Identification of edge removal fault in Boolean networks and disjunctive Boolean networks

Abstract

It is meaningful to identify various faults occurring in dynamic systems as early as possible. This paper explores the identification of edge removal fault in Boolean networks (BNs). At first, with the help of semi-tensor product of matrices, the algebraic formulation is presented for the faulty BNs subject to an edge removal fault. After that, a fault-triggered matrix is constructed to uncover the relationship of algebraic formulations between non-faulty BN and faulty BN, based on which, a kind of fault identification equation is established to identify the two faulty nodes in the single edge removal fault. Furthermore, a fault identification matrix is constructed to identify the faulty nodes in the single and multiple edge removal faults of a disjunctive BN, whose dimension is much smaller than the fault-triggered matrix. Finally, the obtained results are demonstrated by the Drosophila Spz processing model.