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.

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 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 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: 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/0310060v1 Authors: arXiv ID: 0310060v1