Synthesis Problem for Petri Nets with Localities

There is a growing need to introduce and develop computational models capable of faithfully modelling systems whose behaviour combines synchrony with asynchrony in a variety of complicated ways. Examples of such real-life systems can be found from VLSI hardware to systems of cells within which biochemical reactions happen in synchronised pulses. One way of capturing the resulting intricate behaviours is to use Petri nets with localities partitioning transitions into disjoint groups within which execution is synchronous and maximally concurrent. In this paper, we generalise this type of nets by allowing each transition to belong to several localities. Moreover, we define this extension in a generic way for all classes of nets defined by net-types.The semantics of nets with overlapping localities can be defined in different ways, and we here discuss four fundamental interpretations, each of which turns out to be an instance of the general model of nets with policies. Thanks to this fact, it is possible to automatically synthesise nets with localities from behavioural specifications given in terms of finite transition systems. We end the paper outlining some initial ideas concerning net synthesis when the association of transitions to localities is not given and has to be determined by the synthesis algorithm.