Formulation in Terms of Vectors and Matrices
The markings of a Petri net can be regarded as vectors of nonnegative integers of length .
Its transition relation can be described as a pair of by matrices:
- , defined by
- , 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 w, write for the vector that maps every transition to its number of occurrences in w. Then, we have
- is a firing sequence of .
Note that it must be required that w is a firing sequence; allowing arbitrary sequences of transitions will generally produce a larger set.
Read more about this topic: Petri Net
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