A note on observability of Boolean control networks

The observability of Boolean control networks is investigated. The pairs of states are classified into three classes: (i)diagonal, (ii) h-distinguishable, and h-indistinguishable. For h-indistinguishable pairs, we construct a matrix W called the transferable matrix, which indicates the control-transferability among h-indistinguishable pairs. Modifying W yields a matrix U⁰, which is used as the initial matrix for an iterative algorithm. After finite iterations a stable U^k∗ is reached, which is called the observability matrix. It is proved that a Boolean control network is observable, if and only if, the last column for all rows of U^k∗ are one. Some numerical examples are presented.