Entry Test — Graduate Research Program
Business Process Management Team
School of Computing and Information Systems
The University of Melbourne
April 2018
This test aims to assess a range of fundamental skills to undertake a PhD
course in the computational aspects of Business Process Management. We do
not expect a candidate student to possess skills across all the assessed areas.
Rather, the results will indicate areas of strengths of the candidate, and will be
used to inform the choice of PhD topic. Therefore, please attempt to answer as
many questions as possible in a concise but convincing way.
Analytical Skills
Let hN, E, li, be a labeled directed graph, where N is a set of vertices, E ⊆ N ×N
is a set of edges, and l : E → L is a function assigning labels from a set L to
edges. Let source and target be functions on E such that source(s, t) = s and
target(s, t) = t. Formulate the following properties formally:
1. Every label in L is a label of some edge.
2. There are no nodes that are target of more than two edges with identical
labels.
3. There is at least one path of length three where all the edges have identical
labels.
4. There are no nodes that are source of edges with more than two distinct
labels.
1
Process Analysis Skills
Workflow nets are a class of Petri nets for the analysis of business processes. A
Workflow net has a unique source and a unique sink place and all places and
transitions are on a directed path from this source place to this sink place.
A Workflow net is sound if and only if:
a) from every reachable marking a marking can be reached that marks the
sink place (option to complete),
b) every reachable marking that marks the sink place marks it with one token
only and marks no other place (proper completion), and
c) for every transition a marking can be reached that enables this transition
(no dead transitions).
There is a lot of reference material on Workflow nets and soundness available,
for example:
W.M.P. van der Aalst. Verification of Workflow Nets. In P. Azma
and G. Balbo, editors, Application and Theory of Petri Nets 1997,
volume 1248 of Lecture Notes in Computer Science, pages 407–426.
Springer-Verlag, Berlin, 1997.
The above publication is available for download from here: https://goo.gl/
fRWzKv.
1. Create a Workflow net that only violates the option to complete property.
2. Create a Workflow net that only violates the proper completion property.
3. Create a Workflow net that only violates the no dead transitions property.
4. Create a Workflow net that violates the option to complete and proper
completion properties, but not the no dead transitions property.
Explain your answers.
Hint: You may want to construct the reachability/coverability graphs of the
proposed Workflow nets to verify your answer.
2
Conceptual Skills
Undirected graphs consist of nodes and undirected edges between nodes. In
Figures 1(a), 1(b), and 1(c) you can see a conceptual model for undirected
graphs (captured using Object-Role Modeling notation), a sample undirected
graph, and a population of the conceptual model, respectively.
Vertex
v1
v2
… is connected to ...
v3
v4
… is connected to ...
(a)
(b)
v1
v2
v2
v3
v3
v1
v3
v4
(c)
Figure 1: (a) A conceptual model for undirected graphs, (b) a sample undirected
graph, and (c) a population of the model in (a) that encodes (b).
Construct conceptual models for the following types of graphs, using either ORM
(Object-Role Modeling), ER (Entity-Relationship), or UML Class Diagrams:
1. directed graphs Directed graphs consist of nodes and directed edges between nodes.
2. hypergraphs Hypergraphs consist of nodes and hyperedges between these
nodes. A hyperedge has multiple (at least one) sources and a single target.
3. multigraphs Multigraphs consist of nodes and undirected edges between
these nodes. As opposed to undirected graphs, there may be multiple
edges between the same pair of nodes.
For each of your conceptual models create a sample graph and show this graph
as a population of your model.
Examples of the aforementioned types of graphs are shown in Figure 2.
v1
v1
v2
v3
v4
(a)
v2
v5
v1
v2
v3
v4
v4
v3
v6
(b)
(c)
Figure 2: (a) A directed graph, (b) a hypergraph, and (c) a multigraph.
3
If you decide to use ORM, you may wish to consult www.orm.net.
If you decide to use ER, you may wish to consult
www.smartdraw.com/entity-relationship-diagram/.
Finally, if you choose to use UML Class Diagrams, you can consult
www.smartdraw.com/class-diagram/.
Writing Skills
Write a 3–4 paragraph summary (approx. 400 words) of one of the following
articles (choose one article from the list; the articles are available for download
from here: https://goo.gl/FWxN4C):
Luciano Garcı́a-Bañuelos, Nick van Beest, Marlon Dumas, Marcello
La Rosa, Willem Mertens: Complete and Interpretable Conformance
Checking of Business Processes. IEEE Trans. Software Eng. 44(3):
262–290 (2018)
Artem Polyvyanyy, Chun Ouyang, Alistair Barros, Wil M. P. van
der Aalst: Process querying: Enabling business intelligence through
query-based process analytics. Decision Support Systems 100: 41–56
(2017)
Raffaele Conforti, Marcello La Rosa, Arthur H. M. ter Hofstede:
Filtering Out Infrequent Behavior from Business Process Event Logs.
IEEE Trans. Knowl. Data Eng. 29(2): 300–314 (2017)
Please use your own words and demonstrate that you are able to capture the
essence and the significance of the article. What are the main research questions
addressed in the article of your choice?
Programming Skills
Provide evidence of implementation capabilities by discussing a software component that you developed recently. Discuss architectural considerations, choice
of technology, and algorithmic challenges. If you have not developed software
in recent times, discuss an algorithm that you have developed and include a
discussion on its computational complexity.
4