Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

TLDR: A new matrix product, called semi-tensor product of matrices, is used, which can covert the Boolean networks into discrete-time linear dynamic systems and the controllability of Boolean control networks is considered in the paper as an application.

Abstract: A Boolean network is a logical dynamic system, which has been used to describe cellular networks. Using a new matrix product, called semi-tensor product of matrices, a logical function can be expressed as an algebraic function. This expression can covert the Boolean networks into discrete-time linear dynamic systems. Similarly, the Boolean control networks can also be converted into discrete time bilinear dynamic systems. Under these forms the standard matrix analysis can be used to consider the structure and the control problems of Boolean (control) networks. After the detailed description of this new approach, the controllability of Boolean control networks is considered in the paper as an application.