Robust Weak Detectability Analysis of Boolean Networks Subject to Function Perturbation

As a class of state estimation issues, detectability is widely used in fault diagnosis, circuit design, and disease status detection. This brief analyzes the robust weak detectability of Boolean networks (BNs) under function perturbation. A simplified parallel system is constructed for BNs. Based on the transition of state pairs in the simplified parallel system, a new criterion is proposed for the weak detectability of BNs. Using the reachability from perturbed state pairs to attractors in indistinguishable pairs, the robust weak detectability of BNs subject to function perturbation is analyzed. A practical example of p53-MDM2 negative feedback regulatory loop is used to illustrate the obtained criteria.