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

Main Author: Konstantinos Kyritsis
Format: Paper
Language: English
Published: Academic Publications 2018
Subjects:
Online Access: http://cris.teiep.gr/jspui/handle/123456789/1667
Physical Description: 14
Citation: 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: http://www.ijpam.eu doi: 10.12732/ijpam.v120i3.17
ISSN: 1314-3395
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.