Behaviour Preserving Refinement of Petri Nets

In a hierarchic design of a Petri net a host net, which is a ”rough” model, is refined by replacing a transition by a daughter net, that simulates the transition. For the independent design of host and daughter net those daughter nets are of interest that guarantee that an arbitrary host has the same behaviour as the respective refined net. We characterize these daughter nets, called modules, prove that it is decidable whether a net is a module and show how firing sequences and reachable markings of module, host and refined net are interrelated. Our results shed some light on the problem what a homomorphism of Petri nets should be and allow the generation of live Petri nets.