RAIRO-Theor. Inf. Appl.
Volume 52, Number 1, January–March 2018
|Page(s)||55 - 86|
|Published online||18 July 2018|
The inclusion structure of partially lossy queue monoids and their trace submonoids★
Fachgebiet Automaten und Logik, Technische Universität Ilmenau,
* Corresponding author: firstname.lastname@example.org
Accepted: 20 March 2018
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 monoid’s 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. Surprisingly, these are precisely those trace monoids that embed into the direct product of two free monoids – which gives a partial answer to a question raised by Diekert et al. at STACS 1995.
Mathematics Subject Classification: 68Q70 / 20M35
Key words: Lossy queue / transformation monoid
© 2018, EDP Sciences
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