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Axiomatizing Kolmogorov Complexity

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Abstract

We revisit the axiomatization of Kolmogorov complexity given by Alexander Shen, currently available only in Russian language. We derive an axiomatization for conditional plain Kolmogorov complexity. Next we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). In addition we prove that the analogue of Shen’s axiomatic system fails to characterize prefix-free Kolmogorov complexity.

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Acknowledgements

I would like to express my gratitude to Laurent Bienvenu without whom this paper would never had existed. Thanks also to Serge Grigorieff for our numerous discussions during which he helped me progress on this work. Finally, thanks to anonymous reviewers for their help in preparing the final version of this paper.

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Authors and Affiliations

  1. LIAFA, CNRS & Université de Paris 7, Paris Cedex 13, France

    Antoine Taveneaux

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  1. Antoine Taveneaux
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Correspondence to Antoine Taveneaux.

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Taveneaux, A. Axiomatizing Kolmogorov Complexity. Theory Comput Syst 52, 148–161 (2013). https://doi.org/10.1007/s00224-012-9395-2

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  • DOI: https://doi.org/10.1007/s00224-012-9395-2

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