8.1 Determine whether the following statements are correct or not

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Presentation transcript:

8.1 Determine whether the following statements are correct or not (1) If a problem is NP-complete, then it cannot be solved by any polynomial algorithm in worst cases. (2) If a problem is NP-complete, then we have not found any polynomial algorithm to solve it in worst cases. (3) If a problem is NP-complete, then it is unlikely that a polynomial algorithm can be found in the future to solve it in worst cases. (4) If a problem is NP-complete, then it is unlikely that we can find a polynomial algorithm to solve it in average cases. (5) If we can prove that the lower bound of an NP-complete problem is exponential, then we have proved that NP≠P.

(1) If a problem is NP-complete, then it cannot be solved by any polynomial algorithm in worst cases. False, It is still open whether NP is P or not

(2) If a problem is NP-complete, then we have not found any polynomial algorithm to solve it in worst cases. True

(3) If a problem is NP-complete, then it is unlikely that a polynomial algorithm can be found in the future to solve it in worst cases. True

(4) If a problem is NP-complete, then it is unlikely that we can find a polynomial algorithm to solve it in average cases. False, It is possible to solve an NP-complete problem in average polynomial time

(5) If we can prove that the lower bound of an NP-complete problem is exponential, then we have proved that NP≠P. True