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Abstract: Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ! CK 1 all of which are in PSPACE and uniformly hard for PH, such that successors are NP-jumps of their predecessors. This is analgous to the hyperarithmetic hierarchy, which is defined similarly but with the (recursive) Turing degrees. The lack of uniform least upper bounds for ascending sequences of ptime degrees causes (the limit levels of) our ... (Update)
Active bibliography (related documents): More All
1.3: Hyper-Polynomial Hierarchies and the NP-Jump - Fenner, Homer, Pruim, Schaefer (Correct)
0.1: The Mathematical Work of S.C. Kleene - Shoenfield (1995) (Correct)
0.1: Negation and Inductive Norms - McColm (2003) (Correct)
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BibTeX entry: (Update)
@inproceedings{ fenner97hyperpolynomial,
author = "Stephen A. Fenner and Steven Homer and Randall Pruim and Marcus Schaefer",
title = "Hyper-Polynomial Hierarchies and the {NP}-Jump",
booktitle = "{IEEE} Conference on Computational Complexity",
pages = "102-110",
year = "1997",
url = "citeseer.ist.psu.edu/347226.html" }
Citations (may not include all citations):129 Theoretical Computer Science (context) - Stockmeyer, hierarchy - 1977
126 PP is as hard as the polynomial-time hierarchy (context) - Toda - 1991
124 Journal of the ACM (context) - Chandra, Kozen et al. - 1981
94 the structure of polynomial-time reducibility (context) - Ladner - 1975
24 volume 11 of EATCS Monographs on Theoretical Computer Scienc.. (context) - Balcazar, iaz et al. - 1988
14 Higher Recursion Theory (context) - Sacks - 1990
6 Recursive well-orderings (context) - Spector - 1955
3 the relative complexity of hard problems for complexity clas.. (context) - Ambos-Spies - 1989
3 Inverting the Turing jump in complexity theory - Fenner - 1995
Documents on the same site (http://cs-www.bu.edu/faculty/homer/paperlist.html): More
Determining Acceptance Possibility for a Quantum.. - Fenner, Green, Homer.. (1998) (Correct)
Structural Properties of Complete Problems for Exponential Time - Homer (1997) (Correct)
Complements of Multivalued Functions - Frederic Green Clark (Correct)
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