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Surjectivity of functors on grammars

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.

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References

  1. [1]

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

  2. [2]

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

  3. [3]

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

  4. [4]

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

  5. [5]

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

  6. [6]

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

  7. [7]

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

  8. [8]

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

  9. [9]

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

  10. [10]

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

  11. [11]

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

  12. [12]

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

  13. [13]

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

  14. [14]

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

  15. [15]

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

  16. [16]

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

  17. [17]

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

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

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Keywords

  • Computational Mathematic
  • Additional Theorem