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Regular Varieties of Automata and Coequations

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Mathematics of Program Construction (MPC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9129))

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Abstract

In this paper we use a duality result between equations and coequations for automata, proved by Ballester-Bolinches, Cosme-Llópez, and Rutten to characterize nonempty classes of deterministic automata that are closed under products, subautomata, homomorphic images, and sums. One characterization is as classes of automata defined by regular equations and the second one is as classes of automata satisfying sets of coequations called varieties of languages. We show how our results are related to Birkhoff’s theorem for regular varieties.

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Acknowledgements

The research of Julian Salamanca is funded by NWO project 612.001.210. The research of Adolfo Ballester-Bolinches has been supported by the grant 11271085 from the National Natural Science Foundation of China. The research of Enric Cosme-Llópez has been supported by the predoctoral grant AP2010-2764 from the Ministerio de Educación (Spanish Government) and by an internship from CWI. The research of Adolfo Ballester-Bolinches, Enric Cosme-Llópez, and Jan Rutten has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad (Spanish Government).

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Authors and Affiliations

  1. CWI Amsterdam, Amsterdam, The Netherlands

    J. Salamanca, M. M. Bonsangue & J. J. M. M. Rutten

  2. Universitat de València, Valencia, Spain

    A. Ballester-Bolinches & E. Cosme-Llópez

  3. LIACS - Leiden University, Leiden, The Netherlands

    M. M. Bonsangue

  4. Radboud University Nijmegen, Nijmegen, The Netherlands

    J. J. M. M. Rutten

Authors
  1. J. Salamanca
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  2. A. Ballester-Bolinches
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  3. M. M. Bonsangue
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  4. E. Cosme-Llópez
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  5. J. J. M. M. Rutten
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Corresponding author

Correspondence to J. Salamanca .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Ralf Hinze

  2. University of Bonn, Bonn, Germany

    Janis Voigtländer

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Salamanca, J., Ballester-Bolinches, A., Bonsangue, M.M., Cosme-Llópez, E., Rutten, J.J.M.M. (2015). Regular Varieties of Automata and Coequations. In: Hinze, R., Voigtländer, J. (eds) Mathematics of Program Construction. MPC 2015. Lecture Notes in Computer Science(), vol 9129. Springer, Cham. https://doi.org/10.1007/978-3-319-19797-5_11

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  • DOI: https://doi.org/10.1007/978-3-319-19797-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19796-8

  • Online ISBN: 978-3-319-19797-5

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