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  n\Omega\Gamma1/6 n) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom (1993) [17 citations — 1 self]

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by Alexander Razborov, Avi Wigderson
Information Processing Letters
http://www.cs.huji.ac.il/~avi/RaW.ps
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Abstract:

to appear in Information Processing Letters We present a function in ACC 0 such that any depth 3 threshold circuit which computes this function and has AND gates at the bottom must have size n\Omega\Gamma607 n)

Citations

157 Separating the polynomial-time hierarchy by oracles – Yao - 1985
125 Computational limitations on small depth circuits – H˚astad - 1986
115 Parity, circuits and the polynomial time hierarchy – Furst, Saxe, et al. - 1984
108 Threshold circuits of bounded depth – Hajnal, Maass, et al. - 1987
84 On ACC and threshold circuits – Yao - 1990
68 On the power of small-depth threshold circuits – H˚astad, Goldmann - 1991
66 Majority gates vs. general weighted threshold gates – Goldmann, H˚astad, et al. - 1992
48 Variation Ranks of Communication Matrices and Lower Bounds for Depth Two Circuits Having Symmetric Gates with Unbounded Fan-In. FOCS 777–782 – Krause, Waack - 1991
44 Multiparty protocols and logspace-hard pseudorandom sequences – Babai, Nisan, et al. - 1989
22 On proving super-logarithmic depth lower bounds via the direct sum in communication complexity – Karchmer, Raz, et al. - 1991
14 Geometric arguments yield better bounds for threshold circuits and distributed computing – Krause - 1991
14 On small depth threshold circuits – Razborov - 1992
5 O metode poluqeni bolee qem kvadratiqnyh ninih ocenok dl slonosti -shem. Vestnik MGU, ser. matem i mehan., t – Andreev - 1987