(School of Mathematics,Shandong University,Ji'nan250100,China)
Boolean(control) network is an effective mathematical model of simulating gene regulation networks. By quantifying the interactions among genes within cells or a particular genome and related variables, the expression, replication, transcription and other activities of genes can be well reflected by a Boolean network model. Via a novel tool, semi-tensor product, a lot of excellent results on Boolean networks are obtained. In recent years, there have been frequent outbreaks of virus at home and abroad, causing great impact and loss to all aspects of the world. Virus detection technology plays a key role against virus diseases. In view of this, the paper mainly summarizes some recent achievements on observability and detectabitliy of Boolean control networks via semi-tensor product to attract more scholars' attention to such problems and methods. Firstly, the developments of observability and detectabitliy are reviewed. Then, from a theoretical point of view, the relationship among four types of observability and three types of detectability is shown by a network diagram. Moreover, some important works, including state feedback, output feedback, disturbance and so on, are introduced. Finally, following an overview of some applications of observability and detectability, future development is prospected.