Petri Net Reachability Graphs: Decidability Status of First Order   Properties
  We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques. 
Philippe Darondeau (INRIA Rennes Bretagne Atlantique), Stephane Demri   (LSV, ENS Cachan, CNRS, INRIA), Roland Meyer (Univer...
cs.LO