460-6005/03 – Petri Nets (PS)

Gurantor departmentDepartment of Computer ScienceCredits10
Subject guarantorprof. RNDr. Petr Jančar, CSc.Subject version guarantordoc. Ing. Zdeněk Sawa, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
SAW75 doc. Ing. Zdeněk Sawa, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+0

Subject aims expressed by acquired skills and competences

On successful completion of the course, the student - understands the notions from Petri net theory - is able to model and analyse concrete systems by help of software tools based on Petri nets - is able to assess using the methods of Petri net for concrete engineering problems - is able by self-study to master and present an advanced topic in Petri net theory

Teaching methods

Individual consultations
Project work


Petri nets constitute a class of frequently used tools for modelling, design, and analysis of complex systems with distributed states, parallel processes and hierarchical structure. They have numerous applications in the area of data processing, operating systems, distributed databases, and controlling of complex processes. The course presents the basic notions and methods of Petri net theory and with the methodologies of their use in specification, design, analysis and verification of information and other systems.

Compulsory literature:

K.Jensen, L.M.Kristensen: Coloured Petri Nets (Modelling and Validation of Concurrent Systems), Springer, 2009.

Recommended literature:

W.Reisig-G.Rozenberg (Eds.): Lectures on Petri Nets I: Basic Models, LNCS 1491, Springer, 1998. W.Reisig-G.Rozenberg (Eds.): Lectures on Petri Nets II: Applications, LNCS 1492, Springer, 1998. M.A.Marsan, G.Balbo, G.Conte, S.Donatelli, G.Franceschinis: Modelling with Generalised Stochastic Petri Nets. Series in Parallel Computing, John Wiley & Sons, 1995.

Way of continuous check of knowledge in the course of semester

The student writes a concise, cogent and understandable article about a selected advanced topic, which he/she presents during the course.


Other requirements

There are not defined other requirements for student.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Problem of analysis, modelling and design of complex systems with parallelism and hierarchical structure. Net methods to solve the problem. Definition and classification of Petri nets. Informal introduction into modelling by Petri nets I: C/E Petri nets, P/T Petri nets. Petri nets with inhibitors. Informal introduction into modelling by Petri nets II: high-level Petri nets, coloured Petri nets, hierarchical Petri nets. Structures, systems and parametrized systems of Petri nets. Statics and dynamics of Petri nets. Markings, and the reachability set of a PN-system. Reachability graph. Petri nets properties: boundedness, liveness, deadlock-freeness, reversibility, conservativeness. The reachability problem. State analysis of Petri nets. Structure analysis of Petri nets. The fundamental equation. P-invariants, T-invariants, net components. Dual nets. Special types of Petri nets: automata nets, synchronization nets, free-choice nets. Synthesis of safe, live and reversible Petri nets. Hiearachization via substitution of places and transitions. Petri net languages, their relation to Chomsky hierarchy. High Level Petri Nets (HLPN). Coloured Petri Nets (CPN), the most used version of HLPN. CPN nonhierarchical; structure and dynamics. CPN hierarchical. Substitution and invocation of places and transitions. Fusing of places and transitions.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (P0613D140005) Computer Science K Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P0613D140005) Computer Science P Czech Ostrava Choice-compulsory type B study plan
2019/2020 (P0613D140005) Computer Science P Czech Ostrava Choice-compulsory type B study plan
2019/2020 (P0613D140005) Computer Science K Czech Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner