On State Number Calculation Problem in Petri Nets

The state number calculation problem is very important for model checking approach in Petri nets' analysis. It is known that the problem is intractable for general Petri nets. In this paper, we showed that the problem is intractable for a popular subclass of Petri nets, called free choice workflow nets. Then we proposed a polynomial time algorithm to solve the problem for a subclass of free choice workflow nets. We also showed effectiveness of the algorithm through an application example.

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

[2]  Dhanistha Panyasak,et al.  Circuits , 1995, Annals of the New York Academy of Sciences.

[3]  Shingo Yamaguchi,et al.  Convertibility and Conversion Algorithm of Well-Structured Workflow Net to Process Tree , 2013, 2013 First International Symposium on Computing and Networking.

[4]  Manuel Silva Suárez,et al.  Circuits, handles, bridges and nets , 1991, Applications and Theory of Petri Nets.

[5]  Wil M. P. van der Aalst,et al.  Verification of Workflow Nets , 1997, ICATPN.

[6]  K. Tsuji,et al.  NP-Hardness of Liveness Problem of Bounded Asymmetric Choice Net , 2002 .

[7]  M. Nielsen,et al.  Decidability Issues for Petri Nets , 1994 .

[9]  Boudewijn F. van Dongen,et al.  Towards Improving the Representational Bias of Process Mining , 2011, SIMPDA.

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

[11]  Shin Nakajima,et al.  The SPIN Model Checker : Primer and Reference Manual , 2004 .

[12]  Fang Yu,et al.  Number of reachable states for simple classes of Petri nets , 2011, IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.

[13]  Kees M. van Hee,et al.  Workflow Management: Models, Methods, and Systems , 2002, Cooperative information systems.

[14]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[15]  Yamaguchi Shingo,et al.  On Properties and a Decision Method of Bridge-Less Workflow Nets , 2014 .

[16]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[17]  Hsu-Chun Yen,et al.  Normal and Sinkless Petri Nets , 1989, J. Comput. Syst. Sci..