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A system is said to be critically observable if the operator can always determine whether the current state belongs to a set of critical states. Due to the communication failures, systems may suffer from intermittent loss of observations, which makes the system not critically observable. In this sense, to characterize critical observability in a quantitative way, this paper extends the notion of critical observability to stochastic discrete event systems modeled as partially observable probabilistic finite automata. Two new notions, called step-based almost critical observability and almost critical observability are proposed, which describe a measure of critical observability for a given system against intermittent loss of observations. We introduce a new language operation to obtain a probabilistic finite automaton describing the behavior of the plant system under intermittent loss of observations. Based on this structure, we also present verification methodologies to check the aforementioned two notions and analyze the complexity. Finally, the results are applied to a raw coal processing system, which shows the effectiveness of the proposed methods.

This paper addresses the fault diagnosis problem of PLC-based systems that can be modeled as Petri nets under a certain level of abstraction. The existing Petri-net-based fault diagnosis approaches often associate transitions and/or places with sensors and require that any change in sensor readings needs to be treated by a PLC, leading to a situation that the PLC would be too busy processing the changes in sensor readings to perform other tasks. This paper assumes that a PLC does not monitor the changes of readings of sensors all the time, but periodically reads the values of sensors when needed. The system output is defined as a marking sequence interleaved with possible observed transitions. A fault diagnosis algorithm is developed by defining and solving integer linear programing (ILP) problems whose size is regardless of the length of the system output. The proposed approach enjoys high computational efficiency compared with other ILP-based approaches and is more suitable for fault diagnosis of PLC-based systems with low computing power.

This paper investigated the verification of detectability for discrete event systems based on a class of partially observed unbounded Petri nets. In an unbounded net system, all transitions and partial places are assumed to be unobservable. The system administrator can only observe a few observable places, i.e., the number of tokens at these places can be observed, allowing for the estimation of current and subsequent states. The concepts of quasi-observable transitions, truly unobservable transitions, and partial markings are used to construct a basis coverability graph. According to this graph, four sufficient and necessary conditions of detectability are proposed. Correspondingly, a specific example is proposed to prove that the detectability can be verified in the unbounded net system. Furthermore, based on the conclusion of detectability, the system’s ability to detect critical states was explored by using the basis coverability graph, called C-detectability. Two real-world examples are proposed to show that the detectability of discrete event systems has not only pioneered new research methods, but also demonstrated that the real conditions faced by this method are more general, and it has overcome the limitations of relying only on the ideal conditions of bounded systems for verification.

This article explores the foundational mechanisms of the Discrete Event System Specification (DEVS) theory—closure under coupling, universality, and uniqueness—and their critical role in enabling interoperability through modular, hierarchical simulation frameworks. Closure under coupling empowers modelers to compose interconnected models, both atomic and coupled, into unified systems without departing from the DEVS formalism. We show how this modular approach supports the scalable and flexible construction of complex simulation architectures on a firm system-theoretic foundation. Also, we show that facilitating the transformation from non-modular to modular and hierarchical structures endows a major benefit in that existing non-modular models can be accommodated by simply wrapping them in DEVS-compliant format. Therefore, DEVS theory simplifies model maintenance, integration, and extension, thereby promoting interoperability and reuse. Additionally, we demonstrate how DEVS universality and uniqueness guarantee that any system with discrete event interfaces can be structurally represented with the DEVS formalism, ensuring consistency across heterogeneous platforms. We propose that these mechanisms collectively can streamline simulator design and implementation for advancing simulation interoperability.

This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9% accuracy at a 1% threshold and a weighted F1-score of 0.8126, validating its superior performance.

This paper delves into current-state opacity enforcement in partially observed discrete event systems through an innovative application of differential privacy, which is fundamental for security-critical cyber–physical systems. An opaque system implies that an external agent cannot infer the predefined system secret via its observational output, such that the important system information flow cannot be leaked out. Differential privacy emerges as a robust framework that is pivotal for the protection of individual data integrity within these systems. Motivated by the differential privacy mechanism for information protection, this research proposes the secret string adjacency relation as a novel concept, assessing the similarity between potentially compromised strings and system-generated alternatives, thereby shielding the system’s confidential data from external observation. The development of secret string differential privacy is achieved by substituting sensitive strings. These substitution strings are generated by a modified Levenshtein automaton, following exponentially distributed generation probabilities. The verification and illustrative examples of the proposed mechanism are provided.

This paper considers the verification of decentralized fault pattern diagnosability for discrete event systems, where the pattern is modeled as a finite automaton whose accepted language is the objective to be diagnosed. We introduce a notion of codiagnosability to formalize the decentralized fault pattern diagnosability, which requires the pattern to be detected by one of the external local observers within a bounded delay. To this end, a structure, namely a verifier, is proposed to verify the codiagnosability of the system and the fault pattern. By studying an indeterminate cycle of the verifier, sufficient and necessary conditions are provided to test the codiagnosability. It is shown that the proposed method requires polynomial time at most. In addition, we present an approach to extend the proposed verifier structure so that it can be applied to centralized cases.

A think-globally-act-locally (TGAL) technique is proven to be an effective method to address the state explosion issue for complex discrete event systems modeled with Petri nets. This paper introduces a TGAL-based method for computing and analyzing the reachability graph (RG) of Petri net models. Given a net system, the TGAL technique strategically introduces a global idle place (GIP) to iteratively generate its RG by updating the token count. At each step, the reachable markings (RMs) and legal markings (LMs) obtained by the previous iterations are considered to calculate the corresponding states of the current step. According to the enforced control requirement, a system state is required to be computed and classified only once during an iterative process. This method only calculates the necessary number of RMs and reduces computational redundancy, which minimizes the computational cost. Four typical Petri net models from existing studies are employed to demonstrate the method.

Diagnosability of a discrete event system is usually dealt at the system level entailing synchronous composition of component automata leading to state explosion problem. However, many of the systems are modular in nature allowing localized detection and isolation of faults. Moreover, developments in sensor technology allow direct detection of faults based on sensor output which are denoted as observations in this paper. Combining modularity and observations, we propose a new concept of O-diagnosability based on observations at the subsystem or component level to make the diagnosability verification less complex. The concepts of monolithic (system) O-diagnosability and CO-diagnosability (system to component) are introduced and necessary and sufficient conditions for O-diagnosability are derived. Theoretical results on the relation between monolithic O-diagnosability and CO-diagnosability support the system level diagnosability verification through component level analysis in a progressive way. Computational complexity for the proposed diagnosability verification is shown to be of the order of n 2 where n is the largest number of diagnoser states of a component of the system.

In the context of discrete event systems (DESs), critical states usually refer to a system configuration of interest, describing certain important system properties, e.g., fault diagnosability, state/language opacity, and state/event concealment. Technically, a DES is critically observable if an intruder can always unambiguously infer, by observing the system output, whether the plant is currently in a predefined set of critical states or the current state set is disjointed with the critical states. In this paper, given a partially observable DES modeled with a finite-state automaton that is not critically observable, we focus on how to make it critically observable, which is achieved by proposing a novel enforcement mechanism based on differential privacy (DP). Specifically, we consider two observations where one observation cannot determine whether a system is currently in the predefined critical states (i.e., the observation violating the critical observability) while the other is randomly generated by the system. When these two observations are processed separately by the differential privacy mechanism (DPM), the system generates an output, exposed to the intruder, that is randomly modified such that its probability approximates the two observations. In other words, the intruder cannot determine the original input of a system by observing its output. In this way, even if the utilized DPM is published to the intruder, they are unable to identify whether critical observability is violated.