P = NP

TL;DR

This paper claims to prove P=NP by constructing a polynomial-time deterministic Turing machine that decides the existence of accepting paths in NP machines through a novel reduction to linear programming, challenging longstanding complexity theory assumptions.

Contribution

It introduces a constructive proof that P=NP by reducing the problem to linear programming, differing from traditional SAT-based reductions.

Findings

Constructed a polynomial-time deterministic machine for NP acceptance paths.

Reduced the acceptance path problem to linear programming, an NP-complete problem.

Proved that NP problems can be decided in polynomial time using this method.

Abstract

The present work proves that P=NP. The proof, presented in this work, is a constructive one: the program of a polynomial time deterministic multi-tape Turing machine M_ExistsAcceptingPath, that determines if there exists an accepting computational path of a polynomial time non-deterministic single-tape Turing machine M_NP, is constructed (machine M_ExistsAcceptingPath is different for each Turing machine M_NP). Machine M_ExistsAcceptingPath is based on reduction to problem LP (linear programming) instead of reduction to problem 3-CNF-SAT which is commonly used. In more detail, machine M_AcceptingPath uses a reduction of the initial string problem to another string problem TCPE (defined in the paper) that is NP-complete and decidable in polynomial time. The time complexity of machine M_ExistsAcceptingPath is O(t(n)^{272}) wherein t(n) is an upper bound of the time complexity of machine M_NP.