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Statistical properties of finite sequences with high Kolmogorov complexity

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Abstract

We investigate to what extent finite binary sequences with high Kolmogorov complexity are normal (all blocks of equal length occur equally frequently), and the maximal length of all-zero or all-one runs which occur with certainty.

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References

  1. G. J. Chaitin, A theory of program size formally identical to information theory,J. Assoc. Comput. Mach.,22 (1975), 329–340.

    Google Scholar 

  2. T. Corman, C. Leiserson, and R. Rivest,Introduction to Algorithms, McGraw-Hill, New York, 1990.

    Google Scholar 

  3. P. Erdös and J. Spencer,Probabilistic Methods in Combinatorics, Academic Press, New York, 1974.

    Google Scholar 

  4. P. Gács, On the symmetry of algorithmic information,Soviet Math. Dokl,15 (1974), 1477–1480.

    Google Scholar 

  5. R. L. Graham, D. E. Knuth, and O. Patashnik,Concrete Mathematics, Addison-Wesley, Reading, MA, 1989.

    Google Scholar 

  6. D. E. Knuth,Seminumerical Algorithms, Addison-Wesley, Reading, MA, 1981.

    Google Scholar 

  7. A. N. Kolmogorov, Three approaches to the definition of the concept “quantity of information”,Problems Inform. Transmission,1(1) (1965), 1–7.

    Google Scholar 

  8. A. N. Kolmogorov, Combinatorial foundation of information theory and the calculus of probabilities,Russian Math. Surveys,38(4) (1983), 29–40.

    Google Scholar 

  9. L. A. Levin, Laws of information conservation (non-growth) and aspects of the foundation of probability theory,Problems Inform. Transmission,10 (1974), 206–210.

    Google Scholar 

  10. M. Li and P. M. B. Vitányi, Kolmogorov complexity and its applications, in:Handbook of Theoretical Computer Science, Vol. A (J. van Leeuwen, ed.), Elsevier/MIT Press, Amsterdam/Princeton, NJ, 1990, pp. 187–254.

    Google Scholar 

  11. M. Li and P. M. B. Vitányi, Kolmogorov complexity arguments in combinatorics,J. Combin. Theory Ser. A (to appear).

  12. P. Martin-Löf, On the definition of random sequences,Inform, and Control,9 (1966), 602–619.

    Google Scholar 

  13. H. J. Rogers, Jr.,Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967.

    Google Scholar 

  14. V. G. Vovk,Theory Probab. Appl,32 (1987), 413–425.

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Ming Li

  2. Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Paul M. B. Vitányi

Authors
  1. Ming Li
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  2. Paul M. B. Vitányi
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Additional information

Ming Li was supported by NSERC Operating Grant OGP-046506. Paul Vitányi was partially supported by NSERC International Scientific Exchange Award ISE0046203 and by the NWO through NFI Project ALADDIN under Contract Number NF 62-376.

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Li, M., Vitányi, P.M.B. Statistical properties of finite sequences with high Kolmogorov complexity. Math. Systems Theory 27, 365–376 (1994). https://doi.org/10.1007/BF01192146

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  • DOI: https://doi.org/10.1007/BF01192146

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