Here we show that the emptiness problem for E_LBAs is undecidable. The idea is to encode "accepting computation histories" (defined in the video) into an LBA. 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=eWSi1uvK9T0

Credit: https://cs.stackexchange.com/a/60791 Here we give an involved proof to give strong evidence that there is no "pumping lemma for context-sensitive languages." The idea is that if there is one, then one can show that the "infinity" problem for that model is recognizable, but this is impossible for CSLs because that problem is unrecognizable (as we prove with linear bounded automata). Timeline: 0:00 - Intro 1:20 - What does a "pumping lemma" mean? 6:45 - If the predicate exists, then Infinity Problem is recognizable 13:43 - Infinity Problem for LBAs is not recognizable 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=nOJlfXGoqEQ

Here we answer a viewer-submitted question about whether this language {a^n b^n/3 c^(n mod 3) : n at least 1} is context-free. 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=WJAL9FkLAgc

Here we give some explanations as to why every P vs NP proof has failed, so far. P refers to problems that are *solvable* in polynomial time, and NP are those that *can be checked* in polynomial time. A central question in complexity theory is: does P = NP? It is sufficient to show that some NP-hard problem is in P (to show that P = NP), or to show that EVERY NP-hard problem is not in P (to show that P != NP). It is also not ruled out yet that the statement "Does P = NP?" is impossible to solve with current mathematical techniques (or any slight variation). I give a set of reasons for why known "proofs" have failed, so that you can see through why a "proof" is actually false; many people claim to have solved the problem online. I deliberately did not go into details because the video would be insanely long if I did (if there's interest, I can make such videos...eventually...). The truth is: it is unlikely we will see a resolution of P vs NP soon, or even within our lifetimes, because it is so insanely difficult for some of the reasons I go into in the video. The unedited version of this video is here: https://youtu.be/MWZ_p8nXIrQ The humorous (and sadly outdated) P-versus-NP page: https://www.win.tue.nl/~gwoegi/P-versus-NP.htm Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Names are listed in alphabetical order by surname. Dolev Abuhazira, Simone Glinz, Timmy Gy, Josh Hibschman, Patrik Keinonen, Travis Schnider, Tao Su, Micah Wood 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 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=RwcVyWaQ4TQ