155-0991/01 – Modeling of paralel systems by Petri nets (MPSPS)

Gurantor departmentDepartment of Applied InformaticsCredits10
Subject guarantordoc. RNDr. Ivo Martiník, Ph.D.Subject version guarantordoc. RNDr. Ivo Martiník, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageCzech
Year of introduction2020/2021Year of cancellation
Intended for the facultiesEKFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
MAR63 doc. RNDr. Ivo Martiník, 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

1. To obtain basic knowledge about Petri nets and analysis of their properties 2. Understand the principles of modeling parallel and non-parallel systems with using of Petri nets 3. Understand the principles and properties of high-level Petri nets 4. To obtain knowledge about basic properties of well-structured systems and their modeling by Petri nets 5. Understand the principles of modeling and verification of discrete-time dynamic systems by selected classes of time and timed Petri nets 6. To be able to practically apply knowledge of Petri nets in modeling and verification of selected economic systems

Teaching methods

Individual consultations
Project work


The main goal of the course is to deepen theoretical and practical knowledge in the field of modeling and verification of parallel and non-parallel systems through the mathematical apparatus of Petri nets. Various types of low-level and high-level Petri nets, their basic static and dynamic properties and methods of their verification are studied. Attention is also paid to the synthesis of Petri nets in order to preserve their properties. For the purpose of modeling economic parallel systems, a special class of so called process Petri nets has been introduced and its properties related to the problem of so-called well-structured systems and their applications in the field of informatics and economics have been studied.

Compulsory literature:

REISIG, W. Understanding Petri Nets. Modeling Techniques, Analysis Methods, Case Studies. 2nd Edition. Berlin: Springer Verlag. 2013. 230 pp. ISBN 978-3-642-33277-7. REISIG, W. and G. ROZENBERG, G. Lectures on Petri Nets I: Basic Models. 1st Edition. Berlin: Springer-Verlag. 1998. 477 pp. ISBN 978-3540653066. DIAZ, M. Petri Nets: Fundamental Models, Verification and Applications. 1st Edition. London: John Willey. 2009. 656 pp. ISBN 978-1848210790.

Recommended literature:

DAVID, R. and H. ALLA. Discrete, Continuous and Hybrid Petri Nets. 2nd Edition. Berlin: Springer-Verlag. 2010. 550 pp. ISBN 978-3642106682. HUANG, H., JIAO, L., CHEUNG, T. and W. M. MAK. Property-Preserving Petri Net Process Algebra In Software Engineering. 1st Edition. Singapore: World Scientific Publishing. 2012. 318 pp. ISBN 978-981-4324-28-1. REISIG, W. Elements of Distributed Algorithms. 1st Edition. Berlin: Springer-Verlag. 1998. 302 pp. ISBN 978-3540627524.

Way of continuous check of knowledge in the course of semester

- project development - oral exam


Other requirements

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Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Definition and basic properties of low-level Petri nets and their basic classes: C/E Petri nets, P/T Petri nets, Petri nets with inhibitors 2. Basic static and dynamic properties of Petri nets: Petri nets marking, liveness, boudnedness, reversibility, marking reachibility, siphons and traps, etc. 3. P- and T-invariants of Petri nets and their determination. 4. Synthesis of low-level Petri nets and fundamentals of regional theory. 5. Process Petri nets and their basic properties, modeling and verification of economic systems with their using. 6. Well-structured systems, their properties and modeling of these systems with using of process Petri nets. 7. Process algebras over the Petri nets class, Petri Net Process Algebras property-preservation and their application in modeling economic systems. 8. Time and timed Petri nets, discrete-time modeling of economic systems. 9. Definition and properties of basic classes of high-level Petri nets, colored Petri nets. 10. High-level Process Petri nets and their use in modeling economic systems.

Conditions for subject completion

Part-time form (validity from: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (P0311D050019) Systems Engineering and Informatics P Czech Ostrava Choice-compulsory type B study plan
2021/2022 (P0311D050019) Systems Engineering and Informatics K Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P0311D050019) Systems Engineering and Informatics P Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P0311D050019) Systems Engineering and Informatics K Czech Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

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