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arXiv · 0704.1043

On the Kolmogorov-Chaitin Complexity for short sequences

Jean-Paul Delahaye·Hector Zenil
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Abstract

A drawback of Kolmogorov-Chaitin complexity (K) as a function from s to the shortest program producing s is its noncomputability which limits its range of applicability. Moreover, when strings are short, the dependence of K on a particular universal Turing machine U can be arbitrary. In practice one can approximate it by computable compression methods. However, such compression methods do not always provide meaningful approximations--for strings shorter, for example, than typical compiler lengths. In this paper we suggest an empirical approach to overcome this difficulty and to obtain a stable definition of the Kolmogorov-Chaitin complexity for short sequences. Additionally, a correlation in terms of distribution frequencies was found across the output of two models of abstract machines, namely unidimensional cellular automata and deterministic Turing machine.

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Jean-Paul Delahaye, Hector Zenil. 2010-12-17. On the Kolmogorov-Chaitin Complexity for short sequences. https://arxiv.org/abs/0704.1043

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