TY - CONF T1 - Computing with very weak random sources T2 - , 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings Y1 - 1994 A1 - Srinivasan, Aravind A1 - Zuckerman,D. KW - Application software KW - BPP simulations KW - Chor-Goldreich sources KW - computational complexity KW - Computational modeling KW - Computer science KW - Computer simulation KW - cryptography KW - distributed algorithms KW - expander constructions KW - hardness KW - MATHEMATICS KW - min-entropy KW - Physics computing KW - Polynomials KW - probability KW - R-bit string KW - randomness-efficient Leftover Hash Lemma KW - RP algorithms simulation KW - Testing KW - time-space tradeoffs KW - very weak random sources AB - For any fixed ε>0, we show how to simulate RP algorithms in time nO(log n) using the output of a δ-source with min-entropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an R-bit string such that any string has probability at most 2-R(ε). If ε>1-1/(k+1), our BPP simulations take time nO(log(k n)) (log(k) is the logarithm iterated k times). We also give a polynomial-time BPP simulation using Chor-Goldreich sources of min-entropy RΩ(1), which is optimal. We present applications to time-space tradeoffs, expander constructions, and the hardness of approximation. Also of interest is our randomness-efficient Leftover Hash Lemma, found independently by Goldreich and Wigderson JA - , 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings PB - IEEE SN - 0-8186-6580-7 M3 - 10.1109/SFCS.1994.365688 ER -