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A
A
A
B
B
C
C
D
D
D
Fig. 6.
Two fellows and their composition
If
L
,
M
and
N
are pairwise partners, then
L
⊕
M
is a partner of
N
and
⊕
is
associative i.e. (
L
N
).
Likewise, if
L
,
M
and
N
are pairwise fellows, then
L
⊕
M
)
⊕
N
=
L
⊕
(
M
⊕
⊕
M
is a fellow of
N
,
and
⊕
is associative, as described above.
4.5
Open Workflow Nets with Ports
Experience shows that the composition of services requires more flexibility than
offered by oWFN as defined above.
As an example, the composition
A
B
of the beverage service A and its
strategy B of Fig. 4 remains with a fairly unintuitive input place,
tea!
.Intu-
itively,
A
and
B
fit perfectly and consequently their composition
A
⊕
B
should
be a “closed” net, i.e. a net with empty interface. More flexibility is also re-
quired when the issue of
refinement
and
abstraction
istakenintoaccountinthe
sequel.
A fairly simple idea suces to provide oWFNs with the required degree of
flexible composition: The interface places are grouped into
ports
such that each
interface place belongs to exactly one port. The ports are decorated with (pair-
wise different)
names.
As an example, Fig. 7 equips the beverage service
A
of
Fig. 2 with three ports. One of them, “select”, contains two input places “cof-
fee” and “tea”. The other two, “pay” and “offer”, contain one element each.
The graphical representation is obvious. Correspondingly, Fig. 7 identifies three
ports for the strategy
B
of Fig. 4 one for each place.
Composition of two oWFNs with ports,
M
and
N
, say, then follows a simple
rule: Just glue ports of
M
and
N
with identical names. Gluing the ports of
M
and
N
with name
α
then means to identify a place
p
of the
α
-port of
M
with a place
q
of the
α
-port of
N
if and only if
p
=
q
, described in Sect. 4.3.
As an example, Fig. 8 shows the composition of the port equipped oWFN of
Fig. 7.
⊕
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