Here we show that the emptiness problem for context-free grammars (CFGs) is decidable. A variable is "productive" if it can make any string of terminals at all. So we formally define what a productive variable is, and repeatedly mark variables as productive by scanning through the rules. If no new variables are found, we stop and answer whether or not the start variable has been marked. Easy Theory Website: https://www.easytheory.org Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join 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 #easytheory Youtube Live Streaming (Sundays) - subscribe for when these occur. 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 ▶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. ... https://www.youtube.com/watch?v=qFZAblZiO08

Here we show that A_REX is decidable, which is the problem of determining if a given regular expression can generate a given string. We show that this is decidable by converting the regex into an equivalent NFA, and calling the decider for A_NFA on that NFA and the same input string. Since the NFA and regex are equivalent, the answer reported is the same. Since all steps take finite time, this shows A_REX is decidable. Easy Theory Website: https://www.easytheory.org Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join 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 #easytheory Youtube Live Streaming (Sundays) - subscribe for when these occur. 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 ▶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. ... https://www.youtube.com/watch?v=sPzvKqp0MBc

Here we show that undecidable languages are NOT closed under concatenation. The trick is to form two "opposite" languages that are based on unions, such that when concatenation is applied, all strings are included. Credit to: https://cs.stackexchange.com/questions/1549/operations-under-which-the-class-of-undecidable-languages-isnt-closed Easy Theory Website: https://www.easytheory.org Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join 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 #easytheory Youtube Live Streaming (Sundays) - subscribe for when these occur. 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 ▶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. ... https://www.youtube.com/watch?v=jAHKYpRt7h0

Here we give a complete and correct proof of Chomsky Normal Form, which is a restricted form of context-free grammars, and the proof is that every CFG can be converted into CNF. Many proofs out there give a "hand-wavy" argument, but we give a technically sound argument at each step of the way. There are 5 stages - watch the video to find out what the 5 are! Timestamps: 0:00 - Intro 3:00 - Definition of Chomsky Normal Form 7:30 - Proof of Step 1's correctness 12:15 - Proof of Step 2's correctness 20:20 - Proof of Step 3's correctness 27:13 - Proof of Step 4's correctness 30:42 - Proof of Step 5's correctness Easy Theory Website: https://www.easytheory.org 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 #easytheory #gate #theory Youtube Live Streaming (Sundays) - subscribe for when these occur. 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 ▶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. ... https://www.youtube.com/watch?v=lEsDll4Um7Y