Petri Net - Formulation in Terms of Vectors and Matrices

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.