Note for the P versus NP Problem

EasyChair Preprint 11886, version history

Version	Date	Pages	Version notes
1	January 29, 2024	4
2	February 1, 2024	4	We use the 1-in-3 3sat problem
3	February 2, 2024	4	We created a Github repository with the software solution in Python
4	February 3, 2024	4	We show that the Monotone Weighted Xor 2-satisfiability problem ($MWX2SAT$) is $NP$-complete and $P$ at the same time.
5	February 6, 2024	4	We improved the Lemma 1
6	March 10, 2024	4	We changed the abstract and content
7	March 14, 2024	5	We improved the content.
8	March 15, 2024	4	In the previous version, we create two ways to prove that MWX2SAT is in P. In this version, we remove the one that is flawed and we keep the single one that is correct.
9	March 28, 2024	5	We improved the Lemma 1 and added the Discussion section
10	April 8, 2024	5	We replaced in the definition of the K-CLOSURE the content "($u \in V'$ or $v \in V'$) or ($u \notin V'$ or $v \notin V'$)" by "($u \in V'$ and $v \in V'$) or ($u \notin V'$ and $v \notin V'$)"

Keyphrases: completeness, complexity classes, computational algorithm, polynomial time, reduction

BibTeX entry

BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:

@booklet{EasyChair:11886,
  author    = {Frank Vega},
  title     = {Note for the P versus NP Problem},
  howpublished = {EasyChair Preprint 11886},
  year      = {EasyChair, 2024}}