Аннотация:We prove that trace equivalence is undecidable for the very small and natural subclass of Petri nets in which no transition requires more than one token; this subclass corresponds exactly to the calculus BPP of Christensen for which bisimulation equivalence is known to be decidable. We present this result along with a survey of decidability results for various notions of equivalence with respect to various subclasses of Petri nets.