English

P != NP Proof

Computational Complexity 2019-07-01 v9

Abstract

This paper demonstrates that P \not= NP. The way was to generalize the traditional definitions of the classes P and NP, to construct an artificial problem (a generalization to SAT: The XG-SAT, much more difficult than the former) and then to demonstrate that it is in NP but not in P (where the classes P and NP are generalized and called too simply P and NP in this paper, and then it is explained why the traditional classes P and NP should be fixed and replaced by these generalized ones into Theory of Computer Science). The demonstration consists of: 1. Definition of Restricted Type X Program; 2. Definition of the General Extended Problem of Satisfiability of a Boolean Formula - XG-SAT; 3. Generalization to classes P and NP; 4. Demonstration that the XG-SAT is in NP; 5. Demonstration that the XG-SAT is not in P; 6. Demonstration that the Baker-Gill-Solovay Theorem does not refute the proof; 7. Demonstration that the Razborov-Rudich Theorem does not refute the proof; 8. Demonstration that the Aaronson-Wigderson Theorem does not refute the proof.

Cite

@article{arxiv.0907.3965,
  title  = {P != NP Proof},
  author = {André Luiz Barbosa},
  journal= {arXiv preprint arXiv:0907.3965},
  year   = {2019}
}

Comments

25 pages and 3 new great ideas!

R2 v1 2026-06-21T13:28:01.916Z