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The monoid of queue actions

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Abstract

We model the behavior of a fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic algebraic properties such as conjugacy. Moreover, we show that while several properties concerning its rational subsets are undecidable, their uniform membership problem is \({{\mathsf {N}}}{{\mathsf {L}}}\)-complete. Furthermore, we present an algebraic characterization of this monoid’s recognizable subsets. Finally, we prove that it is not Thurston-automatic.

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Notes

  1. This is not the original definition from [7], but it is equivalent by [7, Prop. 5.4].

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Acknowledgements

G. Zetzsche supported by a fellowship within the Postdoc-Program of the German Academic Exchange Service (DAAD).

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Authors and Affiliations

  1. London, UK

    Martin Huschenbett

  2. Institut für Theoretische Informatik, TU Ilmenau, Ilmenau, Germany

    Dietrich Kuske

  3. LSV, CNRS & ENS Cachan, Université Paris-Saclay, Cachan, France

    Georg Zetzsche

Authors
  1. Martin Huschenbett
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  2. Dietrich Kuske
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  3. Georg Zetzsche
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Corresponding author

Correspondence to Dietrich Kuske.

Additional information

Communicated by Markus Lohrey.

The results proved in this paper were announced in the extended abstract [11].

The results of this paper were obtained when Martin Huschenbett was affiliated with Institut für Theoretische Informatik, TU Ilmenau and when Georg Zetzsche was affiliated with Fachbereich Informatik, TU Kaiserslautern.

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Huschenbett, M., Kuske, D. & Zetzsche, G. The monoid of queue actions. Semigroup Forum 95, 475–508 (2017). https://doi.org/10.1007/s00233-016-9835-4

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