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.
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.