Theory and Applications of Petri Nets

Completion:examination (written&verbal)
Type of
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Guarantee:Češka Milan, prof. RNDr., CSc., DITS
Lecturer:Češka Milan, prof. RNDr., CSc., DITS
Instructor:Češka Milan, prof. RNDr., CSc., DITS
Faculty:Faculty of Information Technology BUT
Department:Department of Intelligent Systems FIT BUT
Learning objectives:
  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.
  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.
Knowledge and skills required for the course:
  Basic knowledge of discrete mathematics concepts including graph theory and formal languages concepts,  basic concepts of algorithmic complexity, and principles of computer modelling.
Subject specific learning outcomes and competences:
  Theoretical and practical background for application of Petri nets and supporting tools in system modelling, design, and verification.
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.
Syllabus of lectures:
  • 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.
Syllabus - others, projects and individual work of students:
  • Essay based on selected scientific paper dealing with Petri net application in problems solved in student dissertation.
Fundamental literature:
  • Reisich W.: Petri nets, Springer Verlag 1985
  • Jensen K.: Coloured Petri nets, Springer Verlag 1993
  • Češka M.: Petriho sítě, Akad.nakl. CERM, Brno 1994
Study literature:
  • Reisich W.: Petri nets, Springer Verlag 1985
  • Jensen K.: Coloured Petri nets, Springer Verlag 1993
  • 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
  • http://www.fit.vutbr.cz/study/courses/TI1/public/ti.pdf
Controlled instruction:
  Lectures and essay elaboration.
Progress assessment:
  Short tests in lectures, state of essay elaboration.