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
• http://www.fit.vutbr.cz/study/courses/TI1/public/ti.pdf
• Jensen K.: Coloured Petri Nets, Springer Verlag 1993
• Reisig W.: Petri Nets: An Introduction. Springer-Verlag, Berlin, Heidelberg 1985
• 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

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. Place/Transition Petri nets, analysis problems.
7. Analysis of P/T Petri nets by reachability tree.
8. Invariants of P/T Petri nets.
9. Petri nets languages.
10. Marked graphs and Free choices Petri nets, Petri nets with inhibitors.
11. Coloured Petri nets, CPN Design, applications.
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.

Short tests in lectures, state of essay elaboration.
Lectures and essay elaboration.