Petri net

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A Petri net is a mathematical representation of discrete distributed systems. Petri nets were defined in the 1960s by Carl Adam Petri. Because of their ability to express concurrent events, they generalize automata theory.

A Petri net consists of places, transitions and directed arcs. Arcs connect a place to a transition and vice versa. There are no arcs between two places, nor between two transitions. Places may contain any number of tokens. Transitions fire, that is consume tokens from input positions and produce tokens in output positions. A transition is enabled if there are tokens in every input position.

In its most basic form, tokens in a Petri net are indistinguishable from each other. More complex Petri nets add token coloring, activation time and hierarchy to the network.

Most problems for Petri Nets are decidable, such as Boundedness and Covering by constructing the Karp-Miller Tree. The reachability problem is known to be decidable, however in at least exponential time. All known general algorithms so far, however, employ non-primitive recursive space. Further details, also for special types of nets may be found in this survey.

Application areas

Programming tools

  1. ARP
  2. CoopnTools
  3. CPN-AMI
  4. CPN Tools
  5. CPN ML
  6. DPNSchematic
  7. EZPetri
  8. HiQPN-Tool
  9. HPSim
  10. Integrated Net Analyzer
  11. JARP
  12. JFern
  13. JPetriNet
  14. Maria
  15. Marigold
  16. Model-Checking Kit
  17. NEPTUN
  18. PED
  19. PEP
  20. PetriEdiSim
  21. Platform Independent Petri Net Editor
  22. Petrigen
  23. PetriSim
  24. Petri Net Browser
  25. Petri Net Kernel
  26. Petri Net Simulator
  27. PNES
  28. PNSim
  29. PNtalk
  30. Poseidon
  31. Poses++
  32. Predator
  33. PROD
  34. Romeo
  35. Renew
  36. SEA
  37. SimPRES
  38. SIPN-Editor
  39. SimulaWorks
  40. StpnPlay
  41. Tina
  42. Visual Object Net ++
  43. Visual SimNet
  44. WebSPN
  45. WINSIM
  46. Woflan
  47. XPetri
  48. XRL

See also

References

  • Harald Störrle: Models of Software Architecture - Design and Analysis with UML and Petri-Nets, Books on Demand GmbH, ISBN 3-8311-1330-0
  • Robert-Christoph Riemann: Modelling of Concurrent Systems: Structural and Semantical Methods in the High Level Petri Net Calculus, Herbert Utz Verlag, ISBN 3-89675-629-X
  • Kurt Jensen: Coloured Petri Nets, Springer Verlag, ISBN 3-540-62867-3
  • Janette Cardoso, Heloisa Camargo: Fuzziness in Petri Nets, Physica-Verlag, ISBN 3-7908-1158-0
  • James Lyle Peterson: Petri Net Theory and the Modeling of Systems, Prentice Hall, ISBN 0136619835
  • Wolfgang Reisig: A Primer in Petri Net Design, Springer-Verlag, ISBN 3-540-52044-9
  • Mengchu Zhou, Frank Dicesare: Petri Net Synthesis for Discrete Event Control of Manufacturing Systems, Kluwer Academic Publishers, ISBN 0792392892
  • Mengchu Zhou: Modeling, Simulation, & Control of Flexible Manufacturing Systems: A Petri Net Approach, World Scientific Publishing Company, ISBN 981023029X
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