# Petri net

## English

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### Etymology

Named after Carl Adam Petri (1926–2010), German mathematician and computer scientist.

### Noun

Petri net (plural Petri nets)

1. One of several mathematical representations of discrete distributed systems, a 5-tuple ${\displaystyle (S,T,F,M_{0},W)\!}$, where
1. ${\displaystyle S}$ is a set of places.
2. ${\displaystyle T}$ is a set of transitions.
3. ${\displaystyle S}$ and ${\displaystyle T}$ are disjoint, i.e. no object can be both a place and a transition
4. ${\displaystyle F}$ is a set of arcs known as a flow relation. The set ${\displaystyle F}$ is subject to the constraint that no arc may connect two places or two transitions, or more formally: ${\displaystyle F\subseteq (S\times T)\cup (T\times S)}$.
5. ${\displaystyle M_{0}:S\to \mathbb {N} }$ is an initial marking, where for each place ${\displaystyle s\in S}$, there are ${\displaystyle n_{s}\in \mathbb {N} }$ tokens.
6. ${\displaystyle W:F\to \mathbb {N^{+}} }$ is a set of arc weights, which assigns to each arc ${\displaystyle f\in F}$ some ${\displaystyle n\in \mathbb {N^{+}} }$ denoting how many tokens are consumed from a place by a transition, or alternatively, how many tokens are produced by a transition and put into each place.