PETRI NETS AND THEIR PROPERTIES - Modelling with Generalised Stochastic Petri Nets - page 24

Figure 2.4: The reachability graph of the readers & writers PN system
obtained from the PN model in Fig. 2.1 by letting K = 2

nodes is RS, and whose set of arcs A is defined as follows:

• A ⊆ RS × RS × T
•h M i ,M j ,t i∈ A ⇔ M i [t i M j

(2.6)

M 0 is taken as the initial node of the graph.

We use the notation h M i ,M j ,t i to indicate that a directed arc connects the
node corresponding to marking M i to the node corresponding to marking
M j , and a label t is associated with the arc. Fig. 2.4 shows the RG of the
readers & writers PN system corresponding to the RS of Fig. 2.3.
The algorithm for the construction of the RG is quite similar to that for the
computation of the RS. The only difference is that, in the construction of
the RG, the arcs connecting the markings must be stored. At each iteration,
and for each reached marking, besides adding the marking (if new) to the
RS, the algorithm also adds one arc labelled with the proper transition name
to the set A.