PATCH Graphs: An efficient data structure for completion of finitely presented groups
Identifieur interne : 001816 ( Istex/Corpus ); précédent : 001815; suivant : 001817PATCH Graphs: An efficient data structure for completion of finitely presented groups
Auteurs : Christopher Lynch ; Polina StrogovaSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.
Url:
DOI: 10.1007/3-540-61732-9_57
Links to Exploration step
ISTEX:67DA9E6D9D304D82D80E853240AB62AAA64EF745Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
<author><name sortKey="Lynch, Christopher" sort="Lynch, Christopher" uniqKey="Lynch C" first="Christopher" last="Lynch">Christopher Lynch</name>
<affiliation><mods:affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: lynch@loria.fr</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Strogova, Polina" sort="Strogova, Polina" uniqKey="Strogova P" first="Polina" last="Strogova">Polina Strogova</name>
<affiliation><mods:affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN and INRIA Rocquencourt, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: strogova@loria.fr</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:67DA9E6D9D304D82D80E853240AB62AAA64EF745</idno>
<date when="1996" year="1996">1996</date>
<idno type="doi">10.1007/3-540-61732-9_57</idno>
<idno type="url">https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/fulltext.pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001816</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001816</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
<author><name sortKey="Lynch, Christopher" sort="Lynch, Christopher" uniqKey="Lynch C" first="Christopher" last="Lynch">Christopher Lynch</name>
<affiliation><mods:affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: lynch@loria.fr</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Strogova, Polina" sort="Strogova, Polina" uniqKey="Strogova P" first="Polina" last="Strogova">Polina Strogova</name>
<affiliation><mods:affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN and INRIA Rocquencourt, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: strogova@loria.fr</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title>
<title level="s" type="abbrev">Lect Notes Comput Sci</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: Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.</div>
</front>
</TEI>
<istex><corpusName>springer-ebooks</corpusName>
<author><json:item><name>Christopher Lynch</name>
<affiliations><json:string>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</json:string>
<json:string>E-mail: lynch@loria.fr</json:string>
</affiliations>
</json:item>
<json:item><name>Polina Strogova</name>
<affiliations><json:string>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN and INRIA Rocquencourt, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</json:string>
<json:string>E-mail: strogova@loria.fr</json:string>
</affiliations>
</json:item>
</author>
<arkIstex>ark:/67375/HCB-RHR38WQ5-7</arkIstex>
<language><json:string>eng</json:string>
</language>
<originalGenre><json:string>ReviewPaper</json:string>
</originalGenre>
<abstract>Abstract: Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.</abstract>
<qualityIndicators><score>7.948</score>
<pdfWordCount>8494</pdfWordCount>
<pdfCharCount>35135</pdfCharCount>
<pdfVersion>1.3</pdfVersion>
<pdfPageCount>15</pdfPageCount>
<pdfPageSize>439.28 x 666 pts</pdfPageSize>
<refBibsNative>false</refBibsNative>
<abstractWordCount>79</abstractWordCount>
<abstractCharCount>537</abstractCharCount>
<keywordCount>0</keywordCount>
</qualityIndicators>
<title>PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
<chapterId><json:string>11</json:string>
<json:string>Chap11</json:string>
</chapterId>
<genre><json:string>conference</json:string>
</genre>
<serie><title>Lecture Notes in Computer Science</title>
<language><json:string>unknown</json:string>
</language>
<copyrightDate>1996</copyrightDate>
<issn><json:string>0302-9743</json:string>
</issn>
<eissn><json:string>1611-3349</json:string>
</eissn>
<editor><json:item><name>G. Goos</name>
</json:item>
<json:item><name>J. Hartmanis</name>
</json:item>
<json:item><name>J. van Leeuwen</name>
</json:item>
</editor>
</serie>
<host><title>Artificial Intelligence and Symbolic Mathematical Computation</title>
<language><json:string>unknown</json:string>
</language>
<copyrightDate>1996</copyrightDate>
<doi><json:string>10.1007/3-540-61732-9</json:string>
</doi>
<issn><json:string>0302-9743</json:string>
</issn>
<eissn><json:string>1611-3349</json:string>
</eissn>
<eisbn><json:string>978-3-540-70740-0</json:string>
</eisbn>
<bookId><json:string>3540617329</json:string>
</bookId>
<isbn><json:string>978-3-540-61732-7</json:string>
</isbn>
<volume>1138</volume>
<pages><first>176</first>
<last>190</last>
</pages>
<genre><json:string>book-series</json:string>
</genre>
<editor><json:item><name>Jacques Calmet</name>
</json:item>
<json:item><name>John A. Campbell</name>
</json:item>
<json:item><name>Jochen Pfalzgraf</name>
</json:item>
</editor>
<subject><json:item><value>Computer Science</value>
</json:item>
<json:item><value>Computer Science</value>
</json:item>
<json:item><value>Artificial Intelligence (incl. Robotics)</value>
</json:item>
<json:item><value>Symbolic and Algebraic Manipulation</value>
</json:item>
<json:item><value>Algorithms</value>
</json:item>
<json:item><value>Mathematical Logic and Formal Languages</value>
</json:item>
<json:item><value>Systems and Information Theory in Engineering</value>
</json:item>
</subject>
</host>
<ark><json:string>ark:/67375/HCB-RHR38WQ5-7</json:string>
</ark>
<publicationDate>1996</publicationDate>
<copyrightDate>1996</copyrightDate>
<doi><json:string>10.1007/3-540-61732-9_57</json:string>
</doi>
<id>67DA9E6D9D304D82D80E853240AB62AAA64EF745</id>
<score>1</score>
<fulltext><json:item><extension>pdf</extension>
<original>true</original>
<mimetype>application/pdf</mimetype>
<uri>https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/fulltext.pdf</uri>
</json:item>
<json:item><extension>zip</extension>
<original>false</original>
<mimetype>application/zip</mimetype>
<uri>https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/bundle.zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/fulltext.tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
</titleStmt>
<publicationStmt><authority>ISTEX</authority>
<availability><licence>Springer-Verlag</licence>
</availability>
<date when="1996">1996</date>
</publicationStmt>
<notesStmt><note type="conference" source="proceedings" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</note>
<note type="publication-type" subtype="book-series" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</note>
</notesStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
<author><persName><forename type="first">Christopher</forename>
<surname>Lynch</surname>
</persName>
<email>lynch@loria.fr</email>
<affiliation><orgName type="department">Technopôle de Nancy-Brabois</orgName>
<orgName type="institution">INRIA Lorraine-CRIN</orgName>
<address><postBox>B.P. 101</postBox>
<postCode>54602</postCode>
<settlement>Villers-lès-Nancy Cedex</settlement>
<country key="FR">FRANCE</country>
</address>
</affiliation>
</author>
<author><persName><forename type="first">Polina</forename>
<surname>Strogova</surname>
</persName>
<email>strogova@loria.fr</email>
<affiliation><orgName type="department">Technopôle de Nancy-Brabois</orgName>
<orgName type="institution">INRIA Lorraine-CRIN and INRIA Rocquencourt</orgName>
<address><postBox>B.P. 101</postBox>
<postCode>54602</postCode>
<settlement>Villers-lès-Nancy Cedex</settlement>
<country key="FR">FRANCE</country>
</address>
</affiliation>
</author>
<idno type="istex">67DA9E6D9D304D82D80E853240AB62AAA64EF745</idno>
<idno type="ark">ark:/67375/HCB-RHR38WQ5-7</idno>
<idno type="DOI">10.1007/3-540-61732-9_57</idno>
</analytic>
<monogr><title level="m" type="main">Artificial Intelligence and Symbolic Mathematical Computation</title>
<title level="m" type="sub">International Conference, AISMC-3 Steyr, Austria, September 23–25, 1996 Proceedings</title>
<idno type="DOI">10.1007/3-540-61732-9</idno>
<idno type="book-id">3540617329</idno>
<idno type="ISBN">978-3-540-61732-7</idno>
<idno type="eISBN">978-3-540-70740-0</idno>
<idno type="chapter-id">Chap11</idno>
<editor><persName><forename type="first">Jacques</forename>
<surname>Calmet</surname>
</persName>
</editor>
<editor><persName><forename type="first">John</forename>
<forename type="first">A.</forename>
<surname>Campbell</surname>
</persName>
</editor>
<editor><persName><forename type="first">Jochen</forename>
<surname>Pfalzgraf</surname>
</persName>
</editor>
<imprint><biblScope unit="vol">1138</biblScope>
<biblScope unit="page" from="176">176</biblScope>
<biblScope unit="page" to="190">190</biblScope>
<biblScope unit="chapter-count">23</biblScope>
</imprint>
</monogr>
<series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title>
<title level="s" type="abbrev">Lect Notes Comput Sci</title>
<editor><persName><forename type="first">G.</forename>
<surname>Goos</surname>
</persName>
</editor>
<editor><persName><forename type="first">J.</forename>
<surname>Hartmanis</surname>
</persName>
</editor>
<editor><persName><forename type="first">J.</forename>
<nameLink>van</nameLink>
<surname>Leeuwen</surname>
</persName>
</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>Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.</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. Robotics)</term>
</item>
<label>I17052</label>
<item><term type="Secondary" subtype="priority-2">Symbolic and Algebraic Manipulation</term>
</item>
<label>M14018</label>
<item><term type="Secondary" subtype="priority-3">Algorithms</term>
</item>
<label>I16048</label>
<item><term type="Secondary" subtype="priority-4">Mathematical Logic and Formal Languages</term>
</item>
<label>T11022</label>
<item><term type="Secondary" subtype="priority-5">Systems and Information Theory in Engineering</term>
</item>
</list>
</keywords>
</textClass>
<langUsage><language ident="EN"></language>
</langUsage>
</profileDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item><extension>txt</extension>
<original>false</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/fulltext.txt</uri>
</json:item>
</fulltext>
<metadata><istex:metadataXml wicri:clean="corpus springer-ebooks not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration>
<istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType>
<istex:document><Publisher><PublisherInfo><PublisherName>Springer Berlin Heidelberg</PublisherName>
<PublisherLocation>Berlin, Heidelberg</PublisherLocation>
</PublisherInfo>
<Series><SeriesInfo TocLevels="0"><SeriesID>558</SeriesID>
<SeriesPrintISSN>0302-9743</SeriesPrintISSN>
<SeriesElectronicISSN>1611-3349</SeriesElectronicISSN>
<SeriesTitle Language="En">Lecture Notes in Computer Science</SeriesTitle>
<SeriesAbbreviatedTitle>Lect Notes Comput Sci</SeriesAbbreviatedTitle>
</SeriesInfo>
<SeriesHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>G.</GivenName>
<FamilyName>Goos</FamilyName>
</EditorName>
</Editor>
<Editor><EditorName DisplayOrder="Western"><GivenName>J.</GivenName>
<FamilyName>Hartmanis</FamilyName>
</EditorName>
</Editor>
<Editor><EditorName DisplayOrder="Western"><GivenName>J.</GivenName>
<Particle>van</Particle>
<FamilyName>Leeuwen</FamilyName>
</EditorName>
</Editor>
</EditorGroup>
</SeriesHeader>
<Book Language="En"><BookInfo MediaType="eBook" Language="En" BookProductType="Proceedings" TocLevels="0" NumberingStyle="Unnumbered"><BookID>3540617329</BookID>
<BookTitle>Artificial Intelligence and Symbolic Mathematical Computation</BookTitle>
<BookSubTitle>International Conference, AISMC-3 Steyr, Austria, September 23–25, 1996 Proceedings</BookSubTitle>
<BookVolumeNumber>1138</BookVolumeNumber>
<BookDOI>10.1007/3-540-61732-9</BookDOI>
<BookTitleID>45058</BookTitleID>
<BookPrintISBN>978-3-540-61732-7</BookPrintISBN>
<BookElectronicISBN>978-3-540-70740-0</BookElectronicISBN>
<BookChapterCount>23</BookChapterCount>
<BookCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName>
<CopyrightYear>1996</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="I17052" Priority="2" Type="Secondary">Symbolic and Algebraic Manipulation</BookSubject>
<BookSubject Code="M14018" Priority="3" Type="Secondary">Algorithms</BookSubject>
<BookSubject Code="I16048" Priority="4" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject>
<BookSubject Code="T11022" Priority="5" Type="Secondary">Systems and Information Theory in Engineering</BookSubject>
<SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection>
</BookSubjectGroup>
</BookInfo>
<BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Jacques</GivenName>
<FamilyName>Calmet</FamilyName>
</EditorName>
</Editor>
<Editor><EditorName DisplayOrder="Western"><GivenName>John</GivenName>
<GivenName>A.</GivenName>
<FamilyName>Campbell</FamilyName>
</EditorName>
</Editor>
<Editor><EditorName DisplayOrder="Western"><GivenName>Jochen</GivenName>
<FamilyName>Pfalzgraf</FamilyName>
</EditorName>
</Editor>
</EditorGroup>
</BookHeader>
<Chapter ID="Chap11" Language="En"><ChapterInfo ChapterType="ReviewPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ChapterID>11</ChapterID>
<ChapterDOI>10.1007/3-540-61732-9_57</ChapterDOI>
<ChapterSequenceNumber>11</ChapterSequenceNumber>
<ChapterTitle Language="En">PATCH Graphs: An efficient data structure for completion of finitely presented groups</ChapterTitle>
<ChapterFirstPage>176</ChapterFirstPage>
<ChapterLastPage>190</ChapterLastPage>
<ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName>
<CopyrightYear>1996</CopyrightYear>
</ChapterCopyright>
<ChapterHistory><OnlineDate><Year>2005</Year>
<Month>6</Month>
<Day>2</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>3540617329</BookID>
<BookTitle>Artificial Intelligence and Symbolic Mathematical Computation</BookTitle>
</ChapterContext>
</ChapterInfo>
<ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Christopher</GivenName>
<FamilyName>Lynch</FamilyName>
</AuthorName>
<Contact><Fax>(+33) 83 27 83 19</Fax>
<Email>lynch@loria.fr</Email>
</Contact>
</Author>
<Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Polina</GivenName>
<FamilyName>Strogova</FamilyName>
</AuthorName>
<Contact><Email>strogova@loria.fr</Email>
</Contact>
</Author>
<Affiliation ID="Aff1"><OrgDivision>Technopôle de Nancy-Brabois</OrgDivision>
<OrgName>INRIA Lorraine-CRIN</OrgName>
<OrgAddress><Postbox>B.P. 101</Postbox>
<Postcode>54602</Postcode>
<City>Villers-lès-Nancy Cedex</City>
<Country>France</Country>
</OrgAddress>
</Affiliation>
<Affiliation ID="Aff2"><OrgDivision>Technopôle de Nancy-Brabois</OrgDivision>
<OrgName>INRIA Lorraine-CRIN and INRIA Rocquencourt</OrgName>
<OrgAddress><Postbox>B.P. 101</Postbox>
<Postcode>54602</Postcode>
<City>Villers-lès-Nancy Cedex</City>
<Country>France</Country>
</OrgAddress>
</Affiliation>
</AuthorGroup>
<Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading>
<Para>Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.</Para>
</Abstract>
</ChapterHeader>
<NoBody></NoBody>
</Chapter>
</Book>
</Series>
</Publisher>
</istex:document>
</istex:metadataXml>
<mods version="3.6"><titleInfo lang="en"><title>PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA"><title>PATCH Graphs: An efficient data structure for completion of finitely presented groups</title>
</titleInfo>
<name type="personal"><namePart type="given">Christopher</namePart>
<namePart type="family">Lynch</namePart>
<affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</affiliation>
<affiliation>E-mail: lynch@loria.fr</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Polina</namePart>
<namePart type="family">Strogova</namePart>
<affiliation>Technopôle de Nancy-Brabois, INRIA Lorraine-CRIN and INRIA Rocquencourt, B.P. 101, 54602, Villers-lès-Nancy Cedex, France</affiliation>
<affiliation>E-mail: strogova@loria.fr</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre displayLabel="ReviewPaper" 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">1996</dateIssued>
<copyrightDate encoding="w3cdtf">1996</copyrightDate>
</originInfo>
<language><languageTerm type="code" authority="rfc3066">en</languageTerm>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
</language>
<abstract lang="en">Abstract: Based on a new data structure called PATCH Graph, an efficient completion procedure for finitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH Graph data structure and inference rules complement other extensions of Knuth-Bendix completion for finitely presented groups.</abstract>
<relatedItem type="host"><titleInfo><title>Artificial Intelligence and Symbolic Mathematical Computation</title>
<subTitle>International Conference, AISMC-3 Steyr, Austria, September 23–25, 1996 Proceedings</subTitle>
</titleInfo>
<name type="personal"><namePart type="given">Jacques</namePart>
<namePart type="family">Calmet</namePart>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">John</namePart>
<namePart type="given">A.</namePart>
<namePart type="family">Campbell</namePart>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Jochen</namePart>
<namePart type="family">Pfalzgraf</namePart>
<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">1996</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. Robotics)</topic>
<topic authority="SpringerSubjectCodes" authorityURI="I17052">Symbolic and Algebraic Manipulation</topic>
<topic authority="SpringerSubjectCodes" authorityURI="M14018">Algorithms</topic>
<topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic>
<topic authority="SpringerSubjectCodes" authorityURI="T11022">Systems and Information Theory in Engineering</topic>
</subject>
<identifier type="DOI">10.1007/3-540-61732-9</identifier>
<identifier type="ISBN">978-3-540-61732-7</identifier>
<identifier type="eISBN">978-3-540-70740-0</identifier>
<identifier type="ISSN">0302-9743</identifier>
<identifier type="eISSN">1611-3349</identifier>
<identifier type="BookTitleID">45058</identifier>
<identifier type="BookID">3540617329</identifier>
<identifier type="BookChapterCount">23</identifier>
<identifier type="BookVolumeNumber">1138</identifier>
<part><date>1996</date>
<detail type="volume"><number>1138</number>
<caption>vol.</caption>
</detail>
<extent unit="pages"><start>176</start>
<end>190</end>
</extent>
</part>
<recordInfo><recordOrigin>Springer-Verlag, 1996</recordOrigin>
</recordInfo>
</relatedItem>
<relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title>
</titleInfo>
<name type="personal"><namePart type="given">G.</namePart>
<namePart type="family">Goos</namePart>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">J.</namePart>
<namePart type="family">Hartmanis</namePart>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">J.</namePart>
<namePart type="family">van Leeuwen</namePart>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<originInfo><publisher>Springer</publisher>
<copyrightDate encoding="w3cdtf">1996</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, 1996</recordOrigin>
</recordInfo>
</relatedItem>
<identifier type="istex">67DA9E6D9D304D82D80E853240AB62AAA64EF745</identifier>
<identifier type="ark">ark:/67375/HCB-RHR38WQ5-7</identifier>
<identifier type="DOI">10.1007/3-540-61732-9_57</identifier>
<identifier type="ChapterID">11</identifier>
<identifier type="ChapterID">Chap11</identifier>
<accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1996</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, 1996</recordOrigin>
</recordInfo>
</mods>
<json:item><extension>json</extension>
<original>false</original>
<mimetype>application/json</mimetype>
<uri>https://api.istex.fr/ark:/67375/HCB-RHR38WQ5-7/record.json</uri>
</json:item>
</metadata>
</istex>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001816 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001816 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Istex |étape= Corpus |type= RBID |clé= ISTEX:67DA9E6D9D304D82D80E853240AB62AAA64EF745 |texte= PATCH Graphs: An efficient data structure for completion of finitely presented groups }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |