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signatures. We use previously defined terminological concepts
T
(Def. 1) as the
set of input symbols (i.e. alphabet) to initiate state changes. A path through
this automaton, i.e. a finite sequence of connected states, ending in a final state
represents a concatenation of terminological concepts that defines a language of
Enterprise Service signatures.
Furthermore, we decided for an NFA-
ε
and against a DFA (deterministic
finite automaton) for the following reason. Although we expect SOA governance-
compliant Enterprise Services to correctly employ naming conventions, we can-
not assume them to be exhaustive to completely describe any Enterprise Services
signature. This means that the automaton should be able to ignore parts of the
signature that are unknown, i.e. not defined by a naming rule or where concepts
are not recognized. For this, we included empty-word transitions (
ε
-moves).
Definition 3 (Automaton
A
).
We define the NFA-
ε
as
A
=(
Q, T, M, q
0
,Z
)
with
Q
denoting a finite set of states,
T
used as input symbols,
M
:
Q
×
(
T
∪
{
ε
}
)
→
P
(
Q
)
as the transition function (including
ε
-moves) to a powerset of
Q
,
q
0
∈
Q
denoting a (possibly empty) set of
final states. We further define the powerset of a particular state
P
(
Q
representing the start state and
Z
⊆
{
q
}
)
,
q
∈
Q
as the set of states that can be reached from
q
with input
t
∈
T
and
ε
such that
Q
:
q
t,ε
P
(
{
q
}
{
p
∈
−→
p
}
(
ε
-closure). The powerset of all states is defined as
)=
aunion
P
(
Q
)=
q∈Q
P
(
{
q
}
)
.
Example 3 (NFA-
ε
).
In Figure 3, we depicted an example of an automaton
consisting of nine states
Q
=
{
q
0
,...,q
8
}
, an alphabet of nine symbols
T
=
{
and a set of transitions
M
rep-
resented as edges in Figure 3. We further refer to the following examples of
Enterprise Service signatures (S1) and (S2) that are accepted by this automaton
using the set of transitions
M
S
1
and
M
S
2
. Moreover, Enterprise Service signature
(S2) illustrates the need for
ε
-moves.
t
1
,...,t
8
,ε
}
, two accepting states
Z
=
{
q
7
,q
8
}
(S1)
SalesOrderItemScheduleLineChangeRequestConfirmation In
M
S
1
=
q
0
Φ
(
Sales Order
)
q
1
,q
1
Φ
(
Item
)
q
2
,q
2
Φ
(
Schedule Line
)
{
−−−−−−−−−→
−−−−−→
−−−−−−−−−−−→
q
2
,
q
2
Φ
(
Change
)
q
3
,q
3
Φ
(
Request Confirmation
)
q
5
,q
5
Φ
(
In
)
−−−−−−→
−−−−−−−−−−−−−−−→
−−−→
q
7
}
t
3
:
Change /
İ
t
2
:
Business
Object Node
t
7
:
In
t
5
:
Request
Confirmation
q3
q5
q7
t
3
:
Change
t
8
:
Out
t
1
:
Business
Object
q0
q1
t
2
:
Business
Object Node
q2
t
7
:
In
t
6
:
Query
Response
q4
q6
q8
t
4
:
Read
t
8
:
Out
t
4
:
Read /
İ
Fig. 3.
Example of a NFA-
ε
accepting e.g. Enterprise Service signature (S1) and (S2)
