本論文提出一個在個體無差異 (uniform) 之單向 (Unidirectional) 質數環 (Primal Ring) 上代號指定 (Identity Assignment) 之自我穩定演算法 (Self-stabilizing Algorithm)。
代號指定在分散式系統 (Distributed System) 是很基本的問題，它可使系統上的行程 (processors) 建立完全的順序關係 (total order)。

此篇所提的演算法只用了6n的空間，在複雜度 (Complexity) 上用了 O(n**4) 決定論的時間和常數的期望時間。

Dijkstra在1974年提出了「自我穩定」 (Self-stabilization) 一詞。所謂「自我穩定」即，不論起初的狀態 (Initial Configuration) 為何，它可以在有限步驟使系統達到合法狀態 (Legitimate Configuration)，如無短暫的錯誤 (Transient Fault)，則系統一直在合法狀態。

代號指定 (Identity Assignment) 的問題，為使系統的行程 (Processors) 都有一個唯一的代號，此篇論文用自我穩定的方法作代號指定，這裡的系統為個體無差異 (Uniform) 之單向(Unidirectional) 質數環(Primal ring)，即每個行程執行相同的演算法且只能看左側行程的狀態 (State)。

此篇演算法 (Algorithm) 為法則 (Rule) 的集合。每個法則有兩部份 :條件部份 (Condition Part) 動作部份 (Action Part)。條件部份為自己和左側鄰居的狀態的布林函數(Boolean Function)，如行程的條件部份為真則此有特權 (Privilege)。此演算法作用在同步模式下 (Synchronous Execution model)，首先每個行程檢查條件部份，然後每個有特權的行程執行動作部份。

This paper proposes a silent self-stabilization identity assignment algorithm for uniform unidirectional rings of primal size. The algorithm works on synchronous execution model. Each processor has a unique identity when the ring stabilizes. The algorithm maintains 6n states in each processor, where n is the size of the ring. The number of steps that the system takes to stabilize is O(D+E), where D is a deterministic time whose value equals O(n**4 ) and E is an expected time whose value equals O(1).

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