A Necessary and Sufficient Graphic Condition for the Original Disturbance Decoupling of Boolean Networks

For a Boolean network with disturbances and outputs, a necessary and sufficient graphic condition for the original disturbance decoupling is proposed, and it reveals that the outputs are unaffected by the disturbances if and only if the vertex-colored state transition graph has a concolorous perfect vertex partition (CP-VP). In addition, if the CP-VP is an equal partition, a corresponding system decomposition is implemented. Furthermore, an algorithm is designed to check the existence of a CP-VP.