Here we show that the regular languages are closed under homomorphism, which is a function from Sigma* to itself that has a nice "splitting" property. We use this property in the proof by constructing an NFA for the desired "homomorphism" language, by breaking up every transition into many smaller transitions.<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. Construct an NFA for the example homomorphism given in the video applied to a "starter" DFA.<br />2. Can it be possible for a finite language L to have h(L) be infinite?<br />3. Can it be possible for an infinite language L to have h(L) be finite?<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 of computation, and offer a rich theory using which you can hone your mathematical skills in reasonin<br />...<br /><a href="https://www.youtube.com/watch?v=U_cdiPfykTI" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=U_cdiPfykTI</a>