The Monoid of Queue Actions

  • Martin Huschenbett
  • Dietrich Kuske
  • Georg Zetzsche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8634)


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 NL-complete. Furthermore, we present an algebraic characterization of this monoid’s recognizable subsets. Finally, we prove that it is not Thurston-automatic.


Normal Form Basic Action Cayley Graph Regular Language Free Monoid 
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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Martin Huschenbett
    • 1
  • Dietrich Kuske
    • 1
  • Georg Zetzsche
    • 2
  1. 1.Institut für Theoretische InformatikTU IlmenauIlmenauGermany
  2. 2.Fachbereich InformatikTU KaiserslauternKaiserslauternGermany

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