| Course Unit Code | 460-4146/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type A |
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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
1. The problem of analysis, modelling and design of distributed systems with synchronization, parallelism and hierarchical structure. Petri nets (PN) as a suitable tool to solve this problem.
2. Introduction to modelling using Petri nets. P/T Petri nets. Petri nets with inhibitory edges, with priorities or resets arcs.
3. Petri net structure and system. Statics and dynamics of Petri nets. State (marking) and set of achievable states of the PN-system. Reachability graph.
4. Enabling degree of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
5. Properties of Petri nets: boundness, safeness, liveness, reversibility, deadlock-freeness, conservatism. States analysis of Petri nets using a graph of reachability or coverage.
6. Structural analysis of Petri nets. Graph methods and algebraic methods. Traps and cotraps. Fundamental equation.
7. P-invariants and conservative network components. T-invariants and network repetition components. Dual Petri nets.
8. Special types of Petri nets: state-machine PN, synchronization PN and free choice PN.
9. Synthesis of safe, live and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
10. Languages of Petri nets and their relation to Chomsky's hierarchy of languages.
11. Introduction to modelling using higher-level Petri nets. Timed Petri nets.
12. Coloured Petri nets.
13. State space of colored Petri nets.
Exercises:
1. Examples of modeling and design of systems with parallelism and hierachical structure using Petri nets.
2. Examples of P/T Petri nets and Petri nets with inhibitory arcs, Petri nets with priorities.
3. Examples of the structure and system of a Petri net. Statics and dynamics of Petri nets. State (marking) and set of reachable states of the PN-system. Construction of reachability or coverage graph.
4. Examples of the degree of feasibility of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
5. Examples for determining the properties of Petri nets: boundness, safeness, liveness, reversibility, deadlock-freeness, conservatism. Accessibility problem and coverage problem. Analysis of Petri net's state space.
6. Examples of structural analysis of Petri nets. Graph methods and algebraic methods. Locks and traps. Fundamental equations.
7. Determination of P-invariants and conservative components of the network. Determination of T-invariants and repetitive components of the network. Dual Petri nets. Analysis of Petri nets based on P(T)-invariants.
8. Examples of special types of Petri nets: state-machine nets, synchronization nets and free choice nets.
9. Examples of synthesis of safe, living and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
10. Generation and recognition of Petri net's languages.
11. Examples of special extensions of the concept of Petri nets: timed Petri nets. CPN tool as a tool for editing, simulation and analysis of color Petri nets.
12. Examples of colored Petri nets.
13. Examples of analysis of colored Petri net's state space. |
| Recommended or Required Reading |
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| Required Reading: |
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1. MARKL, J.: Petriho sítě I. Lecture notes in Czech language, VŠB-TU Ostrava, http://drazdilova.cs.vsb.cz/Data/Sites/5/petrinet/petrinetsylabus.pdf
2. REISIG, Wolfgang: Understanding Petri Nets. 2013. |
1. MARKL, J.: Petriho sítě I. Učební texty v elektronické podobě, VŠB-TU Ostrava, http://drazdilova.cs.vsb.cz/Data/Sites/5/petrinet/petrinetsylabus.pdf
2. REISIG, W.: Understanding Petri Nets, Springer-Verlag, 2013.
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| Recommended Reading: |
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1. K. Jensen, G. Rozenberg: High-level Petri nets: theory and application. Springer Science & Business Media, 2012.
2. R.David, H.Alla: Petri Nets and Grafcet /Tools for modelling discrete event systems/. Prentice Hall Ltd., 1992.
3. W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets I: Basic Models, LNCS 149, Springer, 1998.
4. W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets II: Applications, LNCS 1492, Springer, 1998.
5. M.A.Marsan, G.Balbo, G.Conte, S.Donatelli, G.Franceschinis: Modelling with Generalised Stochastic Petri Nets. John Wiley & Sons, 1995.
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1. K. Jensen, G. Rozenberg: High-level Petri nets: theory and application. Springer Science & Business Media, 2012.
2. R.David, H.Alla: Petri Nets and Grafcet /Tools for modelling discrete event systems/. Prentice Hall Ltd., 1992.
3. W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets I: Basic Models, LNCS 149, Springer, 1998.
4. W.Resig-G.Rozenberg (Eds.): Lectures on Petri Nets II: Applications, LNCS 1492, Springer, 1998.
5. M.A.Marsan, G.Balbo, G.Conte, S.Donatelli, G.Franceschinis: Modelling with Generalised Stochastic Petri Nets. John Wiley & Sons, 1995.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| 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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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 40 | 21 |
| Examination | Examination | 60 | 30 |