On Profiles and Footprints – Relational Semantics for Petri Nets

Petri net systems have been successfully applied for modelling business processes and analysing their behavioural properties. In this domain, analysis techniques that are grounded on behavioural relations defined between pairs of transitions emerged recently. However, different use cases motivated different definitions of behavioural relation sets. This paper focusses on two prominent examples, namely behavioural profiles and behavioural footprints. We show that both represent different ends of a spectrum of relation sets for Petri net systems, each inducing a different equivalence class. As such, we provide a generalisation of the known relation sets. We illustrate that different relation sets complement each other for general systems, but form an abstraction hierarchy for distinguished net classes. For these net classes, namely S-WF-systems and sound free-choice WF-systems, we also prove a close relation between the structure and the relational semantics. Finally, we discuss implications of our results for the field of business process modelling and analysis.