Subspace and Coordinate Transformation for Boolean Control Networks using Binary Logic

Based on binary logic, this study presents a new framework to analyze the dynamics of Boolean control networks (BCNs) and investigates the basic problem of state-space approach without using the semi-tensor product (STP). The logical form of BCNs is transformed into a discrete-time bilinear system by resorting to Khatri-Rao product and Boolean minterms. This certainly reduces the computational efforts compared to the STP based method. Subspace and regular subspace of a Boolean state-space are defined for BCNs. Necessary and sufficient conditions for the existence of a regular subspace are presented. Further, a general procedure is given to obtain the logical coordinate transformation. On the same lines, output-friendly subspace is also defined. At last, suitable examples are given to illustrate the validity and benefits of the presented results, and application outlook of this framework.