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We present a parallel algorithm for pseudo-random number generation. Given a seed of n驴 truly random bits for any 驴 0, our algorithm generates n驴 pseuderandom bits for any c 1. This takes poly-log time using n驴驴 processors where 驴驴 = k驴 for some fixed small constant k 1. We show that the pseuds-random bits output by our algorithm can not be distinguished from truly random bits in parallel poly-log time using a polynomial number of processors with probability 1/2 + 1/nO(1) if the multiplicative inverse problem almost always can not be solved in RNC. The proof is interesting and is quite different from previous proofs for sequential pseudo-random number generators.Our generator is fast and its output is provably as effective for RNC algorithms as truly random bits. Our generator passes all the statistical tests in KNUTH[14].Moreover, the existence of our generator has a number of central consequences for complexity theory. Given a randomized parallel algorithm A (over a wide class of machine models such as parallel RAMS and fixed connection networks) with time bound T(n) and processor bound P(n), we show A can be simulated by a parallel algorithm with time bound T(n) + O((log n)(log log n)), processor bound P(n)n驴驴, and only using n驴 truly random bits for any 驴 0.Also, we show that if the multiplicative inverse problem is almost always not in RNC, then RNC is within the class of languages accepted by uniform poly-log depth circuits with unbounded fan-in and strictly sub-exponential size 驴驴 0 2n驴.