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Pré-Publication, Document De Travail Année : 2022

A 3 RD SHORTER SOLUTION OF THE CLAY MILLENNIUM PROBLEM ABOUT P ≠ NP =EXPTIME

Constantine Konstantinos Kyritsis
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Résumé

In this paper I present a 3 rd very short proof that P ≠ NP, and NP=EXPTIME derived by simplification from my 2 previous published proofs, in the context of the Zermelo-Frankel set theory and deterministic Turing machines. The proof also gives that the well-known fact that the complexity class NP is contained in the complexity class EXPTIME, must be stated in the usual formal definition of the NP class (even at the standard formulation of this millennium problem by S Cook) because it is provable that it cannot be derived from the other two usual conditions of the formulation and if no added, the problem would become ILL POSED. The results of these proofs definitely solve the 3rd Clay Millennium Problem about P versus NP, in a simple and transparent away that the general scientific community, but also the experts of the area, can follow, understand and therefore become able to accept.
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Dates et versions

hal-03601593 , version 1 (08-03-2022)
hal-03601593 , version 2 (10-07-2023)
hal-03601593 , version 3 (19-10-2023)

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  • HAL Id : hal-03601593 , version 1

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Constantine Konstantinos Kyritsis. A 3 RD SHORTER SOLUTION OF THE CLAY MILLENNIUM PROBLEM ABOUT P ≠ NP =EXPTIME. 2022. ⟨hal-03601593v1⟩
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