1. Introduction, Finite Automata, Regular Expressions

AI won't ever be able to teach math because AI cannot reason. It handles information very differently than humans do. It is at best a flawed oracle that may lie through omission without you being able to tell. This is supported by the fact that there are hard limits to computation, in terms of both Computability Theory, and Complexity Theory that are often disregarded by the novice and magical thinker alike despite being largely solved fields by experts in Computer Science, at least in terms of Computability Theory. Most of this work was completed in the 1950s. This is not a difficult a subject, but most people online simply are unwilling to do the work to rationally learn this and instead choose to try and hide their own ignorance because they feel inadequate, or perhaps they are engaging in something more malevolent. The reasoning (false justification) doesn't really matter. It is, however; quite telling when expert's have validated these things, and yet any mention contrary to a narrative provokes downvotes in a public forum to remove it from view. A perfect example of intentional actions done by third-parties trying to misinform others about the risks (by those parties actions removing legitimate and valid information). For those with the cajones to actually learn this stuff. Here is a link. It seems very jaron laden but it provides a true understanding of how computers actually work which is sorely lacking in the youth of today. MIT 18.404J Theory of Computation [this video]

> if you require your parens to be balanced, that's no longer a regular language. TIL: [link] As someone who has only recently learned the formal definition of regular language ( Thanks to [this video] as mentioned on this board recently ), I'm interested in the formal proof for this? It feels intuitively true, but I haven't finished the course yet and therefore haven't come across it and can't yet reason well about it. Is the problem then in trying to "encode" whether brackets are balanced, that we would need infinite "levels" of how many more brackets we've opened rather than closed, (i.e a stack) and that violates the finite nature of finite automota? So I've googled it now, and I've found the result is due to the "Pumping lemma": [link]