How to recycle random bits

R. Impagliazzo, D. Zuckerman
1989 30th Annual Symposium on Foundations of Computer Science  
We show 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 2 ) bits are needed to improve this probability to 1 − 2 −k . We also present a different pseudo-random generator that is optimal, up to a constant factor, in this regard: it uses only O(r + k)
more » ... to improve the probability to 1 − 2 −k . This generator is based on random walks on expanders. Our results do not depend on any unproven assumptions. Next we show that our modified versions of the shift register and linear congruential generators can be used to sample from distributions using, in the limit, the information-theoretic lower bound on random bits.
doi:10.1109/sfcs.1989.63486 dblp:conf/focs/ImpagliazzoZ89 fatcat:q5mvnstj35bgzakqan4oqec72e