# 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 $(S,T,F,M_0,W)\!$, where
1. $S$ is a set of places.
2. $T$ is a set of transitions.
3. $S$ and $T$ are disjoint, i.e. no object can be both a place and a transition
4. $F$ is a set of arcs known as a flow relation. The set $F$ is subject to the constraint that no arc may connect two places or two transitions, or more formally: $F \subseteq (S \times T) \cup (T \times S)$.
5. $M_0 : S \to \mathbb{N}$ is an initial marking, where for each place $s \in S$, there are $n_s \in \mathbb{N}$ tokens.
6. $W : F \to \mathbb{N^+}$ is a set of arc weights, which assigns to each arc $f \in F$ some $n \in \mathbb{N^+}$ 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.