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

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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 can be used to solve two subproblems independently, reducing the time complexity. His work suggests that there might be a more efficient way to solve the SUBSET-SUM problem, further supporting the idea that P ≠ NP.
Abstract: Craig Alan Feinstein, a researcher in computer science, presented evidence that the classes of decision problems that can be solved by deterministic polynomial-time algorithms (P) and nondeterministic polynomial-time algorithms (NP) are not equal. He focused on the SUBSET-SUM problem and proposed an algorithm (algorithm A) that can solve it in O(2n^2) time, assuming constant-time arithmetic and linear-time sorting. Feinstein argued that algorithm A has the best running-time for large N and proved this through induction. He also proposed an improved strategy that further reduces the running-time.


Main Text:
Main Research Question: Is P = NP?


Craig Alan Feinstein, a computer scientist, provided 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 focused on the SUBSET-SUM problem, which involves determining whether there exists a vector with specific properties.
Methodology: Feinstein focused on the SUBSET-SUM problem and proposed an algorithm (algorithm A) that can solve it in O(2n^2) time. He used induction to prove that algorithm A has the best running-time for large N.


Feinstein proposed an algorithm, called algorithm A, that can solve the SUBSET-SUM problem in O(2n^2) time. This algorithm works by sorting two sets, b-S- and S+, in ascending order and comparing the first two elements in each list. If there is a match, the algorithm stops and outputs that there is a solution. If not, it compares the greater element with the next element on the other list and continues until there is a match or one of the lists runs out of elements.
Results: Feinstein argued that algorithm A has the best running-time (with respect to n for large N) of all algorithms that solve the SUBSET-SUM problem, assuming constant-time arithmetic and linear-time sorting. He also proposed an improved strategy that further reduces the running-time.


Feinstein argued that algorithm A has the best running-time for large N and can be used to solve two subproblems independently. This reduces the time complexity and suggests that there might be a more efficient way to solve the SUBSET-SUM problem. His work supports the idea that P ≠ NP, as it provides evidence that the two classes are not equal.
Implications: Feinstein's evidence suggests that P ≠ NP, as his algorithm can solve the SUBSET-SUM problem more efficiently than any other known algorithm. This could potentially lead to new algorithms and approaches in computer science and could have implications in other fields that rely on decision problems.


Link to Article: https://arxiv.org/abs/0310060v3
Link to Article: https://arxiv.org/abs/0310060v4
Authors:  
Authors:  
arXiv ID: 0310060v3
arXiv ID: 0310060v4


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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, presented evidence that the classes of decision problems that can be solved by deterministic polynomial-time algorithms (P) and nondeterministic polynomial-time algorithms (NP) are not equal. He focused on the SUBSET-SUM problem and proposed an algorithm (algorithm A) that can solve it in O(2n^2) time, assuming constant-time arithmetic and linear-time sorting. Feinstein argued that algorithm A has the best running-time for large N and proved this through induction. He also proposed an improved strategy that further reduces the running-time.

Main Research Question: Is P = NP?

Methodology: Feinstein focused on the SUBSET-SUM problem and proposed an algorithm (algorithm A) that can solve it in O(2n^2) time. He used induction to prove that algorithm A has the best running-time for large N.

Results: Feinstein argued that algorithm A has the best running-time (with respect to n for large N) of all algorithms that solve the SUBSET-SUM problem, assuming constant-time arithmetic and linear-time sorting. He also proposed an improved strategy that further reduces the running-time.

Implications: Feinstein's evidence suggests that P ≠ NP, as his algorithm can solve the SUBSET-SUM problem more efficiently than any other known algorithm. This could potentially lead to new algorithms and approaches in computer science and could have implications in other fields that rely on decision problems.

Link to Article: https://arxiv.org/abs/0310060v4 Authors: arXiv ID: 0310060v4

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