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time spectrum [30]. Behavioural profiles provide an abstraction which approxi-
mates trace equivalence at the weaker end of this spectrum. Notions of inclusion
are discussed in work on behavioural equivalence [7,8,9]. Recent works calculate
a degree of behavioural similarity between process models based on linguistic,
graph-matching, and state-based concepts, see [31] for an overview. Our work
instead provides a precise definition of how to determine the behavioural intersec-
tion of two process models. There is also work that aims to determine the union
of the behaviour captured by two process models [10,11,12,13]. None of these
works has been integrated and extended towards the definition of an algebra.
The requirements for representing variants of a process have been addressed
by different modelling approaches. In our work we build on the assumption that
the union or intersection of two process models is again a process model. This
approach is in line with work on the configuration of workflow models [6]. Other
approaches use dedicated elements for capturing variation points on the level of
the modelling language. Such languages include Configurable EPCs [5,32], ag-
gregated EPCs [33], Provop [3], or variant rich process models [34], which pick
up ideas and concepts from modelling of software product families [35] and fea-
ture diagrams [36]. These approaches typically assume that variation is identified
and explicitly represented by a human modeller while our algebraic operations
permit the calculation of intersection or union from two model variants.
Similar relations, but not exactly those of behavioural profiles, are used in a
pre-processing step of approaches to synthesize a process model [37]. Please refer
to [38] for a discussion of the conceptual differences between the relations used
in [37] and those of the behavioural profile. Our general idea of defining an algebra
for managing process variants is inspired by an algebra for operating guidelines, a
formal concept for the synthesis of interaction partners for a process [17].
7Conluon
In this paper, we addressed two fundamental challenges of managing process
variants, the specification of formal operations for reasoning with variants, and
the foundation of such operations upon an appropriate behavioural abstraction.
As a solution, we proposed a set algebra for behavioural profiles that enables
conclusions on behavioural commonalities and differences using set-theoretic re-
lations and operations. We showed how these concepts are used to address the
problem of managing process variants. Our case study illustrated the potential
of our approach for harmonisation of process model collections.
Having defined a complete algebra for the (abstracted) behaviour of processes
allows for behavioural analysis way beyond similarity measurement. For instance,
a process model may be used to encode forbidden behaviour. Using our algebraic
operations, a model collection may then be analysed whether it allows for the
forbidden behaviour. Our operations may also be used during the design of
process models. As an example, subsumption of behavioural profiles may hint at
the creation of model fragments that can be found in a model collection already.
