System decomposition with respect to inputs for Boolean control networks

In this paper, the problem of system decomposition with respect to inputs is investigated for Boolean control networks (BCNs). First, based on the linear representation of BCNs, some algebraic equivalent conditions for the decomposability are obtained. Second, the concept of perfect equal vertex partition (PEVP) is proposed for BCNs. A necessary and sufficient graphical condition for the decomposability, i.e. the existence of a PEVP, is proposed. Third, for calculating a PEVP, an algorithm called Vertex Set Uniting Algorithm (VSUA) is designed. Finally, a biological example is analyzed to show the effectiveness of the proposed method.