We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g : {0, 1}n {0, 1} cannot be computed on more th...
We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone error...
The "direct product code" of a function f gives its values on all k-tuples (f(x1), . . . , f(xk)). This basic construct underlies "hardness amplification" in c...
Russell Impagliazzo, Valentine Kabanets, Avi Wigde...