Semi-tensor product-based algebra-logic mixed representation and fault diagnosis for a class of gate networks

This article studies an algebra-logic mixed representation of gate networks and its application to stuck-at fault diagnosis. First, the gate network is characterized through a logic expression of disjoint sum-of-products, and the system structure of the gate network is described based on 2-to-1 multiplexers. Then, by resorting to the semi-tensor product of matrices, a novel algebra-logic mixed representation is proposed for the gate network through its logic expression and system structure. Furthermore, a novel stuck-at fault diagnosis algorithm for the gate network is presented, where the stuck-at fault testability of the gate network is equivalent to the solution existence of the system of linear equations. Finally, the fault diagnosis of the 4-bit carry look-ahead adder is carried out to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms.