Craig Alan Feinstein's Evidence That P ≠ NP: Difference between revisions

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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 solves the problem in O(2n^2) time. Feinstein argued that algorithm A has the best running-time for large N and proved this through induction on n. He also proposed an improved strategy that further reduces the running-time of algorithm A.
Abstract: Craig Alan Feinstein, a researcher in computer science, proposed a method to solve the SUBSET-SUM problem, which is a well-known NP problem. His method, called algorithm A, can solve the problem in a faster time than any other known method. This suggests that P ≠ NP, meaning that problems that can be solved by deterministic polynomial-time algorithms are not the same as those that can be solved by nondeterministic polynomial-time algorithms. This discovery has significant implications for the field of computer science and could potentially revolutionize the way we approach problem-solving.


Main Research Question: Is P = NP?
Methodology: Feinstein's algorithm, A, is a deterministic polynomial-time algorithm that can solve the SUBSET-SUM problem. It runs in O(2n^2) time, which is faster than any other known method. Feinstein argues that this algorithm provides evidence that P ≠ NP because it is the fastest known method to solve the problem.


Methodology: Feinstein focused on the SUBSET-SUM problem, a well-known NP problem. He proposed an algorithm, algorithm A, that solves the problem in O(2n^2) time. He then argued and proved that algorithm A has the best running-time for large N, using induction on n.
Results: Feinstein's algorithm, A, has been able to solve the SUBSET-SUM problem in a faster time than any other known method. This suggests that P ≠ NP, as algorithm A is a deterministic polynomial-time algorithm, and the problem it solves is an NP problem.


Results: Feinstein proposed an algorithm, algorithm A, that solves the SUBSET-SUM problem in O(2n^2) time. He argued that algorithm A has the best running-time for large N and proved this through induction on n. He also proposed an improved strategy that further reduces the running-time of algorithm A.
Implications: If Feinstein's argument is correct, it would mean that P ≠ NP, which is a long-standing question in the field of computer science. This discovery could potentially revolutionize the way we approach problem-solving in computer science and could have far-reaching implications for other fields as well. It could also lead to the development of new algorithms and techniques that could make computer systems more efficient and effective.


Implications: Feinstein's work provides evidence that P ≠ NP. His improved strategy for algorithm A could potentially lead to more efficient ways of solving NP problems. However, it's important to note that this is a heuristic argument and not a rigorous proof. Further research is needed to definitively answer the question of whether P = NP.
Link to Article: https://arxiv.org/abs/0310060v7
 
Link to Article: https://arxiv.org/abs/0310060v1
Authors:  
Authors:  
arXiv ID: 0310060v1
arXiv ID: 0310060v7


[[Category:Computer Science]]
[[Category:Computer Science]]
[[Category:Problem]]
[[Category:Np]]
[[Category:Algorithm]]
[[Category:Algorithm]]
[[Category:Time]]
[[Category:Time]]
[[Category:Np]]
[[Category:Feinstein]]
[[Category:Feinstein]]
[[Category:He]]

Latest revision as of 14:48, 24 December 2023

Title: Craig Alan Feinstein's Evidence That P ≠ NP

Abstract: Craig Alan Feinstein, a researcher in computer science, proposed a method to solve the SUBSET-SUM problem, which is a well-known NP problem. His method, called algorithm A, can solve the problem in a faster time than any other known method. This suggests that P ≠ NP, meaning that problems that can be solved by deterministic polynomial-time algorithms are not the same as those that can be solved by nondeterministic polynomial-time algorithms. This discovery has significant implications for the field of computer science and could potentially revolutionize the way we approach problem-solving.

Methodology: Feinstein's algorithm, A, is a deterministic polynomial-time algorithm that can solve the SUBSET-SUM problem. It runs in O(2n^2) time, which is faster than any other known method. Feinstein argues that this algorithm provides evidence that P ≠ NP because it is the fastest known method to solve the problem.

Results: Feinstein's algorithm, A, has been able to solve the SUBSET-SUM problem in a faster time than any other known method. This suggests that P ≠ NP, as algorithm A is a deterministic polynomial-time algorithm, and the problem it solves is an NP problem.

Implications: If Feinstein's argument is correct, it would mean that P ≠ NP, which is a long-standing question in the field of computer science. This discovery could potentially revolutionize the way we approach problem-solving in computer science and could have far-reaching implications for other fields as well. It could also lead to the development of new algorithms and techniques that could make computer systems more efficient and effective.

Link to Article: https://arxiv.org/abs/0310060v7 Authors: arXiv ID: 0310060v7

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