English

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

Formal Languages and Automata Theory 2018-07-13 v2

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.

Keywords

Cite

@article{arxiv.1705.09695,
  title  = {Regularity of languages generated by non context-free grammars over a singleton terminal alphabet},
  author = {Alberto Pettorossi and Maurizio Proietti},
  journal= {arXiv preprint arXiv:1705.09695},
  year   = {2018}
}