Abstract
AbstractIn 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
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for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to
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and
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, respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is
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-complete for leaderless protocols,
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-complete for symmetric protocols with a leader, and in
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for leaderless symmetric protocols, thereby solving all the problems left open in [17].
Publisher
Springer International Publishing
Cited by
2 articles.
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