Review of 'Note for the P versus NP Problem'

Reviewer: Jorge Félix Martínez Pazos

Publication date of review: 2024-04-01

Bookmark

Jorge Félix Martínez Pazos5

Note for the P versus NP ProblemCrossref ScienceOpen

A significant milestone in computational complexity theory.

Average rating:	    Rated 4.5 of 5.
Level of importance:	    Rated 5 of 5.
Level of validity:	    Rated 5 of 5.
Level of completeness:	    Rated 4 of 5.
Level of comprehensibility:	    Rated 4 of 5.
Competing interests:	None

Reviewed article

Record: found
Abstract: found
Article: found

Is Open Access

Note for the P versus NP Problem

Frank Vega (2024)

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

0 comments Cited 0 times     Rated -3 of 5. – based on 2 reviews

Preprint version 1

Bookmark

Review information

DOI:: 10.14293/S2199-1006.1.SOR-COMPSCI.ACYPMU.v1.RJVRLV

License:

This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

ScienceOpen disciplines: Theoretical computer science

Keywords: completeness,graph,polynomial time,Complexity classes,boolean formula

Review text

Focusing on the famous P versus NP problem, which is a cornerstone of computer science, this paper delves into the complicated field of computational complexity theory. This fundamental problem asks whether efficiently verifiable problems can also be efficiently solved. The distinction between the classes P and NP, where P denotes problems that can be solved by polynomial times and NP denotes problems that can be verified by polynomial times, sets the stage for the profound implications of a possible solution to the P versus NP problem.

One of the key concepts discussed is NP-completeness, a class of problems that are both challenging and ubiquitous in computer science. While these problems are efficiently provable, there are no known efficient algorithms for solving them. The paper highlights the importance of NP-complete problems by presenting examples such as the Boolean Satisfiability Problem (SAT) and the K-CLOSURE problem, shedding light on their complexity and implications in various domains.

In this work, the Monotone Weighted Xor 2 Satisfiability Problem (MWX2SAT) is introduced and its NP-completeness is established, with a detailed lemma and theorem being provided to support this claim. The intricate connections drawn between MWX2SAT and graph theory, particularly concerning vertex cover and independent set problems, underscore the depth of the mathematical reasoning and problem-solving strategies employed in the study.

In addition, the paper considers the potential implications of proving that P equals NP, emphasizing the transformative impact such a breakthrough would have on computer science, mathematics, and various other fields. The discussion extends to the practical implications of efficiently solving NP-complete problems, suggesting a paradigm shift in mathematical research methods and the potential acceleration of theorem-proving processes.

The meticulous analysis and theoretical underpinnings presented in the paper pave the way for a deeper understanding of the challenges and opportunities at the intersection of mathematics and computer science.

Quality Assessment