Algorithmic Manifold and Application to P versus NP Problem

Abstract

About P versus NP problem, it has been studied for long time. Recent literature has shown that the existing proof method using the diagonal argument or the circuit complexity is not effective. On the other hand, as another approach, calculation of time complexity based on the geometric method is also performed, but it is limited to the quantum algorithm, and it is an application example to the existing method of lower band derivation of quantum circuit complexity, it is essentially unchanged. 　In this paper, I introduce algorithmic manifolds that explain algorithms by geometric method and show that they are topologically homogeneous with respect to P versus NP problem. And I will also discuss polynomial-time reduction method of NP problem for class P.