How to recycle random bits

@article{Impagliazzo1989HowTR,
  title={How to recycle random bits},
  author={Russell Impagliazzo and David Zuckerman},
  journal={30th Annual Symposium on Foundations of Computer Science},
  year={1989},
  pages={248-253}
}
  • R. Impagliazzo, D. Zuckerman
  • Published 30 October 1989
  • Computer Science, Mathematics
  • 30th Annual Symposium on Foundations of Computer Science
It is shown that modified versions of the linear congruential generator and the shift register generator are provably good for amplifying the correctness of a probabilistic algorithm. More precisely, if r random bits are needed for a BPP algorithm to be correct with probability at least 2/3, then O(r+k/sup 2/) bits are needed to improve this probability to 1-2/sup -k/. A different pseudorandom generator that is optimal, up to a constant factor, in this regard is also presented. It uses only O(r… 

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