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*.<br /><br />#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem<br /><br />Contribute:<br />Donation (appears on streams): <a href="https://streamlabs.com/easytheory1/tip" target="_blank" rel="nofollow">https://streamlabs.com/easytheory1/tip</a><br />Paypal: <a href="https://paypal.me/easytheory" target="_blank" rel="nofollow">https://paypal.me/easytheory</a><br />Patreon: <a href="https://www.patreon.com/easytheory" target="_blank" rel="nofollow">https://www.patreon.com/easytheory</a><br />Discord: <a href="https://discord.gg/SD4U3hs" target="_blank" rel="nofollow">https://discord.gg/SD4U3hs</a><br /><br />Live Streaming (Sundays 2PM GMT, 2 hours):<br />Twitch: <a href="https://www.twitch.tv/easytheory" target="_blank" rel="nofollow">https://www.twitch.tv/easytheory</a><br />(Youtube also)<br /><br />Social Media:<br />Facebook Page: <a href="https://www.facebook.com/easytheory/" target="_blank" rel="nofollow">https://www.facebook.com/easytheory/</a><br />Facebook group: <a href="https://www.facebook.com/groups/easytheory/" target="_blank" rel="nofollow">https://www.facebook.com/groups/easytheory/</a><br />Twitter: <a href="https://twitter.com/EasyTheory" target="_blank" rel="nofollow">https://twitter.com/EasyTheory</a><br /><br />Merch:<br />Language Hierarchy Apparel: <a href="https://teespring.com/language-hierarchy?pid=2&cid=2122" target="_blank" rel="nofollow">https://teespring.com/language-hierarchy?pid=2&cid=2122</a><br />Pumping Lemma Apparel: <a href="https://teespring.com/pumping-lemma-for-regular-lang" target="_blank" rel="nofollow">https://teespring.com/pumping-lemma-for-regular-lang</a><br /><br />If you like this content, please consider subscribing to my channel: <a href="https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1</a><br /><br />Gold Supporters: Micah Wood<br />Silver Supporters: Timmy Gy <br /><br />▶ADDITIONAL QUESTIONS◀<br />1. Prove that A = CB* is unique.<br /><br />▶SEND ME THEORY QUESTIONS◀<br />[email protected]<br /><br />▶ABOUT ME◀<br />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.<br />...<br /><a href="https://www.youtube.com/watch?v=trBbpsaPkbc" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=trBbpsaPkbc</a>