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Quotients and Atoms of Reversible Languages

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Formal Methods. FM 2019 International Workshops (FM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12233))

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Abstract

We consider several reversible finite automaton models which have been introduced over decades, and study some properties of their languages. In particular, we look at the question whether the quotients and atoms of a specific class of reversible languages also belong to that class or not. We consider bideterministic automata, reversible deterministic finite automata (REV-DFAs), reversible multiple-entry DFAs (REV-MeDFAs), and several variants of reversible nondeterministic finite automata (REV-NFAs). It is known that the class of REV-DFA languages is strictly included in the class of REV-MeDFA languages. We show that the classes of complete REV-DFA languages and complete REV-MeDFA languages are the same. We also show that differently from the general case of a REV-DFA language, the minimal DFA of a complete REV-DFA language is a complete REV-DFA. We also show that atoms of any regular language are accepted by REV-NFAs with a single initial and a single final state.

This work was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13.

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Authors and Affiliations

  1. Department of Software Science, Tallinn University of Technology, Tallinn, Estonia

    Hellis Tamm

Authors
  1. Hellis Tamm
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Correspondence to Hellis Tamm .

Editor information

Editors and Affiliations

  1. McMaster University, Hamilton, ON, Canada

    Emil Sekerinski

  2. University of Porto, Porto, Portugal

    Nelma Moreira

  3. University of Minho, Braga, Portugal

    José N. Oliveira

  4. Argo Ai, Munich, Germany

    Daniel Ratiu

  5. University of Pisa, Pisa, Italy

    Riccardo Guidotti

  6. University of Liverpool, Liverpool, UK

    Marie Farrell

  7. University of Liverpool, Liverpool, UK

    Matt Luckcuck

  8. University of Exeter, Exeter, UK

    Diego Marmsoler

  9. University of Minho, Braga, Portugal

    José Campos

  10. University of Newcastle, Newcastle upon Tyne, UK

    Troy Astarte

  11. Claude Bernard University, Lyon, France

    Laure Gonnord

  12. Nazarbayev University, Nur-Sultan, Kazakhstan

    Antonio Cerone

  13. University of Surrey, Guildford, UK

    Luis Couto

  14. University of Surrey, Guildford, UK

    Brijesh Dongol

  15. University of Giessen, Giessen, Germany

    Martin Kutrib

  16. University of Lisbon, Lisbon, Portugal

    Pedro Monteiro

  17. Airbus Operations S.A.S., Toulouse, France

    David Delmas

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Tamm, H. (2020). Quotients and Atoms of Reversible Languages. In: Sekerinski, E., et al. Formal Methods. FM 2019 International Workshops. FM 2019. Lecture Notes in Computer Science(), vol 12233. Springer, Cham. https://doi.org/10.1007/978-3-030-54997-8_28

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  • DOI: https://doi.org/10.1007/978-3-030-54997-8_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54996-1

  • Online ISBN: 978-3-030-54997-8

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