# why is H = {www | w ∊ (0,1)* } not regular language

I know pumping lemma and also know how to prove if languages are not regular or are regular using proof by contradiction methodology. But I am stuck on this one.Especially, I don't know exact string it produces.

$$H = \{www \mid w ∊ (0,1)^* \}$$

How do I prove this is not regular language? Thanks!

You can use the Myhill–Nerode criterion. Consider the words $0^n1$ for all $n$. These are pairwise inequivalent since $0^n10^n10^n1 \in H$ while $0^m10^n10^n1 \notin H$ if $m \neq n$. Since we have found infinitely many pairwise inequivalent words, it follows that the language is not regular.