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arXiv · 1705.09695

Regularity of languages generated by non context-free grammars over a singleton terminal alphabet

Alberto Pettorossi·Maurizio Proietti
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Abstract

It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any language in this superclass over a singleton terminal alphabet is regular. Our proof is based on a transformational approach and does not rely on Parikh's Theorem. Our result extends previously known results because there are languages that are not context-free, do satisfy the Pumping Lemma, and do not satisfy the hypotheses of Parikh's Theorem.

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Alberto Pettorossi, Maurizio Proietti. 2017-05-26. Regularity of languages generated by non context-free grammars over a singleton terminal alphabet. https://arxiv.org/abs/1705.09695

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