Two Equivalent Regularizations for Tree Adjoining Grammars
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Auteurs : Anna KasprzikSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2009.
Abstract
Abstract: We present and compare two methods of how to make derivation in a Tree Adjoining Grammar a regular process (in the Chomsky hierarchy sense) without loss of expressive power. One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these two two-step approaches by giving a direct translation between lifted and three-dimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.
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DOI: 10.1007/978-3-642-00982-2_40
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One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these two two-step approaches by giving a direct translation between lifted and three-dimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Anna Kasprzik</name><affiliations><json:string>Informatik FB IV, University of Trier, D-54286, Trier,</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We present and compare two methods of how to make derivation in a Tree Adjoining Grammar a regular process (in the Chomsky hierarchy sense) without loss of expressive power. 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One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these two two-step approaches by giving a direct translation between lifted and three-dimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.</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>I16048</label><label>I16005</label><label>I17052</label><label>I1603X</label><label>I17001</label><label>I16013</label><item><term>Computer Science</term></item><item><term>Mathematical Logic and Formal Languages</term></item><item><term>Theory of Computation</term></item><item><term>Symbolic and Algebraic Manipulation</term></item><item><term>Logics and Meanings of Programs</term></item><item><term>Mathematics of 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University</OrgName><OrgAddress><City>Lancaster</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Carnegie Mellon University</OrgName><OrgAddress><City>Pittsburgh</City><State>PA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>University of Surrey</OrgName><OrgAddress><City>Guildford</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgName>Cornell University</OrgName><OrgAddress><City>Ithaca</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgName>ETH Zurich</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford 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" NumberingStyle="Unnumbered" OutputMedium="All" TocLevels="0"><BookID>978-3-642-00982-2</BookID><BookTitle>Language and Automata Theory and Applications</BookTitle><BookSubTitle>Third International Conference, LATA 2009, Tarragona, Spain, April 2-8, 2009. Proceedings</BookSubTitle><BookVolumeNumber>5457</BookVolumeNumber><BookSequenceNumber>5457</BookSequenceNumber><BookDOI>10.1007/978-3-642-00982-2</BookDOI><BookTitleID>186551</BookTitleID><BookPrintISBN>978-3-642-00981-5</BookPrintISBN><BookElectronicISBN>978-3-642-00982-2</BookElectronicISBN><BookChapterCount>63</BookChapterCount><BookCopyright><CopyrightHolderName>Springer Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16048" Priority="1" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I16005" Priority="2" Type="Secondary">Theory of Computation</BookSubject><BookSubject Code="I17052" Priority="3" Type="Secondary">Symbolic and Algebraic Manipulation</BookSubject><BookSubject Code="I1603X" Priority="4" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I17001" Priority="5" Type="Secondary">Mathematics of Computing</BookSubject><BookSubject Code="I16013" Priority="6" Type="Secondary">Computation by Abstract Devices</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Adrian</GivenName><GivenName>Horia</GivenName><FamilyName>Dediu</FamilyName></EditorName><Contact><Email>adrian.dediu@urv.cat</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Armand</GivenName><GivenName>Mihai</GivenName><FamilyName>Ionescu</FamilyName></EditorName><Contact><Email>armandmihai.ionescu@urv.cat</Email></Contact></Editor><Editor AffiliationIDS="Aff18"><EditorName DisplayOrder="Western"><GivenName>Carlos</GivenName><FamilyName>Martín-Vide</FamilyName></EditorName><Contact><Email>carlos.martin@urv.cat</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Research Group on Mathematical Linguistics</OrgDivision><OrgName>Rovira i Virgili University</OrgName><OrgAddress><Street>Av. Catalunya, 35</Street><Postcode>43002</Postcode><City>Tarragona</City><Country>Spain</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Research Group on Mathematical Linguistics</OrgDivision><OrgName>Universitat Rovira i Virgili</OrgName><OrgAddress><City>Tarragona</City><Country>Spain</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgName>European Research Council Executive Agency</OrgName><OrgAddress><Street>16 Place Rogier</Street><Postcode>1210</Postcode><City>Brussels</City><Country>Belgium</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Regular Papers</PartTitle><PartChapterCount>58</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Language and Automata Theory and Applications</BookTitle></PartContext></PartInfo><Chapter ID="Chap40" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>40</ChapterID><ChapterDOI>10.1007/978-3-642-00982-2_40</ChapterDOI><ChapterSequenceNumber>40</ChapterSequenceNumber><ChapterTitle Language="En">Two Equivalent Regularizations for Tree Adjoining Grammars</ChapterTitle><ChapterFirstPage>469</ChapterFirstPage><ChapterLastPage>480</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</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>978-3-642-00982-2</BookID><BookTitle>Language and Automata Theory and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Anna</GivenName><FamilyName>Kasprzik</FamilyName></AuthorName></Author><Affiliation ID="Aff19"><OrgDivision>Informatik FB IV</OrgDivision><OrgName>University of Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country> </Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We present and compare two methods of how to make derivation in a Tree Adjoining Grammar a regular process (in the Chomsky hierarchy sense) without loss of expressive power. One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these two two-step approaches by giving a direct translation between lifted and three-dimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Tree Adjoining Grammar</Keyword><Keyword>Multi-Dimensional Trees</Keyword><Keyword>Lifting</Keyword><Keyword>Regularization</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Two Equivalent Regularizations for Tree Adjoining Grammars</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Two Equivalent Regularizations for Tree Adjoining Grammars</title></titleInfo><name type="personal"><namePart type="given">Anna</namePart><namePart type="family">Kasprzik</namePart><affiliation>Informatik FB IV, University of Trier, D-54286, Trier</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">2009</dateIssued><copyrightDate encoding="w3cdtf">2009</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 and compare two methods of how to make derivation in a Tree Adjoining Grammar a regular process (in the Chomsky hierarchy sense) without loss of expressive power. One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these two two-step approaches by giving a direct translation between lifted and three-dimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.</abstract><relatedItem type="host"><titleInfo><title>Language and Automata Theory and Applications</title><subTitle>Third International Conference, LATA 2009, Tarragona, Spain, April 2-8, 2009. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Adrian</namePart><namePart type="given">Horia</namePart><namePart type="family">Dediu</namePart><affiliation>Research Group on Mathematical Linguistics, Rovira i Virgili University, Av. 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">Armand</namePart><namePart type="given">Mihai</namePart><namePart type="family">Ionescu</namePart><affiliation>Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, Spain</affiliation><affiliation>E-mail: armandmihai.ionescu@urv.cat</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Carlos</namePart><namePart type="family">Martín-Vide</namePart><affiliation>European Research Council Executive Agency, 16 Place Rogier, 1210, Brussels, Belgium</affiliation><affiliation>E-mail: carlos.martin@urv.cat</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2009</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="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I16005">Theory of Computation</topic><topic authority="SpringerSubjectCodes" authorityURI="I17052">Symbolic and Algebraic Manipulation</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I17001">Mathematics of Computing</topic><topic authority="SpringerSubjectCodes" authorityURI="I16013">Computation by Abstract Devices</topic></subject><identifier type="DOI">10.1007/978-3-642-00982-2</identifier><identifier type="ISBN">978-3-642-00981-5</identifier><identifier type="eISBN">978-3-642-00982-2</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">186551</identifier><identifier type="BookID">978-3-642-00982-2</identifier><identifier type="BookChapterCount">63</identifier><identifier type="BookVolumeNumber">5457</identifier><identifier type="BookSequenceNumber">5457</identifier><identifier type="PartChapterCount">58</identifier><part><date>2009</date><detail type="part"><title>Regular Papers</title></detail><detail type="volume"><number>5457</number><caption>vol.</caption></detail><extent unit="pages"><start>469</start><end>480</end></extent></part><recordInfo><recordOrigin>Springer Berlin Heidelberg, 2009</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="family">Hutchison</namePart><affiliation>Lancaster University, Lancaster, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm 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 type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of California, Los Angeles, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Doug</namePart><namePart type="family">Tygar</namePart><affiliation>University of California, Berkeley, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moshe</namePart><namePart type="given">Y.</namePart><namePart type="family">Vardi</namePart><affiliation>Rice University, Houston, TX, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Weikum</namePart><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2009</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 Berlin Heidelberg, 2009</recordOrigin></recordInfo></relatedItem><identifier type="istex">B71467CCB0267521D8E3E195076903E90DAB8787</identifier><identifier type="DOI">10.1007/978-3-642-00982-2_40</identifier><identifier type="ChapterID">40</identifier><identifier type="ChapterID">Chap40</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer Berlin Heidelberg, 2009</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2009</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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