There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions.

1. 10th International Conference on
Business Process Management
September 3-6, 2012 | Tallinn, Estonia
Isotactics as a Foundation for
Alignment and Abstraction
of Behavioral Models
Artem Polyvyanyy* Matthias Weidlich Mathias Weske
BPM Discipline Faculty of Industrial BPT Group
Information Systems School Engineering & Management Hasso Plattner Institute
Faculty of Science & Engineering Technion University of Potsdam
Queensland University of Technology Technion – Israel Institute of Technology Hasso Plattner Institute
Brisbane, Australia Haifa, Israel Potsdam, Germany

2. Modeling
Mapping
Reduction
Pragmatics
[ Weidlich 2011]
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 2

3. Process Modeling
[ Weidlich 2011]
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 3

4. Motivation (Structural Abstraction)
Abstraction is at the core of model creation, which comprises the mapping and reducing the entities
of a problem domain for a certain purpose
In process models, abstraction is achieved by means of sub-processes
A sub-process in an abstract version of an original process model is a contracted to a single vertex
connected, usually single-entry-single-exit, sub-graph of the original model
a In stock
c d e
Receive Ship Send Receive
(a) order products bill payment
Mapping Make
products
α = (a,{s,t})
Not in stock
b Reducing
α β
β = (b,{u,v,w}) Purchase u
... Not in stock
raw
material w
Manufacture
products
Order
Make
production
plan v
s t
Analyze Check
(b) order stock
x y z
Ship Send Receive
products bill payment
In stock
[ Artem Polyvyanyy, Sergey Smirnov, Mathias Weske: The Triconnected Abstraction of Process Models. BPM 2009: 229-244 ]
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 4

5. Beyond Structural Abstraction
Structural abstraction defines a relation on process models with the intuitive behavioral
relation between original models and their abstract versions
Do other (behavioral) abstraction relations on process models exist?
o Which mappings are allowed?
o Which reductions are allowed?
o How behavior is preserved?
Abstraction?
Collect
Select Study
product
product product
info
Perform Perform
analysis analysis
Collect Collect
market market
info info
(a) Abstraction? (b)
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 5

6. Alignment w/o Restrictions
Collect e δ
product
info
g
α
Perform
detailed
a analysis
Study
Collect
product
market
Perform c info
(a) f
initial
analysis
d
γ
Evaluate
Study
analysis
market
results
b
Select
w Collect x
product
product
info
α = ({a},{w,x}) (b) Perform
analysis
β = ({b,c,d},{y,z}) Collect
z
γ = ({c,d,g},{z}) market
y
β
info
δ = ({e,f},{x,y})
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 6

7. Alignment of Petri nets
t10
p12 p11
α t13
p15 t12
e t9 p t8
t2 10
p2 p3
g t11
a t5 p14
p1 t1 t4 p 6 t14 p
p7 f p13 p9 16
(a) t3 c t6
p4 p5 p8 t7
b d
γ
δ t10
p11
t2 t3 t4
p2 p4 p5
w x t8 t9
p1 t1 p3 t7 p9 p12
(b) t6
z
α = ({a},{w,x})
p6 t5 p7 p8 p10 t11
y β = ({b,c,d},{y,z})
β γ = ({c,d,g},{z})
δ = ({e,f},{x,y})
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 7

8. Behavioral Models
Review A arrived
Review B arrived
Dissertation submitted Disputation scheduled
Review C arrived
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 8

9. Process Set Abstraction
t10
p12 p11
t13 e t8
t2 p15 t12 t9 p
10
p2 p3
g t11
a
Net system
t5 p14
p1 t 1 t4 p 6 t14 p
p7 f p13 p9 16
t3 c t6
p4 p5 p8 t7
b d
α δ β γ
...
...
...
...
{α}
e2
abstraction
Process set
c2 c3 {β,γ} {β,γ}
Process
a e2
c1 e1 e4 c
6
e5 c7 e6 c8 e7 c9
e3
c d e5 e7
c4 c5
b e3
{β}
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 9

10. Process Tactic
(http://en.wikipedia.org/wiki/Battle_of_Borodino)
A process tactic is a partition of events
of a process set abstraction, such that:
{α}
e2 {β,γ} {β,γ}
e5 e7
e3
{β} Complex event
(i) all events in a part can have the same ‘label’, and
(ii) every two events from distinct parts are in the same causal relation.
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 10

11. Aligned Process Set Abstractions
α
{α} {α} {α,δ}
e2 {β,γ} {β,γ} e2 e4 {β,γ}
e5 e7 e8
e3 e6
{β} β {β,δ} γ
Set abstraction of Set abstraction of
a process from system (a) a process from system (b)
Two process set abstractions are aligned if and only if:
(i) there exist tactics of their set abstractions, and
abstractions
(ii) there exists a mapping between tactics that
respects alignment and causality.
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 11

12. Tactic Coverage / Isotactics
A system covers the tactic of another system if every process of the latter
system has a corresponding aligned process in the former system …
α
{α} {α} {α,δ}
e2 {β,γ} {β,γ} e2 e4 {β,γ}
e5 e7 e8
e3 e6
{β} β {β,δ} γ
... and the process alignment relation is closed under process extensions.
α
{α} {α} {α,δ}
e2 {β,γ} {β,γ} e2 e4 {β,γ}
{δ} {β,δ}
e5 e7 e8
e3 e11 e6 e'6
{β} {β,δ} γ
δ
β
Two systems are isotactic if they cover the tactic of each other
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 12

13. Abstraction in terms of Tactic Coverage
Let S1 and S2 be two systems. An alignment of S1 and S2 is an abstraction
iff S2 covers the tactic of S1 and the aggregation predicate holds.
Abstraction?
α
β
Select
w Collect x Study
a
product
product product
info
u v c
Perform Perform
analysis analysis
Collect
z Collect
market γ market
info
info y b
δ
(a) (b)
Abstraction?
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 13

14. Abstraction (Example)
{α} {α} {α,β}
Select Collect {α} {α,β}
Select
product
product
{β,γ} product
info
Select
Collect
product
product
info {γ,δ}
Collect
(a)
market Perform
info {β,γ} analysis
{α} {α,β} {β,γ} Collect
Collect market
Select Collect
product info
product market
info
info
{α,β} {α,β}
Study Study
{α,β} {β,γ} product product {γ,δ}
(b)
Collect Perform
Study
product
market {β,γ} {β,γ} analysis
info Collect
Collect market
market info
info
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 14

15. Conclusion
In this work:
Used experience from past works to develop and motivate concepts for reasoning
about alignment and (behavior-based) abstraction of process models
Argued that single-entry-single-exit abstractions preserve isotactics
Showed cases when the order of transition occurrences and concurrent enablement
of transitions is preserved by isotactics
Ongoing and future work:
Isotactics spectrum (linear vs. branching time & interleaving vs. true concurrency)
Develop algorithm(s) for checking isotactics
Discover properties that are preserved by isotactics
Develop model transformations/abstractions that preserve tactic coverage/isotactics
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 15