Preserving behavior in transition systems from event structure models

Two structurally different methods of associating transition system semantics to event structure models are distinguished in the literature. One of them is based on configurations (event sets), the other on residuals (model fragments). In this paper, we consider three kinds of event structures (resolvable conflict structures, extended prime structures, stable structures), translate the other models into resolvable conflict structures and back, provide the isomorphism results on the two types of transition systems, and demonstrate the preservation of some bisimulations on them.