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.
More complex Petri nets add hierarchy to the network.
Tokens in a standard Petri net are indistinguishable from each other. Coloured Petri Nets, often designated with the acronym CPN, add token coloring . Firing of a transition in both standard and coloured Petri nets is fully determined by the presence of tokens in the input places. Stochastic Petri Nets add non-deterministic timing .
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 may be found in this survey [1] and in Kurt Jensen Coloured Petri Nets, and in M. Ajmone Marsan et al. Modelling with Generalized Stochastic Petri Nets.
Application areas
Programming tools
- ARP
- CoopnTools
- CPN-AMI
- CPN Tools
- CPN ML
- DPNSchematic
- EZPetri
- HiQPN-Tool
- HPSim
- Integrated Net Analyzer
- JARP
- JFern
- JPetriNet
- Maria
- Marigold
- Model-Checking Kit
- NEPTUN
- PED
- PEP
- PetriEdiSim
- Platform Independent Petri Net Editor
- Petrigen
- PetriSim
- Petri Net Browser
- Petri Net Kernel
- Petri Net Simulator
- PNES
- PNSim
- PNtalk
- Poseidon
- Poses++
- Predator
- PROD
- Romeo
- Renew
- SEA
- SimPRES
- SIPN-Editor
- SimulaWorks
- StpnPlay
- Tina
- Visual Object Net ++
- Visual SimNet
- WebSPN
- WINSIM
- Woflan
- XPetri
- 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
External links