Small-Bias Probability Spaces: Efficient Constructions and Applications

DMCA

Small-Bias Probability Spaces: Efficient Constructions and Applications (1993)

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Joseph Naor , Moni Naor

Venue:	SIAM J. Comput
Citations:	276 - 13 self

BibTeX

@ARTICLE{Naor93small-biasprobability,
    author = {Joseph Naor and Moni Naor},
    title = {Small-Bias Probability Spaces: Efficient Constructions and Applications},
    journal = {SIAM J. Comput},
    year = {1993},
    volume = {22},
    pages = {838--856}
}

OpenURL

Abstract

We show how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with "almost" equal probability. They are called ffl-biased random variables. The number of random bits needed to generate the random variables is O(log n + log 1 ffl ). Thus, if ffl is polynomially small, then the size of the sample space is also polynomial. Random variables that are ffl-biased can be used to construct "almost" k-wise independent random variables where ffl is a function of k. These probability spaces have various applications: 1. Derandomization of algorithms: many randomized algorithms that require only k- wise independence of their random bits (where k is bounded by O(log n)), can be derandomized by using ffl-biased random variables. 2. Reducing the number of random bits required by certain randomized algorithms, e.g., verification of matrix multiplication. 3. Exhaustive testing of combinatorial circui...

Keyphrases

efficient construction random bit small-bias probability space random variable ffl-biased random variable wise independence probability space small probability space various application exhaustive testing matrix multiplication equal probability binary random variable combinatorial circui certain randomized algorithm sample space k-wise independent random variable

DMCA