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Here we give a proof of Ogden's Lemma, which is a generalization of the pumping lemma for context-free languages. It's the same general idea, except now we can arbitrarily mark a number of symbols in the string, and the decomposition of the string contains some number of marked symbols. This generalizes the usual pumping lemma because the usual PL has "marked" symbols as being all of the symbols in the string. But for Ogden's Lemma, we can have some unmarked characters. Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Names are listed in alphabetical order by surname. Platinum: Micah Wood Silver: Dolev Abuhazira, Simone Glinz, Timmy Gy, Josh Hibschman, Patrik Keinonen, Travis Schnider, and Tao Su Easy Theory Website: https://www.easytheory.org Become a member: / @easytheory Donation (appears on streams): https://streamlabs.com/easytheory1/tip Paypal: https://paypal.me/easytheory Patreon: / easytheory Discord: / discord Merch: Language Hierarchy Apparel: https://teespring.com/language-hierar... Pumping Lemma Apparel: https://teespring.com/pumping-lemma-f... If you like this content, please consider subscribing to my channel: / @easytheory ▶SEND ME THEORY QUESTIONS◀ ryan.e.dougherty@icloud.com ▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.