P = BPP unless E has sub-exponential circuits : Derandomizing the XOR Lemma

@inproceedings{Impagliazzo1996PB,
  title={P = BPP unless E has sub-exponential circuits : Derandomizing the XOR Lemma},
  author={Russell Impagliazzo and Avi Wigderson},
  year={1996}
}
Yao showed that the XOR of independent random instances of a somewhat hard Boolean problem becomes almost completely unpredictable. In this paper we show that, in non-uniform settings, total independence is not necessary for this result to hold. We give a pseudo-random generator which produces n instances of a problem for which the analog of the XOR lemma holds. Combining this generator with the results of [25, 6] gives substantially improved results for hardness vs randomness trade-offs. In… CONTINUE READING
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