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Title: The solution to the 3RD Clay Millennium Problem. A short proof that P not equal to NP and NP = Exptime in the context of Zermelo-Frankel set theory
Authors: Konstantinos Kyritsis 
Keywords: Computational Complexity
Issue Date: 14-Jan-2018
Publisher: Academic Publications
Source: International Journal of Pure and Applied Mathematics Volume 120 No. 3 2018, 497-510 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: doi: 10.12732/ijpam.v120i3.17
Abstract: In this paper I provide a very short but decisive proof that P not equal to NP, and NP = EXPTIME in the context of the Zermelo-Frankel set theory and deterministic Turing machines. We discuss also the subtle implications of considering the P versus NP problem, in different axiomatic theories. The results of the current paper definitely solve the 3rd Clay Millennium problem 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.
ISSN: 1314-3395
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