Here we look at the three conditions for the pumping lemma for regular languages, and discuss whether they are necessary, and where they come from. The surprising answer is that only two of the conditions are actually necessary! All three come from the proof of the pumping lemma, and we can deduce all of them easily from the fact that the given language L is regular (and so it has a DFA). 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 about the three conditions for the pumping lemma for context-free languages? 2. Can you give a formal proof of where we only have the two required conditions? ▶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 progra ... https://www.youtube.com/watch?v=e4dUJ8NLjeA