Too many languages satisfy Ogden's Lemma

Ogden's Lemma for Coupled-Context-Free Languages; the Set of Lyndon Words is not Coupled-Context-Free

Pumping Lemma and Ogden Lemma for Displacement Context-Free Grammars

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 multiplecontext 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 the class of tree-adjoining language...

Ogden's Lemma, Multiple Context-Free Grammars, and the Control Language Hierarchy

Abstract. I present a simple example of a multiple context-free language for which a very weak variant of generalized Ogden’s lemma fails. This language is generated by a non-branching (and hence well-nested) 3MCFG as well as by a (non-well-nested) binary-branching 2-MCFG; it follows that neither the class of well-nested 3-MCFLs nor the class of 2-MCFLs is included in Weir’s control language hi...

Ogden's Lemma for Regular Tree Languages

Pumping lemmata are elementary tools for the analysis of formal languages. While they usually cannot be made strong enough to fully capture a class of languages, it is generally desirable to have as strong pumping lemmata as possible. However, this is counterbalanced by the experience that strong pumping lemmata may be hard to prove, or, worse, hard to use—this experience has been made, for exa...

A Proof of the Pumping Lemma for Context-Free Languages Through Pushdown Automata

The pumping lemma for context-free languages is a result about pushdown automata which is strikingly similar to the well-known pumping lemma for regular languages. However, though the lemma for regular languages is simply proved by using the pigeonhole principle on deterministic automata, the lemma for pushdown automata is proven through an equivalence with context-free languages and through th...