P is not equal to NP by Modus Tollens

Joonmo Kim

P is not equal to NP by Modus Tollens

Computational Complexity 2018-10-12 v7

Authors: Joonmo Kim

Abstract

An artificially designed Turing Machine algorithm $\mathbf{M}_{}^{o}$ generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption $\mathcal{P}=\mathcal{NP}$ , we show that $\mathbf{M}_{}^{o}$ has a certain property, which, without the assumption, $\mathbf{M}_{}^{o}$ does not have. This leads to $\mathcal{P}\neq\mathcal{NP}$ by modus tollens.

Keywords

P vs NP satisfiability problem Turing Machine modus tollens computational complexity algorithm design

Cite

@article{arxiv.1403.4143,
  title  = {P is not equal to NP by Modus Tollens},
  author = {Joonmo Kim},
  journal= {arXiv preprint arXiv:1403.4143},
  year   = {2018}
}

Comments

7 pages. Caution: this solution should not be reported to be correct while this caution stands. Actually, it is quite unlikely that this simple solution is correct. I am sharing this e-print to get comments on the probable mistake that I could not have found yet. If you have a conceptual grasp on Cooks Theory and some related glossaries then there will be no difficulty in reading this paper

P is not equal to NP by Modus Tollens

Abstract

Keywords

Cite

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