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On the (combinatorial) structure of L languages without interactions (Extended Abstract)

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A. Ehrenfeucht,

G. RozenbergAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

Pages 137 - 144

https://doi.org/10.1145/800116.803762

Published: 05 May 1975 Publication History

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Abstract

This paper presents some such results for various families of L languages without interactions (see, e.g., [2] or [9]). We have chosen to investigate L languages (without interactions) because:

(i) they are physically well motivated, see, e.g., [5],

(ii) L systems may very well be algebraically the most natural way to define languages, see, e.g., [1],[7] and [10],

(iii) they contribute to our understanding of the essential differences between sequential and parallel string processing (rewriting), see, e.g. [2], [4], [8] and [11].

In this paper we investigate the families of ET0L and E0L languages and their deterministic subfamilies. After each theorem we present an example of a language that can be proved, using the theorem, to be not in the given family of languages.

References

[1]

Downey, P., Formal languages and recursion schemes, Ph.D. thesis, Harvard University, 1974.

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[2]

Ginsburg, S. and Rozenberg G., T0L schemes and control sets, Information and control, to appear.

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[3]

Herman, G.T. and Rozenberg, G., Developmental systems and languages, North-Holland Publ. Company, 1975.

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[4]

van Leeuwen, J., Notes on pre-set pushdown automata, in {9}.

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[5]

Lindenmayer, A., Developmental systems and languages in their biological context, Contribution to {3}.

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[6]

Rozenberg, G., Extension of tabled 0L systems and languages, International Journal of Computer and Information Sciences, v.2, 311-334, 1973.

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[7]

Rozenberg, G., Theory of L systems: from the point of view of formal language theory, in {9}.

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[8]

Rozenberg, G., On a family of acceptors for some classes of developmental languages, International Journal of Computer Mathematics, to appear.

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[9]

Rozenberg, G. and Salomaa, A (eds.), L systems, Lecture Notes in Computer Science No. 15, Springer-Verlag, 1974.

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[10]

Salomaa, A., Parallelism in rewriting systems, in Automata, Languages and Programming, Lecture Notes in Computer Science No. 14, Springer-Verlag, 1974.

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[11]

Savitch, W.J., Some characterizations of Lindemayer systems in terms of Chomsky-type grammars and stack machines, Information and Control, v.27, 37-60, 1975.

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Rozenberg G(2005)L systems, sequences and languagesGI — 5. Jahrestagung10.1007/3-540-07410-4_621(71-84)Online publication date: 4-Jun-2005
https://doi.org/10.1007/3-540-07410-4_621
Greibach S(1981)Formal LanguagesIEEE Annals of the History of Computing10.1109/MAHC.1981.100063:1(14-41)Online publication date: 1-Jan-1981
https://dl.acm.org/doi/10.1109/MAHC.1981.10006
Greibach S(1979)Formal languagesProceedings of the 20th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1979.19(66-90)Online publication date: 29-Oct-1979
https://dl.acm.org/doi/10.1109/SFCS.1979.19

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On the (combinatorial) structure of L languages without interactions (Extended Abstract)

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STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

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Published: 05 May 1975

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Rozenberg G(2005)L systems, sequences and languagesGI — 5. Jahrestagung10.1007/3-540-07410-4_621(71-84)Online publication date: 4-Jun-2005
https://doi.org/10.1007/3-540-07410-4_621
Greibach S(1981)Formal LanguagesIEEE Annals of the History of Computing10.1109/MAHC.1981.100063:1(14-41)Online publication date: 1-Jan-1981
https://dl.acm.org/doi/10.1109/MAHC.1981.10006
Greibach S(1979)Formal languagesProceedings of the 20th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1979.19(66-90)Online publication date: 29-Oct-1979
https://dl.acm.org/doi/10.1109/SFCS.1979.19

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On (un)predictability of formal languages (Extended Abstract)

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Embedding languages without breaking tools

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Iteration theorems for LL(k) languages (Extended Abstract)

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