Document Type
Article
Publication Title
Theoretical Computer Science
Abstract
Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ω1/CK in PSPACE such that successors are polynomial jumps of their predecessors. Moreover these ptime degrees are all uniformly hard for PH. This is analogous to the hyperarithmetic hierarchy, which is defined similarly but with the (computable) Turing degrees. The lack of uniform least upper bounds for ascending sequences of ptime degrees causes the limit levels of our hyper-polynomial hierarchy to be inherently non-canonical. This problem is investigated in depth, and various possible structures for hyper-polynomial hierarchies are explicated, as are properties of the polynomial jump operator on the languages which are in PSPACE but not in PH.
First Page
241
Last Page
256
DOI
10.1016/S0304-3975(00)00193-6
Publication Date
8-2-2001
Recommended Citation
Fenner, Stephen; Homer, Steven; Pruim, Randall J.; and Schaefer, Marcus, "Hyper-polynomial hierarchies and the polynomial jump" (2001). University Faculty Publications and Creative Works. 481.
https://digitalcommons.calvin.edu/calvin_facultypubs/481