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A non-canonical example to support P is not equal to NP

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Abstract

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.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072, China

    Zhengling Yang  (杨正瓴)

  2. Tianjin Key Laboratory of Process Measurement and Control, Tianjin, 300072, China

    Zhengling Yang  (杨正瓴)

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  1. Zhengling Yang  (杨正瓴)
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Correspondence to Zhengling Yang  (杨正瓴).

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YANG Zhengling, born in 1964, male, Dr, associate Prof.

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Yang, Z. A non-canonical example to support P is not equal to NP. Trans. Tianjin Univ. 17, 446–449 (2011). https://doi.org/10.1007/s12209-011-1593-5

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  • DOI: https://doi.org/10.1007/s12209-011-1593-5

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