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Conditional Lindenmayer Systems with Conditions Defined by Bounded Resources

  • Jürgen DassowEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)

Abstract

An extended conditional tabled Lindenmayer systems is an ET0L systems where each table is associated with a regular set, the so-called condition. A table can only be applied to a sentential form if the form belongs to its associated regular set. We study the power of conditional ET0L systems if the conditions are given by regular languages with a limited state or nonterminal complexity. We show that conditions obtained by regular grammars with two nonterminals and finite automata with three states are sufficient to generate all recursively enumerable languages. Similar results are given for the generation of all context-sensitive languages. Moreover, in the non-extended case, one gets infinite hierarchies for both complexity measures.

Keywords

Regular Language Sentential Form Contextual Grammar Regular Grammar Enumerable Language 
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.

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References

  1. 1.
    Dassow, J.: Conditional grammars with restrictions by syntactic parameters. In: Ito, M., Păun, Gh, Yu, Sh (eds.) Words, Semigroups, Transductions, pp. 59–68. World Scientific, Singapore (2001)CrossRefGoogle Scholar
  2. 2.
    Dassow, J.: Contextual grammars with subregular choice. Fundamenta Informaticae 64, 109–118 (2005)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Dassow, J.: Grammars with commutative, circular, and locally testable conditions. In: Automata, Formal Languages, and Related Topics - Dedicated to Ferenc Gécseg on the occasion of his 70th birthday, University of Szeged, 27–37 (2009)Google Scholar
  4. 4.
    Dassow, J., Hornig, H.: Conditional grammars with subregular conditions. In: Proc. Internat. Conf. Words, Languages and Combinatorics II, World Scientific Singapore, 71–86 (1994)Google Scholar
  5. 5.
    Dassow, J., Manea, F., Truthe, B.: On external contextual grammars with subregular selection languages. Theoretical Computer Science 449, 64–73 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dassow, J., Păun, G.: Regulated Rrewriting in Formal Language Theory. Springer-Verlag, Berlin (1989)CrossRefGoogle Scholar
  7. 7.
    Dassow, J.: Rudolf, St.: Conditional Lindenmayer systems with subregular conditions: the non-extended case. RAIRO -. Theor. Inf. Appl. 48, 127–147 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dassow, J., Rudolf, St.: Conditional Lindenmayer systems with subregular conditions: the extended case. SubmittedGoogle Scholar
  9. 9.
    Dassow, J., Stiebe, R., Truthe, B.: Two collapsing hierarchies of subregularly tree controlled languages. Theoretical Computer Science 410, 3261–3271 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Dassow, J., Stiebe, R., Truthe, B.: Generative capacity of subregularly tree controlled grammars. International Journal of Foundations of Computer Science 21, 723–740 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gruska, J.: On a classification of context-free languages. Kybernetika 1, 22–29 (1967)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Gruska, J.: Some classifications of context-free languages. Information and Control 14, 152–179 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Manea, F., Truthe, B.: On internal contextual grammars with subregular selection languages. In: Kutrib, M., Moreira, N., Reis, R. (eds.) DCFS 2012. LNCS, vol. 7386, pp. 222–235. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Păun, G.: Marcus Contextual Grammars. Kluwer Publ. House, Doordrecht (1998)zbMATHGoogle Scholar
  15. 15.
    Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer-Verlag, Berlin (1997)CrossRefzbMATHGoogle Scholar
  16. 16.
    Rozenberg, G., von Solms, S.H.: Priorities on context conditions in rewriting systems. Inform. Sci. 14, 15–51 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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