Study on the Solution of the Clay Millennium Problem about the P vs NP: A Short Proof that P ≠ NP=EXPTIME in the Context of Deterministic Turing Machines

Abstract

In this paper, I provide a very short but decisive proof that P \(\neq\) 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. The hierarchy theorem is a deeper result compared to the P versus NP problem, and in principle there should exist a not much more complicated proof of the P versus NP problem, compared to the proof of the hierarchy theorem. The proof of the P versus NP problem in the direction P \(\neq\) NP, also means that the standard practice of password setting in the internet, is safe.