On the Complexity of Hard-Core Set Constructions

Chi-Jen Lu, Shi-Chun Tsai, Hsin-Lung Wu

Abstract: We study a fundamental result of Impagliazzo (FOCS’95) known as the hard-core set lemma. Consider any function f:{0,1}n →{0,1} which is “mildly-hard”, in the sense that any circuit of size s must disagree with f on at least δ fraction of inputs. Then the hard-core set lemma says that f must have a hard-core set H of density δ on which it is “extremely hard”, in the sense that any circuit of size