# IFDA: Intermittent Fault Diagnosis Algorithm for Augmented Cubes Under the PMC Model
## 1 Introduction  
As the underlying topology of complex networks [1] and social networks [2], interconnection networks are becoming increasingly important. A significant number of multiprocessor systems adopt interconnection networks as their underlying topological framework. In this context, graphs are commonly adopted to model processors and their interconnections within multiprocessor systems. As the scale of processors in a system expands, the probability of node failures experiences a marked increase. The occurrence of faulty processors constitutes a substantial hazard to the system's stability and the integrity of data. Consequently, it is essential for the system to be equipped with relevant algorithms capable of discriminating between faulty and fault-free processors. The procedure of making such a distinction is referred to as fault diagnosis. For the purpose of maintaining system stability, the fault diagnosis emerges as a particularly important research area. At present, fault diagnosis methods mainly include system-level diagnosis and nonsystem-level diagnosis. Nonsystem-level diagnosis mainly uses hardware test diagnosis; its disadvantage is low efficiency, and the test resource requirements are large and prone to errors, especially for large-scale network systems. System-level diagnosis employs the inherent processors of the network for self-diagnostic purposes. This diagnostic strategy offers several merits, including non-intrusiveness to the system's operational state, highefficiency, and a low error rate, which has led to its widespread application. Within the domain of system-level diagnosis, a diverse array of diagnosis models have been presented to explore the diagnosability characteristics of multiprocessor systems. The PMC model, formulated by [PERSON] et al. [3], is based on the concept of reciprocal testing between adjacent processors. In contrast, the MM model, proposed by [PERSON] and [PERSON] [4] and also known as the comparison model, assumes that each processor must undergo comparison with all of its adjacent processors. A considerable volume of research has been conducted utilizing both the PMC model and the MM model as foundational frameworks [5; 6]. Faults in multiprocessor systems can be classified into two categories: permanent faults and intermittent faults. Permanent fault nodes remain in a faulty state indefinitely within the system, while intermittent fault nodes alternate between faulty and fault-free states, ultimately progressing to a permanent fault over time. Given that the fault states exhibited by intermittent fault nodes are inherently difficult to observe, this fault type has not been given enough emphasis in previous research. Accordingly, this investigation explores intermittent fault diagnosis by employing a system-level model. A system is classified as \(n\)-\(t_{p}\)-diagnosable if all faulty nodes are permanent faults and can be accurately identified without replacement, under the condition that the number of faulty nodes does not exceed \(n\). In circumstances where the number of intermittently faulty nodes is no greater than \(t_{i}\), a system is considered \(t_{i}\)-fault diagnosable if a fault-free node is never incorrectly diagnosed as faulty in any syndrome. [PERSON] et al. [7] introduced conditional diagnosability, which stipulates that each processor must possess at least one fault-free neighbor. [PERSON] et al. [8] proposed the concept of good-neighbor fault diagnosability. Within the context of the PMC model and the MM model, researchers have extensively studied the good-neighbor fault diagnosability of a multitude of well-established networks [9; 10]. Currently, for these multiprocessor systems, research on permanent fault diagnosis has achieved a relatively high level of maturity. However, as evidenced by Table 1, there is a dearth of research on intermittent fault diagnosis. [PERSON] et al. proposed a method for determining the intermittent fault diagnosability of any given system [11]. [PERSON] and [PERSON] et al.