Let $L_1, L_2$ be regular languages over $\Sigma = \{ a,b,c\}$. Prove that the following language is regular as well:
$$L = \{ x\in \Sigma^* | x = uvw; \\ u,v,w \in L_1 ; \\wvu\in L_2;\\ W^R\in L[a^*b^*] \}$$
I think I have to build an automata for this question, involving $L_1, L_2$, since they're regular, but how?
Thank you!
Your language is the intersection of two languages which are both regular. Linking 3 times $L_1$ and $L_2^{-1}$ thus regular.