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- W2912379437 abstract "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 $M_{infty}(alpha)$, defined as $liminf C(alpha_{1:n}|n)$, where $alpha_{1:n}$ denotes the length-$n$ prefix of $alpha$ and $C(x|y)$ stands for conditional Kolmogorov complexity. We show that $C^{0'}(alpha )le M_{infty}(alpha)+O(1)$ and $M_{infty}(alpha)$ is not bounded by any computable function of $C^{0'}(alpha )$, even on the domain of computable sequences." @default.
- W2912379437 created "2019-02-21" @default.
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- W2912379437 date "2019-02-04" @default.
- W2912379437 modified "2023-09-27" @default.
- W2912379437 title "Descriptive Complexity of Computable Sequences Revisited." @default.
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