SAT in Polynomial Time: A Proof of P = NP

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, like SAT, could be solved efficiently, it would imply that all NP problems could be solved efficiently, proving P=NP. This research proposes a groundbreaking claim: SAT, traditionally considered NP-complete, can be solved in polynomial time, establishing the equivalence of P and NP.