Graphics Programs Reference
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π
1
= 0
π
2
= 1
t
1
p
1
t
2
Figure 4.3: An example of boundedness due to priority
t
1
p
1
t
2
Figure 4.4: An example of boundedness due to inhibitor arcs
model that is not live, may become live after the addition of an appropriate
priority structure. Moreover, even if the net with priority is live, the priority
structure could change the maximum enabling degree of transitions. For
example, the PN model in Fig.
4.3
shows a PN model with priority in which
t
2
is 1-live, while in the corresponding PN model without priority the same
transition would be
∞
-live. The reason is that the liveness degree of a
transition is related to the possibility of accumulating tokens in its input
places. Let us consider the subnet in Fig.
4.5:
input place p of transition t
i
receives tokens only from a transition t
j
; let's assume that π
j
< π
i
. Tokens
can accumulate in place p, only if the marking of some other input place
p
0
prevents the enabling of t
i
immediately after the firing of t
j
, and at the
same time no other transition sharing an input place p with t
i
can take the
tokens out from it.
p
0
π
j
π
i
p
t
j
t
i
Figure 4.5:
Influence of the priority on the maximum enabling degree of
transitions
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