Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Exercise 4 (1 pt for each correct answer). For each statement indicate whether i

ID: 3704564 • Letter: E

Question

Exercise 4 (1 pt for each correct answer). For each statement indicate whether it is true, 1. There exists a polynomial-time algorithm that determines whether a given integer is 2. There exists a polynomial-time algorithm that for each integer n, finds two prime false, or unknown. prime or not. True? False? Unknown? numbers p and q such that n p. True? False? Unknown? 3. If one-way functions exist, then there exists a polynomial-time algorithm that deter- mines whether a given Boolean formula is satisfiable or not. True? False? Unknown? Computationally Merlin can convince polynomially bounded unlimited Arthur that a given Boolean formula is unsatisfiable. Or, more formally, there exists an interactive proof system for the set of all unsatisfiable Boolean formulas. True False? Unknown?

Explanation / Answer

1. True, there exists a polynomial time algorithm

2. True, there exists a polynomial time algorithm

3.true, there exists a polynomial time algorithm

4. False no there does not exist a polynomial time algorithm