Quasi-interpretations and Small Space Bounds
Identifieur interne : 003509 ( Istex/Corpus ); précédent : 003508; suivant : 003510Quasi-interpretations and Small Space Bounds
Auteurs : Guillaume Bonfante ; Jean-Yves Marion ; Jean-Yves MoyenSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. They not only combine well with path orderings and provide characterizations of usual complexity classes but also give hints in order to optimize the program. Moreover, the existence of a quasi-interpretation is decidable. In this paper, we present some more characterizations of complexity classes using quasi-interpretations. We mainly focus on small space-bounded complexity classes. On one hand, by restricting quasi-interpretations to sums (that is allowing only affine quasi-interpretations), we obtain a characterization of LinSpace. On the other hand, a strong tiering discipline on programs together with quasi-interpretations yield a characterization of LogSpace. Lastly, we give two new characterizations of Pspace: in the first, the quasi-interpretation has to be strictly decreasing on each rule and in the second, some linearity constraints are added to the system but no assumption concerning the termination proof is made.
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DOI: 10.1007/978-3-540-32033-3_12
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Quasi-interpretations and Small Space Bounds</title><author><name sortKey="Bonfante, Guillaume" sort="Bonfante, Guillaume" uniqKey="Bonfante G" first="Guillaume" last="Bonfante">Guillaume Bonfante</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</mods:affiliation></affiliation></author><author><name sortKey="Marion, Jean Yves" sort="Marion, Jean Yves" uniqKey="Marion J" first="Jean-Yves" last="Marion">Jean-Yves Marion</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</mods:affiliation></affiliation></author><author><name sortKey="Moyen, Jean Yves" sort="Moyen, Jean Yves" uniqKey="Moyen J" first="Jean-Yves" last="Moyen">Jean-Yves Moyen</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>Université Henri Poincaré Nancy I, France</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:DECCC95DF46E0E94FB462E046F0D122082735A12</idno><date when="2005" year="2005">2005</date><idno type="doi">10.1007/978-3-540-32033-3_12</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-46N9XPCH-J/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">003509</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003509</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Quasi-interpretations and Small Space Bounds</title><author><name sortKey="Bonfante, Guillaume" sort="Bonfante, Guillaume" uniqKey="Bonfante G" first="Guillaume" last="Bonfante">Guillaume Bonfante</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</mods:affiliation></affiliation></author><author><name sortKey="Marion, Jean Yves" sort="Marion, Jean Yves" uniqKey="Marion J" first="Jean-Yves" last="Marion">Jean-Yves Marion</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</mods:affiliation></affiliation></author><author><name sortKey="Moyen, Jean Yves" sort="Moyen, Jean Yves" uniqKey="Moyen J" first="Jean-Yves" last="Moyen">Jean-Yves Moyen</name><affiliation><mods:affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>Université Henri Poincaré Nancy I, France</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. They not only combine well with path orderings and provide characterizations of usual complexity classes but also give hints in order to optimize the program. Moreover, the existence of a quasi-interpretation is decidable. In this paper, we present some more characterizations of complexity classes using quasi-interpretations. We mainly focus on small space-bounded complexity classes. On one hand, by restricting quasi-interpretations to sums (that is allowing only affine quasi-interpretations), we obtain a characterization of LinSpace. On the other hand, a strong tiering discipline on programs together with quasi-interpretations yield a characterization of LogSpace. Lastly, we give two new characterizations of Pspace: in the first, the quasi-interpretation has to be strictly decreasing on each rule and in the second, some linearity constraints are added to the system but no assumption concerning the termination proof is made.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>Guillaume Bonfante</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</json:string><json:string>INPL, École Nationale Supérieure des Mines de Nancy, France</json:string></affiliations></json:item><json:item><name>Jean-Yves Marion</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</json:string><json:string>INPL, École Nationale Supérieure des Mines de Nancy, France</json:string></affiliations></json:item><json:item><name>Jean-Yves Moyen</name><affiliations><json:string>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</json:string><json:string>Université Henri Poincaré Nancy I, France</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-46N9XPCH-J</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. 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key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Friedemann</forename><surname>Mattern</surname></persName><affiliation><orgName type="institution">ETH Zurich</orgName><address><country key="CH">SWITZERLAND</country></address></affiliation></editor><editor><persName><forename type="first">John</forename><forename type="first">C.</forename><surname>Mitchell</surname></persName><affiliation><orgName type="institution">Stanford University</orgName><address><settlement>CA</settlement><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Moni</forename><surname>Naor</surname></persName><affiliation><orgName type="institution">Weizmann Institute of Science</orgName><address><settlement>Rehovot</settlement><country key="IL">ISRAEL</country></address></affiliation></editor><editor><persName><forename type="first">Oscar</forename><surname>Nierstrasz</surname></persName><affiliation><orgName type="institution">University of Bern</orgName><address><country key="CH">SWITZERLAND</country></address></affiliation></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName><affiliation><orgName type="institution">Indian Institute of Technology</orgName><address><settlement>Madras</settlement><country key="IN">INDIA</country></address></affiliation></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName><affiliation><orgName type="institution">University of Dortmund</orgName><address><country key="DE">GERMANY</country></address></affiliation></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName><affiliation><orgName type="institution">Massachusetts Institute of Technology</orgName><address><settlement>MA</settlement><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName><affiliation><orgName type="institution">New York University</orgName><address><settlement>NY</settlement><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Dough</forename><surname>Tygar</surname></persName><affiliation><orgName type="institution">University of California</orgName><address><settlement>Berkeley</settlement><region>CA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName><affiliation><orgName type="institution">Rice University</orgName><address><settlement>Houston</settlement><region>TX</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation><orgName type="institution">Max-Planck Institute of Computer Science</orgName><address><settlement>Saarbruecken</settlement><country key="DE">GERMANY</country></address></affiliation></editor><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. They not only combine well with path orderings and provide characterizations of usual complexity classes but also give hints in order to optimize the program. Moreover, the existence of a quasi-interpretation is decidable.</p><p>In this paper, we present some more characterizations of complexity classes using quasi-interpretations. We mainly focus on small space-bounded complexity classes. On one hand, by restricting quasi-interpretations to sums (that is allowing only affine quasi-interpretations), we obtain a characterization of <hi rend="smallCaps">LinSpace</hi>. On the other hand, a strong tiering discipline on programs together with quasi-interpretations yield a characterization of <hi rend="smallCaps">LogSpace</hi>.</p><p>Lastly, we give two new characterizations of <hi rend="smallCaps">Pspace</hi>: in the first, the quasi-interpretation has to be strictly decreasing on each rule and in the second, some linearity constraints are added to the system but no assumption concerning the termination proof is made.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I16048</label><item><term type="Secondary" subtype="priority-1">Mathematical Logic and Formal Languages</term></item><label>I1603X</label><item><term type="Secondary" subtype="priority-2">Logics and Meanings of Programs</term></item><label>I14037</label><item><term type="Secondary" subtype="priority-3">Programming Languages, Compilers, Interpreters</term></item><label>I21017</label><item><term type="Secondary" subtype="priority-4">Artificial Intelligence (incl. 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DisplayOrder="Western"><GivenName>Friedemann</GivenName><FamilyName>Mattern</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff6"><EditorName DisplayOrder="Western"><GivenName>John</GivenName><GivenName>C.</GivenName><FamilyName>Mitchell</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff7"><EditorName DisplayOrder="Western"><GivenName>Moni</GivenName><FamilyName>Naor</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff8"><EditorName DisplayOrder="Western"><GivenName>Oscar</GivenName><FamilyName>Nierstrasz</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff9"><EditorName DisplayOrder="Western"><GivenName>C.</GivenName><FamilyName>Pandu Rangan</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff10"><EditorName DisplayOrder="Western"><GivenName>Bernhard</GivenName><FamilyName>Steffen</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff11"><EditorName DisplayOrder="Western"><GivenName>Madhu</GivenName><FamilyName>Sudan</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff12"><EditorName DisplayOrder="Western"><GivenName>Demetri</GivenName><FamilyName>Terzopoulos</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff13"><EditorName DisplayOrder="Western"><GivenName>Dough</GivenName><FamilyName>Tygar</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff14"><EditorName DisplayOrder="Western"><GivenName>Moshe</GivenName><GivenName>Y.</GivenName><FamilyName>Vardi</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff15"><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Weikum</FamilyName></EditorName></Editor><Affiliation ID="Aff1"><OrgName>Lancaster University</OrgName><OrgAddress><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><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford University</OrgName><OrgAddress><City>CA</City><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><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><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><City>MA</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>New York University</OrgName><OrgAddress><City>NY</City><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>Saarbruecken</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>978-3-540-32033-3</BookID><BookTitle>Term Rewriting and Applications</BookTitle><BookSubTitle>16th International Conference, RTA 2005, Nara, Japan, April 19-21, 2005. Proceedings</BookSubTitle><BookVolumeNumber>3467</BookVolumeNumber><BookSequenceNumber>3467</BookSequenceNumber><BookDOI>10.1007/b135673</BookDOI><BookTitleID>117768</BookTitleID><BookPrintISBN>978-3-540-25596-3</BookPrintISBN><BookElectronicISBN>978-3-540-32033-3</BookElectronicISBN><BookChapterCount>36</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2005</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="I1603X" Priority="2" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I14037" Priority="3" Type="Secondary">Programming Languages, Compilers, Interpreters</BookSubject><BookSubject Code="I21017" Priority="4" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I17052" Priority="5" Type="Secondary">Symbolic and Algebraic Manipulation</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Jürgen</GivenName><FamilyName>Giesl</FamilyName></EditorName><Contact><Email>giesl@informatik.rwth-aachen.de</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>LuFG Informatik 2</OrgDivision><OrgName>RWTH Aachen University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap12" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>12</ChapterID><ChapterDOI>10.1007/978-3-540-32033-3_12</ChapterDOI><ChapterSequenceNumber>12</ChapterSequenceNumber><ChapterTitle Language="En">Quasi-interpretations and Small Space Bounds</ChapterTitle><ChapterFirstPage>150</ChapterFirstPage><ChapterLastPage>164</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2005</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><BookID>978-3-540-32033-3</BookID><BookTitle>Term Rewriting and Applications</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff17 Aff18"><AuthorName DisplayOrder="Western"><GivenName>Guillaume</GivenName><FamilyName>Bonfante</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff17 Aff18"><AuthorName DisplayOrder="Western"><GivenName>Jean-Yves</GivenName><FamilyName>Marion</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff17 Aff19"><AuthorName DisplayOrder="Western"><GivenName>Jean-Yves</GivenName><FamilyName>Moyen</FamilyName></AuthorName></Author><Affiliation ID="Aff17"><OrgName>Loria, Calligramme project</OrgName><OrgAddress><Postbox>B.P. 239</Postbox><Postcode>54506</Postcode><City>Vandœuvre-lès-Nancy Cédex</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgDivision>INPL</OrgDivision><OrgName>École Nationale Supérieure des Mines de Nancy</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff19"><OrgName>Université Henri Poincaré Nancy I</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. They not only combine well with path orderings and provide characterizations of usual complexity classes but also give hints in order to optimize the program. Moreover, the existence of a quasi-interpretation is decidable.</Para><Para>In this paper, we present some more characterizations of complexity classes using quasi-interpretations. We mainly focus on small space-bounded complexity classes. On one hand, by restricting quasi-interpretations to sums (that is allowing only affine quasi-interpretations), we obtain a characterization of <Emphasis Type="SmallCaps">LinSpace</Emphasis>. On the other hand, a strong tiering discipline on programs together with quasi-interpretations yield a characterization of <Emphasis Type="SmallCaps">LogSpace</Emphasis>.</Para><Para>Lastly, we give two new characterizations of <Emphasis Type="SmallCaps">Pspace</Emphasis>: in the first, the quasi-interpretation has to be strictly decreasing on each rule and in the second, some linearity constraints are added to the system but no assumption concerning the termination proof is made.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Quasi-interpretations and Small Space Bounds</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Quasi-interpretations and Small Space Bounds</title></titleInfo><name type="personal"><namePart type="given">Guillaume</namePart><namePart type="family">Bonfante</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</affiliation><affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jean-Yves</namePart><namePart type="family">Marion</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</affiliation><affiliation>INPL, École Nationale Supérieure des Mines de Nancy, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jean-Yves</namePart><namePart type="family">Moyen</namePart><affiliation>Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cédex, France</affiliation><affiliation>Université Henri Poincaré Nancy I, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2005</dateIssued><copyrightDate encoding="w3cdtf">2005</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: Quasi-interpretations are an useful tool to control resources usage of term rewriting systems, either time or space. They not only combine well with path orderings and provide characterizations of usual complexity classes but also give hints in order to optimize the program. Moreover, the existence of a quasi-interpretation is decidable. In this paper, we present some more characterizations of complexity classes using quasi-interpretations. We mainly focus on small space-bounded complexity classes. On one hand, by restricting quasi-interpretations to sums (that is allowing only affine quasi-interpretations), we obtain a characterization of LinSpace. On the other hand, a strong tiering discipline on programs together with quasi-interpretations yield a characterization of LogSpace. Lastly, we give two new characterizations of Pspace: in the first, the quasi-interpretation has to be strictly decreasing on each rule and in the second, some linearity constraints are added to the system but no assumption concerning the termination proof is made.</abstract><relatedItem type="host"><titleInfo><title>Term Rewriting and Applications</title><subTitle>16th International Conference, RTA 2005, Nara, Japan, April 19-21, 2005. 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Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I17052">Symbolic and Algebraic Manipulation</topic></subject><identifier type="DOI">10.1007/b135673</identifier><identifier type="ISBN">978-3-540-25596-3</identifier><identifier type="eISBN">978-3-540-32033-3</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">117768</identifier><identifier type="BookID">978-3-540-32033-3</identifier><identifier type="BookChapterCount">36</identifier><identifier type="BookVolumeNumber">3467</identifier><identifier type="BookSequenceNumber">3467</identifier><part><date>2005</date><detail type="volume"><number>3467</number><caption>vol.</caption></detail><extent unit="pages"><start>150</start><end>164</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2005</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer 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type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH 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, 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, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu 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