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(tk
2
, o
2
, u
2
)}. Note that the combination of user id, secret id,andtoken is
valid only when it represents the same user. For example, none of (u
1
, s
2
),
(u
2
, s
1
), (tk
1
, o
1
, u
2
), and (tk
2
, o
1
, u
1
) is valid using the aforementioned
criterion. Here, for simplicity, we assume two users and two orders.
However, in reality, there can be many users and many orders. We further
note that in the compatibility analysis we only need to know the color set
(i.e., type information) of each place rather than the number of colors a
color set has.
The elements
<
receive
>
,
<
reply
>
,
<
invoke
>
,
<
sequence
>
,
<
are
key ones to describe the control logic of BPEL. Because our work
tackles the issue of service compatibility in the control logic aspect, it
does not consider BPEL constructs such as compensation, fault han-
dler, assign, correlation set, link condition, and variables.
Figure 4.4 illustrates how to transform some BPEL elements into
SWF-net ones. BPEL activities and internal control logic are modeled
with internal places and transitions; the messages exchanged are
modeled with message places. In Figure 4.4, message places are expli-
citly denoted as pm, pm
1
and pm
2
, and other places are all internal
places. In Section 4.3 we illustrate how these two BPEL processes
illustrated in Figure 4.2 are transformed into SWF-nets.
if
>
,
<
pick
>
,
<
flow
>
,
<
while
>
,
<
repeatUntil
>
, and
<
link
>
4.2.2 CPN Formalism for Service Composition
Before defining service composition, we define the fusion of two
colored Petri nets.
Definition 4.2. (Fusion of colored Petri nets)
Given two colored
Petri nets N
i
¼
(P
i
, T
i
, F
i
,
S
i
, C
i
, M
0i
), i
¼
1 and 2, satisfying that P
C
¼
\
6¼
1
,
8
2
¼
¼
¼
P
1
P
2
p
P
C
, C
1
(p)
C
2
(p), andM
01
(p)
M
02
(p), N
(P, T,
S
F,
, C, M
0
) is the fusion of N
1
and N
2
via places if the following
requirements are satisfied:
1. P
¼
P
1
[
P
2
,
2. T
¼
T
1
[
T
2
, T
1
\
T
2
¼
1
,
3. F
¼
F
1
[
F
2
,
4.
8
p
2
P,ifp
2
P
1
, C(p)
¼
C
1
(p); else C(p)
¼
C
2
(p), and
5.
8
p
2
P,ifp
2
P
1
, M
0
(p)
¼
M
01
(p); else M
0
(p)
¼
M
02
(p).
