Descriptive Complexity of Computable Sequences Revisitedстатья
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Аннотация:The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the following two complexities of an infinite computable 0-1-sequence $\alpha$: $C^{0'}(\alpha )$, defined as the minimal length of a program with oracle $0'$ that prints $\alpha$, and $\MM(\alpha)$, defined as $\limsup C(\alpha_{1:n}|n)$, where $\alpha_{1:n}$ denotes the length-$n$ prefix of $\alpha$ and $C(x|y)$ stands for conditional Kolmogorov complexity. We show that $C^{0'}(\alpha )\le \MM(\alpha)+O(1)$ and $\MM(\alpha)$ is not bounded by any computable function of $C^{0'}(\alpha )$, even on the domain of computable sequences. \end{abstract}