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Introduction to Petri Nets. Hugo Andrés López [email protected]. Plan for lectures. 6th November ‘07 Informal Introduction, Intuitions. Formal definition Properties for PNets. 8th November ’07 Examples on specifications. Applications. Petri Nets Variants. Advantages, Limitations. - PowerPoint PPT Presentation
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Plan for lectures
6th November ‘07
Informal Introduction, Intuitions.
Formal definition
Properties for PNets.
8th November ’07
Examples on specifications.
Applications.
Petri Nets Variants.
Advantages, Limitations.
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A little of HistoryC.A. Petri proposes a new model for information flow (early 60’s).
Main ideas: Modelling Systems with asynchronous and Concurrent executions as graphs.
Holt and Petri: “net theory” (mid 70’s)
MIT and ADR: Research in Petri Net Properties and Relations with Automata Theory
Nowadays: Event Structures, Bigraphs, (new) flowcharts, relations with Process algebra.
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Intuitions
A Petri Net (PN) is a formalism for representing concurrent programs in terms of events and transitions.
Defining Static Properties (Structural).
Dynamic Properties (Behavioural).
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Producer - Consumers PNET
Static Structure
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Producer - Consumers PNET
Markings introducethe dynamics of
the system
Initial Marking
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Producer - Consumers PNET (Non-Determinism)
Firing T1 again will leadto multiple production
of tokens in P3
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Producer - Consumers PNET (Non-Determinism)
Firing T6 disable T3Firing T3 disable T6
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PNet Evolutions
Resembles a board game.
A transition can be fired if their input events are marked.
Possible Scenarios:
Concurrent Execution Conflicting Execution
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Formal Model for PNets
Structure
Dynamics
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Occurrence Rule
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Occurrences and Reachability
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Example: An Scheduler
Resources:
A buffer of input processes with k=4.
A dual-core processor.
Buffer of Results with k=4.
Processes are independent.
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Behavioural Properties of Marked Petri Nets
•A marked p/t-net is
terminatingterminating – if there is no infinite occurrence sequence deadlock-freedeadlock-free – if each reachable marking enables a transition livelive – if each reachable marking enables an occurrence sequence containing all transitions boundedbounded - if, for each place p, there is a bound b(p) s.t. m(p) <= b(p) for every reachable marking m1-Safe1-Safe - if b(s) = 1 is a bound for each place sReversibleReversible – if m0 is reachable from each other reachable marking
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A vending machine
5c
Take 15c bar
Deposit 5c
0c
Deposit 10c
Deposit 5c
10c
Deposit 10c
Deposit5c
Deposit 10c20c
Deposit5c
15c
Take 20c bar
-VM is Deadlock-free.
t8
t1
p1
t2
p2
t3
p3
t4
t5
t6 p5
t7
p4
t9
Every marking generated from m0 enables a transition
-VM is Live.
The occurrences generated by m0 contains all the transitions
-VM is bounded by 1 (1-safe)
there are no induced tokens, the constraints used in m0 holds for the system.
-VM is Reversible
It is possible to go back to m0 from every
marking derived from
m0
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Exercise
Show by inspection (or other methods) the properties that holds for the scheduler example.
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BibliographyJ.L. Peterson. “Petri Nets”. Computing Surveys, Vol. 9 No. 3, 1977.
A. Kondratyev et al. “The use of Petri nets for the design and verification of asynchronous circuits and systems”. Journal of Circuits Systems and Computers. 1998.
Balbo et al. Lecture notes of the 21st. Int. Conference on Application and Theory of Petri Nets. 2000.
The World of Petri nets:http://www.daimi.au.dk/PetriNets/
C. Ling. The Petri Net Method. http://www.utdallas.edu/~gupta/courses/semath/petri.ppt