Technical Report CS0438

Title: Generalized Lower Bounds Derived from Hastad's Main Lemma
Authors: Shlomo Moran
Abstract: In [H] it is proven, among other things, that the size of any depth k circuit computing the parity or the majority function is Omega(2^o.1(0.3n)^u(k-1)). In this note we generalize the ptoof given there to yield similar lower bounds for arbitrary symmetric functions of {0,1}^n. This improves results in [FKPS], where it was shown that the non-existence cf polynomial-size, constant-depth circuits for the majority function implies the non-existence of such circuits for other symmetric functions.
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