Advertisement

Lindenmayer Systems and Global Transformations

  • Alexandre Fernandez
  • Luidnel Maignan
  • Antoine SpicherEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)

Abstract

Global transformations, a category-based formalism for capturing computing models which are simultaneously local, synchronous and deterministic, are introduced through the perspective of deterministic Lindenmayer systems, a computing model based on parallel string rewriting. No knowledge of category theory is assumed.

Notes

Acknowledgements

The authors would be like thank the reviewers for their help in improving the quality of this paper. This work was partly supported by the DIM RFSI project Theory and Pratice of Global Transformations, Région Île-de-France.

References

  1. 1.
    Arrighi, P., Dowek, G.: Causal graph dynamics. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 54–66. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31585-5_9CrossRefzbMATHGoogle Scholar
  2. 2.
    Arrighi, P., Martiel, S., Nesme, V.: Cellular automata over generalized Cayley graphs. Math. Struct. Comput. Sci. 28(3), 340–383 (2018)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Grzegorz, R., Hartmut, E., Hans-jorg, K.: Handbook of Graph Grammars and Computing by Graph Transformations, vol. 3: Concurrency, Parallelism, and Distribution. World Scientific (1999)Google Scholar
  4. 4.
    Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical system. Math. Syst. Theor. 3(4), 320–375 (1969)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kurth, W., Kniemeyer, O., Buck-Sorlin, G.: Relational growth grammars – a graph rewriting approach to dynamical systems with a dynamical structure. In: Banâtre, J.-P., Fradet, P., Giavitto, J.-L., Michel, O. (eds.) UPP 2004. LNCS, vol. 3566, pp. 56–72. Springer, Heidelberg (2005).  https://doi.org/10.1007/11527800_5CrossRefGoogle Scholar
  6. 6.
    Maignan, L., Spicher, A.: Global graph transformations. In: GCM@ ICGT, pp. 34–49 (2015)Google Scholar
  7. 7.
    Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer, New York (2012)zbMATHGoogle Scholar
  8. 8.
    Păun, G.: From cells to computers: computing with membranes (P systems). Biosystems 59(3), 139–158 (2001)CrossRefGoogle Scholar
  9. 9.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems, vol. 90. Academic press, New York (1980)zbMATHGoogle Scholar
  10. 10.
    Smith, C., Prusinkiewicz, P., Samavati, F.: Local specification of surface subdivision algorithms. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 313–327. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-25959-6_23CrossRefGoogle Scholar
  11. 11.
    Spicher, A., Giavitto, J.-L.: Interaction-based programming in MGS. In: Adamatzky, A. (ed.) Advances in Unconventional Computing. ECC, vol. 22, pp. 305–342. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-33924-5_13CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexandre Fernandez
    • 1
  • Luidnel Maignan
    • 1
  • Antoine Spicher
    • 1
    Email author
  1. 1.Université Paris-Est Créteil, LACLCréteil CedexFrance

Personalised recommendations