Here we look at the question of how many DFAs accept a given language L, which can be anything. This may seem like a silly question but it turns out to be interesting! If L is not regular, then clearly there is no DFA for L. But if L is regular, we can always add an "unreachable" state to an existing DFA for L as many times as we want. Contribute: Patreon: https://www.patreon.com/easytheory Discord: https://discord.gg/SD4U3hs Live Streaming (Saturdays, Sundays 2PM GMT): 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 ▶ADDITIONAL QUESTIONS◀ 1. How many *minimal* DFAs are there for a regular language L? 2. Can you modify the construction so that you can always add a state that is always reachable? ▶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 hard ... https://www.youtube.com/watch?v=Zbqq6G5CipU

Here we look at and define regular expressions, which allow us to describe, formally, what a language is. They are defined using three "base" cases (empty string, empty set, and a single character), and three "inductive" cases (union, concatenation, and star). Contribute: 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 Gold Supporters: Anonymous (x1), Micah Wood, Ben Pritchard Silver Supporters: Timmy Gy Supporters: Yash Singhal ▶ADDITIONAL QUESTIONS◀ 1. What other operators can be included that can be achieved from union, concatenation, and star? ▶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=7phPFEMcfEs