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Petri net

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Noun

Singular
Petri net

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

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