Abstract
In rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in
for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to
and
, respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is
-complete for leaderless protocols,
-complete for symmetric protocols with a leader, and in
for leaderless symmetric protocols, thereby solving all the problems left open in [17].
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787367 (PaVeS).
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Balasubramanian, A.R., Esparza, J., Raskin, M. (2021). Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy. In: Kiefer, S., Tasson, C. (eds) Foundations of Software Science and Computation Structures. FOSSACS 2021. Lecture Notes in Computer Science(), vol 12650. Springer, Cham. https://doi.org/10.1007/978-3-030-71995-1_3
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