Some Complexity Results for the Soundness Problem of Workflow Nets

Workflow nets (WF-nets) are widely used to model and verify the business process management systems and composite web services. The (weak) soundness of WF-nets is an important criterion for the correctness of these systems. This paper focuses on the complexity of solving the (weak) soundness problem. Aalst et al. have proven that the (weak) soundness problem is decidable. Our previous work has proven that the soundness problem for bounded WF-nets is PSPACE-complete. This paper shows that the weak soundness problem for bounded WF-nets is also PSPACE-complete. Aalst et al. has proven that the soundness problem is polynomially solvable for free-choice WF-nets (FCWF-nets). This paper discovers that the weak soundness problem is equivalent to the soundness problem for FCWF-nets. Therefore, the weak soundness problem for FCWF-nets is also polynomially solvable. Unfortunately, many composite web services are not modeled by FCWF-nets. Lots of them can be modeled by asymmetric-choice WF-nets (ACWF-nets). This paper proves that the soundness problem is co-NP-hard for ACWF-nets even when they are three-bounded. Additionally, this paper proves that the k-soundness problem is equivalent to the weak soundness problem for WF-nets, which implies that the k-soundness problem for bounded WF-nets is also PSPACE-complete.

[1]  Guan Jun Liu.  Complexity of the Soundness Problem of Workflow Nets , 2014, Fundam. Informaticae.

[2]  Ferucio Laurentiu Tiplea,et al.  Decidability Results for Soundness Criteria of Resource-Constrained Workflow Nets , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Wil M. P. van der Aalst,et al.  Service Interaction: Patterns, Formalization, and Analysis , 2009, SFM.

[4]  Wil M. P. van der Aalst,et al.  Loosely coupled interorganizational workflows: : modeling and analyzing workflows crossing organizational boundaries , 2000, Inf. Manag..

[5]  Farhad Arbab,et al.  Formal Design and Verification of Long-Running Transactions with Extensible Coordination Tools , 2013, IEEE Transactions on Services Computing.

[6]  Arjan J. Mooij,et al.  Reducing Adapter Synthesis to Controller Synthesis , 2012, IEEE Transactions on Services Computing.

[7]  Wil M. P. van der Aalst,et al.  Service Mining: Using Process Mining to Discover, Check, and Improve Service Behavior , 2013, IEEE Transactions on Services Computing.

[8]  Moe Thandar Wynn,et al.  Soundness of workflow nets: classification, decidability, and analysis , 2011, Formal Aspects of Computing.

[9]  Ekkart Kindler.  The ePNK: An Extensible Petri Net Tool for PNML , 2011, Petri Nets.

[10]  Yuan-Chun Jiang,et al.  Preventing Temporal Violations in Scientific Workflows: Where and How , 2011, IEEE Transactions on Software Engineering.

[11]  Neil D. Jones,et al.  Complexity of Some Problems in Petri Nets , 1977, Theor. Comput. Sci..

[12]  Carl K. Chang,et al.  Design of Service-Oriented Systems Using SODA , 2010, IEEE Transactions on Services Computing.

[13]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[14]  Kees M. van Hee,et al.  Generalised Soundness of Workflow Nets Is Decidable , 2004, ICATPN.

[15]  Changjun Jiang,et al.  Modeling and monitoring of E-commerce workflows , 2009, Inf. Sci..

[16]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[17]  Jun Sun,et al.  Complexity of the Soundness Problem of Bounded Workflow Nets , 2012, Petri Nets.

[18]  MengChu Zhou,et al.  A Petri-Net-Based Correctness Analysis of Internet Stock Trading Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[19]  Haiyang Sun,et al.  TiCoBTx-Net: A Model to Manage Temporal Consistency of Service-Oriented Business Collaboration , 2012, IEEE Transactions on Services Computing.

[20]  Wolfgang Reisig,et al.  An Operating Guideline Approach to the SOA , 2005 .

[21]  MengChu Zhou,et al.  A Petri Net-Based Method for Compatibility Analysis and Composition of Web Services in Business Process Execution Language , 2009, IEEE Transactions on Automation Science and Engineering.

[22]  Taghi M. Khoshgoftaar,et al.  From Web Service Artifact to a Readable and Verifiable Model , 2009, IEEE Transactions on Services Computing.

[23]  T. Neumann.  Computers And Intractability A Guide To The Theory Of Np Completeness , 2016 .

[24]  Kees M. van Hee,et al.  Soundness and Separability of Workflow Nets in the Stepwise Refinement Approach , 2003, ICATPN.

[25]  Axel Martens,et al.  Analyzing Web Service Based Business Processes , 2005, FASE.

[26]  Karsten Wolf,et al.  Deciding service composition and substitutability using extended operating guidelines , 2009, Data Knowl. Eng..

[27]  Jens Palsberg,et al.  Complexity Results for 1-safe Nets , 1993, FSTTCS.

[28]  Wil M. P. van der Aalst,et al.  Workflow Patterns , 2004, Distributed and Parallel Databases.

[29]  MengChu Zhou,et al.  Interactive Petri Nets , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[30]  MengChu Zhou,et al.  Business and Scientific Workflows: A Web Service-Oriented Approach , 2013 .

[31]  Mathias Weske,et al.  Efficient Consistency Measurement Based on Behavioral Profiles of Process Models , 2011, IEEE Transactions on Software Engineering.

[32]  Dan C. Marinescu,et al.  Structural soundness of workflow nets is decidable , 2005, Inf. Process. Lett..

[33]  Axel Martens.  On Compatibility of Web Services , 2003 .