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, proposed a method to solve the Subset-Sum problem, which is a well-known NP-complete problem. His method, called algorithm A, can solve the problem in O(2n^2) time, assuming constant-time arithmetic and linear-time sorting. Feinstein argued that algorithm A is the best method for solving the problem for large inputs, as it efficiently solves two subproblems that are related to each other. This evidence suggests that P ≠ NP, meaning that problems that can be solved by deterministic polynomial-time algorithms are not equivalent to problems that can be solved by nondeterministic polynomial-time algorithms.
Main Research Question: Can the class of decision problems that can be solved by deterministic polynomial-time algorithms (P) be equivalent to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms (NP)?
Methodology: Feinstein focused on the Subset-Sum problem, which is a common NP problem. He proposed algorithm A, which sorts the input vectors in ascending order and then compares elements from each list until a match is found or one list runs out of elements. Feinstein argued that this method is the best for solving the problem for large inputs because it efficiently solves two related subproblems.
Results: Feinstein's algorithm A can solve the Subset-Sum problem in O(2n^2) time, assuming constant-time arithmetic and linear-time sorting. This is an improvement over other methods, as it efficiently solves two related subproblems. This evidence suggests that P ≠ NP, as algorithm A is the best method for solving the problem for large inputs.
Implications: If Feinstein's method is correct, it would mean that P ≠ NP, which is a long-standing open question in the field of computer science. This would have significant implications for the field, as it would mean that there are problems that can be solved more efficiently by nondeterministic algorithms than by deterministic algorithms. This could potentially lead to new algorithms and techniques for solving complex problems.
Link to Article: https://arxiv.org/abs/0310060v5 Authors: arXiv ID: 0310060v5