Information Technology Reference
In-Depth Information
AB
+
ĺ
+
AB
+
B
A
A
B
A
B
+
A
B
+
+
(a)
(b)
Fig. 3.
The behavioural profile of (a) includes the one of (b)
Inclusion.
An inclusion holds between two behavioural profiles, if one profile
completely subsumes the behavioural constraints of another profile for shared
activities according to the notion of strictness discussed in the previous section.
Definition 5 (Inclusion).
Let
B
1
=
{
1
,
+
1
,
||
1
}
and
B
2
=
{
2
,
+
2
,
||
2
}
be
two behavioural profiles over a set of activities
A
.
B
1
includes
B
2
, denoted by
B
1
⊆B
2
, if and only if for all pairs of activities
(
a
1
,a
2
)
∈
A
×
A
it holds:
◦
a
1
+
1
a
2
implies
a
1
+
2
a
2
,
◦
a
1
1
a
2
implies
a
1
+
2
a
2
or
a
1
2
a
2
,
a
1
−
1
a
2
implies
a
1
+
2
a
2
or
a
1
−
1
◦
a
2
.
1
2
If
B
1
⊆B
2
,butnot
B
1
=
B
2
, we speak of proper inclusion, denoted by
B
1
⊂B
2
.
Fig. 3 illustrates inclusion of behavioural profiles (relations for start and end
nodes are omitted). The profile of model 3(a) includes the one of model 3(b) as
the former is less restrictive. It allows for ordered execution of activities
A
and
B
,
whereas model 3(b) forbids any occurrence of both activities in the same trace.
Due to the assumed behavioural abstraction, inclusion of the behavioural profiles
does not imply inclusion of the respective sets of traces. Still, the behavioural
abstraction allows us to cope with variations as they are visible for activities
'Search GBA Data'
and
'Update GBA Data'
in our example in Fig. 1. Model (
II
)
defines strict order for both activities, whereas model (
I
) completely disallows
joint occurrence of both activities. Hence, the behavioural constraints imposed
by model (
I
) are included in the constraints imposed by model (
II
). Any trace-
based assessment will fail to address such cases.
Emptiness.
A behavioural profile is empty, if it defines all pairs of activities,
except for the start and end activity, to be exclusive. Such a profile forbids the
execution of any activity other than the start and the end activity. As those
activities are assumed to carry no semantic meaning but indicate initialisation
and termination of the process, such a trace is considered to be empty.
Definition 6 (Emptiness).
Let
B
=
{
,
+
,
||}
be a behavioural profile over a
set of activities
A
with
s, e
∈
A
being start and end activities.
B
is
empty
,ifand
only if all activity pairs
(
a
1
,a
2
)
∈
(
A
×
A
)
\{
(
s, e
)
,
(
e, s
)
}
are exclusive,
a
1
+
a
2
.
3.3 Set-Theoretic Operations
We introduce three set operations for behavioural profiles, i.e., complementation,
intersection, and union. Again, we abstract from a correspondence relation, as-
sume that corresponding activities are identical, and focus on the constraints for
shared activities once multiple behavioural profiles are considered.
