  Detectability describes the property of a system to uniquely determine, after
a finite number of observations, the current and subsequent states. In this
paper, to reduce the complexity of checking the detectability properties in the
framework of bounded labeled Petri nets, we use a new tool, which is called
detector, to verifying the strong detectability and periodically strong
detectability. First, an approach, which is based on the reachable graph and
its detector, is proposed. Then, we develop a novel approach which is based on
the analysis of the detector of the basis reachability graph. Without computing
the whole reachability space, and without building the observer, the proposed
approaches are more efficient.
