Finite and infinite basis in P and NP

Koji Kobayashi

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arXiv · 1212.0191

Finite and infinite basis in P and NP

Koji Kobayashi

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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.

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BibTeX RIS

Koji Kobayashi. 2012-12-02. Finite and infinite basis in P and NP. https://arxiv.org/abs/1212.0191

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