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.
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References
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.
Aho, A. V., J. D. Ullman, The Theory of Parsing, Translating and Compiling, volume 1, Prentice Hall, Englewood Cliffs, 1972.
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.
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.
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© 1974 Springer-Verlag Berlin Heidelberg
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Walker, A. (1974). Adult languages of L systems and the Chomsky hierarchy. In: Rozenberg, G., Salomaa, A. (eds) L Systems. Lecture Notes in Computer Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06867-8_16
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DOI: https://doi.org/10.1007/3-540-06867-8_16
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