Computing absolutely normal numbers in nearly linear time
نویسندگان
چکیده
A real number x is absolutely normal if, for every base b≥2, two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion x. This paper presents an explicit algorithm that generates binary x, nth bit appearing after npolylog(n) computation steps. speed achieved by simultaneously computing and diagonalizing against a martingale incorporates Lempel-Ziv parsing algorithms all bases.
منابع مشابه
Computing Absolutely Normal Numbers in Nearly Linear Time
A real number x is absolutely normal if, for every base b ≥ 2, every two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion of x. This paper presents an explicit algorithm that generates the binary expansion of an absolutely normal number x, with the nth bit of x appearing after npolylog(n) computation steps. This speed is achieved by simultaneously co...
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ژورنال
عنوان ژورنال: Information & Computation
سال: 2021
ISSN: ['0890-5401', '1090-2651']
DOI: https://doi.org/10.1016/j.ic.2021.104746