English

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

R2 v1 2026-06-21T22:47:26.934Z