Petri net

Etymology
Named after (1926–2010), German mathematician and computer scientist.

Noun

 * 1) One of several mathematical representations of discrete distributed systems, a 5-tuple $$(S,T,F,M_0,W)\!$$, where
 * 2) $$S$$ is a set of places.
 * 3) $$T$$ is a set of transitions.
 * 4) $$S$$ and $$T$$ are disjoint, i.e. no object can be both a place and a transition
 * 5) $$F$$ 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: $$F \subseteq (S \times T) \cup (T \times S)$$.
 * 6) $$M_0 : S \to \mathbb{N}$$ is an initial marking, where for each place $$s \in S$$, there are $$n_s \in \mathbb{N}$$ tokens.
 * 7) $$W : F \to \mathbb{N^+}$$ 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.

Translations

 * Czech: Petriho síť
 * German: Petri-Netz