How to proof regular/non-regular with Nerode Theorem

Question

$L_{1}=\left\{w \in\{a, b\}^{*} | \#_{a}(w)=0\right\}$

$L_{2}=\left\{w \in\{0,1\}^{*} | w=u v u \text { with } u, v \in\{0,1\}^{*}\right\}$

I'm trying to learn to proof regularity/non-regularity with the nerode theorem.

First off I have tried to learn the theorem but don't really understand it well.

The generel idea is to show that I can find finite nerode classes, yes?

Nerode classes are languages where ux and yx is in the language (u and y don't have to be in the main language?)

How do I do this now for these two?

Thanks for any help

Answer 1

Both languages are regular and there is no need of the Nerode theorem to prove it.

Hint for $L_1$. Directly find a regular expression for this language.

Hint for $L_2$. What happens if you take $u = 1$ in the definition?