Verification of C-detectability using Petri nets

Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and the subsequent states. In this paper, we extend detectability to C-detectability that only requires that a given set of crucial states can be distinguished from other states. We define four types of C-detectability in the framework of labeled Petri nets: strong C-detectability, weak C-detectability, periodically strong C-detectability, and periodically weak C-detectability. Moreover, we propose efficient approaches to verify such properties in the case of bounded labeled Petri net systems. The proposed approaches use the notion of basis marking and thus do not require an exhaustive enumeration of the reachability space.