Theory and Applications of Petri Nets

• 39 hrs lectures
• 8 hrs pc labs

• 70 pts final exam
• 30 pts projects

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.

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

• 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
• 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
• 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
• Jensen K.: Coloured Petri Nets, Springer Verlag 1993
• Reisig W.: Petri Nets: An Introduction. Springer-Verlag, Berlin, Heidelberg 1985
• Jensen K.,Kristensen L.M,: Coloured Petri nets: modelling and validation, Springer Verlag, 2009
• David R., Alla H,: Discrete, Continuos and Hybrid Petri Nets, Springer Verlag, 2010

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.

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.

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.