Towards Synthesis of Petri Nets from Scenarios

Given a set of scenarios, we answer the question whether this set equals the set of all executions of a Petri net. Formally, scenarios are expressed by (isomorphism classes of) labelled partial orders (LPOs), also known as pomsets or partial words. An LPO is an execution of a Petri net if it is a sequentialization of an LPO generated by a process of the net. We propose a definition of regions for a set of LPOs, i.e for a partial language. Given a partial language of scenarios, we prove a necessary and sufficient condition (based on regions) for the partial language of scenarios to be the partial language of executions of a place/transition Petri net. Finally, we prove our notion of regions to be consistent with the notion of regions of trace languages.