Question

Consider the following statements:
I. There exists a non deterministic context free language whose reversal is DCFL.
II. There exists a non regular CSL whose Kleene closure is regular.
Which of the above statements are true ?

Answer 1

I is true,
for example take $L=\left\{a^n{b}^{n}d\right\}\cup \left\{a^n{b}^{2n}d\right\}$.
It's reversal will be $\left[C{a}^n{b}^n\right]L\left\{d{a}^n{b}^{2n}\right]$ which is a DCFL. So, I is okay.

II is also true. lets take $L=\left\{a^n|pisprime\right\}$ If we take its kleene closure .
Then $L^n=ϵ-aa{a}^{\ast }$
Hence II is also correct.

Therefore (a) is the most appropriate choice