Observability of Boolean control networks

We show some new results on the observability of Boolean control networks (BCNs). First, to study the observability, we combine two BCNs with the same transition matrix into a new BCN. Then, we propose the concept of a reachable set that results in a given set of initial states, and we derive four additional necessary and sufficient conditions for the observability of BCNs. In addition, we present an algorithm and construct an observability graph to determine the observability of BCNs. Finally, we illustrate the obtained results using three numerical examples.