Graphics Programs Reference
In-Depth Information
p 1
p 1
p 1
p 1
m n
m
p 3
p 3
p 3
t
t
t
t
n m
n
p 2
p 2
p 2
p 2
(a)
(b)
(c)
(d)
Figure 2.12: Petri nets with equal incidence matrix
incidence matrix is always given by:
t
p 1 1
p 2
C =
+1
(m n)
p 3
It follows that during the construction of the incidence matrix, some infor-
mation is lost with respect to that contained in the Petri net, both because
of inhibitor arcs, and because of places that belong to the input and output
sets of the same transition.
The loss of information due to the fact that the incidence matrix does not
capture the effect of inhibitor and test arcs is due to the decision on dis-
regarding any information on the marking. Indeed, when the marking is
neglected, we can no longer rely on the enabling aspects (that in general
depend on the particular initial marking), but only on the state transforma-
tion aspects, that are marking independent (a transition either fires or not,
but its firing always causes the same state change).
Referring again to our basic example, we can observe that its incidence
matrix is the following:
t 1 t 2 t 3 t 4 t 5 t 6 t 7
p 1 1
0
0
0
0
+1
+1
+1 1 1
p 2
0
0
0
0
0 1
p 3
0
+1
0
0
0
C =
0 1
p 4
0
0
+1
0
0
0 1
p 5
0
0
0
0
+1
0 1
p 6
0
0
0
+1
0
0 1
p 7
0
0
0
0
+1
 
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