Self-stabilizing symmetry breaking in constant-space (extended abstract)

Alain Mayer, Yoram Ofek, Rafail Ostrovsky, Moti Yung
1992 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92  
We i n v estigate the problem of self-stabilizing round-robin token management s c heme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic coin-ipping nite state machine which sends and receives messages. We show that the solution to this problem is equivalent to symmetry breaking i.e., leader election. Requiring only constant-size messages and message-passing model has practical implications: our solution can be implemented in
more » ... speed networks using a universal fast hardware switches i.e., nite state machines of size independent of the size of the network. Our automata-based message-passing model has inherent deadlock possibility i.e., when all processors are waiting for a message which w e assume is detected by an external timeout mechanism. Provided that there is no deadlock to begin with, we show h o w starting from an arbitrary con guration, the system never enters a deadlock state and further stabilizes in polynomial time. We note that Dijkstra showed that the last problem does not have a deterministic solution even when the identical processors possess an arbitrary power: starting from a ring with a multitude of tokens, any deterministic system will either not stabilize or will enter a deadlock state.
doi:10.1145/129712.129777 dblp:conf/stoc/MayerOOY92 fatcat:2prmlah2fjaq3j6xh4h4n73uoi