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

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

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 -pq. 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 satisfable or not. True? False? Unknown? 4. Computationally unlimited Merlin can convince polynomially bounded 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

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