, defined by Then their difference
* can be used to describe the reachable markings in terms of matrix multiplication, as follows.For any sequence of transitions , write for the vector that maps every transition to its number of occurrences in . Then, we have
* .

It must be required that is a firing sequence; allowing arbitrary sequences of transitions will generally produce a larger set.

Category-theoretic formulation

Meseguer and Montanari considered a kind of symmetric monoidal categories

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