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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Corresponding author.
$ maximilian.koenig@hpi.de (M. König); tom.lichtenstein@hpi.de (T. Lichtenstein); anjo.seidel@hpi.de (A. Seidel);
mathias.weske@hpi.de (M. Weske)</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Data Objects with Variables in BPMN</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Maximilian König</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Tom Lichtenstein</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Anjo Seidel</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mathias Weske</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Hasso Plattner Institute, University of Potsdam</institution>
          ,
          <addr-line>Prof.-Dr.-Helmert-Str. 2-3, 14482 Potsdam</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2024</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>Managing the creation and manipulation of data is critical in today's organizations. This is reflected in the emergence of object-centric business processes, whose execution is driven by data objects. Therefore, it comes as a surprise that current activity-centric modeling languages such as BPMN lack comprehensive data modeling capabilities, especially when diferent data objects of the same class have to be processed. This paper proposes to extend BPMN process diagrams with variable identifiers that allow to model precise referencing behavior for diferent objects within a single process instance.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;BPMN</kwd>
        <kwd>Data in Processes</kwd>
        <kwd>Object-centric Processes</kwd>
        <kwd>Variables</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction and Motivation</title>
      <p>
        An important aspect of business process management is helping organizations to maintain an overview of
the complex processes that drive their value creation. For that purpose, a wide variety of methodologies
is provided to support the business process lifecycle, from design and verification to implementation,
monitoring, and evaluation [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Recently, the management of data objects in business processes received
significant attention, leading to the emergence of object-centricity as a novel paradigm [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Instead of
focussing on the order of activities and events based on control flow, processes are considered from
the perspective of the involved data objects, which represent business data manipulated in process
executions [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ].
      </p>
      <p>
        Traditional, well-established activity-centric process modeling languages, such as BPMN process
diagrams [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], struggle with the representation of complex data behavior in interaction with the control
lfow [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Hence, the question arises whether this deficiency can be overcome with concepts from the
currently evolving field. While version 2.0 of the BPMN standard [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] introduced concepts that support
modeling relevant data objects and their impact on process flow, they mainly handle single objects and
have imprecise semantics.
      </p>
      <p>
        In a BPMN process diagram, data object nodes, denoted by a document shape, visualize the existence
of certain types of data. Each reference specifies a data class and a state denoted in square brackets. The
data class defines a set of objects with the same structure or of the same type, while the state defines
an abstraction for the expected data. BPMN does not provide a means to define either data classes or
states in more detail. Hence, related approaches often rely on supplementary data models to explicate
data classes with attributes and relations between them [
        <xref ref-type="bibr" rid="ref6 ref7 ref8">6, 7, 8</xref>
        ].
      </p>
      <p>To reference several data objects of the same class in the same state, a data object node may be
annotated with a multi-instance marker (III), representing a collection of data objects. Data objects
and collections can be read and written by activities. Read operations are visualized in the model
through so-called data associations from data object nodes to activities, and write operations through
associations from activity to data object node. An example is shown in Fig. 1. Read operations imply that
at least one data object in the specified state must exist before an activity is enabled. Write operations
update the referenced object/collection or, if none exists, create a new one. An important assumption in
the BPMN specification is that a data object node always refers to the same data object or data object
collection per process instance [5, p. 206], which makes it impossible to access diferent objects of the
same type.</p>
      <p>The impact of that assumption is exemplified in Fig. 1. On the right, the best paper and the runner-up
are singled out from a collection of accepted papers to individually notify the authors later on. However,
due to the assumption that data object nodes always reference the same objects at runtime, the second
of these two subsequent write operations overwrites the reference to the first object. Hence, only the
runner-up paper can be accessed in the process model later on, while the reference to the best paper is
lost.</p>
      <p>Furthermore, when processing collections of data objects under this assumption, activities can only
transition all objects that are in the same state into the same target state. For example, when deciding
on the acceptance of a collection of submitted papers as shown in Fig. 1, the intended behavior is that
only some papers are accepted while others are rejected or require further discussion. However, this
behavior cannot be captured with traditional BPMN. Essentially, splitting and merging collections of
objects is not possible.</p>
      <p>In the following, this paper aims to overcome the presented deficiencies by extending BPMN with
variables to model dynamic references to diferent objects of the same class.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>There exists a large research corpus on the integration of business processes and data that cannot be
covered holistically in this position paper. In the following, we will therefore highlight works on BPMN
extensions improving its data modeling capabilities and a selection of process modeling approaches
with an emphasis on data.</p>
      <p>
        Meyer et al. present an extension to BPMN to capture object relations by denoting foreign key
relations between objects of diferent classes on data object references [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Another work introduces
a translational semantics for dealing with multiple object collections in BPMN, using the state as an
additional identifier next to the data class [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Combi et al. [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] employ an SQL-based approach to link
BPMN activities to the data classes they operate on. However, in all three approaches, the identification
of diferent objects of the same class was either not tackled or limited to objects’ states. Ghilardi et al.
introduce a supplementary SQL-based language to explicate data access in BPMN models [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] with a
focus on the verification of the resulting compound models.
      </p>
      <p>
        To improve the integration of processes and data, object- and data-centric process modeling notations
have been proposed in the literature. Steinau et al. provide a comprehensive overview [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. After
the publication of their paper, additional approaches have been introduced, including object-centric
Petri nets [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], object-centric behavioral constraints [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], synchronous proclets [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], and object-centric
Petri nets with identifiers [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], all covering diferent subsets of the object-centric modeling features
as introduced by Gianola et al. [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. Compared to these formal approaches, BPMN has the advantage
of being well-understandable and widely adopted in industry [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. Therefore, we decided to extend
BPMN’s data modeling capabilities to better capture data behavior.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Introducing Variables to BPMN</title>
      <p>To address the limitations of the current data semantics of BPMN as outlined above, we extend data
object nodes with variables. In essence, a variable represents an identifier denoted on a data object node
that is bound to one specific data object at runtime. Therewith, the variable can be used to access the
assigned data object again in later steps of the process. Furthermore, variables can be reassigned to
a diferent data object of the same class during process execution. Hence, by using variables, we can
viewing pErexcaisemly mpoldeel tOhe BreJfeEreCncTinSg behavior for multiple data objects of the same class, eliminating the
need for data object nodes of a class to reference the same data object throughout process execution.</p>
      <p>P:Paper
[reviewed]</p>
      <p>Pa1:Paper Pb:Paper Pa2:Paper
[accepted] [borderline] [accepted]</p>
      <p>Pa:Paper
[acceptance
published]
bp:Paper
[acceptance
published]</p>
      <p>rp:Paper
[acceptance
published]</p>
      <p>Review
submission
deadline
passed</p>
      <p>Collect papers</p>
      <p>Decide
acceptance
Pr1:Paper
[rejected]</p>
      <p>Discuss
borderline
papers
Pr2:Paper
[rejected]</p>
      <p>Fig. 2 depicts the paper review process extended with variables. We specify variables in the labels of
data object nodes as a prefix to the associated class separated by a colon, e.g., ‘P:Paper’, where ‘P’ is the
variable for data objects of the class ‘Paper’. As a convention, we use uppercase letters, e.g., ‘P:Paper’,
to refer to collections of data objects, and lowercase letters, e.g., ‘bp:Paper’, to refer to individual data
objects. Given the example, using variables allows distinguishing between the data objects written
by the activities ‘Select best paper’ and ‘Select runner-up best paper’, even though both are of class
‘Paper’. Furthermore, variables enable activities to return multiple data objects of the same class in
diferent states, since each output can still be distinguished. Considering the example in Fig. 2, ‘Decide
acceptance’ can create three collections of the class ‘Paper’, each containing data objects in a diferent
state which can later be identified via the respective variable: ‘Pa1’, ‘Pr1’, and ‘Pb’. As a consequence,
variables efectively address the shortcomings outlined in Section 1.</p>
      <p>In the following, we elaborate on the inclusion of variables in process diagrams by discussing their
impact on create, read, and update operations.</p>
      <p>Create. In the original semantics of BPMN, if an activity writes to a data object node without reading
from a node of the same class, a data object is either created or blindly overwritten. Since variables
support distinguishing multiple data objects of the same class, we modify the semantics to always
create a new data object in this case. Consequently, blind writes are no longer supported. The created
data object is assigned to the variable associated with the data object node. This may include the
reassignment of an already assigned variable. Similarly, the creation of a data object collection assigns
all created data objects to the corresponding variable. Considering Fig. 2, ‘Collect papers’ creates a
collection of papers in ‘reviewed’ that all are assigned to the variable ‘P’ for later reference.</p>
      <p>Read. By associating data object nodes with variables, we limit the scope of read operations to the
data object assigned to the corresponding variable. This ensures that multiple successive reads of the
same variable will access the same data object. However, reading a data object from a variable requires
(1) an existing assignment and (2) that the assigned data object satisfies the class and state constraints
as defined in the process model. Otherwise, the read cannot be performed, thus blocking the execution
of the activity.</p>
      <p>When reading data object collections, all data objects are accessed that are assigned to the variable
and satisfy the state constraints of the node. If an activity reads multiple collections of the same class, the
collections are merged before being processed by the activity. For example, in Fig. 2, ‘Send notification
of acceptance’ reads the union of the collections ‘Pa1’ and ‘Pa2’. Similar to single data object reads, an
assignment to a collection must exist for all read variables, and the union of all collections of the same
class and state must contain at least one suitable data object.</p>
      <p>Update. Updates to data objects can only be achieved by reading and writing a data object of the
same class, as blind updates are no longer supported. An updated data object is assigned to the variable
of the reference that is written to. If diferent variables were used to read and write the data object,
both variables will refer to the same data object after the update, even if the state of the data object has
changed. For example, ‘Send notification of acceptance’, updates the state of all data objects associated
to ‘Pa1’ and ‘Pa2’ to ‘acceptance published’ and assigns the results to ‘Pa’. Nonetheless, ‘Pa1’ and
‘Pa2’ keep their references to the data objects. Therewith, we can specify that the best paper and the
runner-up best paper can only be selected from the papers that were accepted in the first round, which
were stored in collection ‘Pa1’.</p>
      <p>
        Inspired by [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], when updating collections, we do not require that every data object in the collection
receives the same update: The activity ‘Discuss borderline papers’ updates the state of each data object
in ‘Pb’ to either ‘accepted’ or ‘rejected’, efectively splitting the initial collection into ‘Pa2’ and ‘Pr2’.
The decision on how collections are split is delayed to runtime, providing flexibility in execution. It
should be noted that a split may result in an empty collection. For example, ‘Pb’ might be empty if no
paper is considered borderline. Empty collections are still assigned to the corresponding variable.
      </p>
      <p>Finally, reading and writing to data objects of the same class without changing the state allows
for copying references to diferent variables. Given the example in Fig. 2, ‘Select best paper’ copies a
reference of the collection ‘Pa’ to one data object ‘bp’ for future use. In this case, the data object itself is
not changed.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Implications and Challenges</title>
      <p>With the introduction of variables to BPMN data object references, we improve BPMN’s expressiveness
regarding the representation of multiple data objects of the same class. Such data objects can now be
explicitly referenced and independently processed in activity instances. Applying the concept to data
object collection references eliminates the limitation that state transitions always apply to all objects in
a collection. Instead, each element can individually be updated to any of the referenced output states.
Together, this overcomes the deficiencies depicted in Fig. 1. The collection of submitted papers can
be split into ‘accepted’, ‘rejected’, and ‘borderline’ papers, and the best paper and runner-up can be
selected and further processed individually, as illustrated in Fig. 2.</p>
      <p>Besides the advantages, the extension entails a number of challenges. So far, it is possible to create
variables referencing collections that contain data objects in diferent states, as well as collections partly
referring to the same data objects. While that behavior is supported, it may lead to unintuitive behavior
which requires further investigation. Similarly, empty output collections can lead to deadlocks: Given
the example in Fig. 2, if all papers are accepted, ‘Send notification of rejection’ cannot be executed,
resulting in a deadlock. Furthermore, variables must be assigned before being read, which is an additional
aspect model designers have to consider. To overcome this, it is essential to develop guidelines for the
use of variables and to explore methods for the automatic detection of potentially erroneous behavior
through model checking.</p>
      <p>
        Another aspect that may be addressed by using variables in BPMN is object correlation, i.e., the
association of related objects within a process instance. For example, if the decision on a paper’s
acceptance used a collection of reviews as additional input, it should be possible to identify which
reviews were created for which paper in the scope of the variables. While some object-centric approaches
already cover this aspect [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], support in BPMN is still lacking. A starting point for investigation might
be the foreign key relations introduced in [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>So far, the description of the semantics for the novel object variables remains on a conceptual level.
Future studies should investigate suitable formalisms to concisely define the intended behavior.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>BPMN process models currently are insuficiently specified to capture complex data behavior involving
multiple objects of the same class. Therefore, this position paper motivates the introduction of variables
for data object nodes to enable individual access to and processing of diferent objects of the same class.
In addition, the implications of such an extension as well as entailed challenges are outlined, providing
a starting point for future research endeavors.</p>
    </sec>
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