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Abstract: A drawback of Kolmogorov-Chaitin complexity K as a function from s to theshortest program producing s is its noncomputability which limits its range ofapplicability. Moreover, when strings are short, the dependence of K on aparticular universal Turing machine U can be arbitrary. In practice one canapproximate it by computable compression methods. However, such compressionmethods do not always provide meaningful approximations-for strings shorter,for example, than typical compiler lengths. In this paper we suggest anempirical approach to overcome this difficulty and to obtain a stabledefinition of the Kolmogorov-Chaitin complexity for short sequences.Additionally, a correlation in terms of distribution frequencies was foundacross the output of two models of abstract machines, namely unidimensionalcellular automata and deterministic Turing machine.



Author: Jean-Paul Delahaye, Hector Zenil

Source: https://arxiv.org/







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