Congruence Closure Modulo Associativity and Commutativity
Identifieur interne : 001630 ( Istex/Corpus ); précédent : 001629; suivant : 001631Congruence Closure Modulo Associativity and Commutativity
Auteurs : L. Bachmair ; I. V. Ramakrishnan ; A. Tiwari ; L. VigneronSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without the need for AC-simplification orderings total on ground terms. Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground AC-theory. This is done by transforming an AC-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction.
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DOI: 10.1007/10720084_16
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ISTEX:600CDD6FAA7BEE4CB3B01BD92A57BB235C6B07ACLe document en format XML
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Ramakrishnan</name><affiliation><mods:affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ram@cs.sunysb.edu</mods:affiliation></affiliation></author><author><name sortKey="Tiwari, A" sort="Tiwari, A" uniqKey="Tiwari A" first="A." last="Tiwari">A. Tiwari</name><affiliation><mods:affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: astiwari@cs.sunysb.edu</mods:affiliation></affiliation></author><author><name sortKey="Vigneron, L" sort="Vigneron, L" uniqKey="Vigneron L" first="L." last="Vigneron">L. 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Bachmair</name><affiliation><mods:affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: leo@cs.sunysb.edu</mods:affiliation></affiliation></author><author><name sortKey="Ramakrishnan, I V" sort="Ramakrishnan, I V" uniqKey="Ramakrishnan I" first="I. V." last="Ramakrishnan">I. V. Ramakrishnan</name><affiliation><mods:affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: ram@cs.sunysb.edu</mods:affiliation></affiliation></author><author><name sortKey="Tiwari, A" sort="Tiwari, A" uniqKey="Tiwari A" first="A." last="Tiwari">A. 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Vigneron</name><affiliation><mods:affiliation>LORIA, Université Nancy 2, Campus Scientifique, B.P. 239, 54506, Vandœvre-lès-Nancy Cedex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: vigneron@loria.fr</mods:affiliation></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 introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without the need for AC-simplification orderings total on ground terms. Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground AC-theory. This is done by transforming an AC-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>L. 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Vigneron</name><affiliations><json:string>LORIA, Université Nancy 2, Campus Scientifique, B.P. 239, 54506, Vandœvre-lès-Nancy Cedex, France</json:string><json:string>E-mail: vigneron@loria.fr</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-5W0CG1XT-Q</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without the need for AC-simplification orderings total on ground terms. Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground AC-theory. This is done by transforming an AC-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. 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This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground <hi rend="italic">AC</hi>-theories without the need for <hi rend="italic">AC</hi>-simplification orderings total on ground terms.</p><p>Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground <hi rend="italic">AC</hi>-theory. This is done by transforming an <hi rend="italic">AC</hi>-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction.</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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Proceedings</BookSubTitle><BookVolumeNumber>1794</BookVolumeNumber><BookSequenceNumber>1794</BookSequenceNumber><BookDOI>10.1007/10720084</BookDOI><BookTitleID>62762</BookTitleID><BookPrintISBN>978-3-540-67281-4</BookPrintISBN><BookElectronicISBN>978-3-540-46421-1</BookElectronicISBN><BookChapterCount>18</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2000</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><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID><SubSeriesID>1244</SubSeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff6"><EditorName DisplayOrder="Western"><GivenName>Hélène</GivenName><FamilyName>Kirchner</FamilyName></EditorName><Contact><Email>Helene.Kirchner@loria.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff7"><EditorName DisplayOrder="Western"><GivenName>Christophe</GivenName><FamilyName>Ringeissen</FamilyName></EditorName><Contact><Email>Christophe.Ringeissen@loria.fr</Email></Contact></Editor><Affiliation ID="Aff6"><OrgName>INRIA & LORIA</OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>LORIA - INRIA</OrgName><OrgAddress><Street>Campus scientifique, 615, rue du Jardin Botanique</Street><Postcode>54602</Postcode><City>Villers-les-Nancy</City><Country>France</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part9"><PartInfo TocLevels="0"><PartID>9</PartID><PartSequenceNumber>9</PartSequenceNumber><PartTitle>Session 5</PartTitle><PartChapterCount>3</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Frontiers of Combining Systems</BookTitle></PartContext></PartInfo><Chapter ID="Chap16" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>16</ChapterID><ChapterDOI>10.1007/10720084_16</ChapterDOI><ChapterSequenceNumber>16</ChapterSequenceNumber><ChapterTitle Language="En">Congruence Closure Modulo Associativity and Commutativity</ChapterTitle><ChapterFirstPage>245</ChapterFirstPage><ChapterLastPage>259</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2000</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>9</PartID><BookID>978-3-540-46421-1</BookID><BookTitle>Frontiers of Combining Systems</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>L.</GivenName><FamilyName>Bachmair</FamilyName></AuthorName><Contact><Email>leo@cs.sunysb.edu</Email></Contact></Author><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>I.</GivenName><GivenName>V.</GivenName><FamilyName>Ramakrishnan</FamilyName></AuthorName><Contact><Email>ram@cs.sunysb.edu</Email></Contact></Author><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><FamilyName>Tiwari</FamilyName></AuthorName><Contact><Email>astiwari@cs.sunysb.edu</Email></Contact></Author><Author AffiliationIDS="Aff9"><AuthorName DisplayOrder="Western"><GivenName>L.</GivenName><FamilyName>Vigneron</FamilyName></AuthorName><Contact><Email>vigneron@loria.fr</Email></Contact></Author><Affiliation ID="Aff8"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>State University of New York</OrgName><OrgAddress><City>Stony Brook</City><State>NY</State><Postcode>11794-4400</Postcode><Country>U.S.A</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgDivision>LORIA</OrgDivision><OrgName>Université Nancy 2</OrgName><OrgAddress><Street>Campus Scientifique</Street><Postbox>B.P. 239</Postbox><Postcode>54506</Postcode><City>Vandœvre-lès-Nancy Cedex</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We introduce the notion of an <Emphasis Type="Italic">associative-commutative congruence closure</Emphasis> and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground <Emphasis Type="Italic">AC</Emphasis>-theories without the need for <Emphasis Type="Italic">AC</Emphasis>-simplification orderings total on ground terms.</Para><Para>Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground <Emphasis Type="Italic">AC</Emphasis>-theory. This is done by transforming an <Emphasis Type="Italic">AC</Emphasis>-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>The research described in this paper was supported in part by the National Science Foundation under grants CCR-9902031, CCR-9711386 and EIA-9705998.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Congruence Closure Modulo Associativity and Commutativity</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Congruence Closure Modulo Associativity and Commutativity</title></titleInfo><name type="personal"><namePart type="given">L.</namePart><namePart type="family">Bachmair</namePart><affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</affiliation><affiliation>E-mail: leo@cs.sunysb.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">I.</namePart><namePart type="given">V.</namePart><namePart type="family">Ramakrishnan</namePart><affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</affiliation><affiliation>E-mail: ram@cs.sunysb.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Tiwari</namePart><affiliation>Department of Computer Science, State University of New York, 11794-4400, Stony Brook, NY, U.S.A</affiliation><affiliation>E-mail: astiwari@cs.sunysb.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">L.</namePart><namePart type="family">Vigneron</namePart><affiliation>LORIA, Université Nancy 2, Campus Scientifique, B.P. 239, 54506, Vandœvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: vigneron@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">2000</dateIssued><copyrightDate encoding="w3cdtf">2000</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We introduce the notion of an associative-commutative congruence closure and show how such closures can be constructed via completion-like transition rules. This method is based on combining completion algorithms for theories over disjoint signatures to produce a convergent rewrite system over an extended signature. This approach can also be used to solve the word problem for ground AC-theories without the need for AC-simplification orderings total on ground terms. Associative-commutative congruence closure provides a novel way to construct a convergent rewrite system for a ground AC-theory. This is done by transforming an AC-congruence closure, which is described by rewrite rules over an extended signature, to a rewrite system over the original signature. The set of rewrite rules thus obtained is convergent with respect to a new and simpler notion of associative-commutative reduction.</abstract><relatedItem type="host"><titleInfo><title>Frontiers of Combining Systems</title><subTitle>Third International Workshop, FroCoS 2000, Nancy, France, March 22-24, 2000. 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