On the relationship between classes P and NP

TL;DR

This paper explores the P versus NP problem, arguing that the main challenges are methodological and stem from how NP problems are formulated, rather than inherent computational complexity.

Contribution

It provides a perspective that the difficulties in resolving P versus NP are due to problem formulation issues rather than fundamental computational barriers.

Findings

Difficulties in P vs NP are methodological in nature.

Small formulation changes affect algorithmic solvability.

Challenges are linked to NP problem formulations.

Abstract

In this paper we discusses the relationship between the known classes P and NP. We show that the difficulties in solving problem "P versus NP" have methodological in nature. An algorithm for solving any problem is sensitive to even small changes in its formulation. As we will shown in the paper, these difficulties are exactly in the formulation of some problems of the class NP.