Problems of Information Transmission

, Volume 43, Issue 1, pp 48–56 | Cite as

Bound on the cardinality of a covering of an arbitrary randomness test by frequency tests

  • K. Yu. Gorbunov
Large Systems


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∨ ≤ 2 L(1−δ), for sufficiently small δ there exists a polynomial (in 1/δ) set of monotonic selection rules (frequency tests) which guarantee that, for each sequence tS, 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 ln 2 L[δ/ln(1/δ)](1 − 2 ln ln(1/δ)/ln(1/δ)).


Selection Rule Information Transmission Binary Sequence Frequency Test Normal Rule 
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Copyright information

© Pleiades Publishing, Inc. 2007

Authors and Affiliations

  • K. Yu. Gorbunov
    • 1
  1. 1.Kharkevich Institute for Information Transmission ProblemsRASMoscowRussia

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