Information Technology Reference
In-Depth Information
2 Assumptions and Notations
2.1 Event Log Format and Sample
Process discovery techniques usually assume that service interaction logs have
certain format that is useful for analysis. The most common format consists
of mono-valued attributes describing service interaction messages. A message
is generated by a service and represents an explicit or implicit transition in a
process execution. Each message has a set of attributes and their associated
values. We consider the set of attributes in a log as
A
=
{
a
1
,
a
2
, ...,
a
i
}
and
the set of messages in a log as
M
=
. While it is dicult to
ensure a global clock with infinite precision to have a total or partial order for
messages generated by disparate services, we propose to consider the order that
the messages have been inserted in the event log. Therefore, we assume in this
work that one centralized log file is used, having exclusive write access to insure
that we will always have messages inserted one by one as they are captured.
Thus, we define a total order function
{
m
1
,
m
2
, ...,
m
j
}
for messages which corresponds to the
order they have been inserted into the event log. The following notations are
also used in this paper:
≺
-
∀
m
∈
M
,
A
(
m
)
⊂
A
is the set of attributes represented in the message
m
.
-
A
(
m
),
V
(
a
,
m
) is the value of the attribute
a
in the message
m
.
-
V
=
{
∀
a
∈
v
1
, ...,
v
m
}
is the set of values assigned to attributes of messages in
M
.
2.2 Message Correlation
Two messages
m
M
are considered as correlated if a Correlation Condition
(CC) is verified. We follow our previous work [4] for the definition of a CC. We
consider a CC as a relation between attribute's values of messages based on
a correlation function
cf
:
V
,
m
j
∈
i
V
such that
V
(
a
i
,
m
i
)=
cf
(
V
(
a
j
,
m
j
)). For
simplicity reasons, we assume in this paper that
cf
(
x
)=
x
.
The correlation of two messages
m
i
and
m
j
∈
−→
M
is denoted
m
i
≪
m
j
,inwhich
≪
is the correlation relation, iff
m
i
≺
m
j
and
∃
a
k
∈
A
(
m
i
)and
a
l
∈
A
(
m
j
)having
V
(
a
k
,
m
i
)=
V
(
a
l
,
m
j
).
The Correlation Condition (CC) of two correlated messages can be atomic
or composite depending on the number of couples of attributes of the two mes-
sages having equal values. The representation of an atomic CC is denoted as the
equality of two attributes:
a
and we note
ACC
the set of all possible unique
atomic CCs for a given set of attributes. A composite CC is a set of atomic CCs
verified for the same couple of correlated messages. We note a composite CC as
the conjunction of atomic correlation conditions:
a
=
a
i
j
...
For
both atomic and composite correlation conditions, we generalize the definition
of a correlation condition as follows:
=
a
j
∧
a
=
a
l
∧
i
k
Definition 1 (Correlation Condition).
We note the CC of two correlated
messages as a function
CCond
:(
M
,
M
)
−→
P
(
ACC
)
such that
∀
m
i
,
m
j
∈
M
/
m
i
≪
m
j
,
CCond
(
m
i
,
m
j
)
is the set of
all
atomic correlation conditions
verified by the correlated events m
i
and m
j
.
