Graphics Programs Reference
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p
1
t
1
p
3
π
3
= 2
π
1
= 1
t
3
p
5
π
2
= 1
p
2
t
2
p
4
Figure 4.2: An example of indirect conflict
3. the firing of t
3
removes the token from place p
2
, thus taking concession
away from transition t
2
This sequence of events is not interruptible after the firing of t
1
, due to
the priority structure, and eventually results in the disabling of t
2
through
the firing of a higher priority transition (the example can be extended to
a sequence of higher priority transitions).
We call this situation indirect
effective conflict between t
1
and t
2
.
Definition 4.2.2 For any priority PN model
M
π
,
∀
t
i
,t
j
∈
T such that
t
i
6
= t
j
,
∀
M : P
→
IN, transition t
i
is in indirect effective conflict with t
j
in
marking M (denoted t
i
IEC(M) t
j
) iff
•
t
j
has concession in M
•
t
i
∈
E(M)
•∃
σ = t
(1)
,...,t
(k)
such that
1. M[t
i
i
M
(1)
[t
(1)
i
...M
(k)
[t
(k)
i
M
0
, and
2.
∀
1
≤
h
≤
k,π
(h)
> π
j
, and
3. t
(k)
EC(M
(k)
)t
j
.
Notice that this situation cannot occur if priority is removed: if all tran-
sitions are at the same priority level, the sequence “t
1
followed by t
3
” is
interruptible, and a “normal” effective conflict exists only between t
2
and
t
3
. Indirect effective conflict is the proper generalization of the concept
of nonprioritized conflict: in the above example a priority level 1 observer
would not see the firing of t
3
, hence from his point of view, t
1
and t
2
actu-
ally are in EC relation in marking M. In the modified readers & writers
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