Overview of BPMN Model Equivalences.
Towards normalization of BPMN diagrams1
Krzysztof Kluza and Krzysztof Kaczor2
Abstract. In various application domains, there is a desire to stan- Although there are several research papers concerning equiva-
dardize modeling techniques. Business Process Model and Notation lences of Business Process models, most authors do not consider us-
(BPMN) is currently the most widespread language used for mod- ing of the BPMN notation, but analyze equivalences of models for
eling Business Processes (BP). Although there are some guidelines Petri nets [5, 32] or web services [12, 25]. The thorough research in
how to use this notation, the issue of modeling technique is not stan- the area of BPMN models equivalences was carried by Vitus Lam
dardized. The same semantics can be represented in BPMN using and can be found in his papers [14, 15, 16]. Although Lam’s equiv-
various but behaviorally equivalent model structures. In this paper, alences of models are formalized, he analyzes only several equiva-
we present an overview of the BPMN models equivalences topic. lence patterns. Thus, it is advisable to address the issue of BPMN
We point out various possibilities of equivalence patterns. This can models equivalences in a wider range.
help to structure diagrams and decrease their semantic complexity. In this paper, we present an overview of the BPMN models equiv-
Such research can be further useful for such tasks as analyzing simi- alences and show various possibilities of equivalent structures. This
larities or measuring compliance of processes. research can be useful in different areas of BPMN application, such
as: process matching [36], identifying the differences between pro-
1 Introduction cess models [13], analyzing similarities [3, 6, 19] or measuring com-
pliance of processes [2, 8].
Business Process (BP) models constitute a graphical representa- The rest of this paper is organized as follows. In Section 2, BPMN
tion of processes in an organization. Business Process Model and models and elements are introduced. Section 3 provides a review of
Notation (BPMN)3 [1, 23] is a notation for modeling Business various equivalence patterns in BPMN models. The conclusion with
Processes, which contributed significantly in Software Engineering suggested course of action is presented in Section 4.
when it comes to collaboration between developers, software ar-
chitects and business analysts. Although there are many new tools
and methodologies which support the BPMN notation, they neither 2 BPMN models and elements
support some recommended modeling techniques nor make BPMN
models easily comprehensible. A Business Process [34] can be defined as a collection of related tasks
Two models with different structure, but behaviorally equivalent, that produce a specific service or product (serve a particular goal) for
can be both correct and unambiguous. This stems from the BPMN a particular customer. BPMN constitute the most widespread lan-
specification allowing for expressing the same semantics using vari- guage for modeling BPs. It uses a set of predefined graphical el-
ous syntactic structures. However, this can cause difficulties in mod- ements to depict a process and how it is performed. The current
eling or understanding of the model – the modeling challenge. BPMN 2.0 specification defines three models to cover various as-
Although behaviorally equivalent structures can be replaceable, pects of processes:
some of them may be not translatable to other languages in order
to be analyzed or verified [29, 33]. This makes practical problems 1. Process Model — describes the ways in which operations are car-
with model analysis – the analysis challenge. Thus, to avoid such ried out to accomplish the intended objectives of an organization.
problems, a set of best practices for modelers is needed, and it would The process can be modeled on different abstraction levels: public
be useful to normalize the preffered model structures. (collaborative Business 2 Business Processes) or private (internal
The first step towards such a structure normalization process is Business Processes).
to identify behaviorally (or semantically) equivalent structures. One 2. Choreography Model — defines expected behavior between two
model can be transformed to the equivalent model to make it con- or more interacting business participants in the process.
sistent in a way which it might not have been before [14]. While this 3. Collaboration Model — can include Processes and/or Choreogra-
may be done manually, and usually is in the case of ad hoc modeling, phies, and provides a Conversation view (which specifies the log-
it is possible to support a normalization task with tools. The goals of ical relation of message exchanges).
such a normalization can be to maintain compatibility, interoperabil-
ity, safety, repeatability, or quality of models. In most cases, using only the Process Model is sufficient. In our
1 The paper is supported by the BIMLOQ Project funded from 2010–2012
research, the internal Business Process Model is considered. Four
basic categories of elements used to model such processes, presented
resources for science as a research project.
2 AGH University of Science and Technology, Poland, in Fig. 1, are: flow objects (activities, gateways, and events), con-
Email: {kluza,kk}@agh.edu.pl necting objects (sequence flows, message flows, and associations),
3 See: http://www.bpmn.org/.
swimlanes, and artifacts [23].
Flow Objects Connecting Objects Swimlanes Artifacts One can also observe that in many cases multiple gateway struc-
ture can be replaced by a single gateway, as shown in Table 3.
Moreover, Gruhn and Laue described patterns in BPMN models that
Sequence Flow
Data Object deal with OR-gateways which can be replaced by AND- or XOR-
Gateways Pool
gateways [9], as presented in Table 4 (each row contains an equiva-
Annotation text
Message Flow
Text Annotations
lent pair of structures). They claimed that the equivalent model is eas-
Activities
ier to understand, as it is cognitively less complex. Such transforma-
Association Lanes
tion is also consistent with a study on the comprehensibility of BPM
(within a pool)
carried out by Sarshar and Loos [28], which shows that OR-gateways
Events Group
are significantly less comprehended than AND or XOR gateways.
Thus, Mendling et al. recommended to avoid OR-gateways [20].
Figure 1. BPMN core objects
Several researchers noticed that in several situations it is possible
to reduce number of repeated activities [14, 17]. The first example
Activities constitute the main BPMN elements. They denote tasks in Table 5 shows a situation where the same activity is located at
that have to be performed and are represented by rectangles with the last position of all incoming sequence flow paths before a join
rounded corners. The sequence flow between activities, the flow of gateway. It is possible to reduce the number of nodes by moving
control, is depicted by arcs. The directions of arcs depict the order in this activity behind the join gateway. The second one is similar but
which the activities have to be performed. concerns a situation in which the repeated activity is located at the
Events, represented by circles, denote something that happens dur- first position after a split gateway.
ing the lifetime of the process. The icon within the circle denotes the In [10], Jung et al. proposed a transformation from the BPMN-
event type, e.g. envelope for message event, clock for time event. formed business process to its semantically equivalent XPDL pro-
Gateways, represented by diamond shapes, determine forking and cess. Although both BPMN and XPDL are conceived of as a directed
merging of the sequence flow between tasks in a process, depending graph structure and the mapping should be straightforward, there are
on some conditions. some differences between BPMN and XPDL. Thus, in the paper [10]
several BPMN transformations are considered.
One of them concerns a loop mechanism. A loop in a process can
3 Equivalences of BPMN Models loop be depicted as in Fig. 2a. The BPMN 2.0 specification defines the
loop
In various application domains there is a need to compare process loop "testBefore" standard loop attribute, which constitutes a flag that con-
models [32]. One of the possible results of such a comparison can be trols whether the loop condition is evaluated at the beginning (test-
that two structurally different graphical representations of a business Before = true) or at the end (testBefore = false) of the loop iteration.
process are behaviorally (and semantically) equivalent. Thus, BPMN Instead of using this attribute, a loop can be depicted explicitly as in
processes can be regarded as equivalent if both of them can be trans- Fig. 2b (test time: before) and Fig. 2c (test time: after).
formed into a common graphical representation [14].
There is ongoing research in the area of process models equiva- Loop equivalences
lences [5, 32, 35]. However most of the researchers do not consider
A B C
BPMN notation, but e.g. Petri nets [5, 32]. There are tools which can A B C
A B C
prove selected equivalences of BPMN processes [14]. However, this
topic still remains an open research problem [16].
a) Loop modeled as a loop activity
3.1 Basic equivalent structures
Some basic equivalences that follow directly from the semantics of A B C
A B C
model elements described in the BPMN specification [23] are pre- A B C
sented in Table 1.
Other basic equivalences have been presented by Wohed et al. [35]
when defining the five simple control-flow patterns for process con- b) Loop modeled using control flow (test time: before)
A
trol based on the concepts defined by Workflow Management Coali- A
tion [4], such as: A B C
A B C
1. sequence — the ability to depict a sequence of activities, A B C
2. parallel split — the ability to capture a split in a single thread of
control into multiple threads which can execute in parallel, c) Loop modeled using control flow (test time: after)
3. synchronization — the ability to capture a synchronization of mul-
tiple parallel subprocesses/activities into a single thread, Figure 2. Variants
A of a loop structure [10] A
A A
4. exclusive choice — the ability to represent a decision point in A
a workflow process where one of several branches is chosen,
5. simple merge — the ability to depict a point in the workflow pro- Another transformation of loops in B graphs was proposed by
B
cess where two or more alternative branches come together with- Zhongjun Du and Zhengjun Dang in [7]. Based
B on the graph reduc-
out synchronization. tion technique [27], they proposed an algorithm which transforms the
C
loop in the workflow to an acyclic sub-graph. Although their solution
C
Apart from the sequence, the other patterns can be modeled in sev- does not use BPMN, it is rather general andCshould be applicable to
eral ways. The models in each column of the Table 2 are equivalent. BPMN models as well.
A
A
A
B
B
B
some some
simple eq
some
some
simple eq
Simple equivalences
A A A A
simple eq
A A
AA AA
A A
some some
A A
control flows without gateways control flows with gateways
simple eq
A B A B
A A B
A A A
B B
B
model with start and C
B A endAevents C
B model without start
A andBAend
C
events A A
A A A A A
A
A A A
C
AA C C AA
C AA
C C
imple eq
simple eq
intermediate message event start message event
A
A
B B
A A
A A B
C B
B
C A A B
A A
A A A
A A A B
A A A
C CC
C C
B A AA C A C A AA
A A C A
B C C
... ... B ... ...
B simple eq
B
... ... simple...eq ...
... ... ... ...
multiple start event-based gateway multiple intermediate event-based gateway
B
BB ... ... B ... ...
A B
A B B
A B B B
A A A
A Table 1. Equivalences
B of BPMN
A A structures based on the
B semantics of elements
A (based on the BPMNB specification [23])
C C C A A
A C A CC
C
C B A C A B A A A AB A
A B A BA C C
B C C C
C A C A C A
simple eq
Control flow equivalences
C ... ... C ... ...C
Merge Exclusive Choice Synchronization Parallel Split
B
... ... B ... ...
A B B
A A A A B
B A B
A A B
A A
C A C B A
A B A
A B B
C C A
C A C C
A C B A C C CC C
A A C A A C A A CA
BA
B
C
simple eq C C B B
B B C C B C C
B C B C C
with
Krzysztof XOR-gateway,
Krzysztof
Kluza Kluza alt 1 B with XOR gateway, alt 1 B
with AND-gateway7 of 7 7 of 7 with AND-gateway
B
Krzysztof Kluza A 6 of 7
A Krzysztof Kluza A 6 of 7
B Krzysztof Kluza
Krzysztof Kluza CB B
A
A A B A AA B 7 of
7 77
B of A B
B A B
B C C
C
A
A Krzysztof Kluza C
A C C A A C 6 Aof 7 C A
A B A
C
C C B B
B C C C C B C
B B C C
B
with XOR-gateway, alt 2 with XOR gateway, alt 2 partially through sub-Activities implicit
Krzysztof Kluza 6 of 7 6 of 7 29.05.2012
B B B B
A A B
Krzysztof
A Kluza Krzysztof Kluza A A 7 of 7 A 7 of 7
B A B B
C A A A A A A
C C C C
C C B C
A A C A C
C C C C
B
B
B B A B A
C B C B C
B
implicit without XOR-gateway through sub-Activities
C
rzysztof Kluza6 of 7 6 of 7 29.05.2012
A Krzysztof Kluza 6 of 7
A
A Table 2. Basic control-flow patterns in BPMN [35]
A A A
C A
C
C C B A B A
C C C
B B
B
A A C A
B B
B B
C C
B B
6 of 7 29.05.2012
Krzysztof Kluza 6 of 7
Krzysztof Kluza
B B B
A A
A
A A A
C C
C C C
B
B B
morgan
Multiple gateways equivalences
multiplemultiple
multiple gateways
gatewaysgateways B
B
C A B
C A
BB B BB B
B C A
AA A
D CC C AA A CC C
D D
DD D DD D
multiple parallel gateway with a common task single parallel gateway
BB B BB B
AA A
CC C AA A CC C
DD D DD D
multiple parallel gateway single parallel gateway
BB B BB B
AA A
CC C AA A CC C
multiplemultiple
gatewaysgateways
DD D DD D
multiple inclusive gateway single inclusive gateway
B B B B
A A
C C A A C C
D D D D
3 of 7 29.05.2012
multiple exclusive gateway Krzysztof Kluza single exclusive gateway 3
B B B B
Table 3. Equivalences of BPMN structures based on multiple gateway elements
Krzysztof
Krzysztof
Krzysztof Kluza Kluza
Kluza A A 44of
of77 4 of 7
C C A A C C
3.2 Complex Equivalences of BPMN structures
D D
Tantitharanukul and Jumpamule
D D
[31] defined Generalized Busi-
ness Process Modeling Notation (GBPMN) as a notation for dia-
grams which nodes are labeled with the process expression. They
Other transformations considered in [10] concern discrimination and presented an algorithm which converts any BPMN into GBPMN
serialization mechanisms. In Table 6 several examples of the applica- form. It is important to mention that the GBPMN is not a standard-
tion of the discriminator transformation to selected BPMN elements
B B B
ized solution, thus it is not very B
useful in practice. However, one of
are presented. The serialization examples, which transform some- the steps of their algorithm is taken if the existing diagram has more
A
thing serialized implicitly to another thing
A serialized explicitly, are
C C than
A one A start event or end event.
C InCsuch a case, they stipulate adding
shown in Table 7. a new single start event and/or a new single end event, and connect-
ing these events to the existing diagrams by using inclusive gateway
Qing-xiu et al. [24], in order to verify a workflow model D based
D D D
which is capable of capturing whether they simultaneously start or
on Petri net, proposed several reduction actions, such as reduction not. Using single start and end events should be taken into account
of sequential, iterative, or adjacent structure. However, the proposed when modeling, and such a procedure should be considered as a part
reductions are not directly applicable to BPMN models. of a normalization algorithm for business processes as well.
refaktoring
refaktoring
A A A A
refaktoring
refaktoring AA AA
AA AA
Gateways equivalences
A
A A
A
A
AA A A
AA A
A A A A
AA AA
A
A A
A
A
A A
A
A A A A
A A A A
AA AA
A A
A
A A
A A
A
A A A A
AA AA
A
A A
A
AB B
A AB B
A
B B B B
B
A
B
A B
A
B
A
A A A A
BB BB
A A A A
AA AA
B
B B
B
AB B
A AB B
A
B B B B
B
A
B
A B
A
B
A
brackets
brackets
Krzysztof
Krzysztof Kluza
Kluza Table 4. Gateways equivalences of BPMN structures (based on [9]) 5 of57of 7
brackets
brackets Krzysztof
Krzysztof Kluza
Kluza B 5 of57of 7
B B
B
Krzysztof Kluza
Krzysztof Kluza 55 of
of 77
A A B
B
C C Multiple activities equivalences B
B A A
Krzysztof Kluza
Krzysztof Kluza 55 of
of 77
A A C C A A
C C
Krzysztof
Krzysztof Kluza
Kluza 55 of
of 77
C C
B B C C B B
B B C C B B
A A B B B B
A A B B B B
A A
A A
A A C C C C
A A C C C C
Table 5. Multiple activities equivalences of BPMN structures (based on [14, 17])
A B C
AA BB CC
A A B B A A A B B B A
A B A
AA BB AA
B C C A B C
A B C
AA BB CC
Discriminator equivalences of events
A A B B C C A AA B B B CC C A B
A B C A B
C C A B C AA BB CC AA BB
A A
A B D D C DD D
AA BB CC
A A D
DD
boundary intermediate event intermediate event in normal flow
C
A A A A
A A
AA AA
B A B A B B
B
B B
A B A B B
B BB
BB
B C
C C
C multiple
C event
C
a numberC of single events
C
CC
Discriminator equivalences of gatewaysC CC
A A A A
A B C A B C
A A
A B AA C A B AA C
C
B B B B
D D
C
B B
BB D BB D
A
B
termination of a process using terminate
B B
event normal process termination B
B A B
B B B
B A A A BB A BB
AB A
C AA C C AA C
C C
C C C
C CC CC
C
Krzysztof Kluza 2 of 7
2 of 7gateway
multiple event a combination of gateways and2single
of 7 events 29.05.2012
29.05.2012
Krzysztof Kluza
Krzysztof Kluza 2 of27of 7
Krzysztof Kluza A 2 of 7
A Table 6. Discriminator equivalences of BPMN structures (based on [10])
B
B
3.3 Guidelines for modelers eight patterns which reduce the perceived model complexity with-
out changing the abstract syntax of the model and classified them
The normalization process should also take into account the existing according to the following hierarchy [26]:
B guidelines for business modelers. Most of the existing toolsB do not
require to complyA with any guidelines or modeling
B requirements, so 1. Layout Guidance — describes features to modify the process
a user has to adhere to them itself. model layout.
A
C One of the papers with most impact in the business process
C mod- 2. Outline visual mechanisms to emphasize certain aspects:
eling field by Mendling et al. [20] concerns guidelines
C for business (a) Enclosure Highlight — for visually enclosing close a set of log-
process modelers, which should be taken into account when model- ically related model elements,
ing business processes. They formulated seven guidelines
2 of 7 and prior- 29.05.20
itized them with the help of industry experts [20]: (b) Graphical Highlight — to change the visual appearance of
1 of 1 31.05.2012
model elements, such as shape, line thickness and type, etc.
1. Model as structured as possible. (c) Pictorial and Textual Annotation — to assign pictorial ele-
2. Decompose a model with more than 50 elements. ments, such as icons or images, to modeling elements, or to
3. Use as few elements in the model as possible. visually represent free-form text in the canvas, which can be
4. Use verb-object activity labels. attached to modeling elements without changing semantics.
5. Minimize the routing paths per element.
6. Use one start and one end event. 3. Two representation patterns:
7. Avoid OR routing elements. (a) Explicit Representation — to capture process modeling con-
cepts via a dedicated graphical notation,
La Rosa et al. [26] performed a systematic analysis and proposed
a number of concrete syntax modifications for business process mod- (b) Alternative Representation — to capture process modeling con-
els to manage their complexity. They presented a collection of pat- cepts without the use of their primary graphical notation.
terns that generalize and conceptualize various existing mechanisms 4. Naming Guidance — naming conventions or advice for model el-
to change the visual representation of a process model. Their goal ements’ labels, which can be syntactic (e.g. using a verb-object
was to simplify the representation of processes. Thus, they identified style) or semantic (e.g. using a domain-specific vocabulary).
A B C
A B C A
A B C
A B C
D
D
Serialization equivalences for gateways
A A
A A
B
B B
B
C
C C
C
linklink
implicit join explicit join
link Serialization equivalences for links
A A
A A
A
A A
B Z
Z Z A
A A
B Z
Z Z
B B
A B
B B ...
... ... Z A B
B B ...
... ... Z
B ... B ...
internal links in a model a model without links
B B
B B
X
X X A Y
Y Y A
A A
X Y C X
X X Y
Y Y C
C C
Z
Z Z A
A A Z
Z Z
A
A A X Z
ZY Z
Z A Z
Krzysztof Kluza Z
Z Z 2 of 7
KrzysztofA Kluza Z 2 of 7
Z
external links in a model a model without links
Table 7. Serialization equivalences of BPMN structures (based on [10])
4 Conclusion Moreover, we presented several guidelines for modelers, which
should be taken into account when modeling, and considered as a part
of a normalization algorithm for business processes.
Although BPMN is the most widespread notation used by soft-
While normalization can be performed manually, and usually is in
ware architects and business analysts for modeling Business Pro-
the case of ad hoc modeling, it is possible to support such a process
cesses, it is not clear which structures should be preferred and which
Krzysztof Kluza with tools. However, most of the existing tools do not require to com- 24.05.2012
avoided.
Krzysztof Kluza The BPMN specification does not clarify how the notation 1 of1 of1 1 24.05.2012
ply with any guidelines or modeling requirements, so a user has to
should be used for modeling various processes. Thus, the standard-
Krzysztofization
Kluza of such modeling technique in BPMN is desired. 1 of 1
adhere to them itself. 24.05.2012
Furthermore, normalization can help in the future research on
As BPMN allows for expressing the same semantics using var-
structuring diagrams in order to decrease their semantic complexity.
ious syntactic structures, this can cause the modeling and analysis
Our research can be further useful for many purposes, such as pro-
challenges. Cognitive understanding of model semantics can vary in
cess matching, identifying the differences between process models,
case of complex syntactic differences. Furthermore, a behaviorally
analyzing similarities or measuring compliance of processes.
equivalent but syntactically different structures can be analyzed in
In our future research, we will formalize the presented equiva-
different ways or even can be untranslatable to other languages in or-
lences. This will allow for implementing a tool for proving that two
der to be verified. To address these issues, a set of best practices for
models are equivalent or using some of the existing tools for ana-
modelers as well as normalization of BPMN models are needed.
lyzing BPMN patterns for this purpose [15, 17, 18, 30]. Our goal is
In this paper, we prepared the first step towards such a normaliza-
to define the preferable structures of the model, which will consti-
tion process – based on a literature review, we presented an overview
tute a normalization process and a part of a modeling methodology
of the topic of BPMN models equivalences, identified various be-
for modeling business processes integrated with rules [22, 21]. Such
haviorally (or semantically) equivalent structures, and pointed out
process can be further supported by a proper tool framework [11].
possibilities of equivalent patterns.
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