Observability of Boolean networks via STP and graph methods

摘要

This study addresses the observability of Boolean networks (BNs), using semi-tensor product (STP) of matrices. First, unobservable states can be divided into two types, and the first type of unobservable states can be easily determined by blocking idea. Second, it is found that all states reaching to observable states are observable. Based on subgraph of transition matrix and blocking idea, the second type of unobservable states can be also determined. Approaches are obtained to directly determine some observable or unobservable states. An algorithm is designed for determining the observability of BNs as well. Examples are given to illustrate the effectiveness of the given results.