On Periodic Detectability of Probabilistic Boolean Networks

In this paper, we investigate verification of periodic detectability for probabilistic Boolean networks (PBNs) from a brand-new angle. First, the dynamics of a PBN is converted equivalently into a stochastic automaton in the framework of semi-tensor product (STP) theory. Using the previously-proposed observer-based approach in the literature, the necessary and sufficient condition is presented to verify whether a PBN is strongly (resp., weakly) periodically detectable or not. Second, to avoid graph-based symbolic manipulations, we further propose the matrix-based verification criteria that are numerically tractable for the aforementioned two types of periodic detectability. Finally, several examples modeled by the same PBN are provided to instantiate the corresponding theoretical results.