Remarks on the nonexistence of some covering grammars
The problem of covering context-free grammars by grammars in some normal forms is considered. It is shown that certain example grammars cannot be covered by grammars which are in ε-free form or in Greibach normal form or in Chomsky normal form. The results are generalized using a concept called the structural similarity of context-free grammars. Finally, a grammatical transformation method for constructing ε-free covers is given.
KeywordsNormal Form Derivation Tree Empty String Start Symbol Recursive Part
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- 1.Aho, A.V. and J.D. Ullman: The Theory of Parsing, Translation, and Compiling, Vol.I: Parsing. Prentice-Hall, Englewood Cliffs, N.J., 1972.Google Scholar
- 2.Gray, J.N. and M.A. Harrison: On the covering and reduction problems for context-free grammars. J. Assoc. Comput. Mach. 19 (1972), 675–698.Google Scholar
- 3.Nijholt, A.: Cover results and normal forms. In: Proc. 6th Int. Symp. on Mathematical Foundations of Computer Science (ed. J. Gruska), Lect. Notes in Computer Science 53, pp. 420–429, Springer-Verlag, Berlin-Heidelberg-New York, 1977.Google Scholar
- 4.Nijholt,A.: On the covering of left-recursive grammars. Conf. Record of the Fourth ACM Symposium on Principles of Programming Languages, pp. 86–96, 1977.Google Scholar
- 5.Nijholt,A.: Structure preserving transformations on non-left-recursive grammars. Report IR-39, Vrije Universiteit Amsterdam, 1978.Google Scholar
- 6.Salomaa, A.: Formal Languages. Academic Press, New York and London, 1973.Google Scholar
- 7.Ukkonen, E.: Transformations to produce certain covering grammars. In: Proc. 7th Int. Symp. on Mathematical Foundations of Computer Science (ed. J. Winkowski), Lect. Notes in Computer Science 64, pp. 516–525, Springer-Verlag, Berlin-Heidelberg-New York, 1978.Google Scholar