Question: 4. (20 points) Consider the following set defined recursively over = {a,b}. Write S4 as a regular set. (16 points). Explain your answer. (4 points)

4. (20 points) Consider the following set defined recursively over =

4. (20 points) Consider the following set defined recursively over = {a,b}. Write S4 as a regular set. (16 points). Explain your answer. (4 points) (i) Basis: LE S4 (ii) Recursive step: If w E S4, then aaw E S4 and wbb E S4. (iii) Closure: S4 consists of exactly the elements that can be obtained by starting with the basis elements of S4 and applying the recursive step a finite number of times to construct the new elements of S4

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