I need a regular language $ L\subseteq \{0,1\}^{*} $ so that $unary(L)$ is not context free.unary of $L$ is defined by:$$unary(L) = \{0^{1x}  : x \in L  \}$$Example $L = \{0, 11\} $ $\rightarrow  unary(L) = \{00, 0000000\}$ Any help would be great.
a regular language so that $unary(L) \notin $Context Free Languages
formal languages;regular languages;context free
Let $L = 10^*$ and observe that $$\text{unary}(L) = \{ 1, 11, 1111, 11111111, \dots\} = \{1^{2^i} \mid i \in \mathbb{N} \}.$$Can you prove the rest yourself?