Why is {a^nb^n | n >= 0} not regular?

Question

In a CS course I\'m taking there is an example of a language that is not regular:

{a^nb^n | n >= 0}

I can understand that it is not regu

Answer 1

Because you can't write a finite state machine that will 'count' identical sequences of 'a' and 'b' symbols. In a nutshell, FSMs cannot 'count'. Try imagining such a FSM: how many states would you give to symbol 'a'? How many to 'b'? What if your input sequence has more?

Note that if you had n <= X with X an integer value you could prepare such FSM (by having one with a lots of states, but still a finite number); such language would be regular.