Cascading decomposition of Boolean control networks: a graph-theoretical method

Abstract

Two types of cascading decomposition problems of Boolean control networks are investigated using a graph-theoretical method. A new graphic concept called nested perfect equal vertex partition (NPEVP) is proposed. Based on NPEVP, the necessary and sufficient graphic conditions for solvability of the cascading decomposition problems are obtained. Given the proposed graphic conditions, the logical coordinate transformations are constructively obtained to realize the corresponding cascading decomposition forms. Finally, two illustrative examples are provided to validate the results.