Ambient Petri Nets

Both the Ambient Calculus by L. Cardelli and the Elementary Object Systems by R. Valk model the behaviour of mobile systems. The Ambient Calculus is based on the concept of ambient, which is an environment with a given name that is delimited by a boundary, where some internal processes are executed. The main property of these ambients is that they can be moved to a new location thus modeling mobility. Elementary Object Systems are two-level net systems composed of a system net and one or more object nets, which can be seen as high-level token objects of the system net modeling the execution of mobile processes. This paper intends to contribute to the relationship between both frameworks by defining a multilevel extension of Elementary Object Systems, which will be used to provide a denotational semantics of a new process algebra called APBC (Ambient Petri Box Calculus). Such process algebra is an extension of the Petri Box Calculus that includes both ambients and their mobility capabilities, which conversely can be also interpreted as an extension of the Ambient Calculus with the main operations from the PBC.