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 Probl. Peredachi Inf., 2007, Volume 43, Issue 1, Pages 56–66 (Mi ppi6)

Large Systems

Estimation of the Number of Elements in a Covering of an Arbitrary Randomness Test by Frequency Tests

K. Yu. Gorbunov

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We improve a well-known asymptotic bound on the number of monotonic selection rules for covering of an arbitrary randomness test by frequency tests. More precisely, we prove that, for any set $S$ (arbitrary test) of binary sequences of sufficiently large length $L$, where $|S|\le2^{L(1-\delta)}$, for sufficiently small $\delta$ there exists a polynomial (in $1/\delta$) set of monotonic selection rules (frequency tests) which guarantee that, for each sequence $\boldsymbol t\in S$, a subsequence can be selected such that the product of its length by the squared deviation of the fraction of zeros in it from $1/2$ is of the order of at least $0{,}5\ln2 L[\delta/\ln(1/\delta)](1-2\ln\ln(1/\delta)/\ln(1/\delta))$.

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English version:
Problems of Information Transmission, 2007, 43:1, 48–56

Bibliographic databases:

UDC: 621.391.1:519.2

Citation: K. Yu. Gorbunov, “Estimation of the Number of Elements in a Covering of an Arbitrary Randomness Test by Frequency Tests”, Probl. Peredachi Inf., 43:1 (2007), 56–66; Problems Inform. Transmission, 43:1 (2007), 48–56

Citation in format AMSBIB
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