This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation that relates LMCs that can be made (exactly) probabilistically bisimilar by small perturbations of their transition probabilities. We explore how the notions interrelate and establish their connections to other well-known notions like $\varepsilon$-bisimulation.

翻译：本文研究带标签马尔可夫链（LMCs）上各类近似概率互模拟概念。我们提出了弱互模拟与分支互模拟的近似版本，并引入一种ε-扰动互模拟概念，用于描述可通过微小扰动转移概率而成为（精确）概率互模拟的LMCs。我们探讨了这些概念之间的内在联系，并建立了它们与ε-互模拟等其他经典概念的关联。