Graphics Programs Reference
In-Depth Information
t
π
2
= 1
π
4
= 0
p
2
t
4
K
p
1
t
1
p
3
t
3
π
1
= 0
π
3
= 0
Figure 4.6: An example of modified P-invariant due to priority
However, if the priority structure is taken into account it is clear that also
the following P-invariant holds for this model:
M(p
3
)
≤
M
0
(p
3
) = 0
which implies that
M(p
1
) + M(p
2
) = K
.
The problem with such invariant relations is that no general algorithm is
known to compute a minimal set of independent invariants due to priority,
unlike for P- and T-semiflows. Hence, these properties must be proved on a
case-by-case basis, using the intuition and the ingenuity of the modeller.
4.4.2
Graph based analysis
Structural conflict — For PN models without priority, we defined the
notion of structural conflict relation (SC) to identify potentially conflicting
pairs of transitions by inspection of the net structure. Intuitively, two tran-
sitions t
i
and t
j
are in structural conflict if they share at least one input
place or if the output set of t
i
is not disjoint from the inhibition set of t
j
.
The definition does not change for Petri nets with priority.
In this case we can also define the indirect structural conflict (ISC) relation
that gives a necessary condition for two transitions to be in indirect effective
conflict relation in some marking. Intuitively, we have first to find a pair
of transitions t
k
and t
j
such that π
k
> π
j
and t
k
SCt
j
; then we have to
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