Finite and infinite basis in P and NP
Computational Complexity
2015-01-28 v3
Abstract
This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each other in disjunction. That is, NP-Complete problem is in infinite dimension function space that bases are P-Complete. The other hand, any P-Complete problem have at most a finite number of P-Complete basis. The reason is that each P problems have at most finite number of Least fixed point operator. Therefore, we cannot describe NP-Complete problems in P. We can also prove this result from incompleteness of P.
Keywords
Cite
@article{arxiv.1212.0191,
title = {Finite and infinite basis in P and NP},
author = {Koji Kobayashi},
journal= {arXiv preprint arXiv:1212.0191},
year = {2015}
}
Comments
2 pages