Pumping lemma and Ogden lemma for displacement context-free grammars

TL;DR

This paper develops stronger versions of the pumping and Ogden lemmas for displacement context-free grammars, enabling better proofs of non-generability of certain languages and advancing formal language theory.

Contribution

It introduces enhanced pumping and Ogden lemmas for displacement context-free grammars, improving tools for language classification and analysis.

Findings

Stronger pumping lemma for displacement context-free grammars

Ogden lemma analogue for this language family

Certain natural context-sensitive languages cannot be generated by tree-adjoining grammars

Abstract

The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiple-context free languages. However, the statement of lemma is too weak for practical usage. We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for this language family. We also use these statements to prove that some natural context-sensitive languages cannot be generated by tree-adjoining grammars.