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dc.contributor.authorBalcázar Navarro, José Luis
dc.contributor.authorBook, R
dc.contributor.authorSchoening, U
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.contributor.otherFacultat d'Informàtica de Barcelona
dc.identifier.citationBalcazar, J. L., Book, R., Schoening, U. Sparse sets, lowness, and highness. "SIAM journal on computing", Agost 1986, vol. 15, núm. 1, p. 739-747.
dc.description.abstractWe develop the notions of “generalized lowness” for sets in PH (the union of the polynomial-time hierarchy) and of “generalized highness” for arbitrary sets. Also, we develop the notions of “extended lowness” and “extended highness” for arbitrary sets. These notions extend the decomposition of NP into low sets and high sets developed by Schöning [15] and studied by Ko and Schöning [9]. We show that either every sparse set in PH is generalized high or no sparse set in PH is generalized high. Further, either every sparse set is extended high or no sparse set is extended high. In both situations, the former case corresponds to the polynomial-time hierarchy having only finitely many levels while the latter case corresponds to the polynomial-time hierarchy extending infinitely many levels.
dc.format.extent9 p.
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
dc.subject.lcshComplexity, Computational
dc.subject.otherDiscrete mathematics
dc.subject.otherGeneralized lowness
dc.subject.otherGeneralized highness Extended lowness
dc.subject.otherExtended highness
dc.subject.otherSparse sets
dc.subject.otherPolynomial-time hierarchy
dc.titleSparse sets, lowness, and highness
dc.subject.lemacComplexitat computacional
dc.contributor.groupUniversitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorBalcazar, J. L.; Book, R.; Schoening, U.
local.citation.publicationNameSIAM journal on computing

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