Craig Alan Feinstein's Evidence That P ≠ NP: Difference between revisions
Created page with "Title: Craig Alan Feinstein's Evidence That P ≠ NP Abstract: Craig Alan Feinstein, a researcher in computer science, presented evidence that suggests the class of decision problems that can be solved by deterministic polynomial-time algorithms, P, is not equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms, NP. He did this by examining the SUBSET-SUM problem and proposing an algorithm, algorithm A, that solves the p..." |
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Title: Craig Alan Feinstein's Evidence That P ≠ NP | Title: Craig Alan Feinstein's Evidence That P ≠ NP | ||
Abstract: Craig Alan Feinstein, a researcher in computer science, presented evidence that suggests the class of decision problems that can be solved by deterministic polynomial-time algorithms, P, is not equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms, NP. He did this by examining the SUBSET-SUM problem and proposing an algorithm, algorithm A, that | Abstract: Craig Alan Feinstein, a researcher in computer science, presented evidence that suggests the class of decision problems that can be solved by deterministic polynomial-time algorithms, P, is not equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms, NP. He did this by examining the SUBSET-SUM problem and proposing an algorithm, algorithm A, that can solve it in O(2n^2) time. Feinstein argued that algorithm A has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time. This suggests that P ≠ NP, as the improved algorithm can solve the problem more efficiently than any other known algorithm. | ||
Main Research Question: Is P = NP? | Main Research Question: Is P = NP? | ||
Methodology: Feinstein focused on the SUBSET-SUM problem, a well-known NP problem. He proposed an algorithm, algorithm A, that | Methodology: Feinstein focused on the SUBSET-SUM problem, a well-known NP problem. He proposed an algorithm, algorithm A, that can solve the problem in O(2n^2) time. He then argued that algorithm A has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time. | ||
Results: Feinstein | Results: Feinstein's algorithm, algorithm A, can solve the SUBSET-SUM problem in O(2n^2) time. He argued that this algorithm has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time. | ||
Implications: Feinstein's | Implications: Feinstein's evidence suggests that P ≠ NP, as his improved algorithm can solve the SUBSET-SUM problem more efficiently than any other known algorithm. This could have significant implications for the field of computer science, as solving the P = NP problem has been a long-standing challenge in the field. | ||
Link to Article: https://arxiv.org/abs/ | Link to Article: https://arxiv.org/abs/0310060v2 | ||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0310060v2 | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
[[Category:Time]] | |||
[[Category:Algorithm]] | [[Category:Algorithm]] | ||
[[Category: | [[Category:Can]] | ||
[[Category:Problem]] | |||
[[Category:Np]] | [[Category:Np]] | ||
Revision as of 14:47, 24 December 2023
Title: Craig Alan Feinstein's Evidence That P ≠ NP
Abstract: Craig Alan Feinstein, a researcher in computer science, presented evidence that suggests the class of decision problems that can be solved by deterministic polynomial-time algorithms, P, is not equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms, NP. He did this by examining the SUBSET-SUM problem and proposing an algorithm, algorithm A, that can solve it in O(2n^2) time. Feinstein argued that algorithm A has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time. This suggests that P ≠ NP, as the improved algorithm can solve the problem more efficiently than any other known algorithm.
Main Research Question: Is P = NP?
Methodology: Feinstein focused on the SUBSET-SUM problem, a well-known NP problem. He proposed an algorithm, algorithm A, that can solve the problem in O(2n^2) time. He then argued that algorithm A has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time.
Results: Feinstein's algorithm, algorithm A, can solve the SUBSET-SUM problem in O(2n^2) time. He argued that this algorithm has the best running-time for large N and can be improved further for odd numbers, reducing the running-time to 8 units of time.
Implications: Feinstein's evidence suggests that P ≠ NP, as his improved algorithm can solve the SUBSET-SUM problem more efficiently than any other known algorithm. This could have significant implications for the field of computer science, as solving the P = NP problem has been a long-standing challenge in the field.
Link to Article: https://arxiv.org/abs/0310060v2 Authors: arXiv ID: 0310060v2