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Sparse sets, lowness, and highness
dc.contributor.author | Balcázar Navarro, José Luis |
dc.contributor.author | Book, R |
dc.contributor.author | Schoening, U |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Ciències de la Computació |
dc.contributor.other | Facultat d'Informàtica de Barcelona |
dc.date.accessioned | 2017-04-04T07:57:03Z |
dc.date.available | 2017-04-04T07:57:03Z |
dc.date.issued | 1986-08 |
dc.identifier.citation | Balcazar, 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.identifier.issn | 0097-5397 |
dc.identifier.uri | http://hdl.handle.net/2117/103245 |
dc.description.abstract | We 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.extent | 9 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat |
dc.subject.lcsh | Complexity, Computational |
dc.subject.other | Discrete mathematics |
dc.subject.other | Generalized lowness |
dc.subject.other | Generalized highness Extended lowness |
dc.subject.other | Extended highness |
dc.subject.other | Sparse sets |
dc.subject.other | Polynomial-time hierarchy |
dc.title | Sparse sets, lowness, and highness |
dc.type | Article |
dc.subject.lemac | Complexitat computacional |
dc.contributor.group | Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
dc.identifier.doi | 10.1137/0215053 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://epubs.siam.org/doi/abs/10.1137/0215053 |
dc.rights.access | Open Access |
local.identifier.drac | 1625154 |
dc.description.version | Postprint (published version) |
local.citation.author | Balcazar, J. L.; Book, R.; Schoening, U. |
local.citation.publicationName | SIAM journal on computing |
local.citation.volume | 15 |
local.citation.number | 1 |
local.citation.startingPage | 739 |
local.citation.endingPage | 747 |
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