Petri net

S is a set of places.

T is a set of transitions.

S and T are disjoint, i.e. no object can be both a place and a transition

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).

M_0:S→ℕ is an initial marking, where for each place s∈S, there are n_s∈ℕ tokens.

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.