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A NOTE ON THE LEARNING-THEORETIC CHARACTERIZATIONS OF RANDOMNESS AND CONVERGENCE
The Review of Symbolic Logic ( IF 0.6 ) Pub Date : 2021-03-22 , DOI: 10.1017/s1755020321000125
TOMASZ STEIFER

Recently, a connection has been established between two branches of computability theory, namely between algorithmic randomness and algorithmic learning theory. Learning-theoretical characterizations of several notions of randomness were discovered. We study such characterizations based on the asymptotic density of positive answers. In particular, this note provides a new learning-theoretic definition of weak 2-randomness, solving the problem posed by (Zaffora Blando, Rev. Symb. Log. 2019). The note also highlights the close connection between these characterizations and the problem of convergence on random sequences.



中文翻译:

关于随机性和收敛性的学习理论表征的注释

最近,可计算性理论的两个分支,即算法随机性和算法学习理论之间建立了联系。发现了几种随机性概念的学习理论特征。我们基于肯定答案的渐近密度来研究这些特征。特别是,本说明提供了弱 2 随机性的新学习理论定义,解决了 (Zaffora Blando, Rev. Symb. Log. 2019) 提出的问题。该说明还强调了这些特征与随机序列收敛问题之间的密切联系。

更新日期:2021-03-22
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