Petri nets by Barkatllah


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Petri nets by Barkatllah

  1. 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. 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. 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. 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. 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. 6. Activity Diagram
  7. 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. 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. 9. A chemical process example C + O2 → CO2 CO2 + NaOH → NaHCO3 NaHCO3 + HCl → H2O + NaCl + CO2
  10. 10. A chemical process example C + O2 → CO2 C Fired CO2 O2
  11. 11. A chemical process example C + O2 → CO2 CO2 + NaOH → NaHCO3 NaOH C Fired CO2 O2 NaHCO3
  12. 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. 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. 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. 15. Disease processes Example Production Death Healthy Infection Death Infected virion Reproduction Death
  16. 16. a copy + / a+ b X a copy !=0 b - a- b NaN b =0