Petri Net Synthesis from a Reachability Set

Classical Petri net synthesis is a method to generate a Petri net from a labelled transition system. In this paper, by contrast, it is assumed that a (finite) set of markings is given, and an algorithm is described which generates a Petri net of some class having exactly this set as its reachability set. A notion of T-monotonicity simplifying the problem is introduced, but it is also shown that for some non-T-monotonic classes, the synthesis may nevertheless be solved algorithmically.