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Edge, Event and State Removal: The Complexity of Some Basic Techniques that Make Transition Systems Petri Net Implementable

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12734)

Abstract

In Petri net synthesis we ask whether a given transition system A can be implemented by a Petri net N. Depending on the level of accuracy, there are three ways how N can implement A: an embedding, the least accurate implementation, preserves only the diversity of states of A; a language simulation already preserves exactly the language of A; a realization, the most accurate implementation, realizes the behavior of A exactly. However, independent of the implementation sought, a corresponding net does not always exist. In this case, it was suggested to modify the input behavior –of course as little as possible. Since transition systems consist of states, events and edges, these components appear as the natural choice for modifications. In this paper we show that the task of converting an unimplementable transition system into an implementable one by removing as few states or events or edges as possible is NP-complete –regardless of what type of implementation we are aiming for.

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References

  1. van der Aalst, W.M.P.: Process Mining - Discovery, Conformance and Enhancement of Business Processes. Springer (2011). https://doi.org/10.1007/978-3-642-19345-3

  2. Badouel, E., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) CAAP 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59293-8_207

    CrossRef  Google Scholar 

  3. Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. TTCSAES. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47967-4

    CrossRef  MATH  Google Scholar 

  4. Badouel, E., Caillaud, B., Darondeau, P.: Distributing finite automata through Petri net synthesis. Formal Asp. Comput. 13(6), 447–470 (2002). https://doi.org/10.1007/s001650200022

    CrossRef  MATH  Google Scholar 

  5. Best, E., Darondeau, P.: petri net distributability. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 1–18. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29709-0_1

    CrossRef  Google Scholar 

  6. Best, E., Devillers, R.R.: Synthesis and reengineering of persistent systems. Acta Inf. 52(1), 35–60 (2015). https://doi.org/10.1007/s00236-014-0209-7

  7. Carmona, J.: The label splitting problem. Trans. Petri Nets Other Model. Concurr. 6, 1–23 (2012). https://doi.org/10.1007/978-3-642-35179-2_1

  8. Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: A region-based theory for state assignment in speed-independent circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 16(8), 793–812 (1997). https://doi.org/10.1109/43.644602

    CrossRef  MATH  Google Scholar 

  9. Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: Logic Synthesis for Asynchronous Controllers and Interfaces. Springer, Berlin (2013)

    MATH  Google Scholar 

  10. de San Pedro, J., Cortadella, J.: Mining structured petri nets for the visualization of process behavior. In: Ossowski, S. (ed.) Proceedings of the 31st Annual ACM Symposium on Applied Computing, Pisa, Italy, 4–8 April, 2016. pp. 839–846. ACM (2016). https://doi.org/10.1145/2851613.2851645

  11. Schlachter, U., Wimmel, H.: Relabelling LTS for petri net synthesis via solving separation problems. Trans. Petri Nets Other Model. Concurr. 14, 222–254 (2019). https://doi.org/10.1007/978-3-662-60651-3_9

  12. Schlachter, U., Wimmel, H.: Optimal label splitting for embedding an LTS into an arbitrary Petri net reachability graph is NP-complete. CoRR abs/2002.04841 (2020). https://arxiv.org/abs/2002.04841

  13. Tredup, R.: Finding an optimal label-splitting to make a transition system petri net implementable: a complete complexity characterization. In: ICTCS. CEUR Workshop Proceedings, vol. 2756, pp. 131–144. CEUR-WS.org (2020)

    Google Scholar 

  14. Verbeek, H.M.W., Pretorius, A.J., van der Aalst, W.M.P., van Wijk, J.J.: Visualizing State Spaces with Petri Nets. Eindhoven University of Technology, Eindhoven, The Netherlands (2007). https://publications.rwth-aachen.de/record/715007

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Acknowledgements

I would like to thank the anonymous reviewers for their detailed comments and valuable suggestions.

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Correspondence to Ronny Tredup .

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Tredup, R. (2021). Edge, Event and State Removal: The Complexity of Some Basic Techniques that Make Transition Systems Petri Net Implementable. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_13

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