期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1998
卷号：95
期号：18
页码：10367-10372
DOI：10.1073/pnas.95.18.10367
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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.
关键词：normal numbers/maximally irregular/approximate entropy/deficit from equidistribution/combinatorial
