1. $L\_1=\{a^nb^mc^nd^m \mid m,n >0\}$
2. $L\_2=\{a^nb^mc^md^n \mid m,n >0 \}$
3. $L\_3=\{a^mb^n \mid m+n\text{ is a prime number}\}$
4. $L\_4=\{a^mb^n \mid n=m^2\}$
5. $L\_5=\big\{ww^R\#ww^R \mid w \in \{a,b\}^\* \big\}$
6. $L\_6=\big\{wuw^R \mid |w|=|u|, w,u \in \{a,b\}^\* \big\}$
7. $L\_7=\big\{wu \mid |w|=|u|, w,u \in\{a,b\}^\*\big\}$
8. $L\_8=\{a^mb^nc^k \mid k \le \min(m,n) \}$
9. $L\_9=\{a^mb^nc^k \mid k \le \max(m,n) \}$

thanks in advance!