A simple proof of NP != P ?
It is well known that relativization cannot be used to prove or disprove NP not equal to P. This paper question this belief by giving a very simple prove of NP not equal to P using relativization.
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It is well known that relativization cannot be used to prove or disprove NP not equal to P. This paper question this belief by giving a very simple prove of NP not equal to P using relativization.
Folding a square sheet of paper into an arbitrary 3D shape is proved to be NP-hard problem. It is proved by transforming the problem into circle packing problem[1].
[1] arxiv.org/abs/1008.1224: Circle Packing for Origami Design Is Hard
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Vinay Deolalikar, HP Labs researcher, claimed to have proved NP not equal to P. The website is his homepage in HP. You can find his 103 paper in pdf here. And he said he will post the final version when ready. Here is his email claiming to have solved the problem:
Permanent of a matrix is quite similar to that of determinant, though determinant can be found in polynomial time, while permanent is #P-complete (meaning that if you solve it, you can count the number of solution of all NP problem.)
In this paper, I am going to describe a new method to calculate permanent based on a very simple principle: ...