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Efficient Observability Verification for Large-Scale Boolean Control Networks

It is known that verifying observability of Boolean control networks (BCNs) is NP-hard in the number of nodes. In this paper, we use a node aggregation approach to overcome the computational complexity in verifying observability for networks with special structures. First, we define a class of network node aggregations with compatible observability. It is proven for this class of aggregations, the whole BCN being observable does not imply that all corresponding subnetworks are observable, and vice versa. Second, when the aggregations are acyclic, we prove that all corresponding subnetworks being observable implies that the overall BCN is observable, although the converse is not true. Third, we show that finding acyclic aggregations with small subnetworks can tremendously reduce the computational complexity in verifying observability. Finally, we use a BCN T-cell receptor kinetics model from the literature with 37 state nodes and 3 input nodes to illustrate the efficiency of these results. For this model, we derive the unique minimal set of 16 state nodes needed to be observed to make the overall BCN observable.