中文摘要：

带发散性说明的分支互模拟是van Glabbeek和Weijland提出的一个概念,并被用来定义等价关系≈b△.该等价关系应该是最弱的一个发散性保持的并且满足分支互模拟性质的等价关系.然而在概念提出时并没有提供这些重要性质的证明,并且我们认为在原定义的基础上这个证明是不显然的.本文通过co-induction的手段利用染色迹的概念定义了着色完全迹等价,并证明该等价关系是最弱的一个保持发散的并且满足分支互模拟性质的等价关系.然后我们证明了着色完全迹等价关系和≈b△是相同的,因而补充了van Glabbeek和Weijland的工作,即证明了≈b△是最弱的一个保持发散的并且是满足分支互模拟性质的等价关系.

英文摘要：

The notion of branching bisimulation with explicit divergence was introduced by van Glabbeek and Weijland. It is used to define an equivalence relation ≈b△, which means to be the weakest equivalence with the property of branching bisimulation and divergence preservation. However, in that paper it only claims that ≈b△ is an equivalence with such properties without proofs, and as it turns out that the proving is not obvious. In this paper we introduce an equivalence relation called coloured complete trace equivalence, and prove that it is the weakest equivalence which has the property of branching bisimulation equivalence and is also divergence preserving. We then prove that the coloured complete trace equivalence coincides with ≈b△, thus supplementing the work of van Glabbeek and Weijland.