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

The pumping lemma for context-free languages is a result about pushdown\nautomata which is strikingly similar to the well-known pumping lemma for\nregular languages. However, though the lemma for regular languages is simply\nproved by using the pigeonhole principle on deterministic automata, the lemma\nfor pushdown automata is proven through an equivalence with context-free\nlanguages and through the more powerful Ogden's lemma. We present here a proof\nof the pumping lemma for context-free languages which relies on pushdown\nautomata instead of context-free grammars.\n