MadeEasy Subject Test 2019: Theory of Computation - Closure Property

Question

Consider the following Statements :

1. There Exist a non-deterministic CFL whose reversal is DCFL.
2. There exist a non regular CSL whose Kleene Closure is regular.

Which of following are True ?

Explain with reasons.

Answer 1

for 1st statement https://stackoverflow.com/questions/8363833/find-a-non-deterministic-cfl-whose-reverse-is-deterministic

for 2nd statement: L = $a^p$ where p is prime number, whose Kleene Closure is regular.

Comments

For first one {a^2nb^n} U {a^nb^nc} ---->CFL

On reversing {b^na^2n} U {ca^nb^n} ----->DCFL