Petri Nets with Localities and Testing

In this survey paper, we discuss how to enhance the modelling power of Place/Transition-nets with the notions of ‘locality’ of individual transitions and token ‘testing’ using inhibitor and activator arcs (or, more generally, range arcs). As motivation for these extensions we consider membrane systems – a computational model inspired by the way chemical reactions take place in cells that are divided by membranes into compartments. We explain how key features of membrane systems can be in a natural way captured by transitions with localities (to model compartments) and range arcs (to model inhibitors and promoters). For the resulting model of PTRL-nets, we discuss the synchrony and asynchrony in their behaviours and outline how their causal processes can be defined. Both localities and range arcs render problems, such as boundedness, undecidable in the general case. We therefore present conditions under which one can still decide whether a net is bounded.