Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach
Identifieur interne : 001A92 ( Istex/Corpus ); précédent : 001A91; suivant : 001A93Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach
Auteurs : Christophe Costa Florêncio ; Henning FernauSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2010.
Abstract
Abstract: Kanazawa ([8]) has studied the learnability of several parameterized families of classes of categorial grammars. These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. As far as the authors are aware, this is the first such result for learning problems.
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DOI: 10.1007/978-3-642-13089-2_17
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These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. 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They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. 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Ann. Univ. Sci. Budapest, Eötvös Sect. Math</title><publicationDate>1959</publicationDate></host><title>Learning Categorial Grammars The Netherlands</title><publicationDate>1959</publicationDate></json:item><json:item><author><json:item><name>D,S Johnson</name></json:item></author><host><volume>1</volume><pages><last>176</last><first>160</first></pages><issue>1</issue><author></author><title>ACM Transactions on Algorithms</title><publicationDate>2005</publicationDate></host><title>The NP-completeness column</title><publicationDate>2005</publicationDate></json:item><json:item><host><author><json:item><name>M Kanazawa</name></json:item></author><title>Learnable Classes of Categorial Grammars</title><publicationDate>1998</publicationDate></host></json:item><json:item><author><json:item><name>J Köbler</name></json:item><json:item><name>U Schöning</name></json:item><json:item><name>J Torán</name></json:item></author><host><author></author><title>Birkhäuser</title><publicationDate>1993</publicationDate></host><title>Graph Isomorphism Problem: The Structural Complexity</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>T Moriyama</name></json:item><json:item><name>M Sato</name></json:item><json:item><name>S Kobayashi</name></json:item><json:item><name>T Yokomori</name></json:item><json:item><name>K,P Jantke</name></json:item></author><host><pages><last>196</last><first>187</first></pages><author></author><title>Tomita, E ALT 1993</title><publicationDate>1993</publicationDate></host><title>Properties of language classes with finite elasticity</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>K Reinhardt</name></json:item></author><host><pages><last>450</last><first>441</first></pages><author></author><title>FCT 1999</title><publicationDate>1999</publicationDate></host><title>A parallel context-free derivation hierarchy</title><publicationDate>1999</publicationDate></json:item></refBibs><genre><json:string>conference</json:string></genre><serie><editor><json:item><name>David Hutchison</name><affiliations><json:string>Lancaster University, Lancaster, UK</json:string></affiliations></json:item><json:item><name>Takeo Kanade</name><affiliations><json:string>Carnegie Mellon University, Pittsburgh, PA, USA</json:string></affiliations></json:item><json:item><name>Josef Kittler</name><affiliations><json:string>University of Surrey, Guildford, UK</json:string></affiliations></json:item><json:item><name>Jon M. 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These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. As far as the authors are aware, this is the first such result for learning problems.</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>I21017</label><label>I16048</label><label>I2203X</label><label>I1603X</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>Artificial Intelligence (incl. 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University</OrgName><OrgAddress><City>Stanford</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Weizmann Institute of Science</OrgName><OrgAddress><City>Rehovot</City><Country>Israel</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-13089-2</BookID><BookTitle>Language and Automata Theory and Applications</BookTitle><BookSubTitle>4th International Conference, LATA 2010, Trier, Germany, May 24-28, 2010. Proceedings</BookSubTitle><BookVolumeNumber>6031</BookVolumeNumber><BookSequenceNumber>6031</BookSequenceNumber><BookDOI>10.1007/978-3-642-13089-2</BookDOI><BookTitleID>211346</BookTitleID><BookPrintISBN>978-3-642-13088-5</BookPrintISBN><BookElectronicISBN>978-3-642-13089-2</BookElectronicISBN><BookChapterCount>51</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2010</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16013" Priority="1" Type="Secondary">Computation by Abstract Devices</BookSubject><BookSubject Code="I16021" Priority="2" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I21017" Priority="3" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I16048" Priority="4" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I2203X" Priority="5" Type="Secondary">Pattern Recognition</BookSubject><BookSubject Code="I1603X" Priority="6" Type="Secondary">Logics and Meanings of Programs</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Adrian-Horia</GivenName><FamilyName>Dediu</FamilyName></EditorName><Contact><Email>adrian.dediu@urv.cat</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></EditorName><Contact><Email>fernau@informatik.uni-trier.de</Email></Contact></Editor><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Carlos</GivenName><FamilyName>Martín-Vide</FamilyName></EditorName><Contact><Email>cmv@astor.urv.es</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Research Group on Mathematical Linguistics</OrgDivision><OrgName>Universitat Rovira i Virgili</OrgName><OrgAddress><Street>Avinguda Catalunya, 35</Street><Postcode>43002</Postcode><City>Tarragona</City><Country>Spain</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Fachbereich IV - Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Street>Campus II, Behringstraße</Street><Postcode>54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Regular Papers</PartTitle><PartChapterCount>47</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Language and Automata Theory and Applications</BookTitle></PartContext></PartInfo><Chapter ID="Chap17" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>17</ChapterID><ChapterDOI>10.1007/978-3-642-13089-2_17</ChapterDOI><ChapterSequenceNumber>17</ChapterSequenceNumber><ChapterTitle Language="En">Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach</ChapterTitle><ChapterFirstPage>202</ChapterFirstPage><ChapterLastPage>213</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2010</CopyrightYear></ChapterCopyright><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><PartID>2</PartID><BookID>978-3-642-13089-2</BookID><BookTitle>Language and Automata Theory and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>Christophe</GivenName><FamilyName>Costa Florêncio</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Henning</GivenName><FamilyName>Fernau</FamilyName></AuthorName><Contact><Email>fernau@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff18"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>K.U. Leuven</OrgName><OrgAddress><City>Leuven</City><Country>Belgium</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgDivision>FB IV—Abteilung 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>Kanazawa ([8]) has studied the learnability of several parameterized families of classes of categorial grammars. These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar.</Para><Para>The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. As far as the authors are aware, this is the first such result for learning problems.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Finding Consistent Categorial Grammars of Bounded Value: A Parameterized Approach</title></titleInfo><name type="personal"><namePart type="given">Christophe</namePart><namePart type="family">Costa Florêncio</namePart><affiliation>Department of Computer Science, K.U. Leuven, Leuven, Belgium</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>FB IV—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany</affiliation><affiliation>E-mail: fernau@uni-trier.de</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">2010</dateIssued><copyrightDate encoding="w3cdtf">2010</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: Kanazawa ([8]) has studied the learnability of several parameterized families of classes of categorial grammars. These classes were shown to be learnable from text, in the technical sense of identifiability in the limit from positive data. They are defined in terms of bounds on certain parameters of the grammars. Intuitively, these bounds correspond to restrictions on linguistic aspects such as the amount of lexical ambiguity of the grammar. The time complexity of learning these classes has been studied by Costa Florêncio ([4]). It was shown that for most of these classes, selecting a grammar from the class that is consistent with the data is NP-hard. In this paper existing complexity results are sharpened by demonstrating W[2]-hardness. Additional parameters allowing FPT-results are also studied, and it is shown that if these parameters are fixed, these problems become computable in polynomial time. As far as the authors are aware, this is the first such result for learning problems.</abstract><relatedItem type="host"><titleInfo><title>Language and Automata Theory and Applications</title><subTitle>4th International Conference, LATA 2010, Trier, Germany, May 24-28, 2010. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Adrian-Horia</namePart><namePart type="family">Dediu</namePart><affiliation>Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain</affiliation><affiliation>E-mail: adrian.dediu@urv.cat</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Henning</namePart><namePart type="family">Fernau</namePart><affiliation>Fachbereich IV - Informatik, Universität Trier, Campus II, Behringstraße, 54286, Trier, Germany</affiliation><affiliation>E-mail: fernau@informatik.uni-trier.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Carlos</namePart><namePart type="family">Martín-Vide</namePart><affiliation>Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain</affiliation><affiliation>E-mail: cmv@astor.urv.es</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2010</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="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I2203X">Pattern Recognition</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic></subject><identifier type="DOI">10.1007/978-3-642-13089-2</identifier><identifier type="ISBN">978-3-642-13088-5</identifier><identifier type="eISBN">978-3-642-13089-2</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">211346</identifier><identifier type="BookID">978-3-642-13089-2</identifier><identifier type="BookChapterCount">51</identifier><identifier type="BookVolumeNumber">6031</identifier><identifier type="BookSequenceNumber">6031</identifier><identifier type="PartChapterCount">47</identifier><part><date>2010</date><detail type="part"><title>Regular Papers</title></detail><detail 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type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm 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encoding="w3cdtf">2010</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 Berlin Heidelberg, 2010</recordOrigin></recordInfo></relatedItem><identifier type="istex">05B669A8A52C0DD3027866D0B0C80AA55FBB31F7</identifier><identifier type="DOI">10.1007/978-3-642-13089-2_17</identifier><identifier type="ChapterID">17</identifier><identifier type="ChapterID">Chap17</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2010</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2010</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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