Falk Bartels, Ana Sokolova, Erik de Vink:
A hierarchy of probabilistic system types, CMCS03

Abstract
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We arrange various types of probabilistic transition systems studied
in the literature in an expressiveness hierarchy. The expressiveness
criterion is the existence of an embedding of systems of the one class
into those of the other. An embedding here is a system transformation
which preserves and reflects bisimilarity. To facilitate the task, we
define the classes of systems and the corresponding notion of
bisimilarity coalgebraically and use the new technical result that an
embedding arises from a natural transformation with injective
components between the two coalgebra functors under
consideration. Moreover, we argue that coalgebraic bisimilarity,
on which we base our results, coincides with the concrete notions
proposed in the literature for the different system classes, exemplified
by a detailed proof for the case of general Segala-type systems.