Skip to main content
SpringerLink
Log in

Nonterminal Complexity of Programmed Grammars

  • Conference paper
  • First Online:
Machines, Computations, and Universality (MCU 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2055))

Included in the following conference series:

Abstract

We show that, in the case of context-free programmed grammars with appearance checking working under free derivations, three nonterminals are enough to generate every recursively enumerable language. This improves the previously published bound of eight for the nonterminal complexity of these grammars. This also yields an improved nonterminal complexity bound of four for context-free matrix grammars with appearance checking. Moreover, we establish nonterminal complexity bounds for context-free programmed and matrix grammars working under leftmost derivations.

Acknowledgments

We are grateful for immediate answers of our colleagues H.Bordihn and Gh.Păun concerning questions on syntactic complexity and for some discussions with R.F reund and F.Stephan.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Dassow and Gh. Păun. Regulated Rewriting in Formal Language Theory. Berlin: Springer, 1989.

    Google Scholar 

  2. H. Fernau. Unconditional transfer in regulated rewriting. Acta Informatica, 34:837–857, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Fernau. On regulated grammars under leftmost derivation. GRAMMARS, 3:37–62, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Fernau and F. Stephan. Characterizations of recursively enumerable languages by programmed grammars with unconditional transfer. Journal of Automata, Languages and Combinatorics, 4(2):117–142, 1999.

    MATH  MathSciNet  Google Scholar 

  5. R. Freund and Gh. Păun. On the number of non-terminal symbols in graph controlled, programmed and matrix grammars. This volume.

    Google Scholar 

  6. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Reading (MA): Addison-Wesley, 1979.

    MATH  Google Scholar 

  7. T. Kasai. A hierarchy between context-free and context-sensitive languages. Journal of Computer and System Sciences, 4:492–508, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Meduna. Syntactic complexity of scattered context grammars. Acta Informatica, 32:285–298, 1995.

    MATH  MathSciNet  Google Scholar 

  9. A. Meduna. Four-nonterminal scattered context grammars characterize the family of recursively enumerable languages. International Journal of Computer Mathematics, 63:67–83, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Meduna. Generative power of three-nonterminal scattered context grammars. Theoretical Computer Science, 246:279–284, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Meduna and Gy. Horváth. On state grammars. Acta Cybernetica, 8:237–245, 1988.

    MathSciNet  Google Scholar 

  12. Gh. Păun. Six nonterminals are enough for generating each r.e. language by a matrix grammar. International Journal of Computer Mathematics, 15:23–37, 1984.

    Article  MATH  Google Scholar 

  13. D. J. Rosenkrantz. Programmed grammars and classes of formal languages. Journal of the ACM, 16(1):107–131, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  14. C. E. Shannon. A universal Turing machine with two internal states. IN: Automata Studies, pages 157–165. Princeton University Press, 1956.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Täbingen, Sand 13, D-72076, Tübingen, Germany

    Henning Fernau

Authors
  1. Henning Fernau
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LITA, UFR MIM, Université de Metz, Ile du Saulcy, 57045, Metz, Cedex, France

    Maurice Margenstern

  2. Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, 5 Academiei str, 2028, Chiŗinău, Moldova

    Yurii Rogozhin

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fernau, H. (2001). Nonterminal Complexity of Programmed Grammars. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45132-3_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42121-4

  • Online ISBN: 978-3-540-45132-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation