2019•Electronic Notes in Theoretical Computer ScienceOpen access

Some Applications of the Formalization of the Pumping Lemma for Context-Free Languages

Marcus Vinícius Midena Ramos, José Bacelar Almeida, Nelma Moreira, Ruy J. G. B. de Queiroz

Abstract

Context-free languages are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma for Context-Free Languages states a property that is valid for all context-free languages, which makes it a tool for showing the existence of non-context-free languages. This paper presents a formalization, extending the previously formalized Lemma, of the fact that several well-known languages are not context-free. Moreover, we build on those results to construct a formal proof of the well-known property that context-free languages are not closed under intersection. All the formalization has been mechanized in the Coq proof assistant.

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Key concepts: Pumping lemma for regular languages, Abstract family of languages, Lemma (botany), Computer science, Context-free language, Context (archaeology), Formal language, Intersection (aeronautics)