Question: Let L be a regular language. Define L = { xay in Sigma | xy in L , a in Sigma } .

Let L be a regular language. Define L

= {

xay in

\

Sigma

|

xy in L

,

a in

\

Sigma

} .

take the strings in L

,

and add exactly one symbol anywhere in the string for anywhere

it could be placed, even possibly at the beginning or end. Prove that if L is regular,

then so is L

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