On self-reducible sets of low information content
Identifieur interne : 001235 ( Istex/Corpus ); précédent : 001234; suivant : 001236On self-reducible sets of low information content
Auteurs : Martin MundhenkSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1994.
Abstract
Abstract: Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.
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DOI: 10.1007/3-540-57811-0_17
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The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Martin Mundhenk</name><affiliations><json:string>Fachbereich IV - Informatik, Universität Trier, D-54286, Trier, Germany</json:string><json:string>E-mail: mundhenk@uni-trier.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>ReviewPaper</json:string></originalGenre><abstract>Abstract: Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.</abstract><qualityIndicators><score>6.263</score><pdfVersion>1.3</pdfVersion><pdfPageSize>439.28 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>881</abstractCharCount><pdfWordCount>4487</pdfWordCount><pdfCharCount>19604</pdfCharCount><pdfPageCount>10</pdfPageCount><abstractWordCount>148</abstractWordCount></qualityIndicators><title>On self-reducible sets of low information content</title><chapterId><json:string>17</json:string><json:string>Chap17</json:string></chapterId><refBibs><json:item><host><author><json:item><name>V Arvind</name></json:item><json:item><name>Y Hart</name></json:item><json:item><name>L Hemachandra</name></json:item><json:item><name>A K5bler</name></json:item><json:item><name>M Lozano</name></json:item><json:item><name>M Mundhenk</name></json:item><json:item><name>U Ogiwara</name></json:item><json:item><name>R Schsning</name></json:item><json:item><name>T Silvestri</name></json:item><json:item><name> Thierauf</name></json:item></author><title>Reductions to sets of low information content</title><publicationDate>1993</publicationDate></host></json:item><json:item><author><json:item><name>V Arvind</name></json:item><json:item><name>J Ksbler</name></json:item><json:item><name>M Mundhenk</name></json:item></author><host><pages><last>258</last><first>249</first></pages><author></author><title>Proc. 3rd ISAAC</title><publicationDate>1992</publicationDate></host><title>Lowness and the complexity of sparse and tally descriptions</title><publicationDate>1992</publicationDate></json:item><json:item><author><json:item><name>V Arvind</name></json:item><json:item><name>J K6bler</name></json:item><json:item><name>M Mundhenk</name></json:item></author><host><pages><last>241</last><first>232</first></pages><author></author><title>Proc. 18th MFGS</title><publicationDate>1993</publicationDate></host><title>Hausdorff reductions to sparse sets and to sets of high information content</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>J,J L Self-Reducibility</name></json:item><json:item><name>R Balcs</name></json:item><json:item><name>U Book</name></json:item><json:item><name> Schsning</name></json:item></author><host><volume>41</volume><pages><last>388739</last><first>367</first></pages><issue>15</issue><author></author><title>Journal of Computer and System Sciences SIAM Journal on Computing J.L. 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Wagner</name></json:item></author><host><volume>51</volume><pages><last>80</last><first>53</first></pages><author></author><title>Theoretical Computer Science</title><publicationDate>1987</publicationDate></host><title>More comphcated questions about maxima and minima, and some closures of NP</title><publicationDate>1987</publicationDate></json:item></refBibs><genre><json:string>conference</json:string></genre><serie><editor><json:item><name>G. 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The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>I</label><label>I16013</label><label>I16021</label><label>I15017</label><label>M17009</label><item><term>Computer Science</term></item><item><term>Computation by Abstract Devices</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Data 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abstract</ChapterSubTitle><ChapterFirstPage>203</ChapterFirstPage><ChapterLastPage>212</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1994</CopyrightYear></ChapterCopyright><ChapterHistory><OnlineDate><Year>2005</Year><Month>5</Month><Day>26</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>3540578110</BookID><BookTitle>Algorithms and Complexity</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Martin</GivenName><FamilyName>Mundhenk</FamilyName></AuthorName><Contact><Email>mundhenk@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich 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>Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily <Emphasis Type="Italic">all</Emphasis> information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in <Emphasis Type="Italic">APT′)</Emphasis>. Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in P<Superscript>NP</Superscript>, if they are self-reducible in a little more restricted sense of self-reducibility.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Work done at Universität Ulm, Abt. Theoretische Informatik. Supported in part by the DAAD through Acciones Integradas 1992, 313-AI-e-es/zk.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On self-reducible sets of low information content</title><subTitle>Extended abstract</subTitle></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On self-reducible sets of low information content</title><subTitle>Extended abstract</subTitle></titleInfo><name type="personal"><namePart type="given">Martin</namePart><namePart type="family">Mundhenk</namePart><affiliation>Fachbereich IV - Informatik, Universität Trier, D-54286, Trier, Germany</affiliation><affiliation>E-mail: mundhenk@uni-trier.de</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">2005-05-26</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: Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.</abstract><relatedItem type="host"><titleInfo><title>Algorithms and Complexity</title><subTitle>Second Italian Conference, CIAC '94 Rome, Italy, February 23–25, 1994 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Bonuccelli</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">P.</namePart><namePart type="family">Crescenzi</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Petreschi</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="I15017">Data Structures</topic><topic authority="SpringerSubjectCodes" authorityURI="M17009">Combinatorics</topic></subject><identifier type="DOI">10.1007/3-540-57811-0</identifier><identifier type="ISBN">978-3-540-57811-6</identifier><identifier type="eISBN">978-3-540-48337-3</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">39088</identifier><identifier type="BookID">3540578110</identifier><identifier type="BookChapterCount">18</identifier><identifier type="BookVolumeNumber">778</identifier><part><date>1994</date><detail type="volume"><number>778</number><caption>vol.</caption></detail><extent unit="pages"><start>203</start><end>212</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">78B668B1AF663FF55AAE659F4729213F9F640EFC</identifier><identifier type="DOI">10.1007/3-540-57811-0_17</identifier><identifier type="ChapterID">17</identifier><identifier type="ChapterID">Chap17</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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