Summary
For all n ≧2, we construct a context-free language L n for which we prove the following:
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a)
L n , has a cfg of size O(n)
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b)
Any chain rule free cfg for L n has size Ω(n log log n).
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References
Harrison, M.A.: Introduction to formal language theory. Addison-Wesley, 1978
Yehudai, A.: On the complexity of grammar and language problems, Dissertation, Berkeley, 1977
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Blum, N. On the power of chain rules in context free grammars. Acta Informatica 17, 425–433 (1982). https://doi.org/10.1007/BF00264161
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DOI: https://doi.org/10.1007/BF00264161