本篇論文中，我們提出了一個演算法來解決在雙向一致任意大小的環上去同步化相位時鐘的問題。此演算法擁有自我穩定的能力。也就是說，無論在什麼樣的開始設定下，所有處理器的時鐘最終將會有相同的值。 與以往的隨機演算法的方式解決此一問題不同之處在於，以往的演算法從頭到尾都是倚靠隨機選取的方式，來決定下一時間相位時鐘的值的變化；而我們僅用隨機選取的方式來打破對稱的情況，扣除打破對稱情況的動作外，此系統將非隨機地運作。我們用了72個額外的狀態(排除時鐘變數在外)且最差情況下達到穩定所需的時間為O(n^3)。 In this thesis, we propose an algorithm to solve the problem of synchronizing phase clock on bidirectional uniform rings of any size. The algorithm has the self-stabilizing ability. That is, no matter under what initial configuration, clocks on every processors will have the same value eventually. The difference with previous randomized algorithms is that previous ones are totally randomized to decide the value of phase clock of the next step. We just use randomization to break symmetry. Except symmetry breaking, the system works deterministically. We use 72 additional states(exclude the clock variable) and the stabilizing time in the worst case is O(n^3).
