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“…(See [20] for a survey of these prediction models.) We also refer the reader to [22,21] for recent work relating Hausdorff dimension to prediction.…”

confidence: 99%

“…(See [20] for a survey of these prediction models.) We also refer the reader to [22,21] for recent work relating Hausdorff dimension to prediction.…”

confidence: 99%

“…The description of the suggested processes show that they can be used to develop PRNGs with the property in Equation (1). The described processes are generalization of so-called two-faced processes suggested in [20][21][22].…”

confidence: 91%

“…In 1949, Eggleston [7], building on work of Besicovitch [3] and Good [10], proved that, for any probability measure π on a finite alphabet Σ, the set of all sequences in which each symbol a ∈ Σ has asymptotic frequency π(a) has Hausdorff dimension H |Σ| (π), the Shannon entropy of π, normalized to range over [0,1]. In retrospect, Hausdorff dimension is an information-theoretic concept [27], but these developments essentially all took place prior to Shannon's development of information theory [28].…”

confidence: 99%