Search Results (410)

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

Modern AMSs (automated manufacturing systems) on the one hand bring many benefits, but on the other hand, they are cumbersome to coordinate. AMSs consist of various subsystems (e.g., production lines) that share a finite number of resources (robots, machines, buffers, automated guided vehicles, etc.). This forces AMS designers to build flexible and decentralized systems. However, in these cases, the danger of deadlocks exists. Consequently, such a situation requires the application of advanced supervisors. One solution to the deadline problem is the application of Petri nets. This paper is motivated by AMS control based on deadlock prevention by means of ordinary Petri nets (OPNs) and generalized Petri nets (GPNs). This paper examines two areas of AMS Petri net-based model structures and presents methods of deadlock prevention. First, simpler structures of AMSs modeled by OPNs and GPNs will be investigated, and then more complex structures of AMSs modeled by the same kinds of Petri nets (PNs) will be analyzed. The siphon-based approach will be used for deadlock prevention in all of these cases. The principal results are introduced, explained, and illustrated through examples. Key results are introduced, especially in Example 1 and Example 2. Full article

Healthcare delivery systems operate as complex socio-technical Systems-of-Systems (SoS), where autonomous entities—hospitals, insurers, laboratories, and technology vendors—must coordinate to achieve collective outcomes that exceed individual capabilities. Despite substantial investment in interoperability standards and regulatory frameworks, persistent fragmentation undermines care quality, operational efficiency, and systemic adaptability. This fragmentation stems from a fundamental governance paradox: how can independent systems retain operational autonomy while adhering to shared rules that ensure systemic resilience? This paper addresses this challenge by advancing a governance-oriented architecture grounded in Object-Oriented Programming (OOP) principles. We reinterpret core OOP constructs—encapsulation, modularity, inheritance, polymorphism, and interface definition—as governance mechanisms that enable autonomy through principled constraints while fostering structured coordination across heterogeneous systems. Central to this framework is the Confluence Interoperability Covenant (CIC), a socio-technical governance artifact that functions as an adaptive interface mechanism, codifying integrated legal, procedural, and technical standards without dictating internal system architectures. To validate this approach, we develop a functional proof-of-concept simulation using Petri Nets, modeling constituent healthcare systems as autonomous entities interacting through CIC-governed transitions. Comparative simulation results demonstrate that CIC-based governance significantly reduces fragmentation (from 0.8077 to 0.1538) while increasing successful interactions fivefold (from 68 to 339 over 400 steps). This work contributes foundational principles for SoS Engineering and offers practical guidance for designing scalable, interoperable governance architectures in mission-critical socio-technical domains. Full article

The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this metric is well-defined for numerous model types, including, most prominently, Ordinary Differential Equations (ODEs). The basic reproduction number is used in disease modeling to predict the potential of an outbreak and the transmissibility of a disease, as well as by governments to inform public health interventions and resource allocation for controlling the spread of diseases. A Petri Net (PN) is a directed bipartite graph where places, transitions, arcs, and the firing of the arcs determine the dynamic behavior of the system. Petri Net models have been an increasingly used tool within the epidemiology community. However, no generalized method for calculating $R_0$ directly from PN models has been established. Thus, in this paper, we establish a generalized computational framework for calculating $R_0$ directly from Petri Net models. We adapt the next-generation matrix method to be compatible with multiple Petri Net formalisms, including both deterministic Variable Arc Weight Petri Nets (VAPNs) and stochastic continuous-time Petri Nets (SPNs). We demonstrate the method’s versatility on a range of complex epidemiological models, including those with multiple strains, asymptomatic states, and nonlinear dynamics. Crucially, we numerically validate our framework by demonstrating that the analytically derived $R_0$ values are in strong agreement with those estimated from simulation data, thereby confirming the method’s accuracy and practical utility. Full article

Driving safety education remains a critical societal priority, and understanding traffic rules is essential for reducing road accidents and improving driver awareness. This study presents the development and evaluation of a virtual simulator for learning traffic rules, incorporating spherical video technology and interactive training scenarios. The primary objective was to enhance the accessibility and effectiveness of traffic rule education by utilizing modern virtual reality approaches without the need for specialized equipment. A key research component is using Petri net-based models to study the simulator’s dynamic states, enabling the analysis and optimization of system behavior. The developed simulator employs large language models for the automated generation of educational content and test questions, supporting personalized learning experiences. Additionally, a model for determining the camera rotation angle was proposed, ensuring a realistic and immersive presentation of training scenarios within the simulator. The system’s cloud-based, modular software architecture and cross-platform algorithms ensure flexibility, scalability, and compatibility across devices. The simulator allows users to practice traffic rules in realistic road environments with the aid of spherical videos and receive immediate feedback through contextual prompts. The developed system stands out from existing traffic rule learning platforms by combining spherical video technology, large language model-based content generation, and cloud architecture to create a more interactive, adaptive, and realistic learning experience. The experimental results confirm the simulator’s high efficiency in improving users’ knowledge of traffic rules and practical decision-making skills. Full article

The integration of data-driven, intelligent components, particularly those based on Artificial Neural Network (ANN), is pivotal for enabling software systems to adapt to dynamic environments. However, the performance of these hybrid systems is critically dependent on the quality of their training data. Deficiencies in this data can propagate through the ANN, leading to violations of key system properties that are difficult to trace back to their root cause. To address this challenge, this paper introduces $D^{3}MV$, a novel verification-based methodology for tracing system-level property violations back to specific deficient training data. Our approach involves constructing a unified system model (Adaptive Petri Net) that integrates traditional components with ANNs, extracting interpretable fuzzy rules from the trained network to bridge the semantic gap, and employing model checking for formal verification. When a property is violated, a novel inverse mapping technique leverages the implicated fuzzy rules to pinpoint the responsible data samples in the training set. Experimental validation using a manufacturing case study demonstrates that the method $D^{3}MV$ successfully identified deficient data causing property violations. After replacing 200 problematic data samples and updating the model, the revised system met all specified performance metrics. This preliminary result suggests that by improving data quality, our approach helps ensure system reliability. Full article