Mathematical systems theory

, Volume 8, Issue 4, pp 316–341 | Cite as

Description of developmental languages using recurrence systems

  • G. T. Herman
  • A. Lindenmayer
  • G. Rozenberg


Recurrence systems have been devised to describe formally certain types of biological developments. A recurrence system specifies a formal language associated with the development of an organism. The family of languages defined by recurrence systems is an extension of some interesting families of languages, including the family of context-free languages. Some normal-form theorems are proved and the equivalence of the family of recurrence languages to a previously studied family of developmental languages (EOL-languages) is shown. Various families of developmental and other formal languages are characterized using recurrence systems. Some closure properties are also discussed.


Computational Mathematic Biological Development Formal Language Interesting Family Closure Property 
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  1. [1]
    M. Blattner, The unsolvability of the equality problem for sentential forms of contextfree languages,J. Computer System Sciences 7 (1973), 463–468.Google Scholar
  2. [2]
    A. Ehrenfeucht andG. Rozenberg, The equality of EOL languages and codings of OL languages,Internat. J. Computer Math., to appear.Google Scholar
  3. [3]
    R. W. Floyd, On the nonexistence of a phrase structure grammar for algol 60,Comm. ACM 5 (1962), 483–484.Google Scholar
  4. [4]
    S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.Google Scholar
  5. [5]
    S. Ginsburg andH. G. Rice, Two families of languages related to algol,J. ACM 9 (1962), 350–371.Google Scholar
  6. [6]
    G. T. Herman, Closure properties of some families of languages associated with biological systems,Information and Control,24 (1974), 101–121.Google Scholar
  7. [7]
    G. T. Herman, A biologically motivated extension of algol-like languages,Information and Control 22 (1973), 487–502.Google Scholar
  8. [8]
    P. Hogeweg andB. Hesper, Pattern recognition in biology: A methodical analysis using computer experimentation,IV Int. Congress Logic, Methodology, Philosophy of Science (1971), Abstract, 279–280.Google Scholar
  9. [9]
    J. E. Hopcroft andJ. D. Ullman,Formal languages and their Relation to Automata, Addison-Wesley, Reading, Mass., 1969.Google Scholar
  10. [10]
    E. Konrad-Hawkins, Developmental studies of regenerates ofCallithamnion reseum Harvey,Protoplasma 58 (1964), 42–74.Google Scholar
  11. [11]
    A. Lindenmayer, Mathematical models for cellular interactions in development, Part I and Part II,Journal of Theoretical Biology 18 (1968), 280–299, 300–315.Google Scholar
  12. [12]
    A. Lindenmayer, Developmental systems without cellular interactions, their languages and grammars,J. Theoretical Biology 30 (1971), 455–485.Google Scholar
  13. [13]
    A. Lindenmayer andG. Rozenberg, Developmental systems and languages,Proc. 4th Annual ACM Symp. on Theory of Computing (1972), 214–221.Google Scholar
  14. [14]
    G. F. Rose, An extension of algol-like languages,Comm. ACM 7 (1964), 52–61.Google Scholar
  15. [15]
    G. Rozenberg, Direct proofs of the undecidability of the equivalence problem for sentential forms of linear context-free grammars and the equivalence problems for OL-systems,Information Processing Letters 1 (1972), 233–235.Google Scholar
  16. [16]
    G. Rozenberg,L-systems with interactions,J. Computer System Sciences, to appear.Google Scholar
  17. [17]
    G. Rozenberg andP. Doucet, On OL-languages,Information and Control 19 (1971), 302–318.Google Scholar
  18. [18]
    G. Rozenberg andA. Lindenmayer, Developmental systems with locally catenative formulas,Acta Information 2 (1973), 214–248.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1975

Authors and Affiliations

  • G. T. Herman
    • 1
  • A. Lindenmayer
    • 1
  • G. Rozenberg
    • 2
  1. 1.State University of New York at BuffaloUSA
  2. 2.Rijksuniversiteit UtrechtNetherlands

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