2-state alternator for uniform rings with arbitrary size

In the paper, we propose a two-state alternator algorithm for uniform rings with n processors, where n is any positive integer. Gouda and Haddix defined the concept of the alternator. It discusses a set of concurrent processors, which satisfies the following conditions. (1) If one processor executes the critical phase, no neighbor of the processor executes the critical phase in the same computing phase. (2) Along any infinite computing phases, each processor executes the critical phase infinitely often. (3) An alternator is self-stabilizing to the above conditions. The proposed algorithm achieves the maximal performance in the sense that no additional processor can execute the critical phase without violating the first condition of the alternator. The proposed alternator algorithm has the snap property. It always satisfies condition (1) even when some transient faults occur. The proposed algorithm allows each processor to execute the critical phase every three phases in the worst case. It includes an expected number of log(n) phases and a deterministic number of O((n-2)/2) to achieve the maximal performance.