Skip to main content
Log in

On non context-free grammar forms

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

A grammar formF defines via a so-calledinterpretation mechanism, a family of languages

(F). In this paper we establish that for many grammar formsF,

(the family of context-free languages) implies

(F)=

RE (the family of recursively enumerable sets). We conjecture that this is also true in general. Because of this, it seems necessary to use restricted interpretations for non context-free grammar forms, a form giving then rise to a family

We compare the obvious alternatives for restricting interpretations and focus attention on two promising alternatives,

Q (F) and

st(F) and their combination

Q, st(F). Using st-interpretations, surprising families can be generated and strong normal form results can be obtained. Closure results and decidability results are also given. UnderQ, st-interpretation, it is possible to characterize a number of well-known families of languages between

CF and

RE, including the families of EOL, ETOL, matrix and scattered context languages.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. B. Cremers, S. Ginsburg, Context-Free Grammar Forms,J. of Computer and System Sciences 11, 86–117, (1975).

    Google Scholar 

  2. A. B. Cremers, O. Mayer, On Vector Languages.J. of Computer and System Sciences 7, 158–166 (1974).

    Google Scholar 

  3. S. Ginsberg,Algebraic and automata-theoretic properties of formal languages. North Holland, Amsterdam, (1975).

    Google Scholar 

  4. S. Ginsburg, E. Spanier, Substitutions of Grammar Forms.Acta Informatica 5, 377–386 (1975).

    Google Scholar 

  5. H. A. Maurer,Theoretische Grundlagen der Programmiersprachen BI, Mannheim, (1969).

    Google Scholar 

  6. H. A. Maurer, A. Salomaa D. Wood, EOL Forms.Acta Informatica 8, 75–96 (1977).

    Google Scholar 

  7. H. A. Maurer, A. Salomaa, D. Wood, Uniform Interpretations ofL Forms.Information and Control 36, 157–173 (1978).

    Google Scholar 

  8. A. Salomaa,Formal Languages. Academic Press, New York (1973).

    Google Scholar 

  9. W. Savitch, How to make arbitrary Grammars look like Context-Free Grammars.SIAM J. Computing 2, 174–182 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Part of this work was carried out while the third and fourth authors were visiting the University of Karlsruhe. Part of this work was supported by the Natural Sciences and Engineering Research Council of Canada Grant No. A-7700.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maurer, H.A., Penttonen, M., Salomaa, A. et al. On non context-free grammar forms. Math. Systems Theory 12, 297–324 (1978). https://doi.org/10.1007/BF01776580

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01776580

Keywords

Navigation