所謂的自我穩定，是1974年由Dijkstra[D74]所提出，一個自我穩定的系統，不需要任何初始化的動作(Initialization)，也不管其起始的狀態為何，系統本身可以保證在有限時間內自動偵測錯誤並修復，使系統回到合理一穩定狀態(Legitimate states)。
交互執行器，是由M. G. Gouda 以及 F. Haddix [GH99b] 提出，它能夠解決許多同步上的問題。交互執行器是由一堆程緒所組成的網路，並滿足以下三個條件：(1)如果一個程序進入臨界區間內，其相鄰之程序絕對不會同時進入臨界區間。(2)經過無限多的步驟後，每個程序能進入臨界區間的次數也是無限多次。(3)該交互執行器為一自我穩定系統，在一定時間內，會自動滿足以上的條件。在[GH99b]中所提出的交互執行器，只能運行在非個體無差異的網路下，它也不會在任何網路下都是一個最佳交互執行器。

由於[GH99b]的交互執行器在某些特殊的網路之下，其效率不彰，我們便針對了這一點，對特殊的網路設計特別的交互執行器。我們提出了一個方法，使得該方法在環上有著良好的執行效率，在奇數環上更是最佳化的交互執行器。這一個方法可以使用在一般性、個體無差異的環上。其執行模式為同步模式(Synchronous model)。

An alternator is a network of concurrent processes, which satisfies the following conditions. (1) If one process executes the critical step, no neighbor of the process executes the critical step at the same time. (2) Along any infinite time, each process executes the critical step infinitely often. (3) The alternator is self-stabilizing to the above conditions.
In this paper, we proposed a design of alternators for rings. The protocol is optimal in the sense that each node can execute the critical step at least once every three steps when it works on rings of odd size.

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