Information Technology Reference
In-Depth Information
XOR1
...
,
END
Act1
,
END
,
...
XOR1
Fig. 4.
Content of the arcs and nodes of a reachability graph
-
Function
flow
:
(
P
C
) returns the set of sequence flow elements
of the business process model contained in a set of nodes of the reachability
graph.
flow
(
N
)=
P
(
N
)
→P
N
(
M
(
p
c
,n
)=1))
{
p
c
∈
P
c
:
∃
n
∈
}
.
-
Function
activity
:
N
E
BP
returns the flow node of the business process
model contained in the input arc of the current node of the reachability
graph.
activity
(
n
)=
→
{
e
i
∈
E
BP
:
p
c
=(
e
i
,e
o
)
∧
M
(
p
c
,n
)=1
}
.
The node of the reachability graph with no input arrows is called
firstNode
∈
N
:
firstNode
and it is the start node of a reachability graph. The nodes
of the reachability graph with no output arrows, whose input is called END
andwithnotokensinacontrolplaceare
normal
final nodes of the reachability
graph. We will describe
abnormal
final nodes in Section 3.3.
∃•
3.3 Step 3. Object Life Cycle from Reachability Graph
Definition 3.
An
object life cycle of a data object of a business process
is a
2-tuple
OLC
=(
S
OLC
,T
OLC
)
,where:
-
S
OLC
=
{
s
1
,s
2
, ..., s
n
}
is the set of states in which the data object can be.
∀
represent immediately previous and next states of
state
s
i
, respectively. Let
start
s
i
∈
S
OLC
,
•
s
i
and
s
i
•
∈
S
and
end
∈
S
be the start and the final
(
start
end
)=
P
D
=
D
BP
states of the OLC, respectively. Then,
S
OLC
\
-
T
OLC
⊆
(
N
)
is the set of transitions that appear in the
object life cycle. Each transition contains a set of nodes of the reachability
graph from which it has been generated. Function
replace
:
T
OLC
×
S
OLC
×
S
OLC
×P
N
×
P
T
OLC
replaces the set of nodes before node N in the path of a
transition for a specific set of nodes.
(
N
)
→
We have defined Algorithms 1 and 2 to obtain an OLC from a reachability
graph. Algorithm 1 receives the reachability graph resulting from the previous
step and the list of activities of the BP that write the data object. Its out-
put is the OLC together with a set of data anomalies found while creating it.
