Upper bounds for the complexity of sparse and tally descriptions
Identifieur interne : 001341 ( Istex/Corpus ); précédent : 001340; suivant : 001342Upper bounds for the complexity of sparse and tally descriptions
Auteurs : V. Arvind ; J. Köbler ; M. MundhenkSource :
- Mathematical systems theory [ 0025-5661 ] ; 1996-02-01.
Abstract
Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.
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DOI: 10.1007/BF01201814
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Arvind</name><affiliation><mods:affiliation>Department of Computer Science, Institute of Mathematical Sciences, C.I.T. Campus, 600113, Madras, India</mods:affiliation></affiliation></author><author><name sortKey="Kobler, J" sort="Kobler, J" uniqKey="Kobler J" first="J." last="Köbler">J. Köbler</name><affiliation><mods:affiliation>Abteilung für Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany</mods:affiliation></affiliation></author><author><name sortKey="Mundhenk, M" sort="Mundhenk, M" uniqKey="Mundhenk M" first="M." last="Mundhenk">M. Mundhenk</name><affiliation><mods:affiliation>Lehrstuhl IV-Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Mathematical systems theory</title><title level="j" type="abbrev">Math. Systems Theory</title><idno type="ISSN">0025-5661</idno><idno type="eISSN">1433-0490</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-02-01">1996-02-01</date><biblScope unit="volume">29</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="63">63</biblScope><biblScope unit="page" to="94">94</biblScope></imprint><idno type="ISSN">0025-5661</idno></series><idno type="istex">1BE62514B9085FFD1DA6A76728DEBFADE1A09AF8</idno><idno type="DOI">10.1007/BF01201814</idno><idno type="ArticleID">BF01201814</idno><idno type="ArticleID">Art6</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5661</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>V. Arvind</name><affiliations><json:string>Department of Computer Science, Institute of Mathematical Sciences, C.I.T. Campus, 600113, Madras, India</json:string></affiliations></json:item><json:item><name>J. Köbler</name><affiliations><json:string>Abteilung für Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany</json:string></affiliations></json:item><json:item><name>M. Mundhenk</name><affiliations><json:string>Lehrstuhl IV-Informatik, Universität Trier, D-54286, Trier, Germany</json:string></affiliations></json:item></author><articleId><json:string>BF01201814</json:string><json:string>Art6</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</abstract><qualityIndicators><score>6.5</score><pdfVersion>1.3</pdfVersion><pdfPageSize>446.28 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>740</abstractCharCount><pdfWordCount>13272</pdfWordCount><pdfCharCount>58516</pdfCharCount><pdfPageCount>32</pdfPageCount><abstractWordCount>125</abstractWordCount></qualityIndicators><title>Upper bounds for the complexity of sparse and tally descriptions</title><refBibs><json:item><host><author></author><title>Every polynomially well-founded self-reducible set is in DSPACE(2n~</title></host></json:item><json:item><host><author></author><title>Every word-decreasing self-reducible set is in DTIME(2~</title></host></json:item><json:item><host><author></author><title>Every polynomially related self-reducible set in P/poly is Iow for 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Campus, 600113, Madras, India</affiliation></author><author xml:id="author-2"><persName><forename type="first">J.</forename><surname>Köbler</surname></persName><affiliation>Abteilung für Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany</affiliation></author><author xml:id="author-3"><persName><forename type="first">M.</forename><surname>Mundhenk</surname></persName><affiliation>Lehrstuhl IV-Informatik, Universität Trier, D-54286, Trier, Germany</affiliation></author></analytic><monogr><title level="j">Mathematical systems theory</title><title level="j" type="abbrev">Math. Systems Theory</title><idno type="journal-ID">224</idno><idno type="pISSN">0025-5661</idno><idno type="eISSN">1433-0490</idno><idno type="issue-article-count">6</idno><idno type="volume-issue-count">6</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-02-01"></date><biblScope unit="volume">29</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="63">63</biblScope><biblScope unit="page" to="94">94</biblScope></imprint></monogr><idno type="istex">1BE62514B9085FFD1DA6A76728DEBFADE1A09AF8</idno><idno type="DOI">10.1007/BF01201814</idno><idno type="ArticleID">BF01201814</idno><idno type="ArticleID">Art6</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1993-08-03</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</p></abstract><textClass><keywords scheme="Journal-Subject-Group"><list><label>I</label><label>I16005</label><label>M1400X</label><item><term>Computer Science</term></item><item><term>Theory of Computation</term></item><item><term>Computational Mathematics and Numerical Analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1993-08-03">Created</change><change when="1996-02-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-21">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/1BE62514B9085FFD1DA6A76728DEBFADE1A09AF8/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher 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-Verlag</PublisherName><PublisherLocation>New York</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>224</JournalID><JournalPrintISSN>0025-5661</JournalPrintISSN><JournalElectronicISSN>1433-0490</JournalElectronicISSN><JournalTitle>Mathematical systems theory</JournalTitle><JournalAbbreviatedTitle>Math. Systems Theory</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Code="I" Type="Primary">Computer Science</JournalSubject><JournalSubject Code="I16005" Priority="1" Type="Secondary">Theory of Computation</JournalSubject><JournalSubject Code="M1400X" Priority="2" Type="Secondary">Computational Mathematics and Numerical Analysis</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo TocLevels="0" VolumeType="Regular"><VolumeIDStart>29</VolumeIDStart><VolumeIDEnd>29</VolumeIDEnd><VolumeIssueCount>6</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd><IssueArticleCount>6</IssueArticleCount><IssueHistory><CoverDate><Year>1996</Year><Month>2</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Springer-Verlag New York Inc.</CopyrightHolderName><CopyrightYear>1996</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art6"><ArticleInfo ArticleType="OriginalPaper" ContainsESM="No" Language="En" NumberingStyle="Unnumbered" TocLevels="0"><ArticleID>BF01201814</ArticleID><ArticleDOI>10.1007/BF01201814</ArticleDOI><ArticleSequenceNumber>6</ArticleSequenceNumber><ArticleTitle Language="En">Upper bounds for the complexity of sparse and tally descriptions</ArticleTitle><ArticleFirstPage>63</ArticleFirstPage><ArticleLastPage>94</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>2</Month><Day>5</Day></RegistrationDate><Received><Year>1993</Year><Month>8</Month><Day>3</Day></Received><Accepted><Year>1993</Year><Month>12</Month><Day>21</Day></Accepted></ArticleHistory><ArticleCopyright><CopyrightHolderName>Springer-Verlag New York Inc.</CopyrightHolderName><CopyrightYear>1996</CopyrightYear></ArticleCopyright><ArticleGrants 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></ArticleGrants> <ArticleContext><JournalID>224</JournalID><VolumeIDStart>29</VolumeIDStart><VolumeIDEnd>29</VolumeIDEnd><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>V.</GivenName><FamilyName>Arvind</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>J.</GivenName><FamilyName>Köbler</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff3"><AuthorName DisplayOrder="Western"><GivenName>M.</GivenName><FamilyName>Mundhenk</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>Institute of Mathematical Sciences</OrgName><OrgAddress><Street>C.I.T. Campus</Street><Postcode>600113</Postcode><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Abteilung für Theoretische Informatik</OrgDivision><OrgName>Universität Ulm</OrgName><OrgAddress><Postcode>D-89069</Postcode><City>Ulm</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgDivision>Lehrstuhl IV-Informatik</OrgDivision><OrgName>Universität Trier</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 investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a set<Emphasis Type="Italic">A</Emphasis> and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in the<Emphasis Type="Italic">EL</Emphasis><Stack><Subscript>1</Subscript><Superscript>Σ</Superscript></Stack>-level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets in<Emphasis Type="Italic">R</Emphasis><Stack><Subscript>d</Subscript><Superscript>p</Superscript></Stack>(SPARSE) and<Emphasis Type="Italic">R</Emphasis><Stack><Subscript>hd</Subscript><Superscript>p</Superscript></Stack> (<Emphasis Type="Italic">R</Emphasis><Stack><Subscript>c</Subscript><Superscript>p</Superscript></Stack>(SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</Para></Abstract><ArticleNote Type="PresentedAt"><SimplePara>Parts of this work have been presented at ISAAC'92, MFCS'93, and CIAC'94 [AKM2], [AKM3], [Mu]. The work of V. Arvind was done while visiting Universität Ulm and was supported in part by an Alexander von Humboldt research fellowship.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Upper bounds for the complexity of sparse and tally descriptions</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Upper bounds for the complexity of sparse and tally descriptions</title></titleInfo><name type="personal"><namePart type="given">V.</namePart><namePart type="family">Arvind</namePart><affiliation>Department of Computer Science, Institute of Mathematical Sciences, C.I.T. Campus, 600113, Madras, India</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Köbler</namePart><affiliation>Abteilung für Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Mundhenk</namePart><affiliation>Lehrstuhl IV-Informatik, Universität Trier, D-54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">1993-08-03</dateCreated><dateIssued encoding="w3cdtf">1996-02-01</dateIssued><copyrightDate encoding="w3cdtf">1996</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 investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</abstract><relatedItem type="host"><titleInfo><title>Mathematical systems theory</title></titleInfo><titleInfo type="abbreviated"><title>Math. Systems Theory</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1996-02-01</dateIssued><copyrightDate encoding="w3cdtf">1996</copyrightDate></originInfo><subject><genre>Journal-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16005">Theory of Computation</topic><topic authority="SpringerSubjectCodes" authorityURI="M1400X">Computational Mathematics and Numerical Analysis</topic></subject><identifier type="ISSN">0025-5661</identifier><identifier type="eISSN">1433-0490</identifier><identifier type="JournalID">224</identifier><identifier type="IssueArticleCount">6</identifier><identifier type="VolumeIssueCount">6</identifier><part><date>1996</date><detail type="volume"><number>29</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="pages"><start>63</start><end>94</end></extent></part><recordInfo><recordOrigin>Springer-Verlag New York Inc., 1996</recordOrigin></recordInfo></relatedItem><identifier type="istex">1BE62514B9085FFD1DA6A76728DEBFADE1A09AF8</identifier><identifier type="DOI">10.1007/BF01201814</identifier><identifier type="ArticleID">BF01201814</identifier><identifier type="ArticleID">Art6</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag New York Inc., 1996</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag New York Inc., 1996</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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