Here we show that regular languages are closed under reversal, and give some tips on why the "usual" proof is not quite right. The main idea is to take a DFA for the language, and reverse all of its transitions. The problem is that the resulting machine may not necessarily be a DFA or even an NFA. But by observing what the resulting language should be (the reverse of all the strings), we can make some adjustments to it to make it work, which we cover in the video.<br /><br />#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem<br /><br />Contribute:<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 />Mixer: <a href="https://mixer.com/easytheory" target="_blank" rel="nofollow">https://mixer.com/easytheory</a><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 />Ultimate Supporters: (none)<br />Diamond Supporters: (none)<br />Platinum Supporters: (none)<br />Gold Supporters: Anonymous (x1), Micah Wood, Ben Pritchard<br />Silver Supporters: Timmy Gy<br />Supporters: Yash Singhal <br /><br />▶ADDITIONAL QUESTIONS◀<br />1. How large will the "reverse" DFA be in relation to the original one? (after converting from an NFA to DFA)<br />2. What if we ask all strings such that some substring of it is reversed?<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 over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.<br /><br />▶ABOUT THIS CHANNEL◀<br />The theory of computation is perhaps the fundamental theory of computer science. It sets out to define, mathematically, what exactly computation is, what is feasible to solve using a computer, and also what is not possible to solve using a computer. The main objective is to define a computer mathematically, without the reliance on real-world computers, hardware or software, or the plethora of programming languages we have in use today. The notion of a Turing machine serves this purpose and defines what we believe is the crux of all computable functions.<br /><br />This channel is also about weaker forms of computation, concentrating on two classes: regular languages and context-free languages. These two models help understand what we can do with restricted means o<br />...<br /><a href="https://www.youtube.com/watch?v=7OzQ8ItYGSw" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=7OzQ8ItYGSw</a>