Download:
|
by Mitsunori Ogihara, Thomas Thierauf, Fakultat Fur Informatik, Universtat Ulm, Seinosuke Toda, Osamu Watanabe
http://theorie.informatik.uni-ulm.de/papers/../Personen/Thierauf/Papers/numberP-context.ps.gz
Add To MetaCart
Abstract:
For any operator on integer-valued functions, we say that #P is closed under in context PFffi#P if, for every f 2 #P, [f] belongs to PF ffi #P. For several operators , it is shown that the closure properties of #P under in the above sense is closely related to the relationships between P #P[1] and higher classes such as PH PP and PP PP
Citations
|
248
|
The complexity of enumeration and reliability problems
– Valiant
- 1979
|
|
209
|
Computational complexity of probabilistic Turing machines
– Gill
- 1977
|
|
191
|
Parity, circuits and the polynomial-time hierarchy
– Furst, Saxe, et al.
- 1984
|
|
190
|
The complexity of optimization problems
– Krentel
- 1988
|
|
164
|
PP is as hard as the polynomial-time hierarchy
– Toda
- 1991
|
|
137
|
Gap-definable counting classes
– Fenner, Fortnow, et al.
- 1994
|
|
115
|
Log depth circuits for division and related problems
– Beame, Cook, et al.
- 1986
|
|
111
|
The complexity of combinatorial problems with succinct input representations
– Wagner
- 1986
|
|
87
|
Pp is closed under intersection
– Beigel, Reingold, et al.
- 1995
|
|
72
|
Two remarks on the power of counting
– Papadimitriou, Zachos
- 1983
|
|
71
|
On Some Central Problems in Computational Complexity
– Simon
- 1975
|
|
55
|
A complexity theory for feasible closure properties
– Ogiwara, Hemachandra
- 1993
|
|
52
|
On the power of parity polynomial time
– Cai, Hemachandra
- 1990
|
|
49
|
PP is closed under truth-table reductions
– Fortnow, Reingold
- 1991
|
|
29
|
On counting and approximation
– Kobler, Schoning, et al.
- 1989
|
|
18
|
Probabilistic polynomial time is closed under parity reductions
– Beigel, Hemachandra, et al.
- 1991
|
|
18
|
The Power of Counting
– Schoning
- 1990
|
|
18
|
An oracle characterization of the counting hierarchy
– Tor'an
- 1988
|
|
16
|
Some observations on the connection between counting and recursion
– Wagner
- 1986
|
|
9
|
On probabilistic ACC circuits with an exact-threshold output gate
– Beigel, Tarui, et al.
- 1992
|
|
3
|
Simple characterization of P(#P) and complete problems
– Toda
- 1994
|
