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Applied Sciences
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Recent Trends in Petri Net Research: Methods and Innovative Applications
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Recent Trends in Petri Net Research: Methods and Innovative Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Electrical, Electronics and Communications Engineering".

Deadline for manuscript submissions: 20 April 2026 | Viewed by 429

Special Issue Editor

Dr. Marcin Wojnakowski

E-Mail Website
Guest Editor
Institute of Control and Computation Engineering, University of Zielona Góra, Prof. Z. Szafrana 2, 65-516 Zielona Góra, Poland
Interests: Petri net-based systems; analysis of Petri nets; hardware implementation; FPGAs; Verilog
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Petri nets continue to grow as a multipurpose tool across a wide range of scientific and engineering fields. They are a well-established formalism for modeling, analyzing, and verifying concurrent and distributed systems. Their ability to represent complex interactions, synchronization, and resource sharing makes them vital for studying systems. These systems exhibit concurrency, nondeterminism, and asynchronous behavior. Recent trends in Petri net theory and applications have expanded their impact in areas such as manufacturing systems, cyber–physical systems, biochemical networks, communication protocols, and software verification. This Special Issue will bring high-quality research contributions. It focuses on theoretical developments, novel analysis methods, and innovative applications of Petri nets. Topics of interest include, but are not limited to, reachability analysis, invariant computation, model checking, and other extensions (classes) of Petri nets. We particularly welcome studies that address scalability challenges, integrate Petri nets with other modeling paradigms, or demonstrate efficient and effective analysis methods. To promote interdisciplinary collaboration, this Special Issue requests studies covering both foundational research and practical implementations, as well as those contributing to the advancement of Petri net methodologies within the scientific community.

Dr. Marcin Wojnakowski
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Petri nets
  • concurrent control systems
  • model-driven development
  • reachability analysis
  • invariants
  • model checking
  • cyber-physical systems
  • biochemical networks
  • distributed systems

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Published Papers (2 papers)

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24 pages, 1035 KB  
Article
XT-Hypergraph-Based Decomposition and Implementation of Concurrent Control Systems Modeled by Petri Nets
by Łukasz Stefanowicz, Paweł Majdzik and Marcin Witczak
Appl. Sci. 2026, 16(1), 340; https://doi.org/10.3390/app16010340 (registering DOI) - 29 Dec 2025
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Recent Trends in Petri Net Research: Methods and Innovative Applications)
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29 pages, 1877 KB  
Article
The Basic Reproduction Number for Petri Net Models: A Next-Generation Matrix Approach
by Trevor Reckell, Beckett Sterner and Petar Jevtić
Appl. Sci. 2025, 15(23), 12827; https://doi.org/10.3390/app152312827 - 4 Dec 2025
Viewed by 247
Abstract
The basic reproduction number (R0) 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, [...] Read more.
The basic reproduction number (R0) 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 R0 directly from PN models has been established. Thus, in this paper, we establish a generalized computational framework for calculating R0 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 R0 values are in strong agreement with those estimated from simulation data, thereby confirming the method’s accuracy and practical utility. Full article
(This article belongs to the Special Issue Recent Trends in Petri Net Research: Methods and Innovative Applications)
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