, Volume 11, Issue 1, pp 63-70

Pseudorandom bits for constant depth circuits

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For every integerd we explicitly construct a family of functions (pseudo-random bit generators) that convert a polylogarithmic number of truly random bits ton bits that appear random to any family of circuits of polynomial size and depthd. The functions we construct are computable by a uniform family of circuits of polynomial size and constant depth. This allows us to simulate randomized constant depth polynomial size circuits inDSPACE(polylog) and inDTIME(2 polylog ). As a corollary we show that the complexity class AM is equal to the class of languages recognizable in NP with a random oracle. Our technique may be applied in order to get pseudo random generators for other complexity classes as well; a further paper [16] explores these issues.

Part of this work was done while the first author was in U. C. Berkeley, visiting the Hebrew University of Jerusalem.