Arden's Theorem/Lemma Proof

Here we prove Arden's Theorem/Lemma, which says that if we have regexes A and B such that (1) epsilon is not in A, and (2) A = C U AB for some regex C, then we can uniquely write A as CB*. The idea is to "expand" out the right side until we notice a pattern, and then factor C out of the right side. Then we use the definition of star to deduce that it is indeed CB*. #easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem Contribute: Donation (appears on streams): https://streamlabs.com/easytheory1/tip Paypal: https://paypal.me/easytheory Patreon: https://www.patreon.com/easytheory Discord: https://discord.gg/SD4U3hs Live Streaming (Sundays 2PM GMT, 2 hours): Twitch: https://www.twitch.tv/easytheory (Youtube also) Social Media: Facebook Page: https://www.facebook.com/easytheory/ Facebook group: https://www.facebook.com/groups/easytheory/ Twitter: https://twitter.com/EasyTheory Merch: Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122 Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1 Gold Supporters: Micah Wood Silver Supporters: Timmy Gy ▶ADDITIONAL QUESTIONS◀ 1. Prove that A = CB* is unique. ▶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.