Craig Alan Feinstein
نویسنده
چکیده
The question of whether the class of decision problems that can be solved by deterministic polynomial-time algorithms (P ) is equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms (NP) has been open since it was first formulated by Cook, Karp, and Levin in 1971. In this paper, we prove that they are not equal by showing that any algorithm that solves the SUBSET-SUM problem must perform a super-polynomial number of computations for some input of size, O(n), where n is the size of the set in the problem. Disclaimer: This article was authored by Craig Alan Feinstein in his private capacity. No official support or endorsement by the U.S. Government is intended or should be inferred. Date: July 25, 2003.
منابع مشابه
The Collatz 3n+1 Conjecture Is Unprovable
In this paper, we show that any proof of the Collatz 3n + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable.
متن کاملP = Np
The question of whether the class of decision problems that can be solved by deterministic polynomial-time algorithms (P ) is equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms (NP) has been open since it was first formulated by Cook, Karp, and Levin in 1971. In this paper, we prove that they are not equal by showing that any algorithm that...
متن کاملSmooth Solutions to the 3D Navier-Stokes Equations Exist
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...
متن کاملComplexity Theory for Simpletons
In this article, we shall describe some of the most interesting topics in the subject of Complexity Theory for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary understanding of computer programming will be able to follow this article. First, we shall describe the P versus NP problem and its significance. Next, we shall describe...
متن کاملPuzzle: Zermelo-Fraenkel set theory is inconsistent
The question of whether the class of decision problems that can be solved by deterministic polynomial-time algorithms, P , is equal to the class of decision problems that can be solved by nondeterministic polynomial-time algorithms, NP , has been open since it was first formulated by Cook, Karp, and Levin in 1971. In this paper, we give evidence that they are not equal by examining the SUBSET-S...
متن کامل