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⊆(S×T)∪(T×S).
   5. M_0:S→ℕ is an initial marking, where for each place s∈S, there are n_s∈ℕ tokens.
   6. W:F→ℕ⁺ is a set of arc weights, which assigns to each arc f∈F some n∈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.