Matrix expression of Owen values

Zhu, Sanmei; Feng, Jun‐e; Sun, Liying

doi:10.1002/asjc.2738

Cited by 2 publications

(1 citation statement)

References 32 publications

(44 reference statements)

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“…Besides, based on the Boolean function of gate networks, an algebraic representation, that is, a linear form of the product of a matrix and a vector, was proposed through the technology of semi-tensor product of matrices, which was an original theory first proposed by Cheng and Qi in 2009 [22]. Thereafter, extensive superior work has been done on the applications of logic systems based on their algebraic representations, such as state estimation [23,24], detectability, and observability [25][26][27] as well as control of Boolean networks [28][29][30][31][32], synchronization of Boolean networks [33,34], games [35][36][37], fault detection of digital circuits [38][39][40], and transformation of two feedback shift registers [41].…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Shen

Moschoyiannis

et al. 2023

Asian Journal of Control

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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.

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