A recipe for randomness.

نویسندگان

  • S Pincus
  • B H Singer
چکیده

Despite many diverse theories that address closely related themes-e. g., probability theory, algorithmic complexity, cryptoanalysis, and pseudorandom number generation-a near-void remains in constructive methods certified to yield the desired "random" output. Herein, we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences, based on constructions and properties derived from approximate entropy (ApEn), a computable formulation of sequential irregularity. Furthermore, for infinite sequences, we considerably refine normality, by providing methods for constructing diverse classes of normal numbers, classified by the extent to which initial segments deviate from maximal irregularity.

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عنوان ژورنال:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 95 18  شماره 

صفحات  -

تاریخ انتشار 1998