Upper bounds for the complexity of sparse and tally descriptions
Identifieur interne : 002742 ( Main/Exploration ); précédent : 002741; suivant : 002743Upper bounds for the complexity of sparse and tally descriptions
Auteurs : V. Arvind [Inde] ; J. Köbler [Allemagne] ; M. Mundhenk [Allemagne]Source :
- Mathematical systems theory [ 0025-5661 ] ; 1996-02-01.
Abstract
Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.
Url:
DOI: 10.1007/BF01201814
Affiliations:
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Arvind</name><affiliation wicri:level="1"><country xml:lang="fr">Inde</country><wicri:regionArea>Department of Computer Science, Institute of Mathematical Sciences, C.I.T. Campus, 600113, Madras</wicri:regionArea><wicri:noRegion>Madras</wicri:noRegion></affiliation></author><author><name sortKey="Kobler, J" sort="Kobler, J" uniqKey="Kobler J" first="J." last="Köbler">J. Köbler</name><affiliation wicri:level="4"><country xml:lang="fr">Allemagne</country><wicri:regionArea>Abteilung für Theoretische Informatik, Universität Ulm, D-89069, Ulm</wicri:regionArea><placeName><region type="land" nuts="1">Bade-Wurtemberg</region><region type="district" nuts="2">District de Tübingen</region><settlement type="city">Ulm</settlement></placeName><orgName type="university">Université d'Ulm</orgName></affiliation></author><author><name sortKey="Mundhenk, M" sort="Mundhenk, M" uniqKey="Mundhenk M" first="M." last="Mundhenk">M. 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Systems Theory</title><idno type="ISSN">0025-5661</idno><idno type="eISSN">1433-0490</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-02-01">1996-02-01</date><biblScope unit="volume">29</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="63">63</biblScope><biblScope unit="page" to="94">94</biblScope></imprint><idno type="ISSN">0025-5661</idno></series><idno type="istex">1BE62514B9085FFD1DA6A76728DEBFADE1A09AF8</idno><idno type="DOI">10.1007/BF01201814</idno><idno type="ArticleID">BF01201814</idno><idno type="ArticleID">Art6</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5661</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing self-reducible sets in IC[log, poly] are in NP ∩ co-NP and therefore low for NP. We derive similar results for sets inR d p (SPARSE) andR hd p (R c p (SPARSE)), as well as in some nondeterministic reduction classes to sparse sets.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Inde</li></country><region><li>Bade-Wurtemberg</li><li>District de Tübingen</li></region><settlement><li>Ulm</li></settlement><orgName><li>Université d'Ulm</li></orgName></list><tree><country name="Inde"><noRegion><name sortKey="Arvind, V" sort="Arvind, V" uniqKey="Arvind V" first="V." last="Arvind">V. Arvind</name></noRegion></country><country name="Allemagne"><region name="Bade-Wurtemberg"><name sortKey="Kobler, J" sort="Kobler, J" uniqKey="Kobler J" first="J." last="Köbler">J. Köbler</name></region><name sortKey="Mundhenk, M" sort="Mundhenk, M" uniqKey="Mundhenk M" first="M." last="Mundhenk">M. Mundhenk</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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