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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.

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

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