Skip to main content

Conditional Lindenmayer Systems with Conditions Defined by Bounded Resources

  • Chapter
  • First Online:
  • 878 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Chapter  Google Scholar 

  2. Dassow, J.: Contextual grammars with subregular choice. Fundamenta Informaticae 64, 109–118 (2005)

    MathSciNet  MATH  Google Scholar 

  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. 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. Dassow, J., Manea, F., Truthe, B.: On external contextual grammars with subregular selection languages. Theoretical Computer Science 449, 64–73 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dassow, J., Păun, G.: Regulated Rrewriting in Formal Language Theory. Springer-Verlag, Berlin (1989)

    Book  Google Scholar 

  7. Dassow, J.: Rudolf, St.: Conditional Lindenmayer systems with subregular conditions: the non-extended case. RAIRO -. Theor. Inf. Appl. 48, 127–147 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dassow, J., Rudolf, St.: Conditional Lindenmayer systems with subregular conditions: the extended case. Submitted

    Google Scholar 

  9. Dassow, J., Stiebe, R., Truthe, B.: Two collapsing hierarchies of subregularly tree controlled languages. Theoretical Computer Science 410, 3261–3271 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gruska, J.: On a classification of context-free languages. Kybernetika 1, 22–29 (1967)

    MathSciNet  MATH  Google Scholar 

  12. Gruska, J.: Some classifications of context-free languages. Information and Control 14, 152–179 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  14. Păun, G.: Marcus Contextual Grammars. Kluwer Publ. House, Doordrecht (1998)

    MATH  Google Scholar 

  15. Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer-Verlag, Berlin (1997)

    Book  MATH  Google Scholar 

  16. Rozenberg, G., von Solms, S.H.: Priorities on context conditions in rewriting systems. Inform. Sci. 14, 15–51 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jürgen Dassow .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Dassow, J. (2014). Conditional Lindenmayer Systems with Conditions Defined by Bounded Resources. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13350-8_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13349-2

  • Online ISBN: 978-3-319-13350-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics