Skip to main content
SpringerLink
Log in

On the Number of Non-Terminal Symbols in Graph-Controlled, Programmed and Matrix 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 improve the results elaborated in [6] on the number of non-terminal symbols needed in matrix grammars, programmed grammars, and graph-controlled grammars with appearance checking for generating arbitrary recursively enumerable languages. Of special interest is the result that the number of non-terminal symbols used in the appearance checking mode can be restricted to two. In the case of graph controlled (and programmed grammars) with appearance checking also the number of non-terminal symbols can be reduced to three (and four, respectively); in the case of matrix grammars with appearance checking we either need four non-terminal symbols with three of them being used in the appearance checking mode or else again we only need two non-terminal symbols being used in the appearance checking mode, but in that case we cannot bound the total number of non-terminal symbols.

Work supported by Bundesministerium für Bildung, Wissenschaft und Kunst, Austria, grant GZ 55.300/269-VII/D/5a/2000 and by a grant of the NATO Science Committee, Spain, 2000-2001

Acknowledgement

We gratefully acknowledge some interesting discussions with Henning Fernau.

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. C. Calude and Gh. Păun. Computing with Cells and Atoms. Taylor and Francis, London, 2000.

    Google Scholar 

  2. J. Dassow and Gh. Păun. Regulated Rewriting in Formal Language Theory. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  3. H. Fernau. Nonterminal complexity of programmed grammars. This volume.

    Google Scholar 

  4. R. Freund and Gh. Păun. Computing with Membranes: Three More Collapsing Hierarchies. Submitted, 2000 (also presented at the EMCC Meeting in Milano, Italy, November 3rd, 2000).

    Google Scholar 

  5. M. L. Minsky. Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs, New Jersey, USA.

    Google Scholar 

  6. Gh. Păun. Six Nonterminals are Enough for Generating Each R.E. Language by a Matrix Grammar. Intern. J. Computer Math. 15 (1984), pp. 23–37.

    Article  MATH  Google Scholar 

  7. Gh. Păun. Computing with Membranes. Journal of Computer and System Sciences 1, 1 (2000), pp. 108–143.

    Article  Google Scholar 

  8. G. Rozenberg and A. Salomaa (eds.). Handbook of Formal Languages, 3 volumes. Springer-Verlag, Berlin, 1997.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Computer Languages, Vienna University of Technology, Favoritenstraße 9, A-1040, Wien, Austria

    Rudolf Freund

  2. Institute of Mathematics of the Romanian Academy, 1-764, 70700, Bucureşti, Romania

    Gheorghe Păun

Authors
  1. Rudolf Freund
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gheorghe Păun
    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

Freund, R., Păun, G. (2001). On the Number of Non-Terminal Symbols in Graph-Controlled, Programmed and Matrix 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_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-45132-3_14

  • 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