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On the Piecewise Complexity of Words and Periodic Words

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SOFSEM 2024: Theory and Practice of Computer Science (SOFSEM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14519))

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Abstract

The piecewise complexity h(u) of a word is the minimal length of subwords needed to exactly characterise u. Its piecewise minimality index \(\rho (u)\) is the smallest length k such that u is minimal among its order-k class \([u]_k\) in Simon’s congruence.

We study these two measures and provide efficient algorithms for computing h(u) and \(\rho (u)\). We also provide efficient algorithms for the case where u is a periodic word, of the form \(u=v^n\).

Work supported by IRL ReLaX. J. Veron supported by DIGICOSME ANR-11-LABX-0045.

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Notes

  1. 1.

    In fact \(\delta (u,v)\) is a measure of similarity and not of difference, between u and v. The associated distance is actually \(d(u,v){\mathop {=}\limits ^{\text{ def }}}2^{-\delta (u,v)}\) [SS83].

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Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    M. Praveen

  2. CNRS, ReLaX, IRL 2000, Chennai, India

    M. Praveen

  3. Laboratoire Méthodes Formelles, Univ. Paris-Saclay, Gif-sur-Yvette, France

    Ph. Schnoebelen, J. Veron & I. Vialard

Authors
  1. M. Praveen
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  2. Ph. Schnoebelen
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  3. J. Veron
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  4. I. Vialard
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Corresponding author

Correspondence to Ph. Schnoebelen .

Editor information

Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

  2. UNSW Sydney, Sydney, NSW, Australia

    Serge Gaspers

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

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Praveen, M., Schnoebelen, P., Veron, J., Vialard, I. (2024). On the Piecewise Complexity of Words and Periodic Words. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_32

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  • DOI: https://doi.org/10.1007/978-3-031-52113-3_32

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  • Online ISBN: 978-3-031-52113-3

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