## Computing with Very Weak Random Sources (1994)

Citations: | 74 - 7 self |

### BibTeX

@MISC{Srinivasan94computingwith,

author = {Aravind Srinivasan and David Zuckerman},

title = {Computing with Very Weak Random Sources},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

For any fixed 6> 0, we show how to simulate RP algorithms in time nO(‘Ogn) using the output of a 6-source wath min-entropy R‘. Such a weak random source is asked once for R bits; it outputs an R-bit string such that any string has probability at most 2-Rc. If 6> 1- l/(k + l), our BPP simulations take time no(‘og(k)n) (log(k) is the logarithm iterated k times). We also gave a polynomial-time BPP simulation using Chor-Goldreich sources of min-entropy Ro(’), which is optimal. We present applications to time-space tradeoffs, expander constructions, and the hardness of approximation. Also of interest is our randomness-efficient Leflover Hash Lemma, found independently by Goldreich & Wigderson.