, Volume 11, Issue 1, pp 6370
First online:
Pseudorandom bits for constant depth circuits
 Noam NisanAffiliated withDepartment of Computer Science, Hebrew University of Jerusalem
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For every integerd we explicitly construct a family of functions (pseudorandom 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.
AMS subject classification (1980)
68 C 25 Title
 Pseudorandom bits for constant depth circuits
 Journal

Combinatorica
Volume 11, Issue 1 , pp 6370
 Cover Date
 199103
 DOI
 10.1007/BF01375474
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
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 Keywords

 68 C 25
 Industry Sectors
 Authors

 Noam Nisan ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Hebrew University of Jerusalem, Israel