Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several divergence-sensitive refinements of branching and weak probabilistic bisimilarities have been proposed in the literature. Both the definitions of these equivalences and the techniques to investigate them differ significantly. This paper presents a comprehensive comparative study on divergence-sensitive behavioral equivalence relations that refine the branching and weak probabilistic bisimilarities. Additionally, these equivalence relations are shown to have efficient checking algorithms. The techniques of this paper might be of independent interest in a more general setting.

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