Barbed semantics for open reactive systems

Reactive systems (RSs) represent a meta-framework aimed at deriving labelled transition systems from unlabelled ones such that the induced bisimilarity is a congruence. Such a property is desirable, since it allows one to replace a subsystem with an equivalent one without changing the behaviour of the overall system. One of the main drawback of RSs is the restriction to the analysis of ground (i.e., completely specified) systems. Only recently the theory was extended to consider open systems (and rules) and an associated strong bisimulation equivalence. However, the resulting bisimilarity adopted for the formalism turns out to be a congruence only under very restrictive conditions, hindering the applicability of the framework. In this paper we suggest to consider (strong and weak) barbed equivalence as an alternative for open RSs. After proving that it is always a congruence, we instantiate our proposal by addressing the semantics of Asynchronous CCS and of Mobile Ambients.