Peter Linz Edition 4 Exercise 2.3 Question 15 (Page No. 63)

Question

From a language $L$ we create a new language $chop2 (L)$ by removing the two leftmost symbols of
every string in $L$. Specifically,

                            $chop2(L) =$ {$w: vw ∈ L,$ with $|v|= 2$}.

Show that if $L$ is regular, then $chop2 (L)$ is also regular.

Comments

Given that L is regular.

therefore there is no relation btw input alphabet symbols ( i mean no comparission exist btw the alphabet symbols)

List all them = { a, abb,ba,bababa,bbaab,.......} ( for example )

cut the last two symbols then also you can have no relation between the input alphabet symbols  ===> it is RL

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if   W$\epsilon$ (a+b)*

then if you remove first two symbol then also the new strings  formed belongs to (a+b)* thus L will remain regular .

CORRECT ME IF I AM WRONG!!!