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The Transformation Monoid of a Partially Lossy Queue

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Computer Science – Theory and Applications (CSR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10304))

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Abstract

We model the behavior of a lossy fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. To have a common model for reliable and lossy queues, we split the alphabet of the queue into two parts: the forgettable letters and the letters that are transmitted reliably.

We describe this monoid by means of a confluent and terminating semi-Thue system and then study some of the monoids algebraic properties. In particular, we characterize completely when one such monoid can be embedded into another as well as which trace monoids occur as submonoids. The resulting picture is far more diverse than in the case of reliable queues studied before.

C. Köcher and D. Kuske—Supported by the DFG-Project “Speichermechanismen als Monoide”, KU 1107/9-1.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Technische Universität Ilmenau, Ilmenau, Germany

    Chris Köcher & Dietrich Kuske

Authors
  1. Chris Köcher
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  2. Dietrich Kuske
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Corresponding author

Correspondence to Chris Köcher .

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Editors and Affiliations

  1. University of Bordeaux , Talence, France

    Pascal Weil

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Köcher, C., Kuske, D. (2017). The Transformation Monoid of a Partially Lossy Queue. In: Weil, P. (eds) Computer Science – Theory and Applications. CSR 2017. Lecture Notes in Computer Science(), vol 10304. Springer, Cham. https://doi.org/10.1007/978-3-319-58747-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-58747-9_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58746-2

  • Online ISBN: 978-3-319-58747-9

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