Average-Case Lower Bounds For Formula Size
STOC'13: Symposium on Theory of Computing Palo Alto California USA June, 2013(2013)
摘要
We give an explicit function h : {0,1}(n) -> {0, 1} such that any deMorgan formula of size O (n(2.499)) agrees with h on at most 1/2+ epsilon fraction of the inputs, where e is exponentially small (i.e. epsilon = 2(-n Omega(1))). We also show, using the same technique, that any boolean formula of size O(n(1.999)) over the complete basis, agrees with h on at most 1/2 + epsilon fraction of the inputs, where epsilon is exponentially small (i.e. epsilon = epsilon = 2(-n Omega(1))).Our construction is based on Andreev's Omega(n(2.5-o(1))) formula size lower bound that was proved for the case of exact computation [2].
更多查看译文
关键词
deMorgan formulas,lower bounds,Boolean formulas,correlation bounds,average-case hardness
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络