Course detail

Theory and Applications of Petri Nets

FIT-TADAcad. year: 2025/2026

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.

Language of instruction

Czech, English

Mode of study

Not applicable.

Guarantor

doc. Mgr. Adam Rogalewicz, Ph.D.

Department

Department of Intelligent Systems (UITS)

Entry knowledge

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

Rules for evaluation and completion of the course

Discussion within the lectures. Project on a selected topic. In the case when the course is opened as the consulted study discussions with the given literature.

Aims

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.
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.

Study aids

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Češka M.: Petriho sítě, Akad.nakl. CERM, 1994
David R., Alla H,: Discrete, Continuos and Hybrid Petri Nets, Springer Verlag, 2010
Jensen K.: Coloured Petri Nets, Springer Verlag 1993
Jensen K.,Kristensen L.M,: Coloured Petri nets: modelling and validation, Springer Verlag, 2009
M.Češka a kolektiv: Petriho sítě (studijní opora). K dispozici online: https://www.fit.vut.cz/study/course/MBA/private/materialy/Opora_PES-2006.pdf
Reisig W.: Petri Nets: An Introduction. Springer-Verlag, Berlin, Heidelberg 1985
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
Wil van der Aalst and Kees van Hee: Workflow Management: Models, Methods, and Systems MIT Press, 368 pp., ISBN 0-262-01189-1

Classification of course in study plans

  • Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Milan Češka, CSc.

Syllabus

  1. Introduction to Petri nets, basic notions.
  2. Condition/Event Petri nets.
  3. Complementation, case graphs, and applications in C/E systems analysis.
  4. Processes of C/E Petri nets, occurrences nets.
  5. Properties of C/E Petri nets, synchronic distances, facts.
  6. PT Petri nets basic analysis problems.
  7. Analysis of P/T Petri nets by reachability tree and backward analysis.
  8. Invariants of P/T Petri nets.
  9. Petri nets languages, relation to the Chomsky hierarchy.
  10. Marked graphs and Free choices Petri nets, Petri nets with inhibitors.
  11. Coloured Petri nets.
  12. Analysis of Coloured Petri nets.
  13. Hierarchical Coloured Petri nets and Object oriented Petri nets.

Guided consultation in combined form of studies

26 hod., optionally

Teacher / Lecturer

doc. Mgr. Adam Rogalewicz, Ph.D.

Exercise in computer lab

8 hod., compulsory

Teacher / Lecturer

doc. Mgr. Adam Rogalewicz, Ph.D.

Syllabus

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