Does P = NP?

TL;DR

This paper explores the P versus NP problem, analyzing the implications of polynomial-time SAT algorithms and the possibility of unresolved NP problems despite such algorithms.

Contribution

It introduces a proposition regarding the limitations of polynomial-time SAT algorithms and discusses the open question of NP problem instances.

Findings

Polynomial-time SAT algorithms do not necessarily resolve all NP problems.

The existence of certain NP problems remains an open question.

The paper highlights the theoretical possibility of NP problems outside the scope of polynomial algorithms.

Abstract

This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it remains theoretically possible for there to yet exist a non-deterministically polynomial (NP) problem for which the algorithm does not provide a polynomial (P) time solution. The paper leaves open as subject of continuing research the question of existence of instance of conjectured problem.