Information Technology Reference
In-Depth Information
BOpenW rkflowN s
Definition 6 (Open Workflow Net, oWFN)
Let
(
P, T, F
)
be a net,
let in, out
⊆
P with
•
in
=
out
•
=
∅
,
let m
0
be a marking of N,
let Ω be a set of markings of N.
Then N
=(
P,T,F,in,out,m
0
,Ω
)
is an
open workflow net
(oWFN for short).
in
and
out
contain the
input
and
output places
,
I
=
def
in
∪
out
is the
interface
,
J
=
def
P
I
contains the
inner places
of
N
respectively. Whenever
N
is not
obvious from the context, we ax the index
N
,asin
P
N
,T
N
,F
N
,m
0
N
,Ω
N
,in
N
,
out
N
,I
N
,J
N
.
\
Definition 7 (Inner(N))
Let N be an oWFN. Then
inner
(
N
)=
def
(
J
N
,T
N
,F
N
∩
((
J
N
×
T
N
)
∪
(
T
N
×
J
N
)))
,
is the
inner subnet
of N.
Definition 8 (Internally disjoint oWFNs)
Two oWFNs M and N are
internally disjoint
iff
(
P
M
∪
T
M
)
∩
(
P
N
∪
T
N
)
⊆
(
I
M
∩
I
N
)
.
Remark 1.
Two oWFNs can canonically be made internally disjoint: Each shared
internal element is replicated.
General assumption: Two oWFNs
M
and
N
will always be assumed as internally
disjoint.
Definition 9 (Composition of oWFNs)
The
composition
M
⊕
N of two (internally disjoint) oWFNs M and N is the
oWFN
M
⊕
N
=
def
(
P
M
∪
P
N
,T
M
∪
T
N
,F
M
∪
F
N
)
,with
in
M⊕N
=
def
(
in
m
\
out
N
)
∪
(
in
N
\
out
M
)
,
out
M⊕N
=
def
(
out
m
\
in
N
)
∪
(
out
N
\
in
M
)
,
m
0
M ⊕N
=
def
m
0
M
+
m
0
N
,
Ω
M⊕N
=
def
{
m
+
n
|
m
∈
Ω
M
and n
∈
Ω
N
}
.
Definition 10 (Partners)
Two oWFNs M and N are
partners
iff out
M
∩
out
N
=
in
M
∩
in
N
=
∅
.
Definition 11 (Fellows)
Two oWFNs M and N are
fellows
iff out
M
∩
in
N
=
out
N
∩
in
M
=
∅
.