|
Título:
|
Sparse sets, lowness, and highness
|
|
Autor/a:
|
Balcázar Navarro, José Luis; Book, R; Schoening, U
|
|
Otros autores:
|
Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Facultat d'Informàtica de Barcelona; Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
|
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. |
|
Abstract:
|
Peer Reviewed |
|
Materia(s):
|
-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
-Complexity, Computational
-Discrete mathematics
-Generalized lowness
-Generalized highness Extended lowness
-Extended highness
-Sparse sets
-Polynomial-time hierarchy
-Complexitat computacional |
|
Derechos:
|
|
|
Tipo de documento:
|
Artículo - Versión publicada
Artículo |
|
Compartir:
|
|
