Kalman decomposition for Boolean control networks

The Kalman decomposition problem for Boolean control networks (BCNs) is solved completely. A necessary and sufficient condition, described by vertex partitions of digraphs, is proposed for the Kalman decomposition. And, an algorithm is designed to compute the logical coordinate transformation that results in the Kalman decomposition. Finally, two examples are presented. One example illustrates the procedure of realizing the Kalman decomposition. The other one reveals that not all the BCNs can be transformed into the Kalman decomposition form. This is an essential property different from that of the traditional linear control systems.