Note for the P versus NP problem (II)

Frank Vega

doi:10.20944/preprints202409.2053.v2

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preprints.org > computer science and mathematics > data structures, algorithms and complexity > doi: 10.20944/preprints202409.2053.v2 (registering DOI)

Preprint Article Version 2 This version is not peer-reviewed

Note for the P versus NP problem (II)

Frank Vega

Version 1 : Received: 24 September 2024 / Approved: 25 September 2024 / Online: 26 September 2024 (07:44:40 CEST)
Version 2 : Received: 27 September 2024 / Approved: 27 September 2024 / Online: 29 September 2024 (11:14:57 CEST)

How to cite: Vega, F. Note for the P versus NP problem (II). Preprints 2024, 2024092053. https://doi.org/10.20944/preprints202409.2053.v2 Vega, F. Note for the P versus NP problem (II). Preprints 2024, 2024092053. https://doi.org/10.20944/preprints202409.2053.v2

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MDPI and ACS Style

Vega, F. Note for the P versus NP problem (II). Preprints 2024, 2024092053. https://doi.org/10.20944/preprints202409.2053.v2

APA Style

Vega, F. (2024). Note for the P versus NP problem (II). Preprints. https://doi.org/10.20944/preprints202409.2053.v2

Chicago/Turabian Style

Vega, F. 2024 "Note for the P versus NP problem (II)" Preprints. https://doi.org/10.20944/preprints202409.2053.v2

Abstract

The P versus NP problem is a cornerstone of theoretical computer science, asking whether problems that are easy to check are also easy to solve. "Easy" here means solvable in polynomial time, where the computation time grows proportionally to the input size. While this problem's origins can be traced to John Nash's 1955 letter, its formalization is credited to Stephen Cook and Leonid Levin. Despite decades of research, a definitive answer remains elusive. Central to this question is the concept of NP-completeness. If even one NP-complete problem could be solved efficiently, it would imply that all problems in NP could be solved efficiently, proving P equals NP. This research proposes that EXACT CLOSURE, a notoriously difficult NP-complete problem, can be solved efficiently, thereby potentially establishing the equivalence of P and 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.

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