Preliminary Proceedings of the Workshop on Geometry and Topology in Concurrency Theory GETCO ’ 03 Marseille , France , September 6 , 2003

In this paper, we reason that simulation and bisimulation are not adequate in the context of hybrid systems as they are only capable of comparing states that are reachable in a finite number of transitions. To solve this problem we extend labelled transition systems with a topology on the state space. We define topological versions of simulation and bisimulation that are also capable of comparing accumulation states of infinite sequences of transitions. We show that for transition systems with an indiscrete topology, topological (bi-)simulation and standard (bi-)simulation coincide. A similar result is obtained for finite transition systems with a discrete topology.