2 Craig Alan
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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. Even if the reader does not believe the proof, the author believes that he or she will still very much enjoy reading this article. 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: August 1, 2003.
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Craig Alan Feinstein
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...
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تاریخ انتشار 2003