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Approaching Repetition Thresholds via Local Resampling and Entropy Compression

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Developments in Language Theory (DLT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13911))

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Abstract

We analyze a simple algorithm, transforming an input word into a word avoiding certain repetitions such as fractional powers and undirected powers. This transformation can be made reversible by adding the log of the run of the algorithm to the output. We introduce a compression scheme for the logs; its analysis proves that \((1+\frac{1}{d})\)-powers and undirected \((1+\frac{1}{d})\)-powers can be avoided over \(d+O(1)\) letters. These results are closer to the optimum than it is usually expected from a purely information-theoretic considerations. In the second part, we present experimental results obtained by the mentioned algorithm in the extreme case of \((d+1)\)-ary words avoiding \((1+\frac{1}{d})^+\!\)-powers.

Supported by the grant MPM no. ERC 683064 under the EU’s Horizon 2020 Research and Innovation Programme and by the State of Israel through the Center for Absorption in Science of the Ministry of Aliyah and Immigration.

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Authors and Affiliations

  1. Bar Ilan University, Ramat Gan, Israel

    Arseny M. Shur

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  1. Arseny M. Shur
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Correspondence to Arseny M. Shur .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Ural Federal University, Ekaterinburg, Russia

    Mikhail Volkov

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Shur, A.M. (2023). Approaching Repetition Thresholds via Local Resampling and Entropy Compression. In: Drewes, F., Volkov, M. (eds) Developments in Language Theory. DLT 2023. Lecture Notes in Computer Science, vol 13911. Springer, Cham. https://doi.org/10.1007/978-3-031-33264-7_18

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  • DOI: https://doi.org/10.1007/978-3-031-33264-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33263-0

  • Online ISBN: 978-3-031-33264-7

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