L systems, sequences and languages

  • G. Rozenberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 34)


In this paper we provide a short overview of the mathematical theory of L systems. Because of the limitations on the size of this paper the overview is very concise and it treats only the small fragment of the existing theory (the choice of the material covered strongly reflects the personal point of view of the author). Still it is hoped that the reader will get an idea what are the L systems about and may be some of the readers will join the research in this interesting and very promising area.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

V. References

  1. [1].
    J. Carlyle, S. Greibach and A. Paz, A two-dimensional generating system modding growth by binary cell division, 15th Annual Symposium on Switching and Automata Theory, 1974.Google Scholar
  2. [2].
    K. Culik II and A. Lindenmayer, Parallel rewriting on graphs and multidimensional development, Dept. of Computer Science, University of Waterloo, Canada, Techn. Report No. CS-74-22, 1974.Google Scholar
  3. [3].
    P. Downey, Formal languages and recursion schemes, Ph. D. dissertation, Harvard University, 1974.Google Scholar
  4. [4].
    A. Ehrenfeucht and G. Rozenberg, A limit theorem for sets of subwords in deterministic T0L languages, Information Processing Letters, 2, 10–73, 1973.Google Scholar
  5. [5].
    A. Ehrenfeucht and G. Rozenberg, The number of occurrences of letters versus their distribution in some E0L languages, Information and Control, 26, 256–271, 1974.Google Scholar
  6. [6].
    A. Ehrenfeucht and G. Rozenberg, The equality of E0L languages and codings of 0L languages, International Journal of Computer Mathematics, 4, 95–104, 1974.Google Scholar
  7. [7].
    A. Ehrenfeucht and G. Rozenberg, Nonterminals versus homomorphisms in defining languages for some classes of rewriting systems, Acta Informatica, 3, 265–283, 1974.Google Scholar
  8. [8].
    A. Ehrenfeucht and G. Rozenberg, On the (combinatorial) structure of L languages without interactions, 7th Annual ACM Symposium on Theory of Computing, 1975.Google Scholar
  9. [9].
    A. Ehrenfeucht and G. Rozenberg, A characterization theorem for a subclass of ET0L languages, Acta Informatica, to appear.Google Scholar
  10. [10].
    C. Ellis, The validation of parallel co-operating processes, Dept. of Computer Science, University of Colorado at Boulder, U.S.A., Techn. Rep. No. CU-CS-065-75, 1975.Google Scholar
  11. [11].
    G. T. Herman, Simulation of organisms based on L systems, 1974 Conference of Biologically Motivated Automata Theory, 1974.Google Scholar
  12. [12].
    G.T. Herman and G. Rozenberg, Developmental systems and languages, North-Holland Publ. Comp., Amsterdam. 1975.Google Scholar
  13. [13].
    G.T. Herman, A. Lindenmayer and G. Rozenberg, Description of developmental languages using recurrence systems, Mathematical Systems Theory, 8, 316–341, 1975.Google Scholar
  14. [14].
    J. van Leeuwen, Notes on pre-set pushdown automata, in [24], 177–189, 1974.Google Scholar
  15. [15].
    A. Lindenmayer, Mathematical models for cellular interactions in development, Parts I and II, Journal of Theoretical Biology, 18, 280–315, 1968.Google Scholar
  16. [16].
    A. Lindenmayer, Developmental systems and languages in their biological context, Chapter 0 in 12, 1975.Google Scholar
  17. [17].
    A. Lindenmayer, L systems in their biological context, Journ. of Theoretical Biology, to appear.Google Scholar
  18. [18].
    A. Paz and A. Salomaa, Integral sequential word functions and growth equivalence of Lindenmayer systems, Information and Control, 23, 313–343, 1973.Google Scholar
  19. [19].
    G. Rozenberg, T0L systems and languages, Information and Control, 23, 357–381, 1973.Google Scholar
  20. [20].
    G. Rozenberg, Extension of tabled 0L systems and languages, International Journal of Computer and Information Sciences, 2, 311–336, 1973.Google Scholar
  21. [21].
    G. Rozenberg, D0L sequences, Discrete Mathematics, 7, 323–347, 1974.Google Scholar
  22. [22].
    G. Rozenberg, On a family of acceptors for some classes of developmental languages, International Journal of Computer Mathematics, 4. 199–228, 1974.Google Scholar
  23. [23].
    G. Rozenberg and A. Lindenmayer, Developmental systems with locally catenative formulas, Acta Informatica, 2, 214–248, 1973.Google Scholar
  24. [24].
    G. Rozenberg and A. Salomaa (eds), L systems, Lecture Notes in Computer Science, v. 15, Springer-Verlag, 1974.Google Scholar
  25. [25].
    G. Rozenberg and A. Salomaa, The mathematical theory of L systems, Progress in Information Processing (edited by J. Tou), to appear.Google Scholar
  26. [26].
    C. Roman, R systems, Ph. D. thesis, Moore School of Electr. Engineering, 1975.Google Scholar
  27. [27].
    A. Salomaa, On exponential growth in Lindenmayer systems, Indagationes Mathematicae, 35, 23–30, 1973.Google Scholar
  28. [28].
    W. Savitch, Some characterizations of Lindenmayer systems in terms of Chomsky-type grammars and stack machines, Information and Control, 27, 37–60, 1975.Google Scholar
  29. [29].
    A Szilard, Growth functions of Lindenmayer systems, Dept. of Computer Science, University of Western Ontario, Canada, Techn. Rep. No. 4, 1971.Google Scholar
  30. [30].
    P. Vitanyi, Structure of growth in Lindenmayer systems, Indagationes Mathematicae, 35, 247–253, 1973.Google Scholar
  31. [31].
    A. Walker, Adult languages of L systems and the Chomsky hierarchy, in [24], 201–216, 1974.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • G. Rozenberg
    • 1
    • 2
  1. 1.Department of MathematicsAntwerp University, UIAWilrijkBelgium
  2. 2.Institute of MathematicsUtrecht UniversityUtrechtHolland

Personalised recommendations