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I have always though that NP consists of problems solved in a non polynomial time by a deterministic Turing machine. Recently I discovered that NP classifies all the problems solved by a non deterministic Turing machine in polynomial time.

Do those 2 machines solve the same problems? Meaning, can a deterministic Turing machine solve the problems in NP with non polynomial time, and should I consider them equal?

Thank you in advance for you help!

Ceznex
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    No, they are not equal. Non-deterministic refers to the behaviour of the TM while not-polynomial refers to taking more than polynomial work. If you have heard about it, the P vs NP problem would be meaningless if the notions you asked about are equivalent – nir shahar Feb 15 '22 at 17:17

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A non-deterministic machine is basically able to make a lucky guess at any time. There are situations where this doesn't actually help, so there are problems that take polynomial time with a non-deterministic Turing machine, but take the same time with a deterministic one.

Plus decision problems in NP cannot be solved in polynomial time on a non-deterministic Turing machine in all cases, but only in cases where the answer is "YES". If the answer is "NO", then the non-deterministic machine doesn't help.

gnasher729
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