petri nets by barkatllah
TRANSCRIPT
Petri NetsGroup A:
Prepared by:
Barkatullah
Memebers:
Waqas Ahmad
Nawab Shah
Aziz Khan
Ijaz Ali
Najeebullah
Irfan-ul-Haq
Arsalan khan
Yasir Raza Khan
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).
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.
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.
BipartiteMEANS
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
Activity Diagram
A Petri Net Specification ...
consists of three types of components: places (circles), transitions (rectangles/bar) and arcs (arrows): Places represent possible states of the
system
Transitions are events or actions which cause the change of state
Every arc simply connects a place with a transition or a transition with a place.
A place
A transition
A token
Input Arc
Output Arc
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.
A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2
A chemical process example
C + O2 → CO2
C
O2
Fired
CO2
A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
C
O2
Fired
CO2
NaOH
NaHCO3
A chemical process example
O2
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2
C
O2
Fired
CO2
NaOH
NaHCO3
HCl
H2O
NaCl
A chemical process example
C + O2 → CO2
CO2 + NaOH → NaHCO3
NaHCO3 + HCl → H2O + NaCl + CO2
C
O2
CO2
NaOH
NaHCO3
HCl
H2O
NaCl
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.
Disease processes Example
Production
Healthy
Death
Infection
Infected
virion
Reproduction
Death Death
copy
copy
a
a
a
ab
b
b
b + +
- -
/
!=0
=0
NaN
X