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Abstract: The counting class C= P, which captures the notion of "exact counting", while extremely powerful under various nondeterministic reductions, is quite weak under polynomial-time deterministic reductions. We discuss the analogies between NP and co-C = P, which allow us to derive many interesting results for such deterministic reductions to co-C = P. We exploit these results to obtain some interesting oracle separations. Most importantly, we show that there exists an oracle A such that \PhiP A 6` ... (Update)
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...in polynomial time to the following problem EQUALRUN, which is in C by Lemma 5.5: Given two NP Turing machines . Lemma 5. 5 (cf. [28, 14]) EQUALRUN is in C . Let as described in Section 2.2. Let be NP Turing machines which on input ;N 6; 6OJ QP nondeterministically select...
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I N F S Y S R E S E a R C H - Institut Ur Informationssysteme (Correct)
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BibTeX entry: (Update)
F. Green. On the power of deterministic reductions to 5 . Mathematical Systems Theory, 26(2):215-- 233, 1993. http://citeseer.ist.psu.edu/green91power.html More
@misc{ green93power,
author = "F. Green",
title = "the power of deterministic reductions to",
text = "F. Green. On the power of deterministic reductions to 5 . Mathematical
Systems Theory, 26(2):215-- 233, 1993.",
year = "1993",
url = "citeseer.ist.psu.edu/green91power.html" }
Citations (may not include all citations):105 Bounded Query Classes (context) - Wagner - 1990
70 The Boolean Hierarchy I: Structural Properties (context) - Cai, Gunderman et al. - 1988
68 Bounded Queries to SAT and the Boolean Hierarchy - Beigel - 1988
66 PP is Closed Under Intersection - Beigel, Reingold et al. - 1991
44 the computational power of PP and \PhiP (context) - Toda - 1989
37 The Boolean Hierarchy and the Polynomial Hierarchy: a Closer.. - Chang, Kadin - 1990
32 The Strong Exponential Hierarchy Collapses (context) - Hemachandra - 1989
26 A Survey on Counting Classes (context) - Gundermann, Nasser et al. - 1990
23 A Relationship between Difference Hierarchies and Relativize.. - Beigel, Chang et al. - 1991
12 An Oracle Characterization of the Counting Hierarchy (context) - Tor'an - 1988
11 Generalized Boolean Hierarchies and Boolean Hierarchies over.. (context) - Bertoni, Bruschi et al. - 1989
9 Restricted Turing Reducibilities and the Structure of the Po.. (context) - Kadin - 1988
8 Degree Complexity of Boolean Functions and Its Applications .. (context) - Tarui - 1991
6 Compact Descriptions and the Counting Polynomial Time Hierar.. (context) - Wagner - 1986
6 On Truth-table Reducibility to SAT and the Difference Hierar.. - Buss, Hay - 1988
5 Probability One Separation of the Boolean Hierarchy (context) - Cai - 1987
3 E-Mail and the Unexpected Power of Interaction (context) - Babai - 1990
3 On Polynomial-Time Truth-Table Reducibility to C=P Sets (context) - Toda - 1990
3 Counting Classes Are as Hard as the Polynomial- Time Hierarc.. (context) - Toda, Ogiwara - 1991
2 Randomized Polynomials, Threshold Circuits, and the Polynomi.. (context) - Tarui - 1991
1 Generealized Theorems on Relationships Among Reducibility No.. (context) - Ogiwara - 1991
1 Structural Properties of the Counting Hierarchy (context) - Tor'an - 1988
1 Volume II of EATCS Monographs on Theoretical Computer Scienc.. (context) - Balc'azar, D'iaz et al. - 1988
1 BPP and the Polynomial Hierarchy (context) - Lautenmann - 1983
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