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Abstract: We show that probabilistic polynomial time (PP) is closed under polynomial-time parity reductions. As corollaries, we show that several complexity classes are contained in PP. (Update)
Context of citations to this paper: More
...that D p;A k 6 PP S p;A k Gamma2 . We use D p k to denote the complexity class P S p k Gamma1 . Beigel, Hemachandra, and Wechsung [2] showed that P NP[log] PP, and later Beigel, Reingold, and Spielman [3] proved the even stronger P PP[log] PP. A relativization of these...
...#accN (x) where #accN (x) denotes the number of accepting paths of N(x) #P is a tremendously powerful class. Toda ( 42] see also [8, 43, 35]) showed that Turing access to #P suces to accept every set in the polynomial hierarchy. Unfortunately, it is well known that computing...
Cited by: More
PP is Closed Under Intersection - Beigel, Reingold, Spielman (1991) (Correct)
The Polynomial Method in Circuit Complexity - Beigel (1995) (Correct)
On Closure Properties of P in the Context of PF - Ogihara, Thierauf, Toda (Correct)
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11: Computational complexity of probabilistic Turing machines (context) - Gill - 1974
11: PP is Closed under Intersection - Beigel, Reingold et al. - 1991
10: The complexity of combinatorial problems with succinct input representation (context) - Wagner - 1986
BibTeX entry: (Update)
R. Beigel, L. Hemachandra, G. Wechsung. Probabilistic polynomial time is closed under parity reductions. In Information Processing Letters, 37(2):9194, 1991. http://citeseer.ist.psu.edu/beigel91probabilistic.html More
@article{ beigel91probabilistic,
author = "Richard Beigel and Lane A. Hemachandra and Gerd Wechsung",
title = "Probabilistic Polynomial Time is Closed under Parity Reductions",
journal = "Information Processing Letters",
volume = "37",
number = "2",
pages = "91-94",
year = "1991",
url = "citeseer.ist.psu.edu/beigel91probabilistic.html" }
Citations (may not include all citations):151 The complexity of optimization problems (context) - Krentel - 1988
145 Computational complexity of probabilistic Turing machines (context) - Gill - 1977
126 PP is as hard as the polynomial-time hierarchy (context) - Toda - 1991
90 The complexity of combinatorial problems with succinct input.. (context) - Wagner - 1986
68 Bounded queries to SAT and the Boolean hierarchy - Beigel - 1991
55 On Some Central Problems In Computational Complexity (context) - Simon - 1975
44 the power of parity polynomial time (context) - Cai, Hemachandra - 1990
40 and sparse Turing-complete sets for NP (context) - Kadin, NP - 1987
39 and some facets of complexity (context) - Papadimitriou, Yannakakis et al. - 1984
35 On truth table reducibility to SAT - Buss, Hay - 1991
32 The strong exponential hierarchy collapses (context) - Hemachandra - 1987
29 The difference and truth-table hierarchies for NP (context) - Kobler, Schoning et al. - 1987
26 A survey of counting classes (context) - Gundermann, Nasser et al. - 1990
24 volume 11 of EATCS Monographs on Theoretical Computer Scienc.. (context) - Balc'azar, D'iaz et al. - 1988
22 Turing machines with few accepting computations and low sets.. - Kobler, Schoning et al. - 1992
18 Bounded query computations (context) - Wagner - 1988
10 Structural Properties of Complexity Classes (context) - Russo - 1985
8 the computational power of exact counting (context) - Ogiwara - 1990
7 Two remarks on the complexity of counting (context) - Papadimitriou, Zachos - 1983
5 Restricted relativizations of probabilistic polynomial time (context) - Toda - 1991
3 Structural Properties of The Counting Hierarchies (context) - Tor'an - 1988
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