Petri Net Course - Theory & Application

The Petri Net Course is a satellite event of the 46th International Conference on Application and Theory of Petri Nets and Concurrency (Petri Nets 2025). The course offers a thorough introduction to Petri Nets in four half-day modules and two half-day tutorials on applications of Petri Nets and new developments presented by experts in the area.

This year, the first two modules will be offered as videos for time-independent learning. The other two modules and the two tutorials will take place during the conference in Paris - the modules on Monday, the tutorials on Tuesday. Each module of the course can also be taken separately. In particular, the tutorials on Tuesday can be attended as independent lectures.

For the course as a whole, graduate and PhD Students are the intended audience.

For the preparation phase, students who have registered for the entire course will receive material containing preliminaries on the philosophy of net theory, basic notions, small examples, typical application areas, etc. in advance. They will also receive access to the video lectures of the first two modules.

to the resources for preparation
(for participants only)

Module: Basic Net Classes

Lecturer:	Jörg Desel FernUniversität in Hagen joerg.desel@fernuni-hagen.de
Date:	until June 23
offered as video lecture

This is the introductory module to the Petri Net Course and as such provides key concepts and definitions underlying almost every Petri net model. Guided by a motivating example, principles of net theory are discussed highlighting local dynamics and concurrency. Two basic net classes are introduced and investigated: Place/Transition Systems and Elementary Net (EN) Systems. We consider the occurrence rule (token game), reachability, state graph, behavioural properties like deadlock and boundedness, behavioural equivalence and normal forms. The fundamental situations causality, conflict, concurrency, and confusion are explained in the context of EN Systems. We discuss EN system behaviour in terms of sequential and non-sequential observations. Finally, basic analysis techniques to establish structural properties of nets are presented.

to the resources
(for participants only)

Module: Coloured Petri Nets and the CPN Tools

Lecturer:	Lars Michael Kristensen Western Norway University of Applied Sciences Lars.Michael.Kristensen@hvl.no
Date:	until June 23
offered as video lecture

This module focusses on the constructs and definition of the Coloured Petri Nets (CPNs) modelling language. CPNs belong to the class of high-level Petri nets and combines Petri Nets with the functional programming language Standard ML (SML). Petri nets provides the primitives for modelling concurrency, communication, and synchronisation while SML provides the primitives for modelling data manipulation and for creating compact and parameterised models. CPNs and the supporting computer tool CPN Tools have been widely used in practice for modelling and validating a wide range of concurrent and distributed systems. Examples demonstrating the practical use of CPN modelling and verification on industrial-sized systems will be presented. Having completed this module the participants should be able to:

explain and use the basic constructs of the CPN modelling language
explain the syntax and semantics of CPNs
structure CPN models into a hierarchically related set of modules
apply CPN Tools for construction and simulation of CPN models

The module includes hands-on experiments with CPN Tools.

to the resources
(for participants only)

Module: Verification and Model Checking of Petri Nets

Lecturer:	Karsten Wolf University of Rostock karsten.wolf@uni-rostock.de
Date:	Monday, 23 June 2025
Time:	8.30 – 10.00 and 10.30 – 12.00
Room:	... to be announced ...

In the beginning, model checking was just a set of algorithms: given a system model and a specification (written in a temporal logic), decide whether the model satisfies the specification. The problem is challenging, mainly due to the state explosion problem. State explosion can be addressed in various ways. This has led to a wealth of technology: data structures, implementations, and approaches. In this module, model checking differentiated by the application domain. For instance, the main challenge in software model checking is to find appropriate abstractions for the data structures.

Petri net model checking has developed into its own branch of model checking. It can be characterized by:

Absence of data structures (most Petri net model checkers operate on place/transition nets),
Locality, monotonicity, and linearity of the firing rule,
Presence of massive concurrency, and
Availability of results from Petri net theory.

We cover the whole spectrum from basic algorithms to state-of-the-art technology. At every stage, we show where and how our application domain Petri nets impacts the design of a Petri net model checker. We demonstrate the results using the LoLA 2 model checking tool that is freely available.

to the resources
(for participants only)

Module: Timed and Stochastic Petri Nets

Lecturer:	Serge Haddad ENS Paris-Saclay serge.haddad@lmf.cnrs.fr
Date:	Monday, 23 June 2025
Time:	13.30 – 15.00 and 15.30 – 17.00
Room:	... to be announced ...

This module presents different ways to introduce time in Petri nets, focusing on the various policies and ideas explored in literature. In particular, four model classes will be considered in details:

Timed Transitions Petri nets (TTPN), where time is associated to transitions as firing intervals;
Stochastic Petri Nets (SPN), where transitions are associated with an exponential distribution function;
Generalized Stochastic Petri Nets (GSPN), that extend SPN with immediate activities; and
Deterministic & Stochastic Petri Nets (DSPN), that extend GSPN with arbitrary probability distribution functions associated to transition firing times.

The module will introduce the syntax and semantics of these model classes, and develop some standard analysis techniques. For particular kinds of distributions, the module will describe the construction of a continuous time Markov chain (CTMC) or of a Markov Regenerative Processed (MRgP), on which the main performance indices can be computed.

The module will include a short description of Markov chains in order to be self-contained.

to the resources
(for participants only)

Tutorial: Object-centric process modeling and analysis. A short avant-garde journey.

Lecturers:	Jan Martijn van der Werf, Utrecht University Andrey Rivkin, Technical University of Denmark
Date:	Tuesday, 24 June 2025
Time:	8.30 – 10.00 and 10.30 – 12.00
Room:	... to be announced ...

Object-centricity has been among the key trends in the process science community in recent years. In a nutshell, object-centric processes must exhibit two key features: the ability to identify the objects they manipulate and the capacity to represent relations between such objects, where the relations may evolve during process execution. The first feature is typically achieved by introducing tokens with unique identities (similar to colored Petri nets), where the identifier domain consists of countably many elements. The second feature can be obtained in various ways. For instance, one approach involves using places to store tuples of related objects, while another relies on refined execution semantics that enable the simultaneous firing of multiple transitions, which in turn consume or transfer related tokens.

To date, various Petri net classes have been employed for modeling and analyzing object-centric processes. In this tutorial, we will provide a brief overview of these classes and focus on a specific one: typed Petri nets with identifiers (t-PNIDs for short). This class allows to distinguish objects not only by their identifiers but also by their types. Places in t-PNIDs represent relations (with fixed schemas) between objects which in turn means that tokens carry tuples of identifiers. Objects can participate in multiple relations and, throughout net executions, can “migrate” from one relation to another. Additionally, t-PNIDs support the generation of fresh identifiers, allowing for dynamic object creation.

In this tutorial, we will show how t-PNIDs can be used as a modelling tool for object-centric processes. Furthermore, we will discuss key properties of t-PNIDs and their decidability. Among such properties, specific attention will be put on the property of soundness, which is crucial for workflow-like models and plays a significant role in process discovery. In the final part of the tutorial, we will discuss how t-PNIDs (and their sub-classes) can be used in various process mining tasks.

to the resources
(for participants only)

Tutorial: Modeling Complex Systems with High-level Petri Nets

Lecturers:	Daniel Moldt, Laif-Oke Clasen, Marcel Hansson Universität Hamburg moldt@informatik.uni-hamburg.de
Date:	Tuesday, 24 June 2025
Time:	13.30 – 15.00 and 15.30 – 17.00
Room:	... to be announced ...

... to be announced ...

to the resources
(for participants only)