Top-down lower bounds for depth-three circuits
Identifieur interne : 001080 ( Istex/Corpus ); précédent : 001079; suivant : 001081Top-down lower bounds for depth-three circuits
Auteurs : J. H Stad ; S. Jukna ; P. PudlákSource :
- computational complexity [ 1016-3328 ] ; 1995-06-01.
Abstract
Abstract: We present a top-down lower bound method for depth-three ⋎, ⋏, ¬-circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.
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DOI: 10.1007/BF01268140
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H Stad</name><affiliation><mods:affiliation>Royal Institute of Technology, Stockholm, Sweden</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: johanh@nada.kth.se</mods:affiliation></affiliation></author><author><name sortKey="Jukna, S" sort="Jukna, S" uniqKey="Jukna S" first="S." last="Jukna">S. Jukna</name><affiliation><mods:affiliation>Institute of Mathematics, Vilnius, Lithuania</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: jokna@ti.uni-trier.de</mods:affiliation></affiliation></author><author><name sortKey="Pudlak, P" sort="Pudlak, P" uniqKey="Pudlak P" first="P." last="Pudlák">P. 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In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>J. Håstad</name><affiliations><json:string>Royal Institute of Technology, Stockholm, Sweden</json:string><json:string>E-mail: johanh@nada.kth.se</json:string></affiliations></json:item><json:item><name>S. Jukna</name><affiliations><json:string>Institute of Mathematics, Vilnius, Lithuania</json:string><json:string>E-mail: jokna@ti.uni-trier.de</json:string></affiliations></json:item><json:item><name>P. 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This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</abstract><qualityIndicators><score>5.888</score><pdfVersion>1.3</pdfVersion><pdfPageSize>482.28 x 677 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>458</abstractCharCount><pdfWordCount>5135</pdfWordCount><pdfCharCount>22355</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>74</abstractWordCount></qualityIndicators><title>Top-down lower bounds for depth-three circuits</title><refBibs><json:item><author></author><host><volume>24</volume><pages><last>48</last><first>1</first></pages><author></author><title>Ann. Pure and AppI. 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In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Computer Science</head><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Computational Mathematics and Numerical Analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1995-06-01">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="2017-01-20">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/E554537508CD0DB48F68395CD7D52FDA793697DC/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no 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DisplayOrder="Western"><GivenName>J.</GivenName><FamilyName>Håstad</FamilyName></AuthorName><Contact><Email>johanh@nada.kth.se</Email></Contact></Author><Author AffiliationIDS="Aff2" PresentAffiliationID="Aff3"><AuthorName DisplayOrder="Western"><GivenName>S.</GivenName><FamilyName>Jukna</FamilyName></AuthorName><Contact><Email>jokna@ti.uni-trier.de</Email></Contact></Author><Author AffiliationIDS="Aff4"><AuthorName DisplayOrder="Western"><GivenName>P.</GivenName><FamilyName>Pudlák</FamilyName></AuthorName><Contact><Email>pudlak@csearn.bitnet</Email></Contact></Author><Affiliation ID="Aff1"><OrgName>Royal Institute of Technology</OrgName><OrgAddress><City>Stockholm</City><Country>Sweden</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgName>Mathematical Institute</OrgName><OrgAddress><City>Prague</City><Country>Czech Republic</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Institute of Mathematics</OrgName><OrgAddress><City>Vilnius</City><Country>Lithuania</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>University of Trier</OrgName><OrgAddress><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We present a top-down lower bound method for depth-three ⋎, ⋏, ¬-circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least<InlineEquation ID="IE1"><InlineMediaObject><ImageObject FileRef="37_2005_Article_BF01268140_TeX2GIFIE1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX"> $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ </EquationSource></InlineEquation>, respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Computational complexity</Keyword><Keyword>small-depth circuits</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>subject classifications</Heading><Keyword>68Q25</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Top-down lower bounds for depth-three circuits</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Top-down lower bounds for depth-three circuits</title></titleInfo><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Håstad</namePart><affiliation>Royal Institute of Technology, Stockholm, Sweden</affiliation><affiliation>E-mail: johanh@nada.kth.se</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Jukna</namePart><affiliation>Institute of Mathematics, Vilnius, Lithuania</affiliation><affiliation>E-mail: jokna@ti.uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">P.</namePart><namePart type="family">Pudlák</namePart><affiliation>Mathematical Institute, Prague, Czech Republic</affiliation><affiliation>E-mail: pudlak@csearn.bitnet</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Birkhäuser-Verlag</publisher><place><placeTerm type="text">Basel</placeTerm></place><dateIssued encoding="w3cdtf">1995-06-01</dateIssued><copyrightDate encoding="w3cdtf">1995</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 present a top-down lower bound method for depth-three ⋎, ⋏, ¬-circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</abstract><relatedItem type="host"><titleInfo><title>computational complexity</title></titleInfo><titleInfo type="abbreviated"><title>Comput Complexity</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1995-06-01</dateIssued><copyrightDate encoding="w3cdtf">1995</copyrightDate></originInfo><subject><genre>Computer Science</genre><topic>Algorithm Analysis and Problem Complexity</topic><topic>Computational Mathematics and Numerical Analysis</topic></subject><identifier type="ISSN">1016-3328</identifier><identifier type="eISSN">1420-8954</identifier><identifier type="JournalID">37</identifier><identifier type="IssueArticleCount">5</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1995</date><detail type="volume"><number>5</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="pages"><start>99</start><end>112</end></extent></part><recordInfo><recordOrigin>Birkhäuser Verlag, 1995</recordOrigin></recordInfo></relatedItem><identifier type="istex">E554537508CD0DB48F68395CD7D52FDA793697DC</identifier><identifier type="DOI">10.1007/BF01268140</identifier><identifier type="ArticleID">BF01268140</identifier><identifier type="ArticleID">Art1</identifier><accessCondition type="use and reproduction" contentType="copyright">Birkhäuser Verlag, 1995</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Birkhäuser Verlag, 1995</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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