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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
ISBN: 0-8186-2445-0
pp: 777-782
M. Krause , Dortmund Univ., Germany
An exponential lower bound for depth two circuits with arbitrary symmetric gates in the bottom level and with a MOD/sub m/-gate in the top level is proved. This solves a problem posed by R. Smolensky (1990). The method uses the variation rank of communication matrices. A variant of this method is used for deriving lower bounds for the size of depth-two circuits having a threshold gate at the top.
threshold gate, MOD m gate, communication matrices, depth two circuits, symmetric gates, unbounded fan-in, exponential lower bound, variation rank

M. Krause and S. Waack, "Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in," [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 777-782.
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