Nonprimitive recursive complexity and undecidability for Petri net equivalences

The aim of this note is twofold. Firstly, it shows that the undecidability result for bisimilarity in [Theor. Comput. Sci. 148 (1995) 281-301] can be immediately extended for the whole range of equivalences land preorders) on labelled Petri nets. Secondly, it shows that restricting our attention to nets with finite reachable space, the respective (decidable) problems are nonprimitive recursive; this approach also applies to Mayr and Meyer's result [J. ACM 28 (1981) 561-576] for the reachability set equality, yielding a more direct proof. (C) 2001 Elsevier Science B.V. All rights reserved.