The Annals of Mathematical Statistics

On Memory Saved by Randomization

Abstract

It is known that deterministic automata are generally not optimal in the problem of learning with finite memory. It is natural to ask how much memory is saved by randomization. In this note it is shown that the memory saving is arbitrarily large in the sense that for any memory size $m < \infty$, and $\delta > 0$, there exist problems such that all $m$-state deterministic algorithms have probability of error $P(e) \geqq \frac{1}{2} - \delta$, while the optimal two-state randomized algorithm has $P(e) \leqq \delta$.

Article information

Source
Ann. Math. Statist., Volume 42, Number 3 (1971), 1075-1078.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177693334

Digital Object Identifier
doi:10.1214/aoms/1177693334

Mathematical Reviews number (MathSciNet)
MR278853

Zentralblatt MATH identifier
0218.62027

JSTOR