Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Self-stabilizing systems in spite of distributed control
Communications of the ACM
The Theory of Weak Stabilization
WSS '01 Proceedings of the 5th International Workshop on Self-Stabilizing Systems
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Computation in networks of passively mobile finite-state sensors
Distributed Computing - Special issue: PODC 04
Weak vs. Self vs. Probabilistic Stabilization
ICDCS '08 Proceedings of the 2008 The 28th International Conference on Distributed Computing Systems
Quasi-self-stabilization of a distributed system assuming read/write atomicity
Computers & Mathematics with Applications
Self-stabilizing leader election in networks of finite-state anonymous agents
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Stably computable properties of network graphs
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Fast computation by population protocols with a leader
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Self-stabilizing population protocols
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
On utilizing speed in networks of mobile agents
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Improving space complexity of self-stabilizing counting on mobile sensor networks
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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A self-stabilizing protocol guarantees that starting from an arbitrary initial configuration, a system eventually comes to satisfy its specification and keeps the specification forever. Although self-stabilizing protocols show excellent fault-tolerance against any transient faults (e.g. memory crash), designing self-stabilizing protocols is difficult and, what is worse, might be impossible due to the severe requirements. To circumvent the difficulty and impossibility, we introduce a novel notion of loose-stabilization, that relaxes the closure requirement of self-stabilization; starting from an arbitrary configuration, a system comes to satisfy its specification in a relatively short time, and it keeps the specification for a long time, though not forever. To show effectiveness and feasibility of this new concept, we present a probabilistic loosely-stabilizing leader election protocol in the Probabilistic Population Protocol (PPP) model of complete networks. Starting from any configuration, the protocol elects a unique leader within O(nNlogn) expected steps and keeps the unique leader for Ω(NeN) expected steps, where n is the network size (not known to the protocol) and N is a known upper bound of n. This result proves that introduction of the loose-stabilization circumvents the already-known impossibility result; the self-stabilizing leader election problem in the PPP model of complete networks cannot be solved without the knowledge of the exact network size.