14 Facts About Petri nets

Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.

Unlike these standards, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis.

Petri nets are state-transition systems that extend a class of nets called elementary nets.

Similarly, if a Petri nets net is not an elementary net, then the multiset M can be interpreted as representing a non-singleton set of configurations.

One thing that makes Petri nets interesting is that they provide a balance between modeling power and analyzability: many things one would like to know about concurrent systems can be automatically determined for Petri nets, although some of those things are very expensive to determine in the general case.

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Several subclasses of Petri nets have been studied that can still model interesting classes of concurrent systems, while these problems become easier.

Petri nets can be described as having different degrees of liveness.

Petri nets net is called k-bounded, safe, or bounded when all of its places are.

Petri nets net is bounded if and only if its reachability graph is finite.

Extensions that cannot be transformed into Petri nets are sometimes very powerful, but usually lack the full range of mathematical tools available to analyse ordinary Petri nets.

Workflow nets are a subclass of Petri nets intending to model the workflow of process activities.

The WF-Petri nets have additional structural and operational requirements, mainly the addition of a single input place with no previous transitions, and output place with no following transitions.

WF-Petri nets have the soundness property, indicating that a process with a start marking of k tokens in its source place, can reach the termination state marking with k tokens in its sink place .

WRI-WF-Petri nets are G-sound, therefore by using only WRI-WF-net building blocks, one can get WF-Petri nets that are G-sound by construction.