Is it option C?

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L1 would have been regular if n had a fixed value. But it is not regular here.

L2 is regular because {Regular}^{* }is regular

Option(C)

0

Let's say n=4

L1: if after iterating x four times it belongs to the set A (which is regular)

If the condition is true it will be accepted else rejected

L1: if after iterating x four times it belongs to the set A (which is regular)

If the condition is true it will be accepted else rejected

0

For L1.

Suppose {x = 0^{i}1^{j} / i==j and i,j>=0}

and {y = (o^{i}1^{j})^{*}/ i,j>=0} we are taking kleen closure because n>=0. and note that y is a complete language over 0 and 1, hence y contain kleen closure of x's string.

now here x is DCFL and y is regular.

there for L1 is not Regular.

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