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A Characterization of Those Automata That Structurally Generate Finite Groups

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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Abstract

Antonenko and Russyev independently have shown that any Mealy automaton with no cycle with exit—that is, where every cycle in the underlying directed graph is a sink component—generates a finite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper.

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Author information

Authors and Affiliations

  1. Sorbonne Paris Cité, LIAFA, UMR 7089 CNRS, Univ Paris Diderot, F-75013, Paris, France

    Ines Klimann & Matthieu Picantin

Authors
  1. Ines Klimann
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  2. Matthieu Picantin
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Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Klimann, I., Picantin, M. (2014). A Characterization of Those Automata That Structurally Generate Finite Groups. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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