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Structural Equivalence of Regularly Extended E0L Grammars: An Automata Theoretic Proof

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Theory Is Forever

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3113))

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Abstract

Regularly extended E0L grammars allow an infinite number of rules for a given nonterminal provided that the set of right sides of the rules for each nonterminal is a regular language. We show that structural equivalence remains decidable for regularly extended E0L grammars.

The research of the first author was supported under the Natural Sciences and Engineering Research Council of Canada grant OGP0147224 and that of the second was supported under the grant HKUST6166/00E from the Research Grants Council of the Hong Kong SAR.

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References

  1. Albert, J., Giammarresi, D., Wood, D.: Normal form algorithms for extended context-free grammars. Theoret. Comput. Sci. 267, 35–47 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berstel, J., Boasson, L.: Formal properties of XML grammars and languages. Acta Informatica 38, 649–671 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brüggemann-Klein, A., Wood, D.: Caterpillars: A context-specification technique. Mark-up Languages: Theory & Practice 2, 81–106 (2000)

    Article  Google Scholar 

  4. Brüggemann-Klein, A., Wood, D.: The regularity of two-way nondeterministic tree automata languages. Internat. J. of Foundations of Computer Science 13, 67–81 (2002)

    Article  MATH  Google Scholar 

  5. Cameron, H.A., Wood, D.: Structural equivalence of regularly extended contextfree grammars and SGML DTDs (manuscript) (1996)

    Google Scholar 

  6. Gécseg, F., Steinby, M.: Tree Automata, Académiai Kiadó, Budapest (1984)

    Google Scholar 

  7. Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. III, pp. 1–68. Springer, Heidelberg (1997)

    Google Scholar 

  8. Istrate, G.: The strong equivalence of ET0L grammars. Inf. Process. Lett. 62, 171–176 (1997)

    Article  MathSciNet  Google Scholar 

  9. McNaughton, R.: Parenthesis grammars. J. Assoc. Comput. Mach. 14, 490–500 (1967)

    MATH  MathSciNet  Google Scholar 

  10. Niemi, V.: A normal form for structurally equivalent E0L grammars. In: Rozenberg, G., Salomaa, A. (eds.) Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology, pp. 133–148. Springer, Heidelberg (1992)

    Google Scholar 

  11. Ottmann, T., Wood, D.: Defining families of trees with E0L grammars. Discrete Applied Math. 32, 195–209 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ottmann, T., Wood, D.: Simplifications of E0L grammars. In: Rozenberg, G., Salomaa, A. (eds.) Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology, pp. 149–166. Springer, Heidelberg (1992)

    Google Scholar 

  13. Paull, M., Unger, S.: Structural equivalence of context-free grammars. J. Comput. System Sci. 2, 427–463 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  14. Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)

    MATH  Google Scholar 

  15. Salomaa, K., Wood, D., Yu, S.: Complexity of E0L structural equivalence. RAIRO Theoretical Informatics 29, 471–485 (1995)

    MATH  MathSciNet  Google Scholar 

  16. Salomaa, K., Wood, D., Yu, S.: Structural equivalence and ET0L grammars. Theoret. Comput. Sci. 164, 123–140 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  17. Salomaa, K., Yu, S.: Decidability of structural equivalence of E0L grammars. Theoret. Comput. Sci. 82, 131–139 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  18. Salomaa, K., Yu, S.: Decidability of EDT0L structural equivalence. Theoret. Comput. Sci. 276, 245–259 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Thatcher, J.W.: Tree automata: an informal survey. In: Aho, A.V. (ed.) Currents in the Theory of Computing, pp. 143–172. Prentice Hall, Englewood Cliffs (1973)

    Google Scholar 

  20. Wood, D.: Theory of Computation. John Wiley & Sons, New York (1987)

    MATH  Google Scholar 

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Salomaa, K., Wood, D. (2004). Structural Equivalence of Regularly Extended E0L Grammars: An Automata Theoretic Proof. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_23

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  • DOI: https://doi.org/10.1007/978-3-540-27812-2_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22393-1

  • Online ISBN: 978-3-540-27812-2

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