Open Petri Nets: Non-deterministic Processes and Compositionality

We introduce ranked open nets, a reactive extension of Petri nets which generalises a basic open net model introduced in a previous work by allowing for a refined notion of interface. The interface towards the external environment of a ranked open net is given by a subset of places designated as open and used for composition. Additionally, a bound on the number of connections which are allowed on an open place can be specified. We show that the non-deterministic process semantics is compositional with respect to the composition operation over ranked open nets, a result which did not hold for basic open nets.