Here we show 5 different examples of applying Rice's theorem to languages show that each of these languages are undecidable. Easy Theory Website: https://www.easytheory.org Discord: https://discord.gg/SD4U3hs If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1 ▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about it. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes. The views expressed in this video are not reflective of any of my current or former employers. ... https://www.youtube.com/watch?v=n-kBE750AFc

Here we show that the totally quantified boolean formula (TQBF) problem is PSPACE-complete. This is very similar to the Cook-Levin theorem as well as Savitch's theorem, but now we want to make sure that the formula only has polynomial size. The trick is to utilize the "for all" quantifier to encode the recursive calls into one call. 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. Platinum: Micah Wood Silver: Timmy Gy, Josh Hibschman, Patrik Keinonen, Travis Schnider, and Tao Su 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=DxOT5uYcyRA

Here we create a DFA for the union of the languages of two simple DFAs, using a simple "product" construction of the states of the two machines. We just follow the transitions to form the final DFA, and also noting which states are final. We also check that our answer makes sense at the end. Whenever you have a problem to solve with DFAs, if you can break it down into "Problem 1 AND Problem 2" or "Problem 1 OR Problem 2", the product construction is your friend. First make the DFAs for each of Problem 1 and Problem 2, and follow the procedure in the video. The final states for either case correspond to intersection for AND, and union for OR. Recall that a DFA is a 5-tuple (Q, Sigma, delta, q0, F) where Q is the set of states, Sigma is the alphabet, delta is the transition function, q0 is the start state, and F is the set of final state. A computation on a string is the sequence of states that are visited, starting from the start state, on that string. A string is accepted if and only if the computation ends in a final state. In the video, a final state is one with a double circle. Patreon: https://www.patreon.com/easytheory PDF: https://drive.google.com/open?id=1fjO7_UjdwV88KwFaKrOTKb-MEiYGuV8Z Solutions: https://drive.google.com/open?id=1k1Ng4a1opINOboQ7NpGnIXs0HRw59egt If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1 ▶ADDITIONAL QUESTIONS◀ 1. Is this the smallest DFA for this language? 2. Is there an example of applying the product construction, and every state in the resulting DFA is required? ▶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 over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory. ... https://www.youtube.com/watch?v=CWei4YjTj90

Here we do an example on showing that regular languages are closed under suffix. Main video is here: https://www.youtube.com/watch?v=UQRsGun4l7Y #easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem Contribute: Patreon: https://www.patreon.com/easytheory Discord: https://discord.gg/SD4U3hs Live Streaming (Sundays 2PM GMT, 2 hours): Twitch: https://www.twitch.tv/easytheory (Youtube also) Mixer: https://mixer.com/easytheory 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 Ultimate Supporters: (none) Diamond Supporters: (none) Platinum Supporters: (none) Gold Supporters: Anonymous (x1), Micah Wood, Ben Pritchard Silver Supporters: Timmy Gy Supporters: Yash Singhal ▶ADDITIONAL QUESTIONS◀ 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 over 12 courses at two different universities, including several sections of undergraduate and graduate theory-level classes. ... https://www.youtube.com/watch?v=3IJrvxJL-io