算法随机序列

IF 0.3 Q4 MATHEMATICS, APPLIED

Computability-The Journal of the Association CiE Pub Date : 2023-09-13 DOI:10.3233/com-220433

Rodney G. Downey, Noam Greenberg, Andrew Tanggara

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引用次数: 0

摘要

Rademacher (Mathematische Annalen 87 (1922) 112-138)， Steinhaus (Mathematische Zeitschrift 31 (1930) 408-416)， Paley和Zygmund(剑桥哲学学会数学论文集26(1930)337-257，剑桥哲学学会数学论文集26(1930)458-474，剑桥哲学学会数学论文集28(1932)190-205)开创了随机序列的广泛研究。利用可计算性理论和概率论相结合的算法随机性理论，研究了一些经典定理的有效内容。我们将讨论这与Kahane和Bollobás的一个老问题之间的关系。我们还讨论了如何考虑这些关于随机序列的算法问题似乎导致了算法随机性的新概念。

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Algorithmically random series

Rademacher (Mathematische Annalen 87 (1922) 112–138), Steinhaus (Mathematische Zeitschrift 31 (1930) 408–416) and Paley and Zygmund (Mathematical Proceedings of the Cambridge Philosophical Society 26 (1930) 337–257, Mathematical Proceedings of the Cambridge Philosophical Society 26 (1930) 458–474, Mathematical Proceedings of the Cambridge Philosophical Society 28 (1932) 190–205) initiated the extensive study of random series. Using the theory of algorithmic randomness, which is a mix of computability theory and probability theory, we investigate the effective content of some classical theorems. We discuss how this is related to an old question of Kahane and Bollobás. We also discuss how considerations of such algorithmic questions about random series seem to lead to new notions of algorithmic randomness.

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来源期刊

Computability-The Journal of the Association CiE MATHEMATICS, APPLIED-

CiteScore

1.10

自引率

16.70%

发文量