1974年，Dijkstra [D74] 提出“自我穩定”這個名詞。一個自我穩定系統，不需要任何初值化（Initialization）的動作；系統本身可以保證在有限時間內自動偵測錯誤並修復，使系統回到合理的穩定狀態（Legitimate states）下運行。
交互器（Alternator）由M.G. Gouda 以及 F. Haddix [GH99b] 提出，它能夠解決許多同步的問題。交互器是由一群行程（Processes）所組成的網路，並滿足以下三個需求： (1) 兩個相鄰的行程，在同一時間一定不會同時在臨界區間（Critical section）內。(2) 經過無限的步驟（Steps），每個行程能夠進入臨界區間的次數也是無限多次。(3) 該交互器為一自我穩定的系統。在 [GH99b]中所提出的交互器，只能運行在非個體無差異（Non-uniform）的網路下，它也可能不是最佳化交互器（Optimal alternator）。

本論文主要提出一個通用的方法（General approach），用來實做出交互器。本論文利用這個方法，針對hypercube以及mesh，設計出最佳化交互器。同時，這個方法亦可以套用在一般性、個體無差異（Uniform）的網路上。本論文所提出來的自我穩定演算法，執行在同步模式下（Synchronous model）。

In 1974, Dijkstra [D74] introduced the term “self-stabilization” to distinguish any system that has the following property: if the system starts at any, possibly illegitimate state, it is guaranteed to converge to a legitimate state in a finite time.
Alternator was proposed by M.G. Gouda and F. Haddix [GH99b] and can be used in realizing many of synchronization problems. An alternator is a network of processes that satisfy the following three conditions. (1) If one process is in critical section, no neighbor of the process will be in critical section at the same time. (2) Along any infinite time, each process enters critical section infinitely often. (3) The alternator is self-stabilizing to the above conditions. The alternator in [GH99b] works under non-uniform networks and may not be an optimal alternator.

In this thesis, we will propose a general approach to implementing alternators. By using this approach, we designed optimal alternators for hypercube and mesh. The concept of the approach can also be applied in general, uniform networks for optimal alternators. Protocols in this thesis works under synchronous model.

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