Translating Asynchronous Games for Distributed Synthesis

Authors Raven Beutner, Bernd Finkbeiner, Jesko Hecking-Harbusch

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Raven Beutner
  • Saarland University, Saarbrücken, Germany
Bernd Finkbeiner
  • Saarland University, Saarbrücken, Germany
Jesko Hecking-Harbusch
  • Saarland University, Saarbrücken, Germany

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Raven Beutner, Bernd Finkbeiner, and Jesko Hecking-Harbusch. Translating Asynchronous Games for Distributed Synthesis. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In distributed synthesis, a set of process implementations is generated, which together, accomplish an objective against all possible behaviors of the environment. A lot of recent work has focussed on systems with causal memory, i.e., sets of asynchronous processes that exchange their causal histories upon synchronization. Decidability results for this problem have been stated either in terms of control games, which extend Zielonka’s asynchronous automata by partitioning the actions into controllable and uncontrollable, or in terms of Petri games, which extend Petri nets by partitioning the tokens into system and environment players. The precise connection between these two models was so far, however, an open question. In this paper, we provide the first formal connection between control games and Petri games. We establish the equivalence of the two game types based on weak bisimulations between their strategies. For both directions, we show that a game of one type can be translated into an equivalent game of the other type. We provide exponential upper and lower bounds for the translations. Our translations allow to transfer and combine decidability results between the two types of games. Exemplarily, we translate decidability in acyclic communication architectures, originally obtained for control games, to Petri games, and decidability in single-process systems, originally obtained for Petri games, to control games.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • synthesis
  • distributed systems
  • causal memory
  • Petri games
  • control games


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