Randomness is linear in space

Noam Nisan*, David Zuckerman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

464 Scopus citations


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
Issue number1
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.


Dive into the research topics of 'Randomness is linear in space'. Together they form a unique fingerprint.

Cite this