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LATIN 2016: Theoretical Informatics

LATIN 2016: LATIN 2016: Theoretical Informatics pp 605–618Cite as

Trees and Languages with Periodic Signature

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9644))

Abstract

The signature of a labelled tree (and hence of its prefix-closed branch language) is the sequence of the degrees of the nodes of the tree in the breadth-first traversal. In a previous work, we have characterised the signatures of the regular languages. Here, the trees and languages that have the simplest possible signatures, namely the periodic ones, are characterised as the sets of representations of the integers in rational base numeration systems.

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Notes

  1. 1.

    The sequence of degrees observed on the tree in the figure begins indeed with a 1 instead of a 2, the sequence of labels begins at the second term. These discrepancies will be explained later.

  2. 2.

    A word \(a_0\,a_1\,a_2\,\cdots \,a_n\) is increasing if \(a_0<a_1<a_2<\cdots <a_n\).

  3. 3.

    This property was introduced in [10] under the unproper name of Bounded Left Iteration Property, or BLIP for short.

References

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Author information

Authors and Affiliations

  1. LIAFA, Université Denis Diderot, 8 place Aurélie Nemours, 75013, Paris, France

    Victor Marsault

  2. Telecom-ParisTech and CNRS, 46 rue Barrault, 75013, Paris, France

    Jacques Sakarovitch

Authors
  1. Victor Marsault
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  2. Jacques Sakarovitch
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Corresponding author

Correspondence to Victor Marsault .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, ON, Ontario, Canada

    Evangelos Kranakis

  2. University Chile, Santiago, Chile

    Gonzalo Navarro

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Marsault, V., Sakarovitch, J. (2016). Trees and Languages with Periodic Signature. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_45

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  • DOI: https://doi.org/10.1007/978-3-662-49529-2_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49528-5

  • Online ISBN: 978-3-662-49529-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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