I was reading up on finite automata and I came across an interesting fact near the end of the Wikipedia page.
The classic example of a simply described language that no DFA can recognize is bracket or Dyck language, i.e., the language that consists of properly paired brackets such as word "(()())". Intuitively, no DFA can recognize the Dyck language because DFAs are not capable of counting: [...]
Although it is very intuitive the argument they gave, I was wondering if there were a formal proof I could read for this, or if simple enough, reconstruct.
I tried Googling around for a proof, but I think I am missing some sort of a keyword in my search because nothing useful is coming up, it this proof trivial or intuitive enough that no papers have been published on it?