Article
Version 1
This version is not peer-reviewed
Note for the P versus NP problem (II)
Version 1
: Received: 24 September 2024 / Approved: 25 September 2024 / Online: 26 September 2024 (07:44:40 CEST)
How to cite: Vega, F. Note for the P versus NP problem (II). Preprints 2024, 2024092053. https://doi.org/10.20944/preprints202409.2053.v1 Vega, F. Note for the P versus NP problem (II). Preprints 2024, 2024092053. https://doi.org/10.20944/preprints202409.2053.v1
Abstract
The P versus NP problem is a fundamental question in computer science. It asks whether problems whose solutions can be quickly verified can also be quickly solved. Here, "quickly" refers to computational time that grows proportionally to the size of the input (polynomial time). While the problem's roots trace back to a 1955 letter from John Nash, its formalization is attributed to Stephen Cook and Leonid Levin. Despite extensive research, a definitive answer remains elusive. Closely tied to this is the concept of NP-completeness. If a single NP-complete problem could be solved efficiently, it would imply that all problems in NP can be solved efficiently, proving that P equals NP. Our work presents a polynomial-time algorithm for the CLOSURE problem. We implemented a Python-based solution for this polynomial time algorithm, which is available on GitHub under the username "frankvegadelgado". In addition, we propose that CLOSURE is actually an NP-complete problem, which would imply that P equals NP. This work is an expansion and refinement of the article "Note for the P versus NP problem", published in IPI Letters.
Keywords
Complexity classes; Boolean formula; Graph; Completeness; Polynomial time
Subject
Computer Science and Mathematics, Data Structures, Algorithms and Complexity
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment