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Phase-Bounded Broadcast Networks over Topologies of Communication

Authors Lucie Guillou , Arnaud Sangnier , Nathalie Sznajder

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ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Parameterized verification
  • Coverability
  • Broadcast Networks

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Abstract

We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its broadcasts. The coverability problem asks, given a protocol and a state of the protocol, whether there is a topology for the processes such that one of them (at least) reaches the given state. This problem is undecidable [G. Delzanno et al., 2010]. We study here an under-approximation of the problem where processes alternate a bounded number of times k between phases of broadcasting and phases of receiving messages. We show that, if the problem remains undecidable when k is greater than 6, it becomes decidable for k = 2, and ExpSpace-complete for k = 1. Furthermore, we show that if we restrict ourselves to line topologies, the problem is in P for k = 1 and k = 2.

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Lucie Guillou, Arnaud Sangnier, and Nathalie Sznajder. Phase-Bounded Broadcast Networks over Topologies of Communication. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.26

Author Details

Lucie Guillou
  • IRIF, CNRS, Université Paris Cité, France
Arnaud Sangnier
  • DIBRIS, Università di Genova, Italy
Nathalie Sznajder
  • LIP6, CNRS, Sorbonne Université, Paris, France

Funding

  • Guillou, Lucie: ANR project PaVeDyS (ANR-23-CE48-0005)

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