Graph-Based Deterministic Polynomial Algorithm for NP Problems
By: Changryeol Lee
Potential Business Impact:
Solves hard problems as fast as checking answers.
The P = NP problem asks whether every problem whose solution can be verified in polynomial time (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P = NP, demonstrating that every NP problem can be solved deterministically in polynomial time. We introduce a new Computation Model that enables the simulation of a Turing machine, and show that NP problems can be simulated efficiently within this framework. By introducing the concept of a Feasible Graph, we ensure that the simulation can be performed in polynomial time, providing a direct path to resolving the P = NP question. Our result has significant implications for fields such as cryptography, optimization, and artificial intelligence, where NP-complete problems play a central role.
Similar Papers
Graph-Based Deterministic Polynomial Algorithm for NP Problems
Computational Complexity
Solves hard problems as fast as checking answers.
An Invitation to "Fine-grained Complexity of NP-Complete Problems"
Data Structures and Algorithms
Finds faster ways to solve tough computer puzzles.
A Study of NP-Completeness and Undecidable Word Problems in Semigroups
Computational Complexity
Proves some math problems can never be solved by computers.