For Publishers
DiscoveryMetadataPeer reviewHostingPublishing
For Researchers
JoinPublishReviewCollect
Register
Blog
About
Search
Advanced search
My ScienceOpen
Search
For Publishers
For Researchers
Blog
About
742
views
1
references
 Top references
cited by
0
    
2 reviews
 Review
1
comments
 Comment
1
recommends
+1 Recommend
1 collections
    0
    shares
      200
      similar
       All similar

      One-Click Submission System Now Available for SO Preprints, learn more on how this works in our blog post and don't forget to check the video, too!

      scite_
      0
      0
      0
      0
      Smart Citations
      0
      0
      0
      0
      Citing PublicationsSupportingMentioningContrasting
      View Citations

      See how this article has been cited at scite.ai

      scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

      Version and Review History
      Preprint version 3
      2
      Preprint version 2
      Reviewed by Jorge Félix Martínez PazosReviewed by Sergi Simon
      2
      Preprint version 1
      Reviewed by Jorge Félix Martínez PazosReviewed by Sergi Simon
       
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Note for the P versus NP Problem

      Preprint
      research-article
      This is not the latest version for this article. If you want to read the latest version, click here.
      Author(s):   1 ,
      Publication date (Electronic preprint):
      Journal: ScienceOpen Preprints
      Publisher: ScienceOpen
      Keywords: Complexity classes, boolean formula, graph, completeness, polynomial time
      Bookmark

            Revision notes

            We improved the Lemma 1 according to the comments of the reviewer Sergi Simon. Besides, we added a Discussion section where we contributed and included important remarks to the final result. In addition, we picked up the discipline of "Data structures and Algorithms" since it is very close to the scope of the paper as well.

            Abstract

            Content

            Author and article information

            Journal
            Title: ScienceOpen Preprints
            Publisher: ScienceOpen
            Publication date (Electronic preprint): 28 March 2024
            Affiliations
            [1 ] GROUPS PLUS TOURS INC., 9611 Fontainebleau Blvd, Miami, FL, 33172, USA;
            Author notes
            Author information
            https://orcid.org/0000-0001-8210-4126
            Article
            DOI: 10.14293/PR2199.000759.v2
            SO-VID: 5e6e97ed-697f-4685-a43b-6c48e598af02
            License:

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            Date received : 15 March 2024
            Categories

            Data availability: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
            ScienceOpen disciplines: Data structures & Algorithms,Theoretical computer science
            Keywords: boolean formula,completeness,graph,polynomial time,Complexity classes

            References

            1. Fortnow Lance. The status of the P versus NP problem. Communications of the ACM. Vol. 52(9):78–86. 2009. Association for Computing Machinery (ACM). [Cross Ref]

            Comments

            wrote:

            With the help of the reviewer Sergi Simon, we detected a minor detail in this last version. However, that issue was a very simple and small mistake that I commited when I was writing the paper and so, it does not deserve a third version. I fixed and replaced the following statement in latex (over the definition of the K-CLOSURE problem):

            --------------------------------

            Note that in this problem the statement ``either $u \in V'$ or $v \notin V'$'' does mean the same as ($u \in V'$ or $v \in V'$) or ($u \notin V'$ or $v \notin V'$) since the logical implication of the word ``\textbf{Either}'' indicates that at least one of the following statements must be true, but not necessarily both.

            -------------------------------

            by the correct one:

            ------------------------------

            Note that in this problem the phrase ``either $u \in V'$ or $v \notin V'$'' does mean the same as ($u \in V'$ and $v \in V'$) or ($u \notin V'$ and $v \notin V'$) since the logical implication of the words ``\textbf{either ... or ...}'' indicates that exactly one of the following statements can be true.

            ------------------------------

            As you can see it is only one sentence, but the paper would be perfect after that. You may check this change in the following preprint:

             

            https://www.techrxiv.org/users/258307/articles/716221-note-for-the-p-versus-np-problem

             

            I hope this can be taken into account by the readers for their final moment of evaluating this version,

            2024-04-18 19:39 UTC
            +1

            Comment on this article