Coupled similarity is an equivalence on (labeled) transition systems; its distinguishing power lies between (weak) bisimilarity and (may) testing equivalence. Its main feature, compared to weak bisimilarity, is an additional $$\tau $$ τ -law that abstracts from the atomicity of internal choices among several possible branches, thus allowing for gradual commitments. The need for this $$\tau $$ τ -law in applications was motivated by van Glabbeek and Vaandrager in 1988. Parrow and Sjödin coined the term coupled simulation in 1992 as a coinductive proof technique for the comparison of distributed (not “just” concurrent) systems, heavily exploiting gradual commitments. Over the years, coupled similarity also gained significance for the definition and analysis of the correctness of encodings, of action refinement and contraction, and of branching-time semantics for various process calculi. In this paper, we compare variants and formalizations of coupled similarity and highlight its relevance.

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夫妻相似：前32年

耦合相似性是（标记的）转换系统的等价；它的区分能力在于（弱）双相似性和（可能）测试等效性。与弱双相似性相比，它的主要特征是一个额外的 $$\tau $$ τ 律，它从几个可能的分支之间的内部选择的原子性中抽象出来，从而允许逐步承诺。1988 年 van Glabbeek 和 Vaandrager 在应用中需要这种 $$\tau $$ τ 定律。Parrow 和 Sjödin 在 1992 年创造了耦合模拟这个术语，作为一种用于比较分布式（而不是“仅”并发）系统，大量利用逐步承诺。多年来，耦合相似性对于编码正确性、动作细化和收缩的定义和分析也具有重要意义，以及各种进程演算的分支时间语义。在本文中，我们比较了耦合相似性的变体和形式化，并强调了其相关性。