Here we show that if A and B are regular, then A/B is regular, where this is the set of all strings w such that wx is in A for some x in B. We show that this is regular by making a DFA for it by changing the final states of A. The new final states are going to be the ones where reading ANY string from B will result in an ORIGINAL final state of A. This is not a "constructive" method for a DFA, but this shows that the DFA exists, which is all that is needed.<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. Can it be possible that A/B is equal to B/A (without using trivial examples of A, B)?<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 two different universities, including several sections of undergraduate and graduate theory-level classes.<br />...<br /><a href="https://www.youtube.com/watch?v=mtURMW_VSUA" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=mtURMW_VSUA</a>