Necessary and sufficient condition for observability of Boolean control networks

Using semi-tensor product of matrices, Boolean control network is expressed as a discrete-time linear system. Under this framework, a systematic method of controllability and observability of Boolean control networks (BCN) has been developed by professor Cheng in literature, and the controllability is a necessary condition for testing the observability of BCN. In this paper, using controllability of BCN avoiding states set, we give a new necessary and sufficient condition for testing the observability of BCN, which is a generalization of the known result obtained in literature.