Download High Level Petri Nets-Development and Software Engineering-Lecture Slides and more Slides Software Engineering in PDF only on Docsity!
High-Level Petri Nets
๏ The classical Petri net was invented by Carl Adam Petri in 1962. ๏ A lot of research has been conducted (>10,000 publications). ๏ Until 1985 it was mainly used by theoreticians. ๏ Since the 80โs their practical use has increased because of the introduction of high-level Petri nets and the availability of many tools. ๏ High-level Petri nets are Petri nets extended with ๏ colour (for the modelling of attributes) ๏ time (for performance analysis) ๏ hierarchy (for the structuring of models, DFD's)
Why do we need Petri Nets?
๏ Petri Nets can be used to rigorously define a system
(reducing ambiguity, making the operations of a system
clear, allowing us to prove properties of a system etc.)
๏ They are often used for distributed systems (with several
subsystems acting independently) and for systems with
resource sharing.
๏ Since there may be more than one transition in the Petri
Net active at the same time (and we do not know which
will โfireโ first), they are non-deterministic.
The Classical Petri Net Model
Another ( equivalent ) notation is to use a solid bar for the transitions: t p p p p t t We may use either notation since they are equivalent, sometimes one makes the diagram easier to read than the other.. The state of a Petri net is determined by the distribution of tokens over the places (we could represent the above state as (1,2,1,1) for (p1,p2,p3,p4))
Transition t1 has three input places (p1, p2 and p3) and two
output places (p3 and p4).
Place p3 is both an input and an output place of t1.
p p p p t COMP201 - Software Engineering 5
Transitions with Multiple
Inputs and Outputs
docsity.com
Firing
An enabled transition may fire.
Firing corresponds to consuming tokens from the input
places and producing tokens for the output places.
t2 t
Firing is atomic (only one transition fires at a time,
even if more than one is enabled)
An Example Petri Net
Creating/Consuming Tokens
COMP201 - Software Engineering 10
A transition without any input can fire at any time and
produces tokens in the connected places:
After firing 3 times.. T1 (^) T T1 T P1 (^) P P P docsity.com
Creating/Consuming Tokens
COMP201 - Software Engineering 11
A transition without any output must be enabled to fire
and deletes (or consumes) the incoming token(s):
After firing 3 times.. T1 (^) T T1 (^) T P1 (^) P P1 (^) P docsity.com
Modelling
States of a process can be modelled by tokens in places and state transitions leading from one state to another are modelled by transitions. ๏ Tokens can represent resources (humans, goods, machines), information, conditions or states of objects. ๏ Places represent buffers, channels, geographical locations, conditions or states. ๏ Transitions represent events, transformations or transportations.
Modelling a Traffic Light
Example: Traffic Light
rg red amber green yr gy
Two Traffic Lights
- rg - red - amber - green
- yr
- gy - rg - red - amber - green - yr - gy
- rg Two Safe Traffic Lights - red - amber - green
- yr
- gy - rg - red - amber - green - yr - gy
- rg Two Safe and Fair Traffic Lights - red - yellow - green
- yr
- gy - rg - red - yellow - green - yr - gy - safe - safe
Exercise
๏ 1) Can you prove that the Petri net from the previous slide
will never allow two red lights to be shown simultaneously?
