Probabilistic bisimilarity as testing equivalence

Larsen and Skou initiated the study of probabilistic bisimilarity and its characterisation in terms of tests. Later on, van Breugel et al. showed that, for labelled Markov processes with continuous state spaces, probabilistic bisimilarity nicely coincides with a simple notion of testing equivalence. Their proof employs advanced machinery from topology. In the discrete case of finite-state reactive probabilistic processes, we prove that coincidence result with an elementary and more accessible proof.