, Volume 12, Issue 4, pp 449-461

First online:

Pseudorandom generators for space-bounded computation

  • Noam NisanAffiliated withDepartment of Computer Science, Hebrew University of Jerusalem

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Pseudorandom generators are constructed which convertO(SlogR) truly random bits toR bits that appear random to any algorithm that runs inSPACE(S). In particular, any randomized polynomial time algorithm that runs in spaceS can be simulated using onlyO(Slogn) random bits. An application of these generators is an explicit construction of universal traversal sequences (for arbitrary graphs) of lengthn O(logn).

The generators constructed are technically stronger than just appearing random to spacebounded machines, and have several other applications. In particular, applications are given for “deterministic amplification” (i.e. reducing the probability of error of randomized algorithms), as well as generalizations of it.

AMS subject classification code (1991)

68 Q 15