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Petri Net

Type of study Follow-up Master
Language of instruction English
Code 460-4146/02
Abbreviation PES
Course title Petri Net
Credits 4
Coordinating department Department of Computer Science
Course coordinator doc. Mgr. Pavla Dráždilová, Ph.D.

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.

E-learning

Study materials are available in MS Teams for students of the course.

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.

Advised 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.