Understanding Context-Free Grammar and Its Languages

Here we start context-free grammars (CFG) and context-free languages (CFL), which are the languages of CFGs. The idea is to have every rule's right-hand side allowed to have any combination of variables and terminals. We show that every regular grammar is already a context-free grammar, and not necessarily the other way around because we give an example of a CFG for {0^n 1^n : n at least 0}, which is not regular. We then make a CFG for the language of palindromes over {0,1}. What is a context-free grammar? It is a set of 4 items: a set of "variables," a set of "terminals," a "start variable," and a set of rules. Each rule must involve a single variable on its "left side", and any combination of variables and terminals on its right side. Easy Theory Website: https://www.easytheory.org GoFundMe: https://www.gofundme.com/f/easy-theory-video-studio Patreon: https://www.patreon.com/EasyTheoryYT Fourthwall: https://easy-theory-llc-shop.fourthwall.com Problem Solving channel: ​⁠ @easytheoryprobsolve Timestamps: 0:00 - Intro 0:35 - Grammars (generally) 2:35 - Example grammar that has nonregular language 7:45 - Context-Free Grammar (CFG) definition 11:15 - Example CFG for Palindromes If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1