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 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