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Statistical testing of finite sequences based on algorithmic complexity

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Fundamentals of Computation Theory (FCT 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 199))

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Abstract

A mathematical model is presented which enables to give a meaningful interpretation to the assertion "with a probability greater than 1-ɛ the finite sequence of letters under consideration is an initial segment of a relatively simple infinite recursive sequence" and to give an at least potential possibility how to test the validity of such an assertion. The model is based on a modified version of Kolmogorov algorithmic complexity of sequences of letters and the results are compared with those offered by the classical statistical hypothesis testing theory.

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References

  1. A. N. Kolmogorov: Tri podchoda k kvantitativnomu opredeleniju informacii. Problemy peredači informacii vol. 1(1965), pp. 4–7.

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  2. T. L. Fine: Theories of Probability — an Examination of Foundations. Academic Press, New York — London, 1973.

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  3. E. L. Lehmann: Testing Statistical Hypotheses. J. Wiley & Sons — Chapman & Hall, New York — London, 1960.

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  4. J. S. Chow, H. Teicher: Probability Theory — Independence, Interchangeability, Martingales. Springer-Verlag, Berlin — Heidelberg — New York, 1978.

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  5. I. Kramosil: Non-Deterministic Prediction Based on Algorithmic Complexity. Submitted for publication.

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  6. M. Esmenjaud-Bonnardel: Étude statistique des decimals de pí. Rev. française Trait. Inf. vol. 8(1965), pp. 295–306.

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Authors and Affiliations

  1. Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, Pod vodárenskou věží 4, 182 08, Prague, Czechoslovakia

    Ivan Kramosil

Authors
  1. Ivan Kramosil
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Lothar Budach

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© 1985 Springer-Verlag Berlin Heidelberg

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Kramosil, I. (1985). Statistical testing of finite sequences based on algorithmic complexity. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028805

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  • DOI: https://doi.org/10.1007/BFb0028805

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15689-5

  • Online ISBN: 978-3-540-39636-9

  • eBook Packages: Springer Book Archive

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