JUCS - Journal of Universal Computer Science 9(1): 34-50, doi: 10.3217/jucs-009-01-0034
Relativizing Function Classes
expand article infoChristian Glaßer‡, Gerd Wechsung§
‡ Institut für Informatik, Julius-Maximilians-University Würzburg, Würzburg, Germany§ Institut für Informatik, Friedrich-Schiller-University Jena, Jena, Germany

Corresponding author: Christian Glaßer ( glasser@informatik.uni-wuerzburg.de )

© Christian Glaßer, Gerd Wechsung.
This article is freely available under the J.UCS Open Content License.
Citation: Glaßer C, Wechsung G (2003) Relativizing Function Classes. JUCS - Journal of Universal Computer Science 9(1): 34-50. https://doi.org/10.3217/jucs-009-01-0034
Open Access
Abstract
The operators min?, max?, and #? translate classes of the polynomial-time hierarchy to function classes. Although the inclusion relationships between these function classes have been studied in depth, some questions concerning separations remained open. We provide oracle constructions that answer most of these open questions in the relativized case. As a typical instance for the type of results of this paper, we construct a relativized world where min_P #?NP, thus giving evidence for the hardness of proving min?P #?NP in the unrelativized case. The strongest results, proved in the paper, are the constructions of oracles D and E, such that min_coNPD #?PD NPD coNPD and UPE = NPE min?PE #?PE.
Keywords
polynomial-time hierarchy, function classes, oracle separations