摘要
The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.
The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems （languages）, and the second is the distinction be- tween a non-deterministic Turing machine （NTM） and a deterministic Turing machine （DTM）. The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor＇s theorem, it is shown that an NTM is not equipotent to a DTM. This means that ＂generating the power set P （A） of a set A＂ is a non-canonical example to support that P is not equal to NP.
