Skip to main content
SpringerLink
Log in

Surjectivity of functors on grammars

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

We present a procedure for deciding a sufficient condition for equivalence of context-free grammars. The main focus of the paper is on deciding whether a given functor between two grammars is surjective. An additional theorem gives us the means for deciding a certain type of structural similarity which is defined by the existence of such a functor.

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

Access this article

Log in via an institution

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. Y. Bar-Hillel,et al., Measures of syntactic complexity,Machine Translation (edited by A. D. Booth), North Holland, 1967.

  2. D. Benson, Syntax and semantics: a categorical view,Information and Control 17 (1970), 145–160.

    Google Scholar 

  3. E. Bertsch,Existenz- und Entscheidbarkeitsfragen der Übersetzungstheorie, doctoral thesis, Saarbrücken, 1973.

  4. E. Bertsch, Classes of mappings between context-free derivation systems,Lecture Notes in Computer Science 2 (1973), 278–283.

    Google Scholar 

  5. E. Bertsch, A decidability result for sequential grammars,Lecture Notes in Computer Science 14 (1974), 577–583.

    Google Scholar 

  6. S. Ginsburg,The Mathematical Theory of Context-free Languages, McGraw-Hill, 1966.

  7. G. Hotz, Eindeutigkeit und Mehrdeutigkeit formaler Sprachen, Elektr.,Inform. und Kybern. 2 (1966), 235–246.

    Google Scholar 

  8. G. Hotz, Reduktionssätze über eine Klasse formaler Sprachen mit endlich vielen Zuständen,Math. Zeitschrift 104 (1968), 205–221.

    Google Scholar 

  9. G. Hotz, Übertragung automatentheoretischer Sätze auf Chomsky-Sprachen,Computing 4 (1969), 30–42.

    Google Scholar 

  10. G. Hotz andV. Claus,Automatentheorie und formale Sprachen, Vol. III, BI-Verlag, Mannheim, 1972.

    Google Scholar 

  11. H. Maurer,Theoretische Grundlagen der Programmier-Sprachen, BI-Verlag, Mannheim, 1969.

    Google Scholar 

  12. C. Schnorr, Reguläre Untergrammatiken,4th Colloquium on Automata Theory, Munich, 1967.

  13. C. Schnorr, Vier Entscheidbarkeitsprobleme für kontextsensitive Sprachen,Computing 3 (1968), 311–317.

    Google Scholar 

  14. C. Schnorr, Transformational classes of grammars,Information and Control 14 (1969), 252–277.

    Google Scholar 

  15. C. Schnorr andH. Walter, Pullback-Konstruktionen bei Semi-Thue-Systemen,Elektr. Inform. und Kybern. 5 (1969), 27–36.

    Google Scholar 

  16. J. Thatcher, Generalized2 sequential machine maps,J. Computer and System Sciences 4 (1970), 339–367.

    Google Scholar 

  17. H. Walter,Einige topologische Aspekte der syntaktischen Analyse und Übersetzung, Research report AFS-1, TH Darmstadt, 1972.

Download references

Author information

Authors and Affiliations

  1. Fachbereich Angewandte Mathematik, Universität des Saarlandes, 66 Saarbrücken, Germany

    Eberhard Bertsch

Authors
  1. Eberhard Bertsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bertsch, E. Surjectivity of functors on grammars. Math. Systems Theory 9, 298–307 (1975). https://doi.org/10.1007/BF01735147

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01735147

Keywords

Search

Navigation