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The Biconnected Verification
of Workflow Nets
Cooperative Information Systems
October 2010, Crete, Greece
Artem Polyvyanyy...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Correctness of Process Models
A process model is
correct if and o...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Research Problem:
Correctness and Connectedness
Soundness Connect...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity
■ A separating set of a graph is a set of elements, ...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition (I)
A k-connected graph can be d...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition (II)
The connectivity-based grap...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (I)
A graph is (n,e)-c...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (II): Node vs. Edge
Ed...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
Connectivity-based Decomposition
Framework (III): Related Work
O(...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
0
The Biconnected Verification (I)
1. A WF-net can be sound only ...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
1
The Biconnected Verification (II)
Transition t1 and the biconne...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
2
Towards the Triconnected Verification
The Refined Process Struc...
Artem Polyvyanyy | Crete, Greece | October 2010 30.01.15
3
Conclusion
■ Connectivity-based decomposition is a stepwise app...
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The Biconnected Verification of Workflow Nets

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The Biconnected Verification of Workflow Nets

  1. 1. The Biconnected Verification of Workflow Nets Cooperative Information Systems October 2010, Crete, Greece Artem Polyvyanyy Matthias Weidlich Mathias Weske
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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