Pseudorandom bits for constant depth circuits

Noam Nisan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

139 Scopus citations

Abstract

For every integer d we explicitly construct a family of functions (pseudo-random bit generators) that convert a polylogarithmic number of truly random bits to n bits that appear random to any family of circuits of polynomial size and depth d. 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 in DSPACE(polylog) and in DTIME(2polylog). 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.

Original languageAmerican English
Pages (from-to)63-70
Number of pages8
JournalCombinatorica
Volume11
Issue number1
DOIs
StatePublished - Mar 1991

Keywords

  • AMS subject classification (1980): 68C25

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