Nondeterministic Instance Complexity and Hard-to-Prove Tautologies
Identifieur interne : 000D79 ( Istex/Corpus ); précédent : 000D78; suivant : 000D80Nondeterministic Instance Complexity and Hard-to-Prove Tautologies
Auteurs : Vikraman Arvind ; Johannes Köbler ; Martin Mundhenk ; Jacobo ToránSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2000.
Abstract
Abstract: In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic assumptions, that there are infinitely many propositional tautologies that are hard to prove in any sound propositional proof system.
Url:
DOI: 10.1007/3-540-46541-3_26
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ISTEX:28874A2076C489F821A003B62EB091D49D9B5B73Le document en format XML
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Heidelberg</CopyrightHolderName><CopyrightYear>2000</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16005" Priority="1" Type="Secondary">Theory of Computation</BookSubject><BookSubject Code="I14002" Priority="2" Type="Secondary">Software Engineering/Programming and Operating Systems</BookSubject><BookSubject Code="I15009" Priority="3" Type="Secondary">Data Structures, Cryptology and Information Theory</BookSubject><BookSubject Code="I22013" Priority="4" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I17001" Priority="5" Type="Secondary">Mathematics of Computing</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Horst</GivenName><FamilyName>Reichel</FamilyName></EditorName><Contact><Email>reichel@tcs.inf.tu-dresden.de</Email></Contact></Editor><Editor AffiliationIDS="Aff5"><EditorName DisplayOrder="Western"><GivenName>Sophie</GivenName><FamilyName>Tison</FamilyName></EditorName><Contact><Email>Sophie.Tison@lifl.fr</Email></Contact></Editor><Affiliation ID="Aff4"><OrgDivision>Faculty of Computer Science, Dept. of Theoretical Computer Science</OrgDivision><OrgName>Universität Dresden</OrgName><OrgAddress><Postcode>01062</Postcode><City>Dresden</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgName>Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA</OrgName><OrgAddress><Postcode>59655</Postcode><City>Villeneuve d’ASCQ Cedex</City><Country>France</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap26" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" Language="En" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>26</ChapterID><ChapterDOI>10.1007/3-540-46541-3_26</ChapterDOI><ChapterSequenceNumber>26</ChapterSequenceNumber><ChapterTitle Language="En">Nondeterministic Instance Complexity and Hard-to-Prove Tautologies</ChapterTitle><ChapterFirstPage>314</ChapterFirstPage><ChapterLastPage>323</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2000</CopyrightYear></ChapterCopyright><ChapterHistory><RegistrationDate><Year>2000</Year><Month>3</Month><Day>23</Day></RegistrationDate><OnlineDate><Year>2000</Year><Month>3</Month><Day>24</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>3-540-46541-3</BookID><BookTitle>STACS 2000</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff6"><AuthorName DisplayOrder="Western"><GivenName>Vikraman</GivenName><FamilyName>Arvind</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff7"><AuthorName DisplayOrder="Western"><GivenName>Johannes</GivenName><FamilyName>Köbler</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>Martin</GivenName><FamilyName>Mundhenk</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff9"><AuthorName DisplayOrder="Western"><GivenName>Jacobo</GivenName><FamilyName>Torán</FamilyName></AuthorName></Author><Affiliation ID="Aff6"><OrgDivision>Institute of Mathematical Sciences</OrgDivision><OrgName>C.I.T Campus</OrgName><OrgAddress><City>Madras</City><Postcode>600113</Postcode><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgDivision>Institut für Informatik</OrgDivision><OrgName>Humboldt-Universität zu Berlin</OrgName><OrgAddress><Postcode>D-10099</Postcode><City>Berlin</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgDivision>Fachbereich IV — Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgDivision>Theoretische Informatik</OrgDivision><OrgName>Universität Ulm</OrgName><OrgAddress><Postcode>D-89069</Postcode><City>Ulm</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic assumptions, that there are infinitely many propositional tautologies that are hard to prove in any sound propositional proof system.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Nondeterministic Instance Complexity and Hard-to-Prove Tautologies</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Nondeterministic Instance Complexity and Hard-to-Prove Tautologies</title></titleInfo><name type="personal"><namePart type="given">Vikraman</namePart><namePart type="family">Arvind</namePart><affiliation>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">Johannes</namePart><namePart type="family">Köbler</namePart><affiliation>Institut für Informatik, Humboldt-Universität zu Berlin, D-10099, Berlin, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Martin</namePart><namePart type="family">Mundhenk</namePart><affiliation>Fachbereich IV — Informatik, Universität Trier, D-54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jacobo</namePart><namePart type="family">Torán</namePart><affiliation>Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2000-03-24</dateIssued><copyrightDate encoding="w3cdtf">2000</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: In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic assumptions, that there are infinitely many propositional tautologies that are hard to prove in any sound propositional proof system.</abstract><relatedItem type="host"><titleInfo><title>STACS 2000</title><subTitle>17th Annual Symposium on Theoretical Aspects of Computer Science Lille, France, February 17–19, 2000 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Horst</namePart><namePart type="family">Reichel</namePart><affiliation>Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany</affiliation><affiliation>E-mail: reichel@tcs.inf.tu-dresden.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Sophie</namePart><namePart type="family">Tison</namePart><affiliation>Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France</affiliation><affiliation>E-mail: Sophie.Tison@lifl.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2000</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="I16005">Theory of Computation</topic><topic authority="SpringerSubjectCodes" authorityURI="I14002">Software Engineering/Programming and Operating Systems</topic><topic authority="SpringerSubjectCodes" authorityURI="I15009">Data Structures, Cryptology and Information Theory</topic><topic authority="SpringerSubjectCodes" authorityURI="I22013">Computer Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I17001">Mathematics of Computing</topic></subject><identifier type="DOI">10.1007/3-540-46541-3</identifier><identifier type="ISBN">978-3-540-67141-1</identifier><identifier type="eISBN">978-3-540-46541-6</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="BookTitleID">62734</identifier><identifier type="BookID">3-540-46541-3</identifier><identifier type="BookChapterCount">54</identifier><identifier type="BookVolumeNumber">1770</identifier><identifier type="BookSequenceNumber">1770</identifier><part><date>2000</date><detail type="volume"><number>1770</number><caption>vol.</caption></detail><extent unit="pages"><start>314</start><end>323</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2000</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><affiliation>Karlsruhe University, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><affiliation>Cornell University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><affiliation>Utrecht University, The Netherlands</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2000</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2000</recordOrigin></recordInfo></relatedItem><identifier type="istex">28874A2076C489F821A003B62EB091D49D9B5B73</identifier><identifier type="DOI">10.1007/3-540-46541-3_26</identifier><identifier type="ChapterID">26</identifier><identifier type="ChapterID">Chap26</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2000</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2000</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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