# Empty words in regular languages

Let $L_1,L_2$ be any $\Sigma$-Languages, with $l_1\in L_1, l_2\in L_2$

If I have a regular Language $L(l_1(l_2l_1)^*l_2)$ would the word $\omega=l_2$ be recognized? I'm confused because if $\epsilon \in L_1$ then $l_1$could be $\epsilon$, then $L(l_1(l_2l_1)^*l_2)$ would recognize the word with $(l_1 = \epsilon) *((l_2l_1)^0=\epsilon)*l_2 = \omega$

I think this is wrong but I don't know why.

• Please pick a better title, this one does nothing to distinguish your question. – Raphael Dec 4 '17 at 17:30
• Try proving your claim. – Raphael Dec 4 '17 at 17:31
• I don't know how i would approach a proof like that – JDizzle Dec 4 '17 at 17:35
• There's nothing wrong with your argument. – Yuval Filmus Dec 4 '17 at 17:50
• So the empty word would be recognized by my Language? Then, would $(L(l_1))^+$ recognize it? – JDizzle Dec 4 '17 at 17:54