  For a given labelled transition system (LTS), synthesis is the task to find
an unlabelled Petri net with an isomorphic reachability graph. Even when just
demanding an embedding into a reachability graph instead of an isomorphism, a
solution is not guaranteed. In such a case, label splitting is an option, i.e.
relabelling edges of the LTS such that differently labelled edges remain
different. With an appropriate label splitting, we can always obtain a solution
for the synthesis or embedding problem. Using the label splitting, we can
construct a labelled Petri net with the intended bahaviour (e.g. embedding the
given LTS in its reachability graph). As the labelled Petri net can have a
large number of transitions, an optimisation may be desired, limiting the
number of labels produced by the label splitting. We show that such a
limitation will turn the problem from being solvable in polynomial time into an
NP-complete problem.
