On the Representation of Timed Polyhedra
Identifieur interne : 001C69 ( Istex/Corpus ); précédent : 001C68; suivant : 001C70On the Representation of Timed Polyhedra
Auteurs : Olivier Bournez ; Oded MalerSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: In this paper we investigate timed polyhedra, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (convex and non-convex) polyhedra in any dimension. We then develop relatively efficient algorithms for membership, boolean operations, projection and passage of time for this representation.
Url:
DOI: 10.1007/3-540-45022-X_66
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ISTEX:7B6A1ACBA0FA8AAA1495EF5474588E26B98BE2CFLe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On the Representation of Timed Polyhedra</title><author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name><affiliation><mods:affiliation>LORIA, Campus Scientifique, BP 239, 54506, Vandoeuvre lés Nancy, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: Olivier.Bournez@loria.fr</mods:affiliation></affiliation></author><author><name sortKey="Maler, Oded" sort="Maler, Oded" uniqKey="Maler O" first="Oded" last="Maler">Oded Maler</name><affiliation><mods:affiliation>VERIMAG, 2, av. de Vignate, 38610, Giéres, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: maler@imag.fr</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:7B6A1ACBA0FA8AAA1495EF5474588E26B98BE2CF</idno><date when="2000" year="2000">2000</date><idno type="doi">10.1007/3-540-45022-X_66</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-9VCHZRT0-5/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">001C69</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001C69</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On the Representation of Timed Polyhedra</title><author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name><affiliation><mods:affiliation>LORIA, Campus Scientifique, BP 239, 54506, Vandoeuvre lés Nancy, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: Olivier.Bournez@loria.fr</mods:affiliation></affiliation></author><author><name sortKey="Maler, Oded" sort="Maler, Oded" uniqKey="Maler O" first="Oded" last="Maler">Oded Maler</name><affiliation><mods:affiliation>VERIMAG, 2, av. de Vignate, 38610, Giéres, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: maler@imag.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="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: In this paper we investigate timed polyhedra, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (convex and non-convex) polyhedra in any dimension. 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Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (convex and non-convex) polyhedra in any dimension. 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type="first">Juris</forename><surname>Hartmanis</surname></persName><affiliation><orgName type="institution">Cornell University</orgName><address><region>NY</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Jan</forename><nameLink>van</nameLink><surname>Leeuwen</surname></persName><affiliation><orgName type="institution">Utrecht University</orgName><address><country key=""></country></address></affiliation></editor><idno type="pISSN">0302-9743</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>In this paper we investigate <hi rend="italic">timed polyhedra</hi>, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. 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Polyhedra</ChapterTitle><ChapterFirstPage>793</ChapterFirstPage><ChapterLastPage>807</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2000</CopyrightYear></ChapterCopyright><ChapterHistory><RegistrationDate><Year>2002</Year><Month>2</Month><Day>17</Day></RegistrationDate><OnlineDate><Year>2002</Year><Month>2</Month><Day>18</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><PartID>8</PartID><BookID>3-540-45022-X</BookID><BookTitle>Automata, Languages and Programming</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>Olivier</GivenName><FamilyName>Bournez</FamilyName></AuthorName><Contact><Email>Olivier.Bournez@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>Oded</GivenName><FamilyName>Maler</FamilyName></AuthorName><Contact><Email>maler@imag.fr</Email></Contact></Author><Affiliation ID="Aff7"><OrgName>LORIA</OrgName><OrgAddress><Street>Campus Scientifique</Street><Postbox>BP 239</Postbox><Postcode>54506</Postcode><City>Vandoeuvre lés Nancy</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>VERIMAG</OrgName><OrgAddress><Street>2, av. de Vignate</Street><Postcode>38610</Postcode><City>Giéres</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>In this paper we investigate <Emphasis Type="Italic">timed polyhedra</Emphasis>, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (<Emphasis Type="Italic">convex and non-convex</Emphasis>) polyhedra in <Emphasis Type="Italic">any</Emphasis> dimension. We then develop relatively efficient algorithms for membership, boolean operations, projection and passage of time for this representation.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On the Representation of Timed Polyhedra</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On the Representation of Timed Polyhedra</title></titleInfo><name type="personal"><namePart type="given">Olivier</namePart><namePart type="family">Bournez</namePart><affiliation>LORIA, Campus Scientifique, BP 239, 54506, Vandoeuvre lés Nancy, France</affiliation><affiliation>E-mail: Olivier.Bournez@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Oded</namePart><namePart type="family">Maler</namePart><affiliation>VERIMAG, 2, av. de Vignate, 38610, Giéres, France</affiliation><affiliation>E-mail: maler@imag.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: In this paper we investigate timed polyhedra, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (convex and non-convex) polyhedra in any dimension. We then develop relatively efficient algorithms for membership, boolean operations, projection and passage of time for this representation.</abstract><relatedItem type="host"><titleInfo><title>Automata, Languages and Programming</title><subTitle>27th International Colloquium, ICALP 2000 Geneva, Switzerland, July 9–15, 2000 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Ugo</namePart><namePart type="family">Montanari</namePart><affiliation>Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">José</namePart><namePart type="given">D.</namePart><namePart type="given">P.</namePart><namePart type="family">Rolim</namePart><affiliation>Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland</affiliation><role><roleTerm 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