A collective interpretation semantics for reversing Petri nets

• Published in: Theoretical computer science 2022-07, Vol.924, p.148-170
• Main Authors: Philippou, Anna, Psara, Kyriaki
• Format: Article
• Language: English
• Subjects: Collective token interpretation; Controlling reversibility; Local reversibility; Reversing Petri nets; Sodium-potassium pump
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2022.05.016

Reversing Petri nets (RPNs) have recently been proposed as a net-based approach to model causal and out-of-causal order reversibility. They are based on the notion of individual tokens that can be connected together via bonds. In this paper we extend RPNs by allowing multiple tokens of the same type to exist within a net and we implement a notion of local reversibility for the model based on the collective token interpretation of Petri nets. The resulting framework allows us to model a form of out-of-causal-order reversibility, a type of reversibility that arises most notably in biological systems. Furthermore, it is lightweight in the sense that it requires no global control and no history needs to be preserved. Furthermore, we provide a mechanism for controlling reversibility by associating transitions with conditions, which guard their execution. We demonstrate the usefulness of the framework by modelling the functioning of the sodium-potassium pump, a system where transition execution is governed by activation conditions and featuring reversible behaviour. •Introduction of token multiplicity in RPNs.•Local reversibility semantics yielding a form of out-of-causal order reversibility.•Introduction of a mechanism for controlling reversibility based on the association of conditions to transitions.•A model of the sodium-potassium pump.