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A Final Coalgebra for k-regular Sequences

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Horizons of the Mind. A Tribute to Prakash Panangaden

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8464))

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Abstract

We study k-regular sequences from a coalgebraic perspective. Building on the observation that the set of streams over a semiring S can be turned into a final coalgebra, we obtain characterizations of k-regular sequences in terms of finite weighted automata, finite systems of behavioral differential equations, and recognizable power series. The latter characterization is obtained via an isomorphism of final coalgebras based on the k-adic numeration system.

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Author information

Authors and Affiliations

  1. Radboud University Nijmegen, Netherlands

    Helle Hvid Hansen & Jan Rutten

  2. University of Strathclyde, UK

    Clemens Kupke

  3. CWI Amsterdam, UK

    Helle Hvid Hansen, Jan Rutten & Joost Winter

Authors
  1. Helle Hvid Hansen
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  2. Clemens Kupke
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  3. Jan Rutten
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  4. Joost Winter
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, York University, Keele Street, 4700, M3J 1P3, Toronto, ON, Canada

    Franck van Breugel

  2. School of Informatics, Informatics Forum, University of Edinburgh, 10 Crichton Street, EH8 9LE, Edinburgh, UK

    Elham Kashefi

  3. Inria Saclay, Campus de l’École Polytechnique, Bâtiment Alan Turing, 1, rue Honoré d’Estienne d’Orves, 91120, Palaiseau, France

    Catuscia Palamidessi

  4. CWI, P.O. Box 94079, 1090, Amsterdam, GB, The Netherlands

    Jan Rutten

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Hansen, H.H., Kupke, C., Rutten, J., Winter, J. (2014). A Final Coalgebra for k-regular Sequences. In: van Breugel, F., Kashefi, E., Palamidessi, C., Rutten, J. (eds) Horizons of the Mind. A Tribute to Prakash Panangaden. Lecture Notes in Computer Science, vol 8464. Springer, Cham. https://doi.org/10.1007/978-3-319-06880-0_19

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  • DOI: https://doi.org/10.1007/978-3-319-06880-0_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06879-4

  • Online ISBN: 978-3-319-06880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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