We give two different notions of deadlock for systems based on active objects and futures. One is based on blocked objects and conforms with the classical definition of deadlock by Coffman, Jr. et al. The other one is an extended notion of deadlock based on blocked processes which is more general than the classical one. We introduce a technique to prove deadlock freedom of systems of active objects. To check deadlock freedom an abstract version of the program is translated into Petri nets. Extended deadlocks, and then also classical deadlock, can be detected via checking reachability of a distinct marking. Absence of deadlocks in the Petri net constitutes deadlock freedom of the concrete system.

In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well.