Inductive counting below logspace
Identifieur interne : 001071 ( Istex/Corpus ); précédent : 001070; suivant : 001072Inductive counting below logspace
Auteurs : Carsten Damm ; Markus HolzerSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1994.
Abstract
Abstract: We apply the inductive counting technique to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a consequence we obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immerman [6] and Szelepcsényi [12] to space bounds of order o(log n) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds [3, 5, 9].
Url:
DOI: 10.1007/3-540-58338-6_74
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Inductive counting below logspace</title><author><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name><affiliation><mods:affiliation>FB IV-Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Holzer, Markus" sort="Holzer, Markus" uniqKey="Holzer M" first="Markus" last="Holzer">Markus Holzer</name><affiliation><mods:affiliation>Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:2FE43D8A47994F4BC60DE9B37868841FC85743A2</idno><date when="1994" year="1994">1994</date><idno type="doi">10.1007/3-540-58338-6_74</idno><idno type="url">https://api.istex.fr/document/2FE43D8A47994F4BC60DE9B37868841FC85743A2/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001071</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001071</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Inductive counting below logspace</title><author><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name><affiliation><mods:affiliation>FB IV-Informatik, Universität Trier, D-54286, Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Holzer, Markus" sort="Holzer, Markus" uniqKey="Holzer M" first="Markus" last="Holzer">Markus Holzer</name><affiliation><mods:affiliation>Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>1994</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">2FE43D8A47994F4BC60DE9B37868841FC85743A2</idno><idno type="DOI">10.1007/3-540-58338-6_74</idno><idno type="ChapterID">20</idno><idno type="ChapterID">Chap20</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We apply the inductive counting technique to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a consequence we obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immerman [6] and Szelepcsényi [12] to space bounds of order o(log n) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds [3, 5, 9].</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Carsten Damm</name><affiliations><json:string>FB IV-Informatik, Universität Trier, D-54286, Trier, Germany</json:string></affiliations></json:item><json:item><name>Markus Holzer</name><affiliations><json:string>Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>ReviewPaper</json:string></originalGenre><abstract>Abstract: We apply the inductive counting technique to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a consequence we obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immerman [6] and Szelepcsényi [12] to space bounds of order o(log n) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds [3, 5, 9].</abstract><qualityIndicators><score>5.875</score><pdfVersion>1.3</pdfVersion><pdfPageSize>439.2 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>971</abstractCharCount><pdfWordCount>4123</pdfWordCount><pdfCharCount>20299</pdfCharCount><pdfPageCount>10</pdfPageCount><abstractWordCount>146</abstractWordCount></qualityIndicators><title>Inductive counting below logspace</title><chapterId><json:string>20</json:string><json:string>Chap20</json:string></chapterId><refBibs><json:item><author><json:item><name>David,A Barrington</name></json:item></author><host><volume>38</volume><pages><last>164</last><first>150</first></pages><author></author><title>Journal of Computer and Systems Sciences</title><publicationDate>1989</publicationDate></host><title>Bounded width polynomial size branching programs can recognize exactly those languages in NC 1</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>Allen Borodin</name></json:item><json:item><name>Stephen,A Cook</name></json:item><json:item><name>Patrick,W Dymond</name></json:item><json:item><name>Walter,L Ruzzo</name></json:item><json:item><name>Martin Tompa</name></json:item></author><host><volume>18</volume><pages><last>578</last><first>559</first></pages><author></author><title>SIAM Journal on Computing</title><publicationDate>1989</publicationDate></host><title>Two appfications of inductive counting for complementation problems</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>Roma Burchard Yon Brannmfihl</name></json:item><json:item><name>Robert Gengler</name></json:item><json:item><name> Rettinger</name></json:item></author><host><volume>3</volume><pages><last>230</last><first>207</first></pages><author></author><title>Computational Complexity</title><publicationDate>1993</publicationDate></host><title>The alternation hierarchy for sublogarithmic space is infinite</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>Ashok,K Chandra</name></json:item><json:item><name>Dexter,C Kozen</name></json:item><json:item><name>Larry,J Stockmeyer</name></json:item></author><host><volume>28</volume><pages><last>133</last><first>114</first></pages><author></author><title>Alternation. Journal of the AUM</title><publicationDate>1981</publicationDate></host><publicationDate>1981</publicationDate></json:item><json:item><host><author><json:item><name>Villiam Geffert</name></json:item></author><title>A hierarchy that does not collapse: Alternations in low level space. 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DisplayOrder="Western"><GivenName>Carsten</GivenName><FamilyName>Damm</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Markus</GivenName><FamilyName>Holzer</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>FB IV-Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Institut für Informatik</OrgDivision><OrgName>Technische Universität München</OrgName><OrgAddress><Street>Arcisstr. 21</Street><Postcode>D-80290</Postcode><City>München</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We apply the inductive counting technique to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound <Emphasis Type="Italic">s(n)</Emphasis>, the class of languages accepted by <Emphasis Type="Italic">nonuniform</Emphasis> nondeterministic <Emphasis Type="Italic">O(s(n))</Emphasis> space bounded Turing machines is closed under complementation. As a consequence we obtain for arbitrary space bounds <Emphasis Type="Italic">s(n)</Emphasis> that the alternation hierarchy of <Emphasis Type="Italic">nonuniform O(s(n))</Emphasis> space bounded Turing machines collapses to its first level. This improves the previously known result of Immerman [6] and Szelepcsényi [12] to space bounds of order <Emphasis Type="Italic">o</Emphasis>(log <Emphasis Type="Italic">n</Emphasis>) in the nonuniform setting.</Para><Para>This reveals a strong difference to the relations between the corresponding <Emphasis Type="Italic">uniform</Emphasis> complexity classes, since very recently it has been proved that in the <Emphasis Type="Italic">uniform case</Emphasis> the alternating space hierarchy does not collapse for sublogarithmic space bounds [3, 5, 9].</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Partially supported by the Deutsche Forschungsgemeinschaft grant DFG La 618/1-1.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Inductive counting below logspace</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Inductive counting below logspace</title></titleInfo><name type="personal"><namePart type="given">Carsten</namePart><namePart type="family">Damm</namePart><affiliation>FB IV-Informatik, Universität Trier, D-54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Markus</namePart><namePart type="family">Holzer</namePart><affiliation>Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="ReviewPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2005-06-04</dateIssued><copyrightDate encoding="w3cdtf">1994</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 apply the inductive counting technique to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a consequence we obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immerman [6] and Szelepcsényi [12] to space bounds of order o(log n) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds [3, 5, 9].</abstract><relatedItem type="host"><titleInfo><title>Mathematical Foundations of Computer Science 1994</title><subTitle>19th International Symposium, MFCS'94 Košice, Slovakia, August 22–26, 1994 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Igor</namePart><namePart type="family">Prívara</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Branislav</namePart><namePart type="family">Rovan</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Peter</namePart><namePart type="family">Ruzička</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">1994</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="I16013">Computation by Abstract Devices</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I14029">Software Engineering</topic><topic authority="SpringerSubjectCodes" authorityURI="I14037">Programming Languages, Compilers, Interpreters</topic></subject><identifier type="DOI">10.1007/3-540-58338-6</identifier><identifier type="ISBN">978-3-540-58338-7</identifier><identifier type="eISBN">978-3-540-48663-3</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">42007</identifier><identifier type="BookID">3540583386</identifier><identifier type="BookChapterCount">54</identifier><identifier type="BookVolumeNumber">841</identifier><part><date>1994</date><detail type="volume"><number>841</number><caption>vol.</caption></detail><extent unit="pages"><start>276</start><end>285</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1994</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><originInfo><copyrightDate encoding="w3cdtf">1994</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, 1994</recordOrigin></recordInfo></relatedItem><identifier type="istex">2FE43D8A47994F4BC60DE9B37868841FC85743A2</identifier><identifier type="DOI">10.1007/3-540-58338-6_74</identifier><identifier type="ChapterID">20</identifier><identifier type="ChapterID">Chap20</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1994</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag, 1994</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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