Finite-time observability of probabilistic Boolean control networks

In this paper, the finite-time observability (FO) of probabilistic Boolean control networks (PBCNs) based on set reachability and parallel extension is investigated. Under algebraic state space representation of PBCNs, finite-time set reachability (FSR), finite-time single input sequence set reachability (FSSSR), finite-time arbitrary input sequence set reachability (FASSR), as well as finite-time output feedback set reachability (FOSR) are addressed, where some efficient criteria are proposed. In the second part of this paper, several types of FO are provided, which can be converted to the corresponding FSR based on the parallel extension technique. Consequently, the obtained results for FSR are utilized to deal with FO. Finally, two examples including a biological network are given to demonstrate the theoretical results.