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Abstract: We show that any two complexity classes satisfying some general conditions are distinct relative to a generic oracle iff the corresponding type-2 classes are distinct. (Update)
Context of citations to this paper: More
.... separations between the Turing closures of the related type 1 search classes and these separations apply to all generic oracles ( BI87] [CY95]. 2.3 Some simple reductions It is easy to see that SOURCE:OR:SINK m LEAF , by ignoring the direction information on the input graph....
...A ; iii) There exists a generic oracle G such that 5 Figure 2: Reducing Q 1 to Q 2 (CQ 1 ) G (CQ 2 ) G . The proof appears in [CIY97] In order to state the full power of our separation results, we now define a more general form of reduction among total search problems: We...
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6: Generic oracles and oracle classes (context) - Blum, Impagliazzo - 1987
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BibTeX entry: (Update)
S. A. Cook, R. Impagliazzo, and T. Yamakami. A tight relationship between generic oracles and type-2 complexity theory. Information and Computation, 136, 1997. To appear. http://citeseer.ist.psu.edu/cook97tight.html More
@article{ cook97tight,
author = "Stephen Cook and Russell Impagliazzo and Tomoyuki Yamakami",
title = "A Tight Relationship Between Generic Oracles and Type-2 Complexity Theory",
journal = "Information and Computation",
volume = "137",
number = "2",
pages = "159-170",
year = "1997",
url = "citeseer.ist.psu.edu/cook97tight.html" }
Citations (may not include all citations):534 The complexity of theorem-proving procedures (context) - Cook - 1971
172 Algebraic methods for interactive proof systems - Lund, Fortnow et al. - 1992
75 and the polynomial time hierarchy (context) - Furst, Saxe et al. - 1984
60 Generic oracles and oracle classes (context) - Blum, Impagliazzo - 1987
48 Borel sets and circuit complexity (context) - Sipser - 1983
37 Decision trees and downward closures (context) - Impagliazzo, Naor - 1988
32 An oracle builder's toolkit - Fenner, Fortnow et al. - 1993
27 The relative complexity of NP search problems - Beame, Cook et al. - 1995
26 Polynomial and abstract subrecursive classes (context) - Mehlhorn - 1976
18 Are there interactive protocols for co-NP languages - Fortnow, Sipser - 1988
15 Robust machines accept easy sets (context) - Hartmanis, Hemachandra - 1990
13 On graph-theoretic lemmata and complexity classes (context) - Papadimitriou - 1990
11 On some natural complete operators (context) - Ko - 1985
8 Relativized questions involving probabilistic algorithms (context) - Rackoff - 1982
7 Symbolic Logic (context) - Poizat, NQ - 1986
4 One-way functions (context) - Hartmanis, Hemachandra - 1987
3 Provably total functions of intuitionistic bounded arithmeti.. (context) - Harnik - 1992
3 Query complexity (context) - Tardos - 1989
2 and Solovay (context) - Baker, Gill - 1975
1 Generic separations - Fortnow, Yamakami - 1996
1 Computing with polynomials give by black boxes for their eva.. (context) - Kaltofen, Trager - 1990
1 Functional interpretaions of feasibly constructive arithmeti.. (context) - Cook, Urquhart - 1993
1 Type two computable functionals (context) - Constable - 1973
1 A new characterization of type-2 feasibility (context) - Kapron, Cook - 1996
The graph only includes citing articles where the year of publication is known.
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