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Finding a Witness Path for Non-liveness in Free-Choice Nets

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Applications and Theory of Petri Nets (PETRI NETS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6709))

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Abstract

One of the disablers of structural Petri net verification techniques is the lack of diagnosis information that is easily understandable. In this article, we improve this situation for a particular technique: the siphon and trap based verification of liveness in free-choice nets. Instead of the information ”there is a siphon without included marked trap”, we exhibit an execution path that leads from the initial marking to a marking m * and a set of transitions that mutually block each other and are thus dead at m *. The latter information can be much more easily comprehended by non-experts in Petri net theory. We provide experimental results suggesting that our method is competitive to related state space techniques.

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References

  1. Barkaoui, K., Minoux, M.: A Polynomial-Time Graph Algorithm to Decide Liveness of Some Basic Classes of Bounded Petri Nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 62–75. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  2. Barkaoui, K., Pradat-Peyre, J.: On Liveness and Controlled Siphons in Petri Nets. In: Billington, J., Reisig, W. (eds.) ICATPN 1996. LNCS, vol. 1091, pp. 57–72. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  3. Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  4. D’Souza, K., Khator, S.: A survey of Petri net applications in modeling controls for automated manufacturing systems. Computers in Industry 24(1), 5–16 (1994)

    Article  Google Scholar 

  5. Fahland, D., Favre, C., Jobstmann, B., Koehler, J., Lohmann, N., Völzer, H., Wolf, K.: Instantaneous soundness checking of industrial business process models. In: Dayal, U., Eder, J., Koehler, J., Reijers, H.A. (eds.) BPM 2009. LNCS, vol. 5701, Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Hack, M.: Analysis of Production Schemata by Petri Nets. Massachusetts Institute of Technology, 1972. MS Thesis, corrected (1974)

    Google Scholar 

  7. Hack, M.: Decidability Questions for Petri Nets. Massachusetts Institute of Technology, Ph.D. Thesis (1976)

    Google Scholar 

  8. Jones, N., Landweber, L., Lien, Y.: Complexity of some problems in petri nets. Theoretical Computer Science 4, 277–299 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kosaraju, S.R.: Decidability of reachability in vector addition systems. In: Proceedings of the 14th Annual ACM STOC, pp. 267–281 (1982)

    Google Scholar 

  10. Lambert, J.L.: A structure to decide reachability in Petri nets. Theoretical Computer Science 99, 79–104 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lipton, R.J.: The Reachability Problem Requires Exponential Space. Research Report, 62 (1976)

    Google Scholar 

  12. Mayr, E.: An algorithm for the general Petri net reachability problem. SIAM Journal of Computing 13(3), 441–460 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  13. MiniSat. Minimalistic, open-source SAT solver (2007), http://www.minisat.se

  14. Oanea, O., Wimmel, H., Wolf, K.: New Algorithms for Deciding the Siphon-Trap Property. In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 267–286. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Talcott, C., Dill, D.: The pathway logic assistent. In: Third International Workshop on Computational Methods in Systems Biology (2005)

    Google Scholar 

  16. van der Aalst, W.: The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)

    Article  Google Scholar 

  17. Wimmel, H.: Entscheidbarkeit bei Petri Netzen. eXamen.press. Springer, Habilitation Thesis (2008)

    Google Scholar 

  18. Wimmel, H.: Sara – Structures for Automated Reachability Analysis (2010), http://service-technology.org/tools/download

  19. Wimmel, H., Wolf, K.: Applying CEGAR to the Petri Net State Equation. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Wolf, K.: Generating Petri net state spaces. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 29–42. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Wolf, K.: LoLA – A low level analyzer (2010), http://www.informatik.uni-rostock.de/~nl/wiki/tools/lola

  22. Yamauchi, M., Watanabe, T.: Algorithms for Extracting Minimal Siphons Containing Specified Places in a General Petri Net. IEICE Trans. Fundamentals E82-A(11), 2566–2572 (1999)

    Google Scholar 

  23. Yamauchi, M., Watanabe, T.: Time Complexity Analysis of the Minimal Siphon Extraction Problem of Petri Nets. IEICE Trans. Fundamentals E82-A(11), 2558–2565 (1999)

    Google Scholar 

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Wimmel, H., Wolf, K. (2011). Finding a Witness Path for Non-liveness in Free-Choice Nets. In: Kristensen, L.M., Petrucci, L. (eds) Applications and Theory of Petri Nets. PETRI NETS 2011. Lecture Notes in Computer Science, vol 6709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21834-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-21834-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21833-0

  • Online ISBN: 978-3-642-21834-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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