Graphics Programs Reference
In-Depth Information
Mutual exclusion between transitions t and t
0
in a given PN system is checked
by verifying that
6∃
M
∈
RS such that
{
t,t
0
}⊆
E(M)
In the readers & writers PN system with two customers, places p
6
and p
7
are mutually exclusive: this property ensures that the mutual exclusion
requirement between readers and writers in the modelled system is satisfied.
In the same PN system, transitions t
6
and t
7
are mutually exclusive, again
due to the impossibility for read and write accesses to be concurrently active.
Effective conflict and confusion — By inspection of the RG, using the
definition of EC, it is possible to identify all markings in which an effective
conflict arises among transitions; this requires the knowledge of the multiset
E(M) for each marking M
∈
RS.
Some effective conflicts that can be identified on the RG in Fig.
2.4
are:
t
2
EC(M
1
) t
3
, t
3
EC(M
1
) t
2
, t
4
EC(M
10
) t
5
. Notice that in this PN system
every effective conflict is symmetric.
Given a sequence of nonconflicting transition firings that cause the system
to move from marking M to M
0
, all the permutations of the sequence are
present in the RG between the same two markings. An example of this
firing t
3
and t
4
or by firing t
4
and t
3
.
It is important to notice that the EC relation does not capture every situa-
tion where a conflict between activities is solved, because of the possibility
of confusion. Confusion can be easily recognized on the RG by looking for
sets of transition sequences connecting the same two markings (containing
the same transitions although in different order) such that the patterns of
EC relations along the sequences are not the same. For example, there is
confusion in the sequences connecting M
5
and M
15
, since in the first se-
quence the EC relations between t
2
and t
3
at the first step, and between t
4
and t
5
at the second step, can be observed, while in the second sequence
only the effective conflict between t
2
and t
3
occurs. It can thus be deduced
that the conflict between t
4
and t
5
is hidden in the second sequence.
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