The Biconnected Verification of Workflow Nets

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

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

Research Problem: Correctness and Connectedness To which extent … ? Soundness
Connectedness
Strong Connectedness Theorem
A net N for which there exists a marking M 0 , such that (N,M 0 ) is live and bounded, is strongly connected Soundness
Connectedness
live and bounded short-circuit net Strong …

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 C v (edge C e ) connectivity of a graph is the size of the smallest separating set composed of vertices (edges)
C v ≤ C e

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

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

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 (n 1 ,e 1 )-connected graph can be decomposed into (n 2 ,e 2 )-connected components

Connectivity-based Decomposition Framework (II): Node vs. Edge Edge-based decomposition Node-based decomposition

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

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

The Biconnected Verification (II)
Transition t 1 and the biconnected WF-net A3 constitute valuable diagnostic information:
t 1 is never enabled
A3 is not sound (t 4 is never enabled in A3)

Towards the Triconnected Verification The Refined Process Structure Tree The triconnected subnets
Future work: How do separation pairs and triconnected subnets influence soundness?

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

The Biconnected Verification of Workflow Nets

by Artem Polyvyanyy on Oct 29, 2010

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The Biconnected Verification of Workflow Nets — Presentation Transcript