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Branching Frequency and Markov Entropy of Repetition-Free Languages

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Book cover Developments in Language Theory (DLT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12811))

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Abstract

We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language and the parameters of branching of its prefix tree. We show how to compute Markov entropy for a regular language. Finally, we develop a framework for experimental study of Markov entropy by modelling random walks and present the results of experiments with power-free and Abelian-power-free languages.

Supported by the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387).

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Notes

  1. 1.

    Non-uniform distributions are also used in many applications but we do not consider them here.

  2. 2.

    Note that it is not possible in general to find the roots of polynomials exactly.

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Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    Elena A. Petrova & Arseny M. Shur

Authors
  1. Elena A. Petrova
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  2. Arseny M. Shur
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Correspondence to Arseny M. Shur .

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Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Nelma Moreira

  2. University of Porto, Porto, Portugal

    Rogério Reis

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Petrova, E.A., Shur, A.M. (2021). Branching Frequency and Markov Entropy of Repetition-Free Languages. In: Moreira, N., Reis, R. (eds) Developments in Language Theory. DLT 2021. Lecture Notes in Computer Science(), vol 12811. Springer, Cham. https://doi.org/10.1007/978-3-030-81508-0_27

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  • DOI: https://doi.org/10.1007/978-3-030-81508-0_27

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  • Print ISBN: 978-3-030-81507-3

  • Online ISBN: 978-3-030-81508-0

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