A strong pumping lemma for context-free languages

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A context-free language is shown to be equivalent to a set of sentences describable by sequences of strings related by finite substitutions on finite domains, and vice-versa. As a result, a necessary and sufficient version of the Classic Pumping Lemma is established. This result provides a guaranteed method of proving that a language is not context-free when such is the case. An example is given of a language which neither the Classic Pumping Lemma nor Parikh's Theorem can show to be non-context-free, although Ogden's Lemma can. The main result also establishes {anbamn} as a language which is not in the Boolean closure of deterministic context-free languages. © 1976.




Wise, D. S. (1976). A strong pumping lemma for context-free languages. Theoretical Computer Science, 3(3), 359–369. https://doi.org/10.1016/0304-3975(76)90052-9

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