# Place/Transition (P/T) Systems

## Definition

(according to [bd92])

### Transition Rule (interleaving semantics)

Another transition rule given by [jv81] and [win85] differs from the one given in the enabling of "side conditions":

### Concurrent behaviour (step semantics)

Definition according to [dev90] which corresponds to the definition of a "simple step" in [rei85b].

This definition may be extended to a "bag" of transitions, that is informally, to a set with multiplicity (or multiset) which corresponds to the notion of "step" in [bf86]:

## Sample Net

(from [rei87])

## Tools

CPN/AMI CPN/AMI is an interactive toolkit for creation, manipulation, simulation, transformation, analysis and checking of typed graphs with attributes.

MOBY is a simulation tool based on object-oriented features.

POSES is a simulation and development system.

PENECA is a simulation tool.

PESIM is a tool for the structural and performance analysis of nets.

PNS is a public domain Petri Net simulation tool.

TORAS is a tool for analyzing Petri Nets using reachability analysis.

GRAF is an environment for the analysis and simulation of hierarchical nets.

CAPSNET is a simulation tool.

FORSEE is a collection of tools for the development of systems.

INA is a descriptive analysis tool.

PAPETRI is an integrated environment for editing and anlysing Nets.

PEP is a verification tool for parallel systems.

WINPETRI is an analysis tool for Windows.
## References

- W. Reisig:
`Place/Transition Systems` [rei87]
- L. Bernardinello, F. De Cindio:
`A survey of Basic Net Models and Modular Net Classes` [bd92]
- M. Jantzen, R. Valk:
`Formal properties of Place/Transition Nets` [jv81]
- G. Winskel:
`Categories of Models for Concurrency` [win85]
- R. Devillers:
`The semantics of capacities in P/T Nets` [dev90]
- E. Best, C. Fernandez:
`Notations and terminology on Petri Net Theory` [bf86]
- W. Reisig:
`On the semantics of Petri Nets` [rei85b]
- K. Lautenbach:
`Linear Algebraic Techniques for Place/Transition Nets` [lau87]

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