Version 1
: Received: 12 October 2023 / Approved: 13 October 2023 / Online: 13 October 2023 (11:22:55 CEST)
How to cite:
Sinchev, B.; Sinchev, A.; Mukhanova, A. On A Solution of “P vs Np” Millenium Prize Problem Based on the Subset Sum Problem. Preprints2023, 2023100888. https://doi.org/10.20944/preprints202310.0888.v1
Sinchev, B.; Sinchev, A.; Mukhanova, A. On A Solution of “P vs Np” Millenium Prize Problem Based on the Subset Sum Problem. Preprints 2023, 2023100888. https://doi.org/10.20944/preprints202310.0888.v1
Sinchev, B.; Sinchev, A.; Mukhanova, A. On A Solution of “P vs Np” Millenium Prize Problem Based on the Subset Sum Problem. Preprints2023, 2023100888. https://doi.org/10.20944/preprints202310.0888.v1
APA Style
Sinchev, B., Sinchev, A., & Mukhanova, A. (2023). On A Solution of “P vs Np” Millenium Prize Problem Based on the Subset Sum Problem. Preprints. https://doi.org/10.20944/preprints202310.0888.v1
Chicago/Turabian Style
Sinchev, B., Askar Sinchev and Aksulu Mukhanova. 2023 "On A Solution of “P vs Np” Millenium Prize Problem Based on the Subset Sum Problem" Preprints. https://doi.org/10.20944/preprints202310.0888.v1
Abstract
Given a set of distinct non-negative integers X^n and a target certificate S in parametrized form: ∃X^k⊆X^n,∑_(x_i∈X^k)▒x_i =S (k=|X^k |,n=|X^n |). We present a polynomial solution of the subset sum problem with time complexity T≤O(kn)≤O(n^2) and space complexity S≤O(((n-1)n)/2)≤O(n^2 ), so that P = NP.
Keywords
P; NP and NP-complete class; set; subset; potency; time; space
Subject
Computer Science and Mathematics, Computer Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
