Year: 2024
Type: article
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. This work posits that ONE-IN-THREE 3SAT, a notoriously difficult NP-complete problem, can be solved efficiently, thereby establishing the equivalence of P and NP.
Source: IPI Letters
DOI: 10.59973/ipil.122
Author: Frank Vega
Institution: Information Physics Institute
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402549356