Probabilistic transition systems (PTSs) extend classic labeled transition systems via a mechanism to represent probability. In the literature, they have been used as semantic models of probabilistic processes. Labeled Markov processes (LMPs) represent a subset of PTSs that study interacting Markov processes. This paper is focused on the probabilistic bisimulation between LMPs—that is, on a method that relates as equivalent two LMPs if and only if their probabilistic transition schemes have the same probabilistic branching structure.

The paper introduces a novel kind of probabilistic bisimulation between LMPs: event bisimulation (EB). EB is proven to be a generalization of probabilistic bisimulation. Actually, it applies to systems that have a measurable state space, while probabilistic bisimulation works only on analytic spaces.

I enjoyed the paper. It gives a clear snapshot of the related literature, and, in doing so, describes the basic notions one needs to understand to complete the paper. A logical characterization of EB is given by a set of theorems that are explained with examples. Although this is a dense paper, it is easy to read.