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) hh-distinguishable, and (iii) hh-indistinguishable. For hh-indistinguishable pairs, we construct a matrix WW called the transferable matrix, which indicates the control-transferability among hh-indistinguishable pairs. Modifying WW yields a Boolean matrix U0U0, which is used as the initial matrix for an iterative algorithm. After finite iterations a stable U∗U∗ 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 of U∗U∗, Colr+1(U∗)=1r. Some numerical examples are presented.