Closure property

Question

A CFL $\cap$ a DCFL (i.e what is the intersection of a CFL with a DCFL??)

Answer 1

Surely CSL , it may not be CFL..
$L_1 = \left\{a^nb^nc^m, n,m \geq 0\right\}$
$L_2 = \left\{a^mb^nc^n, n,m \geq 0\right\}$
$L = L_1 \cap  L_2 = \left\{a^nb^nc^m, n,m \geq 0\right\} \cap \left\{a^mb^nc^n, n,m \geq 0\right\} = \{a^nb^nc^n, n \geq 0\}$ is CSL and not CFL.

Comments

I think here both L1 and L2 is DCFL na???