Lectures
- 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.
- Introduction to modelling using Petri nets. P/T Petri nets. Petri nets with inhibitory edges, with priorities or resets arcs.
- Petri net structure and system. Statics and dynamics of Petri nets. State (marking) and set of achievable states of the PN-system. Reachability graph.
- Enabling degree of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
- Properties of Petri nets: boundness, safeness, liveness, reversibility, deadlock-freeness, conservatism. States analysis of Petri nets using a graph of reachability or coverage.
- Structural analysis of Petri nets. Graph methods and algebraic methods. Traps and cotraps. Fundamental equation.
- P-invariants and conservative network components. T-invariants and network repetition components. Dual Petri nets.
- Special types of Petri nets: state-machine PN, synchronization PN and free choice PN.
- Synthesis of safe, live and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
- Languages of Petri nets and their relation to Chomsky's hierarchy of languages.
- Introduction to modelling using higher-level Petri nets. Timed Petri nets.
- Coloured Petri nets.
- State space of colored Petri nets.
Exercises:
- Examples of modeling and design of systems with parallelism and hierachical structure using Petri nets.
- Examples of P/T Petri nets and Petri nets with inhibitory arcs, Petri nets with priorities.
- 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.
- Examples of the degree of feasibility of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
- 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.
- Examples of structural analysis of Petri nets. Graph methods and algebraic methods. Locks and traps. Fundamental equations.
- 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.
- Examples of special types of Petri nets: state-machine nets, synchronization nets and free choice nets.
- Examples of synthesis of safe, living and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
- Generation and recognition of Petri net's languages.
- 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.
- Examples of colored Petri nets.
- Examples of analysis of colored Petri net's state space.
- 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.
- Introduction to modelling using Petri nets. P/T Petri nets. Petri nets with inhibitory edges, with priorities or resets arcs.
- Petri net structure and system. Statics and dynamics of Petri nets. State (marking) and set of achievable states of the PN-system. Reachability graph.
- Enabling degree of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
- Properties of Petri nets: boundness, safeness, liveness, reversibility, deadlock-freeness, conservatism. States analysis of Petri nets using a graph of reachability or coverage.
- Structural analysis of Petri nets. Graph methods and algebraic methods. Traps and cotraps. Fundamental equation.
- P-invariants and conservative network components. T-invariants and network repetition components. Dual Petri nets.
- Special types of Petri nets: state-machine PN, synchronization PN and free choice PN.
- Synthesis of safe, live and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
- Languages of Petri nets and their relation to Chomsky's hierarchy of languages.
- Introduction to modelling using higher-level Petri nets. Timed Petri nets.
- Coloured Petri nets.
- State space of colored Petri nets.
Exercises:
- Examples of modeling and design of systems with parallelism and hierachical structure using Petri nets.
- Examples of P/T Petri nets and Petri nets with inhibitory arcs, Petri nets with priorities.
- 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.
- Examples of the degree of feasibility of a transition and relation defined on the set of all transitions: conflict, concurrency, causality, exclusivity, confusion.
- 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.
- Examples of structural analysis of Petri nets. Graph methods and algebraic methods. Locks and traps. Fundamental equations.
- 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.
- Examples of special types of Petri nets: state-machine nets, synchronization nets and free choice nets.
- Examples of synthesis of safe, living and reversible Petri nets. Simple hierarchization by the method of substitution of places and transitions.
- Generation and recognition of Petri net's languages.
- 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.
- Examples of colored Petri nets.
- Examples of analysis of colored Petri net's state space.