(a) If r and s are regular expressions, explain why (r+s)* # r* + s* . (b) Also carefully explain why (r*s*)* = (r + s)* . %3D
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- (a) If r and s are regular expressions, explain why (r+s)* + r* + s* . (b) Also carefully explain why (r*s*)* = (r + s)* .If () statements in R.This is a question of Ocaml: *) (* An employee is a tuple of name, age, and boolean indicating marriage status *)type employee = string * int * bool(* 1. Write a function that takes an employee, and prints out the information in some readable form. *) (*let print_employee_info t =*)
- B. Using Algebraic manipulation, simplify the following function. H(A.B,C,D)=( B + C )(A + D ) + D (AC+AB)2.a Σ : {c,A,G,T}, L = { w : w = CAG™T™C, m = j + n }. For example, CAGTTC E L; CTAGTC ¢ L because the symbols are not in the order specified by the characteristic function; CAGTT ¢ L because it does not end with c; and CAGGTTC € L because the number of T's do not equal the number of A's plus the number of G's. Prove that L¢ RLs using the RL pumping theorem.b) What is the difference between (x+H), (x+-), and (--x). c) Write the purpose for the use of the following: =, |I, //
- : Simplify the following Boolean expressions to a minimum * :number of literals F = abc + (a + c) + ābc3. You are expected to write a recursive function called powy(base, exponent) that, when called, returns baseponent As an example, powy( 6, 5 ) =6*6*6*6*6. Assume that exponent is an integer greater than or equal to 1. Hint: The recursion step would use the relationship baseponent - base baseponent - 1 and the terminating condition occurs when exponent is equal to 1, because base' = baseSimplify each of the following regular expressions. Example: a ((a U b)(b U a) )* U a ( (a Ub) a)* Ua ((b U a) b)* Simplified regular expression: a ((a U b)(b U a))*
- Describe the A * algorithm in detail.Exercise 3. Simplify The following regular expressions a) aa(b* | a) | a(ab* | aa) b) a*(b* + ab*) Exercise 4. Prove the following properties of regular expressions a) * = A b) R*|R² = R*4. Which of the following statements is NOT correct? (a) If LR is regular, then L is regular. ( b) If L is regular, then L is regular. (c) If L∗ is regular, then L is regular. ( d) If L is finite, then L is regular