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Im studing complexity theory and im reading this question on Quora.

According to what the guy is saying : if we are able to solve a NP-Hard problem in polynomial time we have prooved that P=NP. But, in P we find problems that can be solved and checked in polynomial time and in this case we have only prooved that NP problems can be solved in polynomial time, but we dont know if this implies that can be also checked in polynomial time.

Raphael
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Qwerto
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  • NP problems can be 'checked' (=verified) in polynomial time by definition. Also, being solvable in poly-time implies being verifiable in poly-time. I think you should have a good look at the precise definitions involved (again). – Discrete lizard Feb 24 '18 at 11:04
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    Check out our reference question on P and NP. – Yuval Filmus Feb 24 '18 at 11:05
  • Yes, but with a non deterministic turing. P is about deterministic turing machine – Qwerto Feb 24 '18 at 11:27

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