Separation of P and NP

TL;DR

This paper claims a new proof method for P ≠ NP by analyzing Turing machines with increasing time limits, leveraging the halting problem and Rice's theorem to argue the impossibility of solving NP problems efficiently.

Contribution

It introduces a novel proof approach for P ≠ NP based on runtime limits and halting problem considerations, which is a significant theoretical claim.

Findings

Proposes a new proof method for P ≠ NP.

Utilizes the halting problem and Rice's theorem in the proof.

Suggests that NP problems cannot be solved within finite time constraints.

Abstract

There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit goes toward infinity. Due to the halting problem, whether a word is accepted can only be determined at runtime. It can be shown by Rice's theorem, if a finite set of words are to be checked, they all have to be tested by brute force.