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L Systems pp 201-215 | Cite as

Adult languages of L systems and the Chomsky hierarchy

  • Adrian Walker
Different Ways Of Defining L Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 15)

Abstract

Theorems 1 – 4 give us a satisfactory analysis of L systems from the point of view of the adult languages they generate, for they establish direct correspondences with three of the four main classes of languages in the Chomsky hierarchy. The remaining class is that of the regular languages, and it is an easy exercise to restrict the form of the productions of a 0L system to ensure that its adult language is regular. In Walker† it is shown that the result for 2L systems can be extended to 〈k, l〉L systems (see Herman and Rozenberg [45] for the definition of such systems) with k+l≥1, and that the result for P2L systems can be extended to P<k, l>L systems with k, l≥1.

From the point of view of formal language theory, we have given a new characterization, by totally parallel grammars, of each of the classes of languages in the Chomsky hierarchy. From the point of view of biological model building, we have gained access to many of the established results of formal language theory.

Keywords

Turing Machine Regular Language Context Free Language Formal Grammar Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. †.
    Hopcroft, J. E., J. D. Ullman, Formal Languages and their Relation to Automata, Addison-Wesley, Reading, Mass., 1969. From now on we refer to this book simply as H & U.Google Scholar
  2. †.
    Aho, A. V., J. D. Ullman, The Theory of Parsing, Translating and Compiling, volume 1, Prentice Hall, Englewood Cliffs, 1972.Google Scholar
  3. †.
    Walker, A. D., Formal Grammars and the Stability of Biological Organisms, Ph.D. thesis, Department of Computer Science, State University of New York at Buffalo, 1974.Google Scholar
  4. †.
    Walker, A. D., Formal Grammars and the Stability of Biological Organisms, Ph.D. thesis, Department of Computer Science, State University of New York at Buffalo, 1974.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Adrian Walker
    • 1
  1. 1.Department of Computer ScienceState University of New York at BuffaloUSA

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