Analyses of the case studies for the efficiency of pumping lemma for the context-free languages

Abstract

In this study, we investigated the pumping lemma for context-free languages and analyzed some case studies in terms of their efficiency. Pumping lemmas play an important role in formal language theory. Context-free languages (CFL) is the set of languages that can be defined by context-free grammars. Context-free grammars are used to define programming languages, natural language applications (such as grammar correctors), machine protocols and many others. The case studies are used to simplify the process analyses of the efficiency of pumping lemma for Context-Free Languages. To prove that a Language is Not Context-Free using pumping lemma for CFL, we created a guideline presented in the fourth section that contains a proposed algorithmic procedure. Pumping lemma for CFL is used to show the existence of non-context free languages. Insights and argumentations were provided in the end of the paper.