Extensional equivalences for transition systems

Various notions of systems equivalence based on the reactions of systems to stimuli from the outside world are presented and compared. These notions have been proposed in the literature to allow abstraction from unwanted details in models of concurrent and communicating systems. The equivalences, already defined for different theories of concurrency, will be compared by adapting their definitions to labelled transition systems, a model which underlies many others. In the presentation of each equivalence, the aspects of system behaviours which are ignored and the identifications which are forced will be stressed. It will be shown that many equivalences, although defined very differently by following different intuitions about systems behaviour, turn out to be the same or to differ only in minor detail for a large class of transition systems.