Advertisement

Structural Equivalence and ETOL grammars

Extended abstract
  • Kai Salomaa
  • Derick Wood
  • Sheng Yu
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 710)

Abstract

For a given context-sensitive grammar G we construct ET0L grammars G1 and G2 that are structurally equivalent if and only if the language generated by G is empty, which implies that structural equivalence is undecidable for ET0L grammars. This is in contrast to the decidability result for the E0L case. In fact, we show that structural equivalence is undecidable for propagating ET0L grammars even when the number of tables is restricted to be at most two. A stronger notion of equivalence that requires the sets of syntax trees to be isomorphic is shown to be decidable for ET0L grammars.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S. Ginsburg and M. Harrison, Bracketed context-free languages, J. Comput. System Sci. 1 (1967) 1–23.Google Scholar
  2. [2]
    R. McNaughton, Parenthesis grammars, J. Assoc. Comput. Mach. 14 (1967) 490–500.Google Scholar
  3. [3]
    V. Niemi, A normal form for structurally equivalent E0L grammars. In: “Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology”, G. Rozenberg and A. Salomaa (eds.), Springer-Verlag, 1992, pp. 133–148.Google Scholar
  4. [4]
    T. Ottmann and D. Wood, Defining families of trees with E0L grammars, Discrete Applied Math. 32 (1991) 195–209.CrossRefGoogle Scholar
  5. [5]
    T. Ottmann and D. Wood, Simplifications of E0L grammars. In: “Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology”, G. Rozenberg and A. Salomaa (eds.), Springer-Verlag, 1992, pp. 149–166.Google Scholar
  6. [6]
    M. Paull and S. Unger, Structural equivalence of context-free grammars, J. Comput. System Sci. 2 (1968) 427–463.Google Scholar
  7. [7]
    M. Penttonen, One-sided and two-sided context in formal grammars, Inform. Control 25 (1974) 371–392.CrossRefGoogle Scholar
  8. [8]
    G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, New York, 1980.Google Scholar
  9. [9]
    A. Salomaa, Formal Languages. Academic Press, New York, 1973.Google Scholar
  10. [10]
    K. Salomaa and S. Yu, Decidability of structural equivalence of E0L grammars, Theoret. Comput. Sci. 82 (1991) 131–139.CrossRefGoogle Scholar
  11. [11]
    J. W. Thatcher, Tree automata: an informal survey. In: “Currents in the Theory of Computing”, A. V. Aho (ed.), Prentice Hall, Englewood Cliffs, NJ, 1973, pp. 143–172.Google Scholar
  12. [12]
    D. Wood, Theory of Computation. John Wiley & Sons, New York, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Kai Salomaa
    • 1
  • Derick Wood
    • 1
  • Sheng Yu
    • 1
  1. 1.Department of Computer ScienceUniversity of Western OntarioLondonCanada

Personalised recommendations