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June, 1971 On Memory Saved by Randomization
Martin E. Hellman, Thomas M. Cover
Ann. Math. Statist. 42(3): 1075-1078 (June, 1971). DOI: 10.1214/aoms/1177693334

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 $P(e) \leqq \delta$.

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Martin E. Hellman. Thomas M. Cover. "On Memory Saved by Randomization." Ann. Math. Statist. 42 (3) 1075 - 1078, June, 1971. https://doi.org/10.1214/aoms/1177693334

Information

Published: June, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0218.62027
MathSciNet: MR278853
Digital Object Identifier: 10.1214/aoms/1177693334

Rights: Copyright © 1971 Institute of Mathematical Statistics

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Vol.42 • No. 3 • June, 1971
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