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Geometric Interpretation of the Entropy of Sofic Systems

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Abstract

We consider a geometric approach to the notion of metric entropy. We justify the possibility of this approach for the class of Borel invariant ergodic probability measures on sofic systems, which is the first result of such generality for non-Markovian systems.

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References

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Acknowledgments

The author is grateful to his supervisor B.M. Gurevich for setting the problem of geometrical interpretation of entropy and for continued assistance in scientific research. Unfortunately, a few months before the publication, Boris Markovich had passed away, and this article is dedicated to his memory.

The author would also like to thank S.A. Komech for fruitful discussions of the subject and useful comments, M. Guysinsky for valuable advice at the final stage of the preparation of the paper, and the “BASIS” foundation for the support of this work.

The author would specially like to thank Efim Naumovich Malkin for his many years’ support of the author’s interest in scientific research, which played an important role in the appearance of this and two previous publications.

Funding

The research was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS.”

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Authors and Affiliations

  1. Department of Mathematical Statistics and Random Processes, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    G. D. Dvorkin

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  1. G. D. Dvorkin
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Correspondence to G. D. Dvorkin.

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The author of this work declares that he has no conflicts of interest.

Additional information

Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 2, pp. 49–62. https://doi.org/10.31857/S0555292323020043

In memoriam Boris Markovich Gurevich

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Dvorkin, G.D. Geometric Interpretation of the Entropy of Sofic Systems. Probl Inf Transm 59, 115–127 (2023). https://doi.org/10.1134/S0032946023020047

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  • DOI: https://doi.org/10.1134/S0032946023020047

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