Distributed Controller Synthesis for Deadlock Avoidance

Authors Hugo Gimbert, Corto Mascle, Anca Muscholl, Igor Walukiewicz

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Hugo Gimbert
  • Université de Bordeaux, CNRS, France
Corto Mascle
  • Université de Bordeaux, France
Anca Muscholl
  • Université de Bordeaux, France
Igor Walukiewicz
  • Université de Bordeaux, CNRS, France

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Hugo Gimbert, Corto Mascle, Anca Muscholl, and Igor Walukiewicz. Distributed Controller Synthesis for Deadlock Avoidance. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 125:1-125:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We consider the distributed control synthesis problem for systems with locks. The goal is to find local controllers so that the global system does not deadlock. With no restriction this problem is undecidable even for three processes each using a fixed number of locks. We propose two restrictions that make distributed control decidable. The first one is to allow each process to use at most two locks. The problem then becomes complete for the second level of the polynomial time hierarchy, and even in Ptime under some additional assumptions. The dining philosophers problem satisfies these assumptions. The second restriction is a nested usage of locks. In this case the synthesis problem is Nexptime-complete. The drinking philosophers problem falls in this case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Distributed Synthesis
  • Concurrency
  • Lock Synchronisation
  • Deadlock Avoidance


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