State T/F. If someone proves P = NP, then it would imply that every decision problem can be solved in polynomial time. I think it is false. Am I right?
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You are right. But you should elaborate on why you think it is false to see if you are right for the right reasons. – Solarflare Nov 13 '16 at 09:19
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I think the P is the set of decision problem that can be solved in polynomial time. But it not means every decision problem can be solved in polynomial time. – sower Nov 13 '16 at 22:37
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If P = NP, it means that any decision problem in NP can be solved in polynomial time. That is, any decision problem where "yes" answers could be verified efficiently could be solved in polynomial time.
This is not the same as saying that all decision problems can be solved in polynomial time. For example, some decision problems (such as the halting problem) are undecidable, meaning that they can't be decided at all. Proving P = NP doesn't change that.
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