The Gateway to Computer Science Excellence

0 votes

Let $L$ be any language. Define $\text{Even} (W)$ as the strings obtained by extracting from $W$ the letters in the even-numbered positions and $\text{Even}(L) = \{ \text{Even} (W) \mid W \in L\}.$ We define another language $\text{Chop} (L)$ by removing the two leftmost symbols of every string in $L$ given by $\text{Chop}(L) = \{W \mid \mathcal{v} W \in L,$ with $\mid \mathcal{v} \mid =2\}.$ If $L$ is regular language then

- $\text{Even(L)}$ is regular and $\text{Chop(L)}$ is not regular
- Both $\text{Even(L)}$ and $\text{Chop(L)}$ are regular
- $\text{Even(L)}$ is not regular and $\text{Chop(L)}$ is regular
- Both $\text{Even(L)}$ and $\text{Chop(L)}$ are not regular

52,345 questions

60,517 answers

201,939 comments

95,368 users