-
1
-
-
84887465752
-
Bounded depth arithmetic circuits: Counting and closure
-
p. 149-158
-
Allender E., Ambainis A., Mix Barrington D., Datta S., LêThanh H. Bounded depth arithmetic circuits: Counting and closure. Proc. 26th International Colloquium on Automata, Languages, and Programming (ICALP). 1999;. p. 149-158.
-
(1999)
Proc. 26th International Colloquium on Automata, Languages, and Programming (ICALP)
-
-
Allender, E.1
Ambainis, A.2
Mix Barrington, D.3
Datta, S.4
Lêthanh, H.5
-
2
-
-
0008651743
-
Depth reduction for circuits of unbounded fan-in
-
Allender E., Hertrampf U. Depth reduction for circuits of unbounded fan-in. Inform. and Comput. 112:1994;217-238.
-
(1994)
Inform. and Comput.
, vol.112
, pp. 217-238
-
-
Allender, E.1
Hertrampf, U.2
-
4
-
-
38049091720
-
A very hard log-space counting class
-
Álvarez C., Jenner B. A very hard log-space counting class. Theoret. Comput. Sci. 107:1993;3-30.
-
(1993)
Theoret. Comput. Sci.
, vol.107
, pp. 3-30
-
-
Álvarez, C.1
Jenner, B.2
-
5
-
-
0002507290
-
Noncommutative arithmetic circuits: Depth reduction and size lower bounds
-
Allender E., Jiao J., Mahajan M., Vinay V. Noncommutative arithmetic circuits: depth reduction and size lower bounds. Theoret. Comput. Sci. 209:1998;47-86.
-
(1998)
Theoret. Comput. Sci.
, vol.209
, pp. 47-86
-
-
Allender, E.1
Jiao, J.2
Mahajan, M.3
Vinay, V.4
-
6
-
-
0003944654
-
The permanent requires large uniform threshold circuits
-
Allender E. The permanent requires large uniform threshold circuits. Chicago J. Theoret. Comput. Sci. 7:1999.
-
(1999)
Chicago J. Theoret. Comput. Sci.
, vol.7
-
-
Allender, E.1
-
7
-
-
0024754676
-
P-uniform circuit complexity
-
Allender E. P-uniform circuit complexity. J. Assoc. Comput. Mach. 36:1989;912-928.
-
(1989)
J. Assoc. Comput. Mach.
, vol.36
, pp. 912-928
-
-
Allender, E.1
-
11
-
-
0022811668
-
Log depth circuits for division and related problems
-
Beame P., Cook S., Hoover H. J. Log depth circuits for division and related problems. SIAM J. Comput. 15:1986;994-1003.
-
(1986)
SIAM J. Comput.
, vol.15
, pp. 994-1003
-
-
Beame, P.1
Cook, S.2
Hoover, H.J.3
-
12
-
-
0026813292
-
An arithmetical model of computation equivalent to threshold circuits
-
Boyar J., Frandsen G., Sturtivant G. An arithmetical model of computation equivalent to threshold circuits. Theoret. Comput. Sci. 93:1992;303-319.
-
(1992)
Theoret. Comput. Sci.
, vol.93
, pp. 303-319
-
-
Boyar, J.1
Frandsen, G.2
Sturtivant, G.3
-
18
-
-
0022761884
-
Definability by constant-depth polynomial-size circuits
-
Denenberg L., Gurevich Y., Shelah S. Definability by constant-depth polynomial-size circuits. Inform. and Control. 70:1986;216-240.
-
(1986)
Inform. and Control
, vol.70
, pp. 216-240
-
-
Denenberg, L.1
Gurevich, Y.2
Shelah, S.3
-
19
-
-
0026204808
-
Fast parallel arithmetic via modular representation
-
Davida G. I., Litow B. Fast parallel arithmetic via modular representation. SIAM J. Comput. 20:1991;756-765.
-
(1991)
SIAM J. Comput.
, vol.20
, pp. 756-765
-
-
Davida, G.I.1
Litow, B.2
-
21
-
-
0031164818
-
Counting quantifiers, successor relations, and logarithmic space
-
Etessami K. Counting quantifiers, successor relations, and logarithmic space. J. Comput. System Sci. 54:1997;400-411.
-
(1997)
J. Comput. System Sci.
, vol.54
, pp. 400-411
-
-
Etessami, K.1
-
23
-
-
0022050260
-
Bounded-depth, polynomial-size circuits for symmetric functions
-
Fagin R., Klawe M., Pippenger N., Stockmeyer L. Bounded-depth, polynomial-size circuits for symmetric functions. Theoret. Comput. Sci. 36:1985;239-250.
-
(1985)
Theoret. Comput. Sci.
, vol.36
, pp. 239-250
-
-
Fagin, R.1
Klawe, M.2
Pippenger, N.3
Stockmeyer, L.4
-
25
-
-
0000595574
-
Computational complexity of probabilistic Turing machines
-
Gill J. Computational complexity of probabilistic Turing machines. SIAM J. Comput. 6:1977;675-695.
-
(1977)
SIAM J. Comput.
, vol.6
, pp. 675-695
-
-
Gill, J.1
-
27
-
-
0343298010
-
The complexity of iterated multiplication
-
Immerman N., Landau S. The complexity of iterated multiplication. Inform. and Comput. 116:1995;103-116.
-
(1995)
Inform. and Comput.
, vol.116
, pp. 103-116
-
-
Immerman, N.1
Landau, S.2
-
28
-
-
0013446879
-
On iterated integer product
-
Litow B. On iterated integer product. Inform. Process. Lett. 42:1992;269-272.
-
(1992)
Inform. Process. Lett.
, vol.42
, pp. 269-272
-
-
Litow, B.1
-
29
-
-
0000310033
-
Space-efficient deterministic simulation of probabilistic automata
-
Macarie I. Space-efficient deterministic simulation of probabilistic automata. SIAM J. Comput. 27:1998;448-465.
-
(1998)
SIAM J. Comput.
, vol.27
, pp. 448-465
-
-
Macarie, I.1
-
32
-
-
0024019151
-
Parallel computation with threshold functions
-
Parberry I., Schnitger G. Parallel computation with threshold functions. J. Comput. System Sci. 36:1988;278-302.
-
(1988)
J. Comput. System Sci.
, vol.36
, pp. 278-302
-
-
Parberry, I.1
Schnitger, G.2
-
33
-
-
0000883554
-
Lower bounds on the size of bounded depth networks over a complete basis with logical addition
-
Razborov A. A. Lower bounds on the size of bounded depth networks over a complete basis with logical addition. Math. Zametki. 41:1987;598-607.
-
(1987)
Math. Zametki
, vol.41
, pp. 598-607
-
-
Razborov, A.A.1
-
35
-
-
0026932814
-
On threshold circuits and polynomial computation
-
Reif J., Tate S. On threshold circuits and polynomial computation. SIAM J. Comput. 21:1992;896-908.
-
(1992)
SIAM J. Comput.
, vol.21
, pp. 896-908
-
-
Reif, J.1
Tate, S.2
-
36
-
-
0019572555
-
On uniform circuit complexity
-
Ruzzo W. On uniform circuit complexity. J. Comput. System. Sci. 21:1981;365-383.
-
(1981)
J. Comput. System. Sci.
, vol.21
, pp. 365-383
-
-
Ruzzo, W.1
-
37
-
-
0023570259
-
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
-
p. 77-82
-
Smolensky R. Algebraic methods in the theory of lower bounds for Boolean circuit complexity. Proceedings, 19th ACM Symposium on Theory of Computing. 1987;. p. 77-82.
-
(1987)
Proceedings, 19th ACM Symposium on Theory of Computing
-
-
Smolensky, R.1
-
38
-
-
0040098265
-
Verifying the determinant in parallel
-
Santha M., Tan S. Verifying the determinant in parallel. Comput. Complexity. 7:1998;128-151.
-
(1998)
Comput. Complexity
, vol.7
, pp. 128-151
-
-
Santha, M.1
Tan, S.2
-
40
-
-
0041887590
-
Classes of arithmetic circuits capturing the complexity of computing the determinant
-
Toda S. Classes of arithmetic circuits capturing the complexity of computing the determinant. IEICE Trans. Inform. and Systems. E75-D:1992;116-124.
-
(1992)
IEICE Trans. Inform. and Systems
, vol.75
, pp. 116-124
-
-
Toda, S.1
-
42
-
-
49249151236
-
The complexity of computing the Permanent
-
Valiant L. The complexity of computing the Permanent. Theoret. Comput. Sci. 8:1979;189-201.
-
(1979)
Theoret. Comput. Sci.
, vol.8
, pp. 189-201
-
-
Valiant, L.1
-
43
-
-
0003370550
-
Why is boolean complexity theory difficult?
-
M. S. Paterson. Boolean Function Complexity. Cambridge: Cambridge University Press
-
Valiant L. Why is boolean complexity theory difficult? Paterson M. S. Boolean Function Complexity. London Mathematical Society Lecture Notes Series. 169:1992;84-94 Cambridge University Press, Cambridge.
-
(1992)
London Mathematical Society Lecture Notes Series
, vol.169
, pp. 84-94
-
-
Valiant, L.1
-
44
-
-
0026902139
-
Circuit definitions of nondeterministic complexity classes
-
Venkateswaran H. Circuit definitions of nondeterministic complexity classes. SIAM J. Comput. 21:1992;655-670.
-
(1992)
SIAM J. Comput.
, vol.21
, pp. 655-670
-
-
Venkateswaran, H.1
-
45
-
-
0026375502
-
Counting auxiliary pushdown automata and semi unbounded arithmetic circuits
-
p. 270-284
-
Vinay V. Counting auxiliary pushdown automata and semi unbounded arithmetic circuits. Proc. 6th IEEE Structure in Complexity Theory Conference. 1991;. p. 270-284.
-
(1991)
Proc. 6th IEEE Structure in Complexity Theory Conference
-
-
Vinay, V.1
-
46
-
-
0022733806
-
The complexity of combinatorial problems with succinct input representation
-
Wagner K. W. The complexity of combinatorial problems with succinct input representation. Acta Inform. 23:1986;325-356.
-
(1986)
Acta Inform.
, vol.23
, pp. 325-356
-
-
Wagner, K.W.1
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