A faster solver for general systems of equations
Identifieur interne : 001399 ( Istex/Corpus ); précédent : 001398; suivant : 001400A faster solver for general systems of equations
Auteurs : Christian Fecht ; Helmut SeidlSource :
- Science of Computer Programming [ 0167-6423 ] ; 1999.
Abstract
We present a new algorithm which computes a partial approximate solution for a system of equations. It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.
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DOI: 10.1016/S0167-6423(99)00009-X
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It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. 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It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.</abstract><qualityIndicators><score>6.596</score><pdfVersion>1.2</pdfVersion><pdfPageSize>409 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>4</keywordCount><abstractCharCount>843</abstractCharCount><pdfWordCount>10357</pdfWordCount><pdfCharCount>52561</pdfCharCount><pdfPageCount>25</pdfPageCount><abstractWordCount>133</abstractWordCount></qualityIndicators><title>A faster solver for general systems of equations</title><pii><json:string>S0167-6423(99)00009-X</json:string></pii><refBibs><json:item><author><json:item><name>A Arnold</name></json:item><json:item><name>P Crubille</name></json:item></author><host><volume>29</volume><pages><last>66</last><first>57</first></pages><author></author><title>Inform. Process. 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It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Generic local fixpoint iteration</term></item><item><term>Worklist algorithms</term></item><item><term>Abstract interpretation</term></item><item><term>Program analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1999">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-20">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-13">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-16">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/7E6BFE05ED25DB8A60695A71D6FAF7AB8A372A73/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier converted-article found"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>SCICO</jid><aid>570</aid><ce:pii>S0167-6423(99)00009-X</ce:pii><ce:doi>10.1016/S0167-6423(99)00009-X</ce:doi><ce:copyright type="full-transfer" year="1999">Elsevier Science B.V.</ce:copyright></item-info><head><ce:title>A faster solver for general systems of equations</ce:title><ce:author-group><ce:author><ce:given-name>Christian</ce:given-name><ce:surname>Fecht</ce:surname><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Helmut</ce:given-name><ce:surname>Seidl</ce:surname><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref><ce:cross-ref refid="CORR1">*</ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>Fachbereich IV - Informatik, Universität Trier, D-54286 Trier, Germany</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author</ce:text></ce:correspondence></ce:author-group><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We present a new algorithm which computes a partial approximate solution for a system of equations. It is <ce:italic>local</ce:italic> in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is <ce:italic>generic</ce:italic> in that it makes no assumptions on the application domain, and it is <ce:italic>general</ce:italic> in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Generic local fixpoint iteration</ce:text></ce:keyword><ce:keyword><ce:text>Worklist algorithms</ce:text></ce:keyword><ce:keyword><ce:text>Abstract interpretation</ce:text></ce:keyword><ce:keyword><ce:text>Program analysis</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>A faster solver for general systems of equations</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A faster solver for general systems of equations</title></titleInfo><name type="personal"><namePart type="given">Christian</namePart><namePart type="family">Fecht</namePart><affiliation>Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Helmut</namePart><namePart type="family">Seidl</namePart><affiliation>Fachbereich IV - Informatik, Universität Trier, D-54286 Trier, Germany</affiliation><affiliation>Corresponding author</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1999</dateIssued><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">We present a new algorithm which computes a partial approximate solution for a system of equations. It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.</abstract><subject><genre>Keywords</genre><topic>Generic local fixpoint iteration</topic><topic>Worklist algorithms</topic><topic>Abstract interpretation</topic><topic>Program analysis</topic></subject><relatedItem type="host"><titleInfo><title>Science of Computer Programming</title></titleInfo><titleInfo type="abbreviated"><title>SCICO</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">199911</dateIssued></originInfo><identifier type="ISSN">0167-6423</identifier><identifier type="PII">S0167-6423(00)X0026-3</identifier><part><date>199911</date><detail type="volume"><number>35</number><caption>vol.</caption></detail><detail type="issue"><number>2–3</number><caption>no.</caption></detail><extent unit="issue pages"><start>77</start><end>256</end></extent><extent unit="pages"><start>137</start><end>161</end></extent></part></relatedItem><identifier type="istex">7E6BFE05ED25DB8A60695A71D6FAF7AB8A372A73</identifier><identifier type="DOI">10.1016/S0167-6423(99)00009-X</identifier><identifier type="PII">S0167-6423(99)00009-X</identifier><accessCondition type="use and reproduction" contentType="copyright">©1999 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Elsevier Science B.V., ©1999</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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