On the observability of free Boolean networks via the semi-tensor product method

This paper investigates the observability of free Boolean networks by using the semi-tensor product method, and presents some new results. First, the concept of observability for free Boolean networks is proposed, based on which and the algebraic form of Boolean networks, a kind of observability matrix is constructed. Second, by the observability matrix, a new necessary and sufficient condition is given for the observability of Boolean networks. Third, the concept of observability index for observable Boolean networks is defined, and an algorithm is established to calculate the observability index. Finally, a practical example of D. Melanogaster segmentation polarity gene networks is studied to support our new results. The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.