1. Petri Nets
Group A:
Prepared by:
Barkatullah
Memebers:
Waqas Ahmad
Nawab Shah
Aziz Khan
Ijaz Ali
Najeebullah
Irfan-ul-Haq
Arsalan khan
Yasir Raza Khan

2. PETRI NETS

A Petri net (also known as a place/transition net or P/T net) is one of
several mathematical modeling languages for the description
of distributed systems.

Used as a visual communication aid to model the system behavior.

A Petri net is a directed bipartite graph, in which the nodes represent
transitions (i.e. events that may occur, signified by bars) and places
(i.e. conditions, signified by circles).

The directed arcs describe which places are pre- and/or
postconditions for which transitions (signified by arrows).

3. Applications:

Like industry standards such as UML activity diagrams Petri nets offer
a graphical notation for stepwise processes that include iteration,
and concurrent execution.

modelling concurrent and/or distributed systems

communication protocols, computer networks, manufacturing system, public
transport systems etc.

4. Carl Adam Petri

Carl Adam Petri (12 July 1926 – 2 July
2010) was
a German mathematician and computer
scientist.

Petri nets were invented in August 1939 at
the age of 13 for the purpose of describing
chemical processes..

He documented the Petri net in 1962 as
part of his PhD thesis.

5. Bipartite
MEANS
Having or consisting of two parts.
A bipartite graph, also called a bigraph, is
a set of graph vertices decomposed into two
disjoint sets such that no two graph vertices
within the same set are adjacent.
OR
a bipartite graph (or bigraph) is a graph
whose vertices can be divided into two
disjoint sets U and V such that every edge
connects a vertex in U to one in V

6. Activity Diagram

7. A Petri Net Specification ...
A place

consists of three types of components:
places (circles), transitions
(rectangles/bar) and arcs (arrows):

Transitions are events or actions which cause the
change of state
A transition
Places represent possible states of the system

Input Arc

Every arc simply connects a place with a
transition or a transition with a place.
Output Arc
A token

8. A Change of State …

is denoted by a movement of token from place to place
and is caused by the firing of a transition.

The firing represents an occurrence of the event or an
action taken.

The firing is subject to the input conditions, denoted by
token availability.

A transition is firable or enabled when there are
sufficient tokens in its input places.

After firing, tokens will be transferred from the input
places (old state) to the output places, denoting the
new state.

9. A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2

10. A chemical process example
C + O2 → CO2
C
Fired
CO2
O2

11. A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaOH
C
Fired
CO2
O2
NaHCO3

12. A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2
NaOH
HCl
H2O
C
Fired
CO2
O2
O2
NaHCO3
NaCl

13. A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2
NaOH
HCl
H2O
C
CO2
O2
NaHCO3
NaCl

14. Disease processes Example

An example discussed on Azimuth. It describes the virus
that causes AIDS. The species
are healthy cell, infected cell, and virion. The transitions
are for infection, production of healthy cells, reproduction
of virions within an infected cell, death of healthy cells,
death of infected cells, and death of virions.

15. Disease processes Example
Production
Death
Healthy
Infection
Death
Infected
virion
Reproduction
Death

16. a
copy
+
/
a+ b
X
a
copy
!=0
b
-
a- b
NaN
b
=0