Weak (approximate) detectability of labeled Petri net systems with inhibitor arcs

Weak (approximate) detectability of a labeled Petri net (LPN) system (with inhibitor arcs) is a property such that if the property is satisfied then there exists an infinite label sequence generated by the system such that all markings after a time step can determined (in a prescribed subset of reachable markings) by the label sequence. Specifically, we prove that the problems of deciding weak detectability of LPN systems with inhibitor arcs and weak approximate detectability of LPN systems are both undecidable.