Give a recursive algorithm to produce a regular expression, Computer Engineering

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Give a recursive algorithm to produce a regular expression

Problem

L is a language and a is a letter, we define the quotient of L by a, written La-1, as follows. La-1 consists of all those strings that would be in L if you appended an a to them - formally, La-1 = w : wa ∈ L. Prove that if S is any regular expression, and a is any letter, then L(S)a-1 is a regular language. Give a recursive algorithm to produce a regular expression for this language.

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