(Enter summary)
Abstract: Continuing a line of investigation that has studied the function
classes #P [Val79b], #SAC
[Val79a, Vin91, AJMV], #L [AJ93b,
Vin91, AO94], and #NC
[CMTV96], we study the class of functions
. One way to define #AC
is as the class of functions computed
by constant-depth polynomial-size arithmetic circuits of unbounded
fan-in addition and multiplication gates. In contrast to the preceding
# Part of this research was done while visiting the University of Ulm under an Alexander
von... (Update)
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BibTeX entry: (Update)
@article{ agrawal00tc,
author = "Manindra Agrawal and Eric Allender and Samir Datta",
title = "On {TC} 0 , {AC} 0 , and Arithmetic Circuits",
journal = "Journal of Computer and System Sciences",
volume = "60",
number = "2",
pages = "395-421",
year = "2000",
url = "citeseer.ist.psu.edu/article/agrawal00tc.html" }
Citations (may not include all citations):
439
An Introduction to the Theory of Numbers (context) - Hardy, Wright - 1979
251
The complexity of computing the Permanent (context) - Valiant - 1979
189
Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolensky - 1987
145
Computational complexity of probabilistic Turing machines (context) - Gill - 1977
125
On uniform circuit complexity (context) - Ruzzo - 1981
94
Information Processing Letters (context) - Litow, integer - 1992
92
Constant depth reducibility (context) - Chandra, Stockmeyer et al. - 1984
91
Log depth circuits for division and related problems (context) - Beame, Cook et al. - 1986
90
The complexity of combinatorial problems with succinct input.. (context) - Wagner
86
Gap-definable counting classes
- Fenner, Fortnow et al. - 1994
60
On uniformity within NC (context) - Barrington, Immerman et al. - 1990
56
Finite monoids and the fine structure of NC (context) - Barrington, Therien - 1988
54
and logarithmic space (context) - Etessami, successor - 1997
54
Lower bounds on the size of bounded depth networks over a co.. (context) - Razborov - 1987
52
A very hard log-space counting class (context) - Alvarez, Jenner - 1993
51
On threshold circuits and polynomial computation
- Reif, Tate - 1992
46
Counting auxiliary pushdown automata and semiunbounded arith.. (context) - Vinay - 1991
44
Journal of Computer and System Sciences (context) - Razborov, Rudich - 1997
38
Nondeterministic NC computation
- Caussinus, McKenzie et al. - 1998
38
The complexity of iterated multiplication
- Immerman, Landau - 1995
35
Circuit definitions of nondeterministic complexity classes (context) - Venkateswaran - 1992
31
Parallel computation with threshold functions (context) - Parberry, Schnitger - 1988
29
Completeness classes in algebra (context) - Valiant - 1979
28
The complexity of matrix rank and feasible systems of linear..
- Allender, Beals et al. - 1996
26
Counting problems computationally equivalent to the determin.. (context) - Toda
21
uniform circuit complexity (context) - Allender - 1989
20
Classes of arithmetic circuits capturing the complexity of c.. (context) - Toda - 1992
20
polynomial-size circuits for symmetric functions (context) - Fagin, Klawe et al. - 1985
19
Fast parallel arithmetic via modular representation (context) - Davida, Litow - 1991
18
Definability by constant-depth polynomial-size circuits (context) - Denenberg, Gurevich et al. - 1986
15
Computational Complexity (context) - Beigel, Tarui - 1994
15
Depth Reduction for Circuits of Unbounded Fan
- Allender, Hertrampf - 1994
14
On counting AC circuits with negative constants
- Ambainis, Barrington et al. - 1998
14
Noncommutative arithmetic circuits: depth reduction and size..
- Allender, Jiao et al. - 1998
13
The permanent requires large uniform threshold circuits
- Allender
12
Bits and relative order from residues (context) - Dietz, Macarie et al. - 1994
12
Chicago Journal of Theoretical Computer Science (context) - Mahajan, Vinay et al. - 1997
10
Bounded Depth Arithmetic Circuits: Counting and Closure
- Allender, Ambainis et al. - 1999
8
A note on uniform circuit lower bounds for the counting hier.. (context) - Allender - 1996
7
Why is boolean complexity theory di#cult (context) - Valiant - 1992
5
An arithmetical model of computation equivalent to threshold.. (context) - Boyar, Frandsen et al. - 1992
5
Some results on uniform arithmetic circuit complexity (context) - Frandsen, Valence et al. - 1994
4
Semantical counting circuits
- Noilhan, Santha
3
Verifying the determinant in parallel
- Santha, Tan - 1998
2
cient deterministic simulation of probabilistic automata (context) - Macarie - 1998
1
To appear in Computational Complexity (context) - Allender, Ogihara et al. - 1994
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