Course details

Petri Nets

PES Acad. year 2008/2009 Summer semester 5 credits

Current academic year

Basic concepts of Petri nets and their use in modelling of discrete-event systems, classification of Petri nets, the theory of C/E Petri nets, methods of analysis of C/E Petri nets, the theory of P/T Petri nets, methods of analysis of P/T Petri nets, Petri net languages, computability and complexity of Petri net-related problems, the problem of an automatic synthesis of Petri nets, restrictions and extensions of P/T Petri nets, coloured Petri nets, hierarchical and object-oriented Petri nets, Petri net-based tools, applications of Petri nets.


Language of instruction



Examination (written+oral)

Time span

39 hrs lectures, 6 hrs pc labs, 7 hrs projects

Assessment points

50 exam, 30 mid-term test, 20 exercises




Novosad Petr, Ing. (DITS FIT BUT)

Subject specific learning outcomes and competences

The acquired knowledge and experience will allow the students to actively use Petri nets and the computer-aided tools based on them in modelling, design, verification, and implementation of various classes of systems. Based on the acquired theoretical knowledge, the student is able to transfer approaches of the Petri net theory to the domain of other formal models too.

Generic learning outcomes and competences

Abilities to apply and develop advanced information technologies based on suitable formal models, to propose and use such models and theories for automating the design, implementation, and verification of computer-based systems.

Learning objectives

To acquire the basic concepts and methods of the theory of Petri nets and its applications in system modelling, design, and verification. To be able to practically use Petri net-based computer-aided tools in typical applications.


Prerequisite kwnowledge and skills

Basic knowledge of discrete mathematics concepts including graph theory and formal languages concepts,  basic concepts of algorithmic complexity, and principles of computer modelling.

Study literature

  • Reisig, W.: Petri Nets, An Introduction, Springer Verlag, 1985. ISBN: 0-387-13723-8
  • Jensen, K.: Coloured Petri Nets, Basic Concepts, Analysis Methods and Practical Use, Springer Verlag, 1993. ISBN: 3-540-60943-1

Fundamental literature

  • Reisig, W.: Petri Nets, An Introduction, Springer Verlag, 1985. ISBN: 0-387-13723-8
  • Jensen, K.: Coloured Petri Nets, Basic Concepts, Analysis Methods and Practical Use, Springer Verlag, 1993. ISBN: 3-540-60943-1
  • Girault, C., Valk, R.: Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications, Springer Verlag, 2002. ISBN 3-540-41217-4
  • Desel, J., Reisig, W., Rozenberg, G.: Lectures on Concurrency and Petri Nets, Advances in Petri Nets, Lecture Notes in Computer Science, vol. 3098, Springer Verlag, 2004. ISBN 3-540-22261-8

Syllabus of lectures

  1. An introduction to Petri nets, their philosophy and applications, the notion of a net and of the derived basic terms
  2. Condition/Event (C/E) Petri nets, cases and steps, the state space of C/E systems, cyclic and live C/E systems, equivalence of C/E systems.
  3. Contact-free C/E systems, complementation, case graphs and their application for analysing C/E systems.
  4. Processes of C/E systems, occurrence nets, properties of properties and composition of processes.
  5. Complementation of C/E systems, the synchronic distance, special synchronic distances, C/E systems and the propositional calculus, facts.
  6. Place/Transition (P/T) Petri nets, their definition, evolution rules, their state space, basic analytical problems (safety, boundedness, conservativeness, liveness).
  7. Representing the possibly infinite state space of Petri nets by a reachability tree, computing and using reachability trees for analysing P/T Petri nets.
  8. P and T invariants of P/T Petri nets, their definition, the ways of computing them and using them for analysing P/T Petri nets.
  9. Subclasses and extensions of P/T Petri nets, state machines, marked graphs, free-choice Petri nets, Petri nets with inhibitors, timed and stochastic Petri nets.
  10. The notion of a Petri net language, types of such languages, their closure properties, their relation to the Chomsky hierarchy. Computability and complexity of some selected Petri net-related problems.
  11. Coloured Petri nets (CPNs), their basic modelling primitives, an inscription language, CPN Design as an example of a tool based on CPNs.
  12. Analysis of CPNs, occurrence graphs, invariants, and their use in analysing systems.
  13. Hierarchical and object-oriented Petri nets, basic concepts of a hierarchical design, substitution and invocation, adding object-oriented features on top of Petri nets, PNtalk as a language based on object-oriented Petri nets.

Syllabus - others, projects and individual work of students

  • An application of C/E systems.
  • An application of P/T Petri nets.
  • An application of CPNS.
  • An application of object-oriented Petri nets.

Each project implies modelling of a non-trivial system (or its part) by means of a Petri net of the given class and its simulation, analysis, and verification. Suitable computer-aided tools (e.g., PESIM, INA, PEP, TimeNET, CPN Design, Maria, PNtalk, etc.) will be used in the projects.

Progress assessment

A mid-term exam evaluation and an evaluation of projects.

Controlled instruction

A written mid-term exam, a regular evaluation of projects.

Course inclusion in study plans

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