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Kolmogorov complexity and Hausdorff dimension

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Fundamentals of Computation Theory (FCT 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 380))

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References

  1. Billingsley, P., Ergodic Theory and Information. Wiley, New York 1965.

    Google Scholar 

  2. Daley, R.P., The extent and density of sequences within the minimal-program complexity hierarchies. J. Comput. System Sci. 15 (1974), 151–163.

    Google Scholar 

  3. DeLuca, A., On the entropy of a formal language. In: Automata Theory and Formal Languages, Proc. 2nd GI Conference (H. Brakhage, Ed.), Lect. Notes Comput Sci. 33, Springer-Verlag, Berlin 1975, 103–109.

    Google Scholar 

  4. Eilenberg, S., Automata, Languages, and Machines. Vol. A, Academic Press, New York 1974.

    Google Scholar 

  5. Hoogeboom, H.J. and Rozenberg, G., Infinitary languages: Basic theory and applications to concurrent systems. In: Current Trends in Concurrency — Overviews and Tutorials (J.W. de Bakker, W.-P. de Roever and G. Rozenberg, Eds.), Lect. Notes Comput. Sci. 224, Springer-Verlag, Berlin 1986, 266–342.

    Google Scholar 

  6. Katseff, H.P. and Sipser, M., Several results in program size complexity. Theoret. Comput Sci. 15 (1981), 291–309.

    Article  Google Scholar 

  7. Kuich, W., On the entropy of context-free languages. Inform. and Control 16 (1970)2, 173–200.

    Article  Google Scholar 

  8. Leung-Yan-Cheong, S.K. and Cover, T., Some equivalences between Shannon entropy and Kolmogorov complexity. IEEE Trans. Inform. Theory IT-24 (1978), 331–338.

    Article  Google Scholar 

  9. Mi, L., and Vitanyi, P.M.B., Two decades of applied Kolmogorov complexity. In: Proc. 3rd IEEE Structure in Complexity Conference, 1988.

    Google Scholar 

  10. Lindner, R. and Staiger, L., Algebraische Codierungstheorie — Theorie der sequentiellen Codierungen. Akademie-Verlag, Berlin 1977.

    Google Scholar 

  11. Ryabko, B.Ya., Noiseless coding of combinatorial sources, Hausdoff dimension and Kolmogorov complexity. Problemy Peredachi Informatsii 22 (1986) 3, 16–26. [Russian]

    Google Scholar 

  12. Salomaa, A., Theory of Automata. Pergamon, Oxford 1969.

    Google Scholar 

  13. Schnorr, C.P., De Zufälligkeit und Wahrscheinlichkeit. Lect. Notes Math. 218, Springer-Verlag, Berlin 1971.

    Google Scholar 

  14. Schnorr, C.P., Process complexity and effective random tests. J. Comput. System Sci. 7 (1973) 4, 376–388.

    Google Scholar 

  15. Staiger, L., Complexity and entropy. In: Mathematical Foundations of Computer Science (J. Gruska and M. Chytil, Eds.), Lect. Notes Comput. Sci. 118, Springer-Verlag, Berlin 1981, 508–514.

    Google Scholar 

  16. Staiger, L., The entropy of finite-state ω-languages. Probl. Control and Inform. Theory 14 (1985) 5, 383–392.

    Google Scholar 

  17. Staiger, L., Hierarchies of recursive ω-languages. J. Inform. Process. Cybern. EIK 22 (1986) 5/6, 219–241.

    Google Scholar 

  18. Staiger, L., Research in the theory of ω-languages. J. Inform. Process. Cybern. EIK 23 (1987) 8/9, 415–439.

    Google Scholar 

  19. Staiger, L., Ein Satz über die Entropie von Untermonoiden. Theoret. Comput. Sci. 61 (1988) (2,3), 279–282.

    Article  Google Scholar 

  20. Staiger, L., Quadtrees and the Hausdorff dimension of pictures. In: Proc. GEOBILD '89 (A. Hübler, W. Nagel, B.D. Ripley and G. Werner, Eds), Mathematical Research 51, Akademie-Verlag, Berlin 1989

    Google Scholar 

  21. Staiger, L., Combinatorial properties of the Hausdorff dimension. J. Statist. Plann. Inference 22 (1989), to appear.

    Google Scholar 

  22. Thomas, W., Automata on infinite objects. Aachener Informatik-Berichte 88-17.

    Google Scholar 

  23. van Lambalgen, M., Random sequences. Ph.D. Thesis, Univ. of Amsterdam, 1987.

    Google Scholar 

  24. Zvonkin, A.K. and Levin, L.A., Complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russian Math. Surveys 25 (1970), 83–124.

    Google Scholar 

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J. Csirik J. Demetrovics F. Gécseg

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Staiger, L. (1989). Kolmogorov complexity and Hausdorff dimension. In: Csirik, J., Demetrovics, J., Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1989. Lecture Notes in Computer Science, vol 380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51498-8_42

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  • DOI: https://doi.org/10.1007/3-540-51498-8_42

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