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Transformation of Petri Nets into Context-Dependent Fusion Grammars

  • Hans-Jörg Kreowski
  • Sabine Kuske
  • Aaron LyeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)

Abstract

In this paper, we introduce context-dependent fusion grammars as a new type of hypergraph grammars where the application of fusion rules is restricted by positive and negative context conditions. Our main result is that Petri nets can be transformed into these grammars such that the reachable markings are in one-to-one correspondence to the members of the generated language. As a corollary, we get that the membership problem for context-dependent fusion grammars is at least as hard as the reachability problem of Petri nets.

References

  1. 1.
    Kreowski, H.-J., Kuske, S., Lye, A.: Fusion grammars: a novel approach to the generation of graph languages. In: de Lara, J., Plump, D. (eds.) ICGT 2017. LNCS, vol. 10373, pp. 90–105. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-61470-0_6CrossRefzbMATHGoogle Scholar
  2. 2.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  3. 3.
    Czerwinski, W., Lasota, S., Lazic, R., Leroux, J., Mazowiecki, F.: The reachability problem for Petri nets is not elementary. CoRR. arXiv.org, abs/1809.07115 (2018)
  4. 4.
    Kreowski, H.-J.: A comparison between petri-nets and graph grammars. In: Noltemeier, H. (ed.) WG 1980. LNCS, vol. 100, pp. 306–317. Springer, Heidelberg (1981).  https://doi.org/10.1007/3-540-10291-4_22CrossRefGoogle Scholar
  5. 5.
    Corradini, A.: Concurrent computing: from Petri nets to graph grammars. Electron. Notes Theoret. Comput. Sci. 2, 56–70 (1995)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ehrig, H., Padberg, J.: Graph grammars and Petri net transformations. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 496–536. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-27755-2_14CrossRefzbMATHGoogle Scholar
  7. 7.
    Desel, J., Reisig, W.: Place/transition Petri nets. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 122–173. Springer, Heidelberg (1998).  https://doi.org/10.1007/3-540-65306-6_15CrossRefzbMATHGoogle Scholar
  8. 8.
    Girault, C., Valk, R.: Petri Nets for Systems Engineering. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-662-05324-9CrossRefzbMATHGoogle Scholar
  9. 9.
    Priese, L., Wimmel, H.: Petri-Netze. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-76971-2CrossRefzbMATHGoogle Scholar
  10. 10.
    Best, E., Wimmel, H.: Structure theory of Petri nets. In: Jensen, K., van der Aalst, W.M.P., Balbo, G., Koutny, M., Wolf, K. (eds.) Transactions on Petri Nets and Other Models of Concurrency VII. LNCS, vol. 7480, pp. 162–224. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38143-0_5CrossRefzbMATHGoogle Scholar
  11. 11.
    Reisig, W.: Understanding Petri Nets - Modeling Techniques, Analysis Methods, Case Studies. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-33278-4CrossRefzbMATHGoogle Scholar
  12. 12.
    Ehrig, H., Habel, A.: Graph grammars with application conditions. In: Rozenberg, G., Salomaa, A. (eds.) The Book of L, pp. 87–100. Springer, Berlin (1986).  https://doi.org/10.1007/978-3-642-95486-3_7CrossRefGoogle Scholar
  13. 13.
    Habel, A., Heckel, R., Taentzer, G.: Graph grammars with negative application conditions. Fundamenta Inform. 26(3,4), 287–313 (1996)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Dediu, A.-H., Klempien-Hinrichs, R., Kreowski, H.-J., Nagy, B.: Contextual hypergraph grammars – a new approach to the generation of hypergraph languages. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 327–338. Springer, Heidelberg (2006).  https://doi.org/10.1007/11779148_30CrossRefGoogle Scholar
  15. 15.
    Ehrig, H., Hermann, F., Sartorius, C.: Completeness and correctness of model transformations based on triple graph grammars with negative application conditions. In: Proceedings of the 8th International Workshop on Graph Transformation and Visual Modeling Techniques, vol. 18, pp. 1–18 (2009)Google Scholar
  16. 16.
    Kreowski, H.-J., Kuske, S., Lye, A.: Splicing/fusion grammars and their relation to hypergraph grammars. In: Lambers, L., Weber, J. (eds.) ICGT 2018. LNCS, vol. 10887, pp. 3–19. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-92991-0_1CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of Bremen, Department of Computer Science and MathematicsBremenGermany

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