Geodesic
A short essay towards if $P$ not equal $NP$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 2, pp. 258-260

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We find a computational algorithmic task and prove that it is solvable in polynomial time by a non-deterministic Turing machine and cannot be solved in polynomial time by any deterministic Turing machine. The point is that our task does not look as very canonical one and if it may be classified as computational problem in standard terms.
Keywords: deterministic computations, non-deterministic computations. 
Vladimir V. Rybakov. A short essay towards if $P$ not equal $NP$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 2, pp. 258-260. http://geodesic.mathdoc.fr/item/JSFU_2021_14_2_a13/
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[1] S.A. Cook, “The complexity of theorem proving procedures”, Proceedings of the Third Annual ACM Symposium on Theory of Computing, 1971, 151–158 | DOI | MR | Zbl

[2] https://en.wikipedia.org/wiki/P_versus_NP_problem

[3] Javier A. Arroyo-Figueroa, The Existence of the Tau One-Way Functions Class as a Proof that P!= NP, 2016, arXiv: 1604.03758

[4] Mathias Hauptmann, On Alternation and the Union Theorem, Mathematics, Computer Science, 2016, arXiv: 1602.04781