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<p><b>Abstract</b>—This paper proposes a self-stabilizing asynchronous phase synchronization protocol for uniform unidirectional rings. Consider applications with phase bound K, i.e., the phases are phase 0, phase 1, <tmath>\ldots</tmath>, phase K-1, phase 0, phase 1, etc. Under the protocol, when the ring is stabilized, it satisfies the following criterion: No node begins to execute phase <tmath>(k+1)</tmath><it>mod</it> K until all nodes have executed phase <it>k</it>, and after all nodes have executed their phase <it>k</it>, each node eventually executes phase <tmath>(k+1)</tmath><it>mod</it> K. Besides the variable used to denote the phase that a node is working on, each node maintains only one auxiliary variable with <it>b</it> states, where <it>b</it> can be any number greater than or equal to the ring size. Provided that K and <it>b</it> satisfy the limitation: <tmath>{\rm{K}}\times b>n(b-1)</tmath>, the proposed protocol is correct under the parallel model and takes at most <tmath>2({\rm{K}}\times b)</tmath> rounds to stabilize.</p>
Phase synchronization, self-stabilization, transient fault, uniform ring.

T. Liu, S. Hung and S. Huang, "Asynchronous Phase Synchronization in Uniform Unidirectional Rings," in IEEE Transactions on Parallel & Distributed Systems, vol. 15, no. , pp. 378-384, 2004.
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