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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

  1. $\text{Even(L)}$ is regular and $\text{Chop(L)}$ is not regular
  2. Both $\text{Even(L)}$ and $\text{Chop(L)}$ are regular
  3. $\text{Even(L)}$ is not regular and $\text{Chop(L)}$ is regular
  4. Both $\text{Even(L)}$ and $\text{Chop(L)}$ are not regular
in Theory of Computation by
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2 Answers

+1 vote

Since in both case the word obtained after removal belongs to that particular language L. and the language L is regular

so both the Languages defined by even and Chop are regular

by
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Ans: B Both even(L) and Chop(L) are regular

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