460-4146/01 – Petri Net (PES)
| Gurantor department | Department of Computer Science | Credits | 4 |
| Subject guarantor | Mgr. Pavla Dráždilová, Ph.D. | Subject version guarantor | Mgr. Pavla Dráždilová, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory type A |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2022/2023 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
Project work
Summary
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.
Compulsory literature:
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.
Recommended literature:
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.
Way of continuous check of knowledge in the course of semester
Continuous control of the study:
Problems given in exercises for independent (home) solution.
Working with software tools for Petri nets freely available on the web.
Semester work - design of a Petri net modeling a real problem and its analysis - the scope of the net is specified in agreement with the lecturer. Presentation of semester work.
Credit test at the end of the semester.
Credit conditions:
Obtaining at least 12 points (out of 25 possible) from the credit test at the end of the semester.
Obtaining at least 7 points (out of 15 possible) for the activity during the semester (solving the assigned tasks, knowledge of working with program tools, semester work).
The point evaluation of the whole subject consists of three items:
- Credit test at the end of the semester max 25 points (min 12 points),
- Semester work max 15 points (min 7 points),
- Final written exam max 60 points (min 30 points).
E-learning
Other requirements
Additional requirements are not placed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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