Abstract
Four semantic domains for Place/Transition Petri nets and their relationships are considered. They are monoids of respectively: firing sequences, processes, traces and dependence graphs. For each of them the analysis and synthesis problem is stated and solved. The monoid of processes is defined in a non-standard way. Nets under consideration involve weights of arrows and capacities (finite or infinite) of places. However, the analysis and synthesis tasks require nets to be pure, i.e. each of their transition must have the pre-set and post-set disjoint.