Problem 1 Given an alphabet Σ, a string constructed from the alphabet is a concatenation of symbols in that alphabet. Given a string w = w₁W₂... wn where w; E Σ, the reverse of string w, written as wrev, is the string w in reverse order, i.e., wrev = Wn Wn-1... w₁. For any language A, let Arev = {wrev | w € A}. Show that if A is regular, so is Arev. Hint: Use regular expressions.

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Problem 1 Given an alphabet Σ, a string constructed from the alphabet is a concatenation of
symbols in that alphabet. Given a string w = w₁W2 . Wn where wi
written as wrev, is the string w in reverse order, i.e., wrev = Wn Wn-1.
Arev = {wrev | w ¤ A}. Show that if A is regular, so is Arev.
Σ, the reverse of string w,
w₁. For any language A, let
Hint: Use regular expressions.
Transcribed Image Text:Problem 1 Given an alphabet Σ, a string constructed from the alphabet is a concatenation of symbols in that alphabet. Given a string w = w₁W2 . Wn where wi written as wrev, is the string w in reverse order, i.e., wrev = Wn Wn-1. Arev = {wrev | w ¤ A}. Show that if A is regular, so is Arev. Σ, the reverse of string w, w₁. For any language A, let Hint: Use regular expressions.
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