1.
The Biconnected Verification
of Workflow Nets
Cooperative Information Systems
October 2010, Crete, Greece
Artem Polyvyanyy
Matthias Weidlich
Mathias Weske

2.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Correctness of Process Models
A process model is
correct if and only if the
corresponding workflow
net is sound
A sound workflow net
always terminates properly
and each transition can
contribute to the
completion of the net

3.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Research Problem:
Correctness and Connectedness
Soundness Connectedness
To which extent …
Strong Connectedness Theorem
A net N for which there exists a marking M0, such that (N,M0) is live and
bounded, is strongly connected
Soundness Connectedness
live and bounded
short-circuit net
Strong …

4.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity
■ A separating set of a graph is a set of elements, each a vertex or an edge,
whose removal renders the graph disconnected
■ A graph is k-connected if it has no separating set of size k−1
■ The vertex Cv (edge Ce) connectivity of a graph is the size of the smallest
separating set composed of vertices (edges)
Cv ≤ Ce

5.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition (I)
A k-connected graph can be decomposed into (k+1)-connected components
If a connected graph has no
separating sets, then the
graph is complete

6.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition (II)
The connectivity-based graph decomposition produces
separating sets, connected components, and their relations “ ”
The derived structural
information can be used for
analysis purposes
1
2
3 4
1
2

7.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (I)
A graph is (n,e)-connected if there exists no set of n nodes and there exists no
set of e edges, whose removal renders the graph disconnected
An (n,e)-connected graph
An (n1,e1)-connected graph
can be decomposed into
(n2,e2)-connected
components

8.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (II): Node vs. Edge
Edge-based decomposition Node-based decomposition

9.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (III): Related Work
O(|G|)*
O(|G|n+e-1
)**
single-entry-
single-exit edge
(SESE-edge)
[Johnson et al 94]
single-entry-
single-exit node
(SESE-node)
[Tarjan and Valdes 80,
Vanhatalo et al 08,
Polyvyanyy et al 10]
* |G| is the size of the graph
** n,e are parameters of the (n,e)-connected decomposition

10.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
0
The Biconnected Verification (I)
1. A WF-net can be sound only if all the
cutvertices of the corresponding
short-circuit net are places
2. Each biconnected WF-net of a WF-net
is safe and sound, if and only if the WF-
net is safe and sound

11.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
1
The Biconnected Verification (II)
Transition t1 and the biconnected
WF-net A3 constitute valuable
diagnostic information:
■ t1 is never enabled
■ A3 is not sound
(t4 is never enabled in A3)

12.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
2
Towards the Triconnected Verification
The Refined Process Structure Tree
The triconnected subnets
Future work: How do separation
pairs and triconnected subnets
influence soundness?

13.
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
3
Conclusion
■ Connectivity-based decomposition is a stepwise approach to a discovery of structural
information in WF-nets, i.e., separating sets, connected subnets, and their relations
■ Connectivity-based decomposition has various applications: Translation between
process languages, control-flow and data-flow analysis, process comparison and
merging, process abstraction, process comprehension, model layout, pattern
application in process modeling, etc
■ In this work, we have investigated the relation between the connectivity property of a
workflow net and its behavioral correctness (soundness)
■ In case of unsoundness, the method provides diagnostic information
■ The biconnected verification can be performed in linear time and requires linear space
to the size of the WF-net, whereas more fine grained decomposition steps can be
accomplished in low-polynomial time
■ Future Work: Follow the research agenda defined by the decomposition framework
to obtain new results on behavioral correctness