How strong is Nisan's pseudo-random generator?

Authors:
Matei David;Periklis A. Papakonstantinou;Anastasios Sidiropoulos
Affiliations:
Center for Computational Intractability, Princeton University, United States;Tsinghua University, Institute for Theoretical Computer Science, 1-208 FIT Building, Beijing, China;Toyota Technological Institute, Chicago, United States
Venue:
Information Processing Letters
Year:
2011

Citing 5
Cited 0

A fast parallel algorithm to compute the rank of a matrix over an arbitrary field

Combinatorica
On read-once vs. multiple access to randomness in logspace

Theoretical Computer Science - Special issue on structure in complexity theory
Pseudorandomness for network algorithms

STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomization and Derandomization in Space-Bounded Computation

CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Computational Complexity: A Modern Approach

Computational Complexity: A Modern Approach

Quantified Score

Hi-index	0.89

Visualization

Abstract

We study the resilience of the classical pseudo-random generator (PRG) of Nisan (1992) [6] against space-bounded machines that make multiple passes over the input. Nisan@?s PRG is known to fool log-space machines that read the input once. We ask what are the limits of this PRG regarding log-space machines that make multiple passes over the input. We show that for every constant k Nisan@?s PRG fools log-space machines that make log^kn passes over the input, using a seed of length log^k^^^'n, for some k^'k. We complement this result by showing that in general Nisan@?s PRG cannot fool log-space machines that make n^O^(^1^) passes even for a seed of length 2^@Q^(^l^o^g^n^). The observations made in this note outline a more general approach in understanding the difficulty of derandomizing BPNC^1.