Improved Average-Case Lower Bounds for De Morgan Formula Size: Matching Worst-Case Lower Bound

SIAM J. Comput., Volume 46, Issue 1, 2017, Pages 37-57.

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Abstract:

We give an explicit function $h:{0,1}^n to {0,1}$ such that every de Morgan formula of size $n^{3-o(1)}/r^2$ agrees with $h$ on at most a fraction of $frac{1}{2}+2^{-Omega(r)}$ of the inputs. Our technical contributions include a theorem that shows that the “expected shrinkage” result of Haastad [SIAM J. Comput., 27 (1998), pp. 48--64] ac...More

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