Randomness is linear in space

Noam Nisan*, David Zuckerman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

464 Scopus citations

Abstract

We show that any randomized algorithm that runs in space S and time T and uses poly(S) random bits can be simulated using only O(S) random bits in space S and time T+poly(S). A deterministic simulation in space S follows. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.

Original languageAmerican English
Pages (from-to)43-52
Number of pages10
JournalJournal of Computer and System Sciences
Volume52
Issue number1
DOIs
StatePublished - Feb 1996

Bibliographical note

Funding Information:
-Supported by USA Israel BSF Grants 89-00126 and 92-00043 and by a Wolfson research award administered by the Israeli Academy of Sciences. Part of this research was done while the author visited IBM Almaden.

Funding Information:
Most of this research was done while the author was affiliated with MIT and supported by an NSF Postdoctoral Fellowship, NSF Grant 92-12184 CCR, and DARPA Grant N00014-92-J-1799. Part of this research was done while the author visited The Hebrew University in Jerusalem, Princeton University through DIMACS, and the International Computer Science Institute in Berkeley.

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