xoEPC - Jan Mendling

3.4. EPC Semantics 55
c1
c2
e1
f1
e2
f2
e4
a1
a2
a3
a4
a5
a6
f3
e3
a9
a8
a7
(a) One OR-Join Loop EPC (b) Two OR-Join Loop EPC
c3
c4
e5
f5
e6
f6
e9
a11
a12
a13
a14
a15
a16
a23 a24
Figure 3.6: EPCs (a) with one OR-join and (b) with two OR-joins on the loop
from function f1 to the OR-join c1. The question is whether c1 can fire. If it could fire,
then it would be possible for a token to arrive on arc a9 from f3 to the join. This would
imply that it should wait and not fire. On the other hand, if it must wait, it is not possible
that a token might arrive at a9. Figure 3.6(b) depicts an EPC with two OR-joins, c3 and
c5, on a loop which are both enabled (cf. [ADK02]). Here, the question is whether both
or none of them can fire. Since the situation is symmetrical, it seems unreasonable that
only one of them should be allowed to fire.
The situation might be even more complicated, as Figure 3.7 illustrates (cf. [Kin03,
Kin04, Kin06]). This EPC includes a loop with three OR-joins: c1, c3, and c5, all of
which are enabled. Following the informal semantics, the first OR-join c1 is allowed to
fire if it is not possible for a token to arrive on arc a21 from the AND-split c6. To put it
differently, if c1 is allowed to fire, it is possible for a token to arrive on arc a7 that leads
to the OR-join c3. Furthermore, the OR-join c5 could eventually fire. Finally, the first
OR-join c1 would have to wait for that token before firing. To put it short, if c1 could
fire, it would have to wait. One can show that this also holds the other way around: if it
e7
f7
e8
f8
e10
a17
a18
a19
a20
a21
a22
c5
c6