Markov automata (MA) and weak bisimulation have been proposed by Eisentraut,
Hermanns and Zhang in [10]. In this paper we propose early and late semantics of
Markovian automata, and then introduce early and late weak bisimulations correspondingly.
We show that early weak bisimulation coincides with the weak bisimulation in [10], and late
weak bisimulation is strictly coarser. Further, we extend our results to simulations.

Weak bisimilarity is a distribution-based equivalence notion for Markov automata. It has
gained some popularity as the coarsest reasonable behavioural equivalence on Markov
automata. This paper studies a strictly coarser notion: Late weak bisimilarity enjoys valuable
properties if restricting to important subclasses of schedulers: Trace distribution equivalence
is implied for partial information schedulers, and compositionality is preserved by distributed
schedulers. The intersection of the two scheduler classes thus spans a coarser and still …