Petri Nets with Localities and Testing

Kleijn, J; Koutny, M

doi:10.1007/978-3-642-13675-7

Petri Nets with Localities and Testing

Lookup NU author(s): Professor Maciej Koutny ORCiD

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Abstract

In this paper, we discuss how to enhance the modelling power of Place/Transition-nets using the notions of `locality' of individual transitions and token `testing' using inhibitor and activator arcs (or, more generally, range arcs). As a motivation for such an extension we consider membrane systems -- a computational model inspired by the way living cells are divided by membranes into compartments where chemical reactions may take place. We explain how key features of membrane systems canbe 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 outlinehow their causal processes can be defined. Both localities and range arcs render problems, such as boundedness, undecidable in the general case. We therefore discuss conditions under which one can still decide whether a net is bounded.