Here we celebrate getting 500 thousand views on the channel. We also do a pumping lemma problem example, and a cool result on the number of strings a DFA accepts of a certain length. 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: Dolev Abuhazira, Simone Glinz, 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=HLox-pqUecU

Here we go over the definition of Turing Machines, as well as an example of one and how to compute with it using the Turing Machine tape. This was recorded on 3 April 2017. 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=aDK5E868lfg

Here we make a short introduction into my research, which is about the intersection of math and computer science, specifically in software testing and making it as efficient as possible. Covering arrays are one model of testing that is very well studied, and this video shows a way of proving the existence of covering arrays with a very low cost compared to exhaustive testing, via a technique called the "probabilistic method." Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben 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 ▶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=m1j4OBs1wsY

Here we show that the problem of checking whether a DFA's language is infinite is decidable. The idea is to appeal to the pumping lemma for regular languages, and then make a certain DFA with the property that its language is empty if and only if the original DFA's language was finite (or infinite). Then the question boils down to asking whether the constructed DFA's language is empty (which is decidable). Patreon: https://www.patreon.com/easytheory Facebook: https://www.facebook.com/easytheory/ Twitter: https://twitter.com/EasyTheory If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1 ▶ADDITIONAL QUESTIONS◀ 1. Can we do a similar question with PDAs/CFGs? 2. What about with Turing Machines? ▶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. ▶ABOUT THIS CHANNEL◀ 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. 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 reasoning with simple machines and the languages they define. However, they are not simply there as a weak form of computation--the most attractive aspect of them is that problems formulated on them are tractable, i.e. we can build efficient algorithms to reason with objects such as finite automata, context-free grammars and pushdown automata. For example, we can model a piece of hardware (a circuit) as a finite-state system and solve whether the circuit satisfies a property (like whether it performs addition of 16-bit registers correctly). We can model the syntax of a programming language using a grammar, and build algorithms that check if a string parses according to this grammar. On the other hand, most problems that ask properties about Turing machines are undecidable. This Youtube channel will help you see ... https://www.youtube.com/watch?v=iwuu6Ox88CI