English

Topological approach to solve P versus NP

Computational Complexity 2012-10-16 v9

Abstract

This paper talks about difference between P and NP by using topological space that mean resolution principle. I pay attention to restrictions of antecedent and consequent in resolution, and show what kind of influence the restrictions have for difference of structure between P and NP regarding relations of relation. First, I show the restrictions of antecedent and consequent in resolution principle. Antecedents connect each other, and consequent become a linkage between these antecedents. And we can make consequent as antecedents product by using some resolutions which have same joint variable. We can determine these consequents reducible and irreducible. Second, I introduce RCNF that mean topology of resolution principle in CNF. RCNF is HornCNF and that variable values are presence of restrictions of CNF formula clauses. RCNF is P-Complete. Last, I introduce TCNF that have 3CNF's character which relate 2 variables relations with 1 variable. I show CNF complexity by using CCNF that combine some TCNF. TCNF is NP-Complete and product irreducible. I introduce CCNF that connect TCNF like Moore graph. We cannot reduce CCNF to RCNF with polynomial size. Therefore, TCNF is not in P.

Cite

@article{arxiv.1202.1194,
  title  = {Topological approach to solve P versus NP},
  author = {Koji Kobayashi},
  journal= {arXiv preprint arXiv:1202.1194},
  year   = {2012}
}

Comments

7 pages, English and Japanese (see Other formats - Source)

R2 v1 2026-06-21T20:15:30.915Z