D-54286, Trier, Germany</affiliation><affiliation>E-mail: seidl@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2002-09-05</dateIssued><copyrightDate encoding="w3cdtf">2002</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: We exhibit a rich class of Horn clauses, which we call $$ \mathcal{H}_{\text{1}} $$ , whose least models, though possibly infinite, can be computed effectively. We show that the least model of an $$ \mathcal{H}_{\text{1}} $$ clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of $$ \mathcal{H}_{\text{1}} $$ clauses, which we call $$ \mathcal{H}_{\text{2}} $$ , where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside $$ \mathcal{H}_{\text{2}} $$ , we exhibit a fragment $$ \mathcal{H}_{\text{3}} $$ where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].</abstract><relatedItem type="host"><titleInfo><title>Static Analysis</title><subTitle>9th International Symposium, SAS 2002 Madrid, Spain, September 17–20, 2002 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Manuel</namePart><namePart type="given">V.</namePart><namePart type="family">Hermenegildo</namePart><affiliation>Department of Computer Science Facultad de Informática, Technical University of Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain</affiliation><affiliation>E-mail: herme@fi.upm.es</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Germán</namePart><namePart type="family">Puebla</namePart><affiliation>Department of Computer Science Facultad de Informática, Technical University of Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain</affiliation><affiliation>E-mail: german@fi.upm.es</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2002</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="I14037">Programming Languages, Compilers, Interpreters</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I14029">Software Engineering</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I14010">Programming Techniques</topic></subject><identifier type="DOI">10.1007/3-540-45789-5</identifier><identifier type="ISBN">978-3-540-44235-6</identifier><identifier type="eISBN">978-3-540-45789-3</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="BookTitleID">72502</identifier><identifier type="BookID">3-540-45789-5</identifier><identifier type="BookChapterCount">35</identifier><identifier type="BookVolumeNumber">2477</identifier><identifier type="BookSequenceNumber">2477</identifier><part><date>2002</date><detail type="volume"><number>2477</number><caption>vol.</caption></detail><extent unit="pages"><start>20</start><end>35</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2002</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><copyrightDate encoding="w3cdtf">2002</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2002</recordOrigin></recordInfo></relatedItem><identifier type="istex">86E718368D98B82C7571E0E8936C2D6F2896A139</identifier><identifier type="DOI">10.1007/3-540-45789-5_5</identifier><identifier type="ChapterID">5</identifier><identifier type="ChapterID">Chap5</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2002</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2002</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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