Unraveling Unstructured Process Models Marlon Dumas University of Tartu, Estonia Joint work with...

Unraveling Unstructured Process Models

Marlon Dumas

University of Tartu, Estonia

Joint work with Artem Polyvyanyy and Luciano García-Bañuelos

Invited Talk, BPMN’2010 Workshop, Potsdam, 14 Oct. 2010

Poll: Which desk do you prefer?

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Poll: Which model do you prefer?

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The Problem

• Sometimes, structured is “preferable”– Easier to understand– Easier to analyze– Easier to automatically layout– Easier to abstract (zoom-out)

• But not all models are structured – often for a good reason!

• We know not all models can be structured…

• Which ones can, which ones can’t? 4

Analysis of Structured Models

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CTparallel = Max{T1, T2,…, TM}

CT = p1T1+p2T2+…+pmTm=

m

1iiiTp

CT = T/(1-r)

CT = T1+T2+…+ Tm

Laguna & Marklund (2005): Business Process Modeling, Simulation and Design

Automated Layout and Abstraction

6Wil van der Aalst et al., Process Mining Tutorial

A Bit of History

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1968 1969 1970s (and 80s)

20 years (and 200 papers) later…

• Everything can be structured if you accept to break and continue

• Everyone forgot to release their implementation (they were ashamed since it was full of GOTOs)

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40 years (and 400 papers) later• We can structure any BPMN

diagram, except:– “Incorrect” ones– Cycles with multiple exit points– Z-structures– Inclusive join gateways, complex

gateways and other demons

• Try it out: http://sep.cs.ut.ee/Main/bpstruct 9

Corollary (if you care)

• Any (sound) BPMN model can be transformed into an equivalent (readable) BPEL process definition

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• If BPEL had break/continue statements or we use boolean variables to simulate break/continue statememts• And the BPMN model does not have inclusive join gateways, complex gateways and other demons• And some other minor details not worth mentioning

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Behavioral Equivalence

B

A C

D

B

A C

D

Preserves the level of concurrency in a process model

Sequential simulation of a process model

Fully concurrent bisimilar (FCB)

WeaklybisimilarWeaklybisimilar

Sequential simulation of a process model

C D

A

D C

C D

B

D C

C D

A

D C

C D

B

D C

Starting Point – Process Structure Tree

12Johnson et al. (PLDI’1994), Vanhatalo et al. (BPM’2008)

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Taxonomy of Process Fragments

Process fragment

Trivial Polygon Bond Rigid

■ Trivials, polygons, and bonds are structured fragments■ Rigids are “unstructured”

Homogeneous Heterogeneous

XOR AND

Acyclic Cyclic

Acyclic Cyclic

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P1

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B1

P2

P3

a

b

c

d

e f

i ot

u

v

w

x y z

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Homogeneous XOR Rigid

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Homogeneous AND Rigid

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Block-structured version…

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Homogeneous AND Rigid that cannot be structured

• Causal rules:– {A, B} { C }– { B } { D }

• Overlap on the left-hand side of the rules

Compare to this…

• Causal relations– {A, B} {C, D}

Heterogeneous Acyclic Rigid

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Equivalent Structured Fragment

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The Key Ingredient: Unfoldings

A

B

ct,aet,a

ct

ct,bet,b

ca,u

cb,v

eu

ev

cw

cx

c'w

c'x

ew,c

ex,d

C1

D1

cw,c

cx,d

C2

D2

c'w,c

c'x,d

cc,y

cd,y

c'c,y

c'd,y

ey co

c'oe'y

e'w,c

e'x,d

ci ei

ea

eb

ec

ed

e'c

e'd

A

tt,a

pi

B

tt,b

pt

pt,a

pt,b

tu

tv

pa,u

pb,v

pw

px

C

D

pw,c

px,d

tw,c

tx,d

ty

pc,y

pd,y

poti

ta

tb

tc

td

An unfolding is arepresentation of a net without “merge” points

A complete prefix unfolding is a finite initial part of the unfolding that contains full information about the reachable states

A

B

ct,aet,a

ct

ct,bet,b

ca,u

cb,v

eu

ev

cw

cx

c'w

c'x

ew,c

ex,d

C1

D1

cw,c

cx,d

cc,y

cd,y

ey co

ci ei

ea

eb

ec

ed

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B

A C

D

Ordering Relations

■ Two transitions of an occurrence net are in one of the following relations:

□ A and B are in causal relation (A>B), iff there exists a path from A to B

□ A and B are in conflict (A#B), iff there are two transitions t1, t2 that share an input place and there is a path from t1 to A and a path from t2 to B

□ A and B are in concurrency (A||B) relation iff A and B are neither in causal, nor in conflict relation

A

B

ct,aet,a

ct

ct,bet,b

ca,u

cb,v

eu

ev

cw

cx

c'w

c'x

ew,c

ex,d

C1

D1

cw,c

cx,d

C2

D2

c'w,c

c'x,d

cc,y

cd,y

c'c,y

c'd,y

ey co

c'oe'y

e'w,c

e'x,d

ci ei

ea

eb

ec

ed

e'c

e'd

A>C1

B>D2

B#AA#D2

C2||D2

D2||C2

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FCB and Ordering Relations

A B C DA

B

C

D

>#

||

>> >#

||

<<<<

B

A C

D B

A C

D

A B C DA

B

C

D

>#

||

>> >#

||

<<<<

Two process models are FCB-equivalent …

… if and only if, (complete prefix) unfoldings of both models expose same ordering relations

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Structuring Process Models

B

A C

D

B

A C

D

Compute ordering relationsof the (unstructured) process model

Construct a block-structuredprocess model from ordering

relations

A B C DA

B

C

D

>#

||

>> >#

||

<<<<

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Ordering Relations Graph

A B C DA

B

C

D

>#

||

>> >#

||

<<<<

An ordering relations graph

A

B

C

D

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Modular Decomposition Tree (MDT)

L1

C1 C2

A

B

C

D

A

B

C

D

C1

A

B

C

D

C1 C2

The MDT is unique and can be computed in linear time

A

B

C

D

C1 C2

L1

B

A C

D

The MDT

■ A linear (L) module is a total order on a set of nodes of a graph■ A complete (C) module is a complete graph, or a clique■ A primitive (P) module is neither trivial, nor linear, nor complete

A module is a set of edges with uniform structure

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Structuring Acyclic Process Models

B

A

C

D

E

A B

E

C

D

B

A

C

D

E

A primitive module

Let G be an ordering relations graph. The MDT of G has no primitive module, iff there exists a well-structured process model W such that G is the ordering relations graph of W.

Heterogeneous Cyclic Rigid

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For further details…

Download and try:

• http://sep.cs.ut.ee/Main/bpstruct

• http://code.google.com/p/bpstruct/

Perspectives:

• Analyze

• Decompose (e.g. for distributed execution)

• Refactor (extract duplicate fragments into subprocesses)

• Visualize

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