Course detail

Theory and Applications of Petri Nets

FIT-TADAcad. year: 2020/2021

Basic concepts of Petri nets, typical analysis problems, analysis methods, Petri net languages, restrictions and extensions of basic class of Petri nets, Coloured Petri nets, Hierarchical and Object oriented Petri nets, Petri nets tools, applications.

The state examination topics:

  1. Basic notions and concepts of Petri nets theory.
  2. Classification of Petri nets models.
  3. Analysis of Condition/Event Petri nets based on case graphs.
  4. Processes of C/E Petri nets.
  5. Synchronic distances and facts..
  6. Analysis of P/T Petri nets by reachability tree.
  7. Invariants of P/T Petri nets and their applications.
  8. Petri nets languages.
  9. Marked graphs and Free choices Petri nets, Petri nets with inhibitors.
  10. Coloured and hierarchical Petri nets.

Learning outcomes of the course unit

Theoretical and practical background for application of Petri nets and supporting tools in system modelling, design, and verification.
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.


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


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Češka M.: Petriho sítě, Akad.nakl. CERM, 1994
Wil van der Aalst and Kees van Hee: Workflow Management: Models, Methods, and Systems MIT Press, 368 pp., ISBN 0-262-01189-1 2004
Unifying Petri Nets, Advances in Petri Nets, Ed.: Hartmut Ehrig, Gabriel Juhas, Julia Padberg, Grzegorz Rozenberg, Springer-Verlag Vol.: LNCS 2128, 485 pp., ISBN: 3-540-43067-9 2001
Jensen K.: Coloured Petri nets, Springer Verlag 1993
Češka M.: Petriho sítě, Akad.nakl. CERM, Brno 1994
Reisig W.: Petri Nets: An Introduction. Springer-Verlag, Berlin, Heidelberg 1985
Jensen K.: Coloured Petri nets: modelling and validation, Springer Verlag, 2009
David R., Alla H,: Discrete, Continuos and Hybrid Petri Nets, Springer Verlag, 2010

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Short tests in lectures, state of essay elaboration.

Language of instruction

Czech, English

Work placements

Not applicable.


To understand the basic concepts and methods of system modelling using Petri nets, to adopt the Petri nets theory and applications in problems of system modelling, design, and verification. To gain practical experiences with representative Perti nets tools.

Specification of controlled education, way of implementation and compensation for absences

Lectures and essay elaboration.

Classification of course in study plans

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, elective

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, elective

Type of course unit



39 hours, optionally

Teacher / Lecturer


  • Introduction to Petri nets, basic notions.
  • Condition/Event Petri nets.
  • Complementation, case graphs, and applications in C/E systems analysis.
  • Processes of C/E Petri nets, occurrences nets.
  • Properties of C/E Petri nets, synchronic distances, facts.
  • Place/Transition Petri nets, analysis problems.
  • Analysis of P/T Petri nets by reachability tree.
  • Invariants of P/T Petri nets.
  • Petri nets languages.
  • Marked graphs and Free choices Petri nets, Petri nets with inhibitors.
  • Coloured Petri nets, CPN Design, applications.
  • Analysis of Coloured Petri nets.
  • Hierarchical Coloured Petri nets and Object oriented Petri nets.

Guided consultation in combined form of studies

26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

8 hours, compulsory

Teacher / Lecturer


  • Tools for C/E and P/T Petri nets.
  • Tools for high-level Petri nets (CPN).
  • Tools for object-oriented Petri nets.
  • Tools for modeling and programming of control systems based on Petri nets.