Falk Bartels, Ana Sokolova, Erik de Vink
A hierarchy of probabilistic system types

We study various notions of probabilistic bisimulation from a
coalgebraic point of view, accumulating in a hierarchy of
probabilistic system types. In general, a natural transformation
between two SetCat-functors straightforwardly gives rise to a
transformation of coalgebras for the respective functors. This
latter transformation preserves homomorphisms and thus
bisimulations. For comparison of probabilistic system types we
also need reflection of bisimulation. We build the hierarchy of
probabilistic systems by exploiting the new result that the
transformation also reflects bisimulation in case the natural
transformation is componentwise injective and the first functor
preserves weak pullbacks. Additionally, we illustrate the
correspondence of concrete and coalgebraic bisimulation in the
case of general Segala-type systems.