# IFDA: Intermittent Fault Diagnosis Algorithm for Augmented Cubes Under the PMC Model
## 1 Introduction
provided the necessary and sufficient conditions for the diagnosability of crisp three-cycle networks under the PMC model [12]. Studies on intermittent faults currently have difficulty diagnosing some typical inter-network topologies, such as the augmented cube. The \(n\)-dimensional augmented cube \(AQ_{n}\) is a variant of the \(n\)-dimensional hypercube \(Q_{n}\) developed by [PERSON] and [PERSON] [15]. It has been documented that this structure not only preserves certain favorable properties of the hypercube but also possesses some embedded characteristics that are absent in the hypercube [16; 17]. A substantial body of research has been dedicated to investigating the topological properties and diagnosability of augmented hypercubes [18; 19]. [PERSON] et al. [20] showed that the conditional diagnosability of an \(n\)-dimensional augmented cube \(AQ_{n}\) is \(8n-27\) for \(n\geq 5\). In this paper, we evaluate the intermittent fault diagnosability of \(AQ_{n}\) under the PMC model. We show that the intermittent fault diagnosability of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Multiprocessor System** & **Degree** & **Model** & \(t_{p}\)**-Diagnosability** & \(t_{i}\)**-Diagnosability** \\ \hline Hypercube (\(Q_{n}\)) & \(n\) & PMC & \(n\) for \(n\geq 3\)[13] & \(n-1\) for \(n\geq 3\) \\ Mobius Cube (\(MQ_{n}\)) & \(n\) & PMC & \(n\) for \(n\geq 5\)[14] & unknown \\ BC Network (\(X_{n}\)) & \(n\) & PMC & \(n\) for \(n\geq 3\) & unknown \\ Folded Hypercube (\(FQ_{n}\)) & \(n+1\) & PMC & \(n+1\) for \(n\geq 5\)[14] & unknown \\ Twisted Cube (\(T_{n}\)) & \(n\) & PMC & \(n\) for \(n\geq 5\)[14] & unknown \\ Augmented Cube (\(AQ_{n}\)) & \(2n-1\) & PMC & \(2n-1\) for \(n\geq 4\) & \(2n-2\) for \(n\geq 4\) (this paper) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diagnosability studies of some multiprocessor systems. is \(2n-2\) for \(n\geq 4\). Furthermore, we propose an intermittent fault diagnosis algorithm applicable to augmented cube networks. The instability in the state of intermittent fault nodes makes them more difficult to diagnose. A component composed of intermittent faulty nodes is considered to be in a faulty state if and only if it has no 0-path to any of its adjacent nodes. According to this characteristic, [PERSON] et al. proposed an intermittent fault diagnosis algorithm based on Depth-First Search (DFS) strategy in [21]. However, many of the test result detections between neighboring nodes in this algorithm are unnecessary. In [22], [PERSON] et al. proposed a permanent fault diagnosis algorithm applicable to Hamiltonian networks under the PMC model named _HTAD_; this algorithm determines the node states based on the properties of subpaths after decomposing the Hamiltonian network into subpaths. In [23], we modified the subpath partitioning algorithm for Hamiltonian networks in the HTAD algorithm and proposed a corresponding fault diagnosis algorithm. In [24], [PERSON] et al. extended the aforementioned algorithms to the PMC model and the MM model based on path topology and proposed corresponding fault diagnosis algorithms. The augmented cube studied in this paper belongs to Hamiltonian networks, so we designed a quickly intermittent fault diagnosis algorithm by referencing this strategy, which is named \(IFDA\). The rest of this paper is structured as follows: In Section 2, we provide the terminology, lemmas, and theorems for a system-level fault diagnosis. In Section 3, we supplement the properties of the augmented cubes. In Section 4, we evaluate the intermittent fault diagnosability of \(AQ_{n}\). In Section 5, an intermittent fault diagnosis algorithm is proposed, and its performance is evaluated through simulation experiments in Section 6. Finally, we offer our conclusions.