| Course Unit Code | 460-4006/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| SNE10 | Mgr. Pavla Dráždilová, Ph.D. |
| Summary |
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| Petri nets are one of the most adequate and sound languages for description and analysis of discrete dynamic systems with concurrent processes, distributed states and hierarchical structure. The course covers the fundamentals of the theory and practical use of classical "low-level" Petri nets, i.e. Place/Transition nets and their extensions. |
| Learning Outcomes of the Course Unit |
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To understand the basic concepts and methods of system modelling using Petri nets.
To accept the Petri nets as a an extra suited tool for systems modelling, design, and verification.
To gaine practical experiences with some software tools that support handling with Petri nets.
Acquaintance with fundamentals of modeling, designing, and analysing with Petri net models.
Understanding the main theoretical methods for Petri nets analysis and mastering their using in practice.
Gaining practical experience with program tools supporting Petri nets design and analysis.
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| Course Contents |
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Lectures:
Problems of modelling, analysing and designing complex systems with distributed states, parallel actions and hierarchical structure. Petri nets as a convenient tool to cope with these problems.
Informal introduction to modelling with low-level Petri nets. Condition/Event (C/E) Petri nets. Place/Transition (P/T) Petri nets. Petri nets with inhibitors.
Informal introduction to modelling with high-level Petri nets. Coloured Petri nets. Object-oriented Petri nets. Hierarchical Petri nets.
PN structures, PN systems and parametrized PN systems. Structure and dynamics of P/T Petri nets. States (markings), enabling and firing rule, set of all reachable states. Reachability graph.
Enabling degree of transition. Relations defined on the transition set: conflict, concurrency, causal connection, exclusivity, confusion.
Basic properties of P/T Petri nets: boundness, safeness, liveness, reversibility, deadlock-freeness, conservativity. Reachability and coverability problem. Petri nets state analysis.
Structure analysis of Petri nets. Graph and algebraic methods. Traps and siphons. Change matrix and fundamental equation.
P-invariants, T-invariants and corresponding components. Dual Petri nets and their invariants. Using invariants for Petri nets analysis.
Subclasses of Petri nets according their structure: state-machine PN, synchronization PN, free-choice PN and their properties.
Hierarchical structure of Petri nets. Modular design of Petri nets that are safe, live and reversible.
Formal languages specified by Petri nets and their relation to Chomsky hierarchy of languages.
Some extensions of classical P/T Petri nets: Petri nets with priorities. Timed Petri nets. Transition timed Petri nets with atomic firing.
Exercises:
The content of exercises is determined by the content of lectures. The main goals are:
Confirm understanding of theoretical knowledge by means of simple Petri nets designing and analysing.
Master the basic set of methods for state-space and algebraic analysis and design PN models.
Gain some experience with program systems supporting design, simulation and formal analysis of Petri net models.
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| Recommended or Required Reading |
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| Required Reading: |
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Markl, J.: Petriho sítě I. Lecture notes in Czech language, VŠB-TU Ostrava, http://drazdilova.cs.vsb.cz/Data/Sites/5/petrinet/petrinetsylabus.pdf
Reisig, Wolfgang: Understanding Petri Nets. 2013. |
Markl, J.: Petriho sítě I. Učební texty v elektronické podobě, VŠB-TU Ostrava, http://drazdilova.cs.vsb.cz/Data/Sites/5/petrinet/petrinetsylabus.pdf
Reisig, W.: Understanding Petri Nets, Springer-Verlag, 2013.
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| Recommended Reading: |
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R.David, H.Alla: Petri Nets and Grafcet /Tools for modelling discrete event systems/. Prentice Hall Ltd., 1992.
W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets I: Basic Models, LNCS 149, Springer, 1998.
W.Resig-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. John Wiley & Sons, 1995.
L.Priese, H.Wimmel: Theoretische Informatik Petri-Netze, Springer-Verlag Berlin Heidelberg 2003. |
R.David, H.Alla: Petri Nets and Grafcet /Tools for modelling discrete event systems/. Prentice Hall Ltd., 1992.
W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets I: Basic Models, LNCS 149, Springer, 1998.
W.Resig-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. John Wiley & Sons, 1995.
L.Priese, H.Wimmel: Theoretische Informatik Petri-Netze, Springer-Verlag Berlin Heidelberg 2003. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 40 (40) | 21 |
| Project | Project | 15 | 7 |
| Písemná práce | Written test | 25 | 12 |
| Examination | Examination | 60 | 30 |