1. composition of workflows
Dresden Dec.12, 2016 GK Rosi
Soundness preserving
composition of workflows
Theory of Programming
Prof. Dr. W. Reisig
Wolfgang Reisig

2. Background
Each large system is made of components (workflows, services, … )
A component
has a behavior
has an interface,
interface is used to communicate with other components
A component model
describes behavior as steps,
describes the interface
as a set of – whatever – elements
models communication by composition,
i.e “glueing” corresponding interface elements of components
This talk:
Smart Behavior Modeling
Smart Composition Modeling
The cyclic extension
Include data …

3. Smart Behavior modeling
… using Workflow Nets
1.1 Classes of Workflow Nets
1.2 Sound Workflow Nets

4. 1.1 Classes of Workflow Nets
local ~
global ~
open ~

5. local WF net: A buyer Def.: local WF net: - one start place, p;
Initial marking: 1 token on p.
- one stop place, q;
Final marking: 1 token on q.

6. local WF net: credit based shopping

7. global WF net: Buyer and seller
goods I
Def.: global WF net N: - set *N of start places,
initial marking: 1 token on each p  *N .
- set N* of stop places,
final marking: 1 token on each p  N* .

8. stretched WF net N: restaurant2 1
global WF net: restaurant
stretched WF net N: restaurant
Def.: global WF net N: - set *N of start places,
initial marking: 1 token on each p  *N .
- set N* of stop places,
final marking: 1 token on each p  N* .

9. Observations let N be global. i. N is local iff |*N| = |N*| = 1
ii. N can easily be made local:
Later we see:
no good idea
upon composition

10. Open WF nets
Def.: later

11. inner(N) Lemma: Let N be an open WF net.
Then inner(N) is a global WF net

12. 1.2 Sound workflow nets sound! Def.: Let N be a global WF net.
N is sound iff
no arc goes out of N* ;
starting from *N, each transition can be enabled ;
From each reachable marking M, the marking N* is reachable.
No marking M > N* is reachable.
Soundness is efficiently decidable. (v.d. Aalst)

13. Internet Shopping sound! Def.: Let N be a global WF net.
choose product
send order
rec. product
accept product ib fb
return prod.
sound!
Def.: Let N be a global WF net.
N is sound iff
no arc goes out of N* ;
starting from *N, each transition can be enabled ;
From each reachable marking M, the marking N* is reachable.
No marking M > N* is reachable.
Soundness is efficiently decidable. (v.d. Aalst)

14. not sound Def.: Let N be a global WF net. N is sound iff
choose product
send order
rec. product
accept product ib fb
time out
return prod.
Def.: Let N be a global WF net.
N is sound iff
no arc goes out of N* ;
starting from *N, each transition can be enabled ;
From each reachable marking M, the marking N* is reachable.
No marking M > N* is reachable.
Soundness is efficiently decidable. (v.d. Aalst)

15. because Def.: Let N be a global WF net. N is sound iff
choose product
send order
rec. product
accept product ib fb
time out
return prod.
Def.: Let N be a global WF net.
N is sound iff
no arc goes out of N* ;
starting from *N, each transition can be enabled ;
From each reachable marking M, the marking N* is reachable.
No marking M > N* is reachable.
Soundness is efficiently decidable. (v.d. Aalst)

16. 2. Smart Composition Modeling
2.1 The problem of associative composition
2.2 Left and right port
2.3 Index labelling of a port
2.4 Composition of global WF nets
2.5 Composition of open WF nets

17. 2.1 The problem of associative comp.
Example: a supply chain
composition of business processes
RM $ Su $ Ma $ Di $ Cu $ Co
no brackets!

18. an analogy: adapter $ $
socket $ adapter $ plug

19. an analogy: adapter $ $ ( )
socket $ adapter $ plug
no brackets!

20. a naïve composition operator
(S $ T)
$ U a b c a b b c S U = |
S $
(T $ U) T a b c U S
not associative

21. … summing up On the set of component models, composition should be
total
associative

22. 2.2 Left and right port On the set of component models,
composition should be
total
associative

23. A fundamental observation$
typical left/right ports:
start and stop
input and output
customer and supplier
provider and requester
producer and consumer
buy side and sell side
predecessor and successor
RM $ Su $ Ma $ Di $ C u $ Co
The interface of a component S
is partitioned
into a left and a right port *S and S* !
Central idea:
Exploit this observation!

24. left and right port S right port T* right port S* T U left port *Tb c
right
port T*
right
port S* T b e d f U b e d f
left
port *T
The interface of a component S
is partitioned
into a left and a right port *S and S* !
For S $ T,
compose
S* with *T .
Central idea:
Exploit this observation!

25. composition along portsb c T b e d f U b e d f
(S $ T)
$ U
The interface of a component S
is partitioned
into a left and a right port *S and S* !
For S $ T,
compose
S* with *T .
Central idea:
Exploit this observation!

26. … is associative! = S T U (S $ T) $ U S $ (T $ U)b c T b e d f U b e d f
(S $ T)
$ U =
S $
(T $ U)
The interface of a component S
is partitioned
into a left and a right port *S and S* !
For S $ T,
compose
S* with *T .
Central idea:
Exploit this observation!

27. 2.3 Index labelled composition

28. in case a* and *b fit perfectly
The two “C” labelled places are matching.
The two “D” labelled places are matching.

29. composition a$b
a$b B D D F a b A C C E
* (a$b)
(a$b)*

30. … it is not always that simple*b b E D C F G B D a A C *a a*
The two “C” labelled places are matching.
The two “D” labelled places are matching.

31. … it is not always that simple
a$b C1 G B D D F a b A C C E L1 R2
*(a$b)
(a$b)*

32. this works nicely: C a b B D G F a b A C C E *a a* *b b*
The two “C” labelled places are matching.

33. … unfortunately a b* *b b E D C F E B D a A C *a a*
The two “C” labelled places are matching.
The two “D” labelled places are matching.

34. … unfortunately a$b C1 C2 E B D D F a b A C C E R2 *(a$b) L1 (a$b)*
Two nodes of (a$b)*
are labelled alike!
You can not avoid this!

35. … what to do here ??? ? a b B D D F C a b A C C E *a a* 1 2 *b b*
Idea:
index labelling:
n equally labelled nodes in one port
are indexed 1, … n .
graphical convention:
lower < upper.
Glue
equally labelled and equally indexed nodes.

36. … what to do here ??? a b B D C D F a b A C C E *a a* 1 2 *b b* Idea:
index labelling:
n equally labelled nodes in one port
are indexed 1, … n .
graphical convention:
lower < upper.
Glue
equally labelled and equally indexed nodes.

37. an extreme case a b* *b b A A A A a A 1 2 3 A *a 1 2 a* 1 2 1
all labels alike.

38. an extreme case a b* *b b A 1 A A A a A 1 2 3 A *a 1 2 a* 1 2
all labels alike.

39. an extreme case a$b C1 C2 A A D A a b 2 A A C A R2 *(a$b) L1 1 2
all labels alike.

40. … another extreme case B F D D H a b A E C G C B A D b a G F E H
all labels different.
results in

41. The associativity Theorem
Theorem: Index labelled composition is associative.

42. 2.4 Composition of global WF nets
index labelled
remember:
Def.: global WF net N: - set *N of start places,
initial marking: 1 token on each p  *N .
- set N* of stop places,
final marking: 1 token on each p  N* .
the left port
the right port
index labelled

43. a global, sound workflow, N
add a seller
choose product
send order
rec. product
accept product ib fb
time out
return prod.
rec. returned prod.
handle
rec. order
send product
file record is fs

44. … a reachable state … buyer may want to continue … choose product
send order
rec. product
accept product ib fb
return prod.
buyer may want to continue …
time out
rec. returned prod.
handle
rec. order
send product
file record is fs

45. second purchase, N$N choose product send order ib rec. returned prod.
handle
return prod.
time out
accept product fb
file record fs

46. second purchase choose product send order ib rec. returned prod.
handle
return prod.
time out
accept product fb
file record fs

47. second purchase rec. returned prod. handle return prod. time out
accept product fb
file record fs
rec. product
accept product fb
return prod.
time out
rec. returned prod.
handle
file record
send product
rec. order is fs
choose product
send order ib

48. N$N is a sound WF net, too! N: choose product send order rec. product
accept product ib fb
time out
return prod.
rec. returned prod.
handle
rec. order
send product
file record is fs

49. Properties Let N and M be global WF nets.
Observation: N$M is a global WF net.
Theorem 1. N$M is sound iff both N and M are sound.

50. 2.5 Open WF nets composition
Def.: open WF net N:
- set *N of places and transitions,
subset of places startN  *N,
initial marking: 1 token on each p  startN .
set N* of places and transitions,
subset of places stopN  *N,
final marking: 1 token on each p  stopN .
the left port
the right port
Observation:
An open WF net N is a global WF net
iff *N = startN and N* = stopN .

51. Example: Client and seller
order
receive
pay
seller
obtain
collect
send
subscription
product
cash
subscription
product
cash

52. … not what we wanted Deadlock!! client seller order receive pay obtain
collect
send
subscription
product
cash
Deadlock!!

53. Adapting required behaviour
client
order
receive
pay
bank
subscription
product
cash
seller
obtain
collect
send
subscription
product
cash
subscription
product
cash

54. associativity required!
client
order
receive
pay
subscription
product
cash
bank
subscription
product
cash
seller
obtain
collect
send
subscription
product
cash

55. More liberal compo- sition

56. Composed business processes

57. Properties Observation. Let N and M be open WF nets.
Then N$M is an open WF net.
… no compositional behavior

58. 3. The cyclic extension acB A D a C B a D B C B A
Idea:
To construct ac, compose a* with *a
just as you compose
a* with some *b .

59. remember: Seller and buyer
the Always ready-seller N: N
choose product
send order
rec. product
accept product ib fb *N N*
time out
return prod.
Def.: global WF net N: - set *N of start places,
initial marking: 1 token on each p  *N .
- set N* of stop places,
final marking: 1 token on each p  N* .
with internal init
 M
- set M of inner places
 M
rec. returned prod.
handle
Observations.
Each conventional open WF net
is an open WF net with M = ; as internal init .
ii. Let N and M be open WF nets with internal init.
N$M is an open WF net with internal init. M
rec. order
send product
file record is fs

60. remember: Seller and buyer
the Always ready-seller, Nc Nc N:
choose product
send order
rec. product
accept product ib fb
*(Nc)
(Nc)*
time out
return prod.
Def.: global WF net N: - set *N of start places,
initial marking: 1 token on each p  *N .
- set N* of stop places,
final marking: 1 token on each p  N* .
Closure Nc of a
 MN
Let MN be the “matching”
places of N* and *N.
 MN
rec. returned prod.
handle
Observation: Let N be a global WF net with internal init. Then Nc is a global workflow net with internal init. MN
rec. order
send product
file record is fs is

61. remember: Soundness Def.: Let N be a global WF net. N is sound iff
no arc goes out of N* ;
starting from *N, each transition can be enabled ;
From each reachable marking M, the marking N* is reachable.
No marking K > N* is reachable.
with internal init, M.
 M
 M
 M
Theorem: Let N and M be sound global Wf nets with initial init.
i. N$M is sound.
ii. Nc is sound.

62. global WF net: restaurant2 1 N Nc
*N ={C1, C2, Wf}
*(Nc) ={C1, C2}
N* ={e1, e2, Wf}
(Nc)* ={e1, e2}

63. 4. Include data …

64. data processing open WF nets
x! =
x =
the juice partner:
coin
beverage
coin x!
beverage x
order
order

65. Distinguishable tokens
x! =
x =
the tea partner:
coin
beverage
coin x!
beverage x
order
order

66. The McDonald’s vending machine
x = ...
coin x!
beverage x
order

67. summing up: How to use all this …
Start modelling your system
by small data processing sound open WF nets;
compose them;
You get a sound system model for free!

68. composition of workflows
SOAMED Vorlesung 5. Dez. 2016
Soundness preserving
composition of workflows
do it with
global ,
sound
workflow
nets!
Theory of Programming
Prof. Dr. W. Reisig
Wolfgang Reisig

69. Soundness preserving composition of workflows
A large computer embedded system or business process is usually composed of interacting components. A component may be organized as a workflow. A workflow is a pattern, describing a set of events, to be executed in a “before-after”-relation, or independent form one another, or alternatively. A large workflow may be composed from smaller ones.
A reasonable workflow W is sound: W has a unique initial and a unique terminal state; to every event e of W there exists a sequence of event executions that includes e; W can always reach its terminal state, and upon termination, no “garbage” remains. Soundness of (Petri net models of) workflows is efficiently decidable.
We present a most liberal composition operator for workflows that preserves soundness (i.e. composition of two sound workflows is a sound workflow again). This allows to stay in the world of sound workflows during the construction of large workflows and business processes.