Parameterized Verification of Communicating Automata under Context Bounds

We study the verification problem for parameterized communicating automata (PCA), in which processes synchronize via message passing. A given PCA can be run on any topology of bounded degree (such as pipelines, rings, or ranked trees), and communication may take place between any two processes that are adjacent in the topology. Parameterized verification asks if there is a topology from a given topology class that allows for an accepting run of the given PCA. In general, this problem is undecidable even for synchronous communication and simple pipeline topologies. We therefore consider context-bounded verification, which restricts the behavior of each single process. For several variants of context bounds, we show that parameterized verification over pipelines, rings, and ranked trees is decidable. More precisely, it is PSPACE-complete for pipelines and rings, and EXPTIME-complete for ranked trees. Our approach is automata-theoretic. We build a finite (tree, respectively) automaton that identifies those topologies that allow for an accepting run of the given PCA. The verification problem then reduces to checking nonemptiness of that automaton.

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