The Cayley-Graph of the Queue Monoid: Logic and Decidability

Authors Faried Abu Zaid, Chris Köcher

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Author Details

Faried Abu Zaid
  • Camelot Management Consultants, CoE Artificial Intelligence for Information Management, Munich, Germany
Chris Köcher
  • Technische Universität Ilmenau, Automata and Logics Group, Ilmenau, Germany

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Faried Abu Zaid and Chris Köcher. The Cayley-Graph of the Queue Monoid: Logic and Decidability. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We investigate the decidability of logical aspects of graphs that arise as Cayley-graphs of the so-called queue monoids. These monoids model the behavior of the classical (reliable) fifo-queues. We answer a question raised by Huschenbett, Kuske, and Zetzsche and prove the decidability of the first-order theory of these graphs with the help of an - at least for the authors - new combination of the well-known method from Ferrante and Rackoff and an automata-based approach. On the other hand, we prove that the monadic second-order of the queue monoid's Cayley-graph is undecidable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Models of computation
  • Information systems → Data structures
  • Queues
  • Transformation Monoid
  • Cayley-Graph
  • Logic
  • First-Order Theory
  • MSO Theory
  • Model Checking


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