Information Technology Reference
In-Depth Information
Remarks:
1.
Intuitively, service composition is used to synthesize two
SWF-nets via message places with identical color set and
contrary polarity.
2.
If P
C1
\
P
C2
6¼
1
;8
p
2
P
C1
\
P
C2
, p in N
1
and p in N
2
have
contrary polarity,
that
is,
C
1
p
ðÞC
2
p
ðÞ¼
1, and in
M
,
C
M
p
ðÞ¼
0.
3. N
1
P
C
N
2
is a special case of N
1
P
C1
M
P
C2
N
2
, where
P
C
¼
P
C1
¼
P
C2
, and T
m
¼
F
m
¼
1
.
Now we can give the definition of service compatibility.
Definition 4.6. (Compatibility of Two Services)
Given two SWF-
nets N
1
and N
2
, N is their composition, that is, N
¼
N
1
P
C
N
2
.
M
0
M
2e
. M
i0
and M
ie
are the initial
and end markings of N
i
, respectively. N
1
is compatible with N
2
with
respect to P
C
if the reachability graph of N is well formed, that is,
¼
M
10
M
20
,andM
e
¼
M
1e
8
2 R
ð
;
Þ
, there is a firing sequence
s
and a marking M
s
1.
M
N
M
0
such that M
½
si
M
s
and M
s
M
e
; and
2. Given M
2 Rð
N
;
M
0
Þ
with M
M
e
,if
9
p
2
P
;
M
ð
p
Þ >
M
e
ð
p
Þ;
then p
2
P
M1
[
P
M2
.
In addition, two SWF-nets, N
1
and N
2
, are compatible with mediator
M
if the reachability graph of N
1
P
C1
M
P
C2
N
2
is well formed.
The meaning of Definition 4.6 can be explained as follows:
1. Once the interaction begins, it will complete successfully.
2. When the interaction completes, both services reach their
ending state, and possibly there are remaining messages that
are sent out by one service but not consumed by the other.
Weak soundness [56] requires a stronger condition than the afore-
mentioned compatibility does, and soundness [81] requires even more
thanweak soundness does. This relaxation roots from the observation that
services aremore autonomous and loosely coupled. Hence, Definition 4.6
