Abstract

The purpose of this paper is to answer two questions left open in Durand et al. (2001) [2]. Namely, we consider the following two complexities of an infinite computable 0-1-sequence α: C0′(α), defined as the minimal length of a program with oracle 0′ that prints α, and M∞(α), defined as limsupC(α1:n|n), where α1:n denotes the length-n prefix of α and C(x|y) stands for conditional Kolmogorov complexity. We show that C0′(α)⩽M∞(α)+O(1) and M∞(α) is not bounded by any computable function of C0′(α), even on the domain of computable sequences.

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