Here we cover the regular expression (regex) to NFA conversion. The idea is to revisit the definition of regex, and to make an NFA for each of the 6 pieces of the definition. For the first three, we can make either a 1-state or a 2-state NFA. For the other three (the "inductive" cases), we revisit earlier constructions with NFAs using union, concatenation, and star to make an NFA for the "bigger" regex, using "smaller" NFAs that have already been built. #easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem Contribute: Paypal: https://paypal.me/easytheory 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) 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 ▶ADDITIONAL QUESTIONS◀ 1. What does the NFA for the regex ab look like? ▶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=HLOAwCCYVxE

Here we look at a (rare) double conversion, which is converting from a regular grammar to an NFA (nondeterministic finite automaton) to a regular expression (regex). This comes from a 2017 exam question of mine. I walk through the steps in both of the conversions of how to perform them. For the regular grammar to NFA conversion, make a state for each of the variables of the NFA, as well as a single final state. Then, for each rule that produces a variable, go to that variable with the produced character (or on epsilon if none produced). If a rules makes epsilon or a character, go to the new final state on that character. For the NFA to regex conversion, I walk through this process in this video: https://www.youtube.com/watch?v=UKYvP8aS7fM&list=PLylTVsqZiRXMD7nqoHqEdCKdeGwGuO1KR&index=6&t=0s Patreon: https://www.patreon.com/easytheory Twitch: https://www.twitch.tv/easytheory Mixer: https://mixer.com/easytheory Discord: https://discord.gg/SD4U3hs Facebook: https://www.facebook.com/easytheory/ Twitter: https://twitter.com/EasyTheory Teespring: 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 ▶ADDITIONAL QUESTIONS◀ 1. What is the maximum length of a regex that comes from the NFA to regex process? What about for this specific NFA? 2. Will the regex that comes out of the conversion look the same if we ripped out different states? When is it the case that they are identically the same? ▶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. Ho ... https://www.youtube.com/watch?v=6SyRwpyQF6I

Here we give different proofs that EQ_DFA is decidable: (1) a different formulation of "equality" for two sets (namely regular languages), (2) minimization of DFAs, and (3) using the pumping lemma. 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 Youtube Live Streaming (Sundays) - subscribe for when these occur. 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=ql0rBl29_fQ

Here we convert a context-free grammar into Chomsky Normal Form, and show that it works for any CFG. The process involves 5 stages: (1) ensure the start variable is not on the RHS of any rule, (2) "eliminate" epsilon-rules, (3) "eliminate" unit rules, (4) ensure the RHS is only variables or a single terminal, and (5) reduce "long" RHSes. The order of the rules is important! Timestamps: 0:00 - Intro 1:30 - Step 1 (ensure start var not on RHS) 3:25 - Step 2 ("eliminate" epsilon rules) 9:10 - Step 3 ("eliminate" unit rules) 13:48 - Step 4 (remove mix of terminals and vars) 17:18 - Step 5 (ensure RHSes are of length at most 2) Patreon: https://www.patreon.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 you prove why it is the case that each stage never changes the language of the CFG? 2. What if we have a regular grammar and convert it to CNF? (i.e., every rule is either A to epsilon, A to a single terminal, A to a variable B, or A to xB where x is a terminal, B a variable) ▶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=-SZkkMWHBvQ