A strong pumping lemma for context-free languages

AbstractA 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