US20260228297
2026-08-06
Physics
G06F17/10
The patent application details a groundbreaking method for solving NP problems, specifically the Subset Sum Problem (SSP), in polynomial time. This approach not only finds solutions but also counts and classifies them into equivalence classes, representing them as a compact directed acyclic graph. By solving the SSP, which is an NP-complete problem, this method can be applied to a wide range of fields, transforming previously intractable problems into solvable ones.
NP problems are those where a proposed solution can be verified quickly, in polynomial time. These problems span multiple domains such as technology, engineering, medicine, and artificial intelligence. The difficulty of finding solutions to these problems typically increases exponentially with the size of the problem space, making them challenging to solve efficiently.
NP-complete problems, like the Boolean Circuit Satisfiability Problem and the Subset Sum Problem, represent the most challenging class of NP problems. Solving an NP-complete problem efficiently would imply that all NP problems can be solved efficiently. The patent application addresses this by presenting a method to solve the SSP, thereby offering a solution to the P vs. NP problem.
The described system reduces any NP problem to a SSP, which is then solved in polynomial time. The process involves transforming the SSP into a two-dimensional geometric problem and utilizing a Transformation Graph to explore solution paths. This approach avoids the need for an exponential search by identifying hidden structures within the problem space, enabling efficient solution finding.
The system can classify and count solutions, providing insights into the structure of the solution space. This capability is crucial for applications across various fields, including drug design in medicine and circuit design in engineering. The method's ability to efficiently solve NP problems could lead to significant advancements in technology and scientific research.