Question: Let A be any language. Define DROP-OUT (A) to be the language containing all strings that can be obtained by removing one symbol from a

Let A be any language. Define DROP-OUT (A) to be the language containing all strings that can be obtained by removing one symbol from a string in A. Thus,

DROP-OUT(A) = {xz| xyz A where x, z *,y }. = ?

Show that the class of regular languages is closed under the DROP-OUT? operation. Give both proofs by picture and a more formal proof by construction as in Theorem 1.47.

THEOREM 1.47

The class of regular languages is closed under the concatenation operation.

DROP-OUT(A) = {xz| xyz A where x, z *,y }. =

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