Search Results (415)

The increasing complexity and uncertain system of modern discrete event system (DES) challenge traditional model-based control approaches, while artificial intelligence (AI) techniques offer powerful data-driven decision-making capabilities but lack formal guarantees. This review surveys recent research on the integration of AI with DES and supervisory control theory. Following a systematic literature mapping methodology, the literature is organized using a taxonomy based on three orthogonal perspectives: control and decision paradigm, system capability and property, and application and operational objectives. The review highlights how learning-based methods enhance adaptability and performance in DES, while also exposing persistent challenges related to safety, nonblocking behavior, data efficiency, and interpretability. By structuring existing approaches and identifying open issues, this review provides a coherent overview of the current research landscape and outlines key directions for future work on AI-enabled DES. Full article

As the manufacturing industry continues to advance its digital transformation, intelligent sensing technology has become a key support for achieving precise, efficient and automated quality control. However, current production line monitoring systems predominantly rely on fixed and costly monitoring equipment and sensors, lacking flexible and interactive first-person perspective perception approaches centered on on-site operators. Meanwhile, factory process monitoring often depends solely on visual expression rather than balancing the capabilities of the simulation model and visual state detection, leading to delayed responses to abnormal systems and hindering the adjustment strategy feedback. To address these limitations, this study provides wearable sensing for key workers, enriching the state perception capabilities in industrial scenarios. Furthermore, to achieve dynamic model and real-time visual representation of production line operations, a multi-source information-enhanced Petri nets model is proposed in terms of engineering and user-friendliness. With the solid mathematical basics of the Petri nets and the enriched human–machine data from the product line, this method provides an intuitive, dynamic and accurate reflection of the production system’s real-time operational status, offering a scientific and reliable basis for operational decision-making. The proposed approach has been implemented in a real-world production system for reinforced concrete civil defense doors, and this engineering application can also be extended to many other scenarios. Full article

This paper continues the historical and technical trajectory of fault diagnosis and opacity analysis in discrete event systems (DESs). Whereas the previous work reviewed the foundational developments of event diagnosis and opacity, this survey focuses on recent advances over the past decade by addressing modern challenges such as communication losses, delays, distributed architectures, and cyber-attack scenarios. Specifically, we present a structured overview of diagnosability verification and enforcement across automata, Petri nets, and other DES models under these scenarios. In parallel, we review contemporary results on opacity verification and enforcement, including complexity findings, reduction techniques, and robust or attack-resilient formulations. In addition, this survey provides an updated picture of the evolving research landscape and highlights emerging themes and open problems in diagnosis and opacity for DESs. Full article

Construction management plays a fundamental role in the sustainability of construction projects, as its primary objective is to enhance cost-effectiveness and efficient resource utilization. One of the main challenges encountered at the early stages of a project’s lifecycle, particularly during the planning phase, is the development and agreement of construction schedules among the stakeholders involved. The tools employed for time planning and scheduling during both the planning and construction phases should therefore be capable of modeling complex environments and supporting dynamic updates in response to resource constraints. Petri nets are known for their capability of modeling complex systems, such as resource management. Their use in project management is essential for resource constraint problems. This paper investigates the use of Petri Nets as a tool for the time scheduling of engineering and construction projects. A case study is presented and modeled using Timed Petri nets, enabling dynamic adaptation under time and resource constraints. Through simulation performed with the ROMEO (v3.10.6) software, the study identifies the critical paths and determines the total project duration under various scenarios of sensitivity by adjusting specific project parameters. The results demonstrate the effectiveness of Petri nets in project management and the benefits they offer when used in modeling complex systems, identifying critical activities and calculating resource constraints and time deadlines. Full article

In this scientific article, a quantitative assessment is carried out of the influence of the ERTMS modernisation factor on the practical efficiency of operation and resilience of the Belgian railway lines 50A/51A with the application of methodological triangulation in the MATLAB R2025a Update 1 (25.1.0.2973910) software environment (discrete-event modelling, Petri nets, Markov reliability modelling, and correlation analysis). The modelling reveals that the scenario with an expanded level of automation increases the capacity from 18.3 to 26.0 trains over 2 h (+42.1%) and reduces the average waiting time from 1.53 min (baseline level) to 0.21 min—virtually the theoretical lower bound of zero under favourable conditions. The results of the block-occupancy analysis by means of Petri nets show that a more dynamic distribution of blocks provides higher capacity, and Markov chains reflect the reduction of the impact of control centre unavailability in developing communications and virtualisations. Spearman correlation analysis additionally shows coordinated improvement of the metrics of safety, digital protection, resilience, and performance. Relying on the modelling results, a phased roadmap is proposed, combining technical improvements (development of communication systems, readiness for automation, comparable management of rolling stock movement) with compliance with regulatory requirements and the goals of sustainable development, related to SDGs 9, 11, and 13. Full article

Wind power plants (WPPs), as large-scale cyber–physical systems (CPSs), have become essential to renewable energy generation but are increasingly exposed to cyber threats. Attacks on supervisory control and data acquisition (SCADA) networks can cause cascading physical and economic impacts. The systematic synthesis of cyber risk analysis methods specific to WPPs and cyber–physical energy systems (CPESs) is a need of the hour to identify research gaps and guide the development of resilient protection frameworks. This study employs a Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol to review the state of the art in this area. Peer-reviewed studies published between January 2010 and January 2025 were taken from four major journals using a structured set of nine search queries. After removing duplicates, applying inclusion and exclusion criteria, and screening titles and abstracts, 62 studies were examined for analysis on the basis of a synthesis framework. The studies were classified along three methodological dimensions, qualitative vs. quantitative, model-based vs. data-driven, and informal vs. formal, giving us a unified taxonomy of cyber risk analysis approaches. Among the included studies, 45% appeared to be qualitative or semi-quantitative frameworks such as STRIDE, DREAD, or MITRE ATT&CK; 35% were classified as quantitative or model-based techniques such as Bayesian networks, Markov decision processes, and Petri nets; and 20% adopted data-driven or hybrid AI/ML methods. Only 28% implemented formal verification, and fewer than 10% explicitly linked cyber vulnerabilities to safety consequences. Key research gaps include limited integration of safety–security interdependencies, scarce operational datasets, and inadequate modelling of environmental factors in WPPs. This systematic review highlights a predominance of qualitative approaches and a shortage of data-driven and formally verified frameworks for WPP cybersecurity. Future research should prioritise hybrid methods that integrate formal modelling, synthetic data generation, and machine learning-based risk prioritisation to enhance resilience and operational safety of renewable-energy infrastructures. Full article

Autonomous UAV/UGV swarms increasingly operate in contested environments where purely digital control architectures are vulnerable to cyber compromise, communication denial, and timing faults. This paper presents Guarded Swarms, a hybrid framework that combines digital coordination with hardware-level analog safety enforcement. The architecture builds on Topic-Based Communication Space Petri Nets (TB-CSPN) for structured multi-agent coordination, extending this digital foundation with independent analog guard channels—thrust clamps, attitude limiters, proximity sensors, and emergency stops—that operate in parallel at the actuator interface. Each channel can unilaterally veto unsafe commands within microseconds, independently of software state. The digital–analog interface is formalized via timing contracts that specify sensor-consistency windows and actuation latency bounds. A two-robot case study demonstrates token-based arbitration at the digital level and OR-style inhibition at the analog level. The framework ensures local safety deterministically while maintaining global coordination as a best-effort property. This paper presents an architectural contribution establishing design principles and interface contracts. Empirical validation remains future work. Full article

Self-cleansing intrusion-tolerant systems mitigate attacker intrusions and control through periodic recovery, thereby enhancing both availability and security. However, vulnerabilities in the control link render these systems susceptible to request forgery attacks. Furthermore, existing research on the modeling and performance analysis of such systems remains insufficient. To address these issues, this paper introduces an authentication mechanism to fortify control link security and employs Generalized Stochastic Petri Nets for system evaluation. We constructed Petri net models for three distinct scenarios: a traditional system, a system compromised by forged controller requests, and a system fortified with authentication mechanism. Subsequently, isomorphic Continuous-Time Markov Chains were derived to facilitate theoretical analysis. Quantitative evaluations were performed by deriving steady-state probabilities and conducting simulations on the PIPE platform. To further assess practicality, we conduct scalability analysis under varying system scales and parameter settings, and implement a prototype in a virtualized testbed to experimentally validate the analytical findings. Evaluation results indicate that authentication mechanism ensures the reliable execution of cleansing strategies, thereby improving system availability, enhancing security, and mitigating data leakage risks. Full article

This paper is a theoretical contribution that introduces a new reasoning framework for SAT solving based on resolvable networks (RNs). RNs provide a graph-based representation of propositional satisfiability in which clauses are interpreted as directed reaches between disjoint subsets of Boolean variables (nodes). Building on this framework, we introduce a novel RN-based SAT solver, called RN-Solver, which replaces local assignment-driven branching by global reasoning over token distributions. Token distributions, interpreted as truth assignments, are generated by monotone CNF–DNF dualization applied to white (all-positive) clauses. New white clauses are derived via resolution along private-pivot chains, and the solver’s progression is governed by a taxonomy of token distributions (black-blocked, terminal, active, resolved, and non-resolved). The main results establish the soundness and completeness of the RN-Solver. Experimentally, the solver performs very well on pigeonhole formulas, where the separation between white and black clauses enables effective global reasoning. In contrast, its current implementation performs poorly on random 3-SAT instances, highlighting both practical limitations and significant opportunities for optimization and theoretical refinement. The presented RN-Solver implementation is a proof-of-concept which validates the underlying theory rather than a state-of-the-art competitive solver. One promising direction is the generalization of strongly connected components from directed graphs to resolvable networks. Finally, the token-based perspective naturally suggests a connection to token-superposition Petri net models. Full article

Mathematics, as Bertrand Russell noted, possesses both truth and beauty. In this work, we revisit the classical Fibonacci recurrence thanks to a minimal Petri net. Starting from a minimal layered construction that mirrors the second-order additive rule $F_n=F_{n-1}+F_{n-2}$, we show that the marking dynamics of the associated net generate a combinatorial triangle whose parity structure reveals a self-similar, Sierpiński-like pattern. To the best of our knowledge, this oblique fractal geometry has never been formally documented. We provide a formal definition of the underlying Petri net, analyse its computational properties, and explore the emergence of higher-order harmonics when token markings are considered modulo primes. The study highlights how a classical recurrence gives rise to previously unnoticed geometric regularities at the intersection of mathematics and art. Beyond its mathematical interest, the construction illustrates how minimal Petri net dynamics can be used as formal specification patterns for distributed, event-driven systems. Full article

In modern Industry 4.0 environments, real-time scheduling presents a complex challenge requiring both formal correctness guarantees and optimal performance. Background: Traditional approaches fail to provide an optimal integration between formal correctness guaranteeing and optimization, and such failure either produces suboptimal results or a correct result lacking guarantee, and studies have indicated that poor scheduling decisions could cause productivity losses of up to 20–30% and increased operational costs of up to USD 2.5 million each year in medium-scale manufacturing facilities. Methods: This work proposes a new hybrid approach by integrating Extended Time Petri Nets (ETPNs) and Finite-State Automata (FSAs) with formal modeling, abstracting ETPNs by extending conventional Time Petri Nets to deterministic time and priority systems, accompanied by Genetic Algorithms (GAs) to optimize the solution to tackle a multi-objective optimization problem. Our solution tackles indeterministic problems by incorporating suitable priority resolution methods and GA to pursue optimal solutions to very complex scheduling problems and starting accurately from standard real-time scheduling-policy models such as DM, RM, and EDF-EDF. Results: Experimental evaluation has clearly verified performance gains up to 48% above conventional techniques, covering completely synthetic and practical case studies, including 31–48% improvement on synthetic benchmarks, 24% increase on resource allocation, and total elimination of constraint violations. Conclusions: The new proposed hybrid technique is, to a considerable extent, a dramatic advancement within real-time scheduling techniques and Industry 4.0, successfully and effectively integrating optimal correctness guaranteeing and favorable GA-aided optimization techniques, which particularly guarantee optimal correctness to safe-related applications and provide considerable improvements to support efficient and optimal performance, extremely helpful within Industry 4.0. Full article

This paper presents an integrated approach to the structural decomposition of concurrent control systems using exact transversal hypergraphs (XT-hypergraphs). The proposed method combines formal properties of XT-hypergraphs with invariant-based Petri net analysis to enable automatic partitioning of complex, concurrent specifications into deterministic and independent components. The approach focuses on preserving behavioral correctness while minimizing inter-component dependencies and computational complexity. By exploiting the uniqueness of minimal transversal covers, reducibility, and structural stability of XT-hypergraphs, the method achieves a deterministic decomposition process with polynomial-delay generation of exact transversals. The research provides practical insights into the construction, reduction, and classification of XT structures, together with quality metrics evaluating decomposition efficiency and structural compactness. The developed methodology is validated on representative real-world control and embedded systems, showing its applicability in deterministic modeling, analysis, and implementation of concurrent architectures. Future work includes the integration of XT-hypergraph algorithms with adaptive decomposition and verification frameworks to enhance scalability and automation in modern system design and integration with currently popular AI and machine learning methods. Full article

Chemical emergencies in transport are rare but operationally demanding. This study presents a framework that converts the timeline of a real intervention involving a cyclohexylamine leak after a tanker truck overturned into a Petri net and subsequently into an absorbing Markov model. This provides decision-oriented indicators for the intervention phases and enables what-if analysis. Application to a case study shows that the capacity of the decontamination line has a significant impact on the duration of the incident resolution, while introducing a small probability of returning from technical measures to decontamination slightly prolongs the course while leaving the certainty of successful completion unchanged. Mapping between activities, Petri net locations, and aggregated states promotes transparency and the repeatability of procedures and highlights activities with a high number of repeat visits. The outputs are useful for decision making related to personnel and material resources, post-review analyses, and exercise planning. The limitations lie in calibration to a single incident, the partial use of expertly estimated parameters, and the approximate conversion of “steps” to time. Future work will focus on multiple cases, finer-grained time handling, and explicit capacity modelling. Full article

Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique derived from discrete event systems. A minimal Petri net is created that generates Pascal’s triangle under a simple arithmetic rule. Token counts in each place coincide with binomial coefficients, providing a direct combinatorial interpretation. Two other classical structures emerge from this model: by colouring tokens depending on their parity, the Sierpiński triangle appears; by routing tokens randomly at each branching, the binomial distribution arises, converging to a Gaussian limit as depth increases. As a result, a single Petri construction unifies three mathematical objects: Pascal’s Triangle, Sierpiński’s Triangle, and the Gaussian distribution. This connection illustrates the invaluable potential of Petri nets as unifying tools for modelling discrete mathematical structures and beyond. Full article

Predictive process monitoring estimates the future behaviour of running process instances based on historical event logs, with typical tasks including next-activity prediction, remaining-time estimation, and risk assessment. Existing recurrent and Transformer-based models achieve strong accuracy on individual logs but transfer poorly across processes and underuse the rich graph structure of event data. This paper introduces ProcessGFM, a domain-specific graph pretraining prototype for predictive process monitoring on event graphs. ProcessGFM employs a hierarchical graph neural architecture that jointly encodes event-level, case-level, and resource-level structure and is pretrained in a self-supervised manner on multiple benchmark logs using masked activity reconstruction, temporal order consistency, and pseudo-labelled outcome prediction. A multi-task prediction head and an adversarial domain alignment module adapt the pretrained backbone to downstream tasks and stabilise cross-log generalisation. On the BPI 2012, 2017, and 2019 logs, ProcessGFM improves next-activity accuracy by 2.7 to 4.5 percentage points over the best graph baseline, reaching up to 89.6% accuracy and 87.1% macro-F1. For remaining-time prediction, it attains mean absolute errors between 0.84 and 2.11 days, reducing error by 11.7% to 18.2% relative to the strongest graph baseline. For case-level risk prediction, it achieves area-under-the-curve scores between 0.907 and 0.934 and raises precision at 10% recall by 6.7 to 8.1 percentage points. Cross-log transfer experiments show that ProcessGFM retains between about 90% and 96% of its in-domain next-activity accuracy when applied zero-shot to a different log. Attention-based analysis highlights critical subgraphs that can be projected back to Petri net fragments, providing interpretable links between structural patterns, resource handovers, and late cases. Full article