We provide a fine classification of bisimilarities between states of possibly different labelled Markov processes (LMP). We show that a bisimilarity relation proposed by Panangaden that uses direct sums coincides with "event bisimilarity" from his joint work with Danos, Desharnais, and Laviolette. We also extend Giorgio Bacci's notions of bisimilarity between two different processes to the case of nondeterministic LMP and generalize the game characterization of state bisimilarity by Clerc et al. for the latter.

翻译：我们对可能不同标注马尔可夫过程（LMP）的状态之间的双相似性提供了精细分类。我们证明，Panangaden提出的使用直和的双相似关系与其与Danos、Desharnais和Laviolette合作研究中的“事件双相似性”一致。我们还将Giorgio Bacci关于两个不同过程之间双相似性的概念推广到非确定性LMP的情形，并推广了Clerc等人针对后者提出的状态双相似性的博弈刻画。