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
Albert, J., Giammarresi, D., Wood, D.: Normal form algorithms for extended context-free grammars. Theoret. Comput. Sci. 267, 35–47 (2001)
Berstel, J., Boasson, L.: Formal properties of XML grammars and languages. Acta Informatica 38, 649–671 (2002)
Brüggemann-Klein, A., Wood, D.: Caterpillars: A context-specification technique. Mark-up Languages: Theory & Practice 2, 81–106 (2000)
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)
Cameron, H.A., Wood, D.: Structural equivalence of regularly extended contextfree grammars and SGML DTDs (manuscript) (1996)
Gécseg, F., Steinby, M.: Tree Automata, Académiai Kiadó, Budapest (1984)
Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. III, pp. 1–68. Springer, Heidelberg (1997)
Istrate, G.: The strong equivalence of ET0L grammars. Inf. Process. Lett. 62, 171–176 (1997)
McNaughton, R.: Parenthesis grammars. J. Assoc. Comput. Mach. 14, 490–500 (1967)
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)
Ottmann, T., Wood, D.: Defining families of trees with E0L grammars. Discrete Applied Math. 32, 195–209 (1991)
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)
Paull, M., Unger, S.: Structural equivalence of context-free grammars. J. Comput. System Sci. 2, 427–463 (1968)
Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)
Salomaa, K., Wood, D., Yu, S.: Complexity of E0L structural equivalence. RAIRO Theoretical Informatics 29, 471–485 (1995)
Salomaa, K., Wood, D., Yu, S.: Structural equivalence and ET0L grammars. Theoret. Comput. Sci. 164, 123–140 (1996)
Salomaa, K., Yu, S.: Decidability of structural equivalence of E0L grammars. Theoret. Comput. Sci. 82, 131–139 (1991)
Salomaa, K., Yu, S.: Decidability of EDT0L structural equivalence. Theoret. Comput. Sci. 276, 245–259 (2002)
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)
Wood, D.: Theory of Computation. John Wiley & Sons, New York (1987)
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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
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