We use pumping lemma for regular languages to find a language is regular or not. There is a question in the homework that I don't know how to apply pumping lemma onto the language.
L = {a$b: a,b ∈ {0,1}*, number of zeroes in a equals to the number of ones in b}
$ is just a constant there to split a and b.
There is also a language such that:
L = {ab: a,b ∈ {0,1}*, number of zeroes in a equals to the number of ones in b}
I understand that now there is nothing to split a and b and it's not possible to make assumptions about number of zeroes in a and number of ones in b, right? Or am I mistaken?
How do we apply pumping lemma to these languages to prove them regular or not?
